diff options
Diffstat (limited to 'sysdeps/ieee754')
231 files changed, 23775 insertions, 10 deletions
diff --git a/sysdeps/ieee754/Implies b/sysdeps/ieee754/Implies deleted file mode 100644 index 5c9e98b..0000000 --- a/sysdeps/ieee754/Implies +++ /dev/null @@ -1,2 +0,0 @@ -# For all IEEE machines, use Sun's fdlibm code. -libm-ieee754 diff --git a/sysdeps/ieee754/dbl-64/Dist b/sysdeps/ieee754/dbl-64/Dist new file mode 100644 index 0000000..1bb7be35 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/Dist @@ -0,0 +1 @@ +t_exp2.h diff --git a/sysdeps/ieee754/dbl2mpn.c b/sysdeps/ieee754/dbl-64/dbl2mpn.c index f7dead4..f7dead4 100644 --- a/sysdeps/ieee754/dbl2mpn.c +++ b/sysdeps/ieee754/dbl-64/dbl2mpn.c diff --git a/sysdeps/ieee754/dbl-64/e_acos.c b/sysdeps/ieee754/dbl-64/e_acos.c new file mode 100644 index 0000000..eb4080a --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_acos.c @@ -0,0 +1,144 @@ +/* @(#)e_acos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $"; +#endif + +/* __ieee754_acos(x) + * Method : + * acos(x) = pi/2 - asin(x) + * acos(-x) = pi/2 + asin(x) + * For |x|<=0.5 + * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) + * For x>0.5 + * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) + * = 2asin(sqrt((1-x)/2)) + * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) + * = 2f + (2c + 2s*z*R(z)) + * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term + * for f so that f+c ~ sqrt(z). + * For x<-0.5 + * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) + * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Function needed: __ieee754_sqrt + */ + +#include "math.h" +#include "math_private.h" +#define one qS[0] + +#ifdef __STDC__ +static const double +#else +static double +#endif +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ +pS[] = {1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ + -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ + 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ + -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ + 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ + 3.47933107596021167570e-05}, /* 0x3F023DE1, 0x0DFDF709 */ +qS[] ={1.0, -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ + 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ + -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ + 7.70381505559019352791e-02}; /* 0x3FB3B8C5, 0xB12E9282 */ + +#ifdef __STDC__ + double __ieee754_acos(double x) +#else + double __ieee754_acos(x) + double x; +#endif +{ + double z,p,q,r,w,s,c,df,p1,p2,p3,q1,q2,z2,z4,z6; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x3ff00000) { /* |x| >= 1 */ + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+2.0*pio2_lo; /* acos(-1)= pi */ + } + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3fe00000) { /* |x| < 0.5 */ + if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ + z = x*x; +#ifdef DO_NOT_USE_THIS + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); +#else + p1 = z*pS[0]; z2=z*z; + p2 = pS[1]+z*pS[2]; z4=z2*z2; + p3 = pS[3]+z*pS[4]; z6=z4*z2; + q1 = one+z*qS[1]; + q2 = qS[2]+z*qS[3]; + p = p1 + z2*p2 + z4*p3 + z6*pS[5]; + q = q1 + z2*q2 + z4*qS[4]; +#endif + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*0.5; +#ifdef DO_NOT_USE_THIS + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); +#else + p1 = z*pS[0]; z2=z*z; + p2 = pS[1]+z*pS[2]; z4=z2*z2; + p3 = pS[3]+z*pS[4]; z6=z4*z2; + q1 = one+z*qS[1]; + q2 = qS[2]+z*qS[3]; + p = p1 + z2*p2 + z4*p3 + z6*pS[5]; + q = q1 + z2*q2 + z4*qS[4]; +#endif + s = __ieee754_sqrt(z); + r = p/q; + w = r*s-pio2_lo; + return pi - 2.0*(s+w); + } else { /* x > 0.5 */ + z = (one-x)*0.5; + s = __ieee754_sqrt(z); + df = s; + SET_LOW_WORD(df,0); + c = (z-df*df)/(s+df); +#ifdef DO_NOT_USE_THIS + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); +#else + p1 = z*pS[0]; z2=z*z; + p2 = pS[1]+z*pS[2]; z4=z2*z2; + p3 = pS[3]+z*pS[4]; z6=z4*z2; + q1 = one+z*qS[1]; + q2 = qS[2]+z*qS[3]; + p = p1 + z2*p2 + z4*p3 + z6*pS[5]; + q = q1 + z2*q2 + z4*qS[4]; +#endif + r = p/q; + w = r*s+c; + return 2.0*(df+w); + } +} diff --git a/sysdeps/ieee754/dbl-64/e_acosh.c b/sysdeps/ieee754/dbl-64/e_acosh.c new file mode 100644 index 0000000..27c29cd --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_acosh.c @@ -0,0 +1,69 @@ +/* @(#)e_acosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_acosh.c,v 1.9 1995/05/12 04:57:18 jtc Exp $"; +#endif + +/* __ieee754_acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.0, +ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + +#ifdef __STDC__ + double __ieee754_acosh(double x) +#else + double __ieee754_acosh(x) + double x; +#endif +{ + double t; + int32_t hx; + u_int32_t lx; + EXTRACT_WORDS(hx,lx,x); + if(hx<0x3ff00000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x41b00000) { /* x > 2**28 */ + if(hx >=0x7ff00000) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ + } else if(((hx-0x3ff00000)|lx)==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one))); + } else { /* 1<x<2 */ + t = x-one; + return __log1p(t+__sqrt(2.0*t+t*t)); + } +} diff --git a/sysdeps/ieee754/dbl-64/e_asin.c b/sysdeps/ieee754/dbl-64/e_asin.c new file mode 100644 index 0000000..aa19598 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_asin.c @@ -0,0 +1,143 @@ +/* @(#)e_asin.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_asin.c,v 1.9 1995/05/12 04:57:22 jtc Exp $"; +#endif + +/* __ieee754_asin(x) + * Method : + * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... + * we approximate asin(x) on [0,0.5] by + * asin(x) = x + x*x^2*R(x^2) + * where + * R(x^2) is a rational approximation of (asin(x)-x)/x^3 + * and its remez error is bounded by + * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) + * + * For x in [0.5,1] + * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) + * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; + * then for x>0.98 + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) + * For x<=0.98, let pio4_hi = pio2_hi/2, then + * f = hi part of s; + * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) + * and + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) + * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + + +#include "math.h" +#include "math_private.h" +#define one qS[0] +#ifdef __STDC__ +static const double +#else +static double +#endif +huge = 1.000e+300, +pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ +pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ + /* coefficient for R(x^2) */ +pS[] = {1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ + -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ + 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ + -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ + 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ + 3.47933107596021167570e-05}, /* 0x3F023DE1, 0x0DFDF709 */ +qS[] = {1.0, -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ + 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ + -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ + 7.70381505559019352791e-02}; /* 0x3FB3B8C5, 0xB12E9282 */ + +#ifdef __STDC__ + double __ieee754_asin(double x) +#else + double __ieee754_asin(x) + double x; +#endif +{ + double t,w,p,q,c,r,s,p1,p2,p3,q1,q2,z2,z4,z6; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>= 0x3ff00000) { /* |x|>= 1 */ + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((ix-0x3ff00000)|lx)==0) + /* asin(1)=+-pi/2 with inexact */ + return x*pio2_hi+x*pio2_lo; + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3fe00000) { /* |x|<0.5 */ + if(ix<0x3e400000) { /* if |x| < 2**-27 */ + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } else { + t = x*x; +#ifdef DO_NOT_USE_THIS + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); +#else + p1 = t*pS[0]; z2=t*t; + p2 = pS[1]+t*pS[2]; z4=z2*z2; + p3 = pS[3]+t*pS[4]; z6=z4*z2; + q1 = one+t*qS[1]; + q2 = qS[2]+t*qS[3]; + p = p1 + z2*p2 + z4*p3 + z6*pS[5]; + q = q1 + z2*q2 + z4*qS[4]; +#endif + w = p/q; + return x+x*w; + } + } + /* 1> |x|>= 0.5 */ + w = one-fabs(x); + t = w*0.5; +#ifdef DO_NOT_USE_THIS + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); +#else + p1 = t*pS[0]; z2=t*t; + p2 = pS[1]+t*pS[2]; z4=z2*z2; + p3 = pS[3]+t*pS[4]; z6=z4*z2; + q1 = one+t*qS[1]; + q2 = qS[2]+t*qS[3]; + p = p1 + z2*p2 + z4*p3 + z6*pS[5]; + q = q1 + z2*q2 + z4*qS[4]; +#endif + s = __ieee754_sqrt(t); + if(ix>=0x3FEF3333) { /* if |x| > 0.975 */ + w = p/q; + t = pio2_hi-(2.0*(s+s*w)-pio2_lo); + } else { + w = s; + SET_LOW_WORD(w,0); + c = (t-w*w)/(s+w); + r = p/q; + p = 2.0*s*r-(pio2_lo-2.0*c); + q = pio4_hi-2.0*w; + t = pio4_hi-(p-q); + } + if(hx>0) return t; else return -t; +} diff --git a/sysdeps/ieee754/dbl-64/e_atan2.c b/sysdeps/ieee754/dbl-64/e_atan2.c new file mode 100644 index 0000000..ae7d759 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_atan2.c @@ -0,0 +1,130 @@ +/* @(#)e_atan2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_atan2.c,v 1.8 1995/05/10 20:44:51 jtc Exp $"; +#endif + +/* __ieee754_atan2(y,x) + * Method : + * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). + * 2. Reduce x to positive by (if x and y are unexceptional): + * ARG (x+iy) = arctan(y/x) ... if x > 0, + * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * + * Special cases: + * + * ATAN2((anything), NaN ) is NaN; + * ATAN2(NAN , (anything) ) is NaN; + * ATAN2(+-0, +(anything but NaN)) is +-0 ; + * ATAN2(+-0, -(anything but NaN)) is +-pi ; + * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; + * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; + * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; + * ATAN2(+-INF,+INF ) is +-pi/4 ; + * ATAN2(+-INF,-INF ) is +-3pi/4; + * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +tiny = 1.0e-300, +zero = 0.0, +pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ +pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ +pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ +pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ + +#ifdef __STDC__ + double __ieee754_atan2(double y, double x) +#else + double __ieee754_atan2(y,x) + double y,x; +#endif +{ + double z; + int32_t k,m,hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + ix = hx&0x7fffffff; + EXTRACT_WORDS(hy,ly,y); + iy = hy&0x7fffffff; + if(((ix|((lx|-lx)>>31))>0x7ff00000)|| + ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ + return x+y; + if(((hx-0x3ff00000)|lx)==0) return __atan(y); /* x=1.0 */ + m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if((iy|ly)==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7ff00000) { + if(iy==0x7ff00000) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>20; + if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ + else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ + else z=__atan(fabs(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: { + u_int32_t zh; + GET_HIGH_WORD(zh,z); + SET_HIGH_WORD(z,zh ^ 0x80000000); + } + return z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} diff --git a/sysdeps/ieee754/dbl-64/e_atanh.c b/sysdeps/ieee754/dbl-64/e_atanh.c new file mode 100644 index 0000000..fa4fe67 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_atanh.c @@ -0,0 +1,74 @@ +/* @(#)e_atanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_atanh.c,v 1.8 1995/05/10 20:44:55 jtc Exp $"; +#endif + +/* __ieee754_atanh(x) + * Method : + * 1.Reduced x to positive by atanh(-x) = -atanh(x) + * 2.For x>=0.5 + * 1 2x x + * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * For x<0.5 + * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) + * + * Special cases: + * atanh(x) is NaN if |x| > 1 with signal; + * atanh(NaN) is that NaN with no signal; + * atanh(+-1) is +-INF with signal. + * + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double one = 1.0, huge = 1e300; +#else +static double one = 1.0, huge = 1e300; +#endif + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_atanh(double x) +#else + double __ieee754_atanh(x) + double x; +#endif +{ + double t; + int32_t hx,ix; + u_int32_t lx; + EXTRACT_WORDS(hx,lx,x); + ix = hx&0x7fffffff; + if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3ff00000) + return x/zero; + if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ + SET_HIGH_WORD(x,ix); + if(ix<0x3fe00000) { /* x < 0.5 */ + t = x+x; + t = 0.5*__log1p(t+t*x/(one-x)); + } else + t = 0.5*__log1p((x+x)/(one-x)); + if(hx>=0) return t; else return -t; +} diff --git a/sysdeps/ieee754/dbl-64/e_cosh.c b/sysdeps/ieee754/dbl-64/e_cosh.c new file mode 100644 index 0000000..65106b9 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_cosh.c @@ -0,0 +1,92 @@ +/* @(#)e_cosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $"; +#endif + +/* __ieee754_cosh(x) + * Method : + * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : cosh(x) := ------------------- + * 2 + * 22 <= x <= lnovft : cosh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : cosh(x) := huge*huge (overflow) + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double one = 1.0, half=0.5, huge = 1.0e300; +#else +static double one = 1.0, half=0.5, huge = 1.0e300; +#endif + +#ifdef __STDC__ + double __ieee754_cosh(double x) +#else + double __ieee754_cosh(x) + double x; +#endif +{ + double t,w; + int32_t ix; + u_int32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3fd62e43) { + t = __expm1(fabs(x)); + w = one+t; + if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x40360000) { + t = __ieee754_exp(fabs(x)); + return half*t+half/t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x40862e42) return half*__ieee754_exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + GET_LOW_WORD(lx,x); + if (ix<0x408633ce || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { + w = __ieee754_exp(half*fabs(x)); + t = half*w; + return t*w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} diff --git a/sysdeps/ieee754/dbl-64/e_exp.c b/sysdeps/ieee754/dbl-64/e_exp.c new file mode 100644 index 0000000..ee0b22f --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_exp.c @@ -0,0 +1,162 @@ +/* Double-precision floating point e^x. + Copyright (C) 1997, 1998 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +/* How this works: + The basic design here is from + Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical + Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft., + 17 (1), March 1991, pp. 26-45. + + The input value, x, is written as + + x = n * ln(2)_0 + t/512 + delta[t] + x + n * ln(2)_1 + + where: + - n is an integer, 1024 >= n >= -1075; + - ln(2)_0 is the first 43 bits of ln(2), and ln(2)_1 is the remainder, so + that |ln(2)_1| < 2^-32; + - t is an integer, 177 >= t >= -177 + - delta is based on a table entry, delta[t] < 2^-28 + - x is whatever is left, |x| < 2^-10 + + Then e^x is approximated as + + e^x = 2^n_1 ( 2^n_0 e^(t/512 + delta[t]) + + ( 2^n_0 e^(t/512 + delta[t]) + * ( p(x + n * ln(2)_1) + - n*ln(2)_1 + - n*ln(2)_1 * p(x + n * ln(2)_1) ) ) ) + + where + - p(x) is a polynomial approximating e(x)-1; + - e^(t/512 + delta[t]) is obtained from a table; + - n_1 + n_0 = n, so that |n_0| < DBL_MIN_EXP-1. + + If it happens that n_1 == 0 (this is the usual case), that multiplication + is omitted. + */ +#ifndef _GNU_SOURCE +#define _GNU_SOURCE +#endif +#include <float.h> +#include <ieee754.h> +#include <math.h> +#include <fenv.h> +#include <inttypes.h> +#include <math_private.h> + +extern const float __exp_deltatable[178]; +extern const double __exp_atable[355] /* __attribute__((mode(DF))) */; + +static const volatile double TWO1023 = 8.988465674311579539e+307; +static const volatile double TWOM1000 = 9.3326361850321887899e-302; + +double +__ieee754_exp (double x) +{ + static const double himark = 709.7827128933840868; + static const double lomark = -745.1332191019412221; + /* Check for usual case. */ + if (isless (x, himark) && isgreater (x, lomark)) + { + static const double THREEp42 = 13194139533312.0; + static const double THREEp51 = 6755399441055744.0; + /* 1/ln(2). */ + static const double M_1_LN2 = 1.442695040888963387; + /* ln(2), part 1 */ + static const double M_LN2_0 = .6931471805598903302; + /* ln(2), part 2 */ + static const double M_LN2_1 = 5.497923018708371155e-14; + + int tval, unsafe, n_i; + double x22, n, t, dely, result; + union ieee754_double ex2_u, scale_u; + fenv_t oldenv; + + feholdexcept (&oldenv); +#ifdef FE_TONEAREST + fesetround (FE_TONEAREST); +#endif + + /* Calculate n. */ + n = x * M_1_LN2 + THREEp51; + n -= THREEp51; + x = x - n*M_LN2_0; + + /* Calculate t/512. */ + t = x + THREEp42; + t -= THREEp42; + x -= t; + + /* Compute tval = t. */ + tval = (int) (t * 512.0); + + if (t >= 0) + x -= __exp_deltatable[tval]; + else + x += __exp_deltatable[-tval]; + + /* Now, the variable x contains x + n*ln(2)_1. */ + dely = n*M_LN2_1; + + /* Compute ex2 = 2^n_0 e^(t/512+delta[t]). */ + ex2_u.d = __exp_atable[tval+177]; + n_i = (int)n; + /* 'unsafe' is 1 iff n_1 != 0. */ + unsafe = abs(n_i) >= -DBL_MIN_EXP - 1; + ex2_u.ieee.exponent += n_i >> unsafe; + + /* Compute scale = 2^n_1. */ + scale_u.d = 1.0; + scale_u.ieee.exponent += n_i - (n_i >> unsafe); + + /* Approximate e^x2 - 1, using a fourth-degree polynomial, + with maximum error in [-2^-10-2^-28,2^-10+2^-28] + less than 4.9e-19. */ + x22 = (((0.04166666898464281565 + * x + 0.1666666766008501610) + * x + 0.499999999999990008) + * x + 0.9999999999999976685) * x; + /* Allow for impact of dely. */ + x22 -= dely + dely*x22; + + /* Return result. */ + fesetenv (&oldenv); + + result = x22 * ex2_u.d + ex2_u.d; + if (!unsafe) + return result; + else + return result * scale_u.d; + } + /* Exceptional cases: */ + else if (isless (x, himark)) + { + if (__isinf (x)) + /* e^-inf == 0, with no error. */ + return 0; + else + /* Underflow */ + return TWOM1000 * TWOM1000; + } + else + /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ + return TWO1023*x; +} diff --git a/sysdeps/ieee754/dbl-64/e_fmod.c b/sysdeps/ieee754/dbl-64/e_fmod.c new file mode 100644 index 0000000..2ce6135 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_fmod.c @@ -0,0 +1,140 @@ +/* @(#)e_fmod.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_fmod.c,v 1.8 1995/05/10 20:45:07 jtc Exp $"; +#endif + +/* + * __ieee754_fmod(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double one = 1.0, Zero[] = {0.0, -0.0,}; +#else +static double one = 1.0, Zero[] = {0.0, -0.0,}; +#endif + +#ifdef __STDC__ + double __ieee754_fmod(double x, double y) +#else + double __ieee754_fmod(x,y) + double x,y ; +#endif +{ + int32_t n,hx,hy,hz,ix,iy,sx,i; + u_int32_t lx,ly,lz; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + sx = hx&0x80000000; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ + ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx<=hy) { + if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */ + if(lx==ly) + return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/ + } + + /* determine ix = ilogb(x) */ + if(hx<0x00100000) { /* subnormal x */ + if(hx==0) { + for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; + } else { + for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; + } + } else ix = (hx>>20)-1023; + + /* determine iy = ilogb(y) */ + if(hy<0x00100000) { /* subnormal y */ + if(hy==0) { + for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; + } else { + for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; + } + } else iy = (hy>>20)-1023; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -1022) + hx = 0x00100000|(0x000fffff&hx); + else { /* subnormal x, shift x to normal */ + n = -1022-ix; + if(n<=31) { + hx = (hx<<n)|(lx>>(32-n)); + lx <<= n; + } else { + hx = lx<<(n-32); + lx = 0; + } + } + if(iy >= -1022) + hy = 0x00100000|(0x000fffff&hy); + else { /* subnormal y, shift y to normal */ + n = -1022-iy; + if(n<=31) { + hy = (hy<<n)|(ly>>(32-n)); + ly <<= n; + } else { + hy = ly<<(n-32); + ly = 0; + } + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; + if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} + else { + if((hz|lz)==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + hx = hz+hz+(lz>>31); lx = lz+lz; + } + } + hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; + if(hz>=0) {hx=hz;lx=lz;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + while(hx<0x00100000) { /* normalize x */ + hx = hx+hx+(lx>>31); lx = lx+lx; + iy -= 1; + } + if(iy>= -1022) { /* normalize output */ + hx = ((hx-0x00100000)|((iy+1023)<<20)); + INSERT_WORDS(x,hx|sx,lx); + } else { /* subnormal output */ + n = -1022 - iy; + if(n<=20) { + lx = (lx>>n)|((u_int32_t)hx<<(32-n)); + hx >>= n; + } else if (n<=31) { + lx = (hx<<(32-n))|(lx>>n); hx = sx; + } else { + lx = hx>>(n-32); hx = sx; + } + INSERT_WORDS(x,hx|sx,lx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} diff --git a/sysdeps/ieee754/dbl-64/e_gamma_r.c b/sysdeps/ieee754/dbl-64/e_gamma_r.c new file mode 100644 index 0000000..bd802c2 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_gamma_r.c @@ -0,0 +1,51 @@ +/* Implementation of gamma function according to ISO C. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> +#include <math_private.h> + + +double +__ieee754_gamma_r (double x, int *signgamp) +{ + /* We don't have a real gamma implementation now. We'll use lgamma + and the exp function. But due to the required boundary + conditions we must check some values separately. */ + int32_t hx; + u_int32_t lx; + + EXTRACT_WORDS (hx, lx, x); + + if (((hx & 0x7fffffff) | lx) == 0) + { + /* Return value for x == 0 is NaN with invalid exception. */ + *signgamp = 0; + return x / x; + } + if (hx < 0 && (u_int32_t) hx < 0xfff00000 && __rint (x) == x) + { + /* Return value for integer x < 0 is NaN with invalid exception. */ + *signgamp = 0; + return (x - x) / (x - x); + } + + /* XXX FIXME. */ + return __ieee754_exp (__ieee754_lgamma_r (x, signgamp)); +} diff --git a/sysdeps/ieee754/dbl-64/e_hypot.c b/sysdeps/ieee754/dbl-64/e_hypot.c new file mode 100644 index 0000000..76a77ec --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_hypot.c @@ -0,0 +1,128 @@ +/* @(#)e_hypot.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_hypot.c,v 1.9 1995/05/12 04:57:27 jtc Exp $"; +#endif + +/* __ieee754_hypot(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 32 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, + * y1= y with lower 32 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double __ieee754_hypot(double x, double y) +#else + double __ieee754_hypot(x,y) + double x, y; +#endif +{ + double a,b,t1,t2,y1,y2,w; + int32_t j,k,ha,hb; + + GET_HIGH_WORD(ha,x); + ha &= 0x7fffffff; + GET_HIGH_WORD(hb,y); + hb &= 0x7fffffff; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + SET_HIGH_WORD(a,ha); /* a <- |a| */ + SET_HIGH_WORD(b,hb); /* b <- |b| */ + if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ + k=0; + if(ha > 0x5f300000) { /* a>2**500 */ + if(ha >= 0x7ff00000) { /* Inf or NaN */ + u_int32_t low; + w = a+b; /* for sNaN */ + GET_LOW_WORD(low,a); + if(((ha&0xfffff)|low)==0) w = a; + GET_LOW_WORD(low,b); + if(((hb^0x7ff00000)|low)==0) w = b; + return w; + } + /* scale a and b by 2**-600 */ + ha -= 0x25800000; hb -= 0x25800000; k += 600; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + if(hb < 0x20b00000) { /* b < 2**-500 */ + if(hb <= 0x000fffff) { /* subnormal b or 0 */ + u_int32_t low; + GET_LOW_WORD(low,b); + if((hb|low)==0) return a; + t1=0; + SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ + b *= t1; + a *= t1; + k -= 1022; + } else { /* scale a and b by 2^600 */ + ha += 0x25800000; /* a *= 2^600 */ + hb += 0x25800000; /* b *= 2^600 */ + k -= 600; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + t1 = 0; + SET_HIGH_WORD(t1,ha); + t2 = a-t1; + w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + y1 = 0; + SET_HIGH_WORD(y1,hb); + y2 = b - y1; + t1 = 0; + SET_HIGH_WORD(t1,ha+0x00100000); + t2 = a - t1; + w = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + u_int32_t high; + t1 = 1.0; + GET_HIGH_WORD(high,t1); + SET_HIGH_WORD(t1,high+(k<<20)); + return t1*w; + } else return w; +} diff --git a/sysdeps/ieee754/dbl-64/e_j0.c b/sysdeps/ieee754/dbl-64/e_j0.c new file mode 100644 index 0000000..55e8294 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_j0.c @@ -0,0 +1,531 @@ +/* @(#)e_j0.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/26, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $"; +#endif + +/* __ieee754_j0(x), __ieee754_y0(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j0(x): + * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... + * 2. Reduce x to |x| since j0(x)=j0(-x), and + * for x in (0,2) + * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; + * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) + * for x in (2,inf) + * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * as follow: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (cos(x) + sin(x)) + * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j0(nan)= nan + * j0(0) = 1 + * j0(inf) = 0 + * + * Method -- y0(x): + * 1. For x<2. + * Since + * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) + * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. + * We use the following function to approximate y0, + * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 + * where + * U(z) = u00 + u01*z + ... + u06*z^6 + * V(z) = 1 + v01*z + ... + v04*z^4 + * with absolute approximation error bounded by 2**-72. + * Note: For tiny x, U/V = u0 and j0(x)~1, hence + * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) + * 2. For x>=2. + * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * by the method mentioned above. + * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static double pzero(double), qzero(double); +#else +static double pzero(), qzero(); +#endif + +#ifdef __STDC__ +static const double +#else +static double +#endif +huge = 1e300, +one = 1.0, +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + /* R0/S0 on [0, 2.00] */ +R[] = {0.0, 0.0, 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ + -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ + 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ + -4.61832688532103189199e-09}, /* 0xBE33D5E7, 0x73D63FCE */ +S[] = {0.0, 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ + 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ + 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ + 1.16614003333790000205e-09}; /* 0x3E1408BC, 0xF4745D8F */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_j0(double x) +#else + double __ieee754_j0(x) + double x; +#endif +{ + double z, s,c,ss,cc,r,u,v,r1,r2,s1,s2,z2,z4; + int32_t hx,ix; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return one/(x*x); + x = fabs(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = __sin(x); + c = __cos(x); + ss = s-c; + cc = s+c; + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = -__cos(x+x); + if ((s*c)<zero) cc = z/ss; + else ss = z/cc; + } + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix>0x48000000) z = (invsqrtpi*cc)/__sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*cc-v*ss)/__sqrt(x); + } + return z; + } + if(ix<0x3f200000) { /* |x| < 2**-13 */ + if(huge+x>one) { /* raise inexact if x != 0 */ + if(ix<0x3e400000) return one; /* |x|<2**-27 */ + else return one - 0.25*x*x; + } + } + z = x*x; +#ifdef DO_NOT_USE_THIS + r = z*(R02+z*(R03+z*(R04+z*R05))); + s = one+z*(S01+z*(S02+z*(S03+z*S04))); +#else + r1 = z*R[2]; z2=z*z; + r2 = R[3]+z*R[4]; z4=z2*z2; + r = r1 + z2*r2 + z4*R[5]; + s1 = one+z*S[1]; + s2 = S[2]+z*S[3]; + s = s1 + z2*s2 + z4*S[4]; +#endif + if(ix < 0x3FF00000) { /* |x| < 1.00 */ + return one + z*(-0.25+(r/s)); + } else { + u = 0.5*x; + return((one+u)*(one-u)+z*(r/s)); + } +} + +#ifdef __STDC__ +static const double +#else +static double +#endif +U[] = {-7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ + 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ + -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ + 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ + -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ + 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ + -3.98205194132103398453e-11}, /* 0xBDC5E43D, 0x693FB3C8 */ +V[] = {1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ + 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ + 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ + 4.41110311332675467403e-10}; /* 0x3DFE5018, 0x3BD6D9EF */ + +#ifdef __STDC__ + double __ieee754_y0(double x) +#else + double __ieee754_y0(x) + double x; +#endif +{ + double z, s,c,ss,cc,u,v,z2,z4,z6,u1,u2,u3,v1,v2; + int32_t hx,ix,lx; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ + if(ix>=0x7ff00000) return one/(x+x*x); + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + s = __sin(x); + c = __cos(x); + ss = s-c; + cc = s+c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = -__cos(x+x); + if ((s*c)<zero) cc = z/ss; + else ss = z/cc; + } + if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*ss+v*cc)/__sqrt(x); + } + return z; + } + if(ix<=0x3e400000) { /* x < 2**-27 */ + return(U[0] + tpi*__ieee754_log(x)); + } + z = x*x; +#ifdef DO_NOT_USE_THIS + u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); + v = one+z*(v01+z*(v02+z*(v03+z*v04))); +#else + u1 = U[0]+z*U[1]; z2=z*z; + u2 = U[2]+z*U[3]; z4=z2*z2; + u3 = U[4]+z*U[5]; z6=z4*z2; + u = u1 + z2*u2 + z4*u3 + z6*U[6]; + v1 = one+z*V[0]; + v2 = V[1]+z*V[2]; + v = v1 + z2*v2 + z4*V[3]; +#endif + return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); +} + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +#ifdef __STDC__ +static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ + -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ + -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ + -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ + -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ +}; +#ifdef __STDC__ +static const double pS8[5] = { +#else +static double pS8[5] = { +#endif + 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ + 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ + 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ + 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ + 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ +}; + +#ifdef __STDC__ +static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ + -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ + -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ + -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ + -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ + -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ +}; +#ifdef __STDC__ +static const double pS5[5] = { +#else +static double pS5[5] = { +#endif + 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ + 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ + 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ + 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ + 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ +}; + +#ifdef __STDC__ +static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#else +static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ + -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ + -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ + -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ + -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ + -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ +}; +#ifdef __STDC__ +static const double pS3[5] = { +#else +static double pS3[5] = { +#endif + 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ + 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ + 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ + 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ + 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ +}; + +#ifdef __STDC__ +static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ + -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ + -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ + -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ + -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ + -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ +}; +#ifdef __STDC__ +static const double pS2[5] = { +#else +static double pS2[5] = { +#endif + 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ + 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ + 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ + 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ + 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ +}; + +#ifdef __STDC__ + static double pzero(double x) +#else + static double pzero(x) + double x; +#endif +{ +#ifdef __STDC__ + const double *p,*q; +#else + double *p,*q; +#endif + double z,r,s,z2,z4,r1,r2,r3,s1,s2,s3; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = pR8; q= pS8;} + else if(ix>=0x40122E8B){p = pR5; q= pS5;} + else if(ix>=0x4006DB6D){p = pR3; q= pS3;} + else if(ix>=0x40000000){p = pR2; q= pS2;} + z = one/(x*x); +#ifdef DO_NOT_USE_THIS + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); +#else + r1 = p[0]+z*p[1]; z2=z*z; + r2 = p[2]+z*p[3]; z4=z2*z2; + r3 = p[4]+z*p[5]; + r = r1 + z2*r2 + z4*r3; + s1 = one+z*q[0]; + s2 = q[1]+z*q[2]; + s3 = q[3]+z*q[4]; + s = s1 + z2*s2 + z4*s3; +#endif + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +#ifdef __STDC__ +static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ + 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ + 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ + 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ + 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ +}; +#ifdef __STDC__ +static const double qS8[6] = { +#else +static double qS8[6] = { +#endif + 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ + 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ + 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ + 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ + 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ + -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ +}; + +#ifdef __STDC__ +static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ + 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ + 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ + 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ + 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ + 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ +}; +#ifdef __STDC__ +static const double qS5[6] = { +#else +static double qS5[6] = { +#endif + 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ + 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ + 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ + 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ + 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ + -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ +}; + +#ifdef __STDC__ +static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#else +static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ + 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ + 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ + 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ + 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ + 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ +}; +#ifdef __STDC__ +static const double qS3[6] = { +#else +static double qS3[6] = { +#endif + 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ + 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ + 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ + 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ + 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ + -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ +}; + +#ifdef __STDC__ +static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ + 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ + 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ + 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ + 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ + 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ +}; +#ifdef __STDC__ +static const double qS2[6] = { +#else +static double qS2[6] = { +#endif + 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ + 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ + 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ + 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ + 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ + -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ +}; + +#ifdef __STDC__ + static double qzero(double x) +#else + static double qzero(x) + double x; +#endif +{ +#ifdef __STDC__ + const double *p,*q; +#else + double *p,*q; +#endif + double s,r,z,z2,z4,z6,r1,r2,r3,s1,s2,s3; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = qR8; q= qS8;} + else if(ix>=0x40122E8B){p = qR5; q= qS5;} + else if(ix>=0x4006DB6D){p = qR3; q= qS3;} + else if(ix>=0x40000000){p = qR2; q= qS2;} + z = one/(x*x); +#ifdef DO_NOT_USE_THIS + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); +#else + r1 = p[0]+z*p[1]; z2=z*z; + r2 = p[2]+z*p[3]; z4=z2*z2; + r3 = p[4]+z*p[5]; z6=z4*z2; + r= r1 + z2*r2 + z4*r3; + s1 = one+z*q[0]; + s2 = q[1]+z*q[2]; + s3 = q[3]+z*q[4]; + s = s1 + z2*s2 + z4*s3 +z6*q[5]; +#endif + return (-.125 + r/s)/x; +} diff --git a/sysdeps/ieee754/dbl-64/e_j1.c b/sysdeps/ieee754/dbl-64/e_j1.c new file mode 100644 index 0000000..daf025f --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_j1.c @@ -0,0 +1,532 @@ +/* @(#)e_j1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/26, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_j1.c,v 1.8 1995/05/10 20:45:27 jtc Exp $"; +#endif + +/* __ieee754_j1(x), __ieee754_y1(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j1(x): + * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... + * 2. Reduce x to |x| since j1(x)=-j1(-x), and + * for x in (0,2) + * j1(x) = x/2 + x*z*R0/S0, where z = x*x; + * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) + * for x in (2,inf) + * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * as follow: + * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (sin(x) + cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j1(nan)= nan + * j1(0) = 0 + * j1(inf) = 0 + * + * Method -- y1(x): + * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN + * 2. For x<2. + * Since + * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) + * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. + * We use the following function to approximate y1, + * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 + * where for x in [0,2] (abs err less than 2**-65.89) + * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 + * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 + * Note: For tiny x, 1/x dominate y1 and hence + * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) + * 3. For x>=2. + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * by method mentioned above. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static double pone(double), qone(double); +#else +static double pone(), qone(); +#endif + +#ifdef __STDC__ +static const double +#else +static double +#endif +huge = 1e300, +one = 1.0, +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + /* R0/S0 on [0,2] */ +R[] = {-6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ + 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ + -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ + 4.96727999609584448412e-08}, /* 0x3E6AAAFA, 0x46CA0BD9 */ +S[] = {0.0, 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ + 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ + 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ + 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ + 1.23542274426137913908e-11}; /* 0x3DAB2ACF, 0xCFB97ED8 */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_j1(double x) +#else + double __ieee754_j1(x) + double x; +#endif +{ + double z, s,c,ss,cc,r,u,v,y,r1,r2,s1,s2,s3,z2,z4; + int32_t hx,ix; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return one/x; + y = fabs(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = __sin(y); + c = __cos(y); + ss = -s-c; + cc = s-c; + if(ix<0x7fe00000) { /* make sure y+y not overflow */ + z = __cos(y+y); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* + * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) + * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) + */ + if(ix>0x48000000) z = (invsqrtpi*cc)/__sqrt(y); + else { + u = pone(y); v = qone(y); + z = invsqrtpi*(u*cc-v*ss)/__sqrt(y); + } + if(hx<0) return -z; + else return z; + } + if(ix<0x3e400000) { /* |x|<2**-27 */ + if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ + } + z = x*x; +#ifdef DO_NOT_USE_THIS + r = z*(r00+z*(r01+z*(r02+z*r03))); + s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); + r *= x; +#else + r1 = z*R[0]; z2=z*z; + r2 = R[1]+z*R[2]; z4=z2*z2; + r = r1 + z2*r2 + z4*R[3]; + r *= x; + s1 = one+z*S[1]; + s2 = S[2]+z*S[3]; + s3 = S[4]+z*S[5]; + s = s1 + z2*s2 + z4*s3; +#endif + return(x*0.5+r/s); +} + +#ifdef __STDC__ +static const double U0[5] = { +#else +static double U0[5] = { +#endif + -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ + 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ + -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ + 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ + -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ +}; +#ifdef __STDC__ +static const double V0[5] = { +#else +static double V0[5] = { +#endif + 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ + 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ + 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ + 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ + 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ +}; + +#ifdef __STDC__ + double __ieee754_y1(double x) +#else + double __ieee754_y1(x) + double x; +#endif +{ + double z, s,c,ss,cc,u,v,u1,u2,v1,v2,v3,z2,z4; + int32_t hx,ix,lx; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if(ix>=0x7ff00000) return one/(x+x*x); + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = __sin(x); + c = __cos(x); + ss = -s-c; + cc = s-c; + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = __cos(x+x); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) + * where x0 = x-3pi/4 + * Better formula: + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (cos(x) + sin(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrt(x); + else { + u = pone(x); v = qone(x); + z = invsqrtpi*(u*ss+v*cc)/__sqrt(x); + } + return z; + } + if(ix<=0x3c900000) { /* x < 2**-54 */ + return(-tpi/x); + } + z = x*x; +#ifdef DO_NOT_USE_THIS + u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); + v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); +#else + u1 = U0[0]+z*U0[1];z2=z*z; + u2 = U0[2]+z*U0[3];z4=z2*z2; + u = u1 + z2*u2 + z4*U0[4]; + v1 = one+z*V0[0]; + v2 = V0[1]+z*V0[2]; + v3 = V0[3]+z*V0[4]; + v = v1 + z2*v2 + z4*v3; +#endif + return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); +} + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pone(x)-1-R/S | <= 2 ** ( -60.06) + */ + +#ifdef __STDC__ +static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ + 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ + 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ + 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ + 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ +}; +#ifdef __STDC__ +static const double ps8[5] = { +#else +static double ps8[5] = { +#endif + 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ + 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ + 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ + 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ + 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ +}; + +#ifdef __STDC__ +static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ + 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ + 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ + 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ + 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ + 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ +}; +#ifdef __STDC__ +static const double ps5[5] = { +#else +static double ps5[5] = { +#endif + 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ + 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ + 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ + 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ + 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ +}; + +#ifdef __STDC__ +static const double pr3[6] = { +#else +static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ + 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ + 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ + 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ + 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ + 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ +}; +#ifdef __STDC__ +static const double ps3[5] = { +#else +static double ps3[5] = { +#endif + 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ + 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ + 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ + 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ + 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ +}; + +#ifdef __STDC__ +static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ + 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ + 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ + 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ + 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ + 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ +}; +#ifdef __STDC__ +static const double ps2[5] = { +#else +static double ps2[5] = { +#endif + 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ + 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ + 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ + 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ + 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ +}; + +#ifdef __STDC__ + static double pone(double x) +#else + static double pone(x) + double x; +#endif +{ +#ifdef __STDC__ + const double *p,*q; +#else + double *p,*q; +#endif + double z,r,s,r1,r2,r3,s1,s2,s3,z2,z4; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = pr8; q= ps8;} + else if(ix>=0x40122E8B){p = pr5; q= ps5;} + else if(ix>=0x4006DB6D){p = pr3; q= ps3;} + else if(ix>=0x40000000){p = pr2; q= ps2;} + z = one/(x*x); +#ifdef DO_NOT_USE_THIS + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); +#else + r1 = p[0]+z*p[1]; z2=z*z; + r2 = p[2]+z*p[3]; z4=z2*z2; + r3 = p[4]+z*p[5]; + r = r1 + z2*r2 + z4*r3; + s1 = one+z*q[0]; + s2 = q[1]+z*q[2]; + s3 = q[3]+z*q[4]; + s = s1 + z2*s2 + z4*s3; +#endif + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +#ifdef __STDC__ +static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ + -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ + -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ + -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ + -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ +}; +#ifdef __STDC__ +static const double qs8[6] = { +#else +static double qs8[6] = { +#endif + 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ + 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ + 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ + 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ + 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ + -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ +}; + +#ifdef __STDC__ +static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ + -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ + -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ + -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ + -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ + -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ +}; +#ifdef __STDC__ +static const double qs5[6] = { +#else +static double qs5[6] = { +#endif + 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ + 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ + 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ + 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ + 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ + -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ +}; + +#ifdef __STDC__ +static const double qr3[6] = { +#else +static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ + -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ + -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ + -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ + -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ + -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ +}; +#ifdef __STDC__ +static const double qs3[6] = { +#else +static double qs3[6] = { +#endif + 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ + 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ + 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ + 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ + 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ + -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ +}; + +#ifdef __STDC__ +static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ + -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ + -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ + -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ + -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ + -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ +}; +#ifdef __STDC__ +static const double qs2[6] = { +#else +static double qs2[6] = { +#endif + 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ + 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ + 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ + 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ + 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ + -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ +}; + +#ifdef __STDC__ + static double qone(double x) +#else + static double qone(x) + double x; +#endif +{ +#ifdef __STDC__ + const double *p,*q; +#else + double *p,*q; +#endif + double s,r,z,r1,r2,r3,s1,s2,s3,z2,z4,z6; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = qr8; q= qs8;} + else if(ix>=0x40122E8B){p = qr5; q= qs5;} + else if(ix>=0x4006DB6D){p = qr3; q= qs3;} + else if(ix>=0x40000000){p = qr2; q= qs2;} + z = one/(x*x); +#ifdef DO_NOT_USE_THIS + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); +#else + r1 = p[0]+z*p[1]; z2=z*z; + r2 = p[2]+z*p[3]; z4=z2*z2; + r3 = p[4]+z*p[5]; z6=z4*z2; + r = r1 + z2*r2 + z4*r3; + s1 = one+z*q[0]; + s2 = q[1]+z*q[2]; + s3 = q[3]+z*q[4]; + s = s1 + z2*s2 + z4*s3 + z6*q[5]; +#endif + return (.375 + r/s)/x; +} diff --git a/sysdeps/ieee754/dbl-64/e_jn.c b/sysdeps/ieee754/dbl-64/e_jn.c new file mode 100644 index 0000000..d63d768 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_jn.c @@ -0,0 +1,281 @@ +/* @(#)e_jn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_jn.c,v 1.9 1995/05/10 20:45:34 jtc Exp $"; +#endif + +/* + * __ieee754_jn(n, x), __ieee754_yn(n, x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for n<x, forward recursion us used starting + * from values of j0(x) and j1(x). + * for n>x, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ +one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */ + +#ifdef __STDC__ +static const double zero = 0.00000000000000000000e+00; +#else +static double zero = 0.00000000000000000000e+00; +#endif + +#ifdef __STDC__ + double __ieee754_jn(int n, double x) +#else + double __ieee754_jn(n,x) + int n; double x; +#endif +{ + int32_t i,hx,ix,lx, sgn; + double a, b, temp, di; + double z, w; + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if J(n,NaN) is NaN */ + if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; + if(n<0){ + n = -n; + x = -x; + hx ^= 0x80000000; + } + if(n==0) return(__ieee754_j0(x)); + if(n==1) return(__ieee754_j1(x)); + sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ + x = fabs(x); + if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */ + b = zero; + else if((double)n<=x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + if(ix>=0x52D00000) { /* x > 2**302 */ + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + switch(n&3) { + case 0: temp = __cos(x)+__sin(x); break; + case 1: temp = -__cos(x)+__sin(x); break; + case 2: temp = -__cos(x)-__sin(x); break; + case 3: temp = __cos(x)-__sin(x); break; + } + b = invsqrtpi*temp/__sqrt(x); + } else { + a = __ieee754_j0(x); + b = __ieee754_j1(x); + for(i=1;i<n;i++){ + temp = b; + b = b*((double)(i+i)/x) - a; /* avoid underflow */ + a = temp; + } + } + } else { + if(ix<0x3e100000) { /* x < 2**-29 */ + /* x is tiny, return the first Taylor expansion of J(n,x) + * J(n,x) = 1/n!*(x/2)^n - ... + */ + if(n>33) /* underflow */ + b = zero; + else { + temp = x*0.5; b = temp; + for (a=one,i=2;i<=n;i++) { + a *= (double)i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b/a; + } + } else { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + double t,v; + double q0,q1,h,tmp; int32_t k,m; + w = (n+n)/(double)x; h = 2.0/(double)x; + q0 = w; z = w+h; q1 = w*z - 1.0; k=1; + while(q1<1.0e9) { + k += 1; z += h; + tmp = z*q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n+n; + for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two/x; + tmp = tmp*__ieee754_log(fabs(v*tmp)); + if(tmp<7.09782712893383973096e+02) { + for(i=n-1,di=(double)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + } + } else { + for(i=n-1,di=(double)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if(b>1e100) { + a /= b; + t /= b; + b = one; + } + } + } + b = (t*__ieee754_j0(x)/b); + } + } + if(sgn==1) return -b; else return b; +} + +#ifdef __STDC__ + double __ieee754_yn(int n, double x) +#else + double __ieee754_yn(n,x) + int n; double x; +#endif +{ + int32_t i,hx,ix,lx; + int32_t sign; + double a, b, temp; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if Y(n,NaN) is NaN */ + if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + sign = 1; + if(n<0){ + n = -n; + sign = 1 - ((n&1)<<1); + } + if(n==0) return(__ieee754_y0(x)); + if(n==1) return(sign*__ieee754_y1(x)); + if(ix==0x7ff00000) return zero; + if(ix>=0x52D00000) { /* x > 2**302 */ + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + switch(n&3) { + case 0: temp = __sin(x)-__cos(x); break; + case 1: temp = -__sin(x)-__cos(x); break; + case 2: temp = -__sin(x)+__cos(x); break; + case 3: temp = __sin(x)+__cos(x); break; + } + b = invsqrtpi*temp/__sqrt(x); + } else { + u_int32_t high; + a = __ieee754_y0(x); + b = __ieee754_y1(x); + /* quit if b is -inf */ + GET_HIGH_WORD(high,b); + for(i=1;i<n&&high!=0xfff00000;i++){ + temp = b; + b = ((double)(i+i)/x)*b - a; + GET_HIGH_WORD(high,b); + a = temp; + } + } + if(sign>0) return b; else return -b; +} diff --git a/sysdeps/ieee754/dbl-64/e_lgamma_r.c b/sysdeps/ieee754/dbl-64/e_lgamma_r.c new file mode 100644 index 0000000..92e9556 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_lgamma_r.c @@ -0,0 +1,314 @@ +/* @(#)er_lgamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_lgamma_r.c,v 1.7 1995/05/10 20:45:42 jtc Exp $"; +#endif + +/* __ieee754_lgamma_r(x, signgamp) + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). + * + * Method: + * 1. Argument Reduction for 0 < x <= 8 + * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may + * reduce x to a number in [1.5,2.5] by + * lgamma(1+s) = log(s) + lgamma(s) + * for example, + * lgamma(7.3) = log(6.3) + lgamma(6.3) + * = log(6.3*5.3) + lgamma(5.3) + * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) + * 2. Polynomial approximation of lgamma around its + * minimun ymin=1.461632144968362245 to maintain monotonicity. + * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use + * Let z = x-ymin; + * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) + * where + * poly(z) is a 14 degree polynomial. + * 2. Rational approximation in the primary interval [2,3] + * We use the following approximation: + * s = x-2.0; + * lgamma(x) = 0.5*s + s*P(s)/Q(s) + * with accuracy + * |P/Q - (lgamma(x)-0.5s)| < 2**-61.71 + * Our algorithms are based on the following observation + * + * zeta(2)-1 2 zeta(3)-1 3 + * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... + * 2 3 + * + * where Euler = 0.5771... is the Euler constant, which is very + * close to 0.5. + * + * 3. For x>=8, we have + * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... + * (better formula: + * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) + * Let z = 1/x, then we approximation + * f(z) = lgamma(x) - (x-0.5)(log(x)-1) + * by + * 3 5 11 + * w = w0 + w1*z + w2*z + w3*z + ... + w6*z + * where + * |w - f(z)| < 2**-58.74 + * + * 4. For negative x, since (G is gamma function) + * -x*G(-x)*G(x) = pi/sin(pi*x), + * we have + * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) + * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 + * Hence, for x<0, signgam = sign(sin(pi*x)) and + * lgamma(x) = log(|Gamma(x)|) + * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); + * Note: one should avoid compute pi*(-x) directly in the + * computation of sin(pi*(-x)). + * + * 5. Special Cases + * lgamma(2+s) ~ s*(1-Euler) for tiny s + * lgamma(1)=lgamma(2)=0 + * lgamma(x) ~ -log(x) for tiny x + * lgamma(0) = lgamma(inf) = inf + * lgamma(-integer) = +-inf + * + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */ +a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */ +a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */ +a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */ +a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */ +a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */ +a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */ +a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */ +a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */ +a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */ +a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */ +a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */ +tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */ +tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */ +/* tt = -(tail of tf) */ +tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */ +t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */ +t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */ +t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */ +t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */ +t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */ +t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */ +t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */ +t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */ +t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */ +t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */ +t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */ +t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */ +t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */ +t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */ +t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */ +u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */ +u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */ +u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */ +u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */ +u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */ +v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */ +v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */ +v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */ +v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */ +v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */ +s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */ +s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */ +s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */ +s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */ +s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */ +s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */ +r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */ +r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */ +r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */ +r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */ +r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */ +r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */ +w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */ +w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */ +w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */ +w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */ +w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */ +w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */ +w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */ + +#ifdef __STDC__ +static const double zero= 0.00000000000000000000e+00; +#else +static double zero= 0.00000000000000000000e+00; +#endif + +#ifdef __STDC__ + static double sin_pi(double x) +#else + static double sin_pi(x) + double x; +#endif +{ + double y,z; + int n,ix; + + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = __floor(y); + if(z!=y) { /* inexact anyway */ + y *= 0.5; + y = 2.0*(y - __floor(y)); /* y = |x| mod 2.0 */ + n = (int) (y*4.0); + } else { + if(ix>=0x43400000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x43300000) z = y+two52; /* exact */ + GET_LOW_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __kernel_sin(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cos(pi*(0.5-y),zero); break; + case 3: + case 4: y = __kernel_sin(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cos(pi*(y-1.5),zero); break; + default: y = __kernel_sin(pi*(y-2.0),zero,0); break; + } + return -y; +} + + +#ifdef __STDC__ + double __ieee754_lgamma_r(double x, int *signgamp) +#else + double __ieee754_lgamma_r(x,signgamp) + double x; int *signgamp; +#endif +{ + double t,y,z,nadj,p,p1,p2,p3,q,r,w; + int i,hx,lx,ix; + + EXTRACT_WORDS(hx,lx,x); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + *signgamp = 1; + if ((unsigned int) hx==0xfff00000&&lx==0) + return x-x; + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x*x; + if((ix|lx)==0) return one/fabs(x); + if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */ + if(hx<0) { + *signgamp = -1; + return -__ieee754_log(-x); + } else return -__ieee754_log(x); + } + if(hx<0) { + if(ix>=0x43300000) /* |x|>=2**52, must be -integer */ + return x/zero; + t = sin_pi(x); + if(t==zero) return one/fabsf(t); /* -integer */ + nadj = __ieee754_log(pi/fabs(t*x)); + if(t<zero) *signgamp = -1; + x = -x; + } + + /* purge off 1 and 2 */ + if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0; + /* for x < 2.0 */ + else if(ix<0x40000000) { + if(ix<=0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */ + r = -__ieee754_log(x); + if(ix>=0x3FE76944) {y = one-x; i= 0;} + else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-0.5*y + p1/p2); + } + } + else if(ix<0x40200000) { /* x < 8.0 */ + i = (int)x; + t = zero; + y = x-(double)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+6.0); /* FALLTHRU */ + case 6: z *= (y+5.0); /* FALLTHRU */ + case 5: z *= (y+4.0); /* FALLTHRU */ + case 4: z *= (y+3.0); /* FALLTHRU */ + case 3: z *= (y+2.0); /* FALLTHRU */ + r += __ieee754_log(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x43900000) { + t = __ieee754_log(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = x*(__ieee754_log(x)-one); + if(hx<0) r = nadj - r; + return r; +} diff --git a/sysdeps/ieee754/dbl-64/e_log.c b/sysdeps/ieee754/dbl-64/e_log.c new file mode 100644 index 0000000..851bd30 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_log.c @@ -0,0 +1,165 @@ +/* @(#)e_log.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $"; +#endif + +/* __ieee754_log(x) + * Return the logarithm of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k*ln2 + log(1+f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log(x) is NaN with signal if x < 0 (including -INF) ; + * log(+INF) is +INF; log(0) is -INF with signal; + * log(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" +#define half Lg[8] +#define two Lg[9] +#ifdef __STDC__ +static const double +#else +static double +#endif +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ +ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ + Lg[] = {0.0, + 6.666666666666735130e-01, /* 3FE55555 55555593 */ + 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ + 2.857142874366239149e-01, /* 3FD24924 94229359 */ + 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ + 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ + 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ + 1.479819860511658591e-01, /* 3FC2F112 DF3E5244 */ + 0.5, + 2.0}; +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_log(double x) +#else + double __ieee754_log(x) + double x; +#endif +{ + double hfsq,f,s,z,R,w,dk,t11,t12,t21,t22,w2,zw2; +#ifdef DO_NOT_USE_THIS + double t1,t2; +#endif + int32_t k,hx,i,j; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/(x-x); /* log(+-0)=-inf */ + if (hx<0) return (x-x)/(x-x); /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ + k += (i>>20); + f = x-1.0; + if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ + if(f==zero) { + if(k==0) return zero; else {dk=(double)k; + return dk*ln2_hi+dk*ln2_lo;} + } + R = f*f*(half-0.33333333333333333*f); + if(k==0) return f-R; else {dk=(double)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/(two+f); + dk = (double)k; + z = s*s; + i = hx-0x6147a; + w = z*z; + j = 0x6b851-hx; +#ifdef DO_NOT_USE_THIS + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + R = t2+t1; +#else + t21 = Lg[5]+w*Lg[7]; w2=w*w; + t22 = Lg[1]+w*Lg[3]; zw2=z*w2; + t11 = Lg[4]+w*Lg[6]; + t12 = w*Lg[2]; + R = t12 + w2*t11 + z*t22 + zw2*t21; +#endif + i |= j; + if(i>0) { + hfsq=0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} diff --git a/sysdeps/ieee754/dbl-64/e_log10.c b/sysdeps/ieee754/dbl-64/e_log10.c new file mode 100644 index 0000000..e8a3278 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_log10.c @@ -0,0 +1,98 @@ +/* @(#)e_log10.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_log10.c,v 1.9 1995/05/10 20:45:51 jtc Exp $"; +#endif + +/* __ieee754_log10(x) + * Return the base 10 logarithm of x + * + * Method : + * Let log10_2hi = leading 40 bits of log10(2) and + * log10_2lo = log10(2) - log10_2hi, + * ivln10 = 1/log(10) rounded. + * Then + * n = ilogb(x), + * if(n<0) n = n+1; + * x = scalbn(x,-n); + * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) + * + * Note 1: + * To guarantee log10(10**n)=n, where 10**n is normal, the rounding + * mode must set to Round-to-Nearest. + * Note 2: + * [1/log(10)] rounded to 53 bits has error .198 ulps; + * log10 is monotonic at all binary break points. + * + * Special cases: + * log10(x) is NaN with signal if x < 0; + * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; + * log10(NaN) is that NaN with no signal; + * log10(10**N) = N for N=0,1,...,22. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ +log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ +log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_log10(double x) +#else + double __ieee754_log10(x) + double x; +#endif +{ + double y,z; + int32_t i,k,hx; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/(x-x); /* log(+-0)=-inf */ + if (hx<0) return (x-x)/(x-x); /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + i = ((u_int32_t)k&0x80000000)>>31; + hx = (hx&0x000fffff)|((0x3ff-i)<<20); + y = (double)(k+i); + SET_HIGH_WORD(x,hx); + z = y*log10_2lo + ivln10*__ieee754_log(x); + return z+y*log10_2hi; +} diff --git a/sysdeps/ieee754/dbl-64/e_pow.c b/sysdeps/ieee754/dbl-64/e_pow.c new file mode 100644 index 0000000..1e1496f --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_pow.c @@ -0,0 +1,352 @@ +/* @(#)e_pow.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; +#endif + +/* __ieee754_pow(x,y) return x**y + * + * n + * Method: Let x = 2 * (1+f) + * 1. Compute and return log2(x) in two pieces: + * log2(x) = w1 + w2, + * where w1 has 53-24 = 29 bit trailing zeros. + * 2. Perform y*log2(x) = n+y' by simulating muti-precision + * arithmetic, where |y'|<=0.5. + * 3. Return x**y = 2**n*exp(y'*log2) + * + * Special cases: + * 1. (anything) ** 0 is 1 + * 2. (anything) ** 1 is itself + * 3. (anything) ** NAN is NAN + * 4. NAN ** (anything except 0) is NAN + * 5. +-(|x| > 1) ** +INF is +INF + * 6. +-(|x| > 1) ** -INF is +0 + * 7. +-(|x| < 1) ** +INF is +0 + * 8. +-(|x| < 1) ** -INF is +INF + * 9. +-1 ** +-INF is NAN + * 10. +0 ** (+anything except 0, NAN) is +0 + * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 12. +0 ** (-anything except 0, NAN) is +INF + * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 15. +INF ** (+anything except 0,NAN) is +INF + * 16. +INF ** (-anything except 0,NAN) is +0 + * 17. -INF ** (anything) = -0 ** (-anything) + * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * + * Accuracy: + * pow(x,y) returns x**y nearly rounded. In particular + * pow(integer,integer) + * always returns the correct integer provided it is + * representable. + * + * Constants : + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" +#define zero C[0] +#define one C[1] +#define two C[2] +#define two53 C[3] +#define huge C[4] +#define tiny C[5] +#define L1 C[6] +#define L2 C[7] +#define L3 C[8] +#define L4 C[9] +#define L5 C[10] +#define L6 C[11] +#define P1 C[12] +#define P2 C[13] +#define P3 C[14] +#define P4 C[15] +#define P5 C[16] +#define lg2 C[17] +#define lg2_h C[18] +#define lg2_l C[19] +#define ovt C[20] +#define cp C[21] +#define cp_h C[22] +#define cp_l C[23] +#define ivln2 C[24] +#define ivln2_h C[25] +#define ivln2_l C[26] + +#ifdef __STDC__ +static const double +#else +static double +#endif +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ +dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ +C[] = { +0.0, +1.0, +2.0, +9007199254740992.0 , +1.0e300, +1.0e-300, +5.99999999999994648725e-01 , +4.28571428578550184252e-01 , +3.33333329818377432918e-01 , +2.72728123808534006489e-01 , +2.30660745775561754067e-01 , +2.06975017800338417784e-01 , +1.66666666666666019037e-01 , +-2.77777777770155933842e-03 , +6.61375632143793436117e-05 , +-1.65339022054652515390e-06 , +4.13813679705723846039e-08 , +6.93147180559945286227e-01 , +6.93147182464599609375e-01 , +-1.90465429995776804525e-09 , +8.0085662595372944372e-0017 , +9.61796693925975554329e-01 , +9.61796700954437255859e-01 , +-7.02846165095275826516e-09 , +1.44269504088896338700e+00 , +1.44269502162933349609e+00 , +1.92596299112661746887e-08 }; + +#ifdef __STDC__ + double __ieee754_pow(double x, double y) +#else + double __ieee754_pow(x,y) + double x, y; +#endif +{ + double z,ax,z_h,z_l,p_h,p_l; + double y1,t1,t2,r,s,t,u,v,w, t12,t14,r_1,r_2,r_3; + int32_t i,j,k,yisint,n; + int32_t hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + if((iy|ly)==0) return C[1]; + + /* +-NaN return x+y */ + if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || + iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) + return x+y; + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if(hx<0) { + if(iy>=0x43400000) yisint = 2; /* even integer y */ + else if(iy>=0x3ff00000) { + k = (iy>>20)-0x3ff; /* exponent */ + if(k>20) { + j = ly>>(52-k); + if((u_int32_t)(j<<(52-k))==ly) yisint = 2-(j&1); + } else if(ly==0) { + j = iy>>(20-k); + if((int32_t)(j<<(20-k))==iy) yisint = 2-(j&1); + } + } + } + + /* special value of y */ + if(ly==0) { + if (iy==0x7ff00000) { /* y is +-inf */ + if(((ix-0x3ff00000)|lx)==0) + return y - y; /* inf**+-1 is NaN */ + else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: C[0]; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: C[0]; + } + if(iy==0x3ff00000) { /* y is +-1 */ + if(hy<0) return C[1]/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3fe00000) { /* y is 0.5 */ + if(hx>=0) /* x >= +0 */ + return __ieee754_sqrt(x); + } + } + + ax = fabs(x); + /* special value of x */ + if(lx==0) { + if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = C[1]/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3ff00000)|yisint)==0) { + z = (z-z)/(z-z); /* (-1)**non-int is NaN */ + } else if(yisint==1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + } + + /* (x<0)**(non-int) is NaN */ + if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); + + /* |y| is huge */ + if(iy>0x41e00000) { /* if |y| > 2**31 */ + if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ + if(ix<=0x3fefffff) return (hy<0)? C[4]*C[4]:C[5]*C[5]; + if(ix>=0x3ff00000) return (hy>0)? C[4]*C[4]:C[5]*C[5]; + } + /* over/underflow if x is not close to one */ + if(ix<0x3fefffff) return (hy<0)? C[4]*C[4]:C[5]*C[5]; + if(ix>0x3ff00000) return (hy>0)? C[4]*C[4]:C[5]*C[5]; + /* now |1-x| is tiny <= 2**-20, suffice to compute + log(x) by x-x^2/2+x^3/3-x^4/4 */ + t = x-1; /* t has 20 trailing zeros */ + w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); + u = C[25]*t; /* ivln2_h has 21 sig. bits */ + v = t*C[26]-w*C[24]; + t1 = u+v; + SET_LOW_WORD(t1,0); + t2 = v-(t1-u); + } else { + double s2,s_h,s_l,t_h,t_l,s22,s24,s26,r1,r2,r3; + n = 0; + /* take care subnormal number */ + if(ix<0x00100000) + {ax *= C[3]; n -= 53; GET_HIGH_WORD(ix,ax); } + n += ((ix)>>20)-0x3ff; + j = ix&0x000fffff; + /* determine interval */ + ix = j|0x3ff00000; /* normalize ix */ + if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */ + else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ + else {k=0;n+=1;ix -= 0x00100000;} + SET_HIGH_WORD(ax,ix); + + /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ + u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ + v = C[1]/(ax+bp[k]); + s = u*v; + s_h = s; + SET_LOW_WORD(s_h,0); + /* t_h=ax+bp[k] High */ + t_h = C[0]; + SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18)); + t_l = ax - (t_h-bp[k]); + s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + s2 = s*s; +#ifdef DO_NOT_USE_THIS + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); +#else + r1 = C[10]+s2*C[11]; s22=s2*s2; + r2 = C[8]+s2*C[9]; s24=s22*s22; + r3 = C[6]+s2*C[7]; s26=s24*s22; + r = r3*s22 + r2*s24 + r1*s26; +#endif + r += s_l*(s_h+s); + s2 = s_h*s_h; + t_h = 3.0+s2+r; + SET_LOW_WORD(t_h,0); + t_l = r-((t_h-3.0)-s2); + /* u+v = s*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*s; + /* 2/(3log2)*(s+...) */ + p_h = u+v; + SET_LOW_WORD(p_h,0); + p_l = v-(p_h-u); + z_h = C[22]*p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = C[23]*p_h+p_l*C[21]+dp_l[k]; + /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = (double)n; + t1 = (((z_h+z_l)+dp_h[k])+t); + SET_LOW_WORD(t1,0); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + s = C[1]; /* s (sign of result -ve**odd) = -1 else = 1 */ + if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) + s = -C[1];/* (-ve)**(odd int) */ + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + y1 = y; + SET_LOW_WORD(y1,0); + p_l = (y-y1)*t1+y*t2; + p_h = y1*t1; + z = p_l+p_h; + EXTRACT_WORDS(j,i,z); + if (j>=0x40900000) { /* z >= 1024 */ + if(((j-0x40900000)|i)!=0) /* if z > 1024 */ + return s*C[4]*C[4]; /* overflow */ + else { + if(p_l+C[20]>z-p_h) return s*C[4]*C[4]; /* overflow */ + } + } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ + if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ + return s*C[5]*C[5]; /* underflow */ + else { + if(p_l<=z-p_h) return s*C[5]*C[5]; /* underflow */ + } + } + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>20)-0x3ff; + n = 0; + if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00100000>>(k+1)); + k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ + t = C[0]; + SET_HIGH_WORD(t,n&~(0x000fffff>>k)); + n = ((n&0x000fffff)|0x00100000)>>(20-k); + if(j<0) n = -n; + p_h -= t; + } + t = p_l+p_h; + SET_LOW_WORD(t,0); + u = t*C[18]; + v = (p_l-(t-p_h))*C[17]+t*C[19]; + z = u+v; + w = v-(z-u); + t = z*z; +#ifdef DO_NOT_USE_THIS + t1 = z - t*(C[12]+t*(C[13]+t*(C[14]+t*(C[15]+t*C[16])))); +#else + r_1 = C[15]+t*C[16]; t12 = t*t; + r_2 = C[13]+t*C[14]; t14 = t12*t12; + r_3 = t*C[12]; + t1 = z - r_3 - t12*r_2 - t14*r_1; +#endif + r = (z*t1)/(t1-C[2])-(w+z*w); + z = C[1]-(r-z); + GET_HIGH_WORD(j,z); + j += (n<<20); + if((j>>20)<=0) z = __scalbn(z,n); /* subnormal output */ + else SET_HIGH_WORD(z,j); + return s*z; +} diff --git a/sysdeps/ieee754/dbl-64/e_rem_pio2.c b/sysdeps/ieee754/dbl-64/e_rem_pio2.c new file mode 100644 index 0000000..a8a8cdb --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_rem_pio2.c @@ -0,0 +1,183 @@ +/* @(#)e_rem_pio2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $"; +#endif + +/* __ieee754_rem_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + +#include "math.h" +#include "math_private.h" + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ +#ifdef __STDC__ +static const int32_t two_over_pi[] = { +#else +static int32_t two_over_pi[] = { +#endif +0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, +0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, +0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, +0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, +0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, +0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, +0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, +0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, +0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, +0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, +0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, +}; + +#ifdef __STDC__ +static const int32_t npio2_hw[] = { +#else +static int32_t npio2_hw[] = { +#endif +0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, +0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, +0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, +0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, +0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, +0x404858EB, 0x404921FB, +}; + +/* + * invpio2: 53 bits of 2/pi + * pio2_1: first 33 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 33 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 33 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +#ifdef __STDC__ +static const double +#else +static double +#endif +zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ +half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ +pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ +pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ +pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ +pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ +pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ + +#ifdef __STDC__ + int32_t __ieee754_rem_pio2(double x, double *y) +#else + int32_t __ieee754_rem_pio2(x,y) + double x,y[]; +#endif +{ + double z,w,t,r,fn; + double tx[3]; + int32_t e0,i,j,nx,n,ix,hx; + u_int32_t low; + + GET_HIGH_WORD(hx,x); /* high word of x */ + ix = hx&0x7fffffff; + if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ + {y[0] = x; y[1] = 0; return 0;} + if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ + if(hx>0) { + z = x - pio2_1; + if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ + y[0] = z - pio2_1t; + y[1] = (z-y[0])-pio2_1t; + } else { /* near pi/2, use 33+33+53 bit pi */ + z -= pio2_2; + y[0] = z - pio2_2t; + y[1] = (z-y[0])-pio2_2t; + } + return 1; + } else { /* negative x */ + z = x + pio2_1; + if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ + y[0] = z + pio2_1t; + y[1] = (z-y[0])+pio2_1t; + } else { /* near pi/2, use 33+33+53 bit pi */ + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z-y[0])+pio2_2t; + } + return -1; + } + } + if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ + t = fabs(x); + n = (int32_t) (t*invpio2+half); + fn = (double)n; + r = t-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 85 bit */ + if(n<32&&ix!=npio2_hw[n-1]) { + y[0] = r-w; /* quick check no cancellation */ + } else { + u_int32_t high; + j = ix>>20; + y[0] = r-w; + GET_HIGH_WORD(high,y[0]); + i = j-((high>>20)&0x7ff); + if(i>16) { /* 2nd iteration needed, good to 118 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + GET_HIGH_WORD(high,y[0]); + i = j-((high>>20)&0x7ff); + if(i>49) { /* 3rd iteration need, 151 bits acc */ + t = r; /* will cover all possible cases */ + w = fn*pio2_3; + r = t-w; + w = fn*pio2_3t-((t-r)-w); + y[0] = r-w; + } + } + } + y[1] = (r-y[0])-w; + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + else return n; + } + /* + * all other (large) arguments + */ + if(ix>=0x7ff00000) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-23) */ + GET_LOW_WORD(low,x); + SET_LOW_WORD(z,low); + e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ + SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); + for(i=0;i<2;i++) { + tx[i] = (double)((int32_t)(z)); + z = (z-tx[i])*two24; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + return n; +} diff --git a/sysdeps/ieee754/dbl-64/e_remainder.c b/sysdeps/ieee754/dbl-64/e_remainder.c new file mode 100644 index 0000000..6418081 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_remainder.c @@ -0,0 +1,80 @@ +/* @(#)e_remainder.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_remainder.c,v 1.8 1995/05/10 20:46:05 jtc Exp $"; +#endif + +/* __ieee754_remainder(x,p) + * Return : + * returns x REM p = x - [x/p]*p as if in infinite + * precise arithmetic, where [x/p] is the (infinite bit) + * integer nearest x/p (in half way case choose the even one). + * Method : + * Based on fmod() return x-[x/p]chopped*p exactlp. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + + +#ifdef __STDC__ + double __ieee754_remainder(double x, double p) +#else + double __ieee754_remainder(x,p) + double x,p; +#endif +{ + int32_t hx,hp; + u_int32_t sx,lx,lp; + double p_half; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hp,lp,p); + sx = hx&0x80000000; + hp &= 0x7fffffff; + hx &= 0x7fffffff; + + /* purge off exception values */ + if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7ff00000)|| /* x not finite */ + ((hp>=0x7ff00000)&& /* p is NaN */ + (((hp-0x7ff00000)|lp)!=0))) + return (x*p)/(x*p); + + + if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p); /* now x < 2p */ + if (((hx-hp)|(lx-lp))==0) return zero*x; + x = fabs(x); + p = fabs(p); + if (hp<0x00200000) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = 0.5*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_HIGH_WORD(hx,x); + SET_HIGH_WORD(x,hx^sx); + return x; +} diff --git a/sysdeps/ieee754/dbl-64/e_sinh.c b/sysdeps/ieee754/dbl-64/e_sinh.c new file mode 100644 index 0000000..1701b9b --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_sinh.c @@ -0,0 +1,86 @@ +/* @(#)e_sinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $"; +#endif + +/* __ieee754_sinh(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinh(-x) = -sinh(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) + * 2 + * + * 22 <= x <= lnovft : sinh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : sinh(x) := x*shuge (overflow) + * + * Special cases: + * sinh(x) is |x| if x is +INF, -INF, or NaN. + * only sinh(0)=0 is exact for finite x. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double one = 1.0, shuge = 1.0e307; +#else +static double one = 1.0, shuge = 1.0e307; +#endif + +#ifdef __STDC__ + double __ieee754_sinh(double x) +#else + double __ieee754_sinh(x) + double x; +#endif +{ + double t,w,h; + int32_t ix,jx; + u_int32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix<0x3e300000) /* |x|<2**-28 */ + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + t = __expm1(fabs(x)); + if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x40862e42) return h*__ieee754_exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + GET_LOW_WORD(lx,x); + if (ix<0x408633ce || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { + w = __ieee754_exp(0.5*fabs(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; +} diff --git a/sysdeps/ieee754/dbl-64/e_sqrt.c b/sysdeps/ieee754/dbl-64/e_sqrt.c new file mode 100644 index 0000000..67da545 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_sqrt.c @@ -0,0 +1,452 @@ +/* @(#)e_sqrt.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_sqrt.c,v 1.8 1995/05/10 20:46:17 jtc Exp $"; +#endif + +/* __ieee754_sqrt(x) + * Return correctly rounded sqrt. + * ------------------------------------------ + * | Use the hardware sqrt if you have one | + * ------------------------------------------ + * Method: + * Bit by bit method using integer arithmetic. (Slow, but portable) + * 1. Normalization + * Scale x to y in [1,4) with even powers of 2: + * find an integer k such that 1 <= (y=x*2^(2k)) < 4, then + * sqrt(x) = 2^k * sqrt(y) + * 2. Bit by bit computation + * Let q = sqrt(y) truncated to i bit after binary point (q = 1), + * i 0 + * i+1 2 + * s = 2*q , and y = 2 * ( y - q ). (1) + * i i i i + * + * To compute q from q , one checks whether + * i+1 i + * + * -(i+1) 2 + * (q + 2 ) <= y. (2) + * i + * -(i+1) + * If (2) is false, then q = q ; otherwise q = q + 2 . + * i+1 i i+1 i + * + * With some algebraic manipulation, it is not difficult to see + * that (2) is equivalent to + * -(i+1) + * s + 2 <= y (3) + * i i + * + * The advantage of (3) is that s and y can be computed by + * i i + * the following recurrence formula: + * if (3) is false + * + * s = s , y = y ; (4) + * i+1 i i+1 i + * + * otherwise, + * -i -(i+1) + * s = s + 2 , y = y - s - 2 (5) + * i+1 i i+1 i i + * + * One may easily use induction to prove (4) and (5). + * Note. Since the left hand side of (3) contain only i+2 bits, + * it does not necessary to do a full (53-bit) comparison + * in (3). + * 3. Final rounding + * After generating the 53 bits result, we compute one more bit. + * Together with the remainder, we can decide whether the + * result is exact, bigger than 1/2ulp, or less than 1/2ulp + * (it will never equal to 1/2ulp). + * The rounding mode can be detected by checking whether + * huge + tiny is equal to huge, and whether huge - tiny is + * equal to huge for some floating point number "huge" and "tiny". + * + * Special cases: + * sqrt(+-0) = +-0 ... exact + * sqrt(inf) = inf + * sqrt(-ve) = NaN ... with invalid signal + * sqrt(NaN) = NaN ... with invalid signal for signaling NaN + * + * Other methods : see the appended file at the end of the program below. + *--------------- + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double one = 1.0, tiny=1.0e-300; +#else +static double one = 1.0, tiny=1.0e-300; +#endif + +#ifdef __STDC__ + double __ieee754_sqrt(double x) +#else + double __ieee754_sqrt(x) + double x; +#endif +{ + double z; + int32_t sign = (int)0x80000000; + int32_t ix0,s0,q,m,t,i; + u_int32_t r,t1,s1,ix1,q1; + + EXTRACT_WORDS(ix0,ix1,x); + + /* take care of Inf and NaN */ + if((ix0&0x7ff00000)==0x7ff00000) { + return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf + sqrt(-inf)=sNaN */ + } + /* take care of zero */ + if(ix0<=0) { + if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */ + else if(ix0<0) + return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + } + /* normalize x */ + m = (ix0>>20); + if(m==0) { /* subnormal x */ + while(ix0==0) { + m -= 21; + ix0 |= (ix1>>11); ix1 <<= 21; + } + for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1; + m -= i-1; + ix0 |= (ix1>>(32-i)); + ix1 <<= i; + } + m -= 1023; /* unbias exponent */ + ix0 = (ix0&0x000fffff)|0x00100000; + if(m&1){ /* odd m, double x to make it even */ + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + } + m >>= 1; /* m = [m/2] */ + + /* generate sqrt(x) bit by bit */ + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */ + r = 0x00200000; /* r = moving bit from right to left */ + + while(r!=0) { + t = s0+r; + if(t<=ix0) { + s0 = t+r; + ix0 -= t; + q += r; + } + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + r>>=1; + } + + r = sign; + while(r!=0) { + t1 = s1+r; + t = s0; + if((t<ix0)||((t==ix0)&&(t1<=ix1))) { + s1 = t1+r; + if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1; + ix0 -= t; + if (ix1 < t1) ix0 -= 1; + ix1 -= t1; + q1 += r; + } + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + r>>=1; + } + + /* use floating add to find out rounding direction */ + if((ix0|ix1)!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;} + else if (z>one) { + if (q1==(u_int32_t)0xfffffffe) q+=1; + q1+=2; + } else + q1 += (q1&1); + } + } + ix0 = (q>>1)+0x3fe00000; + ix1 = q1>>1; + if ((q&1)==1) ix1 |= sign; + ix0 += (m <<20); + INSERT_WORDS(z,ix0,ix1); + return z; +} + +/* +Other methods (use floating-point arithmetic) +------------- +(This is a copy of a drafted paper by Prof W. Kahan +and K.C. Ng, written in May, 1986) + + Two algorithms are given here to implement sqrt(x) + (IEEE double precision arithmetic) in software. + Both supply sqrt(x) correctly rounded. The first algorithm (in + Section A) uses newton iterations and involves four divisions. + The second one uses reciproot iterations to avoid division, but + requires more multiplications. Both algorithms need the ability + to chop results of arithmetic operations instead of round them, + and the INEXACT flag to indicate when an arithmetic operation + is executed exactly with no roundoff error, all part of the + standard (IEEE 754-1985). The ability to perform shift, add, + subtract and logical AND operations upon 32-bit words is needed + too, though not part of the standard. + +A. sqrt(x) by Newton Iteration + + (1) Initial approximation + + Let x0 and x1 be the leading and the trailing 32-bit words of + a floating point number x (in IEEE double format) respectively + + 1 11 52 ...widths + ------------------------------------------------------ + x: |s| e | f | + ------------------------------------------------------ + msb lsb msb lsb ...order + + + ------------------------ ------------------------ + x0: |s| e | f1 | x1: | f2 | + ------------------------ ------------------------ + + By performing shifts and subtracts on x0 and x1 (both regarded + as integers), we obtain an 8-bit approximation of sqrt(x) as + follows. + + k := (x0>>1) + 0x1ff80000; + y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits + Here k is a 32-bit integer and T1[] is an integer array containing + correction terms. Now magically the floating value of y (y's + leading 32-bit word is y0, the value of its trailing word is 0) + approximates sqrt(x) to almost 8-bit. + + Value of T1: + static int T1[32]= { + 0, 1024, 3062, 5746, 9193, 13348, 18162, 23592, + 29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215, + 83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581, + 16499, 12183, 8588, 5674, 3403, 1742, 661, 130,}; + + (2) Iterative refinement + + Apply Heron's rule three times to y, we have y approximates + sqrt(x) to within 1 ulp (Unit in the Last Place): + + y := (y+x/y)/2 ... almost 17 sig. bits + y := (y+x/y)/2 ... almost 35 sig. bits + y := y-(y-x/y)/2 ... within 1 ulp + + + Remark 1. + Another way to improve y to within 1 ulp is: + + y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x) + y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x) + + 2 + (x-y )*y + y := y + 2* ---------- ...within 1 ulp + 2 + 3y + x + + + This formula has one division fewer than the one above; however, + it requires more multiplications and additions. Also x must be + scaled in advance to avoid spurious overflow in evaluating the + expression 3y*y+x. Hence it is not recommended uless division + is slow. If division is very slow, then one should use the + reciproot algorithm given in section B. + + (3) Final adjustment + + By twiddling y's last bit it is possible to force y to be + correctly rounded according to the prevailing rounding mode + as follows. Let r and i be copies of the rounding mode and + inexact flag before entering the square root program. Also we + use the expression y+-ulp for the next representable floating + numbers (up and down) of y. Note that y+-ulp = either fixed + point y+-1, or multiply y by nextafter(1,+-inf) in chopped + mode. + + I := FALSE; ... reset INEXACT flag I + R := RZ; ... set rounding mode to round-toward-zero + z := x/y; ... chopped quotient, possibly inexact + If(not I) then { ... if the quotient is exact + if(z=y) { + I := i; ... restore inexact flag + R := r; ... restore rounded mode + return sqrt(x):=y. + } else { + z := z - ulp; ... special rounding + } + } + i := TRUE; ... sqrt(x) is inexact + If (r=RN) then z=z+ulp ... rounded-to-nearest + If (r=RP) then { ... round-toward-+inf + y = y+ulp; z=z+ulp; + } + y := y+z; ... chopped sum + y0:=y0-0x00100000; ... y := y/2 is correctly rounded. + I := i; ... restore inexact flag + R := r; ... restore rounded mode + return sqrt(x):=y. + + (4) Special cases + + Square root of +inf, +-0, or NaN is itself; + Square root of a negative number is NaN with invalid signal. + + +B. sqrt(x) by Reciproot Iteration + + (1) Initial approximation + + Let x0 and x1 be the leading and the trailing 32-bit words of + a floating point number x (in IEEE double format) respectively + (see section A). By performing shifs and subtracts on x0 and y0, + we obtain a 7.8-bit approximation of 1/sqrt(x) as follows. + + k := 0x5fe80000 - (x0>>1); + y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits + + Here k is a 32-bit integer and T2[] is an integer array + containing correction terms. Now magically the floating + value of y (y's leading 32-bit word is y0, the value of + its trailing word y1 is set to zero) approximates 1/sqrt(x) + to almost 7.8-bit. + + Value of T2: + static int T2[64]= { + 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866, + 0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f, + 0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d, + 0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0, + 0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989, + 0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd, + 0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e, + 0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,}; + + (2) Iterative refinement + + Apply Reciproot iteration three times to y and multiply the + result by x to get an approximation z that matches sqrt(x) + to about 1 ulp. To be exact, we will have + -1ulp < sqrt(x)-z<1.0625ulp. + + ... set rounding mode to Round-to-nearest + y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x) + y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x) + ... special arrangement for better accuracy + z := x*y ... 29 bits to sqrt(x), with z*y<1 + z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x) + + Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that + (a) the term z*y in the final iteration is always less than 1; + (b) the error in the final result is biased upward so that + -1 ulp < sqrt(x) - z < 1.0625 ulp + instead of |sqrt(x)-z|<1.03125ulp. + + (3) Final adjustment + + By twiddling y's last bit it is possible to force y to be + correctly rounded according to the prevailing rounding mode + as follows. Let r and i be copies of the rounding mode and + inexact flag before entering the square root program. Also we + use the expression y+-ulp for the next representable floating + numbers (up and down) of y. Note that y+-ulp = either fixed + point y+-1, or multiply y by nextafter(1,+-inf) in chopped + mode. + + R := RZ; ... set rounding mode to round-toward-zero + switch(r) { + case RN: ... round-to-nearest + if(x<= z*(z-ulp)...chopped) z = z - ulp; else + if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp; + break; + case RZ:case RM: ... round-to-zero or round-to--inf + R:=RP; ... reset rounding mod to round-to-+inf + if(x<z*z ... rounded up) z = z - ulp; else + if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp; + break; + case RP: ... round-to-+inf + if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else + if(x>z*z ...chopped) z = z+ulp; + break; + } + + Remark 3. The above comparisons can be done in fixed point. For + example, to compare x and w=z*z chopped, it suffices to compare + x1 and w1 (the trailing parts of x and w), regarding them as + two's complement integers. + + ...Is z an exact square root? + To determine whether z is an exact square root of x, let z1 be the + trailing part of z, and also let x0 and x1 be the leading and + trailing parts of x. + + If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0 + I := 1; ... Raise Inexact flag: z is not exact + else { + j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2 + k := z1 >> 26; ... get z's 25-th and 26-th + fraction bits + I := i or (k&j) or ((k&(j+j+1))!=(x1&3)); + } + R:= r ... restore rounded mode + return sqrt(x):=z. + + If multiplication is cheaper then the foregoing red tape, the + Inexact flag can be evaluated by + + I := i; + I := (z*z!=x) or I. + + Note that z*z can overwrite I; this value must be sensed if it is + True. + + Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be + zero. + + -------------------- + z1: | f2 | + -------------------- + bit 31 bit 0 + + Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd + or even of logb(x) have the following relations: + + ------------------------------------------------- + bit 27,26 of z1 bit 1,0 of x1 logb(x) + ------------------------------------------------- + 00 00 odd and even + 01 01 even + 10 10 odd + 10 00 even + 11 01 even + ------------------------------------------------- + + (4) Special cases (see (4) of Section A). + + */ diff --git a/sysdeps/ieee754/dbl-64/k_cos.c b/sysdeps/ieee754/dbl-64/k_cos.c new file mode 100644 index 0000000..7e38ef7 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/k_cos.c @@ -0,0 +1,107 @@ +/* @(#)k_cos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $"; +#endif + +/* + * __kernel_cos( x, y ) + * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * + * Algorithm + * 1. Since cos(-x) = cos(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. + * 3. cos(x) is approximated by a polynomial of degree 14 on + * [0,pi/4] + * 4 14 + * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x + * where the remez error is + * + * | 2 4 6 8 10 12 14 | -58 + * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 + * | | + * + * 4 6 8 10 12 14 + * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then + * cos(x) = 1 - x*x/2 + r + * since cos(x+y) ~ cos(x) - sin(x)*y + * ~ cos(x) - x*y, + * a correction term is necessary in cos(x) and hence + * cos(x+y) = 1 - (x*x/2 - (r - x*y)) + * For better accuracy when x > 0.3, let qx = |x|/4 with + * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. + * Then + * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). + * Note that 1-qx and (x*x/2-qx) is EXACT here, and the + * magnitude of the latter is at least a quarter of x*x/2, + * thus, reducing the rounding error in the subtraction. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +C[] = { + 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ + 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ + -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ + 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ + -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ + 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ + -1.13596475577881948265e-11}; /* 0xBDA8FAE9, 0xBE8838D4 */ + +#ifdef __STDC__ + double __kernel_cos(double x, double y) +#else + double __kernel_cos(x, y) + double x,y; +#endif +{ + double a,hz,z,r,qx,r1,r2,r3,z1,z2,z3; + int32_t ix; + z = x*x; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; /* ix = |x|'s high word*/ + if(ix<0x3e400000) { /* if x < 2**27 */ + if(((int)x)==0) return C[0]; /* generate inexact */ + } +#ifdef DO_NOT_USE_THIS + r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); +#else + r1=z*C[6];r1=r1+C[5];z1=z*z; + r2=z*C[4];r2=r2+C[3];z2=z1*z; + r3=z*C[2];r3=r3+C[1];z3=z2*z1; + r=z3*r1+z2*r2+z*r3; +#endif + if(ix < 0x3FD33333) /* if |x| < 0.3 */ + return C[0] - (0.5*z - (z*r - x*y)); + else { + if(ix > 0x3fe90000) { /* x > 0.78125 */ + qx = 0.28125; + } else { + INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */ + } + hz = 0.5*z-qx; + a = C[0]-qx; + return a - (hz - (z*r-x*y)); + } +} diff --git a/sysdeps/ieee754/dbl-64/k_rem_pio2.c b/sysdeps/ieee754/dbl-64/k_rem_pio2.c new file mode 100644 index 0000000..ccf1633 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/k_rem_pio2.c @@ -0,0 +1,320 @@ +/* @(#)k_rem_pio2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $"; +#endif + +/* + * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) + * double x[],y[]; int e0,nx,prec; int ipio2[]; + * + * __kernel_rem_pio2 return the last three digits of N with + * y = x - N*pi/2 + * so that |y| < pi/2. + * + * The method is to compute the integer (mod 8) and fraction parts of + * (2/pi)*x without doing the full multiplication. In general we + * skip the part of the product that are known to be a huge integer ( + * more accurately, = 0 mod 8 ). Thus the number of operations are + * independent of the exponent of the input. + * + * (2/pi) is represented by an array of 24-bit integers in ipio2[]. + * + * Input parameters: + * x[] The input value (must be positive) is broken into nx + * pieces of 24-bit integers in double precision format. + * x[i] will be the i-th 24 bit of x. The scaled exponent + * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 + * match x's up to 24 bits. + * + * Example of breaking a double positive z into x[0]+x[1]+x[2]: + * e0 = ilogb(z)-23 + * z = scalbn(z,-e0) + * for i = 0,1,2 + * x[i] = floor(z) + * z = (z-x[i])*2**24 + * + * + * y[] ouput result in an array of double precision numbers. + * The dimension of y[] is: + * 24-bit precision 1 + * 53-bit precision 2 + * 64-bit precision 2 + * 113-bit precision 3 + * The actual value is the sum of them. Thus for 113-bit + * precision, one may have to do something like: + * + * long double t,w,r_head, r_tail; + * t = (long double)y[2] + (long double)y[1]; + * w = (long double)y[0]; + * r_head = t+w; + * r_tail = w - (r_head - t); + * + * e0 The exponent of x[0] + * + * nx dimension of x[] + * + * prec an integer indicating the precision: + * 0 24 bits (single) + * 1 53 bits (double) + * 2 64 bits (extended) + * 3 113 bits (quad) + * + * ipio2[] + * integer array, contains the (24*i)-th to (24*i+23)-th + * bit of 2/pi after binary point. The corresponding + * floating value is + * + * ipio2[i] * 2^(-24(i+1)). + * + * External function: + * double scalbn(), floor(); + * + * + * Here is the description of some local variables: + * + * jk jk+1 is the initial number of terms of ipio2[] needed + * in the computation. The recommended value is 2,3,4, + * 6 for single, double, extended,and quad. + * + * jz local integer variable indicating the number of + * terms of ipio2[] used. + * + * jx nx - 1 + * + * jv index for pointing to the suitable ipio2[] for the + * computation. In general, we want + * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 + * is an integer. Thus + * e0-3-24*jv >= 0 or (e0-3)/24 >= jv + * Hence jv = max(0,(e0-3)/24). + * + * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. + * + * q[] double array with integral value, representing the + * 24-bits chunk of the product of x and 2/pi. + * + * q0 the corresponding exponent of q[0]. Note that the + * exponent for q[i] would be q0-24*i. + * + * PIo2[] double precision array, obtained by cutting pi/2 + * into 24 bits chunks. + * + * f[] ipio2[] in floating point + * + * iq[] integer array by breaking up q[] in 24-bits chunk. + * + * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] + * + * ih integer. If >0 it indicates q[] is >= 0.5, hence + * it also indicates the *sign* of the result. + * + */ + + +/* + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const int init_jk[] = {2,3,4,6}; /* initial value for jk */ +#else +static int init_jk[] = {2,3,4,6}; +#endif + +#ifdef __STDC__ +static const double PIo2[] = { +#else +static double PIo2[] = { +#endif + 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ + 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ + 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ + 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ + 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ + 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ + 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ + 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ +}; + +#ifdef __STDC__ +static const double +#else +static double +#endif +zero = 0.0, +one = 1.0, +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ + +#ifdef __STDC__ + int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2) +#else + int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) + double x[], y[]; int e0,nx,prec; int32_t ipio2[]; +#endif +{ + int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; + double z,fw,f[20],fq[20],q[20]; + + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + jx = nx-1; + jv = (e0-3)/24; if(jv<0) jv=0; + q0 = e0-24*(jv+1); + + /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ + j = jv-jx; m = jx+jk; + for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + for (i=0;i<=jk;i++) { + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; + } + + jz = jk; +recompute: + /* distill q[] into iq[] reversingly */ + for(i=0,j=jz,z=q[jz];j>0;i++,j--) { + fw = (double)((int32_t)(twon24* z)); + iq[i] = (int32_t)(z-two24*fw); + z = q[j-1]+fw; + } + + /* compute n */ + z = __scalbn(z,q0); /* actual value of z */ + z -= 8.0*__floor(z*0.125); /* trim off integer >= 8 */ + n = (int32_t) z; + z -= (double)n; + ih = 0; + if(q0>0) { /* need iq[jz-1] to determine n */ + i = (iq[jz-1]>>(24-q0)); n += i; + iq[jz-1] -= i<<(24-q0); + ih = iq[jz-1]>>(23-q0); + } + else if(q0==0) ih = iq[jz-1]>>23; + else if(z>=0.5) ih=2; + + if(ih>0) { /* q > 0.5 */ + n += 1; carry = 0; + for(i=0;i<jz ;i++) { /* compute 1-q */ + j = iq[i]; + if(carry==0) { + if(j!=0) { + carry = 1; iq[i] = 0x1000000- j; + } + } else iq[i] = 0xffffff - j; + } + if(q0>0) { /* rare case: chance is 1 in 12 */ + switch(q0) { + case 1: + iq[jz-1] &= 0x7fffff; break; + case 2: + iq[jz-1] &= 0x3fffff; break; + } + } + if(ih==2) { + z = one - z; + if(carry!=0) z -= __scalbn(one,q0); + } + } + + /* check if recomputation is needed */ + if(z==zero) { + j = 0; + for (i=jz-1;i>=jk;i--) j |= iq[i]; + if(j==0) { /* need recomputation */ + for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ + + for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ + f[jx+i] = (double) ipio2[jv+i]; + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + jz += k; + goto recompute; + } + } + + /* chop off zero terms */ + if(z==0.0) { + jz -= 1; q0 -= 24; + while(iq[jz]==0) { jz--; q0-=24;} + } else { /* break z into 24-bit if necessary */ + z = __scalbn(z,-q0); + if(z>=two24) { + fw = (double)((int32_t)(twon24*z)); + iq[jz] = (int32_t)(z-two24*fw); + jz += 1; q0 += 24; + iq[jz] = (int32_t) fw; + } else iq[jz] = (int32_t) z ; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = __scalbn(one,q0); + for(i=jz;i>=0;i--) { + q[i] = fw*(double)iq[i]; fw*=twon24; + } + + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for(i=jz;i>=0;i--) { + for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; + fq[jz-i] = fw; + } + + /* compress fq[] into y[] */ + switch(prec) { + case 0: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + break; + case 1: + case 2: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + fw = fq[0]-fw; + for (i=1;i<=jz;i++) fw += fq[i]; + y[1] = (ih==0)? fw: -fw; + break; + case 3: /* painful */ + for (i=jz;i>0;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (i=jz;i>1;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; + if(ih==0) { + y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; + } else { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n&7; +} diff --git a/sysdeps/ieee754/dbl-64/k_sin.c b/sysdeps/ieee754/dbl-64/k_sin.c new file mode 100644 index 0000000..49c5922 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/k_sin.c @@ -0,0 +1,91 @@ +/* @(#)k_sin.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $"; +#endif + +/* __kernel_sin( x, y, iy) + * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). + * + * Algorithm + * 1. Since sin(-x) = -sin(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. + * 3. sin(x) is approximated by a polynomial of degree 13 on + * [0,pi/4] + * 3 13 + * sin(x) ~ x + S1*x + ... + S6*x + * where + * + * |sin(x) 2 4 6 8 10 12 | -58 + * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 + * | x | + * + * 4. sin(x+y) = sin(x) + sin'(x')*y + * ~ sin(x) + (1-x*x/2)*y + * For better accuracy, let + * 3 2 2 2 2 + * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) + * then 3 2 + * sin(x) = x + (S1*x + (x *(r-y/2)+y)) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +S[] = { + 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ + -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ + 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ + -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ + 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ + -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ + 1.58969099521155010221e-10}; /* 0x3DE5D93A, 0x5ACFD57C */ + +#ifdef __STDC__ + double __kernel_sin(double x, double y, int iy) +#else + double __kernel_sin(x, y, iy) + double x,y; int iy; /* iy=0 if y is zero */ +#endif +{ + double z,r,v,z1,r1,r2; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; /* high word of x */ + if(ix<0x3e400000) /* |x| < 2**-27 */ + {if((int)x==0) return x;} /* generate inexact */ + z = x*x; + v = z*x; +#ifdef DO_NOT_USE_THIS + r = S2+z*(S3+z*(S4+z*(S5+z*S6))); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +#else + r1 = S[5]+z*S[6]; z1 = z*z*z; + r2 = S[3]+z*S[4]; + r = S[2] + z*r2 + z1*r1; + if(iy==0) return x+v*(S[1]+z*r); + else return x-((z*(S[0]*y-v*r)-y)-v*S[1]); +#endif +} diff --git a/sysdeps/ieee754/dbl-64/k_tan.c b/sysdeps/ieee754/dbl-64/k_tan.c new file mode 100644 index 0000000..55dafb8 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/k_tan.c @@ -0,0 +1,145 @@ +/* @(#)k_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_tan.c,v 1.8 1995/05/10 20:46:37 jtc Exp $"; +#endif + +/* __kernel_tan( x, y, k ) + * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input k indicates whether tan (if k=1) or + * -1/tan (if k= -1) is returned. + * + * Algorithm + * 1. Since tan(-x) = -tan(x), we need only to consider positive x. + * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0. + * 3. tan(x) is approximated by a odd polynomial of degree 27 on + * [0,0.67434] + * 3 27 + * tan(x) ~ x + T1*x + ... + T13*x + * where + * + * |tan(x) 2 4 26 | -59.2 + * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 + * | x | + * + * Note: tan(x+y) = tan(x) + tan'(x)*y + * ~ tan(x) + (1+x*x)*y + * Therefore, for better accuracy in computing tan(x+y), let + * 3 2 2 2 2 + * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) + * then + * 3 2 + * tan(x+y) = x + (T1*x + (x *(r+y)+y)) + * + * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then + * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) + * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) + */ + +#include "math.h" +#include "math_private.h" +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ +pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */ +T[] = { + 3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */ + 1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */ + 5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */ + 2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */ + 8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */ + 3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */ + 1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */ + 5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */ + 2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */ + 7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */ + 7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */ + -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */ + 2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */ +}; + +#ifdef __STDC__ + double __kernel_tan(double x, double y, int iy) +#else + double __kernel_tan(x, y, iy) + double x,y; int iy; +#endif +{ + double z,r,v,w,s,r1,r2,r3,v1,v2,v3,w2,w4; + int32_t ix,hx; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; /* high word of |x| */ + if(ix<0x3e300000) /* x < 2**-28 */ + {if((int)x==0) { /* generate inexact */ + u_int32_t low; + GET_LOW_WORD(low,x); + if(((ix|low)|(iy+1))==0) return one/fabs(x); + else return (iy==1)? x: -one/x; + } + } + if(ix>=0x3FE59428) { /* |x|>=0.6744 */ + if(hx<0) {x = -x; y = -y;} + z = pio4-x; + w = pio4lo-y; + x = z+w; y = 0.0; + } + z = x*x; + w = z*z; + /* Break x^5*(T[1]+x^2*T[2]+...) into + * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + + * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) + */ +#ifdef DO_NOT_USE_THIS + r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); + v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); +#else + v1 = T[10]+w*T[12]; w2=w*w; + v2 = T[6]+w*T[8]; w4=w2*w2; + v3 = T[2]+w*T[4]; v1=z*v1; + r1 = T[9]+w*T[11]; v2=z*v2; + r2 = T[5]+w*T[7]; v3=z*v3; + r3 = T[1]+w*T[3]; + v = v3 + w2*v2 + w4*v1; + r = r3 + w2*r2 + w4*r1; +#endif + s = z*x; + r = y + z*(s*(r+v)+y); + r += T[0]*s; + w = x+r; + if(ix>=0x3FE59428) { + v = (double)iy; + return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r))); + } + if(iy==1) return w; + else { /* if allow error up to 2 ulp, + simply return -1.0/(x+r) here */ + /* compute -1.0/(x+r) accurately */ + double a,t; + z = w; + SET_LOW_WORD(z,0); + v = r-(z - x); /* z+v = r+x */ + t = a = -1.0/w; /* a = -1.0/w */ + SET_LOW_WORD(t,0); + s = 1.0+t*z; + return t+a*(s+t*v); + } +} diff --git a/sysdeps/ieee754/mpn2dbl.c b/sysdeps/ieee754/dbl-64/mpn2dbl.c index 8145eb9..8145eb9 100644 --- a/sysdeps/ieee754/mpn2dbl.c +++ b/sysdeps/ieee754/dbl-64/mpn2dbl.c diff --git a/sysdeps/ieee754/dbl-64/s_asinh.c b/sysdeps/ieee754/dbl-64/s_asinh.c new file mode 100644 index 0000000..985cfe3 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_asinh.c @@ -0,0 +1,70 @@ +/* @(#)s_asinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $"; +#endif + +/* asinh(x) + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +huge= 1.00000000000000000000e+300; + +#ifdef __STDC__ + double __asinh(double x) +#else + double __asinh(x) + double x; +#endif +{ + double t,w; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ + if(ix< 0x3e300000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x41b00000) { /* |x| > 2**28 */ + w = __ieee754_log(fabs(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabs(x); + w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =__log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); + } + if(hx>0) return w; else return -w; +} +weak_alias (__asinh, asinh) +#ifdef NO_LONG_DOUBLE +strong_alias (__asinh, __asinhl) +weak_alias (__asinh, asinhl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_atan.c b/sysdeps/ieee754/dbl-64/s_atan.c new file mode 100644 index 0000000..cad3ba1 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_atan.c @@ -0,0 +1,163 @@ +/* @(#)s_atan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_atan.c,v 1.8 1995/05/10 20:46:45 jtc Exp $"; +#endif + +/* atan(x) + * Method + * 1. Reduce x to positive by atan(x) = -atan(-x). + * 2. According to the integer k=4t+0.25 chopped, t=x, the argument + * is further reduced to one of the following intervals and the + * arctangent of t is evaluated by the corresponding formula: + * + * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) + * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) + * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) + * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) + * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double atanhi[] = { +#else +static double atanhi[] = { +#endif + 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ + 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ + 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ + 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ +}; + +#ifdef __STDC__ +static const double atanlo[] = { +#else +static double atanlo[] = { +#endif + 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ + 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ + 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ + 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ +}; + +#ifdef __STDC__ +static const double aT[] = { +#else +static double aT[] = { +#endif + 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ + -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ + 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ + -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ + 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ + -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ + 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ + -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ + 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ + -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ + 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ +}; + +#ifdef __STDC__ + static const double +#else + static double +#endif +one = 1.0, +huge = 1.0e300; + +#ifdef __STDC__ + double __atan(double x) +#else + double __atan(x) + double x; +#endif +{ + double w,s1,z,s,w2,w4,s11,s12,s13,s21,s22,s23; + int32_t ix,hx,id; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x44100000) { /* if |x| >= 2^66 */ + u_int32_t low; + GET_LOW_WORD(low,x); + if(ix>0x7ff00000|| + (ix==0x7ff00000&&(low!=0))) + return x+x; /* NaN */ + if(hx>0) return atanhi[3]+atanlo[3]; + else return -atanhi[3]-atanlo[3]; + } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ + if (ix < 0x3e200000) { /* |x| < 2^-29 */ + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabs(x); + if (ix < 0x3ff30000) { /* |x| < 1.1875 */ + if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ + id = 0; x = (2.0*x-one)/(2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (ix < 0x40038000) { /* |x| < 2.4375 */ + id = 2; x = (x-1.5)/(one+1.5*x); + } else { /* 2.4375 <= |x| < 2^66 */ + id = 3; x = -1.0/x; + } + }} + /* end of argument reduction */ + z = x*x; + w = z*z; + /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ +#ifdef DO_NOT_USE_THIS + s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); + s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (hx<0)? -z:z; + } +#else + s11 = aT[8]+w*aT[10]; w2=w*w; + s12 = aT[4]+w*aT[6]; w4=w2*w2; + s13 = aT[0]+w*aT[2]; + s21 = aT[7]+w*aT[9]; + s22 = aT[3]+w*aT[5]; + s23 = w*aT[1]; + s1 = s13 + w2*s12 + w4*s11; + s = s23 + w2*s22 + w4*s21 + z*s1; + if (id<0) return x - x*(s); + else { + z = atanhi[id] - ((x*(s) - atanlo[id]) - x); + return (hx<0)? -z:z; + } +#endif +} +weak_alias (__atan, atan) +#ifdef NO_LONG_DOUBLE +strong_alias (__atan, __atanl) +weak_alias (__atan, atanl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_cbrt.c b/sysdeps/ieee754/dbl-64/s_cbrt.c new file mode 100644 index 0000000..753049d --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_cbrt.c @@ -0,0 +1,76 @@ +/* Compute cubic root of double value. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Dirk Alboth <dirka@uni-paderborn.de> and + Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include "math.h" +#include "math_private.h" + + +#define CBRT2 1.2599210498948731648 /* 2^(1/3) */ +#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */ + +static const double factor[5] = +{ + 1.0 / SQR_CBRT2, + 1.0 / CBRT2, + 1.0, + CBRT2, + SQR_CBRT2 +}; + + +double +__cbrt (double x) +{ + double xm, ym, u, t2; + int xe; + + /* Reduce X. XM now is an range 1.0 to 0.5. */ + xm = __frexp (fabs (x), &xe); + + /* If X is not finite or is null return it (with raising exceptions + if necessary. + Note: *Our* version of `frexp' sets XE to zero if the argument is + Inf or NaN. This is not portable but faster. */ + if (xe == 0 && fpclassify (x) <= FP_ZERO) + return x + x; + + u = (0.354895765043919860 + + ((1.50819193781584896 + + ((-2.11499494167371287 + + ((2.44693122563534430 + + ((-1.83469277483613086 + + (0.784932344976639262 - 0.145263899385486377 * xm) * xm) + * xm)) + * xm)) + * xm)) + * xm)); + + t2 = u * u * u; + + ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3]; + + return __ldexp (x > 0.0 ? ym : -ym, xe / 3); +} +weak_alias (__cbrt, cbrt) +#ifdef NO_LONG_DOUBLE +strong_alias (__cbrt, __cbrtl) +weak_alias (__cbrt, cbrtl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_ceil.c b/sysdeps/ieee754/dbl-64/s_ceil.c new file mode 100644 index 0000000..1b352a6 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_ceil.c @@ -0,0 +1,85 @@ +/* @(#)s_ceil.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_ceil.c,v 1.8 1995/05/10 20:46:53 jtc Exp $"; +#endif + +/* + * ceil(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to ceil(x). + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double huge = 1.0e300; +#else +static double huge = 1.0e300; +#endif + +#ifdef __STDC__ + double __ceil(double x) +#else + double __ceil(x) + double x; +#endif +{ + int32_t i0,i1,j0; + u_int32_t i,j; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;i1=0;} + else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;} + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x00100000)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) { + if(j0==20) i0+=1; + else { + j = i1 + (1<<(52-j0)); + if(j<i1) i0+=1; /* got a carry */ + i1 = j; + } + } + i1 &= (~i); + } + } + INSERT_WORDS(x,i0,i1); + return x; +} +weak_alias (__ceil, ceil) +#ifdef NO_LONG_DOUBLE +strong_alias (__ceil, __ceill) +weak_alias (__ceil, ceill) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_copysign.c b/sysdeps/ieee754/dbl-64/s_copysign.c new file mode 100644 index 0000000..5e35e69 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_copysign.c @@ -0,0 +1,43 @@ +/* @(#)s_copysign.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_copysign.c,v 1.8 1995/05/10 20:46:57 jtc Exp $"; +#endif + +/* + * copysign(double x, double y) + * copysign(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double __copysign(double x, double y) +#else + double __copysign(x,y) + double x,y; +#endif +{ + u_int32_t hx,hy; + GET_HIGH_WORD(hx,x); + GET_HIGH_WORD(hy,y); + SET_HIGH_WORD(x,(hx&0x7fffffff)|(hy&0x80000000)); + return x; +} +weak_alias (__copysign, copysign) +#ifdef NO_LONG_DOUBLE +strong_alias (__copysign, __copysignl) +weak_alias (__copysign, copysignl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_cos.c b/sysdeps/ieee754/dbl-64/s_cos.c new file mode 100644 index 0000000..7edb5de --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_cos.c @@ -0,0 +1,87 @@ +/* @(#)s_cos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_cos.c,v 1.7 1995/05/10 20:47:02 jtc Exp $"; +#endif + +/* cos(x) + * Return cosine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cosine function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double __cos(double x) +#else + double __cos(x) + double x; +#endif +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_cos(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_cos(y[0],y[1]); + case 1: return -__kernel_sin(y[0],y[1],1); + case 2: return -__kernel_cos(y[0],y[1]); + default: + return __kernel_sin(y[0],y[1],1); + } + } +} +weak_alias (__cos, cos) +#ifdef NO_LONG_DOUBLE +strong_alias (__cos, __cosl) +weak_alias (__cos, cosl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_erf.c b/sysdeps/ieee754/dbl-64/s_erf.c new file mode 100644 index 0000000..d8b6629 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_erf.c @@ -0,0 +1,431 @@ +/* @(#)s_erf.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; +#endif + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * Note that + * erf(-x) = -erf(x) + * erfc(-x) = 2 - erfc(x) + * + * Method: + * 1. For |x| in [0, 0.84375] + * erf(x) = x + x*R(x^2) + * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] + * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] + * where R = P/Q where P is an odd poly of degree 8 and + * Q is an odd poly of degree 10. + * -57.90 + * | R - (erf(x)-x)/x | <= 2 + * + * + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. The interval is chosen because the fix + * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is + * near 0.6174), and by some experiment, 0.84375 is chosen to + * guarantee the error is less than one ulp for erf. + * + * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(x) = sign(x) * (c + P1(s)/Q1(s)) + * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 + * 1+(c+P1(s)/Q1(s)) if x < 0 + * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06 + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * That is, we use rational approximation to approximate + * erf(1+s) - (c = (single)0.84506291151) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * where + * P1(s) = degree 6 poly in s + * Q1(s) = degree 6 poly in s + * + * 3. For x in [1.25,1/0.35(~2.857143)], + * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1) + * erf(x) = 1 - erfc(x) + * where + * R1(z) = degree 7 poly in z, (z=1/x^2) + * S1(z) = degree 8 poly in z + * + * 4. For x in [1/0.35,28] + * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 + * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0 + * = 2.0 - tiny (if x <= -6) + * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else + * erf(x) = sign(x)*(1.0 - tiny) + * where + * R2(z) = degree 6 poly in z, (z=1/x^2) + * S2(z) = degree 7 poly in z + * + * Note1: + * To compute exp(-x*x-0.5625+R/S), let s be a single + * precision number and s := x; then + * -x*x = -s*s + (s-x)*(s+x) + * exp(-x*x-0.5626+R/S) = + * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S); + * Note2: + * Here 4 and 5 make use of the asymptotic series + * exp(-x*x) + * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ) + * x*sqrt(pi) + * We use rational approximation to approximate + * g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625 + * Here is the error bound for R1/S1 and R2/S2 + * |R1/S1 - f(x)| < 2**(-62.57) + * |R2/S2 - f(x)| < 2**(-61.52) + * + * 5. For inf > x >= 28 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * = 2 - tiny if x<0 + * + * 7. Special case: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +tiny = 1e-300, +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ + /* c = (float)0.84506291151 */ +erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ +efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */ +pp[] = {1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */ + -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */ + -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */ + -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */ + -2.37630166566501626084e-05}, /* 0xBEF8EAD6, 0x120016AC */ +qq[] = {0.0, 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */ + 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */ + 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ + 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ + -3.96022827877536812320e-06}, /* 0xBED09C43, 0x42A26120 */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +pa[] = {-2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ + 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ + -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */ + 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */ + -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */ + 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */ + -2.16637559486879084300e-03}, /* 0xBF61BF38, 0x0A96073F */ +qa[] = {0.0, 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */ + 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */ + 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */ + 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */ + 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */ + 1.19844998467991074170e-02}, /* 0x3F888B54, 0x5735151D */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +ra[] = {-9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */ + -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */ + -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */ + -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */ + -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */ + -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */ + -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */ + -9.81432934416914548592e+00}, /* 0xC023A0EF, 0xC69AC25C */ +sa[] = {0.0,1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */ + 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */ + 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */ + 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */ + 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */ + 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */ + 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */ + -6.04244152148580987438e-02}, /* 0xBFAEEFF2, 0xEE749A62 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ +rb[] = {-9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */ + -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */ + -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */ + -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */ + -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */ + -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */ + -4.83519191608651397019e+02}, /* 0xC07E384E, 0x9BDC383F */ +sb[] = {0.0,3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */ + 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */ + 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */ + 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */ + 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ + 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ + -2.24409524465858183362e+01}; /* 0xC03670E2, 0x42712D62 */ + +#ifdef __STDC__ + double __erf(double x) +#else + double __erf(x) + double x; +#endif +{ + int32_t hx,ix,i; + double R,S,P,Q,s,y,z,r; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) { /* erf(nan)=nan */ + i = ((u_int32_t)hx>>31)<<1; + return (double)(1-i)+one/x; /* erf(+-inf)=+-1 */ + } + + if(ix < 0x3feb0000) { /* |x|<0.84375 */ + double r1,r2,s1,s2,s3,z2,z4; + if(ix < 0x3e300000) { /* |x|<2**-28 */ + if (ix < 0x00800000) + return 0.125*(8.0*x+efx8*x); /*avoid underflow */ + return x + efx*x; + } + z = x*x; +#ifdef DO_NOT_USE_THIS + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); +#else + r1 = pp[0]+z*pp[1]; z2=z*z; + r2 = pp[2]+z*pp[3]; z4=z2*z2; + s1 = one+z*qq[1]; + s2 = qq[2]+z*qq[3]; + s3 = qq[4]+z*qq[5]; + r = r1 + z2*r2 + z4*pp[4]; + s = s1 + z2*s2 + z4*s3; +#endif + y = r/s; + return x + x*y; + } + if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ + double s2,s4,s6,P1,P2,P3,P4,Q1,Q2,Q3,Q4; + s = fabs(x)-one; +#ifdef DO_NOT_USE_THIS + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); +#else + P1 = pa[0]+s*pa[1]; s2=s*s; + Q1 = one+s*qa[1]; s4=s2*s2; + P2 = pa[2]+s*pa[3]; s6=s4*s2; + Q2 = qa[2]+s*qa[3]; + P3 = pa[4]+s*pa[5]; + Q3 = qa[4]+s*qa[5]; + P4 = s6*pa[6]; + Q4 = s6*qa[6]; + P = P1 + s2*P2 + s4*P3 + s6*P4; + Q = Q1 + s2*Q2 + s4*Q3 + s6*Q4; +#endif + if(hx>=0) return erx + P/Q; else return -erx - P/Q; + } + if (ix >= 0x40180000) { /* inf>|x|>=6 */ + if(hx>=0) return one-tiny; else return tiny-one; + } + x = fabs(x); + s = one/(x*x); + if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */ +#ifdef DO_NOT_USE_THIS + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); +#else + double R1,R2,R3,R4,S1,S2,S3,S4,s2,s4,s6,s8; + R1 = ra[0]+s*ra[1];s2 = s*s; + S1 = one+s*sa[1]; s4 = s2*s2; + R2 = ra[2]+s*ra[3];s6 = s4*s2; + S2 = sa[2]+s*sa[3];s8 = s4*s4; + R3 = ra[4]+s*ra[5]; + S3 = sa[4]+s*sa[5]; + R4 = ra[6]+s*ra[7]; + S4 = sa[6]+s*sa[7]; + R = R1 + s2*R2 + s4*R3 + s6*R4; + S = S1 + s2*S2 + s4*S3 + s6*S4 + s8*sa[8]; +#endif + } else { /* |x| >= 1/0.35 */ +#ifdef DO_NOT_USE_THIS + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); +#else + double R1,R2,R3,S1,S2,S3,S4,s2,s4,s6; + R1 = rb[0]+s*rb[1];s2 = s*s; + S1 = one+s*sb[1]; s4 = s2*s2; + R2 = rb[2]+s*rb[3];s6 = s4*s2; + S2 = sb[2]+s*sb[3]; + R3 = rb[4]+s*rb[5]; + S3 = sb[4]+s*sb[5]; + S4 = sb[6]+s*sb[7]; + R = R1 + s2*R2 + s4*R3 + s6*rb[6]; + S = S1 + s2*S2 + s4*S3 + s6*S4; +#endif + } + z = x; + SET_LOW_WORD(z,0); + r = __ieee754_exp(-z*z-0.5625)*__ieee754_exp((z-x)*(z+x)+R/S); + if(hx>=0) return one-r/x; else return r/x-one; +} +weak_alias (__erf, erf) +#ifdef NO_LONG_DOUBLE +strong_alias (__erf, __erfl) +weak_alias (__erf, erfl) +#endif + +#ifdef __STDC__ + double __erfc(double x) +#else + double __erfc(x) + double x; +#endif +{ + int32_t hx,ix; + double R,S,P,Q,s,y,z,r; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (double)(((u_int32_t)hx>>31)<<1)+one/x; + } + + if(ix < 0x3feb0000) { /* |x|<0.84375 */ + double r1,r2,s1,s2,s3,z2,z4; + if(ix < 0x3c700000) /* |x|<2**-56 */ + return one-x; + z = x*x; +#ifdef DO_NOT_USE_THIS + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); +#else + r1 = pp[0]+z*pp[1]; z2=z*z; + r2 = pp[2]+z*pp[3]; z4=z2*z2; + s1 = one+z*qq[1]; + s2 = qq[2]+z*qq[3]; + s3 = qq[4]+z*qq[5]; + r = r1 + z2*r2 + z4*pp[4]; + s = s1 + z2*s2 + z4*s3; +#endif + y = r/s; + if(hx < 0x3fd00000) { /* x<1/4 */ + return one-(x+x*y); + } else { + r = x*y; + r += (x-half); + return half - r ; + } + } + if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ + double s2,s4,s6,P1,P2,P3,P4,Q1,Q2,Q3,Q4; + s = fabs(x)-one; +#ifdef DO_NOT_USE_THIS + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); +#else + P1 = pa[0]+s*pa[1]; s2=s*s; + Q1 = one+s*qa[1]; s4=s2*s2; + P2 = pa[2]+s*pa[3]; s6=s4*s2; + Q2 = qa[2]+s*qa[3]; + P3 = pa[4]+s*pa[5]; + Q3 = qa[4]+s*qa[5]; + P4 = s6*pa[6]; + Q4 = s6*qa[6]; + P = P1 + s2*P2 + s4*P3 + s6*P4; + Q = Q1 + s2*Q2 + s4*Q3 + s6*Q4; +#endif + if(hx>=0) { + z = one-erx; return z - P/Q; + } else { + z = erx+P/Q; return one+z; + } + } + if (ix < 0x403c0000) { /* |x|<28 */ + x = fabs(x); + s = one/(x*x); + if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/ +#ifdef DO_NOT_USE_THIS + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); +#else + double R1,R2,R3,R4,S1,S2,S3,S4,s2,s4,s6,s8; + R1 = ra[0]+s*ra[1];s2 = s*s; + S1 = one+s*sa[1]; s4 = s2*s2; + R2 = ra[2]+s*ra[3];s6 = s4*s2; + S2 = sa[2]+s*sa[3];s8 = s4*s4; + R3 = ra[4]+s*ra[5]; + S3 = sa[4]+s*sa[5]; + R4 = ra[6]+s*ra[7]; + S4 = sa[6]+s*sa[7]; + R = R1 + s2*R2 + s4*R3 + s6*R4; + S = S1 + s2*S2 + s4*S3 + s6*S4 + s8*sa[8]; +#endif + } else { /* |x| >= 1/.35 ~ 2.857143 */ + double R1,R2,R3,S1,S2,S3,S4,s2,s4,s6; + if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */ +#ifdef DO_NOT_USE_THIS + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); +#else + R1 = rb[0]+s*rb[1];s2 = s*s; + S1 = one+s*sb[1]; s4 = s2*s2; + R2 = rb[2]+s*rb[3];s6 = s4*s2; + S2 = sb[2]+s*sb[3]; + R3 = rb[4]+s*rb[5]; + S3 = sb[4]+s*sb[5]; + S4 = sb[6]+s*sb[7]; + R = R1 + s2*R2 + s4*R3 + s6*rb[6]; + S = S1 + s2*S2 + s4*S3 + s6*S4; +#endif + } + z = x; + SET_LOW_WORD(z,0); + r = __ieee754_exp(-z*z-0.5625)* + __ieee754_exp((z-x)*(z+x)+R/S); + if(hx>0) return r/x; else return two-r/x; + } else { + if(hx>0) return tiny*tiny; else return two-tiny; + } +} +weak_alias (__erfc, erfc) +#ifdef NO_LONG_DOUBLE +strong_alias (__erfc, __erfcl) +weak_alias (__erfc, erfcl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_exp2.c b/sysdeps/ieee754/dbl-64/s_exp2.c new file mode 100644 index 0000000..875d4d6 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_exp2.c @@ -0,0 +1,129 @@ +/* Double-precision floating point 2^x. + Copyright (C) 1997, 1998 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +/* The basic design here is from + Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical + Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft., + 17 (1), March 1991, pp. 26-45. + It has been slightly modified to compute 2^x instead of e^x. + */ +#ifndef _GNU_SOURCE +#define _GNU_SOURCE +#endif +#include <float.h> +#include <ieee754.h> +#include <math.h> +#include <fenv.h> +#include <inttypes.h> +#include <math_private.h> + +#include "t_exp2.h" + +static const volatile double TWO1023 = 8.988465674311579539e+307; +static const volatile double TWOM1000 = 9.3326361850321887899e-302; + +double +__ieee754_exp2 (double x) +{ + static const double himark = (double) DBL_MAX_EXP; + static const double lomark = (double) (DBL_MIN_EXP - DBL_MANT_DIG - 1) - 1.0; + + /* Check for usual case. */ + if (isless (x, himark) && isgreater (x, lomark)) + { + static const double THREEp42 = 13194139533312.0; + int tval, unsafe; + double rx, x22, result; + union ieee754_double ex2_u, scale_u; + fenv_t oldenv; + + feholdexcept (&oldenv); +#ifdef FE_TONEAREST + /* If we don't have this, it's too bad. */ + fesetround (FE_TONEAREST); +#endif + + /* 1. Argument reduction. + Choose integers ex, -256 <= t < 256, and some real + -1/1024 <= x1 <= 1024 so that + x = ex + t/512 + x1. + + First, calculate rx = ex + t/512. */ + rx = x + THREEp42; + rx -= THREEp42; + x -= rx; /* Compute x=x1. */ + /* Compute tval = (ex*512 + t)+256. + Now, t = (tval mod 512)-256 and ex=tval/512 [that's mod, NOT %; and + /-round-to-nearest not the usual c integer /]. */ + tval = (int) (rx * 512.0 + 256.0); + + /* 2. Adjust for accurate table entry. + Find e so that + x = ex + t/512 + e + x2 + where -1e6 < e < 1e6, and + (double)(2^(t/512+e)) + is accurate to one part in 2^-64. */ + + /* 'tval & 511' is the same as 'tval%512' except that it's always + positive. + Compute x = x2. */ + x -= exp2_deltatable[tval & 511]; + + /* 3. Compute ex2 = 2^(t/512+e+ex). */ + ex2_u.d = exp2_accuratetable[tval & 511]; + tval >>= 9; + unsafe = abs(tval) >= -DBL_MIN_EXP - 1; + ex2_u.ieee.exponent += tval >> unsafe; + scale_u.d = 1.0; + scale_u.ieee.exponent += tval - (tval >> unsafe); + + /* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial, + with maximum error in [-2^-10-2^-30,2^-10+2^-30] + less than 10^-19. */ + + x22 = (((.0096181293647031180 + * x + .055504110254308625) + * x + .240226506959100583) + * x + .69314718055994495) * ex2_u.d; + + /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */ + fesetenv (&oldenv); + + result = x22 * x + ex2_u.d; + + if (!unsafe) + return result; + else + return result * scale_u.d; + } + /* Exceptional cases: */ + else if (isless (x, himark)) + { + if (__isinf (x)) + /* e^-inf == 0, with no error. */ + return 0; + else + /* Underflow */ + return TWOM1000 * TWOM1000; + } + else + /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ + return TWO1023*x; +} diff --git a/sysdeps/ieee754/dbl-64/s_expm1.c b/sysdeps/ieee754/dbl-64/s_expm1.c new file mode 100644 index 0000000..bfd15b2 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_expm1.c @@ -0,0 +1,243 @@ +/* @(#)s_expm1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $"; +#endif + +/* expm1(x) + * Returns exp(x)-1, the exponential of x minus 1. + * + * Method + * 1. Argument reduction: + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 + * + * Here a correction term c will be computed to compensate + * the error in r when rounded to a floating-point number. + * + * 2. Approximating expm1(r) by a special rational function on + * the interval [0,0.34658]: + * Since + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ... + * we define R1(r*r) by + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r) + * That is, + * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r) + * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r)) + * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ... + * We use a special Reme algorithm on [0,0.347] to generate + * a polynomial of degree 5 in r*r to approximate R1. The + * maximum error of this polynomial approximation is bounded + * by 2**-61. In other words, + * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5 + * where Q1 = -1.6666666666666567384E-2, + * Q2 = 3.9682539681370365873E-4, + * Q3 = -9.9206344733435987357E-6, + * Q4 = 2.5051361420808517002E-7, + * Q5 = -6.2843505682382617102E-9; + * (where z=r*r, and the values of Q1 to Q5 are listed below) + * with error bounded by + * | 5 | -61 + * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 + * | | + * + * expm1(r) = exp(r)-1 is then computed by the following + * specific way which minimize the accumulation rounding error: + * 2 3 + * r r [ 3 - (R1 + R1*r/2) ] + * expm1(r) = r + --- + --- * [--------------------] + * 2 2 [ 6 - r*(3 - R1*r/2) ] + * + * To compensate the error in the argument reduction, we use + * expm1(r+c) = expm1(r) + c + expm1(r)*c + * ~ expm1(r) + c + r*c + * Thus c+r*c will be added in as the correction terms for + * expm1(r+c). Now rearrange the term to avoid optimization + * screw up: + * ( 2 2 ) + * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) + * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) + * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) + * ( ) + * + * = r - E + * 3. Scale back to obtain expm1(x): + * From step 1, we have + * expm1(x) = either 2^k*[expm1(r)+1] - 1 + * = or 2^k*[expm1(r) + (1-2^-k)] + * 4. Implementation notes: + * (A). To save one multiplication, we scale the coefficient Qi + * to Qi*2^i, and replace z by (x^2)/2. + * (B). To achieve maximum accuracy, we compute expm1(x) by + * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf) + * (ii) if k=0, return r-E + * (iii) if k=-1, return 0.5*(r-E)-0.5 + * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E) + * else return 1.0+2.0*(r-E); + * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1) + * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else + * (vii) return 2^k(1-((E+2^-k)-r)) + * + * Special cases: + * expm1(INF) is INF, expm1(NaN) is NaN; + * expm1(-INF) is -1, and + * for finite argument, only expm1(0)=0 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then expm1(x) overflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" +#define one Q[0] +#ifdef __STDC__ +static const double +#else +static double +#endif +huge = 1.0e+300, +tiny = 1.0e-300, +o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */ +ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */ +ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */ +invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */ + /* scaled coefficients related to expm1 */ +Q[] = {1.0, -3.33333333333331316428e-02, /* BFA11111 111110F4 */ + 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ + -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ + 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ + -2.01099218183624371326e-07}; /* BE8AFDB7 6E09C32D */ + +#ifdef __STDC__ + double __expm1(double x) +#else + double __expm1(x) + double x; +#endif +{ + double y,hi,lo,c,t,e,hxs,hfx,r1,h2,h4,R1,R2,R3; + int32_t k,xsb; + u_int32_t hx; + + GET_HIGH_WORD(hx,x); + xsb = hx&0x80000000; /* sign bit of x */ + if(xsb==0) y=x; else y= -x; /* y = |x| */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out huge and non-finite argument */ + if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */ + if(hx >= 0x40862E42) { /* if |x|>=709.78... */ + if(hx>=0x7ff00000) { + u_int32_t low; + GET_LOW_WORD(low,x); + if(((hx&0xfffff)|low)!=0) + return x+x; /* NaN */ + else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ + } + if(x > o_threshold) return huge*huge; /* overflow */ + } + if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */ + if(x+tiny<0.0) /* raise inexact */ + return tiny-one; /* return -1 */ + } + } + + /* argument reduction */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + if(xsb==0) + {hi = x - ln2_hi; lo = ln2_lo; k = 1;} + else + {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} + } else { + k = invln2*x+((xsb==0)?0.5:-0.5); + t = k; + hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ + lo = t*ln2_lo; + } + x = hi - lo; + c = (hi-x)-lo; + } + else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */ + t = huge+x; /* return x with inexact flags when x!=0 */ + return x - (t-(huge+x)); + } + else k = 0; + + /* x is now in primary range */ + hfx = 0.5*x; + hxs = x*hfx; +#ifdef DO_NOT_USE_THIS + r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); +#else + R1 = one+hxs*Q[1]; h2 = hxs*hxs; + R2 = Q[2]+hxs*Q[3]; h4 = h2*h2; + R3 = Q[4]+hxs*Q[5]; + r1 = R1 + h2*R2 + h4*R3; +#endif + t = 3.0-r1*hfx; + e = hxs*((r1-t)/(6.0 - x*t)); + if(k==0) return x - (x*e-hxs); /* c is 0 */ + else { + e = (x*(e-c)-c); + e -= hxs; + if(k== -1) return 0.5*(x-e)-0.5; + if(k==1) { + if(x < -0.25) return -2.0*(e-(x+0.5)); + else return one+2.0*(x-e); + } + if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ + u_int32_t high; + y = one-(e-x); + GET_HIGH_WORD(high,y); + SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ + return y-one; + } + t = one; + if(k<20) { + u_int32_t high; + SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */ + y = t-(e-x); + GET_HIGH_WORD(high,y); + SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ + } else { + u_int32_t high; + SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */ + y = x-(e+t); + y += one; + GET_HIGH_WORD(high,y); + SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ + } + } + return y; +} +weak_alias (__expm1, expm1) +#ifdef NO_LONG_DOUBLE +strong_alias (__expm1, __expm1l) +weak_alias (__expm1, expm1l) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_fabs.c b/sysdeps/ieee754/dbl-64/s_fabs.c new file mode 100644 index 0000000..1abe943 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_fabs.c @@ -0,0 +1,40 @@ +/* @(#)s_fabs.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_fabs.c,v 1.7 1995/05/10 20:47:13 jtc Exp $"; +#endif + +/* + * fabs(x) returns the absolute value of x. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double __fabs(double x) +#else + double __fabs(x) + double x; +#endif +{ + u_int32_t high; + GET_HIGH_WORD(high,x); + SET_HIGH_WORD(x,high&0x7fffffff); + return x; +} +weak_alias (__fabs, fabs) +#ifdef NO_LONG_DOUBLE +strong_alias (__fabs, __fabsl) +weak_alias (__fabs, fabsl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_finite.c b/sysdeps/ieee754/dbl-64/s_finite.c new file mode 100644 index 0000000..b12ff42 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_finite.c @@ -0,0 +1,40 @@ +/* @(#)s_finite.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_finite.c,v 1.8 1995/05/10 20:47:17 jtc Exp $"; +#endif + +/* + * finite(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int __finite(double x) +#else + int __finite(x) + double x; +#endif +{ + int32_t hx; + GET_HIGH_WORD(hx,x); + return (int)((u_int32_t)((hx&0x7fffffff)-0x7ff00000)>>31); +} +weak_alias (__finite, finite) +#ifdef NO_LONG_DOUBLE +strong_alias (__finite, __finitel) +weak_alias (__finite, finitel) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_floor.c b/sysdeps/ieee754/dbl-64/s_floor.c new file mode 100644 index 0000000..77db9ef --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_floor.c @@ -0,0 +1,86 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_floor.c,v 1.8 1995/05/10 20:47:20 jtc Exp $"; +#endif + +/* + * floor(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floor(x). + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double huge = 1.0e300; +#else +static double huge = 1.0e300; +#endif + +#ifdef __STDC__ + double __floor(double x) +#else + double __floor(x) + double x; +#endif +{ + int32_t i0,i1,j0; + u_int32_t i,j; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=i1=0;} + else if(((i0&0x7fffffff)|i1)!=0) + { i0=0xbff00000;i1=0;} + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00100000)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) { + if(j0==20) i0+=1; + else { + j = i1+(1<<(52-j0)); + if(j<i1) i0 +=1 ; /* got a carry */ + i1=j; + } + } + i1 &= (~i); + } + } + INSERT_WORDS(x,i0,i1); + return x; +} +weak_alias (__floor, floor) +#ifdef NO_LONG_DOUBLE +strong_alias (__floor, __floorl) +weak_alias (__floor, floorl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_fpclassify.c b/sysdeps/ieee754/dbl-64/s_fpclassify.c new file mode 100644 index 0000000..72a1536 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_fpclassify.c @@ -0,0 +1,43 @@ +/* Return classification value corresponding to argument. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +int +__fpclassify (double x) +{ + u_int32_t hx, lx; + int retval = FP_NORMAL; + + EXTRACT_WORDS (hx, lx, x); + lx |= hx & 0xfffff; + hx &= 0x7ff00000; + if ((hx | lx) == 0) + retval = FP_ZERO; + else if (hx == 0) + retval = FP_SUBNORMAL; + else if (hx == 0x7ff00000) + retval = lx != 0 ? FP_NAN : FP_INFINITE; + + return retval; +} diff --git a/sysdeps/ieee754/dbl-64/s_frexp.c b/sysdeps/ieee754/dbl-64/s_frexp.c new file mode 100644 index 0000000..7dbddfd --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_frexp.c @@ -0,0 +1,64 @@ +/* @(#)s_frexp.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_frexp.c,v 1.9 1995/05/10 20:47:24 jtc Exp $"; +#endif + +/* + * for non-zero x + * x = frexp(arg,&exp); + * return a double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg + * with *exp=0. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */ + +#ifdef __STDC__ + double __frexp(double x, int *eptr) +#else + double __frexp(x, eptr) + double x; int *eptr; +#endif +{ + int32_t hx, ix, lx; + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + *eptr = 0; + if(ix>=0x7ff00000||((ix|lx)==0)) return x; /* 0,inf,nan */ + if (ix<0x00100000) { /* subnormal */ + x *= two54; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + *eptr = -54; + } + *eptr += (ix>>20)-1022; + hx = (hx&0x800fffff)|0x3fe00000; + SET_HIGH_WORD(x,hx); + return x; +} +weak_alias (__frexp, frexp) +#ifdef NO_LONG_DOUBLE +strong_alias (__frexp, __frexpl) +weak_alias (__frexp, frexpl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_ilogb.c b/sysdeps/ieee754/dbl-64/s_ilogb.c new file mode 100644 index 0000000..820f01c --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_ilogb.c @@ -0,0 +1,56 @@ +/* @(#)s_ilogb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_ilogb.c,v 1.9 1995/05/10 20:47:28 jtc Exp $"; +#endif + +/* ilogb(double x) + * return the binary exponent of non-zero x + * ilogb(0) = 0x80000001 + * ilogb(inf/NaN) = 0x7fffffff (no signal is raised) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int __ilogb(double x) +#else + int __ilogb(x) + double x; +#endif +{ + int32_t hx,lx,ix; + + GET_HIGH_WORD(hx,x); + hx &= 0x7fffffff; + if(hx<0x00100000) { + GET_LOW_WORD(lx,x); + if((hx|lx)==0) + return FP_ILOGB0; /* ilogb(0) = FP_ILOGB0 */ + else /* subnormal x */ + if(hx==0) { + for (ix = -1043; lx>0; lx<<=1) ix -=1; + } else { + for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1; + } + return ix; + } + else if (hx<0x7ff00000) return (hx>>20)-1023; + else return FP_ILOGBNAN; +} +weak_alias (__ilogb, ilogb) +#ifdef NO_LONG_DOUBLE +strong_alias (__ilogb, __ilogbl) +weak_alias (__ilogb, ilogbl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_isinf.c b/sysdeps/ieee754/dbl-64/s_isinf.c new file mode 100644 index 0000000..4f063d0 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_isinf.c @@ -0,0 +1,32 @@ +/* + * Written by J.T. Conklin <jtc@netbsd.org>. + * Changed to return -1 for -Inf by Ulrich Drepper <drepper@cygnus.com>. + * Public domain. + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_isinf.c,v 1.3 1995/05/11 23:20:14 jtc Exp $"; +#endif + +/* + * isinf(x) returns 1 is x is inf, -1 if x is -inf, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +int +__isinf (double x) +{ + int32_t hx,lx; + EXTRACT_WORDS(hx,lx,x); + lx |= (hx & 0x7fffffff) ^ 0x7ff00000; + lx |= -lx; + return ~(lx >> 31) & (hx >> 30); +} +weak_alias (__isinf, isinf) +#ifdef NO_LONG_DOUBLE +strong_alias (__isinf, __isinfl) +weak_alias (__isinf, isinfl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_isnan.c b/sysdeps/ieee754/dbl-64/s_isnan.c new file mode 100644 index 0000000..86301e1 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_isnan.c @@ -0,0 +1,43 @@ +/* @(#)s_isnan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_isnan.c,v 1.8 1995/05/10 20:47:36 jtc Exp $"; +#endif + +/* + * isnan(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int __isnan(double x) +#else + int __isnan(x) + double x; +#endif +{ + int32_t hx,lx; + EXTRACT_WORDS(hx,lx,x); + hx &= 0x7fffffff; + hx |= (u_int32_t)(lx|(-lx))>>31; + hx = 0x7ff00000 - hx; + return (int)(((u_int32_t)hx)>>31); +} +weak_alias (__isnan, isnan) +#ifdef NO_LONG_DOUBLE +strong_alias (__isnan, __isnanl) +weak_alias (__isnan, isnanl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_llrint.c b/sysdeps/ieee754/dbl-64/s_llrint.c new file mode 100644 index 0000000..8e70bcf --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_llrint.c @@ -0,0 +1,95 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + +static const long double two52[2] = +{ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + + +long long int +__llrint (double x) +{ + int32_t j0; + u_int32_t i1, i0; + long long int result; + volatile double w; + double t; + int sx; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + sx = i0 >> 31; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 < 20) + { + if (j0 < -1) + return 0; + else + { + w = two52[sx] + x; + t = w - two52[sx]; + EXTRACT_WORDS (i0, i1, t); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + i0 &= 0xfffff; + i0 |= 0x100000; + + result = i0 >> (20 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 >= 52) + result = (((long long int) i0 << 32) | i1) << (j0 - 52); + else + { + w = two52[sx] + x; + t = w - two52[sx]; + EXTRACT_WORDS (i0, i1, t); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + i0 &= 0xfffff; + i0 |= 0x100000; + + result = ((long long int) i0 << (j0 - 20)) | (i1 >> (52 - j0)); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__llrint, llrint) +#ifdef NO_LONG_DOUBLE +strong_alias (__llrint, __llrintl) +weak_alias (__llrint, llrintl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_llround.c b/sysdeps/ieee754/dbl-64/s_llround.c new file mode 100644 index 0000000..92ce10f --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_llround.c @@ -0,0 +1,81 @@ +/* Round double value to long long int. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +long long int +__llround (double x) +{ + int32_t j0; + u_int32_t i1, i0; + long long int result; + int sign; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + sign = (i0 & 0x80000000) != 0 ? -1 : 1; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 < 20) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else + { + i0 += 0x80000 >> j0; + + result = i0 >> (20 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 >= 52) + result = (((long long int) i0 << 32) | i1) << (j0 - 52); + else + { + u_int32_t j = i1 + (0x80000000 >> (j0 - 20)); + if (j < i1) + ++i0; + + if (j0 == 20) + result = (long long int) i0; + else + result = ((long long int) i0 << (j0 - 20)) | (j >> (52 - j0)); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long long int) x; + } + + return sign * result; +} + +weak_alias (__llround, llround) +#ifdef NO_LONG_DOUBLE +strong_alias (__llround, __llroundl) +weak_alias (__llround, llroundl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_log1p.c b/sysdeps/ieee754/dbl-64/s_log1p.c new file mode 100644 index 0000000..0a9801a --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_log1p.c @@ -0,0 +1,191 @@ +/* @(#)s_log1p.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_log1p.c,v 1.8 1995/05/10 20:47:46 jtc Exp $"; +#endif + +/* double log1p(double x) + * + * Method : + * 1. Argument Reduction: find k and f such that + * 1+x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * Note. If k=0, then f=x is exact. However, if k!=0, then f + * may not be representable exactly. In that case, a correction + * term is need. Let u=1+x rounded. Let c = (1+x)-u, then + * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u), + * and add back the correction term c/u. + * (Note: when x > 2**53, one can simply return log(x)) + * + * 2. Approximation of log1p(f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s + * (the values of Lp1 to Lp7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lp1*s +...+Lp7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log1p(f) = f - (hfsq - s*(hfsq+R)). + * + * 3. Finally, log1p(x) = k*ln2 + log1p(f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log1p(x) is NaN with signal if x < -1 (including -INF) ; + * log1p(+INF) is +INF; log1p(-1) is -INF with signal; + * log1p(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + * + * Note: Assuming log() return accurate answer, the following + * algorithm can be used to compute log1p(x) to within a few ULP: + * + * u = 1+x; + * if(u==1.0) return x ; else + * return log(u)*(x/(u-1.0)); + * + * See HP-15C Advanced Functions Handbook, p.193. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ +ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lp[] = {0.0, 6.666666666666735130e-01, /* 3FE55555 55555593 */ + 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ + 2.857142874366239149e-01, /* 3FD24924 94229359 */ + 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ + 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ + 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ + 1.479819860511658591e-01}; /* 3FC2F112 DF3E5244 */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __log1p(double x) +#else + double __log1p(x) + double x; +#endif +{ + double hfsq,f,c,s,z,R,u,z2,z4,z6,R1,R2,R3,R4; + int32_t k,hx,hu,ax; + + GET_HIGH_WORD(hx,x); + ax = hx&0x7fffffff; + + k = 1; + if (hx < 0x3FDA827A) { /* x < 0.41422 */ + if(ax>=0x3ff00000) { /* x <= -1.0 */ + if(x==-1.0) return -two54/(x-x);/* log1p(-1)=+inf */ + else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ + } + if(ax<0x3e200000) { /* |x| < 2**-29 */ + if(two54+x>zero /* raise inexact */ + &&ax<0x3c900000) /* |x| < 2**-54 */ + return x; + else + return x - x*x*0.5; + } + if(hx>0||hx<=((int32_t)0xbfd2bec3)) { + k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */ + } + if (hx >= 0x7ff00000) return x+x; + if(k!=0) { + if(hx<0x43400000) { + u = 1.0+x; + GET_HIGH_WORD(hu,u); + k = (hu>>20)-1023; + c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */ + c /= u; + } else { + u = x; + GET_HIGH_WORD(hu,u); + k = (hu>>20)-1023; + c = 0; + } + hu &= 0x000fffff; + if(hu<0x6a09e) { + SET_HIGH_WORD(u,hu|0x3ff00000); /* normalize u */ + } else { + k += 1; + SET_HIGH_WORD(u,hu|0x3fe00000); /* normalize u/2 */ + hu = (0x00100000-hu)>>2; + } + f = u-1.0; + } + hfsq=0.5*f*f; + if(hu==0) { /* |f| < 2**-20 */ + if(f==zero) { + if(k==0) return zero; + else {c += k*ln2_lo; return k*ln2_hi+c;} + } + R = hfsq*(1.0-0.66666666666666666*f); + if(k==0) return f-R; else + return k*ln2_hi-((R-(k*ln2_lo+c))-f); + } + s = f/(2.0+f); + z = s*s; +#ifdef DO_NOT_USE_THIS + R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); +#else + R1 = z*Lp[1]; z2=z*z; + R2 = Lp[2]+z*Lp[3]; z4=z2*z2; + R3 = Lp[4]+z*Lp[5]; z6=z4*z2; + R4 = Lp[6]+z*Lp[7]; + R = R1 + z2*R2 + z4*R3 + z6*R4; +#endif + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); +} +weak_alias (__log1p, log1p) +#ifdef NO_LONG_DOUBLE +strong_alias (__log1p, __log1pl) +weak_alias (__log1p, log1pl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_log2.c b/sysdeps/ieee754/dbl-64/s_log2.c new file mode 100644 index 0000000..7379ce8 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_log2.c @@ -0,0 +1,136 @@ +/* Adapted for log2 by Ulrich Drepper <drepper@cygnus.com>. */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __log2(x) + * Return the logarithm to base 2 of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k + log(1+f). + * = k+(f-(hfsq-(s*(hfsq+R)))) + * + * Special cases: + * log2(x) is NaN with signal if x < 0 (including -INF) ; + * log2(+INF) is +INF; log(0) is -INF with signal; + * log2(NaN) is that NaN with no signal. + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +ln2 = 0.69314718055994530942, +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __log2(double x) +#else + double __log2(x) + double x; +#endif +{ + double hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,hx,i,j; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/(x-x); /* log(+-0)=-inf */ + if (hx<0) return (x-x)/(x-x); /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ + k += (i>>20); + dk = (double) k; + f = x-1.0; + if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ + if(f==zero) return dk; + R = f*f*(0.5-0.33333333333333333*f); + return dk-(R-f)/ln2; + } + s = f/(2.0+f); + z = s*s; + i = hx-0x6147a; + w = z*z; + j = 0x6b851-hx; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=0.5*f*f; + return dk-((hfsq-(s*(hfsq+R)))-f)/ln2; + } else { + return dk-((s*(f-R))-f)/ln2; + } +} + +weak_alias (__log2, log2) +#ifdef NO_LONG_DOUBLE +strong_alias (__log2, __log2l) +weak_alias (__log2, log2l) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_logb.c b/sysdeps/ieee754/dbl-64/s_logb.c new file mode 100644 index 0000000..4668cf7 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_logb.c @@ -0,0 +1,47 @@ +/* @(#)s_logb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_logb.c,v 1.8 1995/05/10 20:47:50 jtc Exp $"; +#endif + +/* + * double logb(x) + * IEEE 754 logb. Included to pass IEEE test suite. Not recommend. + * Use ilogb instead. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double __logb(double x) +#else + double __logb(x) + double x; +#endif +{ + int32_t lx,ix; + EXTRACT_WORDS(ix,lx,x); + ix &= 0x7fffffff; /* high |x| */ + if((ix|lx)==0) return -1.0/fabs(x); + if(ix>=0x7ff00000) return x*x; + if((ix>>=20)==0) /* IEEE 754 logb */ + return -1022.0; + else + return (double) (ix-1023); +} +weak_alias (__logb, logb) +#ifdef NO_LONG_DOUBLE +strong_alias (__logb, __logbl) +weak_alias (__logb, logbl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_lrint.c b/sysdeps/ieee754/dbl-64/s_lrint.c new file mode 100644 index 0000000..8f0d717 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_lrint.c @@ -0,0 +1,95 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + +static const double two52[2] = +{ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + + +long int +__lrint (double x) +{ + int32_t j0; + u_int32_t i0,i1; + volatile double w; + double t; + long int result; + int sx; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + sx = i0 >> 31; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 < 20) + { + if (j0 < -1) + return 0; + else + { + w = two52[sx] + x; + t = w - two52[sx]; + EXTRACT_WORDS (i0, i1, t); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + i0 &= 0xfffff; + i0 |= 0x100000; + + result = i0 >> (20 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 >= 52) + result = ((long int) i0 << (j0 - 20)) | (i1 << (j0 - 52)); + else + { + w = two52[sx] + x; + t = w - two52[sx]; + EXTRACT_WORDS (i0, i1, t); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + i0 &= 0xfffff; + i0 |= 0x100000; + + result = ((long int) i0 << (j0 - 20)) | (i1 >> (52 - j0)); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__lrint, lrint) +#ifdef NO_LONG_DOUBLE +strong_alias (__lrint, __lrintl) +weak_alias (__lrint, lrintl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_lround.c b/sysdeps/ieee754/dbl-64/s_lround.c new file mode 100644 index 0000000..49be12f --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_lround.c @@ -0,0 +1,78 @@ +/* Round double value to long int. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +long int +__lround (double x) +{ + int32_t j0; + u_int32_t i1, i0; + long int result; + int sign; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + sign = (i0 & 0x80000000) != 0 ? -1 : 1; + i0 &= 0xfffff; + i0 |= 0x100000; + + if (j0 < 20) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else + { + i0 += 0x80000 >> j0; + + result = i0 >> (20 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 >= 52) + result = ((long int) i0 << (j0 - 20)) | (i1 << (j0 - 52)); + else + { + u_int32_t j = i1 + (0x80000000 >> (j0 - 20)); + if (j < i1) + ++i0; + + result = ((long int) i0 << (j0 - 20)) | (j >> (52 - j0)); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long int) x; + } + + return sign * result; +} + +weak_alias (__lround, lround) +#ifdef NO_LONG_DOUBLE +strong_alias (__lround, __lroundl) +weak_alias (__lround, lroundl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_modf.c b/sysdeps/ieee754/dbl-64/s_modf.c new file mode 100644 index 0000000..7851f675 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_modf.c @@ -0,0 +1,85 @@ +/* @(#)s_modf.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_modf.c,v 1.8 1995/05/10 20:47:55 jtc Exp $"; +#endif + +/* + * modf(double x, double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double one = 1.0; +#else +static double one = 1.0; +#endif + +#ifdef __STDC__ + double __modf(double x, double *iptr) +#else + double __modf(x, iptr) + double x,*iptr; +#endif +{ + int32_t i0,i1,j0; + u_int32_t i; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; /* exponent of x */ + if(j0<20) { /* integer part in high x */ + if(j0<0) { /* |x|<1 */ + INSERT_WORDS(*iptr,i0&0x80000000,0); /* *iptr = +-0 */ + return x; + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) { /* x is integral */ + *iptr = x; + INSERT_WORDS(x,i0&0x80000000,0); /* return +-0 */ + return x; + } else { + INSERT_WORDS(*iptr,i0&(~i),0); + return x - *iptr; + } + } + } else if (j0>51) { /* no fraction part */ + *iptr = x*one; + /* We must handle NaNs separately. */ + if (j0 == 0x400 && ((i0 & 0xfffff) | i1)) + return x*one; + INSERT_WORDS(x,i0&0x80000000,0); /* return +-0 */ + return x; + } else { /* fraction part in low x */ + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) { /* x is integral */ + *iptr = x; + INSERT_WORDS(x,i0&0x80000000,0); /* return +-0 */ + return x; + } else { + INSERT_WORDS(*iptr,i0,i1&(~i)); + return x - *iptr; + } + } +} +weak_alias (__modf, modf) +#ifdef NO_LONG_DOUBLE +strong_alias (__modf, __modfl) +weak_alias (__modf, modfl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_nearbyint.c b/sysdeps/ieee754/dbl-64/s_nearbyint.c new file mode 100644 index 0000000..32f5bf9 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_nearbyint.c @@ -0,0 +1,98 @@ +/* Adapted for use as nearbyint by Ulrich Drepper <drepper@cygnus.com>. */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_rint.c,v 1.8 1995/05/10 20:48:04 jtc Exp $"; +#endif + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include <fenv.h> +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +#ifdef __STDC__ + double __nearbyint(double x) +#else + double __nearbyint(x) + double x; +#endif +{ + fenv_t env; + int32_t i0,j0,sx; + u_int32_t i,i1; + double w,t; + EXTRACT_WORDS(i0,i1,x); + sx = (i0>>31)&1; + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { + if(((i0&0x7fffffff)|i1)==0) return x; + i1 |= (i0&0x0fffff); + i0 &= 0xfffe0000; + i0 |= ((i1|-i1)>>12)&0x80000; + SET_HIGH_WORD(x,i0); + feholdexcept (&env); + w = TWO52[sx]+x; + t = w-TWO52[sx]; + fesetenv (&env); + GET_HIGH_WORD(i0,t); + SET_HIGH_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + i>>=1; + if(((i0&i)|i1)!=0) { + if(j0==19) i1 = 0x40000000; else + i0 = (i0&(~i))|((0x20000)>>j0); + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + i>>=1; + if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20)); + } + INSERT_WORDS(x,i0,i1); + feholdexcept (&env); + w = TWO52[sx]+x; + t = w-TWO52[sx]; + fesetenv (&env); + return t; +} +weak_alias (__nearbyint, nearbyint) +#ifdef NO_LONG_DOUBLE +strong_alias (__nearbyint, __nearbyintl) +weak_alias (__nearbyint, nearbyintl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_nexttoward.c b/sysdeps/ieee754/dbl-64/s_nexttoward.c new file mode 100644 index 0000000..c68ba98 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_nexttoward.c @@ -0,0 +1 @@ +/* This function is the same as nextafter so we use an alias there. */ diff --git a/sysdeps/ieee754/dbl-64/s_remquo.c b/sysdeps/ieee754/dbl-64/s_remquo.c new file mode 100644 index 0000000..6e32efb --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_remquo.c @@ -0,0 +1,113 @@ +/* Compute remainder and a congruent to the quotient. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +static const double zero = 0.0; + + +double +__remquo (double x, double y, int *quo) +{ + int32_t hx,hy; + u_int32_t sx,lx,ly; + int cquo, qs; + + EXTRACT_WORDS (hx, lx, x); + EXTRACT_WORDS (hy, ly, y); + sx = hx & 0x80000000; + qs = sx ^ (hy & 0x80000000); + hy &= 0x7fffffff; + hx &= 0x7fffffff; + + /* Purge off exception values. */ + if ((hy | ly) == 0) + return (x * y) / (x * y); /* y = 0 */ + if ((hx >= 0x7ff00000) /* x not finite */ + || ((hy >= 0x7ff00000) /* p is NaN */ + && (((hy - 0x7ff00000) | ly) != 0))) + return (x * y) / (x * y); + + if (hy <= 0x7fbfffff) + x = __ieee754_fmod (x, 8 * y); /* now x < 8y */ + + if (((hx - hy) | (lx - ly)) == 0) + { + *quo = qs ? -1 : 1; + return zero * x; + } + + x = fabs (x); + y = fabs (y); + cquo = 0; + + if (x >= 4 * y) + { + x -= 4 * y; + cquo += 4; + } + if (x >= 2 * y) + { + x -= 2 * y; + cquo += 2; + } + + if (hy < 0x00200000) + { + if (x + x > y) + { + x -= y; + ++cquo; + if (x + x >= y) + { + x -= y; + ++cquo; + } + } + } + else + { + double y_half = 0.5 * y; + if (x > y_half) + { + x -= y; + ++cquo; + if (x >= y_half) + { + x -= y; + ++cquo; + } + } + } + + *quo = qs ? -cquo : cquo; + + if (sx) + x = -x; + return x; +} +weak_alias (__remquo, remquo) +#ifdef NO_LONG_DOUBLE +strong_alias (__remquo, __remquol) +weak_alias (__remquo, remquol) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_rint.c b/sysdeps/ieee754/dbl-64/s_rint.c new file mode 100644 index 0000000..e5f2412 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_rint.c @@ -0,0 +1,91 @@ +/* @(#)s_rint.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_rint.c,v 1.8 1995/05/10 20:48:04 jtc Exp $"; +#endif + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +#ifdef __STDC__ + double __rint(double x) +#else + double __rint(x) + double x; +#endif +{ + int32_t i0,j0,sx; + u_int32_t i,i1; + double w,t; + EXTRACT_WORDS(i0,i1,x); + sx = (i0>>31)&1; + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { + if(((i0&0x7fffffff)|i1)==0) return x; + i1 |= (i0&0x0fffff); + i0 &= 0xfffe0000; + i0 |= ((i1|-i1)>>12)&0x80000; + SET_HIGH_WORD(x,i0); + w = TWO52[sx]+x; + t = w-TWO52[sx]; + GET_HIGH_WORD(i0,t); + SET_HIGH_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + i>>=1; + if(((i0&i)|i1)!=0) { + if(j0==19) i1 = 0x40000000; else + i0 = (i0&(~i))|((0x20000)>>j0); + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + i>>=1; + if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20)); + } + INSERT_WORDS(x,i0,i1); + w = TWO52[sx]+x; + return w-TWO52[sx]; +} +weak_alias (__rint, rint) +#ifdef NO_LONG_DOUBLE +strong_alias (__rint, __rintl) +weak_alias (__rint, rintl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_round.c b/sysdeps/ieee754/dbl-64/s_round.c new file mode 100644 index 0000000..fdb17f8 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_round.c @@ -0,0 +1,97 @@ +/* Round double to integer away from zero. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +static const double huge = 1.0e300; + + +double +__round (double x) +{ + int32_t i0, j0; + u_int32_t i1; + + EXTRACT_WORDS (i0, i1, x); + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + if (j0 < 20) + { + if (j0 < 0) + { + if (huge + x > 0.0) + { + i0 &= 0x80000000; + if (j0 == -1) + i0 |= 0x3ff00000; + i1 = 0; + } + } + else + { + u_int32_t i = 0x000fffff >> j0; + if (((i0 & i) | i1) == 0) + /* X is integral. */ + return x; + if (huge + x > 0.0) + { + /* Raise inexact if x != 0. */ + i0 += 0x00080000 >> j0; + i0 &= ~i; + i1 = 0; + } + } + } + else if (j0 > 51) + { + if (j0 == 0x400) + /* Inf or NaN. */ + return x + x; + else + return x; + } + else + { + u_int32_t i = 0xffffffff >> (j0 - 20); + if ((i1 & i) == 0) + /* X is integral. */ + return x; + + if (huge + x > 0.0) + { + /* Raise inexact if x != 0. */ + u_int32_t j = i1 + (1 << (51 - j0)); + if (j < i1) + i0 += 1; + i1 = j; + } + i1 &= ~i; + } + + INSERT_WORDS (x, i0, i1); + return x; +} +weak_alias (__round, round) +#ifdef NO_LONG_DOUBLE +strong_alias (__round, __roundl) +weak_alias (__round, roundl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_scalbln.c b/sysdeps/ieee754/dbl-64/s_scalbln.c new file mode 100644 index 0000000..aa6134f --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_scalbln.c @@ -0,0 +1,70 @@ +/* @(#)s_scalbn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_scalbn.c,v 1.8 1995/05/10 20:48:08 jtc Exp $"; +#endif + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ +huge = 1.0e+300, +tiny = 1.0e-300; + +#ifdef __STDC__ + double __scalbln (double x, long int n) +#else + double __scalbln (x,n) + double x; long int n; +#endif +{ + int32_t k,hx,lx; + EXTRACT_WORDS(hx,lx,x); + k = (hx&0x7ff00000)>>20; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ + x *= two54; + GET_HIGH_WORD(hx,x); + k = ((hx&0x7ff00000)>>20) - 54; + } + if (k==0x7ff) return x+x; /* NaN or Inf */ + k = k+n; + if (n> 50000 || k > 0x7fe) + return huge*__copysign(huge,x); /* overflow */ + if (n< -50000) return tiny*__copysign(tiny,x); /*underflow*/ + if (k > 0) /* normal result */ + {SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;} + if (k <= -54) + return tiny*__copysign(tiny,x); /*underflow*/ + k += 54; /* subnormal result */ + SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); + return x*twom54; +} +weak_alias (__scalbln, scalbln) +#ifdef NO_LONG_DOUBLE +strong_alias (__scalbln, __scalblnl) +weak_alias (__scalbln, scalblnl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_scalbn.c b/sysdeps/ieee754/dbl-64/s_scalbn.c new file mode 100644 index 0000000..3dbfe8f --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_scalbn.c @@ -0,0 +1,70 @@ +/* @(#)s_scalbn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_scalbn.c,v 1.8 1995/05/10 20:48:08 jtc Exp $"; +#endif + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ +huge = 1.0e+300, +tiny = 1.0e-300; + +#ifdef __STDC__ + double __scalbn (double x, int n) +#else + double __scalbn (x,n) + double x; int n; +#endif +{ + int32_t k,hx,lx; + EXTRACT_WORDS(hx,lx,x); + k = (hx&0x7ff00000)>>20; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ + x *= two54; + GET_HIGH_WORD(hx,x); + k = ((hx&0x7ff00000)>>20) - 54; + } + if (k==0x7ff) return x+x; /* NaN or Inf */ + k = k+n; + if (n> 50000 || k > 0x7fe) + return huge*__copysign(huge,x); /* overflow */ + if (n< -50000) return tiny*__copysign(tiny,x); /*underflow*/ + if (k > 0) /* normal result */ + {SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;} + if (k <= -54) + return tiny*__copysign(tiny,x); /*underflow*/ + k += 54; /* subnormal result */ + SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); + return x*twom54; +} +weak_alias (__scalbn, scalbn) +#ifdef NO_LONG_DOUBLE +strong_alias (__scalbn, __scalbnl) +weak_alias (__scalbn, scalbnl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_signbit.c b/sysdeps/ieee754/dbl-64/s_signbit.c new file mode 100644 index 0000000..ee34003 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_signbit.c @@ -0,0 +1,32 @@ +/* Return nonzero value if number is negative. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + +int +__signbit (double x) +{ + int32_t hx; + + GET_HIGH_WORD (hx, x); + return hx & 0x80000000; +} diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c new file mode 100644 index 0000000..376c69e --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_sin.c @@ -0,0 +1,87 @@ +/* @(#)s_sin.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_sin.c,v 1.7 1995/05/10 20:48:15 jtc Exp $"; +#endif + +/* sin(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double __sin(double x) +#else + double __sin(x) + double x; +#endif +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_sin(y[0],y[1],1); + case 1: return __kernel_cos(y[0],y[1]); + case 2: return -__kernel_sin(y[0],y[1],1); + default: + return -__kernel_cos(y[0],y[1]); + } + } +} +weak_alias (__sin, sin) +#ifdef NO_LONG_DOUBLE +strong_alias (__sin, __sinl) +weak_alias (__sin, sinl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_sincos.c b/sysdeps/ieee754/dbl-64/s_sincos.c new file mode 100644 index 0000000..5bc564b --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_sincos.c @@ -0,0 +1,78 @@ +/* Compute sine and cosine of argument. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +void +__sincos (double x, double *sinx, double *cosx) +{ + int32_t ix; + + /* High word of x. */ + GET_HIGH_WORD (ix, x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if (ix <= 0x3fe921fb) + { + *sinx = __kernel_sin (x, 0.0, 0); + *cosx = __kernel_cos (x, 0.0); + } + else if (ix>=0x7ff00000) + { + /* sin(Inf or NaN) is NaN */ + *sinx = *cosx = x - x; + } + else + { + /* Argument reduction needed. */ + double y[2]; + int n; + + n = __ieee754_rem_pio2 (x, y); + switch (n & 3) + { + case 0: + *sinx = __kernel_sin (y[0], y[1], 1); + *cosx = __kernel_cos (y[0], y[1]); + break; + case 1: + *sinx = __kernel_cos (y[0], y[1]); + *cosx = -__kernel_sin (y[0], y[1], 1); + break; + case 2: + *sinx = -__kernel_sin (y[0], y[1], 1); + *cosx = -__kernel_cos (y[0], y[1]); + break; + default: + *sinx = -__kernel_cos (y[0], y[1]); + *cosx = __kernel_sin (y[0], y[1], 1); + break; + } + } +} +weak_alias (__sincos, sincos) +#ifdef NO_LONG_DOUBLE +strong_alias (__sincos, __sincosl) +weak_alias (__sincos, sincosl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_tan.c b/sysdeps/ieee754/dbl-64/s_tan.c new file mode 100644 index 0000000..714cf27 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_tan.c @@ -0,0 +1,81 @@ +/* @(#)s_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_tan.c,v 1.7 1995/05/10 20:48:18 jtc Exp $"; +#endif + +/* tan(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tan ... tangent function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double __tan(double x) +#else + double __tan(x) + double x; +#endif +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); + + /* tan(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; /* NaN */ + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} +weak_alias (__tan, tan) +#ifdef NO_LONG_DOUBLE +strong_alias (__tan, __tanl) +weak_alias (__tan, tanl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_tanh.c b/sysdeps/ieee754/dbl-64/s_tanh.c new file mode 100644 index 0000000..944f963 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_tanh.c @@ -0,0 +1,93 @@ +/* @(#)s_tanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $"; +#endif + +/* Tanh(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanh(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanh(-x) = -tanh(x). + * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) + * -t + * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) + * t + 2 + * 2 + * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) + * t + 2 + * 22.0 < x <= INF : tanh(x) := 1. + * + * Special cases: + * tanh(NaN) is NaN; + * only tanh(0)=0 is exact for finite argument. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double one=1.0, two=2.0, tiny = 1.0e-300; +#else +static double one=1.0, two=2.0, tiny = 1.0e-300; +#endif + +#ifdef __STDC__ + double __tanh(double x) +#else + double __tanh(x) + double x; +#endif +{ + double t,z; + int32_t jx,ix,lx; + + /* High word of |x|. */ + EXTRACT_WORDS(jx,lx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x40360000) { /* |x|<22 */ + if ((ix | lx) == 0) + return x; /* x == +-0 */ + if (ix<0x3c800000) /* |x|<2**-55 */ + return x*(one+x); /* tanh(small) = small */ + if (ix>=0x3ff00000) { /* |x|>=1 */ + t = __expm1(two*fabs(x)); + z = one - two/(t+two); + } else { + t = __expm1(-two*fabs(x)); + z= -t/(t+two); + } + /* |x| > 22, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (jx>=0)? z: -z; +} +weak_alias (__tanh, tanh) +#ifdef NO_LONG_DOUBLE +strong_alias (__tanh, __tanhl) +weak_alias (__tanh, tanhl) +#endif diff --git a/sysdeps/ieee754/dbl-64/s_trunc.c b/sysdeps/ieee754/dbl-64/s_trunc.c new file mode 100644 index 0000000..07b4951 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/s_trunc.c @@ -0,0 +1,61 @@ +/* Truncate argument to nearest integral value not larger than the argument. + Copyright (C) 1997, 1998 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +double +__trunc (double x) +{ + int32_t i0, j0; + u_int32_t i1; + int sx; + + EXTRACT_WORDS (i0, i1, x); + sx = i0 & 0x80000000; + j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; + if (j0 < 20) + { + if (j0 < 0) + /* The magnitude of the number is < 1 so the result is +-0. */ + INSERT_WORDS (x, sx, 0); + else + INSERT_WORDS (x, sx | (i0 & ~(0x000fffff >> j0)), 0); + } + else if (j0 > 51) + { + if (j0 == 0x400) + /* x is inf or NaN. */ + return x + x; + } + else + { + INSERT_WORDS (x, i0, i1 & ~(0xffffffffu >> (j0 - 20))); + } + + return x; +} +weak_alias (__trunc, trunc) +#ifdef NO_LONG_DOUBLE +strong_alias (__trunc, __truncl) +weak_alias (__trunc, truncl) +#endif diff --git a/sysdeps/ieee754/dbl-64/t_exp.c b/sysdeps/ieee754/dbl-64/t_exp.c new file mode 100644 index 0000000..b02b4f5 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/t_exp.c @@ -0,0 +1,436 @@ +/* Accurate tables for exp(). + Copyright (C) 1998 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +/* This table has the property that, for all integers -177 <= i <= 177, + exp(i/512.0 + __exp_deltatable[abs(i)]) == __exp_atable[i+177] + r + for some -2^-64 < r < 2^-64 (abs(r) < 2^-65 if i <= 0); and that + __exp_deltatable[abs(i)] == t * 2^-60 + for integer t so that abs(t) <= 8847927 * 2^8. */ + +#define W52 (2.22044605e-16) +#define W55 (2.77555756e-17) +#define W58 (3.46944695e-18) +#define W59 (1.73472348e-18) +#define W60 (8.67361738e-19) +const float __exp_deltatable[178] = { + 0*W60, 16558714*W60, -10672149*W59, 1441652*W60, + -15787963*W55, 462888*W60, 7291806*W60, 1698880*W60, + -14375103*W58, -2021016*W60, 728829*W60, -3759654*W60, + 3202123*W60, -10916019*W58, -251570*W60, -1043086*W60, + 8207536*W60, -409964*W60, -5993931*W60, -475500*W60, + 2237522*W60, 324170*W60, -244117*W60, 32077*W60, + 123907*W60, -1019734*W60, -143*W60, 813077*W60, + 743345*W60, 462461*W60, 629794*W60, 2125066*W60, + -2339121*W60, -337951*W60, 9922067*W60, -648704*W60, + 149407*W60, -2687209*W60, -631608*W60, 2128280*W60, + -4882082*W60, 2001360*W60, 175074*W60, 2923216*W60, + -538947*W60, -1212193*W60, -1920926*W60, -1080577*W60, + 3690196*W60, 2643367*W60, 2911937*W60, 671455*W60, + -1128674*W60, 593282*W60, -5219347*W60, -1941490*W60, + 11007953*W60, 239609*W60, -2969658*W60, -1183650*W60, + 942998*W60, 699063*W60, 450569*W60, -329250*W60, + -7257875*W60, -312436*W60, 51626*W60, 555877*W60, + -641761*W60, 1565666*W60, 884327*W60, -10960035*W60, + -2004679*W60, -995793*W60, -2229051*W60, -146179*W60, + -510327*W60, 1453482*W60, -3778852*W60, -2238056*W60, + -4895983*W60, 3398883*W60, -252738*W60, 1230155*W60, + 346918*W60, 1109352*W60, 268941*W60, -2930483*W60, + -1036263*W60, -1159280*W60, 1328176*W60, 2937642*W60, + -9371420*W60, -6902650*W60, -1419134*W60, 1442904*W60, + -1319056*W60, -16369*W60, 696555*W60, -279987*W60, + -7919763*W60, 252741*W60, 459711*W60, -1709645*W60, + 354913*W60, 6025867*W60, -421460*W60, -853103*W60, + -338649*W60, 962151*W60, 955965*W60, 784419*W60, + -3633653*W60, 2277133*W60, -8847927*W52, 1223028*W60, + 5907079*W60, 623167*W60, 5142888*W60, 2599099*W60, + 1214280*W60, 4870359*W60, 593349*W60, -57705*W60, + 7761209*W60, -5564097*W60, 2051261*W60, 6216869*W60, + 4692163*W60, 601691*W60, -5264906*W60, 1077872*W60, + -3205949*W60, 1833082*W60, 2081746*W60, -987363*W60, + -1049535*W60, 2015244*W60, 874230*W60, 2168259*W60, + -1740124*W60, -10068269*W60, -18242*W60, -3013583*W60, + 580601*W60, -2547161*W60, -535689*W60, 2220815*W60, + 1285067*W60, 2806933*W60, -983086*W60, -1729097*W60, + -1162985*W60, -2561904*W60, 801988*W60, 244351*W60, + 1441893*W60, -7517981*W60, 271781*W60, -15021588*W60, + -2341588*W60, -919198*W60, 1642232*W60, 4771771*W60, + -1220099*W60, -3062372*W60, 628624*W60, 1278114*W60, + 13083513*W60, -10521925*W60, 3180310*W60, -1659307*W60, + 3543773*W60, 2501203*W60, 4151*W60, -340748*W60, + -2285625*W60, 2495202*W60 +}; + +const double __exp_atable[355] /* __attribute__((mode(DF))) */ = { + 0.707722561055888932371, /* 0x0.b52d4e46605c27ffd */ + 0.709106182438804188967, /* 0x0.b587fb96f75097ffb */ + 0.710492508843861281234, /* 0x0.b5e2d649899167ffd */ + 0.711881545564593931623, /* 0x0.b63dde74d36bdfffe */ + 0.713273297897442870573, /* 0x0.b699142f945f87ffc */ + 0.714667771153751463236, /* 0x0.b6f477909c4ea0001 */ + 0.716064970655995725059, /* 0x0.b75008aec758f8004 */ + 0.717464901723956938193, /* 0x0.b7abc7a0eea7e0002 */ + 0.718867569715736398602, /* 0x0.b807b47e1586c7ff8 */ + 0.720272979947266023271, /* 0x0.b863cf5d10e380003 */ + 0.721681137825144314297, /* 0x0.b8c01855195c37ffb */ + 0.723092048691992950199, /* 0x0.b91c8f7d213740004 */ + 0.724505717938892290800, /* 0x0.b97934ec5002d0007 */ + 0.725922150953176470431, /* 0x0.b9d608b9c92ea7ffc */ + 0.727341353138962865022, /* 0x0.ba330afcc29e98003 */ + 0.728763329918453162104, /* 0x0.ba903bcc8618b7ffc */ + 0.730188086709957051568, /* 0x0.baed9b40591ba0000 */ + 0.731615628948127705309, /* 0x0.bb4b296f931e30002 */ + 0.733045962086486091436, /* 0x0.bba8e671a05617ff9 */ + 0.734479091556371366251, /* 0x0.bc06d25dd49568001 */ + 0.735915022857225542529, /* 0x0.bc64ed4bce8f6fff9 */ + 0.737353761441304711410, /* 0x0.bcc33752f915d7ff9 */ + 0.738795312814142124419, /* 0x0.bd21b08af98e78005 */ + 0.740239682467211168593, /* 0x0.bd80590b65e9a8000 */ + 0.741686875913991849885, /* 0x0.bddf30ebec4a10000 */ + 0.743136898669507939299, /* 0x0.be3e38443c84e0007 */ + 0.744589756269486091620, /* 0x0.be9d6f2c1d32a0002 */ + 0.746045454254026796384, /* 0x0.befcd5bb59baf8004 */ + 0.747503998175051087583, /* 0x0.bf5c6c09ca84c0003 */ + 0.748965393601880857739, /* 0x0.bfbc322f5b18b7ff8 */ + 0.750429646104262104698, /* 0x0.c01c2843f776fffff */ + 0.751896761271877989160, /* 0x0.c07c4e5fa18b88002 */ + 0.753366744698445112140, /* 0x0.c0dca49a5fb18fffd */ + 0.754839601988627206827, /* 0x0.c13d2b0c444db0005 */ + 0.756315338768691947122, /* 0x0.c19de1cd798578006 */ + 0.757793960659406629066, /* 0x0.c1fec8f623723fffd */ + 0.759275473314173443536, /* 0x0.c25fe09e8a0f47ff8 */ + 0.760759882363831851927, /* 0x0.c2c128dedc88f8000 */ + 0.762247193485956486805, /* 0x0.c322a1cf7d6e7fffa */ + 0.763737412354726363781, /* 0x0.c3844b88cb9347ffc */ + 0.765230544649828092739, /* 0x0.c3e626232bd8f7ffc */ + 0.766726596071518051729, /* 0x0.c44831b719bf18002 */ + 0.768225572321911687194, /* 0x0.c4aa6e5d12d078001 */ + 0.769727479119219348810, /* 0x0.c50cdc2da64a37ffb */ + 0.771232322196981678892, /* 0x0.c56f7b41744490001 */ + 0.772740107296721268087, /* 0x0.c5d24bb1259e70004 */ + 0.774250840160724651565, /* 0x0.c6354d95640dd0007 */ + 0.775764526565368872643, /* 0x0.c6988106fec447fff */ + 0.777281172269557396602, /* 0x0.c6fbe61eb1bd0ffff */ + 0.778800783068235302750, /* 0x0.c75f7cf560942fffc */ + 0.780323364758801041312, /* 0x0.c7c345a3f1983fffe */ + 0.781848923151573727006, /* 0x0.c8274043594cb0002 */ + 0.783377464064598849602, /* 0x0.c88b6cec94b3b7ff9 */ + 0.784908993312207869935, /* 0x0.c8efcbb89cba27ffe */ + 0.786443516765346961618, /* 0x0.c9545cc0a88c70003 */ + 0.787981040257604625744, /* 0x0.c9b9201dc643bfffa */ + 0.789521569657452682047, /* 0x0.ca1e15e92a5410007 */ + 0.791065110849462849192, /* 0x0.ca833e3c1ae510005 */ + 0.792611669712891875319, /* 0x0.cae8992fd84667ffd */ + 0.794161252150049179450, /* 0x0.cb4e26ddbc207fff8 */ + 0.795713864077794763584, /* 0x0.cbb3e75f301b60003 */ + 0.797269511407239561694, /* 0x0.cc19dacd978cd8002 */ + 0.798828200086368567220, /* 0x0.cc8001427e55d7ffb */ + 0.800389937624300440456, /* 0x0.cce65ade24d360006 */ + 0.801954725261124767840, /* 0x0.cd4ce7a5de839fffb */ + 0.803522573691593189330, /* 0x0.cdb3a7c79a678fffd */ + 0.805093487311204114563, /* 0x0.ce1a9b563965ffffc */ + 0.806667472122675088819, /* 0x0.ce81c26b838db8000 */ + 0.808244534127439906441, /* 0x0.cee91d213f8428002 */ + 0.809824679342317166307, /* 0x0.cf50ab9144d92fff9 */ + 0.811407913793616542005, /* 0x0.cfb86dd5758c2ffff */ + 0.812994243520784198882, /* 0x0.d0206407c20e20005 */ + 0.814583674571603966162, /* 0x0.d0888e4223facfff9 */ + 0.816176213022088536960, /* 0x0.d0f0ec9eb3f7c8002 */ + 0.817771864936188586101, /* 0x0.d1597f377d6768002 */ + 0.819370636400374108252, /* 0x0.d1c24626a46eafff8 */ + 0.820972533518165570298, /* 0x0.d22b41865ff1e7ff9 */ + 0.822577562404315121269, /* 0x0.d2947170f32ec7ff9 */ + 0.824185729164559344159, /* 0x0.d2fdd60097795fff8 */ + 0.825797039949601741075, /* 0x0.d3676f4fb796d0001 */ + 0.827411500902565544264, /* 0x0.d3d13d78b5f68fffb */ + 0.829029118181348834154, /* 0x0.d43b40960546d8001 */ + 0.830649897953322891022, /* 0x0.d4a578c222a058000 */ + 0.832273846408250750368, /* 0x0.d50fe617a3ba78005 */ + 0.833900969738858188772, /* 0x0.d57a88b1218e90002 */ + 0.835531274148056613016, /* 0x0.d5e560a94048f8006 */ + 0.837164765846411529371, /* 0x0.d6506e1aac8078003 */ + 0.838801451086016225394, /* 0x0.d6bbb1204074e0001 */ + 0.840441336100884561780, /* 0x0.d72729d4c28518004 */ + 0.842084427144139224814, /* 0x0.d792d8530e12b0001 */ + 0.843730730487052604790, /* 0x0.d7febcb61273e7fff */ + 0.845380252404570153833, /* 0x0.d86ad718c308dfff9 */ + 0.847032999194574087728, /* 0x0.d8d727962c69d7fff */ + 0.848688977161248581090, /* 0x0.d943ae49621ce7ffb */ + 0.850348192619261200615, /* 0x0.d9b06b4d832ef8005 */ + 0.852010651900976245816, /* 0x0.da1d5ebdc22220005 */ + 0.853676361342631029337, /* 0x0.da8a88b555baa0006 */ + 0.855345327311054837175, /* 0x0.daf7e94f965f98004 */ + 0.857017556155879489641, /* 0x0.db6580a7c98f7fff8 */ + 0.858693054267390953857, /* 0x0.dbd34ed9617befff8 */ + 0.860371828028939855647, /* 0x0.dc4153ffc8b65fff9 */ + 0.862053883854957292436, /* 0x0.dcaf90368bfca8004 */ + 0.863739228154875360306, /* 0x0.dd1e0399328d87ffe */ + 0.865427867361348468455, /* 0x0.dd8cae435d303fff9 */ + 0.867119807911702289458, /* 0x0.ddfb9050b1cee8006 */ + 0.868815056264353846599, /* 0x0.de6aa9dced8448001 */ + 0.870513618890481399881, /* 0x0.ded9fb03db7320006 */ + 0.872215502247877139094, /* 0x0.df4983e1380657ff8 */ + 0.873920712852848668986, /* 0x0.dfb94490ffff77ffd */ + 0.875629257204025623884, /* 0x0.e0293d2f1cb01fff9 */ + 0.877341141814212965880, /* 0x0.e0996dd786fff0007 */ + 0.879056373217612985183, /* 0x0.e109d6a64f5d57ffc */ + 0.880774957955916648615, /* 0x0.e17a77b78e72a7ffe */ + 0.882496902590150900078, /* 0x0.e1eb5127722cc7ff8 */ + 0.884222213673356738383, /* 0x0.e25c63121fb0c8006 */ + 0.885950897802399772740, /* 0x0.e2cdad93ec5340003 */ + 0.887682961567391237685, /* 0x0.e33f30c925fb97ffb */ + 0.889418411575228162725, /* 0x0.e3b0ecce2d05ffff9 */ + 0.891157254447957902797, /* 0x0.e422e1bf727718006 */ + 0.892899496816652704641, /* 0x0.e4950fb9713fc7ffe */ + 0.894645145323828439008, /* 0x0.e50776d8b0e60fff8 */ + 0.896394206626591749641, /* 0x0.e57a1739c8fadfffc */ + 0.898146687421414902124, /* 0x0.e5ecf0f97c5798007 */ + 0.899902594367530173098, /* 0x0.e660043464e378005 */ + 0.901661934163603406867, /* 0x0.e6d3510747e150006 */ + 0.903424713533971135418, /* 0x0.e746d78f06cd97ffd */ + 0.905190939194458810123, /* 0x0.e7ba97e879c91fffc */ + 0.906960617885092856864, /* 0x0.e82e92309390b0007 */ + 0.908733756358986566306, /* 0x0.e8a2c6845544afffa */ + 0.910510361377119825629, /* 0x0.e9173500c8abc7ff8 */ + 0.912290439722343249336, /* 0x0.e98bddc30f98b0002 */ + 0.914073998177417412765, /* 0x0.ea00c0e84bc4c7fff */ + 0.915861043547953501680, /* 0x0.ea75de8db8094fffe */ + 0.917651582652244779397, /* 0x0.eaeb36d09d3137ffe */ + 0.919445622318405764159, /* 0x0.eb60c9ce4ed3dffff */ + 0.921243169397334638073, /* 0x0.ebd697a43995b0007 */ + 0.923044230737526172328, /* 0x0.ec4ca06fc7768fffa */ + 0.924848813220121135342, /* 0x0.ecc2e44e865b6fffb */ + 0.926656923710931002014, /* 0x0.ed39635df34e70006 */ + 0.928468569126343790092, /* 0x0.edb01dbbc2f5b7ffa */ + 0.930283756368834757725, /* 0x0.ee2713859aab57ffa */ + 0.932102492359406786818, /* 0x0.ee9e44d9342870004 */ + 0.933924784042873379360, /* 0x0.ef15b1d4635438005 */ + 0.935750638358567643520, /* 0x0.ef8d5a94f60f50007 */ + 0.937580062297704630580, /* 0x0.f0053f38f345cffff */ + 0.939413062815381727516, /* 0x0.f07d5fde3a2d98001 */ + 0.941249646905368053689, /* 0x0.f0f5bca2d481a8004 */ + 0.943089821583810716806, /* 0x0.f16e55a4e497d7ffe */ + 0.944933593864477061592, /* 0x0.f1e72b028a2827ffb */ + 0.946780970781518460559, /* 0x0.f2603cd9fb5430001 */ + 0.948631959382661205081, /* 0x0.f2d98b497d2a87ff9 */ + 0.950486566729423554277, /* 0x0.f353166f63e3dffff */ + 0.952344799896018723290, /* 0x0.f3ccde6a11ae37ffe */ + 0.954206665969085765512, /* 0x0.f446e357f66120000 */ + 0.956072172053890279009, /* 0x0.f4c12557964f0fff9 */ + 0.957941325265908139014, /* 0x0.f53ba48781046fffb */ + 0.959814132734539637840, /* 0x0.f5b66106555d07ffa */ + 0.961690601603558903308, /* 0x0.f6315af2c2027fffc */ + 0.963570739036113010927, /* 0x0.f6ac926b8aeb80004 */ + 0.965454552202857141381, /* 0x0.f728078f7c5008002 */ + 0.967342048278315158608, /* 0x0.f7a3ba7d66a908001 */ + 0.969233234469444204768, /* 0x0.f81fab543e1897ffb */ + 0.971128118008140250896, /* 0x0.f89bda33122c78007 */ + 0.973026706099345495256, /* 0x0.f9184738d4cf97ff8 */ + 0.974929006031422851235, /* 0x0.f994f284d3a5c0008 */ + 0.976835024947348973265, /* 0x0.fa11dc35bc7820002 */ + 0.978744770239899142285, /* 0x0.fa8f046b4fb7f8007 */ + 0.980658249138918636210, /* 0x0.fb0c6b449ab1cfff9 */ + 0.982575468959622777535, /* 0x0.fb8a10e1088fb7ffa */ + 0.984496437054508843888, /* 0x0.fc07f5602d79afffc */ + 0.986421160608523028820, /* 0x0.fc8618e0e55e47ffb */ + 0.988349647107594098099, /* 0x0.fd047b83571b1fffa */ + 0.990281903873210800357, /* 0x0.fd831d66f4c018002 */ + 0.992217938695037382475, /* 0x0.fe01fead3320bfff8 */ + 0.994157757657894713987, /* 0x0.fe811f703491e8006 */ + 0.996101369488558541238, /* 0x0.ff007fd5744490005 */ + 0.998048781093141101932, /* 0x0.ff801ffa9b9280007 */ + 1.000000000000000000000, /* 0x1.00000000000000000 */ + 1.001955033605393285965, /* 0x1.0080200565d29ffff */ + 1.003913889319761887310, /* 0x1.0100802aa0e80fff0 */ + 1.005876574715736104818, /* 0x1.01812090377240007 */ + 1.007843096764807100351, /* 0x1.020201541aad7fff6 */ + 1.009813464316352327214, /* 0x1.0283229c4c9820007 */ + 1.011787683565730677817, /* 0x1.030484836910a000e */ + 1.013765762469146736174, /* 0x1.0386272b9c077fffe */ + 1.015747708536026694351, /* 0x1.04080ab526304fff0 */ + 1.017733529475172815584, /* 0x1.048a2f412375ffff0 */ + 1.019723232714418781378, /* 0x1.050c94ef7ad5e000a */ + 1.021716825883923762690, /* 0x1.058f3be0f1c2d0004 */ + 1.023714316605201180057, /* 0x1.06122436442e2000e */ + 1.025715712440059545995, /* 0x1.06954e0fec63afff2 */ + 1.027721021151397406936, /* 0x1.0718b98f41c92fff6 */ + 1.029730250269221158939, /* 0x1.079c66d49bb2ffff1 */ + 1.031743407506447551857, /* 0x1.082056011a9230009 */ + 1.033760500517691527387, /* 0x1.08a487359ebd50002 */ + 1.035781537016238873464, /* 0x1.0928fa93490d4fff3 */ + 1.037806524719013578963, /* 0x1.09adb03b3e5b3000d */ + 1.039835471338248051878, /* 0x1.0a32a84e9e5760004 */ + 1.041868384612101516848, /* 0x1.0ab7e2eea5340ffff */ + 1.043905272300907460835, /* 0x1.0b3d603ca784f0009 */ + 1.045946142174331239262, /* 0x1.0bc3205a042060000 */ + 1.047991002016745332165, /* 0x1.0c4923682a086fffe */ + 1.050039859627715177527, /* 0x1.0ccf698898f3a000d */ + 1.052092722826109660856, /* 0x1.0d55f2dce5d1dfffb */ + 1.054149599440827866881, /* 0x1.0ddcbf86b09a5fff6 */ + 1.056210497317612961855, /* 0x1.0e63cfa7abc97fffd */ + 1.058275424318780855142, /* 0x1.0eeb23619c146fffb */ + 1.060344388322010722446, /* 0x1.0f72bad65714bffff */ + 1.062417397220589476718, /* 0x1.0ffa9627c38d30004 */ + 1.064494458915699715017, /* 0x1.1082b577d0eef0003 */ + 1.066575581342167566880, /* 0x1.110b18e893a90000a */ + 1.068660772440545025953, /* 0x1.1193c09c267610006 */ + 1.070750040138235936705, /* 0x1.121cacb4959befff6 */ + 1.072843392435016474095, /* 0x1.12a5dd543cf36ffff */ + 1.074940837302467588937, /* 0x1.132f529d59552000b */ + 1.077042382749654914030, /* 0x1.13b90cb250d08fff5 */ + 1.079148036789447484528, /* 0x1.14430bb58da3dfff9 */ + 1.081257807444460983297, /* 0x1.14cd4fc984c4a000e */ + 1.083371702785017154417, /* 0x1.1557d910df9c7000e */ + 1.085489730853784307038, /* 0x1.15e2a7ae292d30002 */ + 1.087611899742884524772, /* 0x1.166dbbc422d8c0004 */ + 1.089738217537583819804, /* 0x1.16f9157586772ffff */ + 1.091868692357631731528, /* 0x1.1784b4e533cacfff0 */ + 1.094003332327482702577, /* 0x1.18109a360fc23fff2 */ + 1.096142145591650907149, /* 0x1.189cc58b155a70008 */ + 1.098285140311341168136, /* 0x1.1929370751ea50002 */ + 1.100432324652149906842, /* 0x1.19b5eecdd79cefff0 */ + 1.102583706811727015711, /* 0x1.1a42ed01dbdba000e */ + 1.104739294993289488947, /* 0x1.1ad031c69a2eafff0 */ + 1.106899097422573863281, /* 0x1.1b5dbd3f66e120003 */ + 1.109063122341542140286, /* 0x1.1beb8f8fa8150000b */ + 1.111231377994659874592, /* 0x1.1c79a8dac6ad0fff4 */ + 1.113403872669181282605, /* 0x1.1d0809445a97ffffc */ + 1.115580614653132185460, /* 0x1.1d96b0effc9db000e */ + 1.117761612217810673898, /* 0x1.1e25a001332190000 */ + 1.119946873713312474002, /* 0x1.1eb4d69bdb2a9fff1 */ + 1.122136407473298902480, /* 0x1.1f4454e3bfae00006 */ + 1.124330221845670330058, /* 0x1.1fd41afcbb48bfff8 */ + 1.126528325196519908506, /* 0x1.2064290abc98c0001 */ + 1.128730725913251964394, /* 0x1.20f47f31c9aa7000f */ + 1.130937432396844410880, /* 0x1.21851d95f776dfff0 */ + 1.133148453059692917203, /* 0x1.2216045b6784efffa */ + 1.135363796355857157764, /* 0x1.22a733a6692ae0004 */ + 1.137583470716100553249, /* 0x1.2338ab9b3221a0004 */ + 1.139807484614418608939, /* 0x1.23ca6c5e27aadfff7 */ + 1.142035846532929888057, /* 0x1.245c7613b7f6c0004 */ + 1.144268564977221958089, /* 0x1.24eec8e06b035000c */ + 1.146505648458203463465, /* 0x1.258164e8cea85fff8 */ + 1.148747105501412235671, /* 0x1.26144a5180d380009 */ + 1.150992944689175123667, /* 0x1.26a7793f5de2efffa */ + 1.153243174560058870217, /* 0x1.273af1d712179000d */ + 1.155497803703682491111, /* 0x1.27ceb43d81d42fff1 */ + 1.157756840726344771440, /* 0x1.2862c097a3d29000c */ + 1.160020294239811677834, /* 0x1.28f7170a74cf4fff1 */ + 1.162288172883275239058, /* 0x1.298bb7bb0faed0004 */ + 1.164560485298402170388, /* 0x1.2a20a2ce920dffff4 */ + 1.166837240167474476460, /* 0x1.2ab5d86a4631ffff6 */ + 1.169118446164539637555, /* 0x1.2b4b58b36d5220009 */ + 1.171404112007080167155, /* 0x1.2be123cf786790002 */ + 1.173694246390975415341, /* 0x1.2c7739e3c0aac000d */ + 1.175988858069749065617, /* 0x1.2d0d9b15deb58fff6 */ + 1.178287955789017793514, /* 0x1.2da4478b627040002 */ + 1.180591548323240091978, /* 0x1.2e3b3f69fb794fffc */ + 1.182899644456603782686, /* 0x1.2ed282d76421d0004 */ + 1.185212252993012693694, /* 0x1.2f6a11f96c685fff3 */ + 1.187529382762033236513, /* 0x1.3001ecf60082ffffa */ + 1.189851042595508889847, /* 0x1.309a13f30f28a0004 */ + 1.192177241354644978669, /* 0x1.31328716a758cfff7 */ + 1.194507987909589896687, /* 0x1.31cb4686e1e85fffb */ + 1.196843291137896336843, /* 0x1.32645269dfd04000a */ + 1.199183159977805113226, /* 0x1.32fdaae604c39000f */ + 1.201527603343041317132, /* 0x1.339750219980dfff3 */ + 1.203876630171082595692, /* 0x1.3431424300e480007 */ + 1.206230249419600664189, /* 0x1.34cb8170b3fee000e */ + 1.208588470077065268869, /* 0x1.35660dd14dbd4fffc */ + 1.210951301134513435915, /* 0x1.3600e78b6bdfc0005 */ + 1.213318751604272271958, /* 0x1.369c0ec5c38ebfff2 */ + 1.215690830512196507537, /* 0x1.373783a718d29000f */ + 1.218067546930756250870, /* 0x1.37d3465662f480007 */ + 1.220448909901335365929, /* 0x1.386f56fa770fe0008 */ + 1.222834928513994334780, /* 0x1.390bb5ba5fc540004 */ + 1.225225611877684750397, /* 0x1.39a862bd3c7a8fff3 */ + 1.227620969111500981433, /* 0x1.3a455e2a37bcafffd */ + 1.230021009336254911271, /* 0x1.3ae2a8287dfbefff6 */ + 1.232425741726685064472, /* 0x1.3b8040df76f39fffa */ + 1.234835175450728295084, /* 0x1.3c1e287682e48fff1 */ + 1.237249319699482263931, /* 0x1.3cbc5f151b86bfff8 */ + 1.239668183679933477545, /* 0x1.3d5ae4e2cc0a8000f */ + 1.242091776620540377629, /* 0x1.3df9ba07373bf0006 */ + 1.244520107762172811399, /* 0x1.3e98deaa0d8cafffe */ + 1.246953186383919165383, /* 0x1.3f3852f32973efff0 */ + 1.249391019292643401078, /* 0x1.3fd816ffc72b90001 */ + 1.251833623164381181797, /* 0x1.40782b17863250005 */ + 1.254280999953110153911, /* 0x1.41188f42caf400000 */ + 1.256733161434815393410, /* 0x1.41b943b42945bfffd */ + 1.259190116985283935980, /* 0x1.425a4893e5f10000a */ + 1.261651875958665236542, /* 0x1.42fb9e0a2df4c0009 */ + 1.264118447754797758244, /* 0x1.439d443f608c4fff9 */ + 1.266589841787181258708, /* 0x1.443f3b5bebf850008 */ + 1.269066067469190262045, /* 0x1.44e183883e561fff7 */ + 1.271547134259576328224, /* 0x1.45841cecf7a7a0001 */ + 1.274033051628237434048, /* 0x1.462707b2c43020009 */ + 1.276523829025464573684, /* 0x1.46ca44023aa410007 */ + 1.279019475999373156531, /* 0x1.476dd2045d46ffff0 */ + 1.281520002043128991825, /* 0x1.4811b1e1f1f19000b */ + 1.284025416692967214122, /* 0x1.48b5e3c3edd74fff4 */ + 1.286535729509738823464, /* 0x1.495a67d3613c8fff7 */ + 1.289050950070396384145, /* 0x1.49ff3e396e19d000b */ + 1.291571087985403654081, /* 0x1.4aa4671f5b401fff1 */ + 1.294096152842774794011, /* 0x1.4b49e2ae56d19000d */ + 1.296626154297237043484, /* 0x1.4befb10fd84a3fff4 */ + 1.299161101984141142272, /* 0x1.4c95d26d41d84fff8 */ + 1.301701005575179204100, /* 0x1.4d3c46f01d9f0fff3 */ + 1.304245874766450485904, /* 0x1.4de30ec21097d0003 */ + 1.306795719266019562007, /* 0x1.4e8a2a0ccce3d0002 */ + 1.309350548792467483458, /* 0x1.4f3198fa10346fff5 */ + 1.311910373099227200545, /* 0x1.4fd95bb3be8cffffd */ + 1.314475201942565174546, /* 0x1.50817263bf0e5fffb */ + 1.317045045107389400535, /* 0x1.5129dd3418575000e */ + 1.319619912422941299109, /* 0x1.51d29c4f01c54ffff */ + 1.322199813675649204855, /* 0x1.527bafde83a310009 */ + 1.324784758729532718739, /* 0x1.5325180cfb8b3fffd */ + 1.327374757430096474625, /* 0x1.53ced504b2bd0fff4 */ + 1.329969819671041886272, /* 0x1.5478e6f02775e0001 */ + 1.332569955346704748651, /* 0x1.55234df9d8a59fff8 */ + 1.335175174370685002822, /* 0x1.55ce0a4c5a6a9fff6 */ + 1.337785486688218616860, /* 0x1.56791c1263abefff7 */ + 1.340400902247843806217, /* 0x1.57248376aef21fffa */ + 1.343021431036279800211, /* 0x1.57d040a420c0bfff3 */ + 1.345647083048053138662, /* 0x1.587c53c5a630f0002 */ + 1.348277868295411074918, /* 0x1.5928bd063fd7bfff9 */ + 1.350913796821875845231, /* 0x1.59d57c9110ad60006 */ + 1.353554878672557082439, /* 0x1.5a8292913d68cfffc */ + 1.356201123929036356254, /* 0x1.5b2fff3212db00007 */ + 1.358852542671913132777, /* 0x1.5bddc29edcc06fff3 */ + 1.361509145047255398051, /* 0x1.5c8bdd032ed16000f */ + 1.364170941142184734180, /* 0x1.5d3a4e8a5bf61fff4 */ + 1.366837941171020309735, /* 0x1.5de9176042f1effff */ + 1.369510155261156381121, /* 0x1.5e9837b062f4e0005 */ + 1.372187593620959988833, /* 0x1.5f47afa69436cfff1 */ + 1.374870266463378287715, /* 0x1.5ff77f6eb3f8cfffd */ + 1.377558184010425845733, /* 0x1.60a7a734a9742fff9 */ + 1.380251356531521533853, /* 0x1.6158272490016000c */ + 1.382949794301995272203, /* 0x1.6208ff6a8978a000f */ + 1.385653507605306700170, /* 0x1.62ba3032c0a280004 */ + 1.388362506772382154503, /* 0x1.636bb9a994784000f */ + 1.391076802081129493127, /* 0x1.641d9bfb29a7bfff6 */ + 1.393796403973427855412, /* 0x1.64cfd7545928b0002 */ + 1.396521322756352656542, /* 0x1.65826be167badfff8 */ + 1.399251568859207761660, /* 0x1.663559cf20826000c */ + 1.401987152677323100733, /* 0x1.66e8a14a29486fffc */ + 1.404728084651919228815, /* 0x1.679c427f5a4b6000b */ + 1.407474375243217723560, /* 0x1.68503d9ba0add000f */ + 1.410226034922914983815, /* 0x1.690492cbf6303fff9 */ + 1.412983074197955213304, /* 0x1.69b9423d7b548fff6 */ +}; diff --git a/sysdeps/ieee754/dbl-64/t_exp2.h b/sysdeps/ieee754/dbl-64/t_exp2.h new file mode 100644 index 0000000..1fd7333 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/t_exp2.h @@ -0,0 +1,585 @@ +/* These values are accurate to 52+12 bits when represented as + a double. */ +static const double exp2_accuratetable[512] = { +0.707106781187802013759 /* 0x0.b504f333fb3f80007 */, +0.708064712808760599040 /* 0x0.b543baa0f71b38000 */, +0.709023942160304065938 /* 0x0.b58297d3a8d518002 */, +0.709984470998547667624 /* 0x0.b5c18ad39b4ba0001 */, +0.710946301084324217006 /* 0x0.b60093a85e8d30001 */, +0.711909434180505784637 /* 0x0.b63fb25984e628005 */, +0.712873872052760648733 /* 0x0.b67ee6eea3b5f8003 */, +0.713839616467838999908 /* 0x0.b6be316f518c98001 */, +0.714806669195984345523 /* 0x0.b6fd91e328d148007 */, +0.715775032009894562898 /* 0x0.b73d0851c69e20002 */, +0.716744706683768884058 /* 0x0.b77c94c2c9b3d0003 */, +0.717715694995770148178 /* 0x0.b7bc373dd52eb0003 */, +0.718687998724665488852 /* 0x0.b7fbefca8cd530004 */, +0.719661619652575468291 /* 0x0.b83bbe70981da8001 */, +0.720636559564428180758 /* 0x0.b87ba337a194b0006 */, +0.721612820246623098989 /* 0x0.b8bb9e27556508004 */, +0.722590403488338473025 /* 0x0.b8fbaf4762c798006 */, +0.723569311081411870036 /* 0x0.b93bd69f7be1d0000 */, +0.724549544820974333906 /* 0x0.b97c1437567828007 */, +0.725531106502312561633 /* 0x0.b9bc6816a87ae8002 */, +0.726513997924421062181 /* 0x0.b9fcd2452bee00000 */, +0.727498220889519875430 /* 0x0.ba3d52ca9e6148002 */, +0.728483777200401694265 /* 0x0.ba7de9aebe05c8003 */, +0.729470668664712662563 /* 0x0.babe96f94e62a8002 */, +0.730458897090379144517 /* 0x0.baff5ab2134df0004 */, +0.731448464287988597833 /* 0x0.bb4034e0d38ab0000 */, +0.732439372072965166897 /* 0x0.bb81258d5b2d60001 */, +0.733431622260458326859 /* 0x0.bbc22cbf75fd28001 */, +0.734425216668725511232 /* 0x0.bc034a7ef32c00001 */, +0.735420157118880535324 /* 0x0.bc447ed3a50fe0005 */, +0.736416445434497690674 /* 0x0.bc85c9c560b350001 */, +0.737414083433310718618 /* 0x0.bcc72b5bf4b4e0000 */, +0.738413072966152328496 /* 0x0.bd08a39f5417a8007 */, +0.739413415848264365956 /* 0x0.bd4a32974abcd0002 */, +0.740415113911250699637 /* 0x0.bd8bd84bb68300002 */, +0.741418168994518067562 /* 0x0.bdcd94c47ddd30003 */, +0.742422582936659858376 /* 0x0.be0f6809865968006 */, +0.743428357577745613238 /* 0x0.be515222b72530003 */, +0.744435494762383687126 /* 0x0.be935317fc6ba0002 */, +0.745443996335090397492 /* 0x0.bed56af1423de8001 */, +0.746453864145572798553 /* 0x0.bf1799b67a6248007 */, +0.747465100043933849969 /* 0x0.bf59df6f970e70002 */, +0.748477705883256683178 /* 0x0.bf9c3c248dbee8001 */, +0.749491683518965001732 /* 0x0.bfdeafdd568308000 */, +0.750507034813367890373 /* 0x0.c0213aa1f0fc38004 */, +0.751523761622240105153 /* 0x0.c063dc7a559ca0003 */, +0.752541865811731880422 /* 0x0.c0a6956e883ed8000 */, +0.753561349247157341600 /* 0x0.c0e965868bd220006 */, +0.754582213796583967110 /* 0x0.c12c4cca664cb8002 */, +0.755604461332336940791 /* 0x0.c16f4b42225350006 */, +0.756628093726406381068 /* 0x0.c1b260f5ca2c48002 */, +0.757653112855631305506 /* 0x0.c1f58ded6d72d8001 */, +0.758679520599333412360 /* 0x0.c238d2311e7d08001 */, +0.759707318837184453227 /* 0x0.c27c2dc8f00368005 */, +0.760736509456435783249 /* 0x0.c2bfa0bcfd1400000 */, +0.761767094336480043995 /* 0x0.c3032b155818d0000 */, +0.762799075372231349951 /* 0x0.c346ccda248cc0001 */, +0.763832454453522768941 /* 0x0.c38a8613805488005 */, +0.764867233473625618441 /* 0x0.c3ce56c98d1ca8005 */, +0.765903414329434539816 /* 0x0.c4123f04708d80002 */, +0.766940998920452976510 /* 0x0.c4563ecc532dc0001 */, +0.767979989148100838946 /* 0x0.c49a56295f9f88006 */, +0.769020386915772125040 /* 0x0.c4de8523c2b0a0001 */, +0.770062194131770905170 /* 0x0.c522cbc3ae94e0003 */, +0.771105412703856241146 /* 0x0.c5672a1154e6b8004 */, +0.772150044545352520777 /* 0x0.c5aba014ed5f18003 */, +0.773196091570364285606 /* 0x0.c5f02dd6b09288003 */, +0.774243555696622731700 /* 0x0.c634d35edb1260003 */, +0.775292438842697939641 /* 0x0.c67990b5aa5c18004 */, +0.776342742931542928455 /* 0x0.c6be65e360bed8000 */, +0.777394469888802008854 /* 0x0.c70352f0437f50004 */, +0.778447621641124243320 /* 0x0.c74857e498fd00006 */, +0.779502200118583399303 /* 0x0.c78d74c8ab5b60000 */, +0.780558207255445668515 /* 0x0.c7d2a9a4c959f8000 */, +0.781615644985491186966 /* 0x0.c817f681412f80002 */, +0.782674515247667956808 /* 0x0.c85d5b6666c150006 */, +0.783734819983036512536 /* 0x0.c8a2d85c904760003 */, +0.784796561133562109454 /* 0x0.c8e86d6c14f850002 */, +0.785859740645942328471 /* 0x0.c92e1a9d513ec8002 */, +0.786924360469767103536 /* 0x0.c973dff8a4b390007 */, +0.787990422552312885808 /* 0x0.c9b9bd866c6440007 */, +0.789057928854407064640 /* 0x0.c9ffb34f1444b0001 */, +0.790126881326406182996 /* 0x0.ca45c15afcc570001 */, +0.791197281930050233534 /* 0x0.ca8be7b292db38000 */, +0.792269132620954885659 /* 0x0.cad2265e3cbee8000 */, +0.793342435380726906957 /* 0x0.cb187d667d3d38006 */, +0.794417192158282659010 /* 0x0.cb5eecd3b33158006 */, +0.795493404931386649540 /* 0x0.cba574ae5d2e80001 */, +0.796571075671306805268 /* 0x0.cbec14fef2a348004 */, +0.797650206352955137846 /* 0x0.cc32cdcdef0000000 */, +0.798730798954342069432 /* 0x0.cc799f23d11d18000 */, +0.799812855456121796232 /* 0x0.ccc089091abb28004 */, +0.800896377841454287795 /* 0x0.cd078b86505c18003 */, +0.801981368096190028208 /* 0x0.cd4ea6a3f97720007 */, +0.803067828208752554378 /* 0x0.cd95da6aa057b8007 */, +0.804155760170129796375 /* 0x0.cddd26e2d21b28001 */, +0.805245165974338261710 /* 0x0.ce248c151f3330001 */, +0.806336047619038653883 /* 0x0.ce6c0a0a1c1350001 */, +0.807428407102107836855 /* 0x0.ceb3a0ca5d6be0006 */, +0.808522246427078927792 /* 0x0.cefb505e7e2550007 */, +0.809617567597010201484 /* 0x0.cf4318cf18a268002 */, +0.810714372621179513182 /* 0x0.cf8afa24ce1c98004 */, +0.811812663508675536069 /* 0x0.cfd2f4683f9810005 */, +0.812912442272482604912 /* 0x0.d01b07a2126188003 */, +0.814013710929394895825 /* 0x0.d06333daeff618001 */, +0.815116471495287542325 /* 0x0.d0ab791b80d028006 */, +0.816220725993571205593 /* 0x0.d0f3d76c75b330000 */, +0.817326476447408967199 /* 0x0.d13c4ed67f1cf8000 */, +0.818433724883006474832 /* 0x0.d184df6250e3b0001 */, +0.819542473330909460055 /* 0x0.d1cd8918a3a328004 */, +0.820652723822034690935 /* 0x0.d2164c02305fa0002 */, +0.821764478391968422618 /* 0x0.d25f2827b53fb0005 */, +0.822877739077315761840 /* 0x0.d2a81d91f188b8000 */, +0.823992507918612782109 /* 0x0.d2f12c49a8d290005 */, +0.825108786960634610365 /* 0x0.d33a5457a35e40003 */, +0.826226578247117093869 /* 0x0.d38395c4a84848007 */, +0.827345883828319528258 /* 0x0.d3ccf09985d958004 */, +0.828466705754248966560 /* 0x0.d41664df0a1320005 */, +0.829589046080638992111 /* 0x0.d45ff29e094330000 */, +0.830712906863802391671 /* 0x0.d4a999df585a20005 */, +0.831838290163696481037 /* 0x0.d4f35aabd04a60006 */, +0.832965198041969556729 /* 0x0.d53d350c4be258002 */, +0.834093632565442222342 /* 0x0.d5872909aba050007 */, +0.835223595802037643865 /* 0x0.d5d136acd138e8006 */, +0.836355089820669306292 /* 0x0.d61b5dfe9f7780004 */, +0.837488116698010487424 /* 0x0.d6659f0801afa8005 */, +0.838622678508982644113 /* 0x0.d6aff9d1e147d8004 */, +0.839758777333464490056 /* 0x0.d6fa6e652d19e0000 */, +0.840896415254110962690 /* 0x0.d744fccad70d00003 */, +0.842035594355151628676 /* 0x0.d78fa50bd2c3b0000 */, +0.843176316724478125433 /* 0x0.d7da673117e730007 */, +0.844318584453106590905 /* 0x0.d8254343a19038003 */, +0.845462399634695271912 /* 0x0.d870394c6dbf30003 */, +0.846607764365415071965 /* 0x0.d8bb49547d37c0004 */, +0.847754680744707056494 /* 0x0.d9067364d45608003 */, +0.848903150873708822763 /* 0x0.d951b7867953b0006 */, +0.850053176859071113491 /* 0x0.d99d15c2787a30006 */, +0.851204760807439786431 /* 0x0.d9e88e21de11a0003 */, +0.852357904828824897169 /* 0x0.da3420adba1508003 */, +0.853512611037803181642 /* 0x0.da7fcd6f2184d8005 */, +0.854668881550406100980 /* 0x0.dacb946f2afaf8000 */, +0.855826718478671755185 /* 0x0.db1775b6e8ad48000 */, +0.856986123964844970247 /* 0x0.db63714f8e0818006 */, +0.858147100114499461478 /* 0x0.dbaf87422625b8000 */, +0.859309649060962410524 /* 0x0.dbfbb797daa460002 */, +0.860473772936213743282 /* 0x0.dc480259d3a710001 */, +0.861639473872910177676 /* 0x0.dc9467913a0f48006 */, +0.862806754008130227807 /* 0x0.dce0e7473b9b28003 */, +0.863975615481124226159 /* 0x0.dd2d8185086c20006 */, +0.865146060433749419813 /* 0x0.dd7a3653d38168005 */, +0.866318091005120138881 /* 0x0.ddc705bcccd628000 */, +0.867491709362415264210 /* 0x0.de13efc9434100004 */, +0.868666917636779056818 /* 0x0.de60f4825df9b8005 */, +0.869843717989716047624 /* 0x0.deae13f16599c0003 */, +0.871022112578215268471 /* 0x0.defb4e1f9dc388002 */, +0.872202103559697183859 /* 0x0.df48a3164a92f0001 */, +0.873383693097737778847 /* 0x0.df9612deb6e878007 */, +0.874566883362160263365 /* 0x0.dfe39d82348310001 */, +0.875751676517234511901 /* 0x0.e031430a0f0688000 */, +0.876938074732511840819 /* 0x0.e07f037f97e548001 */, +0.878126080186539592654 /* 0x0.e0ccdeec2a75e0006 */, +0.879315695055312818168 /* 0x0.e11ad5591f4078001 */, +0.880506921518618312932 /* 0x0.e168e6cfd2f880004 */, 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+1.316296388365203462468 /* 0x1.50f8ccd3df1840003 */, +1.318079601265708777911 /* 0x1.516daa2cf60020002 */, +1.319865229921343141607 /* 0x1.51e2b00da3c2b0007 */, +1.321653277603506371251 /* 0x1.5257de83f5512000d */, +1.323443747588034513690 /* 0x1.52cd359dfc7d5000e */, +1.325236643161341820781 /* 0x1.5342b569d6baa000f */, +1.327031967602244177939 /* 0x1.53b85df59921b0000 */, +1.328829724206201046165 /* 0x1.542e2f4f6b17e0006 */, +1.330629916266568235675 /* 0x1.54a4298571b27000e */, +1.332432547083447937938 /* 0x1.551a4ca5d97190009 */, +1.334237619959296017340 /* 0x1.559098bed16bf0008 */, +1.336045138203900251029 /* 0x1.56070dde90c800000 */, +1.337855105129210686631 /* 0x1.567dac13510cd0009 */, +1.339667524053662184301 /* 0x1.56f4736b52e2c000c */, +1.341482398296830025383 /* 0x1.576b63f4d8333000f */, +1.343299731186792467254 /* 0x1.57e27dbe2c40e0003 */, +1.345119526053918823702 /* 0x1.5859c0d59cd37000f */, +1.346941786233264881662 /* 0x1.58d12d497cd9a0005 */, +1.348766515064854010261 /* 0x1.5948c32824b87000c */, +1.350593715891792223641 /* 0x1.59c0827ff03890007 */, +1.352423392064920459908 /* 0x1.5a386b5f43a3e0006 */, +1.354255546937278120764 /* 0x1.5ab07dd485af1000c */, +1.356090183865519494030 /* 0x1.5b28b9ee21085000f */, +1.357927306213322804534 /* 0x1.5ba11fba8816e000b */, +1.359766917346459269620 /* 0x1.5c19af482f8f2000f */, +1.361609020638567812980 /* 0x1.5c9268a594cc00004 */, +1.363453619463660171403 /* 0x1.5d0b4be135916000c */, +1.365300717204201985683 /* 0x1.5d84590998eeb0005 */, +1.367150317245710233754 /* 0x1.5dfd902d494e40001 */, +1.369002422974674892971 /* 0x1.5e76f15ad22c40008 */, +1.370857037789471544224 /* 0x1.5ef07ca0cc166000b */, +1.372714165088220639199 /* 0x1.5f6a320dcf5280006 */, +1.374573808273481745378 /* 0x1.5fe411b0790800009 */, +1.376435970755022220096 /* 0x1.605e1b976e4b1000e */, +1.378300655944092456600 /* 0x1.60d84fd155d15000e */, +1.380167867259843417228 /* 0x1.6152ae6cdf0030003 */, +1.382037608124419003675 /* 0x1.61cd3778bc879000d */, +1.383909881963391264069 /* 0x1.6247eb03a4dc40009 */, +1.385784692209972801544 /* 0x1.62c2c91c56d9b0002 */, +1.387662042298923203992 /* 0x1.633dd1d1930ec0001 */, +1.389541935670444372533 /* 0x1.63b90532200630004 */, +1.391424375772021271329 /* 0x1.6434634ccc4cc0007 */, +1.393309366052102982208 /* 0x1.64afec30677e90008 */, +1.395196909966106124701 /* 0x1.652b9febc8e0f000d */, +1.397087010973788290271 /* 0x1.65a77e8dcc7f10004 */, +1.398979672539331309267 /* 0x1.66238825534170000 */, +1.400874898129892187656 /* 0x1.669fbcc1415600008 */, +1.402772691220124823310 /* 0x1.671c1c708328e000a */, +1.404673055288671035301 /* 0x1.6798a7420988b000d */, +1.406575993818903302975 /* 0x1.68155d44ca77a000f */, +1.408481510297352468121 /* 0x1.68923e87bf70e000a */, +1.410389608216942924956 /* 0x1.690f4b19e8f74000c */, +1.412300291075172076232 /* 0x1.698c830a4c94c0008 */ +}; +#define S (1.0/4503599627370496.0) /* 2^-52 */ +static const float exp2_deltatable[512] = { + 11527*S, -963*S, 884*S, -781*S, -2363*S, -3441*S, 123*S, 526*S, + -6*S, 1254*S, -1138*S, 1519*S, 1576*S, -65*S, 1040*S, 793*S, + -1662*S, -5063*S, -387*S, 968*S, -941*S, 984*S, -2856*S, -545*S, + 495*S, -5246*S, -2109*S, 1281*S, 2075*S, 909*S, -1642*S,-78233*S, +-31653*S, -265*S, 130*S, 430*S, 2482*S, -742*S, 1616*S, -2213*S, + -519*S, 20*S, -3134*S,-13981*S, 1343*S, -1740*S, 247*S, 1679*S, + -1097*S, 3131*S, 871*S, -1480*S, 1936*S, -1827*S, 17325*S, 528*S, + -322*S, 1404*S, -152*S, -1845*S, -212*S, 2639*S, -476*S, 2960*S, + -962*S, -1012*S, -1231*S, 3030*S, 1659*S, -486*S, 2154*S, 1728*S, + -2793*S, 699*S, -1560*S, -2125*S, 2156*S, 142*S, -1888*S, 4426*S, +-13443*S, 1970*S, -50*S, 1771*S,-43399*S, 4979*S, -2448*S, -370*S, + 1414*S, 1075*S, 232*S, 206*S, 873*S, 2141*S, 2970*S, 1279*S, + -2331*S, 336*S, -2595*S, 753*S, -3384*S, -616*S, 89*S, -818*S, + 5755*S, -241*S, -528*S, -661*S, -3777*S, -354*S, 250*S, 3881*S, + 2632*S, -2131*S, 2565*S, -316*S, 1746*S, -2541*S, -1324*S, -50*S, + 2564*S, -782*S, 1176*S, 6452*S, -1002*S, 1288*S, 336*S, -185*S, + 3063*S, 3784*S, 2169*S, 686*S, 328*S, -400*S, 312*S, -4517*S, + -1457*S, 1046*S, -1530*S, -685*S, 1328*S,-49815*S, -895*S, 1063*S, + -2091*S, -672*S, -1710*S, -665*S, 1545*S, 1819*S,-45265*S, 3548*S, + -554*S, -568*S, 4752*S, -1907*S,-13738*S, 675*S, 9611*S, -1115*S, + -815*S, 408*S, -1281*S, -937*S,-16376*S, -4772*S, -1440*S, 992*S, + 788*S, 10364*S, -1602*S, -661*S, -1783*S, -265*S, -20*S, -3781*S, + -861*S, -345*S, -994*S, 1364*S, -5339*S, 1620*S, 9390*S, -1066*S, + -305*S, -170*S, 175*S, 2461*S, -490*S, -769*S, -1450*S, 3315*S, + 2418*S, -45*S, -852*S, -1295*S, -488*S, -96*S, 1142*S, -2639*S, + 7905*S, -9306*S, -3859*S, 760*S, 1057*S, -1570*S, 3977*S, 209*S, + -514*S, 7151*S, 1646*S, 627*S, 599*S, -774*S, -1468*S, 633*S, + -473*S, 851*S, 2406*S, 143*S, 74*S, 4260*S, 1177*S, -913*S, + 2670*S, -3298*S, -1662*S, -120*S, -3264*S, -2148*S, 410*S, 2078*S, + -2098*S, -926*S, 3580*S, -1289*S, 2450*S, -1158*S, 907*S, -590*S, + 986*S, 1801*S, 1145*S, -1677*S, 3455*S, 956*S, 710*S, 144*S, + 153*S, -255*S, -1898*S, 28102*S, 2748*S, 1194*S, -3009*S, 7076*S, + 0*S, -2720*S, 711*S, 1225*S, -3034*S, -473*S, 378*S, -1046*S, + 962*S, -2006*S, 4647*S, 3206*S, 1769*S, -2665*S, 1254*S, 2025*S, + -2430*S, 6193*S, 1224*S, -856*S, -1592*S, -325*S, -1521*S, 1827*S, + -264*S, 2403*S, -1065*S, 967*S, -681*S, -2106*S, -474*S, 1333*S, + -893*S, 2296*S, 592*S, -1220*S, -326*S, 990*S, 139*S, 206*S, + -779*S, -1683*S, 1238*S, 6098*S, 136*S, 1197*S, 790*S, -107*S, + -1004*S, -2449*S, 939*S, 5568*S, 156*S, 1812*S, 2792*S, -1094*S, + -2677*S, -251*S, 2297*S, 943*S, -1329*S, 2883*S, -853*S, -2626*S, +-105929*S, -6552*S, 1095*S, -1508*S, 1003*S, 5039*S, -2600*S, -749*S, + 1790*S, 890*S, 2016*S, -1073*S, 624*S, -2084*S, -1536*S, -1330*S, + 358*S, 2444*S, -179*S,-25759*S, -243*S, -552*S, -124*S, 3766*S, + 1192*S, -1614*S, 6*S, -1227*S, 345*S, -981*S, -295*S, -1006*S, + -995*S, -1195*S, 706*S, 2512*S, -1758*S, -734*S, -6286*S, -922*S, + 1530*S, 1542*S, 1223*S, 61*S, -83*S, 522*S,116937*S, -914*S, + -418*S, -7339*S, 249*S, -520*S, -762*S, 426*S, -505*S, 2664*S, + -1093*S, -1035*S, 2130*S, 4878*S, 1982*S, 1551*S, 2304*S, 193*S, + 1532*S, -7268*S, 24357*S, 531*S, 2676*S, -1170*S, 1465*S, -1917*S, + 2143*S, 1466*S, -7*S, -7300*S, 3297*S, -1197*S, -289*S, -1548*S, + 26226*S, 4401*S, 4123*S, -1588*S, 4243*S, 4069*S, -1276*S, -2010*S, + 1407*S, 1478*S, 488*S, -2366*S, -2909*S, -2534*S, -1285*S, 7095*S, + -645*S, -2089*S, -944*S, -40*S, -1363*S, -833*S, 917*S, 1609*S, + 1286*S, 1677*S, 1613*S, -2295*S, -1248*S, 40*S, 26*S, 2038*S, + 698*S, 2675*S, -1755*S, -3522*S, -1614*S, -6111*S, 270*S, 1822*S, + -234*S, -2844*S, -1201*S, -830*S, 1193*S, 2354*S, 47*S, 1522*S, + -78*S, -640*S, 2425*S, -1596*S, 1563*S, 1169*S, -1006*S, -83*S, + 2362*S, -3521*S, -314*S, 1814*S, -1751*S, 305*S, 1715*S, -3741*S, + 7847*S, 1291*S, 1206*S, 36*S, 1397*S, -1419*S, -1194*S, -2014*S, + 1742*S, -578*S, -207*S, 875*S, 1539*S, 2826*S, -1165*S, -909*S, + 1849*S, 927*S, 2018*S, -981*S, 1637*S, -463*S, 905*S, 6618*S, + 400*S, 630*S, 2614*S, 900*S, 2323*S, -1094*S, -1858*S, -212*S, + -2069*S, 747*S, 1845*S, -1450*S, 444*S, -213*S, -438*S, 1158*S, + 4738*S, 2497*S, -370*S, -2016*S, -518*S, -1160*S, -1510*S, 123*S +}; +/* Maximum magnitude in above table: 116937 */ +#undef S diff --git a/sysdeps/ieee754/dbl-64/w_exp.c b/sysdeps/ieee754/dbl-64/w_exp.c new file mode 100644 index 0000000..445c578 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/w_exp.c @@ -0,0 +1,58 @@ +/* @(#)w_exp.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_exp.c,v 1.6 1995/05/10 20:48:51 jtc Exp $"; +#endif + +/* + * wrapper exp(x) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ +u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */ + +#ifdef __STDC__ + double __exp(double x) /* wrapper exp */ +#else + double __exp(x) /* wrapper exp */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_exp(x); +#else + double z; + z = __ieee754_exp(x); + if(_LIB_VERSION == _IEEE_) return z; + if(__finite(x)) { + if(x>o_threshold) + return __kernel_standard(x,x,6); /* exp overflow */ + else if(x<u_threshold) + return __kernel_standard(x,x,7); /* exp underflow */ + } + return z; +#endif +} +weak_alias (__exp, exp) +#ifdef NO_LONG_DOUBLE +strong_alias (__exp, __expl) +weak_alias (__exp, expl) +#endif diff --git a/sysdeps/ieee754/flt-32/Dist b/sysdeps/ieee754/flt-32/Dist new file mode 100644 index 0000000..045ac80 --- /dev/null +++ b/sysdeps/ieee754/flt-32/Dist @@ -0,0 +1 @@ +t_exp2f.h diff --git a/sysdeps/ieee754/flt-32/e_acosf.c b/sysdeps/ieee754/flt-32/e_acosf.c new file mode 100644 index 0000000..0d85c42 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_acosf.c @@ -0,0 +1,89 @@ +/* e_acosf.c -- float version of e_acos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_acosf.c,v 1.5 1995/05/12 04:57:16 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +one = 1.0000000000e+00, /* 0x3F800000 */ +pi = 3.1415925026e+00, /* 0x40490fda */ +pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ +pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ +pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ +pS1 = -3.2556581497e-01, /* 0xbea6b090 */ +pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ +pS3 = -4.0055535734e-02, /* 0xbd241146 */ +pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ +pS5 = 3.4793309169e-05, /* 0x3811ef08 */ +qS1 = -2.4033949375e+00, /* 0xc019d139 */ +qS2 = 2.0209457874e+00, /* 0x4001572d */ +qS3 = -6.8828397989e-01, /* 0xbf303361 */ +qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ + +#ifdef __STDC__ + float __ieee754_acosf(float x) +#else + float __ieee754_acosf(x) + float x; +#endif +{ + float z,p,q,r,w,s,c,df; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix==0x3f800000) { /* |x|==1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */ + } else if(ix>0x3f800000) { /* |x| >= 1 */ + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3f000000) { /* |x| < 0.5 */ + if(ix<=0x23000000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ + z = x*x; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*(float)0.5; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + s = __ieee754_sqrtf(z); + r = p/q; + w = r*s-pio2_lo; + return pi - (float)2.0*(s+w); + } else { /* x > 0.5 */ + int32_t idf; + z = (one-x)*(float)0.5; + s = __ieee754_sqrtf(z); + df = s; + GET_FLOAT_WORD(idf,df); + SET_FLOAT_WORD(df,idf&0xfffff000); + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + w = r*s+c; + return (float)2.0*(df+w); + } +} diff --git a/sysdeps/ieee754/flt-32/e_acoshf.c b/sysdeps/ieee754/flt-32/e_acoshf.c new file mode 100644 index 0000000..c607f72 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_acoshf.c @@ -0,0 +1,57 @@ +/* e_acoshf.c -- float version of e_acosh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_acoshf.c,v 1.5 1995/05/12 04:57:20 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +one = 1.0, +ln2 = 6.9314718246e-01; /* 0x3f317218 */ + +#ifdef __STDC__ + float __ieee754_acoshf(float x) +#else + float __ieee754_acoshf(x) + float x; +#endif +{ + float t; + int32_t hx; + GET_FLOAT_WORD(hx,x); + if(hx<0x3f800000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x4d800000) { /* x > 2**28 */ + if(hx >=0x7f800000) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_logf(x)+ln2; /* acosh(huge)=log(2x) */ + } else if (hx==0x3f800000) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_logf((float)2.0*x-one/(x+__ieee754_sqrtf(t-one))); + } else { /* 1<x<2 */ + t = x-one; + return __log1pf(t+__sqrtf((float)2.0*t+t*t)); + } +} diff --git a/sysdeps/ieee754/flt-32/e_asinf.c b/sysdeps/ieee754/flt-32/e_asinf.c new file mode 100644 index 0000000..5270f31 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_asinf.c @@ -0,0 +1,93 @@ +/* e_asinf.c -- float version of e_asin.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_asinf.c,v 1.5 1995/05/12 04:57:25 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +one = 1.0000000000e+00, /* 0x3F800000 */ +huge = 1.000e+30, +pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ +pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ +pio4_hi = 7.8539818525e-01, /* 0x3f490fdb */ + /* coefficient for R(x^2) */ +pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ +pS1 = -3.2556581497e-01, /* 0xbea6b090 */ +pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ +pS3 = -4.0055535734e-02, /* 0xbd241146 */ +pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ +pS5 = 3.4793309169e-05, /* 0x3811ef08 */ +qS1 = -2.4033949375e+00, /* 0xc019d139 */ +qS2 = 2.0209457874e+00, /* 0x4001572d */ +qS3 = -6.8828397989e-01, /* 0xbf303361 */ +qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ + +#ifdef __STDC__ + float __ieee754_asinf(float x) +#else + float __ieee754_asinf(x) + float x; +#endif +{ + float t,w,p,q,c,r,s; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix==0x3f800000) { + /* asin(1)=+-pi/2 with inexact */ + return x*pio2_hi+x*pio2_lo; + } else if(ix> 0x3f800000) { /* |x|>= 1 */ + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3f000000) { /* |x|<0.5 */ + if(ix<0x32000000) { /* if |x| < 2**-27 */ + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } else { + t = x*x; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + w = p/q; + return x+x*w; + } + } + /* 1> |x|>= 0.5 */ + w = one-fabsf(x); + t = w*(float)0.5; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + s = __ieee754_sqrtf(t); + if(ix>=0x3F79999A) { /* if |x| > 0.975 */ + w = p/q; + t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo); + } else { + int32_t iw; + w = s; + GET_FLOAT_WORD(iw,w); + SET_FLOAT_WORD(w,iw&0xfffff000); + c = (t-w*w)/(s+w); + r = p/q; + p = (float)2.0*s*r-(pio2_lo-(float)2.0*c); + q = pio4_hi-(float)2.0*w; + t = pio4_hi-(p-q); + } + if(hx>0) return t; else return -t; +} diff --git a/sysdeps/ieee754/flt-32/e_atan2f.c b/sysdeps/ieee754/flt-32/e_atan2f.c new file mode 100644 index 0000000..8b3398c --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_atan2f.c @@ -0,0 +1,105 @@ +/* e_atan2f.c -- float version of e_atan2.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_atan2f.c,v 1.4 1995/05/10 20:44:53 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +tiny = 1.0e-30, +zero = 0.0, +pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */ +pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */ +pi = 3.1415927410e+00, /* 0x40490fdb */ +pi_lo = -8.7422776573e-07; /* 0xb3bbbd2e */ + +#ifdef __STDC__ + float __ieee754_atan2f(float y, float x) +#else + float __ieee754_atan2f(y,x) + float y,x; +#endif +{ + float z; + int32_t k,m,hx,hy,ix,iy; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + GET_FLOAT_WORD(hy,y); + iy = hy&0x7fffffff; + if((ix>0x7f800000)|| + (iy>0x7f800000)) /* x or y is NaN */ + return x+y; + if(hx==0x3f800000) return __atanf(y); /* x=1.0 */ + m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if(iy==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7f800000) { + if(iy==0x7f800000) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>23; + if(k > 60) z=pi_o_2+(float)0.5*pi_lo; /* |y/x| > 2**60 */ + else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ + else z=__atanf(fabsf(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: { + u_int32_t zh; + GET_FLOAT_WORD(zh,z); + SET_FLOAT_WORD(z,zh ^ 0x80000000); + } + return z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} diff --git a/sysdeps/ieee754/flt-32/e_atanhf.c b/sysdeps/ieee754/flt-32/e_atanhf.c new file mode 100644 index 0000000..f26a15b --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_atanhf.c @@ -0,0 +1,58 @@ +/* e_atanhf.c -- float version of e_atanh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_atanhf.c,v 1.4 1995/05/10 20:44:56 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float one = 1.0, huge = 1e30; +#else +static float one = 1.0, huge = 1e30; +#endif + +#ifdef __STDC__ +static const float zero = 0.0; +#else +static float zero = 0.0; +#endif + +#ifdef __STDC__ + float __ieee754_atanhf(float x) +#else + float __ieee754_atanhf(x) + float x; +#endif +{ + float t; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if (ix>0x3f800000) /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3f800000) + return x/zero; + if(ix<0x31800000&&(huge+x)>zero) return x; /* x<2**-28 */ + SET_FLOAT_WORD(x,ix); + if(ix<0x3f000000) { /* x < 0.5 */ + t = x+x; + t = (float)0.5*__log1pf(t+t*x/(one-x)); + } else + t = (float)0.5*__log1pf((x+x)/(one-x)); + if(hx>=0) return t; else return -t; +} diff --git a/sysdeps/ieee754/flt-32/e_coshf.c b/sysdeps/ieee754/flt-32/e_coshf.c new file mode 100644 index 0000000..223fbee --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_coshf.c @@ -0,0 +1,72 @@ +/* e_coshf.c -- float version of e_cosh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_coshf.c,v 1.6 1996/04/08 15:43:41 phil Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float huge = 1.0e30; +static const float one = 1.0, half=0.5; +#else +static float one = 1.0, half=0.5, huge = 1.0e30; +#endif + +#ifdef __STDC__ + float __ieee754_coshf(float x) +#else + float __ieee754_coshf(x) + float x; +#endif +{ + float t,w; + int32_t ix; + + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3eb17218) { + t = __expm1f(fabsf(x)); + w = one+t; + if (ix<0x24000000) return w; /* cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x41b00000) { + t = __ieee754_expf(fabsf(x)); + return half*t+half/t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x42b17180) return half*__ieee754_expf(fabsf(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x42b2d4fc) { + w = __ieee754_expf(half*fabsf(x)); + t = half*w; + return t*w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} diff --git a/sysdeps/ieee754/flt-32/e_expf.c b/sysdeps/ieee754/flt-32/e_expf.c new file mode 100644 index 0000000..e8a9c9d --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_expf.c @@ -0,0 +1,140 @@ +/* Single-precision floating point e^x. + Copyright (C) 1997, 1998 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +/* How this works: + + The input value, x, is written as + + x = n * ln(2) + t/512 + delta[t] + x; + + where: + - n is an integer, 127 >= n >= -150; + - t is an integer, 177 >= t >= -177 + - delta is based on a table entry, delta[t] < 2^-28 + - x is whatever is left, |x| < 2^-10 + + Then e^x is approximated as + + e^x = 2^n ( e^(t/512 + delta[t]) + + ( e^(t/512 + delta[t]) + * ( p(x + delta[t] + n * ln(2)) - delta ) ) ) + + where + - p(x) is a polynomial approximating e(x)-1; + - e^(t/512 + delta[t]) is obtained from a table. + + The table used is the same one as for the double precision version; + since we have the table, we might as well use it. + + It turns out to be faster to do calculations in double precision than + to perform an 'accurate table method' expf, because of the range reduction + overhead (compare exp2f). + */ +#ifndef _GNU_SOURCE +#define _GNU_SOURCE +#endif +#include <float.h> +#include <ieee754.h> +#include <math.h> +#include <fenv.h> +#include <inttypes.h> +#include <math_private.h> + +extern const float __exp_deltatable[178]; +extern const double __exp_atable[355] /* __attribute__((mode(DF))) */; + +static const volatile float TWOM100 = 7.88860905e-31; +static const volatile float TWO127 = 1.7014118346e+38; + +float +__ieee754_expf (float x) +{ + static const float himark = 88.72283935546875; + static const float lomark = -103.972084045410; + /* Check for usual case. */ + if (isless (x, himark) && isgreater (x, lomark)) + { + static const float THREEp42 = 13194139533312.0; + static const float THREEp22 = 12582912.0; + /* 1/ln(2). */ +#undef M_1_LN2 + static const float M_1_LN2 = 1.44269502163f; + /* ln(2) */ +#undef M_LN2 + static const double M_LN2 = .6931471805599452862; + + int tval; + double x22, t, result, dx; + float n, delta; + union ieee754_double ex2_u; + fenv_t oldenv; + + feholdexcept (&oldenv); +#ifdef FE_TONEAREST + fesetround (FE_TONEAREST); +#endif + + /* Calculate n. */ + n = x * M_1_LN2 + THREEp22; + n -= THREEp22; + dx = x - n*M_LN2; + + /* Calculate t/512. */ + t = dx + THREEp42; + t -= THREEp42; + dx -= t; + + /* Compute tval = t. */ + tval = (int) (t * 512.0); + + if (t >= 0) + delta = - __exp_deltatable[tval]; + else + delta = __exp_deltatable[-tval]; + + /* Compute ex2 = 2^n e^(t/512+delta[t]). */ + ex2_u.d = __exp_atable[tval+177]; + ex2_u.ieee.exponent += (int) n; + + /* Approximate e^(dx+delta) - 1, using a second-degree polynomial, + with maximum error in [-2^-10-2^-28,2^-10+2^-28] + less than 5e-11. */ + x22 = (0.5000000496709180453 * dx + 1.0000001192102037084) * dx + delta; + + /* Return result. */ + fesetenv (&oldenv); + + result = x22 * ex2_u.d + ex2_u.d; + return (float) result; + } + /* Exceptional cases: */ + else if (isless (x, himark)) + { + if (__isinff (x)) + /* e^-inf == 0, with no error. */ + return 0; + else + /* Underflow */ + return TWOM100 * TWOM100; + } + else + /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ + return TWO127*x; +} diff --git a/sysdeps/ieee754/flt-32/e_fmodf.c b/sysdeps/ieee754/flt-32/e_fmodf.c new file mode 100644 index 0000000..47b3123 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_fmodf.c @@ -0,0 +1,113 @@ +/* e_fmodf.c -- float version of e_fmod.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_fmodf.c,v 1.4 1995/05/10 20:45:10 jtc Exp $"; +#endif + +/* + * __ieee754_fmodf(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float one = 1.0, Zero[] = {0.0, -0.0,}; +#else +static float one = 1.0, Zero[] = {0.0, -0.0,}; +#endif + +#ifdef __STDC__ + float __ieee754_fmodf(float x, float y) +#else + float __ieee754_fmodf(x,y) + float x,y ; +#endif +{ + int32_t n,hx,hy,hz,ix,iy,sx,i; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + sx = hx&0x80000000; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if(hy==0||(hx>=0x7f800000)|| /* y=0,or x not finite */ + (hy>0x7f800000)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx<hy) return x; /* |x|<|y| return x */ + if(hx==hy) + return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/ + + /* determine ix = ilogb(x) */ + if(hx<0x00800000) { /* subnormal x */ + for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1; + } else ix = (hx>>23)-127; + + /* determine iy = ilogb(y) */ + if(hy<0x00800000) { /* subnormal y */ + for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1; + } else iy = (hy>>23)-127; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -126) + hx = 0x00800000|(0x007fffff&hx); + else { /* subnormal x, shift x to normal */ + n = -126-ix; + hx = hx<<n; + } + if(iy >= -126) + hy = 0x00800000|(0x007fffff&hy); + else { /* subnormal y, shift y to normal */ + n = -126-iy; + hy = hy<<n; + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy; + if(hz<0){hx = hx+hx;} + else { + if(hz==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + hx = hz+hz; + } + } + hz=hx-hy; + if(hz>=0) {hx=hz;} + + /* convert back to floating value and restore the sign */ + if(hx==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + while(hx<0x00800000) { /* normalize x */ + hx = hx+hx; + iy -= 1; + } + if(iy>= -126) { /* normalize output */ + hx = ((hx-0x00800000)|((iy+127)<<23)); + SET_FLOAT_WORD(x,hx|sx); + } else { /* subnormal output */ + n = -126 - iy; + hx >>= n; + SET_FLOAT_WORD(x,hx|sx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} diff --git a/sysdeps/ieee754/flt-32/e_gammaf_r.c b/sysdeps/ieee754/flt-32/e_gammaf_r.c new file mode 100644 index 0000000..926905e --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_gammaf_r.c @@ -0,0 +1,50 @@ +/* Implementation of gamma function according to ISO C. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> +#include <math_private.h> + + +float +__ieee754_gammaf_r (float x, int *signgamp) +{ + /* We don't have a real gamma implementation now. We'll use lgamma + and the exp function. But due to the required boundary + conditions we must check some values separately. */ + int32_t hx; + + GET_FLOAT_WORD (hx, x); + + if ((hx & 0x7fffffff) == 0) + { + /* Return value for x == 0 is NaN with invalid exception. */ + *signgamp = 0; + return x / x; + } + if (hx < 0 && (u_int32_t) hx < 0xff800000 && __rintf (x) == x) + { + /* Return value for integer x < 0 is NaN with invalid exception. */ + *signgamp = 0; + return (x - x) / (x - x); + } + + /* XXX FIXME. */ + return __ieee754_expf (__ieee754_lgammaf_r (x, signgamp)); +} diff --git a/sysdeps/ieee754/flt-32/e_hypotf.c b/sysdeps/ieee754/flt-32/e_hypotf.c new file mode 100644 index 0000000..d6b1520 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_hypotf.c @@ -0,0 +1,87 @@ +/* e_hypotf.c -- float version of e_hypot.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_hypotf.c,v 1.5 1995/05/12 04:57:30 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + float __ieee754_hypotf(float x, float y) +#else + float __ieee754_hypot(x,y) + float x, y; +#endif +{ + float a,b,t1,t2,y1,y2,w; + int32_t j,k,ha,hb; + + GET_FLOAT_WORD(ha,x); + ha &= 0x7fffffff; + GET_FLOAT_WORD(hb,y); + hb &= 0x7fffffff; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + SET_FLOAT_WORD(a,ha); /* a <- |a| */ + SET_FLOAT_WORD(b,hb); /* b <- |b| */ + if((ha-hb)>0xf000000) {return a+b;} /* x/y > 2**30 */ + k=0; + if(ha > 0x58800000) { /* a>2**50 */ + if(ha >= 0x7f800000) { /* Inf or NaN */ + w = a+b; /* for sNaN */ + if(ha == 0x7f800000) w = a; + if(hb == 0x7f800000) w = b; + return w; + } + /* scale a and b by 2**-60 */ + ha -= 0x5d800000; hb -= 0x5d800000; k += 60; + SET_FLOAT_WORD(a,ha); + SET_FLOAT_WORD(b,hb); + } + if(hb < 0x26800000) { /* b < 2**-50 */ + if(hb <= 0x007fffff) { /* subnormal b or 0 */ + if(hb==0) return a; + SET_FLOAT_WORD(t1,0x3f000000); /* t1=2^126 */ + b *= t1; + a *= t1; + k -= 126; + } else { /* scale a and b by 2^60 */ + ha += 0x5d800000; /* a *= 2^60 */ + hb += 0x5d800000; /* b *= 2^60 */ + k -= 60; + SET_FLOAT_WORD(a,ha); + SET_FLOAT_WORD(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + SET_FLOAT_WORD(t1,ha&0xfffff000); + t2 = a-t1; + w = __ieee754_sqrtf(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + SET_FLOAT_WORD(y1,hb&0xfffff000); + y2 = b - y1; + SET_FLOAT_WORD(t1,ha+0x00800000); + t2 = a - t1; + w = __ieee754_sqrtf(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + SET_FLOAT_WORD(t1,0x3f800000+(k<<23)); + return t1*w; + } else return w; +} diff --git a/sysdeps/ieee754/flt-32/e_j0f.c b/sysdeps/ieee754/flt-32/e_j0f.c new file mode 100644 index 0000000..eed171c --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_j0f.c @@ -0,0 +1,444 @@ +/* e_j0f.c -- float version of e_j0.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_j0f.c,v 1.4 1995/05/10 20:45:25 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static float pzerof(float), qzerof(float); +#else +static float pzerof(), qzerof(); +#endif + +#ifdef __STDC__ +static const float +#else +static float +#endif +huge = 1e30, +one = 1.0, +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +tpi = 6.3661974669e-01, /* 0x3f22f983 */ + /* R0/S0 on [0, 2.00] */ +R02 = 1.5625000000e-02, /* 0x3c800000 */ +R03 = -1.8997929874e-04, /* 0xb947352e */ +R04 = 1.8295404516e-06, /* 0x35f58e88 */ +R05 = -4.6183270541e-09, /* 0xb19eaf3c */ +S01 = 1.5619102865e-02, /* 0x3c7fe744 */ +S02 = 1.1692678527e-04, /* 0x38f53697 */ +S03 = 5.1354652442e-07, /* 0x3509daa6 */ +S04 = 1.1661400734e-09; /* 0x30a045e8 */ + +#ifdef __STDC__ +static const float zero = 0.0; +#else +static float zero = 0.0; +#endif + +#ifdef __STDC__ + float __ieee754_j0f(float x) +#else + float __ieee754_j0f(x) + float x; +#endif +{ + float z, s,c,ss,cc,r,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return one/(x*x); + x = fabsf(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = __sinf(x); + c = __cosf(x); + ss = s-c; + cc = s+c; + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = -__cosf(x+x); + if ((s*c)<zero) cc = z/ss; + else ss = z/cc; + } + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix>0x48000000) z = (invsqrtpi*cc)/__sqrtf(x); + else { + u = pzerof(x); v = qzerof(x); + z = invsqrtpi*(u*cc-v*ss)/__sqrtf(x); + } + return z; + } + if(ix<0x39000000) { /* |x| < 2**-13 */ + if(huge+x>one) { /* raise inexact if x != 0 */ + if(ix<0x32000000) return one; /* |x|<2**-27 */ + else return one - (float)0.25*x*x; + } + } + z = x*x; + r = z*(R02+z*(R03+z*(R04+z*R05))); + s = one+z*(S01+z*(S02+z*(S03+z*S04))); + if(ix < 0x3F800000) { /* |x| < 1.00 */ + return one + z*((float)-0.25+(r/s)); + } else { + u = (float)0.5*x; + return((one+u)*(one-u)+z*(r/s)); + } +} + +#ifdef __STDC__ +static const float +#else +static float +#endif +u00 = -7.3804296553e-02, /* 0xbd9726b5 */ +u01 = 1.7666645348e-01, /* 0x3e34e80d */ +u02 = -1.3818567619e-02, /* 0xbc626746 */ +u03 = 3.4745343146e-04, /* 0x39b62a69 */ +u04 = -3.8140706238e-06, /* 0xb67ff53c */ +u05 = 1.9559013964e-08, /* 0x32a802ba */ +u06 = -3.9820518410e-11, /* 0xae2f21eb */ +v01 = 1.2730483897e-02, /* 0x3c509385 */ +v02 = 7.6006865129e-05, /* 0x389f65e0 */ +v03 = 2.5915085189e-07, /* 0x348b216c */ +v04 = 4.4111031494e-10; /* 0x2ff280c2 */ + +#ifdef __STDC__ + float __ieee754_y0f(float x) +#else + float __ieee754_y0f(x) + float x; +#endif +{ + float z, s,c,ss,cc,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ + if(ix>=0x7f800000) return one/(x+x*x); + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + s = __sinf(x); + c = __cosf(x); + ss = s-c; + cc = s+c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = -__cosf(x+x); + if ((s*c)<zero) cc = z/ss; + else ss = z/cc; + } + if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrtf(x); + else { + u = pzerof(x); v = qzerof(x); + z = invsqrtpi*(u*ss+v*cc)/__sqrtf(x); + } + return z; + } + if(ix<=0x32000000) { /* x < 2**-27 */ + return(u00 + tpi*__ieee754_logf(x)); + } + z = x*x; + u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); + v = one+z*(v01+z*(v02+z*(v03+z*v04))); + return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x))); +} + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +#ifdef __STDC__ +static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.0000000000e+00, /* 0x00000000 */ + -7.0312500000e-02, /* 0xbd900000 */ + -8.0816707611e+00, /* 0xc1014e86 */ + -2.5706311035e+02, /* 0xc3808814 */ + -2.4852163086e+03, /* 0xc51b5376 */ + -5.2530439453e+03, /* 0xc5a4285a */ +}; +#ifdef __STDC__ +static const float pS8[5] = { +#else +static float pS8[5] = { +#endif + 1.1653436279e+02, /* 0x42e91198 */ + 3.8337448730e+03, /* 0x456f9beb */ + 4.0597855469e+04, /* 0x471e95db */ + 1.1675296875e+05, /* 0x47e4087c */ + 4.7627726562e+04, /* 0x473a0bba */ +}; +#ifdef __STDC__ +static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + -1.1412546255e-11, /* 0xad48c58a */ + -7.0312492549e-02, /* 0xbd8fffff */ + -4.1596107483e+00, /* 0xc0851b88 */ + -6.7674766541e+01, /* 0xc287597b */ + -3.3123129272e+02, /* 0xc3a59d9b */ + -3.4643338013e+02, /* 0xc3ad3779 */ +}; +#ifdef __STDC__ +static const float pS5[5] = { +#else +static float pS5[5] = { +#endif + 6.0753936768e+01, /* 0x42730408 */ + 1.0512523193e+03, /* 0x44836813 */ + 5.9789707031e+03, /* 0x45bad7c4 */ + 9.6254453125e+03, /* 0x461665c8 */ + 2.4060581055e+03, /* 0x451660ee */ +}; + +#ifdef __STDC__ +static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#else +static float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + -2.5470459075e-09, /* 0xb12f081b */ + -7.0311963558e-02, /* 0xbd8fffb8 */ + -2.4090321064e+00, /* 0xc01a2d95 */ + -2.1965976715e+01, /* 0xc1afba52 */ + -5.8079170227e+01, /* 0xc2685112 */ + -3.1447946548e+01, /* 0xc1fb9565 */ +}; +#ifdef __STDC__ +static const float pS3[5] = { +#else +static float pS3[5] = { +#endif + 3.5856033325e+01, /* 0x420f6c94 */ + 3.6151397705e+02, /* 0x43b4c1ca */ + 1.1936077881e+03, /* 0x44953373 */ + 1.1279968262e+03, /* 0x448cffe6 */ + 1.7358093262e+02, /* 0x432d94b8 */ +}; + +#ifdef __STDC__ +static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + -8.8753431271e-08, /* 0xb3be98b7 */ + -7.0303097367e-02, /* 0xbd8ffb12 */ + -1.4507384300e+00, /* 0xbfb9b1cc */ + -7.6356959343e+00, /* 0xc0f4579f */ + -1.1193166733e+01, /* 0xc1331736 */ + -3.2336456776e+00, /* 0xc04ef40d */ +}; +#ifdef __STDC__ +static const float pS2[5] = { +#else +static float pS2[5] = { +#endif + 2.2220300674e+01, /* 0x41b1c32d */ + 1.3620678711e+02, /* 0x430834f0 */ + 2.7047027588e+02, /* 0x43873c32 */ + 1.5387539673e+02, /* 0x4319e01a */ + 1.4657617569e+01, /* 0x416a859a */ +}; + +#ifdef __STDC__ + static float pzerof(float x) +#else + static float pzerof(x) + float x; +#endif +{ +#ifdef __STDC__ + const float *p,*q; +#else + float *p,*q; +#endif + float z,r,s; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = pR8; q= pS8;} + else if(ix>=0x40f71c58){p = pR5; q= pS5;} + else if(ix>=0x4036db68){p = pR3; q= pS3;} + else if(ix>=0x40000000){p = pR2; q= pS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +#ifdef __STDC__ +static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.0000000000e+00, /* 0x00000000 */ + 7.3242187500e-02, /* 0x3d960000 */ + 1.1768206596e+01, /* 0x413c4a93 */ + 5.5767340088e+02, /* 0x440b6b19 */ + 8.8591972656e+03, /* 0x460a6cca */ + 3.7014625000e+04, /* 0x471096a0 */ +}; +#ifdef __STDC__ +static const float qS8[6] = { +#else +static float qS8[6] = { +#endif + 1.6377603149e+02, /* 0x4323c6aa */ + 8.0983447266e+03, /* 0x45fd12c2 */ + 1.4253829688e+05, /* 0x480b3293 */ + 8.0330925000e+05, /* 0x49441ed4 */ + 8.4050156250e+05, /* 0x494d3359 */ + -3.4389928125e+05, /* 0xc8a7eb69 */ +}; + +#ifdef __STDC__ +static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + 1.8408595828e-11, /* 0x2da1ec79 */ + 7.3242180049e-02, /* 0x3d95ffff */ + 5.8356351852e+00, /* 0x40babd86 */ + 1.3511157227e+02, /* 0x43071c90 */ + 1.0272437744e+03, /* 0x448067cd */ + 1.9899779053e+03, /* 0x44f8bf4b */ +}; +#ifdef __STDC__ +static const float qS5[6] = { +#else +static float qS5[6] = { +#endif + 8.2776611328e+01, /* 0x42a58da0 */ + 2.0778142090e+03, /* 0x4501dd07 */ + 1.8847289062e+04, /* 0x46933e94 */ + 5.6751113281e+04, /* 0x475daf1d */ + 3.5976753906e+04, /* 0x470c88c1 */ + -5.3543427734e+03, /* 0xc5a752be */ +}; + +#ifdef __STDC__ +static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#else +static float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + 4.3774099900e-09, /* 0x3196681b */ + 7.3241114616e-02, /* 0x3d95ff70 */ + 3.3442313671e+00, /* 0x405607e3 */ + 4.2621845245e+01, /* 0x422a7cc5 */ + 1.7080809021e+02, /* 0x432acedf */ + 1.6673394775e+02, /* 0x4326bbe4 */ +}; +#ifdef __STDC__ +static const float qS3[6] = { +#else +static float qS3[6] = { +#endif + 4.8758872986e+01, /* 0x42430916 */ + 7.0968920898e+02, /* 0x44316c1c */ + 3.7041481934e+03, /* 0x4567825f */ + 6.4604252930e+03, /* 0x45c9e367 */ + 2.5163337402e+03, /* 0x451d4557 */ + -1.4924745178e+02, /* 0xc3153f59 */ +}; + +#ifdef __STDC__ +static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + 1.5044444979e-07, /* 0x342189db */ + 7.3223426938e-02, /* 0x3d95f62a */ + 1.9981917143e+00, /* 0x3fffc4bf */ + 1.4495602608e+01, /* 0x4167edfd */ + 3.1666231155e+01, /* 0x41fd5471 */ + 1.6252708435e+01, /* 0x4182058c */ +}; +#ifdef __STDC__ +static const float qS2[6] = { +#else +static float qS2[6] = { +#endif + 3.0365585327e+01, /* 0x41f2ecb8 */ + 2.6934811401e+02, /* 0x4386ac8f */ + 8.4478375244e+02, /* 0x44533229 */ + 8.8293585205e+02, /* 0x445cbbe5 */ + 2.1266638184e+02, /* 0x4354aa98 */ + -5.3109550476e+00, /* 0xc0a9f358 */ +}; + +#ifdef __STDC__ + static float qzerof(float x) +#else + static float qzerof(x) + float x; +#endif +{ +#ifdef __STDC__ + const float *p,*q; +#else + float *p,*q; +#endif + float s,r,z; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = qR8; q= qS8;} + else if(ix>=0x40f71c58){p = qR5; q= qS5;} + else if(ix>=0x4036db68){p = qR3; q= qS3;} + else if(ix>=0x40000000){p = qR2; q= qS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (-(float).125 + r/s)/x; +} diff --git a/sysdeps/ieee754/flt-32/e_j1f.c b/sysdeps/ieee754/flt-32/e_j1f.c new file mode 100644 index 0000000..e6f14a1 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_j1f.c @@ -0,0 +1,444 @@ +/* e_j1f.c -- float version of e_j1.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_j1f.c,v 1.4 1995/05/10 20:45:31 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static float ponef(float), qonef(float); +#else +static float ponef(), qonef(); +#endif + +#ifdef __STDC__ +static const float +#else +static float +#endif +huge = 1e30, +one = 1.0, +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +tpi = 6.3661974669e-01, /* 0x3f22f983 */ + /* R0/S0 on [0,2] */ +r00 = -6.2500000000e-02, /* 0xbd800000 */ +r01 = 1.4070566976e-03, /* 0x3ab86cfd */ +r02 = -1.5995563444e-05, /* 0xb7862e36 */ +r03 = 4.9672799207e-08, /* 0x335557d2 */ +s01 = 1.9153760746e-02, /* 0x3c9ce859 */ +s02 = 1.8594678841e-04, /* 0x3942fab6 */ +s03 = 1.1771846857e-06, /* 0x359dffc2 */ +s04 = 5.0463624390e-09, /* 0x31ad6446 */ +s05 = 1.2354227016e-11; /* 0x2d59567e */ + +#ifdef __STDC__ +static const float zero = 0.0; +#else +static float zero = 0.0; +#endif + +#ifdef __STDC__ + float __ieee754_j1f(float x) +#else + float __ieee754_j1f(x) + float x; +#endif +{ + float z, s,c,ss,cc,r,u,v,y; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return one/x; + y = fabsf(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = __sinf(y); + c = __cosf(y); + ss = -s-c; + cc = s-c; + if(ix<0x7f000000) { /* make sure y+y not overflow */ + z = __cosf(y+y); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* + * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) + * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) + */ + if(ix>0x48000000) z = (invsqrtpi*cc)/__sqrtf(y); + else { + u = ponef(y); v = qonef(y); + z = invsqrtpi*(u*cc-v*ss)/__sqrtf(y); + } + if(hx<0) return -z; + else return z; + } + if(ix<0x32000000) { /* |x|<2**-27 */ + if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */ + } + z = x*x; + r = z*(r00+z*(r01+z*(r02+z*r03))); + s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); + r *= x; + return(x*(float)0.5+r/s); +} + +#ifdef __STDC__ +static const float U0[5] = { +#else +static float U0[5] = { +#endif + -1.9605709612e-01, /* 0xbe48c331 */ + 5.0443872809e-02, /* 0x3d4e9e3c */ + -1.9125689287e-03, /* 0xbafaaf2a */ + 2.3525259166e-05, /* 0x37c5581c */ + -9.1909917899e-08, /* 0xb3c56003 */ +}; +#ifdef __STDC__ +static const float V0[5] = { +#else +static float V0[5] = { +#endif + 1.9916731864e-02, /* 0x3ca3286a */ + 2.0255257550e-04, /* 0x3954644b */ + 1.3560879779e-06, /* 0x35b602d4 */ + 6.2274145840e-09, /* 0x31d5f8eb */ + 1.6655924903e-11, /* 0x2d9281cf */ +}; + +#ifdef __STDC__ + float __ieee754_y1f(float x) +#else + float __ieee754_y1f(x) + float x; +#endif +{ + float z, s,c,ss,cc,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if(ix>=0x7f800000) return one/(x+x*x); + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = __sinf(x); + c = __cosf(x); + ss = -s-c; + cc = s-c; + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = __cosf(x+x); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) + * where x0 = x-3pi/4 + * Better formula: + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (cos(x) + sin(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrtf(x); + else { + u = ponef(x); v = qonef(x); + z = invsqrtpi*(u*ss+v*cc)/__sqrtf(x); + } + return z; + } + if(ix<=0x24800000) { /* x < 2**-54 */ + return(-tpi/x); + } + z = x*x; + u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); + v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); + return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(x)-one/x)); +} + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pone(x)-1-R/S | <= 2 ** ( -60.06) + */ + +#ifdef __STDC__ +static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.0000000000e+00, /* 0x00000000 */ + 1.1718750000e-01, /* 0x3df00000 */ + 1.3239480972e+01, /* 0x4153d4ea */ + 4.1205184937e+02, /* 0x43ce06a3 */ + 3.8747453613e+03, /* 0x45722bed */ + 7.9144794922e+03, /* 0x45f753d6 */ +}; +#ifdef __STDC__ +static const float ps8[5] = { +#else +static float ps8[5] = { +#endif + 1.1420736694e+02, /* 0x42e46a2c */ + 3.6509309082e+03, /* 0x45642ee5 */ + 3.6956207031e+04, /* 0x47105c35 */ + 9.7602796875e+04, /* 0x47bea166 */ + 3.0804271484e+04, /* 0x46f0a88b */ +}; + +#ifdef __STDC__ +static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + 1.3199052094e-11, /* 0x2d68333f */ + 1.1718749255e-01, /* 0x3defffff */ + 6.8027510643e+00, /* 0x40d9b023 */ + 1.0830818176e+02, /* 0x42d89dca */ + 5.1763616943e+02, /* 0x440168b7 */ + 5.2871520996e+02, /* 0x44042dc6 */ +}; +#ifdef __STDC__ +static const float ps5[5] = { +#else +static float ps5[5] = { +#endif + 5.9280597687e+01, /* 0x426d1f55 */ + 9.9140142822e+02, /* 0x4477d9b1 */ + 5.3532670898e+03, /* 0x45a74a23 */ + 7.8446904297e+03, /* 0x45f52586 */ + 1.5040468750e+03, /* 0x44bc0180 */ +}; + +#ifdef __STDC__ +static const float pr3[6] = { +#else +static float pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + 3.0250391081e-09, /* 0x314fe10d */ + 1.1718686670e-01, /* 0x3defffab */ + 3.9329774380e+00, /* 0x407bb5e7 */ + 3.5119403839e+01, /* 0x420c7a45 */ + 9.1055007935e+01, /* 0x42b61c2a */ + 4.8559066772e+01, /* 0x42423c7c */ +}; +#ifdef __STDC__ +static const float ps3[5] = { +#else +static float ps3[5] = { +#endif + 3.4791309357e+01, /* 0x420b2a4d */ + 3.3676245117e+02, /* 0x43a86198 */ + 1.0468714600e+03, /* 0x4482dbe3 */ + 8.9081134033e+02, /* 0x445eb3ed */ + 1.0378793335e+02, /* 0x42cf936c */ +}; + +#ifdef __STDC__ +static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + 1.0771083225e-07, /* 0x33e74ea8 */ + 1.1717621982e-01, /* 0x3deffa16 */ + 2.3685150146e+00, /* 0x401795c0 */ + 1.2242610931e+01, /* 0x4143e1bc */ + 1.7693971634e+01, /* 0x418d8d41 */ + 5.0735230446e+00, /* 0x40a25a4d */ +}; +#ifdef __STDC__ +static const float ps2[5] = { +#else +static float ps2[5] = { +#endif + 2.1436485291e+01, /* 0x41ab7dec */ + 1.2529022980e+02, /* 0x42fa9499 */ + 2.3227647400e+02, /* 0x436846c7 */ + 1.1767937469e+02, /* 0x42eb5bd7 */ + 8.3646392822e+00, /* 0x4105d590 */ +}; + +#ifdef __STDC__ + static float ponef(float x) +#else + static float ponef(x) + float x; +#endif +{ +#ifdef __STDC__ + const float *p,*q; +#else + float *p,*q; +#endif + float z,r,s; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = pr8; q= ps8;} + else if(ix>=0x40f71c58){p = pr5; q= ps5;} + else if(ix>=0x4036db68){p = pr3; q= ps3;} + else if(ix>=0x40000000){p = pr2; q= ps2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +#ifdef __STDC__ +static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.0000000000e+00, /* 0x00000000 */ + -1.0253906250e-01, /* 0xbdd20000 */ + -1.6271753311e+01, /* 0xc1822c8d */ + -7.5960174561e+02, /* 0xc43de683 */ + -1.1849806641e+04, /* 0xc639273a */ + -4.8438511719e+04, /* 0xc73d3683 */ +}; +#ifdef __STDC__ +static const float qs8[6] = { +#else +static float qs8[6] = { +#endif + 1.6139537048e+02, /* 0x43216537 */ + 7.8253862305e+03, /* 0x45f48b17 */ + 1.3387534375e+05, /* 0x4802bcd6 */ + 7.1965775000e+05, /* 0x492fb29c */ + 6.6660125000e+05, /* 0x4922be94 */ + -2.9449025000e+05, /* 0xc88fcb48 */ +}; + +#ifdef __STDC__ +static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + -2.0897993405e-11, /* 0xadb7d219 */ + -1.0253904760e-01, /* 0xbdd1fffe */ + -8.0564479828e+00, /* 0xc100e736 */ + -1.8366960144e+02, /* 0xc337ab6b */ + -1.3731937256e+03, /* 0xc4aba633 */ + -2.6124443359e+03, /* 0xc523471c */ +}; +#ifdef __STDC__ +static const float qs5[6] = { +#else +static float qs5[6] = { +#endif + 8.1276550293e+01, /* 0x42a28d98 */ + 1.9917987061e+03, /* 0x44f8f98f */ + 1.7468484375e+04, /* 0x468878f8 */ + 4.9851425781e+04, /* 0x4742bb6d */ + 2.7948074219e+04, /* 0x46da5826 */ + -4.7191835938e+03, /* 0xc5937978 */ +}; + +#ifdef __STDC__ +static const float qr3[6] = { +#else +static float qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + -5.0783124372e-09, /* 0xb1ae7d4f */ + -1.0253783315e-01, /* 0xbdd1ff5b */ + -4.6101160049e+00, /* 0xc0938612 */ + -5.7847221375e+01, /* 0xc267638e */ + -2.2824453735e+02, /* 0xc3643e9a */ + -2.1921012878e+02, /* 0xc35b35cb */ +}; +#ifdef __STDC__ +static const float qs3[6] = { +#else +static float qs3[6] = { +#endif + 4.7665153503e+01, /* 0x423ea91e */ + 6.7386511230e+02, /* 0x4428775e */ + 3.3801528320e+03, /* 0x45534272 */ + 5.5477290039e+03, /* 0x45ad5dd5 */ + 1.9031191406e+03, /* 0x44ede3d0 */ + -1.3520118713e+02, /* 0xc3073381 */ +}; + +#ifdef __STDC__ +static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + -1.7838172539e-07, /* 0xb43f8932 */ + -1.0251704603e-01, /* 0xbdd1f475 */ + -2.7522056103e+00, /* 0xc0302423 */ + -1.9663616180e+01, /* 0xc19d4f16 */ + -4.2325313568e+01, /* 0xc2294d1f */ + -2.1371921539e+01, /* 0xc1aaf9b2 */ +}; +#ifdef __STDC__ +static const float qs2[6] = { +#else +static float qs2[6] = { +#endif + 2.9533363342e+01, /* 0x41ec4454 */ + 2.5298155212e+02, /* 0x437cfb47 */ + 7.5750280762e+02, /* 0x443d602e */ + 7.3939318848e+02, /* 0x4438d92a */ + 1.5594900513e+02, /* 0x431bf2f2 */ + -4.9594988823e+00, /* 0xc09eb437 */ +}; + +#ifdef __STDC__ + static float qonef(float x) +#else + static float qonef(x) + float x; +#endif +{ +#ifdef __STDC__ + const float *p,*q; +#else + float *p,*q; +#endif + float s,r,z; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = qr8; q= qs8;} + else if(ix>=0x40f71c58){p = qr5; q= qs5;} + else if(ix>=0x4036db68){p = qr3; q= qs3;} + else if(ix>=0x40000000){p = qr2; q= qs2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return ((float).375 + r/s)/x; +} diff --git a/sysdeps/ieee754/flt-32/e_jnf.c b/sysdeps/ieee754/flt-32/e_jnf.c new file mode 100644 index 0000000..9e5279c --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_jnf.c @@ -0,0 +1,213 @@ +/* e_jnf.c -- float version of e_jn.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_jnf.c,v 1.5 1995/05/10 20:45:37 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +two = 2.0000000000e+00, /* 0x40000000 */ +one = 1.0000000000e+00; /* 0x3F800000 */ + +#ifdef __STDC__ +static const float zero = 0.0000000000e+00; +#else +static float zero = 0.0000000000e+00; +#endif + +#ifdef __STDC__ + float __ieee754_jnf(int n, float x) +#else + float __ieee754_jnf(n,x) + int n; float x; +#endif +{ + int32_t i,hx,ix, sgn; + float a, b, temp, di; + float z, w; + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if J(n,NaN) is NaN */ + if(ix>0x7f800000) return x+x; + if(n<0){ + n = -n; + x = -x; + hx ^= 0x80000000; + } + if(n==0) return(__ieee754_j0f(x)); + if(n==1) return(__ieee754_j1f(x)); + sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ + x = fabsf(x); + if(ix==0||ix>=0x7f800000) /* if x is 0 or inf */ + b = zero; + else if((float)n<=x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + a = __ieee754_j0f(x); + b = __ieee754_j1f(x); + for(i=1;i<n;i++){ + temp = b; + b = b*((float)(i+i)/x) - a; /* avoid underflow */ + a = temp; + } + } else { + if(ix<0x30800000) { /* x < 2**-29 */ + /* x is tiny, return the first Taylor expansion of J(n,x) + * J(n,x) = 1/n!*(x/2)^n - ... + */ + if(n>33) /* underflow */ + b = zero; + else { + temp = x*(float)0.5; b = temp; + for (a=one,i=2;i<=n;i++) { + a *= (float)i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b/a; + } + } else { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + float t,v; + float q0,q1,h,tmp; int32_t k,m; + w = (n+n)/(float)x; h = (float)2.0/(float)x; + q0 = w; z = w+h; q1 = w*z - (float)1.0; k=1; + while(q1<(float)1.0e9) { + k += 1; z += h; + tmp = z*q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n+n; + for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two/x; + tmp = tmp*__ieee754_logf(fabsf(v*tmp)); + if(tmp<(float)8.8721679688e+01) { + for(i=n-1,di=(float)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + } + } else { + for(i=n-1,di=(float)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if(b>(float)1e10) { + a /= b; + t /= b; + b = one; + } + } + } + b = (t*__ieee754_j0f(x)/b); + } + } + if(sgn==1) return -b; else return b; +} + +#ifdef __STDC__ + float __ieee754_ynf(int n, float x) +#else + float __ieee754_ynf(n,x) + int n; float x; +#endif +{ + int32_t i,hx,ix; + u_int32_t ib; + int32_t sign; + float a, b, temp; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if Y(n,NaN) is NaN */ + if(ix>0x7f800000) return x+x; + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + sign = 1; + if(n<0){ + n = -n; + sign = 1 - ((n&1)<<1); + } + if(n==0) return(__ieee754_y0f(x)); + if(n==1) return(sign*__ieee754_y1f(x)); + if(ix==0x7f800000) return zero; + + a = __ieee754_y0f(x); + b = __ieee754_y1f(x); + /* quit if b is -inf */ + GET_FLOAT_WORD(ib,b); + for(i=1;i<n&&ib!=0xff800000;i++){ + temp = b; + b = ((float)(i+i)/x)*b - a; + GET_FLOAT_WORD(ib,b); + a = temp; + } + if(sign>0) return b; else return -b; +} diff --git a/sysdeps/ieee754/flt-32/e_lgammaf_r.c b/sysdeps/ieee754/flt-32/e_lgammaf_r.c new file mode 100644 index 0000000..f744d53 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_lgammaf_r.c @@ -0,0 +1,250 @@ +/* e_lgammaf_r.c -- float version of e_lgamma_r.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_lgammaf_r.c,v 1.3 1995/05/10 20:45:47 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +two23= 8.3886080000e+06, /* 0x4b000000 */ +half= 5.0000000000e-01, /* 0x3f000000 */ +one = 1.0000000000e+00, /* 0x3f800000 */ +pi = 3.1415927410e+00, /* 0x40490fdb */ +a0 = 7.7215664089e-02, /* 0x3d9e233f */ +a1 = 3.2246702909e-01, /* 0x3ea51a66 */ +a2 = 6.7352302372e-02, /* 0x3d89f001 */ +a3 = 2.0580807701e-02, /* 0x3ca89915 */ +a4 = 7.3855509982e-03, /* 0x3bf2027e */ +a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ +a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ +a7 = 5.1006977446e-04, /* 0x3a05b634 */ +a8 = 2.2086278477e-04, /* 0x39679767 */ +a9 = 1.0801156895e-04, /* 0x38e28445 */ +a10 = 2.5214456400e-05, /* 0x37d383a2 */ +a11 = 4.4864096708e-05, /* 0x383c2c75 */ +tc = 1.4616321325e+00, /* 0x3fbb16c3 */ +tf = -1.2148628384e-01, /* 0xbdf8cdcd */ +/* tt = -(tail of tf) */ +tt = 6.6971006518e-09, /* 0x31e61c52 */ +t0 = 4.8383611441e-01, /* 0x3ef7b95e */ +t1 = -1.4758771658e-01, /* 0xbe17213c */ +t2 = 6.4624942839e-02, /* 0x3d845a15 */ +t3 = -3.2788541168e-02, /* 0xbd064d47 */ +t4 = 1.7970675603e-02, /* 0x3c93373d */ +t5 = -1.0314224288e-02, /* 0xbc28fcfe */ +t6 = 6.1005386524e-03, /* 0x3bc7e707 */ +t7 = -3.6845202558e-03, /* 0xbb7177fe */ +t8 = 2.2596477065e-03, /* 0x3b141699 */ +t9 = -1.4034647029e-03, /* 0xbab7f476 */ +t10 = 8.8108185446e-04, /* 0x3a66f867 */ +t11 = -5.3859531181e-04, /* 0xba0d3085 */ +t12 = 3.1563205994e-04, /* 0x39a57b6b */ +t13 = -3.1275415677e-04, /* 0xb9a3f927 */ +t14 = 3.3552918467e-04, /* 0x39afe9f7 */ +u0 = -7.7215664089e-02, /* 0xbd9e233f */ +u1 = 6.3282704353e-01, /* 0x3f2200f4 */ +u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ +u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ +u4 = 2.2896373272e-01, /* 0x3e6a7578 */ +u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ +v1 = 2.4559779167e+00, /* 0x401d2ebe */ +v2 = 2.1284897327e+00, /* 0x4008392d */ +v3 = 7.6928514242e-01, /* 0x3f44efdf */ +v4 = 1.0422264785e-01, /* 0x3dd572af */ +v5 = 3.2170924824e-03, /* 0x3b52d5db */ +s0 = -7.7215664089e-02, /* 0xbd9e233f */ +s1 = 2.1498242021e-01, /* 0x3e5c245a */ +s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ +s3 = 1.4635047317e-01, /* 0x3e15dce6 */ +s4 = 2.6642270386e-02, /* 0x3cda40e4 */ +s5 = 1.8402845599e-03, /* 0x3af135b4 */ +s6 = 3.1947532989e-05, /* 0x3805ff67 */ +r1 = 1.3920053244e+00, /* 0x3fb22d3b */ +r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ +r3 = 1.7193385959e-01, /* 0x3e300f6e */ +r4 = 1.8645919859e-02, /* 0x3c98bf54 */ +r5 = 7.7794247773e-04, /* 0x3a4beed6 */ +r6 = 7.3266842264e-06, /* 0x36f5d7bd */ +w0 = 4.1893854737e-01, /* 0x3ed67f1d */ +w1 = 8.3333335817e-02, /* 0x3daaaaab */ +w2 = -2.7777778450e-03, /* 0xbb360b61 */ +w3 = 7.9365057172e-04, /* 0x3a500cfd */ +w4 = -5.9518753551e-04, /* 0xba1c065c */ +w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ +w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ + +#ifdef __STDC__ +static const float zero= 0.0000000000e+00; +#else +static float zero= 0.0000000000e+00; +#endif + +#ifdef __STDC__ + static float sin_pif(float x) +#else + static float sin_pif(x) + float x; +#endif +{ + float y,z; + int n,ix; + + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = __floorf(y); + if(z!=y) { /* inexact anyway */ + y *= (float)0.5; + y = (float)2.0*(y - __floorf(y)); /* y = |x| mod 2.0 */ + n = (int) (y*(float)4.0); + } else { + if(ix>=0x4b800000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x4b000000) z = y+two23; /* exact */ + GET_FLOAT_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __kernel_sinf(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break; + case 3: + case 4: y = __kernel_sinf(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break; + default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break; + } + return -y; +} + + +#ifdef __STDC__ + float __ieee754_lgammaf_r(float x, int *signgamp) +#else + float __ieee754_lgammaf_r(x,signgamp) + float x; int *signgamp; +#endif +{ + float t,y,z,nadj,p,p1,p2,p3,q,r,w; + int i,hx,ix; + + GET_FLOAT_WORD(hx,x); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + *signgamp = 1; + if ((unsigned int)hx==0xff800000) + return x-x; + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return x*x; + if(ix==0) return one/fabsf(x); + if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */ + if(hx<0) { + *signgamp = -1; + return -__ieee754_logf(-x); + } else return -__ieee754_logf(x); + } + if(hx<0) { + if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ + return x/zero; + t = sin_pif(x); + if(t==zero) return one/fabsf(t); /* -integer */ + nadj = __ieee754_logf(pi/fabsf(t*x)); + if(t<zero) *signgamp = -1; + x = -x; + } + + /* purge off 1 and 2 */ + if (ix==0x3f800000||ix==0x40000000) r = 0; + /* for x < 2.0 */ + else if(ix<0x40000000) { + if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ + r = -__ieee754_logf(x); + if(ix>=0x3f3b4a20) {y = one-x; i= 0;} + else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-(float)0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-(float)0.5*y + p1/p2); + } + } + else if(ix<0x41000000) { /* x < 8.0 */ + i = (int)x; + t = zero; + y = x-(float)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+(float)6.0); /* FALLTHRU */ + case 6: z *= (y+(float)5.0); /* FALLTHRU */ + case 5: z *= (y+(float)4.0); /* FALLTHRU */ + case 4: z *= (y+(float)3.0); /* FALLTHRU */ + case 3: z *= (y+(float)2.0); /* FALLTHRU */ + r += __ieee754_logf(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x5c800000) { + t = __ieee754_logf(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = x*(__ieee754_logf(x)-one); + if(hx<0) r = nadj - r; + return r; +} diff --git a/sysdeps/ieee754/flt-32/e_log10f.c b/sysdeps/ieee754/flt-32/e_log10f.c new file mode 100644 index 0000000..cea3d91 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_log10f.c @@ -0,0 +1,67 @@ +/* e_log10f.c -- float version of e_log10.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_log10f.c,v 1.5 1995/05/10 20:45:53 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +two25 = 3.3554432000e+07, /* 0x4c000000 */ +ivln10 = 4.3429449201e-01, /* 0x3ede5bd9 */ +log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */ +log10_2lo = 7.9034151668e-07; /* 0x355427db */ + +#ifdef __STDC__ +static const float zero = 0.0; +#else +static float zero = 0.0; +#endif + +#ifdef __STDC__ + float __ieee754_log10f(float x) +#else + float __ieee754_log10f(x) + float x; +#endif +{ + float y,z; + int32_t i,k,hx; + + GET_FLOAT_WORD(hx,x); + + k=0; + if (hx < 0x00800000) { /* x < 2**-126 */ + if ((hx&0x7fffffff)==0) + return -two25/(x-x); /* log(+-0)=-inf */ + if (hx<0) return (x-x)/(x-x); /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(hx,x); + } + if (hx >= 0x7f800000) return x+x; + k += (hx>>23)-127; + i = ((u_int32_t)k&0x80000000)>>31; + hx = (hx&0x007fffff)|((0x7f-i)<<23); + y = (float)(k+i); + SET_FLOAT_WORD(x,hx); + z = y*log10_2lo + ivln10*__ieee754_logf(x); + return z+y*log10_2hi; +} diff --git a/sysdeps/ieee754/flt-32/e_logf.c b/sysdeps/ieee754/flt-32/e_logf.c new file mode 100644 index 0000000..de8f869 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_logf.c @@ -0,0 +1,99 @@ +/* e_logf.c -- float version of e_log.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_logf.c,v 1.4 1995/05/10 20:45:54 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ +ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ +two25 = 3.355443200e+07, /* 0x4c000000 */ +Lg1 = 6.6666668653e-01, /* 3F2AAAAB */ +Lg2 = 4.0000000596e-01, /* 3ECCCCCD */ +Lg3 = 2.8571429849e-01, /* 3E924925 */ +Lg4 = 2.2222198546e-01, /* 3E638E29 */ +Lg5 = 1.8183572590e-01, /* 3E3A3325 */ +Lg6 = 1.5313838422e-01, /* 3E1CD04F */ +Lg7 = 1.4798198640e-01; /* 3E178897 */ + +#ifdef __STDC__ +static const float zero = 0.0; +#else +static float zero = 0.0; +#endif + +#ifdef __STDC__ + float __ieee754_logf(float x) +#else + float __ieee754_logf(x) + float x; +#endif +{ + float hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,ix,i,j; + + GET_FLOAT_WORD(ix,x); + + k=0; + if (ix < 0x00800000) { /* x < 2**-126 */ + if ((ix&0x7fffffff)==0) + return -two25/(x-x); /* log(+-0)=-inf */ + if (ix<0) return (x-x)/(x-x); /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(ix,x); + } + if (ix >= 0x7f800000) return x+x; + k += (ix>>23)-127; + ix &= 0x007fffff; + i = (ix+(0x95f64<<3))&0x800000; + SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ + k += (i>>23); + f = x-(float)1.0; + if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */ + if(f==zero) { + if(k==0) return zero; else {dk=(float)k; + return dk*ln2_hi+dk*ln2_lo;} + } + R = f*f*((float)0.5-(float)0.33333333333333333*f); + if(k==0) return f-R; else {dk=(float)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/((float)2.0+f); + dk = (float)k; + z = s*s; + i = ix-(0x6147a<<3); + w = z*z; + j = (0x6b851<<3)-ix; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=(float)0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} diff --git a/sysdeps/ieee754/flt-32/e_powf.c b/sysdeps/ieee754/flt-32/e_powf.c new file mode 100644 index 0000000..4798340 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_powf.c @@ -0,0 +1,253 @@ +/* e_powf.c -- float version of e_pow.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_powf.c,v 1.7 1996/04/08 15:43:44 phil Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +static const float huge = 1.0e+30, tiny = 1.0e-30; + +#ifdef __STDC__ +static const float +#else +static float +#endif +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ +dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ +zero = 0.0, +one = 1.0, +two = 2.0, +two24 = 16777216.0, /* 0x4b800000 */ + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 6.0000002384e-01, /* 0x3f19999a */ +L2 = 4.2857143283e-01, /* 0x3edb6db7 */ +L3 = 3.3333334327e-01, /* 0x3eaaaaab */ +L4 = 2.7272811532e-01, /* 0x3e8ba305 */ +L5 = 2.3066075146e-01, /* 0x3e6c3255 */ +L6 = 2.0697501302e-01, /* 0x3e53f142 */ +P1 = 1.6666667163e-01, /* 0x3e2aaaab */ +P2 = -2.7777778450e-03, /* 0xbb360b61 */ +P3 = 6.6137559770e-05, /* 0x388ab355 */ +P4 = -1.6533901999e-06, /* 0xb5ddea0e */ +P5 = 4.1381369442e-08, /* 0x3331bb4c */ +lg2 = 6.9314718246e-01, /* 0x3f317218 */ +lg2_h = 6.93145752e-01, /* 0x3f317200 */ +lg2_l = 1.42860654e-06, /* 0x35bfbe8c */ +ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */ +cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */ +cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */ +cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */ +ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */ +ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/ +ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ + +#ifdef __STDC__ + float __ieee754_powf(float x, float y) +#else + float __ieee754_powf(x,y) + float x, y; +#endif +{ + float z,ax,z_h,z_l,p_h,p_l; + float y1,t1,t2,r,s,t,u,v,w; + int32_t i,j,k,yisint,n; + int32_t hx,hy,ix,iy,is; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + if(iy==0) return one; + + /* +-NaN return x+y */ + if(ix > 0x7f800000 || + iy > 0x7f800000) + return x+y; + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if(hx<0) { + if(iy>=0x4b800000) yisint = 2; /* even integer y */ + else if(iy>=0x3f800000) { + k = (iy>>23)-0x7f; /* exponent */ + j = iy>>(23-k); + if((j<<(23-k))==iy) yisint = 2-(j&1); + } + } + + /* special value of y */ + if (iy==0x7f800000) { /* y is +-inf */ + if (ix==0x3f800000) + return y - y; /* inf**+-1 is NaN */ + else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zero; + } + if(iy==0x3f800000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3f000000) { /* y is 0.5 */ + if(hx>=0) /* x >= +0 */ + return __ieee754_sqrtf(x); + } + + ax = fabsf(x); + /* special value of x */ + if(ix==0x7f800000||ix==0||ix==0x3f800000){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3f800000)|yisint)==0) { + z = (z-z)/(z-z); /* (-1)**non-int is NaN */ + } else if(yisint==1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + + /* (x<0)**(non-int) is NaN */ + if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); + + /* |y| is huge */ + if(iy>0x4d000000) { /* if |y| > 2**27 */ + /* over/underflow if x is not close to one */ + if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny; + if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny; + /* now |1-x| is tiny <= 2**-20, suffice to compute + log(x) by x-x^2/2+x^3/3-x^4/4 */ + t = x-1; /* t has 20 trailing zeros */ + w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25)); + u = ivln2_h*t; /* ivln2_h has 16 sig. bits */ + v = t*ivln2_l-w*ivln2; + t1 = u+v; + GET_FLOAT_WORD(is,t1); + SET_FLOAT_WORD(t1,is&0xfffff000); + t2 = v-(t1-u); + } else { + float s2,s_h,s_l,t_h,t_l; + n = 0; + /* take care subnormal number */ + if(ix<0x00800000) + {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); } + n += ((ix)>>23)-0x7f; + j = ix&0x007fffff; + /* determine interval */ + ix = j|0x3f800000; /* normalize ix */ + if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */ + else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */ + else {k=0;n+=1;ix -= 0x00800000;} + SET_FLOAT_WORD(ax,ix); + + /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ + u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ + v = one/(ax+bp[k]); + s = u*v; + s_h = s; + GET_FLOAT_WORD(is,s_h); + SET_FLOAT_WORD(s_h,is&0xfffff000); + /* t_h=ax+bp[k] High */ + SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21)); + t_l = ax - (t_h-bp[k]); + s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + s2 = s*s; + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); + r += s_l*(s_h+s); + s2 = s_h*s_h; + t_h = (float)3.0+s2+r; + GET_FLOAT_WORD(is,t_h); + SET_FLOAT_WORD(t_h,is&0xfffff000); + t_l = r-((t_h-(float)3.0)-s2); + /* u+v = s*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*s; + /* 2/(3log2)*(s+...) */ + p_h = u+v; + GET_FLOAT_WORD(is,p_h); + SET_FLOAT_WORD(p_h,is&0xfffff000); + p_l = v-(p_h-u); + z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l*p_h+p_l*cp+dp_l[k]; + /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = (float)n; + t1 = (((z_h+z_l)+dp_h[k])+t); + GET_FLOAT_WORD(is,t1); + SET_FLOAT_WORD(t1,is&0xfffff000); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) + s = -one; /* (-ve)**(odd int) */ + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + GET_FLOAT_WORD(is,y); + SET_FLOAT_WORD(y1,is&0xfffff000); + p_l = (y-y1)*t1+y*t2; + p_h = y1*t1; + z = p_l+p_h; + GET_FLOAT_WORD(j,z); + if (j>0x43000000) /* if z > 128 */ + return s*huge*huge; /* overflow */ + else if (j==0x43000000) { /* if z == 128 */ + if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ + } + else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */ + return s*tiny*tiny; /* underflow */ + else if ((u_int32_t) j==0xc3160000){ /* z == -150 */ + if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ + } + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>23)-0x7f; + n = 0; + if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00800000>>(k+1)); + k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */ + SET_FLOAT_WORD(t,n&~(0x007fffff>>k)); + n = ((n&0x007fffff)|0x00800000)>>(23-k); + if(j<0) n = -n; + p_h -= t; + } + t = p_l+p_h; + GET_FLOAT_WORD(is,t); + SET_FLOAT_WORD(t,is&0xfffff000); + u = t*lg2_h; + v = (p_l-(t-p_h))*lg2+t*lg2_l; + z = u+v; + w = v-(z-u); + t = z*z; + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + r = (z*t1)/(t1-two)-(w+z*w); + z = one-(r-z); + GET_FLOAT_WORD(j,z); + j += (n<<23); + if((j>>23)<=0) z = __scalbnf(z,n); /* subnormal output */ + else SET_FLOAT_WORD(z,j); + return s*z; +} diff --git a/sysdeps/ieee754/flt-32/e_rem_pio2f.c b/sysdeps/ieee754/flt-32/e_rem_pio2f.c new file mode 100644 index 0000000..4b8c446 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_rem_pio2f.c @@ -0,0 +1,196 @@ +/* e_rem_pio2f.c -- float version of e_rem_pio2.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_rem_pio2f.c,v 1.5 1995/05/10 20:46:03 jtc Exp $"; +#endif + +/* __ieee754_rem_pio2f(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2f() + */ + +#include "math.h" +#include "math_private.h" + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ +#ifdef __STDC__ +static const int32_t two_over_pi[] = { +#else +static int32_t two_over_pi[] = { +#endif +0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC, +0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, +0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63, +0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A, +0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09, +0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, +0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44, +0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41, +0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C, +0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, +0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11, +0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF, +0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E, +0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, +0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92, +0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08, +0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0, +0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, +0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85, +0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80, +0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA, +0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B, +}; + +/* This array is like the one in e_rem_pio2.c, but the numbers are + single precision and the last 8 bits are forced to 0. */ +#ifdef __STDC__ +static const int32_t npio2_hw[] = { +#else +static int32_t npio2_hw[] = { +#endif +0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00, +0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00, +0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100, +0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00, +0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00, +0x4242c700, 0x42490f00 +}; + +/* + * invpio2: 24 bits of 2/pi + * pio2_1: first 17 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 17 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 17 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +#ifdef __STDC__ +static const float +#else +static float +#endif +zero = 0.0000000000e+00, /* 0x00000000 */ +half = 5.0000000000e-01, /* 0x3f000000 */ +two8 = 2.5600000000e+02, /* 0x43800000 */ +invpio2 = 6.3661980629e-01, /* 0x3f22f984 */ +pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */ +pio2_1t = 1.0804334124e-05, /* 0x37354443 */ +pio2_2 = 1.0804273188e-05, /* 0x37354400 */ +pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */ +pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */ +pio2_3t = 6.1232342629e-17; /* 0x248d3132 */ + +#ifdef __STDC__ + int32_t __ieee754_rem_pio2f(float x, float *y) +#else + int32_t __ieee754_rem_pio2f(x,y) + float x,y[]; +#endif +{ + float z,w,t,r,fn; + float tx[3]; + int32_t e0,i,j,nx,n,ix,hx; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ + {y[0] = x; y[1] = 0; return 0;} + if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ + if(hx>0) { + z = x - pio2_1; + if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ + y[0] = z - pio2_1t; + y[1] = (z-y[0])-pio2_1t; + } else { /* near pi/2, use 24+24+24 bit pi */ + z -= pio2_2; + y[0] = z - pio2_2t; + y[1] = (z-y[0])-pio2_2t; + } + return 1; + } else { /* negative x */ + z = x + pio2_1; + if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ + y[0] = z + pio2_1t; + y[1] = (z-y[0])+pio2_1t; + } else { /* near pi/2, use 24+24+24 bit pi */ + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z-y[0])+pio2_2t; + } + return -1; + } + } + if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */ + t = fabsf(x); + n = (int32_t) (t*invpio2+half); + fn = (float)n; + r = t-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 40 bit */ + if(n<32&&(int32_t)(ix&0xffffff00)!=npio2_hw[n-1]) { + y[0] = r-w; /* quick check no cancellation */ + } else { + u_int32_t high; + j = ix>>23; + y[0] = r-w; + GET_FLOAT_WORD(high,y[0]); + i = j-((high>>23)&0xff); + if(i>8) { /* 2nd iteration needed, good to 57 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + GET_FLOAT_WORD(high,y[0]); + i = j-((high>>23)&0xff); + if(i>25) { /* 3rd iteration need, 74 bits acc */ + t = r; /* will cover all possible cases */ + w = fn*pio2_3; + r = t-w; + w = fn*pio2_3t-((t-r)-w); + y[0] = r-w; + } + } + } + y[1] = (r-y[0])-w; + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + else return n; + } + /* + * all other (large) arguments + */ + if(ix>=0x7f800000) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-7) */ + e0 = (ix>>23)-134; /* e0 = ilogb(z)-7; */ + SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23))); + for(i=0;i<2;i++) { + tx[i] = (float)((int32_t)(z)); + z = (z-tx[i])*two8; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi); + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + return n; +} diff --git a/sysdeps/ieee754/flt-32/e_remainderf.c b/sysdeps/ieee754/flt-32/e_remainderf.c new file mode 100644 index 0000000..90d0d36 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_remainderf.c @@ -0,0 +1,73 @@ +/* e_remainderf.c -- float version of e_remainder.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_remainderf.c,v 1.4 1995/05/10 20:46:08 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float zero = 0.0; +#else +static float zero = 0.0; +#endif + + +#ifdef __STDC__ + float __ieee754_remainderf(float x, float p) +#else + float __ieee754_remainderf(x,p) + float x,p; +#endif +{ + int32_t hx,hp; + u_int32_t sx; + float p_half; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hp,p); + sx = hx&0x80000000; + hp &= 0x7fffffff; + hx &= 0x7fffffff; + + /* purge off exception values */ + if(hp==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7f800000)|| /* x not finite */ + ((hp>0x7f800000))) /* p is NaN */ + return (x*p)/(x*p); + + + if (hp<=0x7effffff) x = __ieee754_fmodf(x,p+p); /* now x < 2p */ + if ((hx-hp)==0) return zero*x; + x = fabsf(x); + p = fabsf(p); + if (hp<0x01000000) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = (float)0.5*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_FLOAT_WORD(hx,x); + SET_FLOAT_WORD(x,hx^sx); + return x; +} diff --git a/sysdeps/ieee754/flt-32/e_sinhf.c b/sysdeps/ieee754/flt-32/e_sinhf.c new file mode 100644 index 0000000..045f6f1 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_sinhf.c @@ -0,0 +1,68 @@ +/* e_sinhf.c -- float version of e_sinh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_sinhf.c,v 1.4 1995/05/10 20:46:15 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float one = 1.0, shuge = 1.0e37; +#else +static float one = 1.0, shuge = 1.0e37; +#endif + +#ifdef __STDC__ + float __ieee754_sinhf(float x) +#else + float __ieee754_sinhf(x) + float x; +#endif +{ + float t,w,h; + int32_t ix,jx; + + GET_FLOAT_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x41b00000) { /* |x|<22 */ + if (ix<0x31800000) /* |x|<2**-28 */ + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + t = __expm1f(fabsf(x)); + if(ix<0x3f800000) return h*((float)2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x42b17180) return h*__ieee754_expf(fabsf(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x42b2d4fc) { + w = __ieee754_expf((float)0.5*fabsf(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; +} diff --git a/sysdeps/ieee754/flt-32/e_sqrtf.c b/sysdeps/ieee754/flt-32/e_sqrtf.c new file mode 100644 index 0000000..7648ef4 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_sqrtf.c @@ -0,0 +1,97 @@ +/* e_sqrtf.c -- float version of e_sqrt.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_sqrtf.c,v 1.4 1995/05/10 20:46:19 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float one = 1.0, tiny=1.0e-30; +#else +static float one = 1.0, tiny=1.0e-30; +#endif + +#ifdef __STDC__ + float __ieee754_sqrtf(float x) +#else + float __ieee754_sqrtf(x) + float x; +#endif +{ + float z; + int32_t sign = (int)0x80000000; + int32_t ix,s,q,m,t,i; + u_int32_t r; + + GET_FLOAT_WORD(ix,x); + + /* take care of Inf and NaN */ + if((ix&0x7f800000)==0x7f800000) { + return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf + sqrt(-inf)=sNaN */ + } + /* take care of zero */ + if(ix<=0) { + if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */ + else if(ix<0) + return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + } + /* normalize x */ + m = (ix>>23); + if(m==0) { /* subnormal x */ + for(i=0;(ix&0x00800000)==0;i++) ix<<=1; + m -= i-1; + } + m -= 127; /* unbias exponent */ + ix = (ix&0x007fffff)|0x00800000; + if(m&1) /* odd m, double x to make it even */ + ix += ix; + m >>= 1; /* m = [m/2] */ + + /* generate sqrt(x) bit by bit */ + ix += ix; + q = s = 0; /* q = sqrt(x) */ + r = 0x01000000; /* r = moving bit from right to left */ + + while(r!=0) { + t = s+r; + if(t<=ix) { + s = t+r; + ix -= t; + q += r; + } + ix += ix; + r>>=1; + } + + /* use floating add to find out rounding direction */ + if(ix!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (z>one) + q += 2; + else + q += (q&1); + } + } + ix = (q>>1)+0x3f000000; + ix += (m <<23); + SET_FLOAT_WORD(z,ix); + return z; +} diff --git a/sysdeps/ieee754/flt-32/k_cosf.c b/sysdeps/ieee754/flt-32/k_cosf.c new file mode 100644 index 0000000..b232cab --- /dev/null +++ b/sysdeps/ieee754/flt-32/k_cosf.c @@ -0,0 +1,64 @@ +/* k_cosf.c -- float version of k_cos.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_cosf.c,v 1.4 1995/05/10 20:46:23 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +one = 1.0000000000e+00, /* 0x3f800000 */ +C1 = 4.1666667908e-02, /* 0x3d2aaaab */ +C2 = -1.3888889225e-03, /* 0xbab60b61 */ +C3 = 2.4801587642e-05, /* 0x37d00d01 */ +C4 = -2.7557314297e-07, /* 0xb493f27c */ +C5 = 2.0875723372e-09, /* 0x310f74f6 */ +C6 = -1.1359647598e-11; /* 0xad47d74e */ + +#ifdef __STDC__ + float __kernel_cosf(float x, float y) +#else + float __kernel_cosf(x, y) + float x,y; +#endif +{ + float a,hz,z,r,qx; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* ix = |x|'s high word*/ + if(ix<0x32000000) { /* if x < 2**27 */ + if(((int)x)==0) return one; /* generate inexact */ + } + z = x*x; + r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); + if(ix < 0x3e99999a) /* if |x| < 0.3 */ + return one - ((float)0.5*z - (z*r - x*y)); + else { + if(ix > 0x3f480000) { /* x > 0.78125 */ + qx = (float)0.28125; + } else { + SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */ + } + hz = (float)0.5*z-qx; + a = one-qx; + return a - (hz - (z*r-x*y)); + } +} diff --git a/sysdeps/ieee754/flt-32/k_rem_pio2f.c b/sysdeps/ieee754/flt-32/k_rem_pio2f.c new file mode 100644 index 0000000..2783480 --- /dev/null +++ b/sysdeps/ieee754/flt-32/k_rem_pio2f.c @@ -0,0 +1,213 @@ +/* k_rem_pio2f.c -- float version of k_rem_pio2.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_rem_pio2f.c,v 1.4 1995/05/10 20:46:28 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +/* In the float version, the input parameter x contains 8 bit + integers, not 24 bit integers. 113 bit precision is not supported. */ + +#ifdef __STDC__ +static const int init_jk[] = {4,7,9}; /* initial value for jk */ +#else +static int init_jk[] = {4,7,9}; +#endif + +#ifdef __STDC__ +static const float PIo2[] = { +#else +static float PIo2[] = { +#endif + 1.5703125000e+00, /* 0x3fc90000 */ + 4.5776367188e-04, /* 0x39f00000 */ + 2.5987625122e-05, /* 0x37da0000 */ + 7.5437128544e-08, /* 0x33a20000 */ + 6.0026650317e-11, /* 0x2e840000 */ + 7.3896444519e-13, /* 0x2b500000 */ + 5.3845816694e-15, /* 0x27c20000 */ + 5.6378512969e-18, /* 0x22d00000 */ + 8.3009228831e-20, /* 0x1fc40000 */ + 3.2756352257e-22, /* 0x1bc60000 */ + 6.3331015649e-25, /* 0x17440000 */ +}; + +#ifdef __STDC__ +static const float +#else +static float +#endif +zero = 0.0, +one = 1.0, +two8 = 2.5600000000e+02, /* 0x43800000 */ +twon8 = 3.9062500000e-03; /* 0x3b800000 */ + +#ifdef __STDC__ + int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2) +#else + int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2) + float x[], y[]; int e0,nx,prec; int32_t ipio2[]; +#endif +{ + int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; + float z,fw,f[20],fq[20],q[20]; + + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + jx = nx-1; + jv = (e0-3)/8; if(jv<0) jv=0; + q0 = e0-8*(jv+1); + + /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ + j = jv-jx; m = jx+jk; + for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + for (i=0;i<=jk;i++) { + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; + } + + jz = jk; +recompute: + /* distill q[] into iq[] reversingly */ + for(i=0,j=jz,z=q[jz];j>0;i++,j--) { + fw = (float)((int32_t)(twon8* z)); + iq[i] = (int32_t)(z-two8*fw); + z = q[j-1]+fw; + } + + /* compute n */ + z = __scalbnf(z,q0); /* actual value of z */ + z -= (float)8.0*__floorf(z*(float)0.125); /* trim off integer >= 8 */ + n = (int32_t) z; + z -= (float)n; + ih = 0; + if(q0>0) { /* need iq[jz-1] to determine n */ + i = (iq[jz-1]>>(8-q0)); n += i; + iq[jz-1] -= i<<(8-q0); + ih = iq[jz-1]>>(7-q0); + } + else if(q0==0) ih = iq[jz-1]>>8; + else if(z>=(float)0.5) ih=2; + + if(ih>0) { /* q > 0.5 */ + n += 1; carry = 0; + for(i=0;i<jz ;i++) { /* compute 1-q */ + j = iq[i]; + if(carry==0) { + if(j!=0) { + carry = 1; iq[i] = 0x100- j; + } + } else iq[i] = 0xff - j; + } + if(q0>0) { /* rare case: chance is 1 in 12 */ + switch(q0) { + case 1: + iq[jz-1] &= 0x7f; break; + case 2: + iq[jz-1] &= 0x3f; break; + } + } + if(ih==2) { + z = one - z; + if(carry!=0) z -= __scalbnf(one,q0); + } + } + + /* check if recomputation is needed */ + if(z==zero) { + j = 0; + for (i=jz-1;i>=jk;i--) j |= iq[i]; + if(j==0) { /* need recomputation */ + for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ + + for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ + f[jx+i] = (float) ipio2[jv+i]; + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + jz += k; + goto recompute; + } + } + + /* chop off zero terms */ + if(z==(float)0.0) { + jz -= 1; q0 -= 8; + while(iq[jz]==0) { jz--; q0-=8;} + } else { /* break z into 8-bit if necessary */ + z = __scalbnf(z,-q0); + if(z>=two8) { + fw = (float)((int32_t)(twon8*z)); + iq[jz] = (int32_t)(z-two8*fw); + jz += 1; q0 += 8; + iq[jz] = (int32_t) fw; + } else iq[jz] = (int32_t) z ; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = __scalbnf(one,q0); + for(i=jz;i>=0;i--) { + q[i] = fw*(float)iq[i]; fw*=twon8; + } + + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for(i=jz;i>=0;i--) { + for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; + fq[jz-i] = fw; + } + + /* compress fq[] into y[] */ + switch(prec) { + case 0: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + break; + case 1: + case 2: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + fw = fq[0]-fw; + for (i=1;i<=jz;i++) fw += fq[i]; + y[1] = (ih==0)? fw: -fw; + break; + case 3: /* painful */ + for (i=jz;i>0;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (i=jz;i>1;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; + if(ih==0) { + y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; + } else { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n&7; +} diff --git a/sysdeps/ieee754/flt-32/k_sinf.c b/sysdeps/ieee754/flt-32/k_sinf.c new file mode 100644 index 0000000..4fec15e --- /dev/null +++ b/sysdeps/ieee754/flt-32/k_sinf.c @@ -0,0 +1,54 @@ +/* k_sinf.c -- float version of k_sin.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_sinf.c,v 1.4 1995/05/10 20:46:33 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +half = 5.0000000000e-01,/* 0x3f000000 */ +S1 = -1.6666667163e-01, /* 0xbe2aaaab */ +S2 = 8.3333337680e-03, /* 0x3c088889 */ +S3 = -1.9841270114e-04, /* 0xb9500d01 */ +S4 = 2.7557314297e-06, /* 0x3638ef1b */ +S5 = -2.5050759689e-08, /* 0xb2d72f34 */ +S6 = 1.5896910177e-10; /* 0x2f2ec9d3 */ + +#ifdef __STDC__ + float __kernel_sinf(float x, float y, int iy) +#else + float __kernel_sinf(x, y, iy) + float x,y; int iy; /* iy=0 if y is zero */ +#endif +{ + float z,r,v; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* high word of x */ + if(ix<0x32000000) /* |x| < 2**-27 */ + {if((int)x==0) return x;} /* generate inexact */ + z = x*x; + v = z*x; + r = S2+z*(S3+z*(S4+z*(S5+z*S6))); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +} diff --git a/sysdeps/ieee754/flt-32/k_tanf.c b/sysdeps/ieee754/flt-32/k_tanf.c new file mode 100644 index 0000000..eb1a670 --- /dev/null +++ b/sysdeps/ieee754/flt-32/k_tanf.c @@ -0,0 +1,101 @@ +/* k_tanf.c -- float version of k_tan.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_tanf.c,v 1.4 1995/05/10 20:46:39 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" +#ifdef __STDC__ +static const float +#else +static float +#endif +one = 1.0000000000e+00, /* 0x3f800000 */ +pio4 = 7.8539812565e-01, /* 0x3f490fda */ +pio4lo= 3.7748947079e-08, /* 0x33222168 */ +T[] = { + 3.3333334327e-01, /* 0x3eaaaaab */ + 1.3333334029e-01, /* 0x3e088889 */ + 5.3968254477e-02, /* 0x3d5d0dd1 */ + 2.1869488060e-02, /* 0x3cb327a4 */ + 8.8632395491e-03, /* 0x3c11371f */ + 3.5920790397e-03, /* 0x3b6b6916 */ + 1.4562094584e-03, /* 0x3abede48 */ + 5.8804126456e-04, /* 0x3a1a26c8 */ + 2.4646313977e-04, /* 0x398137b9 */ + 7.8179444245e-05, /* 0x38a3f445 */ + 7.1407252108e-05, /* 0x3895c07a */ + -1.8558637748e-05, /* 0xb79bae5f */ + 2.5907305826e-05, /* 0x37d95384 */ +}; + +#ifdef __STDC__ + float __kernel_tanf(float x, float y, int iy) +#else + float __kernel_tanf(x, y, iy) + float x,y; int iy; +#endif +{ + float z,r,v,w,s; + int32_t ix,hx; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; /* high word of |x| */ + if(ix<0x31800000) /* x < 2**-28 */ + {if((int)x==0) { /* generate inexact */ + if((ix|(iy+1))==0) return one/fabsf(x); + else return (iy==1)? x: -one/x; + } + } + if(ix>=0x3f2ca140) { /* |x|>=0.6744 */ + if(hx<0) {x = -x; y = -y;} + z = pio4-x; + w = pio4lo-y; + x = z+w; y = 0.0; + } + z = x*x; + w = z*z; + /* Break x^5*(T[1]+x^2*T[2]+...) into + * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + + * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) + */ + r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); + v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); + s = z*x; + r = y + z*(s*(r+v)+y); + r += T[0]*s; + w = x+r; + if(ix>=0x3f2ca140) { + v = (float)iy; + return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r))); + } + if(iy==1) return w; + else { /* if allow error up to 2 ulp, + simply return -1.0/(x+r) here */ + /* compute -1.0/(x+r) accurately */ + float a,t; + int32_t i; + z = w; + GET_FLOAT_WORD(i,z); + SET_FLOAT_WORD(z,i&0xfffff000); + v = r-(z - x); /* z+v = r+x */ + t = a = -(float)1.0/w; /* a = -1.0/w */ + GET_FLOAT_WORD(i,t); + SET_FLOAT_WORD(t,i&0xfffff000); + s = (float)1.0+t*z; + return t+a*(s+t*v); + } +} diff --git a/sysdeps/ieee754/mpn2flt.c b/sysdeps/ieee754/flt-32/mpn2flt.c index a409b45..a409b45 100644 --- a/sysdeps/ieee754/mpn2flt.c +++ b/sysdeps/ieee754/flt-32/mpn2flt.c diff --git a/sysdeps/ieee754/flt-32/s_asinhf.c b/sysdeps/ieee754/flt-32/s_asinhf.c new file mode 100644 index 0000000..fac256d --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_asinhf.c @@ -0,0 +1,58 @@ +/* s_asinhf.c -- float version of s_asinh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_asinhf.c,v 1.5 1995/05/12 04:57:39 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +one = 1.0000000000e+00, /* 0x3F800000 */ +ln2 = 6.9314718246e-01, /* 0x3f317218 */ +huge= 1.0000000000e+30; + +#ifdef __STDC__ + float __asinhf(float x) +#else + float __asinhf(x) + float x; +#endif +{ + float t,w; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return x+x; /* x is inf or NaN */ + if(ix< 0x38000000) { /* |x|<2**-14 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x47000000) { /* |x| > 2**14 */ + w = __ieee754_logf(fabsf(x))+ln2; + } else if (ix>0x40000000) { /* 2**14 > |x| > 2.0 */ + t = fabsf(x); + w = __ieee754_logf((float)2.0*t+one/(__ieee754_sqrtf(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-14 */ + t = x*x; + w =__log1pf(fabsf(x)+t/(one+__ieee754_sqrtf(one+t))); + } + if(hx>0) return w; else return -w; +} +weak_alias (__asinhf, asinhf) diff --git a/sysdeps/ieee754/flt-32/s_atanf.c b/sysdeps/ieee754/flt-32/s_atanf.c new file mode 100644 index 0000000..a68933f --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_atanf.c @@ -0,0 +1,120 @@ +/* s_atanf.c -- float version of s_atan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_atanf.c,v 1.4 1995/05/10 20:46:47 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float atanhi[] = { +#else +static float atanhi[] = { +#endif + 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ + 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ + 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ + 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ +}; + +#ifdef __STDC__ +static const float atanlo[] = { +#else +static float atanlo[] = { +#endif + 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */ + 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */ + 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */ + 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */ +}; + +#ifdef __STDC__ +static const float aT[] = { +#else +static float aT[] = { +#endif + 3.3333334327e-01, /* 0x3eaaaaaa */ + -2.0000000298e-01, /* 0xbe4ccccd */ + 1.4285714924e-01, /* 0x3e124925 */ + -1.1111110449e-01, /* 0xbde38e38 */ + 9.0908870101e-02, /* 0x3dba2e6e */ + -7.6918758452e-02, /* 0xbd9d8795 */ + 6.6610731184e-02, /* 0x3d886b35 */ + -5.8335702866e-02, /* 0xbd6ef16b */ + 4.9768779427e-02, /* 0x3d4bda59 */ + -3.6531571299e-02, /* 0xbd15a221 */ + 1.6285819933e-02, /* 0x3c8569d7 */ +}; + +#ifdef __STDC__ + static const float +#else + static float +#endif +one = 1.0, +huge = 1.0e30; + +#ifdef __STDC__ + float __atanf(float x) +#else + float __atanf(x) + float x; +#endif +{ + float w,s1,s2,z; + int32_t ix,hx,id; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x50800000) { /* if |x| >= 2^34 */ + if(ix>0x7f800000) + return x+x; /* NaN */ + if(hx>0) return atanhi[3]+atanlo[3]; + else return -atanhi[3]-atanlo[3]; + } if (ix < 0x3ee00000) { /* |x| < 0.4375 */ + if (ix < 0x31000000) { /* |x| < 2^-29 */ + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabsf(x); + if (ix < 0x3f980000) { /* |x| < 1.1875 */ + if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */ + id = 0; x = ((float)2.0*x-one)/((float)2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (ix < 0x401c0000) { /* |x| < 2.4375 */ + id = 2; x = (x-(float)1.5)/(one+(float)1.5*x); + } else { /* 2.4375 <= |x| < 2^66 */ + id = 3; x = -(float)1.0/x; + } + }} + /* end of argument reduction */ + z = x*x; + w = z*z; + /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ + s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); + s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (hx<0)? -z:z; + } +} +weak_alias (__atanf, atanf) diff --git a/sysdeps/ieee754/flt-32/s_cbrtf.c b/sysdeps/ieee754/flt-32/s_cbrtf.c new file mode 100644 index 0000000..fa0fef9 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_cbrtf.c @@ -0,0 +1,64 @@ +/* Compute cubic root of float value. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Dirk Alboth <dirka@uni-paderborn.de> and + Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include "math.h" +#include "math_private.h" + + +#define CBRT2 1.2599210498948731648 /* 2^(1/3) */ +#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */ + +static const double factor[5] = +{ + 1.0 / SQR_CBRT2, + 1.0 / CBRT2, + 1.0, + CBRT2, + SQR_CBRT2 +}; + + +float +__cbrtf (float x) +{ + float xm, ym, u, t2; + int xe; + + /* Reduce X. XM now is an range 1.0 to 0.5. */ + xm = __frexpf (fabsf (x), &xe); + + /* If X is not finite or is null return it (with raising exceptions + if necessary. + Note: *Our* version of `frexp' sets XE to zero if the argument is + Inf or NaN. This is not portable but faster. */ + if (xe == 0 && fpclassify (x) <= FP_ZERO) + return x + x; + + u = (0.492659620528969547 + (0.697570460207922770 + - 0.191502161678719066 * xm) * xm); + + t2 = u * u * u; + + ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3]; + + return __ldexpf (x > 0.0 ? ym : -ym, xe / 3); +} +weak_alias (__cbrtf, cbrtf) diff --git a/sysdeps/ieee754/flt-32/s_ceilf.c b/sysdeps/ieee754/flt-32/s_ceilf.c new file mode 100644 index 0000000..29ccadb --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_ceilf.c @@ -0,0 +1,62 @@ +/* s_ceilf.c -- float version of s_ceil.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_ceilf.c,v 1.4 1995/05/10 20:46:55 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float huge = 1.0e30; +#else +static float huge = 1.0e30; +#endif + +#ifdef __STDC__ + float __ceilf(float x) +#else + float __ceilf(x) + float x; +#endif +{ + int32_t i0,j0; + u_int32_t i; + + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;} + else if(i0!=0) { i0=0x3f800000;} + } + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} +weak_alias (__ceilf, ceilf) diff --git a/sysdeps/ieee754/flt-32/s_copysignf.c b/sysdeps/ieee754/flt-32/s_copysignf.c new file mode 100644 index 0000000..a4e84e5 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_copysignf.c @@ -0,0 +1,42 @@ +/* s_copysignf.c -- float version of s_copysign.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_copysignf.c,v 1.4 1995/05/10 20:46:59 jtc Exp $"; +#endif + +/* + * copysignf(float x, float y) + * copysignf(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + float __copysignf(float x, float y) +#else + float __copysignf(x,y) + float x,y; +#endif +{ + u_int32_t ix,iy; + GET_FLOAT_WORD(ix,x); + GET_FLOAT_WORD(iy,y); + SET_FLOAT_WORD(x,(ix&0x7fffffff)|(iy&0x80000000)); + return x; +} +weak_alias (__copysignf, copysignf) diff --git a/sysdeps/ieee754/flt-32/s_cosf.c b/sysdeps/ieee754/flt-32/s_cosf.c new file mode 100644 index 0000000..86c59d4 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_cosf.c @@ -0,0 +1,60 @@ +/* s_cosf.c -- float version of s_cos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_cosf.c,v 1.4 1995/05/10 20:47:03 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float one=1.0; +#else +static float one=1.0; +#endif + +#ifdef __STDC__ + float __cosf(float x) +#else + float __cosf(x) + float x; +#endif +{ + float y[2],z=0.0; + int32_t n,ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fd8) return __kernel_cosf(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,y); + switch(n&3) { + case 0: return __kernel_cosf(y[0],y[1]); + case 1: return -__kernel_sinf(y[0],y[1],1); + case 2: return -__kernel_cosf(y[0],y[1]); + default: + return __kernel_sinf(y[0],y[1],1); + } + } +} +weak_alias (__cosf, cosf) diff --git a/sysdeps/ieee754/flt-32/s_erff.c b/sysdeps/ieee754/flt-32/s_erff.c new file mode 100644 index 0000000..774714c --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_erff.c @@ -0,0 +1,225 @@ +/* s_erff.c -- float version of s_erf.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_erff.c,v 1.4 1995/05/10 20:47:07 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +tiny = 1e-30, +half= 5.0000000000e-01, /* 0x3F000000 */ +one = 1.0000000000e+00, /* 0x3F800000 */ +two = 2.0000000000e+00, /* 0x40000000 */ + /* c = (subfloat)0.84506291151 */ +erx = 8.4506291151e-01, /* 0x3f58560b */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +efx = 1.2837916613e-01, /* 0x3e0375d4 */ +efx8= 1.0270333290e+00, /* 0x3f8375d4 */ +pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ +pp1 = -3.2504209876e-01, /* 0xbea66beb */ +pp2 = -2.8481749818e-02, /* 0xbce9528f */ +pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ +pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ +qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ +qq2 = 6.5022252500e-02, /* 0x3d852a63 */ +qq3 = 5.0813062117e-03, /* 0x3ba68116 */ +qq4 = 1.3249473704e-04, /* 0x390aee49 */ +qq5 = -3.9602282413e-06, /* 0xb684e21a */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ +pa1 = 4.1485610604e-01, /* 0x3ed46805 */ +pa2 = -3.7220788002e-01, /* 0xbebe9208 */ +pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ +pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ +pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ +pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ +qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ +qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ +qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ +qa4 = 1.2617121637e-01, /* 0x3e013307 */ +qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ +qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +ra0 = -9.8649440333e-03, /* 0xbc21a093 */ +ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ +ra2 = -1.0558626175e+01, /* 0xc128f022 */ +ra3 = -6.2375331879e+01, /* 0xc2798057 */ +ra4 = -1.6239666748e+02, /* 0xc322658c */ +ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ +ra6 = -8.1287437439e+01, /* 0xc2a2932b */ +ra7 = -9.8143291473e+00, /* 0xc11d077e */ +sa1 = 1.9651271820e+01, /* 0x419d35ce */ +sa2 = 1.3765776062e+02, /* 0x4309a863 */ +sa3 = 4.3456588745e+02, /* 0x43d9486f */ +sa4 = 6.4538726807e+02, /* 0x442158c9 */ +sa5 = 4.2900814819e+02, /* 0x43d6810b */ +sa6 = 1.0863500214e+02, /* 0x42d9451f */ +sa7 = 6.5702495575e+00, /* 0x40d23f7c */ +sa8 = -6.0424413532e-02, /* 0xbd777f97 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ +rb0 = -9.8649431020e-03, /* 0xbc21a092 */ +rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ +rb2 = -1.7757955551e+01, /* 0xc18e104b */ +rb3 = -1.6063638306e+02, /* 0xc320a2ea */ +rb4 = -6.3756646729e+02, /* 0xc41f6441 */ +rb5 = -1.0250950928e+03, /* 0xc480230b */ +rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ +sb1 = 3.0338060379e+01, /* 0x41f2b459 */ +sb2 = 3.2579251099e+02, /* 0x43a2e571 */ +sb3 = 1.5367296143e+03, /* 0x44c01759 */ +sb4 = 3.1998581543e+03, /* 0x4547fdbb */ +sb5 = 2.5530502930e+03, /* 0x451f90ce */ +sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ +sb7 = -2.2440952301e+01; /* 0xc1b38712 */ + +#ifdef __STDC__ + float __erff(float x) +#else + float __erff(x) + float x; +#endif +{ + int32_t hx,ix,i; + float R,S,P,Q,s,y,z,r; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) { /* erf(nan)=nan */ + i = ((u_int32_t)hx>>31)<<1; + return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */ + } + + if(ix < 0x3f580000) { /* |x|<0.84375 */ + if(ix < 0x31800000) { /* |x|<2**-28 */ + if (ix < 0x04000000) + /*avoid underflow */ + return (float)0.125*((float)8.0*x+efx8*x); + return x + efx*x; + } + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + return x + x*y; + } + if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ + s = fabsf(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) return erx + P/Q; else return -erx - P/Q; + } + if (ix >= 0x40c00000) { /* inf>|x|>=6 */ + if(hx>=0) return one-tiny; else return tiny-one; + } + x = fabsf(x); + s = one/(x*x); + if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/0.35 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(z,ix&0xfffff000); + r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S); + if(hx>=0) return one-r/x; else return r/x-one; +} +weak_alias (__erff, erff) + +#ifdef __STDC__ + float __erfcf(float x) +#else + float __erfcf(x) + float x; +#endif +{ + int32_t hx,ix; + float R,S,P,Q,s,y,z,r; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (float)(((u_int32_t)hx>>31)<<1)+one/x; + } + + if(ix < 0x3f580000) { /* |x|<0.84375 */ + if(ix < 0x23800000) /* |x|<2**-56 */ + return one-x; + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + if(hx < 0x3e800000) { /* x<1/4 */ + return one-(x+x*y); + } else { + r = x*y; + r += (x-half); + return half - r ; + } + } + if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ + s = fabsf(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) { + z = one-erx; return z - P/Q; + } else { + z = erx+P/Q; return one+z; + } + } + if (ix < 0x41e00000) { /* |x|<28 */ + x = fabsf(x); + s = one/(x*x); + if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/.35 ~ 2.857143 */ + if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(z,ix&0xfffff000); + r = __ieee754_expf(-z*z-(float)0.5625)* + __ieee754_expf((z-x)*(z+x)+R/S); + if(hx>0) return r/x; else return two-r/x; + } else { + if(hx>0) return tiny*tiny; else return two-tiny; + } +} +weak_alias (__erfcf, erfcf) diff --git a/sysdeps/ieee754/flt-32/s_exp2f.c b/sysdeps/ieee754/flt-32/s_exp2f.c new file mode 100644 index 0000000..8229885 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_exp2f.c @@ -0,0 +1,127 @@ +/* Single-precision floating point 2^x. + Copyright (C) 1997, 1998 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +/* The basic design here is from + Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical + Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft., + 17 (1), March 1991, pp. 26-45. + It has been slightly modified to compute 2^x instead of e^x, and for + single-precision. + */ +#ifndef _GNU_SOURCE +# define _GNU_SOURCE +#endif +#include <float.h> +#include <ieee754.h> +#include <math.h> +#include <fenv.h> +#include <inttypes.h> +#include <math_private.h> + +#include "t_exp2f.h" + +static const volatile float TWOM100 = 7.88860905e-31; +static const volatile float TWO127 = 1.7014118346e+38; + +float +__ieee754_exp2f (float x) +{ + static const float himark = (float) FLT_MAX_EXP; + static const float lomark = (float) (FLT_MIN_EXP - FLT_MANT_DIG - 1) - 1.0; + + /* Check for usual case. */ + if (isless (x, himark) && isgreater (x, lomark)) + { + static const float THREEp14 = 49152.0; + int tval, unsafe; + float rx, x22, result; + union ieee754_float ex2_u, scale_u; + fenv_t oldenv; + + feholdexcept (&oldenv); +#ifdef FE_TONEAREST + /* If we don't have this, it's too bad. */ + fesetround (FE_TONEAREST); +#endif + + /* 1. Argument reduction. + Choose integers ex, -128 <= t < 128, and some real + -1/512 <= x1 <= 1/512 so that + x = ex + t/512 + x1. + + First, calculate rx = ex + t/256. */ + rx = x + THREEp14; + rx -= THREEp14; + x -= rx; /* Compute x=x1. */ + /* Compute tval = (ex*256 + t)+128. + Now, t = (tval mod 256)-128 and ex=tval/256 [that's mod, NOT %; and + /-round-to-nearest not the usual c integer /]. */ + tval = (int) (rx * 256.0f + 128.0f); + + /* 2. Adjust for accurate table entry. + Find e so that + x = ex + t/256 + e + x2 + where -7e-4 < e < 7e-4, and + (float)(2^(t/256+e)) + is accurate to one part in 2^-64. */ + + /* 'tval & 255' is the same as 'tval%256' except that it's always + positive. + Compute x = x2. */ + x -= __exp2f_deltatable[tval & 255]; + + /* 3. Compute ex2 = 2^(t/255+e+ex). */ + ex2_u.f = __exp2f_atable[tval & 255]; + tval >>= 8; + unsafe = abs(tval) >= -FLT_MIN_EXP - 1; + ex2_u.ieee.exponent += tval >> unsafe; + scale_u.f = 1.0; + scale_u.ieee.exponent += tval - (tval >> unsafe); + + /* 4. Approximate 2^x2 - 1, using a second-degree polynomial, + with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14] + less than 1.3e-10. */ + + x22 = (.24022656679f * x + .69314736128f) * ex2_u.f; + + /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */ + fesetenv (&oldenv); + + result = x22 * x + ex2_u.f; + + if (!unsafe) + return result; + else + return result * scale_u.f; + } + /* Exceptional cases: */ + else if (isless (x, himark)) + { + if (__isinff (x)) + /* e^-inf == 0, with no error. */ + return 0; + else + /* Underflow */ + return TWOM100 * TWOM100; + } + else + /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ + return TWO127*x; +} diff --git a/sysdeps/ieee754/flt-32/s_expm1f.c b/sysdeps/ieee754/flt-32/s_expm1f.c new file mode 100644 index 0000000..375e334 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_expm1f.c @@ -0,0 +1,135 @@ +/* s_expm1f.c -- float version of s_expm1.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_expm1f.c,v 1.5 1995/05/10 20:47:11 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +static const volatile float huge = 1.0e+30, tiny = 1.0e-30; + +#ifdef __STDC__ +static const float +#else +static float +#endif +one = 1.0, +o_threshold = 8.8721679688e+01,/* 0x42b17180 */ +ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ +ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ +invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ + /* scaled coefficients related to expm1 */ +Q1 = -3.3333335072e-02, /* 0xbd088889 */ +Q2 = 1.5873016091e-03, /* 0x3ad00d01 */ +Q3 = -7.9365076090e-05, /* 0xb8a670cd */ +Q4 = 4.0082177293e-06, /* 0x36867e54 */ +Q5 = -2.0109921195e-07; /* 0xb457edbb */ + +#ifdef __STDC__ + float __expm1f(float x) +#else + float __expm1f(x) + float x; +#endif +{ + float y,hi,lo,c,t,e,hxs,hfx,r1; + int32_t k,xsb; + u_int32_t hx; + + GET_FLOAT_WORD(hx,x); + xsb = hx&0x80000000; /* sign bit of x */ + if(xsb==0) y=x; else y= -x; /* y = |x| */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out huge and non-finite argument */ + if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ + if(hx >= 0x42b17218) { /* if |x|>=88.721... */ + if(hx>0x7f800000) + return x+x; /* NaN */ + if(hx==0x7f800000) + return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ + if(x > o_threshold) return huge*huge; /* overflow */ + } + if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ + if(x+tiny<(float)0.0) /* raise inexact */ + return tiny-one; /* return -1 */ + } + } + + /* argument reduction */ + if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ + if(xsb==0) + {hi = x - ln2_hi; lo = ln2_lo; k = 1;} + else + {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} + } else { + k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); + t = k; + hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ + lo = t*ln2_lo; + } + x = hi - lo; + c = (hi-x)-lo; + } + else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ + t = huge+x; /* return x with inexact flags when x!=0 */ + return x - (t-(huge+x)); + } + else k = 0; + + /* x is now in primary range */ + hfx = (float)0.5*x; + hxs = x*hfx; + r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); + t = (float)3.0-r1*hfx; + e = hxs*((r1-t)/((float)6.0 - x*t)); + if(k==0) return x - (x*e-hxs); /* c is 0 */ + else { + e = (x*(e-c)-c); + e -= hxs; + if(k== -1) return (float)0.5*(x-e)-(float)0.5; + if(k==1) { + if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); + else return one+(float)2.0*(x-e); + } + if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ + int32_t i; + y = one-(e-x); + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + return y-one; + } + t = one; + if(k<23) { + int32_t i; + SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ + y = t-(e-x); + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + } else { + int32_t i; + SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ + y = x-(e+t); + y += one; + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + } + } + return y; +} +weak_alias (__expm1f, expm1f) diff --git a/sysdeps/ieee754/flt-32/s_fabsf.c b/sysdeps/ieee754/flt-32/s_fabsf.c new file mode 100644 index 0000000..6b14513 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_fabsf.c @@ -0,0 +1,39 @@ +/* s_fabsf.c -- float version of s_fabs.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_fabsf.c,v 1.4 1995/05/10 20:47:15 jtc Exp $"; +#endif + +/* + * fabsf(x) returns the absolute value of x. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + float __fabsf(float x) +#else + float __fabsf(x) + float x; +#endif +{ + u_int32_t ix; + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x7fffffff); + return x; +} +weak_alias (__fabsf, fabsf) diff --git a/sysdeps/ieee754/flt-32/s_finitef.c b/sysdeps/ieee754/flt-32/s_finitef.c new file mode 100644 index 0000000..baafc31 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_finitef.c @@ -0,0 +1,39 @@ +/* s_finitef.c -- float version of s_finite.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_finitef.c,v 1.4 1995/05/10 20:47:18 jtc Exp $"; +#endif + +/* + * finitef(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int __finitef(float x) +#else + int __finitef(x) + float x; +#endif +{ + int32_t ix; + GET_FLOAT_WORD(ix,x); + return (int)((u_int32_t)((ix&0x7fffffff)-0x7f800000)>>31); +} +weak_alias (__finitef, finitef) diff --git a/sysdeps/ieee754/flt-32/s_floorf.c b/sysdeps/ieee754/flt-32/s_floorf.c new file mode 100644 index 0000000..e8822b0 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_floorf.c @@ -0,0 +1,71 @@ +/* s_floorf.c -- float version of s_floor.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_floorf.c,v 1.4 1995/05/10 20:47:22 jtc Exp $"; +#endif + +/* + * floorf(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floorf(x). + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float huge = 1.0e30; +#else +static float huge = 1.0e30; +#endif + +#ifdef __STDC__ + float __floorf(float x) +#else + float __floorf(x) + float x; +#endif +{ + int32_t i0,j0; + u_int32_t i; + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=0;} + else if((i0&0x7fffffff)!=0) + { i0=0xbf800000;} + } + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} +weak_alias (__floorf, floorf) diff --git a/sysdeps/ieee754/flt-32/s_fpclassifyf.c b/sysdeps/ieee754/flt-32/s_fpclassifyf.c new file mode 100644 index 0000000..a6b35cf --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_fpclassifyf.c @@ -0,0 +1,42 @@ +/* Return classification value corresponding to argument. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +int +__fpclassifyf (float x) +{ + u_int32_t wx; + int retval = FP_NORMAL; + + GET_FLOAT_WORD (wx, x); + wx &= 0x7fffffff; + if (wx == 0) + retval = FP_ZERO; + else if (wx < 0x1000000) + retval = FP_SUBNORMAL; + else if (wx >= 0x7f800000) + retval = wx > 0x7f800000 ? FP_NAN : FP_INFINITE; + + return retval; +} diff --git a/sysdeps/ieee754/flt-32/s_frexpf.c b/sysdeps/ieee754/flt-32/s_frexpf.c new file mode 100644 index 0000000..a984457 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_frexpf.c @@ -0,0 +1,53 @@ +/* s_frexpf.c -- float version of s_frexp.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_frexpf.c,v 1.5 1995/05/10 20:47:26 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +two25 = 3.3554432000e+07; /* 0x4c000000 */ + +#ifdef __STDC__ + float __frexpf(float x, int *eptr) +#else + float __frexpf(x, eptr) + float x; int *eptr; +#endif +{ + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + *eptr = 0; + if(ix>=0x7f800000||(ix==0)) return x; /* 0,inf,nan */ + if (ix<0x00800000) { /* subnormal */ + x *= two25; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + *eptr = -25; + } + *eptr += (ix>>23)-126; + hx = (hx&0x807fffff)|0x3f000000; + *(int*)&x = hx; + return x; +} +weak_alias (__frexpf, frexpf) diff --git a/sysdeps/ieee754/flt-32/s_ilogbf.c b/sysdeps/ieee754/flt-32/s_ilogbf.c new file mode 100644 index 0000000..e652b93 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_ilogbf.c @@ -0,0 +1,44 @@ +/* s_ilogbf.c -- float version of s_ilogb.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_ilogbf.c,v 1.4 1995/05/10 20:47:31 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int __ilogbf(float x) +#else + int __ilogbf(x) + float x; +#endif +{ + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + hx &= 0x7fffffff; + if(hx<0x00800000) { + if(hx==0) + return FP_ILOGB0; /* ilogb(0) = FP_ILOGB0 */ + else /* subnormal x */ + for (ix = -126,hx<<=8; hx>0; hx<<=1) ix -=1; + return ix; + } + else if (hx<0x7f800000) return (hx>>23)-127; + else return FP_ILOGBNAN; +} +weak_alias (__ilogbf, ilogbf) diff --git a/sysdeps/ieee754/flt-32/s_isinff.c b/sysdeps/ieee754/flt-32/s_isinff.c new file mode 100644 index 0000000..efc0935 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_isinff.c @@ -0,0 +1,28 @@ +/* + * Written by J.T. Conklin <jtc@netbsd.org>. + * Public domain. + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_isinff.c,v 1.3 1995/05/11 23:20:21 jtc Exp $"; +#endif + +/* + * isinff(x) returns 1 if x is inf, -1 if x is -inf, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +int +__isinff (float x) +{ + int32_t ix,t; + GET_FLOAT_WORD(ix,x); + t = ix & 0x7fffffff; + t ^= 0x7f800000; + t |= -t; + return ~(t >> 31) & (ix >> 30); +} +weak_alias (__isinff, isinff) diff --git a/sysdeps/ieee754/flt-32/s_isnanf.c b/sysdeps/ieee754/flt-32/s_isnanf.c new file mode 100644 index 0000000..9ec412f --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_isnanf.c @@ -0,0 +1,41 @@ +/* s_isnanf.c -- float version of s_isnan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_isnanf.c,v 1.4 1995/05/10 20:47:38 jtc Exp $"; +#endif + +/* + * isnanf(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int __isnanf(float x) +#else + int __isnanf(x) + float x; +#endif +{ + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + ix = 0x7f800000 - ix; + return (int)(((u_int32_t)(ix))>>31); +} +weak_alias (__isnanf, isnanf) diff --git a/sysdeps/ieee754/flt-32/s_llrintf.c b/sysdeps/ieee754/flt-32/s_llrintf.c new file mode 100644 index 0000000..a812377 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_llrintf.c @@ -0,0 +1,78 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + +static const double two23[2] = +{ + 8.3886080000e+06, /* 0x4B000000 */ + -8.3886080000e+06, /* 0xCB000000 */ +}; + + +long long int +__llrintf (float x) +{ + int32_t j0; + u_int32_t i0; + volatile float w; + float t; + long long int result; + int sx; + + GET_FLOAT_WORD (i0, x); + + sx = i0 >> 31; + j0 = ((i0 >> 23) & 0xff) - 0x7f; + i0 &= 0x7fffff; + i0 |= 0x800000; + + if (j0 < (int32_t) (sizeof (long long int) * 8) - 1) + { + if (j0 < -1) + return 0; + else if (j0 >= 23) + result = (long long int) i0 << (j0 - 23); + else + { + w = two23[sx] + x; + t = w - two23[sx]; + GET_FLOAT_WORD (i0, t); + j0 = ((i0 >> 23) & 0xff) - 0x7f; + i0 &= 0x7fffff; + i0 |= 0x800000; + + result = i0 >> (23 - j0); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__llrintf, llrintf) diff --git a/sysdeps/ieee754/flt-32/s_llroundf.c b/sysdeps/ieee754/flt-32/s_llroundf.c new file mode 100644 index 0000000..9aad81f --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_llroundf.c @@ -0,0 +1,63 @@ +/* Round float value to long long int. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +long long int +__llroundf (float x) +{ + int32_t j0; + u_int32_t i; + long long int result; + int sign; + + GET_FLOAT_WORD (i, x); + j0 = ((i >> 23) & 0xff) - 0x7f; + sign = (i & 0x80000000) != 0 ? -1 : 1; + i &= 0x7fffff; + i |= 0x800000; + + if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else if (j0 >= 23) + result = (long long int) i << (j0 - 23); + else + { + i += 0x400000 >> j0; + + result = i >> (23 - j0); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long long int) x; + } + + return sign * result; +} + +weak_alias (__llroundf, llroundf) diff --git a/sysdeps/ieee754/flt-32/s_log1pf.c b/sysdeps/ieee754/flt-32/s_log1pf.c new file mode 100644 index 0000000..bd3d576 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_log1pf.c @@ -0,0 +1,115 @@ +/* s_log1pf.c -- float version of s_log1p.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_log1pf.c,v 1.4 1995/05/10 20:47:48 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ +ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ +two25 = 3.355443200e+07, /* 0x4c000000 */ +Lp1 = 6.6666668653e-01, /* 3F2AAAAB */ +Lp2 = 4.0000000596e-01, /* 3ECCCCCD */ +Lp3 = 2.8571429849e-01, /* 3E924925 */ +Lp4 = 2.2222198546e-01, /* 3E638E29 */ +Lp5 = 1.8183572590e-01, /* 3E3A3325 */ +Lp6 = 1.5313838422e-01, /* 3E1CD04F */ +Lp7 = 1.4798198640e-01; /* 3E178897 */ + +#ifdef __STDC__ +static const float zero = 0.0; +#else +static float zero = 0.0; +#endif + +#ifdef __STDC__ + float __log1pf(float x) +#else + float __log1pf(x) + float x; +#endif +{ + float hfsq,f,c,s,z,R,u; + int32_t k,hx,hu,ax; + + GET_FLOAT_WORD(hx,x); + ax = hx&0x7fffffff; + + k = 1; + if (hx < 0x3ed413d7) { /* x < 0.41422 */ + if(ax>=0x3f800000) { /* x <= -1.0 */ + if(x==(float)-1.0) return -two25/(x-x); /* log1p(-1)=+inf */ + else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ + } + if(ax<0x31000000) { /* |x| < 2**-29 */ + if(two25+x>zero /* raise inexact */ + &&ax<0x24800000) /* |x| < 2**-54 */ + return x; + else + return x - x*x*(float)0.5; + } + if(hx>0||hx<=((int32_t)0xbe95f61f)) { + k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */ + } + if (hx >= 0x7f800000) return x+x; + if(k!=0) { + if(hx<0x5a000000) { + u = (float)1.0+x; + GET_FLOAT_WORD(hu,u); + k = (hu>>23)-127; + /* correction term */ + c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); + c /= u; + } else { + u = x; + GET_FLOAT_WORD(hu,u); + k = (hu>>23)-127; + c = 0; + } + hu &= 0x007fffff; + if(hu<0x3504f7) { + SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ + } else { + k += 1; + SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ + hu = (0x00800000-hu)>>2; + } + f = u-(float)1.0; + } + hfsq=(float)0.5*f*f; + if(hu==0) { /* |f| < 2**-20 */ + if(f==zero) { + if(k==0) return zero; + else {c += k*ln2_lo; return k*ln2_hi+c;} + } + R = hfsq*((float)1.0-(float)0.66666666666666666*f); + if(k==0) return f-R; else + return k*ln2_hi-((R-(k*ln2_lo+c))-f); + } + s = f/((float)2.0+f); + z = s*s; + R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); +} +weak_alias (__log1pf, log1pf) diff --git a/sysdeps/ieee754/flt-32/s_log2f.c b/sysdeps/ieee754/flt-32/s_log2f.c new file mode 100644 index 0000000..2377acd --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_log2f.c @@ -0,0 +1,91 @@ +/* e_logf.c -- float version of e_log.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * adapted for log2 by Ulrich Drepper <drepper@cygnus.com> + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +ln2 = 0.69314718055994530942, +two25 = 3.355443200e+07, /* 0x4c000000 */ +Lg1 = 6.6666668653e-01, /* 3F2AAAAB */ +Lg2 = 4.0000000596e-01, /* 3ECCCCCD */ +Lg3 = 2.8571429849e-01, /* 3E924925 */ +Lg4 = 2.2222198546e-01, /* 3E638E29 */ +Lg5 = 1.8183572590e-01, /* 3E3A3325 */ +Lg6 = 1.5313838422e-01, /* 3E1CD04F */ +Lg7 = 1.4798198640e-01; /* 3E178897 */ + +#ifdef __STDC__ +static const float zero = 0.0; +#else +static float zero = 0.0; +#endif + +#ifdef __STDC__ + float __log2f(float x) +#else + float __log2f(x) + float x; +#endif +{ + float hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,ix,i,j; + + GET_FLOAT_WORD(ix,x); + + k=0; + if (ix < 0x00800000) { /* x < 2**-126 */ + if ((ix&0x7fffffff)==0) + return -two25/(x-x); /* log(+-0)=-inf */ + if (ix<0) return (x-x)/(x-x); /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(ix,x); + } + if (ix >= 0x7f800000) return x+x; + k += (ix>>23)-127; + ix &= 0x007fffff; + i = (ix+(0x95f64<<3))&0x800000; + SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ + k += (i>>23); + dk = (float)k; + f = x-(float)1.0; + if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */ + if(f==zero) return dk; + R = f*f*((float)0.5-(float)0.33333333333333333*f); + return dk-(R-f)/ln2; + } + s = f/((float)2.0+f); + z = s*s; + i = ix-(0x6147a<<3); + w = z*z; + j = (0x6b851<<3)-ix; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=(float)0.5*f*f; + return dk-((hfsq-(s*(hfsq+R)))-f)/ln2; + } else { + return dk-((s*(f-R))-f)/ln2; + } +} +weak_alias (__log2f, log2f) diff --git a/sysdeps/ieee754/flt-32/s_logbf.c b/sysdeps/ieee754/flt-32/s_logbf.c new file mode 100644 index 0000000..ade892a --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_logbf.c @@ -0,0 +1,40 @@ +/* s_logbf.c -- float version of s_logb.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_logbf.c,v 1.4 1995/05/10 20:47:51 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + float __logbf(float x) +#else + float __logbf(x) + float x; +#endif +{ + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* high |x| */ + if(ix==0) return (float)-1.0/fabsf(x); + if(ix>=0x7f800000) return x*x; + if((ix>>=23)==0) /* IEEE 754 logb */ + return -126.0; + else + return (float) (ix-127); +} +weak_alias (__logbf, logbf) diff --git a/sysdeps/ieee754/flt-32/s_lrintf.c b/sysdeps/ieee754/flt-32/s_lrintf.c new file mode 100644 index 0000000..210ffec --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_lrintf.c @@ -0,0 +1,78 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + +static const double two23[2] = +{ + 8.3886080000e+06, /* 0x4B000000 */ + -8.3886080000e+06, /* 0xCB000000 */ +}; + + +long int +__lrintf (float x) +{ + int32_t j0; + u_int32_t i0; + volatile float w; + float t; + long int result; + int sx; + + GET_FLOAT_WORD (i0, x); + + sx = i0 >> 31; + j0 = ((i0 >> 23) & 0xff) - 0x7f; + i0 &= 0x7fffff; + i0 |= 0x800000; + + if (j0 < (int32_t) (sizeof (long int) * 8) - 1) + { + if (j0 < -1) + return 0; + else if (j0 >= 23) + result = (long int) i0 << (j0 - 23); + else + { + w = two23[sx] + x; + t = w - two23[sx]; + GET_FLOAT_WORD (i0, t); + j0 = ((i0 >> 23) & 0xff) - 0x7f; + i0 &= 0x7fffff; + i0 |= 0x800000; + + result = i0 >> (23 - j0); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__lrintf, lrintf) diff --git a/sysdeps/ieee754/flt-32/s_lroundf.c b/sysdeps/ieee754/flt-32/s_lroundf.c new file mode 100644 index 0000000..df1d242 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_lroundf.c @@ -0,0 +1,63 @@ +/* Round float value to long int. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +long int +__lroundf (float x) +{ + int32_t j0; + u_int32_t i; + long int result; + int sign; + + GET_FLOAT_WORD (i, x); + j0 = ((i >> 23) & 0xff) - 0x7f; + sign = (i & 0x80000000) != 0 ? -1 : 1; + i &= 0x7fffff; + i |= 0x800000; + + if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else if (j0 >= 23) + result = (long int) i << (j0 - 23); + else + { + i += 0x400000 >> j0; + + result = i >> (23 - j0); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long int) x; + } + + return sign * result; +} + +weak_alias (__lroundf, lroundf) diff --git a/sysdeps/ieee754/flt-32/s_modff.c b/sysdeps/ieee754/flt-32/s_modff.c new file mode 100644 index 0000000..e6c22b2 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_modff.c @@ -0,0 +1,66 @@ +/* s_modff.c -- float version of s_modf.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_modff.c,v 1.4 1995/05/10 20:47:56 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float one = 1.0; +#else +static float one = 1.0; +#endif + +#ifdef __STDC__ + float __modff(float x, float *iptr) +#else + float __modff(x, iptr) + float x,*iptr; +#endif +{ + int32_t i0,j0; + u_int32_t i; + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; /* exponent of x */ + if(j0<23) { /* integer part in x */ + if(j0<0) { /* |x|<1 */ + SET_FLOAT_WORD(*iptr,i0&0x80000000); /* *iptr = +-0 */ + return x; + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) { /* x is integral */ + u_int32_t ix; + *iptr = x; + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x80000000); /* return +-0 */ + return x; + } else { + SET_FLOAT_WORD(*iptr,i0&(~i)); + return x - *iptr; + } + } + } else { /* no fraction part */ + *iptr = x*one; + /* We must handle NaNs separately. */ + if (j0 == 0x80 && (i0 & 0x7fffff)) + return x*one; + SET_FLOAT_WORD(x,i0&0x80000000); /* return +-0 */ + return x; + } +} +weak_alias (__modff, modff) diff --git a/sysdeps/ieee754/flt-32/s_nearbyintf.c b/sysdeps/ieee754/flt-32/s_nearbyintf.c new file mode 100644 index 0000000..7d6f262 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_nearbyintf.c @@ -0,0 +1,77 @@ +/* s_rintf.c -- float version of s_rint.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ +/* Adapted for use as nearbyint by Ulrich Drepper <drepper@cygnus.com>. */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + + +#include <fenv.h> +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +TWO23[2]={ + 8.3886080000e+06, /* 0x4b000000 */ + -8.3886080000e+06, /* 0xcb000000 */ +}; + +#ifdef __STDC__ + float __nearbyintf(float x) +#else + float __nearbyintf(x) + float x; +#endif +{ + fenv_t env; + int32_t i0,j0,sx; + u_int32_t i,i1; + float w,t; + GET_FLOAT_WORD(i0,x); + sx = (i0>>31)&1; + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { + if((i0&0x7fffffff)==0) return x; + i1 = (i0&0x07fffff); + i0 &= 0xfff00000; + i0 |= ((i1|-i1)>>9)&0x400000; + SET_FLOAT_WORD(x,i0); + feholdexcept (&env); + w = TWO23[sx]+x; + t = w-TWO23[sx]; + fesetenv (&env); + GET_FLOAT_WORD(i0,t); + SET_FLOAT_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + i>>=1; + if((i0&i)!=0) i0 = (i0&(~i))|((0x100000)>>j0); + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + feholdexcept (&env); + w = TWO23[sx]+x; + t = w-TWO23[sx]; + fesetenv (&env); + return t; +} +weak_alias (__nearbyintf, nearbyintf) diff --git a/sysdeps/ieee754/flt-32/s_nextafterf.c b/sysdeps/ieee754/flt-32/s_nextafterf.c new file mode 100644 index 0000000..611742b --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_nextafterf.c @@ -0,0 +1,71 @@ +/* s_nextafterf.c -- float version of s_nextafter.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_nextafterf.c,v 1.4 1995/05/10 20:48:01 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + float __nextafterf(float x, float y) +#else + float __nextafterf(x,y) + float x,y; +#endif +{ + int32_t hx,hy,ix,iy; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffff; /* |y| */ + + if((ix>0x7f800000) || /* x is nan */ + (iy>0x7f800000)) /* y is nan */ + return x+y; + if(x==y) return y; /* x=y, return y */ + if(ix==0) { /* x == 0 */ + SET_FLOAT_WORD(x,(hy&0x80000000)|1);/* return +-minsubnormal */ + y = x*x; + if(y==x) return y; else return x; /* raise underflow flag */ + } + if(hx>=0) { /* x > 0 */ + if(hx>hy) { /* x > y, x -= ulp */ + hx -= 1; + } else { /* x < y, x += ulp */ + hx += 1; + } + } else { /* x < 0 */ + if(hy>=0||hx>hy){ /* x < y, x -= ulp */ + hx -= 1; + } else { /* x > y, x += ulp */ + hx += 1; + } + } + hy = hx&0x7f800000; + if(hy>=0x7f800000) return x+x; /* overflow */ + if(hy<0x00800000) { /* underflow */ + y = x*x; + if(y!=x) { /* raise underflow flag */ + SET_FLOAT_WORD(y,hx); + return y; + } + } + SET_FLOAT_WORD(x,hx); + return x; +} +weak_alias (__nextafterf, nextafterf) diff --git a/sysdeps/ieee754/flt-32/s_remquof.c b/sysdeps/ieee754/flt-32/s_remquof.c new file mode 100644 index 0000000..2ffd16c --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_remquof.c @@ -0,0 +1,108 @@ +/* Compute remainder and a congruent to the quotient. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +static const float zero = 0.0; + + +float +__remquof (float x, float y, int *quo) +{ + int32_t hx,hy; + u_int32_t sx; + int cquo, qs; + + GET_FLOAT_WORD (hx, x); + GET_FLOAT_WORD (hy, y); + sx = hx & 0x80000000; + qs = sx ^ (hy & 0x80000000); + hy &= 0x7fffffff; + hx &= 0x7fffffff; + + /* Purge off exception values. */ + if (hy == 0) + return (x * y) / (x * y); /* y = 0 */ + if ((hx >= 0x7f800000) /* x not finite */ + || (hy > 0x7f800000)) /* y is NaN */ + return (x * y) / (x * y); + + if (hy <= 0x7dffffff) + x = __ieee754_fmodf (x, 8 * y); /* now x < 8y */ + + if ((hx - hy) == 0) + { + *quo = qs ? -1 : 1; + return zero * x; + } + + x = fabsf (x); + y = fabsf (y); + cquo = 0; + + if (x >= 4 * y) + { + x -= 4 * y; + cquo += 4; + } + if (x >= 2 * y) + { + x -= 2 * y; + cquo += 2; + } + + if (hy < 0x01000000) + { + if (x + x > y) + { + x -= y; + ++cquo; + if (x + x >= y) + { + x -= y; + ++cquo; + } + } + } + else + { + float y_half = 0.5 * y; + if (x > y_half) + { + x -= y; + ++cquo; + if (x >= y_half) + { + x -= y; + ++cquo; + } + } + } + + *quo = qs ? -cquo : cquo; + + if (sx) + x = -x; + return x; +} +weak_alias (__remquof, remquof) diff --git a/sysdeps/ieee754/flt-32/s_rintf.c b/sysdeps/ieee754/flt-32/s_rintf.c new file mode 100644 index 0000000..4e5b409 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_rintf.c @@ -0,0 +1,72 @@ +/* s_rintf.c -- float version of s_rint.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_rintf.c,v 1.4 1995/05/10 20:48:06 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +TWO23[2]={ + 8.3886080000e+06, /* 0x4b000000 */ + -8.3886080000e+06, /* 0xcb000000 */ +}; + +#ifdef __STDC__ + float __rintf(float x) +#else + float __rintf(x) + float x; +#endif +{ + int32_t i0,j0,sx; + u_int32_t i,i1; + float w,t; + GET_FLOAT_WORD(i0,x); + sx = (i0>>31)&1; + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { + if((i0&0x7fffffff)==0) return x; + i1 = (i0&0x07fffff); + i0 &= 0xfff00000; + i0 |= ((i1|-i1)>>9)&0x400000; + SET_FLOAT_WORD(x,i0); + w = TWO23[sx]+x; + t = w-TWO23[sx]; + GET_FLOAT_WORD(i0,t); + SET_FLOAT_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + i>>=1; + if((i0&i)!=0) i0 = (i0&(~i))|((0x100000)>>j0); + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + w = TWO23[sx]+x; + return w-TWO23[sx]; +} +weak_alias (__rintf, rintf) diff --git a/sysdeps/ieee754/flt-32/s_roundf.c b/sysdeps/ieee754/flt-32/s_roundf.c new file mode 100644 index 0000000..5dc0e36 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_roundf.c @@ -0,0 +1,73 @@ +/* Round float to integer away from zero. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +static const float huge = 1.0e30; + + +float +__roundf (float x) +{ + int32_t i0, j0; + + GET_FLOAT_WORD (i0, x); + j0 = ((i0 >> 23) & 0xff) - 0x7f; + if (j0 < 23) + { + if (j0 < 0) + { + if (huge + x > 0.0F) + { + i0 &= 0x80000000; + if (j0 == -1) + i0 |= 0x3f800000; + } + } + else + { + u_int32_t i = 0x007fffff >> j0; + if ((i0 & i) == 0) + /* X is integral. */ + return x; + if (huge + x > 0.0F) + { + /* Raise inexact if x != 0. */ + i0 += 0x00400000 >> j0; + i0 &= ~i; + } + } + } + else + { + if (j0 == 0x80) + /* Inf or NaN. */ + return x + x; + else + return x; + } + + SET_FLOAT_WORD (x, i0); + return x; +} +weak_alias (__roundf, roundf) diff --git a/sysdeps/ieee754/flt-32/s_scalblnf.c b/sysdeps/ieee754/flt-32/s_scalblnf.c new file mode 100644 index 0000000..4ed4873 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_scalblnf.c @@ -0,0 +1,63 @@ +/* s_scalbnf.c -- float version of s_scalbn.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_scalbnf.c,v 1.4 1995/05/10 20:48:10 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +two25 = 3.355443200e+07, /* 0x4c000000 */ +twom25 = 2.9802322388e-08, /* 0x33000000 */ +huge = 1.0e+30, +tiny = 1.0e-30; + +#ifdef __STDC__ + float __scalblnf (float x, long int n) +#else + float __scalblnf (x,n) + float x; long int n; +#endif +{ + int32_t k,ix; + GET_FLOAT_WORD(ix,x); + k = (ix&0x7f800000)>>23; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((ix&0x7fffffff)==0) return x; /* +-0 */ + x *= two25; + GET_FLOAT_WORD(ix,x); + k = ((ix&0x7f800000)>>23) - 25; + } + if (k==0xff) return x+x; /* NaN or Inf */ + k = k+n; + if (n> 50000 || k > 0xfe) + return huge*copysignf(huge,x); /* overflow */ + if (n< -50000) + return tiny*copysignf(tiny,x); /*underflow*/ + if (k > 0) /* normal result */ + {SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); return x;} + if (k <= -25) + return tiny*copysignf(tiny,x); /*underflow*/ + k += 25; /* subnormal result */ + SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); + return x*twom25; +} +weak_alias (__scalblnf, scalblnf) diff --git a/sysdeps/ieee754/flt-32/s_scalbnf.c b/sysdeps/ieee754/flt-32/s_scalbnf.c new file mode 100644 index 0000000..11b77bd --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_scalbnf.c @@ -0,0 +1,63 @@ +/* s_scalbnf.c -- float version of s_scalbn.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_scalbnf.c,v 1.4 1995/05/10 20:48:10 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +two25 = 3.355443200e+07, /* 0x4c000000 */ +twom25 = 2.9802322388e-08, /* 0x33000000 */ +huge = 1.0e+30, +tiny = 1.0e-30; + +#ifdef __STDC__ + float __scalbnf (float x, int n) +#else + float __scalbnf (x,n) + float x; int n; +#endif +{ + int32_t k,ix; + GET_FLOAT_WORD(ix,x); + k = (ix&0x7f800000)>>23; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((ix&0x7fffffff)==0) return x; /* +-0 */ + x *= two25; + GET_FLOAT_WORD(ix,x); + k = ((ix&0x7f800000)>>23) - 25; + } + if (k==0xff) return x+x; /* NaN or Inf */ + k = k+n; + if (n> 50000 || k > 0xfe) + return huge*copysignf(huge,x); /* overflow */ + if (n< -50000) + return tiny*copysignf(tiny,x); /*underflow*/ + if (k > 0) /* normal result */ + {SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); return x;} + if (k <= -25) + return tiny*copysignf(tiny,x); /*underflow*/ + k += 25; /* subnormal result */ + SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); + return x*twom25; +} +weak_alias (__scalbnf, scalbnf) diff --git a/sysdeps/ieee754/flt-32/s_signbitf.c b/sysdeps/ieee754/flt-32/s_signbitf.c new file mode 100644 index 0000000..85418ea --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_signbitf.c @@ -0,0 +1,32 @@ +/* Return nonzero value if number is negative. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + +int +__signbitf (float x) +{ + int32_t hx; + + GET_FLOAT_WORD (hx, x); + return hx & 0x80000000; +} diff --git a/sysdeps/ieee754/flt-32/s_sincosf.c b/sysdeps/ieee754/flt-32/s_sincosf.c new file mode 100644 index 0000000..0fd7b0c --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_sincosf.c @@ -0,0 +1,74 @@ +/* Compute sine and cosine of argument. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +void +__sincosf (float x, float *sinx, float *cosx) +{ + int32_t ix; + + /* High word of x. */ + GET_FLOAT_WORD (ix, x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if (ix <= 0x3f490fd8) + { + *sinx = __kernel_sinf (x, 0.0, 0); + *cosx = __kernel_cosf (x, 0.0); + } + else if (ix>=0x7ff00000) + { + /* sin(Inf or NaN) is NaN */ + *sinx = *cosx = x - x; + } + else + { + /* Argument reduction needed. */ + float y[2]; + int n; + + n = __ieee754_rem_pio2f (x, y); + switch (n & 3) + { + case 0: + *sinx = __kernel_sinf (y[0], y[1], 1); + *cosx = __kernel_cosf (y[0], y[1]); + break; + case 1: + *sinx = __kernel_cosf (y[0], y[1]); + *cosx = -__kernel_sinf (y[0], y[1], 1); + break; + case 2: + *sinx = -__kernel_sinf (y[0], y[1], 1); + *cosx = -__kernel_cosf (y[0], y[1]); + break; + default: + *sinx = -__kernel_cosf (y[0], y[1]); + *cosx = __kernel_sinf (y[0], y[1], 1); + break; + } + } +} +weak_alias (__sincosf, sincosf) diff --git a/sysdeps/ieee754/flt-32/s_sinf.c b/sysdeps/ieee754/flt-32/s_sinf.c new file mode 100644 index 0000000..76a7c21 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_sinf.c @@ -0,0 +1,54 @@ +/* s_sinf.c -- float version of s_sin.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_sinf.c,v 1.4 1995/05/10 20:48:16 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + float __sinf(float x) +#else + float __sinf(x) + float x; +#endif +{ + float y[2],z=0.0; + int32_t n, ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fd8) return __kernel_sinf(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,y); + switch(n&3) { + case 0: return __kernel_sinf(y[0],y[1],1); + case 1: return __kernel_cosf(y[0],y[1]); + case 2: return -__kernel_sinf(y[0],y[1],1); + default: + return -__kernel_cosf(y[0],y[1]); + } + } +} +weak_alias (__sinf, sinf) diff --git a/sysdeps/ieee754/flt-32/s_tanf.c b/sysdeps/ieee754/flt-32/s_tanf.c new file mode 100644 index 0000000..e8f6016 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_tanf.c @@ -0,0 +1,49 @@ +/* s_tanf.c -- float version of s_tan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_tanf.c,v 1.4 1995/05/10 20:48:20 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + float __tanf(float x) +#else + float __tanf(x) + float x; +#endif +{ + float y[2],z=0.0; + int32_t n, ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fda) return __kernel_tanf(x,z,1); + + /* tan(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; /* NaN */ + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,y); + return __kernel_tanf(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} +weak_alias (__tanf, tanf) diff --git a/sysdeps/ieee754/flt-32/s_tanhf.c b/sysdeps/ieee754/flt-32/s_tanhf.c new file mode 100644 index 0000000..2a0ca9f --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_tanhf.c @@ -0,0 +1,67 @@ +/* s_tanhf.c -- float version of s_tanh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_tanhf.c,v 1.4 1995/05/10 20:48:24 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float one=1.0, two=2.0, tiny = 1.0e-30; +#else +static float one=1.0, two=2.0, tiny = 1.0e-30; +#endif + +#ifdef __STDC__ + float __tanhf(float x) +#else + float __tanhf(x) + float x; +#endif +{ + float t,z; + int32_t jx,ix; + + GET_FLOAT_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x41b00000) { /* |x|<22 */ + if (ix == 0) + return x; /* x == +-0 */ + if (ix<0x24000000) /* |x|<2**-55 */ + return x*(one+x); /* tanh(small) = small */ + if (ix>=0x3f800000) { /* |x|>=1 */ + t = __expm1f(two*fabsf(x)); + z = one - two/(t+two); + } else { + t = __expm1f(-two*fabsf(x)); + z= -t/(t+two); + } + /* |x| > 22, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (jx>=0)? z: -z; +} +weak_alias (__tanhf, tanhf) diff --git a/sysdeps/ieee754/flt-32/s_truncf.c b/sysdeps/ieee754/flt-32/s_truncf.c new file mode 100644 index 0000000..feb6b6f --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_truncf.c @@ -0,0 +1,52 @@ +/* Truncate argument to nearest integral value not larger than the argument. + Copyright (C) 1997, 1998 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +float +__truncf (float x) +{ + int32_t i0, j0; + int sx; + + GET_FLOAT_WORD (i0, x); + sx = i0 & 0x80000000; + j0 = ((i0 >> 23) & 0xff) - 0x7f; + if (j0 < 23) + { + if (j0 < 0) + /* The magnitude of the number is < 1 so the result is +-0. */ + SET_FLOAT_WORD (x, sx); + else + SET_FLOAT_WORD (x, sx | (i0 & ~(0x007fffff >> j0))); + } + else + { + if (j0 == 0x80) + /* x is inf or NaN. */ + return x + x; + } + + return x; +} +weak_alias (__truncf, truncf) diff --git a/sysdeps/ieee754/flt-32/t_exp2f.h b/sysdeps/ieee754/flt-32/t_exp2f.h new file mode 100644 index 0000000..e15d157 --- /dev/null +++ b/sysdeps/ieee754/flt-32/t_exp2f.h @@ -0,0 +1,352 @@ +/* Accurate tables for exp2f(). + Copyright (C) 1998 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +/* This table has the property that, for all integers -128 <= i <= 127, + exp(i/256.0 + __exp2f_deltatable[i-128]) == __exp2f_atable[i+128] + r + for some -2^-35 < r < 2^-35 (abs(r) < 2^-36 if i <= 0); and that + __exp2f_deltatable[i+128] == t * 2^-30 + for integer t so that abs(t) <= 43447 * 2^0. */ + +#define W30 (9.31322575e-10) +static const float __exp2f_deltatable[256] = { + -810*W30, 283*W30, -1514*W30, 1304*W30, + -1148*W30, -98*W30, -744*W30, -156*W30, + -419*W30, -155*W30, 474*W30, 167*W30, + -1984*W30, -826*W30, 692*W30, 781*W30, + -578*W30, -411*W30, -129*W30, -1500*W30, + 654*W30, -141*W30, -816*W30, -53*W30, + 148*W30, 493*W30, -2214*W30, 760*W30, + 260*W30, 750*W30, -1300*W30, 1424*W30, + -1445*W30, -339*W30, -680*W30, -349*W30, + -922*W30, 531*W30, 193*W30, -2892*W30, + 290*W30, -2145*W30, -276*W30, 485*W30, + -695*W30, 215*W30, -7093*W30, 412*W30, + -4596*W30, 367*W30, 592*W30, -615*W30, + -97*W30, -1066*W30, 972*W30, -226*W30, + -625*W30, -374*W30, -5647*W30, -180*W30, + 20349*W30, -447*W30, 111*W30, -4164*W30, + -87*W30, -21*W30, -251*W30, 66*W30, + -517*W30, 2093*W30, -263*W30, 182*W30, + -601*W30, 475*W30, -483*W30, -1251*W30, + -373*W30, 1471*W30, -92*W30, -215*W30, + -97*W30, -190*W30, 0*W30, -290*W30, + -2647*W30, 1940*W30, -582*W30, 28*W30, + 833*W30, 1493*W30, 34*W30, 321*W30, + 3327*W30, -35*W30, 177*W30, -135*W30, + -796*W30, -428*W30, 129*W30, 9332*W30, + -12*W30, -69*W30, -1743*W30, 6508*W30, + -60*W30, 359*W30, 43447*W30, 15*W30, + -23*W30, -305*W30, -375*W30, -652*W30, + 667*W30, 269*W30, -1575*W30, 185*W30, + -329*W30, 200*W30, 6002*W30, 163*W30, + -647*W30, 19*W30, -603*W30, -755*W30, + 742*W30, -438*W30, 3587*W30, 2560*W30, + 0*W30, -520*W30, -241*W30, -299*W30, + -1270*W30, -991*W30, -1138*W30, 255*W30, + -1192*W30, 1722*W30, 1023*W30, 3700*W30, + -1388*W30, -1551*W30, -2549*W30, 27*W30, + 282*W30, 673*W30, 113*W30, 1561*W30, + 72*W30, 873*W30, 87*W30, -395*W30, + -433*W30, 629*W30, 3440*W30, -284*W30, + -592*W30, -103*W30, -46*W30, -3844*W30, + 1712*W30, 303*W30, 1555*W30, -631*W30, + -1400*W30, -961*W30, -854*W30, -276*W30, + 407*W30, 833*W30, -345*W30, -1501*W30, + 121*W30, -1581*W30, 400*W30, 150*W30, + 1224*W30, -139*W30, -563*W30, 879*W30, + 933*W30, 2939*W30, 788*W30, 211*W30, + 530*W30, -192*W30, 706*W30, -13347*W30, + 1065*W30, 3*W30, 111*W30, -208*W30, + -360*W30, -532*W30, -291*W30, 483*W30, + 987*W30, -33*W30, -1373*W30, -166*W30, + -1174*W30, -3955*W30, 1601*W30, -280*W30, + 1405*W30, 600*W30, -1659*W30, -23*W30, + 390*W30, 449*W30, 570*W30, -13143*W30, + -9*W30, -1646*W30, 1201*W30, 294*W30, + 2181*W30, -1173*W30, 1388*W30, -4504*W30, + 190*W30, -2304*W30, 211*W30, 239*W30, + 48*W30, -817*W30, 1018*W30, 1828*W30, + -663*W30, 1408*W30, 408*W30, -36*W30, + 1295*W30, -230*W30, 1341*W30, 9*W30, + 40*W30, 705*W30, 186*W30, 376*W30, + 557*W30, 5866*W30, 363*W30, -1558*W30, + 718*W30, 669*W30, 1369*W30, -2972*W30, + -468*W30, -121*W30, -219*W30, 667*W30, + 29954*W30, 366*W30, 48*W30, -203*W30 +}; + +static const float __exp2f_atable[256] /* __attribute__((mode(SF))) */ = { + 0.707106411447, /* 0x0.b504ecfff */ + 0.709024071690, /* 0x0.b58299fff */ + 0.710945606239, /* 0x0.b60088000 */ + 0.712874472142, /* 0x0.b67ef1000 */ + 0.714806139464, /* 0x0.b6fd88fff */ + 0.716744661340, /* 0x0.b77c94000 */ + 0.718687653549, /* 0x0.b7fbea000 */ + 0.720636486992, /* 0x0.b87ba1fff */ + 0.722590208040, /* 0x0.b8fbabfff */ + 0.724549472323, /* 0x0.b97c12fff */ + 0.726514220228, /* 0x0.b9fcd5fff */ + 0.728483855735, /* 0x0.ba7deb000 */ + 0.730457961549, /* 0x0.baff4afff */ + 0.732438981522, /* 0x0.bb811efff */ + 0.734425544748, /* 0x0.bc0350000 */ + 0.736416816713, /* 0x0.bc85d0000 */ + 0.738412797450, /* 0x0.bd089efff */ + 0.740414917465, /* 0x0.bd8bd4fff */ + 0.742422521111, /* 0x0.be0f66fff */ + 0.744434773914, /* 0x0.be9346fff */ + 0.746454179287, /* 0x0.bf179f000 */ + 0.748477637755, /* 0x0.bf9c3afff */ + 0.750506639473, /* 0x0.c02133fff */ + 0.752541840064, /* 0x0.c0a694fff */ + 0.754582285889, /* 0x0.c12c4e000 */ + 0.756628334525, /* 0x0.c1b265000 */ + 0.758678436269, /* 0x0.c238bffff */ + 0.760736882681, /* 0x0.c2bfa6fff */ + 0.762799203401, /* 0x0.c346cf000 */ + 0.764867603790, /* 0x0.c3ce5d000 */ + 0.766940355298, /* 0x0.c45633fff */ + 0.769021093841, /* 0x0.c4de90fff */ + 0.771104693409, /* 0x0.c5671dfff */ + 0.773195922364, /* 0x0.c5f02afff */ + 0.775292098512, /* 0x0.c6798afff */ + 0.777394294745, /* 0x0.c70350000 */ + 0.779501736166, /* 0x0.c78d6d000 */ + 0.781615912910, /* 0x0.c817fafff */ + 0.783734917628, /* 0x0.c8a2d9fff */ + 0.785858273516, /* 0x0.c92e02000 */ + 0.787990570071, /* 0x0.c9b9c0000 */ + 0.790125787245, /* 0x0.ca45aefff */ + 0.792268991467, /* 0x0.cad223fff */ + 0.794417440881, /* 0x0.cb5ef0fff */ + 0.796570718287, /* 0x0.cbec0efff */ + 0.798730909811, /* 0x0.cc79a0fff */ + 0.800892710672, /* 0x0.cd074dfff */ + 0.803068041795, /* 0x0.cd95ddfff */ + 0.805242776881, /* 0x0.ce2464000 */ + 0.807428598393, /* 0x0.ceb3a3fff */ + 0.809617877002, /* 0x0.cf431dfff */ + 0.811812341211, /* 0x0.cfd2eefff */ + 0.814013659956, /* 0x0.d06333000 */ + 0.816220164311, /* 0x0.d0f3ce000 */ + 0.818434238424, /* 0x0.d184e7fff */ + 0.820652604094, /* 0x0.d21649fff */ + 0.822877407074, /* 0x0.d2a818000 */ + 0.825108587751, /* 0x0.d33a51000 */ + 0.827342867839, /* 0x0.d3ccbdfff */ + 0.829588949684, /* 0x0.d45ff1000 */ + 0.831849217401, /* 0x0.d4f411fff */ + 0.834093391880, /* 0x0.d58724fff */ + 0.836355149750, /* 0x0.d61b5f000 */ + 0.838620424257, /* 0x0.d6afd3fff */ + 0.840896368027, /* 0x0.d744fc000 */ + 0.843176305293, /* 0x0.d7da66fff */ + 0.845462262643, /* 0x0.d87037000 */ + 0.847754716864, /* 0x0.d90673fff */ + 0.850052893157, /* 0x0.d99d10fff */ + 0.852359056469, /* 0x0.da3433fff */ + 0.854668736446, /* 0x0.dacb91fff */ + 0.856986224651, /* 0x0.db6373000 */ + 0.859309315673, /* 0x0.dbfbb1fff */ + 0.861639738080, /* 0x0.dc946bfff */ + 0.863975346095, /* 0x0.dd2d7d000 */ + 0.866317391394, /* 0x0.ddc6f9fff */ + 0.868666708472, /* 0x0.de60f1000 */ + 0.871022939695, /* 0x0.defb5c000 */ + 0.873383641229, /* 0x0.df9611fff */ + 0.875751554968, /* 0x0.e03141000 */ + 0.878126025200, /* 0x0.e0ccde000 */ + 0.880506813521, /* 0x0.e168e4fff */ + 0.882894217966, /* 0x0.e2055afff */ + 0.885287821299, /* 0x0.e2a239000 */ + 0.887686729423, /* 0x0.e33f6ffff */ + 0.890096127973, /* 0x0.e3dd56fff */ + 0.892507970338, /* 0x0.e47b67000 */ + 0.894928157336, /* 0x0.e51a03000 */ + 0.897355020043, /* 0x0.e5b90efff */ + 0.899788379682, /* 0x0.e65888000 */ + 0.902227103705, /* 0x0.e6f85afff */ + 0.904673457151, /* 0x0.e798ae000 */ + 0.907128036008, /* 0x0.e8398afff */ + 0.909585535528, /* 0x0.e8da99000 */ + 0.912051796915, /* 0x0.e97c3a000 */ + 0.914524436003, /* 0x0.ea1e46000 */ + 0.917003571999, /* 0x0.eac0bf000 */ + 0.919490039339, /* 0x0.eb63b2fff */ + 0.921983361257, /* 0x0.ec071a000 */ + 0.924488604054, /* 0x0.ecab48fff */ + 0.926989555360, /* 0x0.ed4f30000 */ + 0.929502844812, /* 0x0.edf3e6000 */ + 0.932021975503, /* 0x0.ee98fdfff */ + 0.934553921208, /* 0x0.ef3eecfff */ + 0.937083780759, /* 0x0.efe4b8fff */ + 0.939624726786, /* 0x0.f08b3f000 */ + 0.942198514924, /* 0x0.f133ebfff */ + 0.944726586343, /* 0x0.f1d99a000 */ + 0.947287976728, /* 0x0.f28176fff */ + 0.949856162070, /* 0x0.f329c5fff */ + 0.952431440345, /* 0x0.f3d28bfff */ + 0.955013573175, /* 0x0.f47bc5000 */ + 0.957603693021, /* 0x0.f52584000 */ + 0.960199773321, /* 0x0.f5cfa7000 */ + 0.962801992906, /* 0x0.f67a31000 */ + 0.965413510788, /* 0x0.f72556fff */ + 0.968030691152, /* 0x0.f7d0dc000 */ + 0.970655620084, /* 0x0.f87ce2fff */ + 0.973290979849, /* 0x0.f92998fff */ + 0.975926160805, /* 0x0.f9d64bfff */ + 0.978571653370, /* 0x0.fa83ac000 */ + 0.981225252139, /* 0x0.fb3193fff */ + 0.983885228626, /* 0x0.fbdfe6fff */ + 0.986552715296, /* 0x0.fc8eb7fff */ + 0.989228487027, /* 0x0.fd3e14000 */ + 0.991909801964, /* 0x0.fdedcd000 */ + 0.994601726545, /* 0x0.fe9e38000 */ + 0.997297704209, /* 0x0.ff4ee6fff */ + 1.000000000000, /* 0x1.000000000 */ + 1.002710938457, /* 0x1.00b1aa000 */ + 1.005429744692, /* 0x1.0163d7ffe */ + 1.008155703526, /* 0x1.02167dffe */ + 1.010888457284, /* 0x1.02c995fff */ + 1.013629436498, /* 0x1.037d38000 */ + 1.016377568250, /* 0x1.043152000 */ + 1.019134163841, /* 0x1.04e5f9ffe */ + 1.021896362316, /* 0x1.059b00000 */ + 1.024668931945, /* 0x1.0650b3ffe */ + 1.027446627635, /* 0x1.0706be001 */ + 1.030234098408, /* 0x1.07bd6bffe */ + 1.033023953416, /* 0x1.087441ffe */ + 1.035824656494, /* 0x1.092bce000 */ + 1.038632392900, /* 0x1.09e3d0001 */ + 1.041450142840, /* 0x1.0a9c79ffe */ + 1.044273972530, /* 0x1.0b558a001 */ + 1.047105550795, /* 0x1.0c0f1c001 */ + 1.049944162390, /* 0x1.0cc924001 */ + 1.052791833895, /* 0x1.0d83c4001 */ + 1.055645227426, /* 0x1.0e3ec3fff */ + 1.058507919326, /* 0x1.0efa60001 */ + 1.061377286898, /* 0x1.0fb66bfff */ + 1.064254641510, /* 0x1.1072fdffe */ + 1.067140102389, /* 0x1.113018000 */ + 1.070034146304, /* 0x1.11edc1fff */ + 1.072937250162, /* 0x1.12ac04001 */ + 1.075843691823, /* 0x1.136a7dfff */ + 1.078760385496, /* 0x1.1429a3ffe */ + 1.081685543070, /* 0x1.14e958000 */ + 1.084618330005, /* 0x1.15a98c000 */ + 1.087556362176, /* 0x1.166a18001 */ + 1.090508937863, /* 0x1.172b98001 */ + 1.093464612954, /* 0x1.17ed4bfff */ + 1.096430182434, /* 0x1.18afa5ffe */ + 1.099401354802, /* 0x1.19725e000 */ + 1.102381587017, /* 0x1.1a35adfff */ + 1.105370759965, /* 0x1.1af994000 */ + 1.108367800686, /* 0x1.1bbdfdffe */ + 1.111373305331, /* 0x1.1c82f6000 */ + 1.114387035385, /* 0x1.1d4878001 */ + 1.117408752440, /* 0x1.1e0e7ffff */ + 1.120437502874, /* 0x1.1ed4fe000 */ + 1.123474478729, /* 0x1.1f9c06000 */ + 1.126521706601, /* 0x1.2063ba001 */ + 1.129574775716, /* 0x1.212bd0001 */ + 1.132638812065, /* 0x1.21f49e000 */ + 1.135709524130, /* 0x1.22bddbffe */ + 1.138789534565, /* 0x1.2387b5fff */ + 1.141876101508, /* 0x1.2451fe000 */ + 1.144971728301, /* 0x1.251cddffe */ + 1.148077130296, /* 0x1.25e861ffe */ + 1.151189923305, /* 0x1.26b462001 */ + 1.154312610610, /* 0x1.278107ffe */ + 1.157440662410, /* 0x1.284e08001 */ + 1.160578370109, /* 0x1.291baa001 */ + 1.163725256932, /* 0x1.29e9e6000 */ + 1.166879892324, /* 0x1.2ab8a3ffe */ + 1.170044302935, /* 0x1.2b8805fff */ + 1.173205971694, /* 0x1.2c5739ffe */ + 1.176397800428, /* 0x1.2d2867ffe */ + 1.179586529747, /* 0x1.2df962001 */ + 1.182784795737, /* 0x1.2ecafbffe */ + 1.185991406414, /* 0x1.2f9d21ffe */ + 1.189206838636, /* 0x1.306fdc001 */ + 1.192430973067, /* 0x1.314328000 */ + 1.195664167430, /* 0x1.32170c001 */ + 1.198906540890, /* 0x1.32eb8a001 */ + 1.202157497408, /* 0x1.33c098000 */ + 1.205416083326, /* 0x1.349625fff */ + 1.208683252332, /* 0x1.356c43fff */ + 1.211961269402, /* 0x1.364318001 */ + 1.215246438983, /* 0x1.371a64000 */ + 1.218539118740, /* 0x1.37f22dffe */ + 1.221847295770, /* 0x1.38cafc000 */ + 1.225158572187, /* 0x1.39a3fdfff */ + 1.228481650325, /* 0x1.3a7dc5ffe */ + 1.231811761846, /* 0x1.3b5803fff */ + 1.235149741144, /* 0x1.3c32c5ffe */ + 1.238499879811, /* 0x1.3d0e53ffe */ + 1.241858124726, /* 0x1.3dea69fff */ + 1.245225191102, /* 0x1.3ec713fff */ + 1.248601436624, /* 0x1.3fa458000 */ + 1.251975655584, /* 0x1.40817a001 */ + 1.255380749731, /* 0x1.4160a2001 */ + 1.258783102010, /* 0x1.423f9bffe */ + 1.262198328973, /* 0x1.431f6e000 */ + 1.265619754780, /* 0x1.43ffa7fff */ + 1.269052743928, /* 0x1.44e0a4001 */ + 1.272490739830, /* 0x1.45c1f4000 */ + 1.275942921659, /* 0x1.46a432001 */ + 1.279397487615, /* 0x1.478697ffe */ + 1.282870173427, /* 0x1.486a2dffe */ + 1.286346316319, /* 0x1.494dfdffe */ + 1.289836049094, /* 0x1.4a32b2001 */ + 1.293333172770, /* 0x1.4b17e1ffe */ + 1.296839594835, /* 0x1.4bfdadfff */ + 1.300354957560, /* 0x1.4ce40fffe */ + 1.303882122055, /* 0x1.4dcb38001 */ + 1.307417988757, /* 0x1.4eb2f1ffe */ + 1.310960650439, /* 0x1.4f9b1dfff */ + 1.314516782746, /* 0x1.50842bfff */ + 1.318079948424, /* 0x1.516daffff */ + 1.321653246888, /* 0x1.5257de000 */ + 1.325237751030, /* 0x1.5342c8001 */ + 1.328829526907, /* 0x1.542e2c000 */ + 1.332433700535, /* 0x1.551a5fffe */ + 1.336045145966, /* 0x1.56070dffe */ + 1.339667558645, /* 0x1.56f473ffe */ + 1.343300342533, /* 0x1.57e287ffe */ + 1.346941947961, /* 0x1.58d130001 */ + 1.350594043714, /* 0x1.59c087ffe */ + 1.354256033883, /* 0x1.5ab085fff */ + 1.357932448365, /* 0x1.5ba175ffe */ + 1.361609339707, /* 0x1.5c926dfff */ + 1.365299344044, /* 0x1.5d8441ffe */ + 1.369003057507, /* 0x1.5e76fc001 */ + 1.372714757920, /* 0x1.5f6a3c000 */ + 1.376437187179, /* 0x1.605e2fffe */ + 1.380165219333, /* 0x1.615282001 */ + 1.383909463864, /* 0x1.6247e3ffe */ + 1.387661933907, /* 0x1.633dd0000 */ + 1.391424179060, /* 0x1.64345fffe */ + 1.395197510706, /* 0x1.652ba9fff */ + 1.399006724329, /* 0x1.66254dffe */ + 1.402773022651, /* 0x1.671c22000 */ + 1.406576037403, /* 0x1.68155dfff */ + 1.410389423392, /* 0x1.690f48001 */ +}; diff --git a/sysdeps/ieee754/flt-32/w_expf.c b/sysdeps/ieee754/flt-32/w_expf.c new file mode 100644 index 0000000..ad38fac --- /dev/null +++ b/sysdeps/ieee754/flt-32/w_expf.c @@ -0,0 +1,59 @@ +/* w_expf.c -- float version of w_exp.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_expf.c,v 1.3 1995/05/10 20:48:53 jtc Exp $"; +#endif + +/* + * wrapper expf(x) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +o_threshold= 8.8721679688e+01, /* 0x42b17180 */ +u_threshold= -1.0397208405e+02; /* 0xc2cff1b5 */ + +#ifdef __STDC__ + float __expf(float x) /* wrapper expf */ +#else + float __expf(x) /* wrapper expf */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_expf(x); +#else + float z; + z = __ieee754_expf(x); + if(_LIB_VERSION == _IEEE_) return z; + if(__finitef(x)) { + if(x>o_threshold) + /* exp overflow */ + return (float)__kernel_standard((double)x,(double)x,106); + else if(x<u_threshold) + /* exp underflow */ + return (float)__kernel_standard((double)x,(double)x,107); + } + return z; +#endif +} +weak_alias (__expf, expf) diff --git a/sysdeps/ieee754/k_standard.c b/sysdeps/ieee754/k_standard.c new file mode 100644 index 0000000..2230065 --- /dev/null +++ b/sysdeps/ieee754/k_standard.c @@ -0,0 +1,943 @@ +/* @(#)k_standard.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_standard.c,v 1.6 1995/05/10 20:46:35 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" +#include <errno.h> + +#include <assert.h> + +#ifndef _USE_WRITE +#include <stdio.h> /* fputs(), stderr */ +#define WRITE2(u,v) fputs(u, stderr) +#else /* !defined(_USE_WRITE) */ +#include <unistd.h> /* write */ +#define WRITE2(u,v) write(2, u, v) +#undef fflush +#endif /* !defined(_USE_WRITE) */ + +/* XXX gcc versions until now don't delay the 0.0/0.0 division until + runtime but produce NaN at copile time. This is wrong since the + exceptions are not set correctly. */ +#if 0 && defined __STDC__ +static const double zero = 0.0; /* used as const */ +#else +static double zero = 0.0; /* used as const */ +#endif + +/* + * Standard conformance (non-IEEE) on exception cases. + * Mapping: + * 1 -- acos(|x|>1) + * 2 -- asin(|x|>1) + * 3 -- atan2(+-0,+-0) + * 4 -- hypot overflow + * 5 -- cosh overflow + * 6 -- exp overflow + * 7 -- exp underflow + * 8 -- y0(0) + * 9 -- y0(-ve) + * 10-- y1(0) + * 11-- y1(-ve) + * 12-- yn(0) + * 13-- yn(-ve) + * 14-- lgamma(finite) overflow + * 15-- lgamma(-integer) + * 16-- log(0) + * 17-- log(x<0) + * 18-- log10(0) + * 19-- log10(x<0) + * 20-- pow(0.0,0.0) + * 21-- pow(x,y) overflow + * 22-- pow(x,y) underflow + * 23-- pow(0,negative) + * 24-- pow(neg,non-integral) + * 25-- sinh(finite) overflow + * 26-- sqrt(negative) + * 27-- fmod(x,0) + * 28-- remainder(x,0) + * 29-- acosh(x<1) + * 30-- atanh(|x|>1) + * 31-- atanh(|x|=1) + * 32-- scalb overflow + * 33-- scalb underflow + * 34-- j0(|x|>X_TLOSS) + * 35-- y0(x>X_TLOSS) + * 36-- j1(|x|>X_TLOSS) + * 37-- y1(x>X_TLOSS) + * 38-- jn(|x|>X_TLOSS, n) + * 39-- yn(x>X_TLOSS, n) + * 40-- tgamma(finite) overflow + * 41-- tgamma(-integer) + * 42-- pow(NaN,0.0) + * 43-- +0**neg + * 44-- exp2 overflow + * 45-- exp2 underflow + * 46-- exp10 overflow + * 47-- exp10 underflow + */ + + +#ifdef __STDC__ + double __kernel_standard(double x, double y, int type) +#else + double __kernel_standard(x,y,type) + double x,y; int type; +#endif +{ + struct exception exc; +#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */ +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + +#ifdef _USE_WRITE + (void) fflush(stdout); +#endif + exc.arg1 = x; + exc.arg2 = y; + switch(type) { + case 1: + case 101: + case 201: + /* acos(|x|>1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "acos" : (type < 200 + ? "acosf" : "acosl");; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = NAN; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if(_LIB_VERSION == _SVID_) { + (void) WRITE2("acos: DOMAIN error\n", 19); + } + __set_errno (EDOM); + } + break; + case 2: + case 102: + case 202: + /* asin(|x|>1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "asin" : (type < 200 + ? "asinf" : "asinl"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = NAN; + if(_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if(_LIB_VERSION == _SVID_) { + (void) WRITE2("asin: DOMAIN error\n", 19); + } + __set_errno (EDOM); + } + break; + case 3: + case 103: + case 203: + /* atan2(+-0,+-0) */ + exc.arg1 = y; + exc.arg2 = x; + exc.type = DOMAIN; + exc.name = type < 100 ? "atan2" : (type < 200 + ? "atan2f" : "atan2l"); + assert (_LIB_VERSION == _SVID_); + exc.retval = HUGE; + if(_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if(_LIB_VERSION == _SVID_) { + (void) WRITE2("atan2: DOMAIN error\n", 20); + } + __set_errno (EDOM); + } + break; + case 4: + case 104: + case 204: + /* hypot(finite,finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "hypot" : (type < 200 + ? "hypotf" : "hypotl"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 5: + case 105: + case 205: + /* cosh(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "cosh" : (type < 200 + ? "coshf" : "coshl"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 6: + case 106: + case 206: + /* exp(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "exp" : (type < 200 + ? "expf" : "expl"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 7: + case 107: + case 207: + /* exp(finite) underflow */ + exc.type = UNDERFLOW; + exc.name = type < 100 ? "exp" : (type < 200 + ? "expf" : "expl"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 8: + case 108: + case 208: + /* y0(0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = type < 100 ? "y0" : (type < 200 ? "y0f" : "y0l"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y0: DOMAIN error\n", 17); + } + __set_errno (EDOM); + } + break; + case 9: + case 109: + case 209: + /* y0(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = type < 100 ? "y0" : (type < 200 ? "y0f" : "y0l"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y0: DOMAIN error\n", 17); + } + __set_errno (EDOM); + } + break; + case 10: + case 110: + case 210: + /* y1(0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = type < 100 ? "y1" : (type < 200 ? "y1f" : "y1l"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y1: DOMAIN error\n", 17); + } + __set_errno (EDOM); + } + break; + case 11: + case 111: + case 211: + /* y1(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = type < 100 ? "y1" : (type < 200 ? "y1f" : "y1l"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y1: DOMAIN error\n", 17); + } + __set_errno (EDOM); + } + break; + case 12: + case 112: + case 212: + /* yn(n,0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = type < 100 ? "yn" : (type < 200 ? "ynf" : "ynl"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("yn: DOMAIN error\n", 17); + } + __set_errno (EDOM); + } + break; + case 13: + case 113: + case 213: + /* yn(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = type < 100 ? "yn" : (type < 200 ? "ynf" : "ynl"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("yn: DOMAIN error\n", 17); + } + __set_errno (EDOM); + } + break; + case 14: + case 114: + case 214: + /* lgamma(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "lgamma" : (type < 200 + ? "lgammaf" : "lgammal"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 15: + case 115: + case 215: + /* lgamma(-integer) or lgamma(0) */ + exc.type = SING; + exc.name = type < 100 ? "lgamma" : (type < 200 + ? "lgammaf" : "lgammal"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("lgamma: SING error\n", 19); + } + __set_errno (EDOM); + } + break; + case 16: + case 116: + case 216: + /* log(0) */ + exc.type = SING; + exc.name = type < 100 ? "log" : (type < 200 ? "logf" : "logl"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log: SING error\n", 16); + } + __set_errno (EDOM); + } + break; + case 17: + case 117: + case 217: + /* log(x<0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "log" : (type < 200 ? "logf" : "logl"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = NAN; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log: DOMAIN error\n", 18); + } + __set_errno (EDOM); + } + break; + case 18: + case 118: + case 218: + /* log10(0) */ + exc.type = SING; + exc.name = type < 100 ? "log10" : (type < 200 + ? "log10f" : "log10l"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log10: SING error\n", 18); + } + __set_errno (EDOM); + } + break; + case 19: + case 119: + case 219: + /* log10(x<0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "log10" : (type < 200 + ? "log10f" : "log10l"); + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = NAN; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log10: DOMAIN error\n", 20); + } + __set_errno (EDOM); + } + break; + case 20: + case 120: + case 220: + /* pow(0.0,0.0) */ + /* error only if _LIB_VERSION == _SVID_ */ + exc.type = DOMAIN; + exc.name = type < 100 ? "pow" : (type < 200 ? "powf" : "powl"); + exc.retval = zero; + if (_LIB_VERSION != _SVID_) exc.retval = 1.0; + else if (!matherr(&exc)) { + (void) WRITE2("pow(0,0): DOMAIN error\n", 23); + __set_errno (EDOM); + } + break; + case 21: + case 121: + case 221: + /* pow(x,y) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "pow" : (type < 200 ? "powf" : "powl"); + if (_LIB_VERSION == _SVID_) { + exc.retval = HUGE; + y *= 0.5; + if(x<zero&&__rint(y)!=y) exc.retval = -HUGE; + } else { + exc.retval = HUGE_VAL; + y *= 0.5; + if(x<zero&&__rint(y)!=y) exc.retval = -HUGE_VAL; + } + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 22: + case 122: + case 222: + /* pow(x,y) underflow */ + exc.type = UNDERFLOW; + exc.name = type < 100 ? "pow" : (type < 200 ? "powf" : "powl"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 23: + case 123: + case 223: + /* -0**neg */ + exc.type = DOMAIN; + exc.name = type < 100 ? "pow" : (type < 200 ? "powf" : "powl"); + if (_LIB_VERSION == _SVID_) + exc.retval = zero; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("pow(0,neg): DOMAIN error\n", 25); + } + __set_errno (EDOM); + } + break; + case 43: + case 143: + case 243: + /* +0**neg */ + exc.type = DOMAIN; + exc.name = type < 100 ? "pow" : (type < 200 ? "powf" : "powl"); + if (_LIB_VERSION == _SVID_) + exc.retval = zero; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("pow(0,neg): DOMAIN error\n", 25); + } + __set_errno (EDOM); + } + break; + case 24: + case 124: + case 224: + /* neg**non-integral */ + exc.type = DOMAIN; + exc.name = type < 100 ? "pow" : (type < 200 ? "powf" : "powl"); + if (_LIB_VERSION == _SVID_) + exc.retval = zero; + else + exc.retval = zero/zero; /* X/Open allow NaN */ + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("neg**non-integral: DOMAIN error\n", 32); + } + __set_errno (EDOM); + } + break; + case 25: + case 125: + case 225: + /* sinh(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "sinh" : (type < 200 + ? "sinhf" : "sinhl"); + if (_LIB_VERSION == _SVID_) + exc.retval = ( (x>zero) ? HUGE : -HUGE); + else + exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL); + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 26: + case 126: + case 226: + /* sqrt(x<0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "sqrt" : (type < 200 + ? "sqrtf" : "sqrtl"); + if (_LIB_VERSION == _SVID_) + exc.retval = zero; + else + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("sqrt: DOMAIN error\n", 19); + } + __set_errno (EDOM); + } + break; + case 27: + case 127: + case 227: + /* fmod(x,0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "fmod" : (type < 200 + ? "fmodf" : "fmodl"); + if (_LIB_VERSION == _SVID_) + exc.retval = x; + else + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("fmod: DOMAIN error\n", 20); + } + __set_errno (EDOM); + } + break; + case 28: + case 128: + case 228: + /* remainder(x,0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "remainder" : (type < 200 + ? "remainderf" + : "remainderl"); + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("remainder: DOMAIN error\n", 24); + } + __set_errno (EDOM); + } + break; + case 29: + case 129: + case 229: + /* acosh(x<1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "acosh" : (type < 200 + ? "acoshf" : "acoshl"); + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("acosh: DOMAIN error\n", 20); + } + __set_errno (EDOM); + } + break; + case 30: + case 130: + case 230: + /* atanh(|x|>1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "atanh" : (type < 200 + ? "atanhf" : "atanhl"); + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("atanh: DOMAIN error\n", 20); + } + __set_errno (EDOM); + } + break; + case 31: + case 131: + case 231: + /* atanh(|x|=1) */ + exc.type = SING; + exc.name = type < 100 ? "atanh" : (type < 200 + ? "atanhf" : "atanhl"); + exc.retval = x/zero; /* sign(x)*inf */ + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("atanh: SING error\n", 18); + } + __set_errno (EDOM); + } + break; + case 32: + case 132: + case 232: + /* scalb overflow; SVID also returns +-HUGE_VAL */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "scalb" : (type < 200 + ? "scalbf" : "scalbl"); + exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 33: + case 133: + case 233: + /* scalb underflow */ + exc.type = UNDERFLOW; + exc.name = type < 100 ? "scalb" : (type < 200 + ? "scalbf" : "scalbl"); + exc.retval = __copysign(zero,x); + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 34: + case 134: + case 234: + /* j0(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "j0" : (type < 200 ? "j0f" : "j0l"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + __set_errno (ERANGE); + } + break; + case 35: + case 135: + case 235: + /* y0(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "y0" : (type < 200 ? "y0f" : "y0l"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + __set_errno (ERANGE); + } + break; + case 36: + case 136: + case 236: + /* j1(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "j1" : (type < 200 ? "j1f" : "j1l"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + __set_errno (ERANGE); + } + break; + case 37: + case 137: + case 237: + /* y1(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "y1" : (type < 200 ? "y1f" : "y1l"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + __set_errno (ERANGE); + } + break; + case 38: + case 138: + case 238: + /* jn(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "jn" : (type < 200 ? "jnf" : "jnl"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + __set_errno (ERANGE); + } + break; + case 39: + case 139: + case 239: + /* yn(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "yn" : (type < 200 ? "ynf" : "ynl"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + __set_errno (ERANGE); + } + break; + case 40: + case 140: + case 240: + /* gamma(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "tgamma" : (type < 200 + ? "tgammaf" : "tgammal"); + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 41: + case 141: + case 241: + /* gamma(-integer) or gamma(0) */ + exc.type = SING; + exc.name = type < 100 ? "tgamma" : (type < 200 + ? "tgammaf" : "tgammal"); + exc.retval = NAN; + if (_LIB_VERSION == _POSIX_) + __set_errno (EDOM); + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("tgamma: SING error\n", 18); + exc.retval = HUGE_VAL; + } + __set_errno (EDOM); + } + break; + case 42: + case 142: + case 242: + /* pow(NaN,0.0) */ + /* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */ + exc.type = DOMAIN; + exc.name = type < 100 ? "pow" : (type < 200 ? "powf" : "powl"); + exc.retval = x; + if (_LIB_VERSION == _IEEE_ || + _LIB_VERSION == _POSIX_) exc.retval = 1.0; + else if (!matherr(&exc)) { + __set_errno (EDOM); + } + break; + + case 44: + case 144: + case 244: + /* exp(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "exp2" : (type < 200 + ? "exp2f" : "exp2l"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 45: + case 145: + case 245: + /* exp(finite) underflow */ + exc.type = UNDERFLOW; + exc.name = type < 100 ? "exp2" : (type < 200 + ? "exp2f" : "exp2l"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + + case 46: + case 146: + case 246: + /* exp(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "exp10" : (type < 200 + ? "exp10f" : "exp10l"); + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + case 47: + case 147: + case 247: + /* exp(finite) underflow */ + exc.type = UNDERFLOW; + exc.name = type < 100 ? "exp10" : (type < 200 + ? "exp10f" : "exp10l"); + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + __set_errno (ERANGE); + else if (!matherr(&exc)) { + __set_errno (ERANGE); + } + break; + /* #### Last used is 47/147/247 ### */ + } + return exc.retval; +} diff --git a/sysdeps/ieee754/ldbl-128/e_acoshl.c b/sysdeps/ieee754/ldbl-128/e_acoshl.c new file mode 100644 index 0000000..7f79340 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/e_acoshl.c @@ -0,0 +1,68 @@ +/* e_acoshl.c -- long double version of e_acosh.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_acoshl(x) + * Method : + * Based on + * acoshl(x) = logl [ x + sqrtl(x*x-1) ] + * we have + * acoshl(x) := logl(x)+ln2, if x is large; else + * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else + * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acoshl(x) is NaN with signal if x<1. + * acoshl(NaN) is NaN without signal. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +one = 1.0, +ln2 = 0.6931471805599453094172321214581766L; + +#ifdef __STDC__ + long double __ieee754_acoshl(long double x) +#else + long double __ieee754_acoshl(x) + long double x; +#endif +{ + long double t; + u_int64_t lx; + int64_t hx; + GET_LDOUBLE_WORDS64(hx,lx,x); + if(hx<0x3fff000000000000LL) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x401b000000000000LL) { /* x > 2**28 */ + if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */ + } else if(((hx-0x3fff000000000000LL)|lx)==0) { + return 0.0L; /* acosh(1) = 0 */ + } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_logl(2.0L*x-one/(x+__ieee754_sqrtl(t-one))); + } else { /* 1<x<2 */ + t = x-one; + return __log1pl(t+__sqrtl(2.0L*t+t*t)); + } +} diff --git a/sysdeps/ieee754/ldbl-128/e_atan2l.c b/sysdeps/ieee754/ldbl-128/e_atan2l.c new file mode 100644 index 0000000..2e081d3 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/e_atan2l.c @@ -0,0 +1,129 @@ +/* e_atan2l.c -- long double version of e_atan2.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_atan2l(y,x) + * Method : + * 1. Reduce y to positive by atan2l(y,x)=-atan2l(-y,x). + * 2. Reduce x to positive by (if x and y are unexceptional): + * ARG (x+iy) = arctan(y/x) ... if x > 0, + * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * + * Special cases: + * + * ATAN2((anything), NaN ) is NaN; + * ATAN2(NAN , (anything) ) is NaN; + * ATAN2(+-0, +(anything but NaN)) is +-0 ; + * ATAN2(+-0, -(anything but NaN)) is +-pi ; + * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; + * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; + * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; + * ATAN2(+-INF,+INF ) is +-pi/4 ; + * ATAN2(+-INF,-INF ) is +-3pi/4; + * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +tiny = 1.0e-4900L, +zero = 0.0, +pi_o_4 = 7.85398163397448309615660845819875699e-01L, /* 3ffe921fb54442d18469898cc51701b8 */ +pi_o_2 = 1.57079632679489661923132169163975140e+00L, /* 3fff921fb54442d18469898cc51701b8 */ +pi = 3.14159265358979323846264338327950280e+00L, /* 4000921fb54442d18469898cc51701b8 */ +pi_lo = 8.67181013012378102479704402604335225e-35L; /* 3f8dcd129024e088a67cc74020bbea64 */ + +#ifdef __STDC__ + long double __ieee754_atan2l(long double y, long double x) +#else + long double __ieee754_atan2l(y,x) + long double y,x; +#endif +{ + long double z; + int64_t k,m,hx,hy,ix,iy; + u_int64_t lx,ly; + + GET_LDOUBLE_WORDS64(hx,lx,x); + ix = hx&0x7fffffffffffffffLL; + GET_LDOUBLE_WORDS64(hy,ly,y); + iy = hy&0x7fffffffffffffffLL; + if(((ix|((lx|-lx)>>63))>0x7fff000000000000LL)|| + ((iy|((ly|-ly)>>63))>0x7fff000000000000LL)) /* x or y is NaN */ + return x+y; + if((hx-0x3fff000000000000LL|lx)==0) return __atanl(y); /* x=1.0L */ + m = ((hy>>63)&1)|((hx>>62)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if((iy|ly)==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7fff000000000000LL) { + if(iy==0x7fff000000000000LL) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return 3.0L*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return -3.0L*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7fff000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>48; + if(k > 120) z=pi_o_2+0.5L*pi_lo; /* |y/x| > 2**120 */ + else if(hx<0&&k<-120) z=0.0L; /* |y|/x < -2**120 */ + else z=__atanl(fabsl(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: { + u_int64_t zh; + GET_LDOUBLE_MSW64(zh,z); + SET_LDOUBLE_MSW64(z,zh ^ 0x8000000000000000ULL); + } + return z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} diff --git a/sysdeps/ieee754/ldbl-128/e_fmodl.c b/sysdeps/ieee754/ldbl-128/e_fmodl.c new file mode 100644 index 0000000..1043f69 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/e_fmodl.c @@ -0,0 +1,138 @@ +/* e_fmodl.c -- long double version of e_fmod.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __ieee754_fmodl(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double one = 1.0, Zero[] = {0.0, -0.0,}; +#else +static long double one = 1.0, Zero[] = {0.0, -0.0,}; +#endif + +#ifdef __STDC__ + long double __ieee754_fmodl(long double x, long double y) +#else + long double __ieee754_fmodl(x,y) + long double x,y; +#endif +{ + int64_t n,hx,hy,hz,ix,iy,sx,i; + u_int64_t lx,ly,lz; + + GET_LDOUBLE_WORDS64(hx,lx,x); + GET_LDOUBLE_WORDS64(hy,ly,y); + sx = hx&0x8000000000000000ULL; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffffffffffffLL; /* |y| */ + + /* purge off exception values */ + if((hy|ly)==0||(hx>=0x7fff000000000000LL)|| /* y=0,or x not finite */ + ((hy|((ly|-ly)>>63))>0x7fff000000000000LL)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx<=hy) { + if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */ + if(lx==ly) + return Zero[(u_int64_t)sx>>63]; /* |x|=|y| return x*0*/ + } + + /* determine ix = ilogb(x) */ + if(hx<0x0001000000000000LL) { /* subnormal x */ + if(hx==0) { + for (ix = -16431, i=lx; i>0; i<<=1) ix -=1; + } else { + for (ix = -16382, i=hx<<15; i>0; i<<=1) ix -=1; + } + } else ix = (hx>>48)-0x3fff; + + /* determine iy = ilogb(y) */ + if(hy<0x0001000000000000LL) { /* subnormal y */ + if(hy==0) { + for (iy = -16431, i=ly; i>0; i<<=1) iy -=1; + } else { + for (iy = -16382, i=hy<<15; i>0; i<<=1) iy -=1; + } + } else iy = (hy>>48)-0x3fff; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -16382) + hx = 0x0001000000000000LL|(0x0000ffffffffffffLL&hx); + else { /* subnormal x, shift x to normal */ + n = -16382-ix; + if(n<=63) { + hx = (hx<<n)|(lx>>(64-n)); + lx <<= n; + } else { + hx = lx<<(n-64); + lx = 0; + } + } + if(iy >= -16382) + hy = 0x0001000000000000LL|(0x0000ffffffffffffLL&hy); + else { /* subnormal y, shift y to normal */ + n = -16382-iy; + if(n<=63) { + hy = (hy<<n)|(ly>>(64-n)); + ly <<= n; + } else { + hy = ly<<(n-64); + ly = 0; + } + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; + if(hz<0){hx = hx+hx+(lx>>63); lx = lx+lx;} + else { + if((hz|lz)==0) /* return sign(x)*0 */ + return Zero[(u_int64_t)sx>>63]; + hx = hz+hz+(lz>>63); lx = lz+lz; + } + } + hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; + if(hz>=0) {hx=hz;lx=lz;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) /* return sign(x)*0 */ + return Zero[(u_int64_t)sx>>63]; + while(hx<0x0001000000000000LL) { /* normalize x */ + hx = hx+hx+(lx>>63); lx = lx+lx; + iy -= 1; + } + if(iy>= -16382) { /* normalize output */ + hx = ((hx-0x0001000000000000LL)|((iy+16383)<<48)); + SET_LDOUBLE_WORDS64(x,hx|sx,lx); + } else { /* subnormal output */ + n = -16382 - iy; + if(n<=48) { + lx = (lx>>n)|((u_int64_t)hx<<(64-n)); + hx >>= n; + } else if (n<=63) { + lx = (hx<<(64-n))|(lx>>n); hx = sx; + } else { + lx = hx>>(n-64); hx = sx; + } + SET_LDOUBLE_WORDS64(x,hx|sx,lx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} diff --git a/sysdeps/ieee754/ldbl-128/e_gammal_r.c b/sysdeps/ieee754/ldbl-128/e_gammal_r.c new file mode 100644 index 0000000..f77350f --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/e_gammal_r.c @@ -0,0 +1,52 @@ +/* Implementation of gamma function according to ISO C. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> +#include <math_private.h> + + +long double +__ieee754_gammal_r (long double x, int *signgamp) +{ + /* We don't have a real gamma implementation now. We'll use lgamma + and the exp function. But due to the required boundary + conditions we must check some values separately. */ + int64_t hx; + u_int64_t lx; + + GET_LDOUBLE_WORDS64 (hx, lx, x); + + if (((hx & 0x7fffffffffffffffLL) | lx) == 0) + { + /* Return value for x == 0 is NaN with invalid exception. */ + *signgamp = 0; + return x / x; + } + if (hx < 0 && (u_int64_t) hx < 0xffff000000000000ULL && __rintl (x) == x) + { + /* Return value for integer x < 0 is NaN with invalid exception. */ + *signgamp = 0; + return (x - x) / (x - x); + } + + /* XXX FIXME. */ + return __ieee754_expl (__ieee754_lgammal_r (x, signgamp)); +} diff --git a/sysdeps/ieee754/ldbl-128/e_remainderl.c b/sysdeps/ieee754/ldbl-128/e_remainderl.c new file mode 100644 index 0000000..81af247 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/e_remainderl.c @@ -0,0 +1,78 @@ +/* e_fmodl.c -- long double version of e_fmod.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_remainderl(x,p) + * Return : + * returns x REM p = x - [x/p]*p as if in infinite + * precise arithmetic, where [x/p] is the (infinite bit) + * integer nearest x/p (in half way case choose the even one). + * Method : + * Based on fmodl() return x-[x/p]chopped*p exactlp. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double zero = 0.0L; +#else +static long double zero = 0.0L; +#endif + + +#ifdef __STDC__ + long double __ieee754_remainderl(long double x, long double p) +#else + long double __ieee754_remainderl(x,p) + long double x,p; +#endif +{ + int64_t hx,hp; + u_int64_t sx,lx,lp; + long double p_half; + + GET_LDOUBLE_WORDS64(hx,lx,x); + GET_LDOUBLE_WORDS64(hp,lp,p); + sx = hx&0x8000000000000000ULL; + hp &= 0x7fffffffffffffffLL; + hx &= 0x7fffffffffffffffLL; + + /* purge off exception values */ + if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7fff000000000000LL)|| /* x not finite */ + ((hp>=0x7fff000000000000LL)&& /* p is NaN */ + (((hp-0x7fff000000000000LL)|lp)!=0))) + return (x*p)/(x*p); + + + if (hp<=0x7ffdffffffffffffLL) x = __ieee754_fmodl(x,p+p); /* now x < 2p */ + if (((hx-hp)|(lx-lp))==0) return zero*x; + x = fabsl(x); + p = fabsl(p); + if (hp<0x0002000000000000LL) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = 0.5L*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_LDOUBLE_MSW64(hx,x); + SET_LDOUBLE_MSW64(x,hx^sx); + return x; +} diff --git a/sysdeps/ieee754/ldbl-128/ieee754.h b/sysdeps/ieee754/ldbl-128/ieee754.h new file mode 100644 index 0000000..c3b2f38 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/ieee754.h @@ -0,0 +1,171 @@ +/* Copyright (C) 1992, 1995, 1996, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#ifndef _IEEE754_H + +#define _IEEE754_H 1 +#include <features.h> + +#include <endian.h> + +__BEGIN_DECLS + +union ieee754_float + { + float f; + + /* This is the IEEE 754 single-precision format. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:8; + unsigned int mantissa:23; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + unsigned int mantissa:23; + unsigned int exponent:8; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee; + + /* This format makes it easier to see if a NaN is a signalling NaN. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:8; + unsigned int quiet_nan:1; + unsigned int mantissa:22; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + unsigned int mantissa:22; + unsigned int quiet_nan:1; + unsigned int exponent:8; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee_nan; + }; + +#define IEEE754_FLOAT_BIAS 0x7f /* Added to exponent. */ + + +union ieee754_double + { + double d; + + /* This is the IEEE 754 double-precision format. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:11; + /* Together these comprise the mantissa. */ + unsigned int mantissa0:20; + unsigned int mantissa1:32; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + /* Together these comprise the mantissa. */ + unsigned int mantissa1:32; + unsigned int mantissa0:20; + unsigned int exponent:11; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee; + + /* This format makes it easier to see if a NaN is a signalling NaN. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:11; + unsigned int quiet_nan:1; + /* Together these comprise the mantissa. */ + unsigned int mantissa0:19; + unsigned int mantissa1:32; +#else + /* Together these comprise the mantissa. */ + unsigned int mantissa1:32; + unsigned int mantissa0:19; + unsigned int quiet_nan:1; + unsigned int exponent:11; + unsigned int negative:1; +#endif + } ieee_nan; + }; + +#define IEEE754_DOUBLE_BIAS 0x3ff /* Added to exponent. */ + + +union ieee854_long_double + { + long double d; + + /* This is the IEEE 854 quad-precision format. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:15; + /* Together these comprise the mantissa. */ + unsigned int mantissa0:16; + unsigned int mantissa1:32; + unsigned int mantissa2:32; + unsigned int mantissa3:32; +#endif /* Big endian. */ +#if __BYTE_ORDER == __LITTLE_ENDIAN + /* Together these comprise the mantissa. */ + unsigned int mantissa3:32; + unsigned int mantissa2:32; + unsigned int mantissa1:32; + unsigned int mantissa0:16; + unsigned int exponent:15; + unsigned int negative:1; +#endif /* Little endian. */ + } ieee; + + /* This format makes it easier to see if a NaN is a signalling NaN. */ + struct + { +#if __BYTE_ORDER == __BIG_ENDIAN + unsigned int negative:1; + unsigned int exponent:15; + unsigned int quiet_nan:1; + /* Together these comprise the mantissa. */ + unsigned int mantissa0:15; + unsigned int mantissa1:32; + unsigned int mantissa2:32; + unsigned int mantissa3:32; +#else + /* Together these comprise the mantissa. */ + unsigned int mantissa3:32; + unsigned int mantissa2:32; + unsigned int mantissa1:32; + unsigned int mantissa0:15; + unsigned int quiet_nan:1; + unsigned int exponent:15; + unsigned int negative:1; +#endif + } ieee_nan; + }; + +#define IEEE854_LONG_DOUBLE_BIAS 0x3fff /* Added to exponent. */ + +__END_DECLS + +#endif /* ieee754.h */ diff --git a/sysdeps/ieee754/ldbl-128/ldbl2mpn.c b/sysdeps/ieee754/ldbl-128/ldbl2mpn.c new file mode 100644 index 0000000..68ecea8 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/ldbl2mpn.c @@ -0,0 +1,137 @@ +/* Copyright (C) 1995, 1996, 1997, 1998, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include "longlong.h" +#include <ieee754.h> +#include <float.h> +#include <math.h> +#include <stdlib.h> + +/* Convert a `long double' in IEEE854 quad-precision format to a + multi-precision integer representing the significand scaled up by its + number of bits (113 for long double) and an integral power of two + (MPN frexpl). */ + +mp_size_t +__mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size, + int *expt, int *is_neg, + long double value) +{ + union ieee854_long_double u; + u.d = value; + + *is_neg = u.ieee.negative; + *expt = (int) u.ieee.exponent - IEEE854_LONG_DOUBLE_BIAS; + +#if BITS_PER_MP_LIMB == 32 + res_ptr[0] = u.ieee.mantissa3; /* Low-order 32 bits of fraction. */ + res_ptr[1] = u.ieee.mantissa2; + res_ptr[2] = u.ieee.mantissa1; + res_ptr[3] = u.ieee.mantissa0; /* High-order 32 bits. */ + #define N 4 +#elif BITS_PER_MP_LIMB == 64 + /* Hopefully the compiler will combine the two bitfield extracts + and this composition into just the original quadword extract. */ + res_ptr[0] = ((unsigned long int) u.ieee.mantissa2 << 32) | u.ieee.mantissa3; + res_ptr[1] = ((unsigned long int) u.ieee.mantissa0 << 32) | u.ieee.mantissa1; + #define N 2 +#else + #error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif +/* The format does not fill the last limb. There are some zeros. */ +#define NUM_LEADING_ZEROS (BITS_PER_MP_LIMB \ + - (LDBL_MANT_DIG - ((N - 1) * BITS_PER_MP_LIMB))) + + if (u.ieee.exponent == 0) + { + /* A biased exponent of zero is a special case. + Either it is a zero or it is a denormal number. */ + if (res_ptr[0] == 0 && res_ptr[1] == 0 + && res_ptr[N - 2] == 0 && res_ptr[N - 1] == 0) /* Assumes N<=4. */ + /* It's zero. */ + *expt = 0; + else + { + /* It is a denormal number, meaning it has no implicit leading + one bit, and its exponent is in fact the format minimum. */ + int cnt; + +#if N == 2 + if (res_ptr[N - 1] != 0) + { + count_leading_zeros (cnt, res_ptr[N - 1]); + cnt -= NUM_LEADING_ZEROS; + res_ptr[N - 1] = res_ptr[N - 1] << cnt + | (res_ptr[0] >> (BITS_PER_MP_LIMB - cnt)); + res_ptr[0] <<= cnt; + *expt = LDBL_MIN_EXP - 1 - cnt; + } + else + { + count_leading_zeros (cnt, res_ptr[0]); + if (cnt >= NUM_LEADING_ZEROS) + { + res_ptr[N - 1] = res_ptr[0] << (cnt - NUM_LEADING_ZEROS); + res_ptr[0] = 0; + } + else + { + res_ptr[N - 1] = res_ptr[0] >> (NUM_LEADING_ZEROS - cnt); + res_ptr[0] <<= BITS_PER_MP_LIMB - (NUM_LEADING_ZEROS - cnt); + } + *expt = LDBL_MIN_EXP - 1 + - (BITS_PER_MP_LIMB - NUM_LEADING_ZEROS) - cnt; + } +#else + int j, k, l; + + for (j = N - 1; j > 0; j++) + if (res_ptr[j] != 0) + break; + + count_leading_zeros (cnt, res_ptr[j]); + cnt -= NUM_LEADING_ZEROS; + l = N - 1 - j; + if (cnt < 0) + { + cnt += BITS_PER_MP_LIMB; + l++; + } + if (!cnt) + for (k = N - 1; k >= l; k--) + res_ptr[k] = res_ptr[k-l]; + else + for (k = N - 1; k >= l; k--) + res_ptr[k] = res_ptr[k-l] << cnt + | res_ptr[k-l-1] >> (BITS_PER_MP_LIMB - cnt); + res_ptr[k--] = res_ptr[0] << cnt; + + for (; k >= 0; k--) + res_ptr[k] = 0; + *expt = LDBL_MIN_EXP - 1 - 3 * BITS_PER_MP_LIMB - cnt; +#endif + } + } + else + /* Add the implicit leading one bit for a normalized number. */ + res_ptr[N - 1] |= 1L << (LDBL_MANT_DIG - 1 - ((N - 1) * BITS_PER_MP_LIMB)); + + return N; +} diff --git a/sysdeps/ieee754/ldbl-128/math_ldbl.h b/sysdeps/ieee754/ldbl-128/math_ldbl.h new file mode 100644 index 0000000..aecb20a --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/math_ldbl.h @@ -0,0 +1,82 @@ +#ifndef _MATH_PRIVATE_H_ +#error "Never use <math_ldbl.h> directly; include <math_private.h> instead." +#endif + +/* A union which permits us to convert between a long double and + four 32 bit ints or two 64 bit ints. */ + +#if __FLOAT_WORD_ORDER == BIG_ENDIAN + +typedef union +{ + long double value; + struct + { + u_int64_t msw; + u_int64_t lsw; + } parts64; + struct + { + u_int32_t w0, w1, w2, w3; + } parts32; +} ieee854_long_double_shape_type; + +#endif + +#if __FLOAT_WORD_ORDER == LITTLE_ENDIAN + +typedef union +{ + long double value; + struct + { + u_int64_t lsw; + u_int64_t msw; + } parts64; + struct + { + u_int32_t w3, w2, w1, w0; + } parts32; +} ieee854_long_double_shape_type; + +#endif + +/* Get two 64 bit ints from a long double. */ + +#define GET_LDOUBLE_WORDS64(ix0,ix1,d) \ +do { \ + ieee854_long_double_shape_type qw_u; \ + qw_u.value = (d); \ + (ix0) = qw_u.parts64.msw; \ + (ix1) = qw_u.parts64.lsw; \ +} while (0) + +/* Set a long double from two 64 bit ints. */ + +#define SET_LDOUBLE_WORDS64(d,ix0,ix1) \ +do { \ + ieee854_long_double_shape_type qw_u; \ + qw_u.parts64.msw = (ix0); \ + qw_u.parts64.lsw = (ix1); \ + (d) = qw_u.value; \ +} while (0) + +/* Get the more significant 64 bits of a long double mantissa. */ + +#define GET_LDOUBLE_MSW64(v,d) \ +do { \ + ieee854_long_double_shape_type sh_u; \ + sh_u.value = (d); \ + (v) = sh_u.parts64.msw; \ +} while (0) + +/* Set the more significant 64 bits of a long double mantissa from an int. */ + +#define SET_LDOUBLE_MSW64(d,v) \ +do { \ + ieee854_long_double_shape_type sh_u; \ + sh_u.value = (d); \ + sh_u.parts64.msw = (v); \ + (d) = sh_u.value; \ +} while (0) + diff --git a/sysdeps/ieee754/ldbl-128/mpn2ldbl.c b/sysdeps/ieee754/ldbl-128/mpn2ldbl.c new file mode 100644 index 0000000..d9cc452 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/mpn2ldbl.c @@ -0,0 +1,51 @@ +/* Copyright (C) 1995, 1996, 1997, 1998, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include <ieee754.h> +#include <float.h> +#include <math.h> + +/* Convert a multi-precision integer of the needed number of bits (113 for + long double) and an integral power of two to a `long double' in IEEE854 + quad-precision format. */ + +long double +__mpn_construct_long_double (mp_srcptr frac_ptr, int expt, int sign) +{ + union ieee854_long_double u; + + u.ieee.negative = sign; + u.ieee.exponent = expt + IEEE854_LONG_DOUBLE_BIAS; +#if BITS_PER_MP_LIMB == 32 + u.ieee.mantissa3 = frac_ptr[0]; + u.ieee.mantissa2 = frac_ptr[1]; + u.ieee.mantissa1 = frac_ptr[2]; + u.ieee.mantissa0 = frac_ptr[3] & ((1 << (LDBL_MANT_DIG - 96)) - 1); +#elif BITS_PER_MP_LIMB == 64 + u.ieee.mantissa3 = frac_ptr[0] & ((1L << 32) - 1); + u.ieee.mantissa2 = frac_ptr[0] >> 32; + u.ieee.mantissa1 = frac_ptr[1] & ((1L << 32) - 1); + u.ieee.mantissa0 = (frac_ptr[1] >> 32) & ((1 << (LDBL_MANT_DIG - 96)) - 1); +#else + #error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" +#endif + + return u.d; +} diff --git a/sysdeps/ieee754/ldbl-128/printf_fphex.c b/sysdeps/ieee754/ldbl-128/printf_fphex.c new file mode 100644 index 0000000..e25d668 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/printf_fphex.c @@ -0,0 +1,84 @@ +/* Print floating point number in hexadecimal notation according to + ISO C 9X. + Copyright (C) 1997, 1998, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#define PRINT_FPHEX_LONG_DOUBLE \ +do { \ + /* We have 112 bits of mantissa plus one implicit digit. Since \ + 112 bits are representable without rest using hexadecimal \ + digits we use only the implicit digits for the number before \ + the decimal point. */ \ + unsigned long long int num0, num1; \ + \ + assert (sizeof (long double) == 16); \ + \ + num0 = (((unsigned long long int) fpnum.ldbl.ieee.mantissa0) << 32 \ + | fpnum.ldbl.ieee.mantissa1); \ + num1 = (((unsigned long long int) fpnum.ldbl.ieee.mantissa2) << 32 \ + | fpnum.ldbl.ieee.mantissa3); \ + \ + zero_mantissa = (num0|num1) == 0; \ + \ + if (sizeof (unsigned long int) > 6) \ + numstr = _itoa_word (num1, numbuf + sizeof numbuf, 16, \ + info->spec == 'A'); \ + else \ + numstr = _itoa (num1, numbuf + sizeof numbuf, 16, \ + info->spec == 'A'); \ + \ + while (numstr > numbuf + (sizeof numbuf - 64 / 4)) \ + *--numstr = '0'; \ + \ + if (sizeof (unsigned long int) > 6) \ + numstr = _itoa_word (num0, numstr, 16, info->spec == 'A'); \ + else \ + numstr = _itoa (num0, numstr, 16, info->spec == 'A'); \ + \ + /* Fill with zeroes. */ \ + while (numstr > numbuf + (sizeof numbuf - 112 / 4)) \ + *--numstr = '0'; \ + \ + leading = fpnum.ldbl.ieee.exponent == 0 ? '0' : '1'; \ + \ + exponent = fpnum.ldbl.ieee.exponent; \ + \ + if (exponent == 0) \ + { \ + if (zero_mantissa) \ + expnegative = 0; \ + else \ + { \ + /* This is a denormalized number. */ \ + expnegative = 1; \ + exponent = IEEE854_LONG_DOUBLE_BIAS - 1; \ + } \ + } \ + else if (exponent >= IEEE854_LONG_DOUBLE_BIAS) \ + { \ + expnegative = 0; \ + exponent -= IEEE854_LONG_DOUBLE_BIAS; \ + } \ + else \ + { \ + expnegative = 1; \ + exponent = -(exponent - IEEE854_LONG_DOUBLE_BIAS); \ + } \ +} while (0) + +#include <sysdeps/generic/printf_fphex.c> diff --git a/sysdeps/ieee754/ldbl-128/s_ceill.c b/sysdeps/ieee754/ldbl-128/s_ceill.c new file mode 100644 index 0000000..f241554 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_ceill.c @@ -0,0 +1,84 @@ +/* s_ceill.c -- long double version of s_ceil.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * ceill(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to ceil(x). + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double huge = 1.0e4930; +#else +static long double huge = 1.0e4930; +#endif + +#ifdef __STDC__ + long double __ceill(long double x) +#else + long double __ceill(x) + long double x; +#endif +{ + int64_t i0,i1,j0; + u_int64_t i,j; + GET_LDOUBLE_WORDS64(i0,i1,x); + j0 = ((i0>>48)&0x7fff)-0x3fff; + if(j0<48) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x8000000000000000ULL;i1=0;} + else if((i0|i1)!=0) { i0=0x3fff000000000000ULL;i1=0;} + } + } else { + i = (0x7fffffffffffffffULL)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x0001000000000000LL)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>111) { + if(j0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = -1ULL>>(j0-48); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) { + if(j0==48) i0+=1; + else { + j = i1+(1LL<<(112-j0)); + if(j<i1) i0 +=1 ; /* got a carry */ + i1=j; + } + } + i1 &= (~i); + } + } + SET_LDOUBLE_WORDS64(x,i0,i1); + return x; +} +weak_alias (__ceill, ceill) diff --git a/sysdeps/ieee754/ldbl-128/s_copysignl.c b/sysdeps/ieee754/ldbl-128/s_copysignl.c new file mode 100644 index 0000000..cece4f2 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_copysignl.c @@ -0,0 +1,43 @@ +/* s_copysignl.c -- long double version of s_copysign.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * copysignl(long double x, long double y) + * copysignl(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __copysignl(long double x, long double y) +#else + long double __copysignl(x,y) + long double x,y; +#endif +{ + u_int64_t hx,hy; + GET_LDOUBLE_MSW64(hx,x); + GET_LDOUBLE_MSW64(hy,y); + SET_LDOUBLE_MSW64(x,(hx&0x7fffffffffffffffULL) + |(hy&0x8000000000000000ULL)); + return x; +} +weak_alias (__copysignl, copysignl) diff --git a/sysdeps/ieee754/ldbl-128/s_cosl.c b/sysdeps/ieee754/ldbl-128/s_cosl.c new file mode 100644 index 0000000..d1258b2 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_cosl.c @@ -0,0 +1,83 @@ +/* s_cosl.c -- long double version of s_cos.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* cosl(x) + * Return cosine function of x. + * + * kernel function: + * __kernel_sinl ... sine function on [-pi/4,pi/4] + * __kernel_cosl ... cosine function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __cosl(long double x) +#else + long double __cosl(x) + long double x; +#endif +{ + long double y[2],z=0.0L; + int64_t n, ix; + + /* High word of x. */ + GET_LDOUBLE_MSW64(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if(ix <= 0x3ffe921fb54442d1LL) + return __kernel_cosl(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7fff000000000000LL) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + switch(n&3) { + case 0: return __kernel_cosl(y[0],y[1]); + case 1: return -__kernel_sinl(y[0],y[1],1); + case 2: return -__kernel_cosl(y[0],y[1]); + default: + return __kernel_sinl(y[0],y[1],1); + } + } +} +weak_alias (__cosl, cosl) diff --git a/sysdeps/ieee754/ldbl-128/s_fabsl.c b/sysdeps/ieee754/ldbl-128/s_fabsl.c new file mode 100644 index 0000000..c0fd05a --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_fabsl.c @@ -0,0 +1,39 @@ +/* s_fabsl.c -- long double version of s_fabs.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * fabsl(x) returns the absolute value of x. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __fabsl(long double x) +#else + long double __fabsl(x) + long double x; +#endif +{ + u_int64_t hx; + GET_LDOUBLE_MSW64(hx,x); + SET_LDOUBLE_MSW64(x,hx&0x7fffffffffffffffLL); + return x; +} +weak_alias (__fabsl, fabsl) diff --git a/sysdeps/ieee754/ldbl-128/s_finitel.c b/sysdeps/ieee754/ldbl-128/s_finitel.c new file mode 100644 index 0000000..dd176c1 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_finitel.c @@ -0,0 +1,40 @@ +/* s_finitel.c -- long double version of s_finite.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * finitel(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int __finitel(long double x) +#else + int __finitel(x) + long double x; +#endif +{ + int64_t hx; + GET_LDOUBLE_MSW64(hx,x); + return (int)((u_int64_t)((hx&0x7fffffffffffffffLL) + -0x7fff000000000000LL)>>63); +} +weak_alias (__finitel, finitel) diff --git a/sysdeps/ieee754/ldbl-128/s_floorl.c b/sysdeps/ieee754/ldbl-128/s_floorl.c new file mode 100644 index 0000000..c9b8b70 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_floorl.c @@ -0,0 +1,85 @@ +/* s_floorl.c -- long double version of s_floor.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * floorl(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floor(x). + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double huge = 1.0e4930; +#else +static long double huge = 1.0e4930; +#endif + +#ifdef __STDC__ + long double __floorl(long double x) +#else + long double __floorl(x) + long double x; +#endif +{ + int64_t i0,i1,j0; + u_int64_t i,j; + GET_LDOUBLE_WORDS64(i0,i1,x); + j0 = ((i0>>48)&0x7fff)-0x3fff; + if(j0<48) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=i1=0;} + else if(((i0&0x7fffffffffffffffLL)|i1)!=0) + { i0=0xbfff000000000000ULL;i1=0;} + } + } else { + i = (0x7fffffffffffffffULL)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x0001000000000000LL)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>111) { + if(j0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = -1ULL>>(j0-48); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) { + if(j0==48) i0+=1; + else { + j = i1+(1LL<<(112-j0)); + if(j<i1) i0 +=1 ; /* got a carry */ + i1=j; + } + } + i1 &= (~i); + } + } + SET_LDOUBLE_WORDS64(x,i0,i1); + return x; +} +weak_alias (__floorl, floorl) diff --git a/sysdeps/ieee754/ldbl-128/s_fpclassifyl.c b/sysdeps/ieee754/ldbl-128/s_fpclassifyl.c new file mode 100644 index 0000000..868c3c4 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_fpclassifyl.c @@ -0,0 +1,44 @@ +/* Return classification value corresponding to argument. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +int +__fpclassifyl (long double x) +{ + u_int64_t hx, lx; + int retval = FP_NORMAL; + + GET_LDOUBLE_WORDS64 (hx, lx, x); + lx |= (hx & 0x0000ffffffffffffLL); + hx &= 0x7fff000000000000LL; + if ((hx | lx) == 0) + retval = FP_ZERO; + else if (hx == 0) + retval = FP_SUBNORMAL; + else if (hx == 0x7fff000000000000LL) + retval = lx != 0 ? FP_NAN : FP_INFINITE; + + return retval; +} diff --git a/sysdeps/ieee754/ldbl-128/s_frexpl.c b/sysdeps/ieee754/ldbl-128/s_frexpl.c new file mode 100644 index 0000000..6dbb60e --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_frexpl.c @@ -0,0 +1,63 @@ +/* s_frexpl.c -- long double version of s_frexp.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * for non-zero x + * x = frexpl(arg,&exp); + * return a long double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexpl(arg,&exp) returns arg + * with *exp=0. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +two114 = 2.0769187434139310514121985316880384E+34L; /* 0x4071000000000000, 0 */ + +#ifdef __STDC__ + long double __frexpl(long double x, int *eptr) +#else + long double __frexpl(x, eptr) + long double x; int *eptr; +#endif +{ + u_int64_t hx, lx, ix; + GET_LDOUBLE_WORDS64(hx,lx,x); + ix = 0x7fffffffffffffffULL&hx; + *eptr = 0; + if(ix>=0x7fff000000000000ULL||((ix|lx)==0)) return x; /* 0,inf,nan */ + if (ix<0x0001000000000000ULL) { /* subnormal */ + x *= two114; + GET_LDOUBLE_MSW64(hx,x); + ix = hx&0x7fffffffffffffffULL; + *eptr = -114; + } + *eptr += (ix>>48)-16382; + hx = (hx&0x8000ffffffffffffULL) | 0x3ffe000000000000ULL; + SET_LDOUBLE_MSW64(x,hx); + return x; +} +weak_alias (__frexpl, frexpl) diff --git a/sysdeps/ieee754/ldbl-128/s_ilogbl.c b/sysdeps/ieee754/ldbl-128/s_ilogbl.c new file mode 100644 index 0000000..d2acfd3 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_ilogbl.c @@ -0,0 +1,55 @@ +/* s_ilogbl.c -- long double version of s_ilogb.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* ilogbl(long double x) + * return the binary exponent of non-zero x + * ilogbl(0) = 0x80000001 + * ilogbl(inf/NaN) = 0x7fffffff (no signal is raised) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int __ilogbl(long double x) +#else + int __ilogbl(x) + long double x; +#endif +{ + int64_t hx,lx; + int ix; + + GET_LDOUBLE_WORDS64(hx,lx,x); + hx &= 0x7fffffffffffffffLL; + if(hx <= 0x0001000000000000LL) { + if((hx|lx)==0) + return FP_ILOGB0; /* ilogbl(0) = FP_ILOGB0 */ + else /* subnormal x */ + if(hx==0) { + for (ix = -16431; lx>0; lx<<=1) ix -=1; + } else { + for (ix = -16382, hx<<=15; hx>0; hx<<=1) ix -=1; + } + return ix; + } + else if (hx<0x7fff000000000000LL) return (hx>>48)-0x3fff; + else return FP_ILOGBNAN; +} +weak_alias (__ilogbl, ilogbl) diff --git a/sysdeps/ieee754/ldbl-128/s_isinfl.c b/sysdeps/ieee754/ldbl-128/s_isinfl.c new file mode 100644 index 0000000..038c294 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_isinfl.c @@ -0,0 +1,28 @@ +/* + * Written by J.T. Conklin <jtc@netbsd.org>. + * Change for long double by Jakub Jelinek <jj@ultra.linux.cz> + * Public domain. + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * isinfl(x) returns 1 if x is inf, -1 if x is -inf, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +int +__isinfl (long double x) +{ + int64_t hx,lx; + GET_LDOUBLE_WORDS64(hx,lx,x); + lx |= (hx & 0x7fffffffffffffffLL) ^ 0x7fff000000000000LL; + lx |= -lx; + return ~(lx >> 63) & (hx >> 62); +} +weak_alias (__isinfl, isinfl) diff --git a/sysdeps/ieee754/ldbl-128/s_isnanl.c b/sysdeps/ieee754/ldbl-128/s_isnanl.c new file mode 100644 index 0000000..d2fb403 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_isnanl.c @@ -0,0 +1,42 @@ +/* s_isnanl.c -- long double version of s_isnan.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * isnanl(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int __isnanl(long double x) +#else + int __isnanl(x) + long double x; +#endif +{ + int64_t hx,lx; + GET_LDOUBLE_WORDS64(hx,lx,x); + hx &= 0x7fffffffffffffffLL; + hx |= (u_int64_t)(lx|(-lx))>>63; + hx = 0x7fff000000000000LL - hx; + return (int)((u_int64_t)hx>>63); +} +weak_alias (__isnanl, isnanl) diff --git a/sysdeps/ieee754/ldbl-128/s_llrintl.c b/sysdeps/ieee754/ldbl-128/s_llrintl.c new file mode 100644 index 0000000..389a65d --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_llrintl.c @@ -0,0 +1,75 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + +static const long double two112[2] = +{ + 5.19229685853482762853049632922009600E+33L, /* 0x406F000000000000, 0 */ + -5.19229685853482762853049632922009600E+33L /* 0xC06F000000000000, 0 */ +}; + +long long int +__llrintl (long double x) +{ + int32_t j0; + u_int64_t i0,i1; + volatile long double w; + long double t; + long long int result; + int sx; + + GET_LDOUBLE_WORDS64 (i0, i1, x); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + sx = i0 >> 63; + i0 &= 0x0000ffffffffffffLL; + i0 |= 0x0001000000000000LL; + + if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 < -1) + return 0; + w = two112[sx] + x; + t = w - two112[sx]; + GET_LDOUBLE_WORDS64 (i0, i1, x); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + i0 &= 0x0000ffffffffffffLL; + i0 |= 0x0001000000000000LL; + + if (j0 <= 48) + result = i0 >> (48 - j0); + else + result = ((long long int) i0 << (j0 - 48)) | (i1 >> (112 - j0)); + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__llrintl, llrintl) diff --git a/sysdeps/ieee754/ldbl-128/s_llroundl.c b/sysdeps/ieee754/ldbl-128/s_llroundl.c new file mode 100644 index 0000000..82395a7 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_llroundl.c @@ -0,0 +1,74 @@ +/* Round long double value to long long int. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +long long int +__llroundl (long double x) +{ + int64_t j0; + u_int64_t i1, i0; + long long int result; + int sign; + + GET_LDOUBLE_WORDS64 (i0, i1, x); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + sign = (i0 & 0x8000000000000000ULL) != 0 ? -1 : 1; + i0 &= 0x0000ffffffffffffLL; + i0 |= 0x0001000000000000LL; + + if (j0 < 48) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else + { + i0 += 0x0000800000000000LL >> j0; + result = i0 >> (48 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 >= 112) + result = ((long long int) i0 << (j0 - 48)) | (i1 << (j0 - 112)); + else + { + u_int64_t j = i1 + (0x8000000000000000ULL >> (j0 - 48)); + if (j < i1) + ++i0; + + result = ((long long int) i0 << (j0 - 48)) | (j >> (112 - j0)); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long long int) x; + } + + return sign * result; +} + +weak_alias (__llroundl, llroundl) diff --git a/sysdeps/ieee754/ldbl-128/s_logbl.c b/sysdeps/ieee754/ldbl-128/s_logbl.c new file mode 100644 index 0000000..1fda289 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_logbl.c @@ -0,0 +1,46 @@ +/* s_logbl.c -- long double version of s_logb.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * long double logbl(x) + * IEEE 754 logb. Included to pass IEEE test suite. Not recommend. + * Use ilogb instead. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __logbl(long double x) +#else + long double __logbl(x) + long double x; +#endif +{ + int64_t lx,hx; + GET_LDOUBLE_WORDS64(hx,lx,x); + hx &= 0x7fffffffffffffffLL; /* high |x| */ + if((hx|lx)==0) return -1.0/fabs(x); + if(hx>=0x7fff000000000000LL) return x*x; + if((hx>>=48)==0) /* IEEE 754 logb */ + return -16382.0; + else + return (long double) (hx-0x3fff); +} +weak_alias (__logbl, logbl) diff --git a/sysdeps/ieee754/ldbl-128/s_lrintl.c b/sysdeps/ieee754/ldbl-128/s_lrintl.c new file mode 100644 index 0000000..434aa31 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_lrintl.c @@ -0,0 +1,91 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + +static const long double two112[2] = +{ + 5.19229685853482762853049632922009600E+33L, /* 0x406F000000000000, 0 */ + -5.19229685853482762853049632922009600E+33L /* 0xC06F000000000000, 0 */ +}; + +long int +__lrintl (long double x) +{ + int32_t j0; + u_int64_t i0,i1; + volatile long double w; + long double t; + long int result; + int sx; + + GET_LDOUBLE_WORDS64 (i0, i1, x); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + sx = i0 >> 63; + i0 &= 0x0000ffffffffffffLL; + i0 |= 0x0001000000000000LL; + + if (j0 < 48) + { + if (j0 < -1) + return 0; + else + { + w = two112[sx] + x; + t = w - two112[sx]; + GET_LDOUBLE_WORDS64 (i0, i1, x); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + i0 &= 0x0000ffffffffffffLL; + i0 |= 0x0001000000000000LL; + + result = i0 >> (48 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 >= 112) + result = ((long int) i0 << (j0 - 48)) | (i1 << (j0 - 112)); + else + { + w = two112[sx] + x; + t = w - two112[sx]; + GET_LDOUBLE_WORDS64 (i0, i1, x); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + i0 &= 0x0000ffffffffffffLL; + i0 |= 0x0001000000000000LL; + + result = ((long int) i0 << (j0 - 48)) | (i1 >> (112 - j0)); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__lrintl, lrintl) diff --git a/sysdeps/ieee754/ldbl-128/s_lroundl.c b/sysdeps/ieee754/ldbl-128/s_lroundl.c new file mode 100644 index 0000000..ea82f4c --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_lroundl.c @@ -0,0 +1,74 @@ +/* Round long double value to long int. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +long int +__lroundl (long double x) +{ + int64_t j0; + u_int64_t i1, i0; + long int result; + int sign; + + GET_LDOUBLE_WORDS64 (i0, i1, x); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + sign = (i0 & 0x8000000000000000ULL) != 0 ? -1 : 1; + i0 &= 0x0000ffffffffffffLL; + i0 |= 0x0001000000000000LL; + + if (j0 < 48) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else + { + i0 += 0x0000800000000000LL >> j0; + result = i0 >> (48 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 >= 112) + result = ((long int) i0 << (j0 - 48)) | (i1 << (j0 - 112)); + else + { + u_int64_t j = i1 + (0x8000000000000000ULL >> (j0 - 48)); + if (j < i1) + ++i0; + + result = ((long int) i0 << (j0 - 48)) | (j >> (112 - j0)); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long int) x; + } + + return sign * result; +} + +weak_alias (__lroundl, lroundl) diff --git a/sysdeps/ieee754/ldbl-128/s_modfl.c b/sysdeps/ieee754/ldbl-128/s_modfl.c new file mode 100644 index 0000000..63d66e7 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_modfl.c @@ -0,0 +1,88 @@ +/* s_modfl.c -- long double version of s_modf.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * modfl(long double x, long double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double one = 1.0; +#else +static long double one = 1.0; +#endif + +#ifdef __STDC__ + long double __modfl(long double x, long double *iptr) +#else + long double __modfl(x, iptr) + long double x,*iptr; +#endif +{ + int64_t i0,i1,j0; + u_int64_t i; + GET_LDOUBLE_WORDS64(i0,i1,x); + j0 = ((i0>>48)&0x7fff)-0x3fff; /* exponent of x */ + if(j0<48) { /* integer part in high x */ + if(j0<0) { /* |x|<1 */ + /* *iptr = +-0 */ + SET_LDOUBLE_WORDS64(*iptr,i0&0x8000000000000000ULL,0); + return x; + } else { + i = (0x0000ffffffffffffLL)>>j0; + if(((i0&i)|i1)==0) { /* x is integral */ + *iptr = x; + /* return +-0 */ + SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0); + return x; + } else { + SET_LDOUBLE_WORDS64(*iptr,i0&(~i),0); + return x - *iptr; + } + } + } else if (j0>111) { /* no fraction part */ + *iptr = x*one; + /* We must handle NaNs separately. */ + if (j0 == 0x4000 && ((i0 & 0x0000ffffffffffffLL) | i1)) + return x*one; + /* return +-0 */ + SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0); + return x; + } else { /* fraction part in low x */ + i = -1ULL>>(j0-48); + if((i1&i)==0) { /* x is integral */ + *iptr = x; + /* return +-0 */ + SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0); + return x; + } else { + SET_LDOUBLE_WORDS64(*iptr,i0,i1&(~i)); + return x - *iptr; + } + } +} +weak_alias (__modfl, modfl) diff --git a/sysdeps/ieee754/ldbl-128/s_nearbyintl.c b/sysdeps/ieee754/ldbl-128/s_nearbyintl.c new file mode 100644 index 0000000..bea3183 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_nearbyintl.c @@ -0,0 +1,93 @@ +/* s_nearbyintl.c -- long double version of s_nearbyint.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * nearbyintl(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rintl(x). + */ + +#include <fenv.h> +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +TWO112[2]={ + 5.19229685853482762853049632922009600E+33L, /* 0x406F000000000000, 0 */ + -5.19229685853482762853049632922009600E+33L /* 0xC06F000000000000, 0 */ +}; + +#ifdef __STDC__ + long double __nearbyintl(long double x) +#else + long double __nearbyintl(x) + long double x; +#endif +{ + fenv_t env; + int64_t i0,j0,sx; + u_int64_t i,i1; + long double w,t; + GET_LDOUBLE_WORDS64(i0,i1,x); + sx = (((u_int64_t)i0)>>63); + j0 = ((i0>>48)&0x7fff)-0x3fff; + if(j0<48) { + if(j0<0) { + if(((i0&0x7fffffffffffffffLL)|i1)==0) return x; + i1 |= (i0&0x0000ffffffffffffLL); + i0 &= 0xffffe00000000000ULL; + i0 |= ((i1|-i1)>>16)&0x0000800000000000LL; + SET_LDOUBLE_MSW64(x,i0); + feholdexcept (&env); + w = TWO112[sx]+x; + t = w-TWO112[sx]; + fesetenv (&env); + GET_LDOUBLE_MSW64(i0,t); + SET_LDOUBLE_MSW64(t,(i0&0x7fffffffffffffffLL)|(sx<<63)); + return t; + } else { + i = (0x0000ffffffffffffLL)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + i>>=1; + if(((i0&i)|i1)!=0) { + if(j0==47) i1 = 0x4000000000000000ULL; else + i0 = (i0&(~i))|((0x0000200000000000LL)>>j0); + } + } + } else if (j0>111) { + if(j0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = -1ULL>>(j0-48); + if((i1&i)==0) return x; /* x is integral */ + i>>=1; + if((i1&i)!=0) i1 = (i1&(~i))|((0x4000000000000000LL)>>(j0-48)); + } + SET_LDOUBLE_WORDS64(x,i0,i1); + feholdexcept (&env); + w = TWO112[sx]+x; + t = w-TWO112[sx]; + fesetenv (&env); + return t; +} +weak_alias (__nearbyintl, nearbyintl) diff --git a/sysdeps/ieee754/ldbl-128/s_nextafterl.c b/sysdeps/ieee754/ldbl-128/s_nextafterl.c new file mode 100644 index 0000000..d3df668 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_nextafterl.c @@ -0,0 +1,85 @@ +/* s_nextafterl.c -- long double version of s_nextafter.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* IEEE functions + * nextafterl(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __nextafterl(long double x, long double y) +#else + long double __nextafterl(x,y) + long double x,y; +#endif +{ + int64_t hx,hy,ix,iy; + u_int64_t lx,ly; + + GET_LDOUBLE_WORDS64(hx,lx,x); + GET_LDOUBLE_WORDS64(hy,ly,y); + ix = hx&0x7fffffffffffffffLL; /* |x| */ + iy = hy&0x7fffffffffffffffLL; /* |y| */ + + if(((ix>=0x7fff000000000000LL)&&((ix-0x7fff000000000000LL)|lx)!=0) || /* x is nan */ + ((iy>=0x7fff000000000000LL)&&((iy-0x7fff000000000000LL)|ly)!=0)) /* y is nan */ + return x+y; + if(x==y) return y; /* x=y, return y */ + if((ix|lx)==0) { /* x == 0 */ + SET_LDOUBLE_WORDS64(x,hy&0x8000000000000000ULL,1);/* return +-minsubnormal */ + y = x*x; + if(y==x) return y; else return x; /* raise underflow flag */ + } + if(hx>=0) { /* x > 0 */ + if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */ + if(lx==0) hx--; + lx--; + } else { /* x < y, x += ulp */ + lx++; + if(lx==0) hx++; + } + } else { /* x < 0 */ + if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */ + if(lx==0) hx--; + lx--; + } else { /* x > y, x += ulp */ + lx++; + if(lx==0) hx++; + } + } + hy = hx&0x7fff000000000000LL; + if(hy==0x7fff000000000000LL) return x+x;/* overflow */ + if(hy==0) { /* underflow */ + y = x*x; + if(y!=x) { /* raise underflow flag */ + SET_LDOUBLE_WORDS64(y,hx,lx); + return y; + } + } + SET_LDOUBLE_WORDS64(x,hx,lx); + return x; +} +weak_alias (__nextafterl, nextafterl) +strong_alias (__nextafterl, __nexttowardl) +weak_alias (__nextafterl, nexttowardl) diff --git a/sysdeps/ieee754/ldbl-128/s_nexttoward.c b/sysdeps/ieee754/ldbl-128/s_nexttoward.c new file mode 100644 index 0000000..f121be2 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_nexttoward.c @@ -0,0 +1,97 @@ +/* s_nexttoward.c + * Conversion from s_nextafter.c by Ulrich Drepper, Cygnus Support, + * drepper@cygnus.com and Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* IEEE functions + * nexttoward(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double __nexttoward(double x, long double y) +#else + double __nexttoward(x,y) + double x; + long double y; +#endif +{ + int32_t hx,ix; + int64_t hy,iy; + u_int32_t lx; + u_int64_t ly; + + EXTRACT_WORDS(hx,lx,x); + GET_LDOUBLE_WORDS64(hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffffffffffffLL; /* |y| */ + + if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ + ((iy>=0x7fff000000000000LL)&&((iy-0x7fff000000000000LL)|ly)!=0)) + /* y is nan */ + return x+y; + if((long double) x==y) return x; /* x=y, return x */ + if((ix|lx)==0) { /* x == 0 */ + double x2; + INSERT_WORDS(x,(u_int32_t)((hy>>32)&0x80000000),1);/* return +-minsub */ + x2 = x*x; + if(x2==x) return x2; else return x; /* raise underflow flag */ + } + if(hx>=0) { /* x > 0 */ + if (hy<0||(ix>>20)>(iy>>48)-0x3c00 + || ((ix>>20)==(iy>>48)-0x3c00 + && (((((int64_t)hx)<<28)|(lx>>4))>(hy&0x0000ffffffffffffLL) + || (((((int64_t)hx)<<28)|(lx>>4))==(hy&0x0000ffffffffffffLL) + && (lx&0xf)>(ly>>60))))) { /* x > y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x < y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } else { /* x < 0 */ + if (hy>=0||(ix>>20)>(iy>>48)-0x3c00 + || ((ix>>20)==(iy>>48)-0x3c00 + && (((((int64_t)hx)<<28)|(lx>>4))>(hy&0x0000ffffffffffffLL) + || (((((int64_t)hx)<<28)|(lx>>4))==(hy&0x0000ffffffffffffLL) + && (lx&0xf)>(ly>>60))))) { /* x < y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x > y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } + hy = hx&0x7ff00000; + if(hy>=0x7ff00000) return x+x; /* overflow */ + if(hy<0x00100000) { /* underflow */ + double x2 = x*x; + if(x2!=x) { /* raise underflow flag */ + INSERT_WORDS(x2,hx,lx); + return x2; + } + } + INSERT_WORDS(x,hx,lx); + return x; +} +weak_alias (__nexttoward, nexttoward) diff --git a/sysdeps/ieee754/ldbl-128/s_nexttowardf.c b/sysdeps/ieee754/ldbl-128/s_nexttowardf.c new file mode 100644 index 0000000..1a22e01 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_nexttowardf.c @@ -0,0 +1,81 @@ +/* s_nexttowardf.c -- float version of s_nextafter.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com + * and Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + float __nexttowardf(float x, long double y) +#else + float __nexttowardf(x,y) + float x; + long double y; +#endif +{ + int32_t hx,ix; + int64_t hy,iy; + u_int64_t ly; + + GET_FLOAT_WORD(hx,x); + GET_LDOUBLE_WORDS64(hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffffffffffffLL; /* |y| */ + + if((ix>0x7f800000) || /* x is nan */ + ((iy>=0x7fff000000000000LL)&&((iy-0x7fff000000000000LL)|ly)!=0)) + /* y is nan */ + return x+y; + if((long double) x==y) return y; /* x=y, return y */ + if(ix==0) { /* x == 0 */ + float x2; + SET_FLOAT_WORD(x,(u_int32_t)((hy>>32)&0x80000000)|1);/* return +-minsub*/ + x2 = x*x; + if(x2==x) return x2; else return x; /* raise underflow flag */ + } + if(hx>=0) { /* x > 0 */ + if(hy<0||(ix>>23)>(iy>>48)-0x3f80 + || ((ix>>23)==(iy>>48)-0x3f80 + && (ix&0x7fffff)>((hy>>25)&0x7fffff))) {/* x > y, x -= ulp */ + hx -= 1; + } else { /* x < y, x += ulp */ + hx += 1; + } + } else { /* x < 0 */ + if(hy>=0||(ix>>23)>(iy>>48)-0x3f80 + || ((ix>>23)==(iy>>48)-0x3f80 + && (ix&0x7fffff)>((hy>>25)&0x7fffff))) {/* x < y, x -= ulp */ + hx -= 1; + } else { /* x > y, x += ulp */ + hx += 1; + } + } + hy = hx&0x7f800000; + if(hy>=0x7f800000) return x+x; /* overflow */ + if(hy<0x00800000) { /* underflow */ + float x2 = x*x; + if(x2!=x) { /* raise underflow flag */ + SET_FLOAT_WORD(x2,hx); + return x2; + } + } + SET_FLOAT_WORD(x,hx); + return x; +} +weak_alias (__nexttowardf, nexttowardf) diff --git a/sysdeps/ieee754/ldbl-128/s_remquol.c b/sysdeps/ieee754/ldbl-128/s_remquol.c new file mode 100644 index 0000000..0d26958 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_remquol.c @@ -0,0 +1,110 @@ +/* Compute remainder and a congruent to the quotient. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +static const long double zero = 0.0; + + +long double +__remquol (long double x, long double y, int *quo) +{ + int64_t hx,hy; + u_int64_t sx,lx,ly; + int cquo,qs; + + GET_LDOUBLE_WORDS64 (hx, lx, x); + GET_LDOUBLE_WORDS64 (hy, ly, y); + sx = hx & 0x8000000000000000ULL; + qs = sx ^ (hy & 0x8000000000000000ULL); + hy &= 0x7fffffffffffffffLL; + hx &= 0x7fffffffffffffffLL; + + /* Purge off exception values. */ + if ((hy | ly) == 0) + return (x * y) / (x * y); /* y = 0 */ + if ((hx >= 0x7fff000000000000LL) /* x not finite */ + || ((hy >= 0x7fff000000000000LL) /* y is NaN */ + && (((hy - 0x7fff000000000000LL) | ly) != 0))) + return (x * y) / (x * y); + + if (hy <= 0x7ffbffffffffffffLL) + x = __ieee754_fmodl (x, 8 * y); /* now x < 8y */ + + if (((hx - hy) | (lx - ly)) == 0) + { + *quo = qs ? -1 : 1; + return zero * x; + } + + x = fabsl (x); + y = fabsl (y); + cquo = 0; + + if (x >= 4 * y) + { + x -= 4 * y; + cquo += 4; + } + if (x >= 2 * y) + { + x -= 2 * y; + cquo += 2; + } + + if (hy < 0x0002000000000000LL) + { + if (x + x > y) + { + x -= y; + ++cquo; + if (x + x >= y) + { + x -= y; + ++cquo; + } + } + } + else + { + long double y_half = 0.5L * y; + if (x > y_half) + { + x -= y; + ++cquo; + if (x >= y_half) + { + x -= y; + ++cquo; + } + } + } + + *quo = qs ? -cquo : cquo; + + if (sx) + x = -x; + return x; +} +weak_alias (__remquol, remquol) diff --git a/sysdeps/ieee754/ldbl-128/s_rintl.c b/sysdeps/ieee754/ldbl-128/s_rintl.c new file mode 100644 index 0000000..c3fc3ba --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_rintl.c @@ -0,0 +1,90 @@ +/* s_rintl.c -- long double version of s_rint.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * rintl(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rintl(x). + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +TWO112[2]={ + 5.19229685853482762853049632922009600E+33L, /* 0x406F000000000000, 0 */ + -5.19229685853482762853049632922009600E+33L /* 0xC06F000000000000, 0 */ +}; + +#ifdef __STDC__ + long double __rintl(long double x) +#else + long double __rintl(x) + long double x; +#endif +{ + int64_t i0,j0,sx; + u_int64_t i,i1; + long double w,t; + GET_LDOUBLE_WORDS64(i0,i1,x); + sx = (((u_int64_t)i0)>>63); + j0 = ((i0>>48)&0x7fff)-0x3fff; + if(j0<48) { + if(j0<0) { + if(((i0&0x7fffffffffffffffLL)|i1)==0) return x; + i1 |= (i0&0x0000ffffffffffffLL); + i0 &= 0xffffe00000000000ULL; + i0 |= ((i1|-i1)>>16)&0x0000800000000000LL; + SET_LDOUBLE_MSW64(x,i0); + w = TWO112[sx]+x; + t = w-TWO112[sx]; + GET_LDOUBLE_MSW64(i0,t); + SET_LDOUBLE_MSW64(t,(i0&0x7fffffffffffffffLL)|(sx<<63)); + return t; + } else { + i = (0x0000ffffffffffffLL)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + i>>=1; + if(((i0&i)|i1)!=0) { + if(j0==47) i1 = 0x4000000000000000ULL; else + i0 = (i0&(~i))|((0x0000200000000000LL)>>j0); + } + } + } else if (j0>111) { + if(j0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = -1ULL>>(j0-48); + if((i1&i)==0) return x; /* x is integral */ + i>>=1; + if((i1&i)!=0) i1 = (i1&(~i))|((0x4000000000000000LL)>>(j0-48)); + } + SET_LDOUBLE_WORDS64(x,i0,i1); + w = TWO112[sx]+x; + return w-TWO112[sx]; +} +weak_alias (__rintl, rintl) diff --git a/sysdeps/ieee754/ldbl-128/s_roundl.c b/sysdeps/ieee754/ldbl-128/s_roundl.c new file mode 100644 index 0000000..f9fff48 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_roundl.c @@ -0,0 +1,94 @@ +/* Round long double to integer away from zero. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +static const long double huge = 1.0E4930L; + + +long double +__roundl (long double x) +{ + int32_t j0; + u_int64_t se, i1, i0; + + GET_LDOUBLE_WORDS64 (i0, i1, x); + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + if (j0 < 31) + { + if (j0 < 0) + { + if (huge + x > 0.0) + { + i0 &= 0x8000000000000000ULL; + if (j0 == -1) + i0 |= 0x3fff000000000000LL; + i1 = 0; + } + } + else + { + u_int64_t i = 0x0000ffffffffffffLL >> j0; + if (((i0 & i) | i1) == 0) + /* X is integral. */ + return x; + if (huge + x > 0.0) + { + /* Raise inexact if x != 0. */ + i0 += 0x0000800000000000LL >> j0; + i0 &= ~i; + i1 = 0; + } + } + } + else if (j0 > 111) + { + if (j0 == 0x4000) + /* Inf or NaN. */ + return x + x; + else + return x; + } + else + { + u_int64_t i = -1ULL >> (j0 - 48); + if ((i1 & i) == 0) + /* X is integral. */ + return x; + + if (huge + x > 0.0) + { + /* Raise inexact if x != 0. */ + u_int64_t j = i1 + (1LL << (111 - j0)); + if (j < i1) + i0 += 1; + i1 = j; + } + i1 &= ~i; + } + + SET_LDOUBLE_WORDS64 (x, i0, i1); + return x; +} +weak_alias (__roundl, roundl) diff --git a/sysdeps/ieee754/ldbl-128/s_scalblnl.c b/sysdeps/ieee754/ldbl-128/s_scalblnl.c new file mode 100644 index 0000000..5e8b58b --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_scalblnl.c @@ -0,0 +1,70 @@ +/* s_scalblnl.c -- long double version of s_scalbn.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* @(#)s_scalbn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * scalblnl (long double x, long int n) + * scalblnl(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +two114 = 2.0769187434139310514121985316880384E+34L, /* 0x4071000000000000, 0 */ +twom114 = 4.8148248609680896326399448564623183E-35L, /* 0x3F8D000000000000, 0 */ +huge = 1.0E+4900L, +tiny = 1.0E-4900L; + +#ifdef __STDC__ + long double __scalblnl (long double x, long int n) +#else + long double __scalblnl (x,n) + long double x; long int n; +#endif +{ + int64_t k,hx,lx; + GET_LDOUBLE_WORDS64(hx,lx,x); + k = (hx>>48)&0x7fff; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffffffffffffULL))==0) return x; /* +-0 */ + x *= two114; + GET_LDOUBLE_MSW64(hx,x); + k = ((hx>>48)&0x7fff) - 114; + } + if (k==0x7fff) return x+x; /* NaN or Inf */ + k = k+n; + if (n> 50000 || k > 0x7ffe) + return huge*__copysignl(huge,x); /* overflow */ + if (n< -50000) return tiny*__copysignl(tiny,x); /*underflow*/ + if (k > 0) /* normal result */ + {SET_LDOUBLE_MSW64(x,(hx&0x8000ffffffffffffULL)|(k<<48)); return x;} + if (k <= -114) + return tiny*__copysignl(tiny,x); /*underflow*/ + k += 114; /* subnormal result */ + SET_LDOUBLE_MSW64(x,(hx&0x8000ffffffffffffULL)|(k<<48)); + return x*twom114; +} +weak_alias (__scalblnl, scalblnl) diff --git a/sysdeps/ieee754/ldbl-128/s_scalbnl.c b/sysdeps/ieee754/ldbl-128/s_scalbnl.c new file mode 100644 index 0000000..c54f064 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_scalbnl.c @@ -0,0 +1,70 @@ +/* s_scalbnl.c -- long double version of s_scalbn.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* @(#)s_scalbn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * scalbnl (long double x, int n) + * scalbnl(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +two114 = 2.0769187434139310514121985316880384E+34L, /* 0x4071000000000000, 0 */ +twom114 = 4.8148248609680896326399448564623183E-35L, /* 0x3F8D000000000000, 0 */ +huge = 1.0E+4900L, +tiny = 1.0E-4900L; + +#ifdef __STDC__ + long double __scalbnl (long double x, int n) +#else + long double __scalbnl (x,n) + long double x; int n; +#endif +{ + int64_t k,hx,lx; + GET_LDOUBLE_WORDS64(hx,lx,x); + k = (hx>>48)&0x7fff; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffffffffffffULL))==0) return x; /* +-0 */ + x *= two114; + GET_LDOUBLE_MSW64(hx,x); + k = ((hx>>48)&0x7fff) - 114; + } + if (k==0x7fff) return x+x; /* NaN or Inf */ + k = k+n; + if (n> 50000 || k > 0x7ffe) + return huge*__copysignl(huge,x); /* overflow */ + if (n< -50000) return tiny*__copysignl(tiny,x); /*underflow*/ + if (k > 0) /* normal result */ + {SET_LDOUBLE_MSW64(x,(hx&0x8000ffffffffffffULL)|(k<<48)); return x;} + if (k <= -114) + return tiny*__copysignl(tiny,x); /*underflow*/ + k += 114; /* subnormal result */ + SET_LDOUBLE_MSW64(x,(hx&0x8000ffffffffffffULL)|(k<<48)); + return x*twom114; +} +weak_alias (__scalbnl, scalbnl) diff --git a/sysdeps/ieee754/ldbl-128/s_signbitl.c b/sysdeps/ieee754/ldbl-128/s_signbitl.c new file mode 100644 index 0000000..52a0afb --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_signbitl.c @@ -0,0 +1,32 @@ +/* Return nonzero value if number is negative. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + +int +__signbitl (long double x) +{ + int64_t e; + + GET_LDOUBLE_MSW64 (e, x); + return e < 0; +} diff --git a/sysdeps/ieee754/ldbl-128/s_sincosl.c b/sysdeps/ieee754/ldbl-128/s_sincosl.c new file mode 100644 index 0000000..2d74e72 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_sincosl.c @@ -0,0 +1,77 @@ +/* Compute sine and cosine of argument. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + +/* Note: We should probably introduce __kernel_sincosl to speed things up, + because __kernel_{cos,sin}l sometimes compute both sine and cosine. */ + +void +__sincosl (long double x, long double *sinx, long double *cosx) +{ + int64_t ix; + + /* High word of x. */ + GET_LDOUBLE_MSW64 (ix, x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if (ix <= 0x3ffe921fb54442d1LL) + { + *sinx = __kernel_sinl (x, 0.0, 0); + *cosx = __kernel_cosl (x, 0.0); + } + else if (ix >= 0x7fff000000000000LL) + { + /* sin(Inf or NaN) is NaN */ + *sinx = *cosx = x - x; + } + else + { + /* Argument reduction needed. */ + long double y[2]; + int n; + + n = __ieee754_rem_pio2l (x, y); + switch (n & 3) + { + case 0: + *sinx = __kernel_sinl (y[0], y[1], 1); + *cosx = __kernel_cosl (y[0], y[1]); + break; + case 1: + *sinx = __kernel_cosl (y[0], y[1]); + *cosx = -__kernel_sinl (y[0], y[1], 1); + break; + case 2: + *sinx = -__kernel_sinl (y[0], y[1], 1); + *cosx = -__kernel_cosl (y[0], y[1]); + break; + default: + *sinx = -__kernel_cosl (y[0], y[1]); + *cosx = __kernel_sinl (y[0], y[1], 1); + break; + } + } +} +weak_alias (__sincosl, sincosl) diff --git a/sysdeps/ieee754/ldbl-128/s_sinl.c b/sysdeps/ieee754/ldbl-128/s_sinl.c new file mode 100644 index 0000000..446a75f --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_sinl.c @@ -0,0 +1,83 @@ +/* s_sinl.c -- long double version of s_sin.c. + * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* sinl(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sinl ... sine function on [-pi/4,pi/4] + * __kernel_cosl ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __sinl(long double x) +#else + long double __sinl(x) + long double x; +#endif +{ + long double y[2],z=0.0L; + int64_t n, ix; + + /* High word of x. */ + GET_LDOUBLE_MSW64(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if(ix <= 0x3ffe921fb54442d1LL) + return __kernel_sinl(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7fff000000000000LL) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + switch(n&3) { + case 0: return __kernel_sinl(y[0],y[1],1); + case 1: return __kernel_cosl(y[0],y[1]); + case 2: return -__kernel_sinl(y[0],y[1],1); + default: + return -__kernel_cosl(y[0],y[1]); + } + } +} +weak_alias (__sinl, sinl) diff --git a/sysdeps/ieee754/ldbl-128/s_tanl.c b/sysdeps/ieee754/ldbl-128/s_tanl.c new file mode 100644 index 0000000..ea9d053 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_tanl.c @@ -0,0 +1,77 @@ +/* s_tanl.c -- long double version of s_tan.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* @(#)s_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* tanl(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tanl ... tangent function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __tanl(long double x) +#else + long double __tanl(x) + long double x; +#endif +{ + long double y[2],z=0.0L; + int64_t n, ix; + + /* High word of x. */ + GET_LDOUBLE_MSW64(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffffffffffffLL; + if(ix <= 0x3ffe921fb54442d1LL) return __kernel_tanl(x,z,1); + + /* tanl(Inf or NaN) is NaN */ + else if (ix>=0x7fff000000000000LL) return x-x; /* NaN */ + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + return __kernel_tanl(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} +weak_alias (__tanl, tanl) diff --git a/sysdeps/ieee754/ldbl-128/s_truncl.c b/sysdeps/ieee754/ldbl-128/s_truncl.c new file mode 100644 index 0000000..bbff5a4 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_truncl.c @@ -0,0 +1,57 @@ +/* Truncate argument to nearest integral value not larger than the argument. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and + Jakub Jelinek <jj@ultra.linux.cz>, 1999. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +long double +__truncl (long double x) +{ + int32_t j0; + u_int64_t i0, i1, sx; + + GET_LDOUBLE_WORDS64 (i0, i1, x); + sx = i0 & 0x8000000000000000ULL; + j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; + if (j0 < 48) + { + if (j0 < 0) + /* The magnitude of the number is < 1 so the result is +-0. */ + SET_LDOUBLE_WORDS64 (x, sx, 0); + else + SET_LDOUBLE_WORDS64 (x, i0 & ~(0x0000ffffffffffffLL >> j0), 0); + } + else if (j0 > 111) + { + if (j0 == 0x4000) + /* x is inf or NaN. */ + return x + x; + } + else + { + SET_LDOUBLE_WORDS64 (x, i0, i1 & ~(0xffffffffffffffffULL >> (j0 - 48))); + } + + return x; +} +weak_alias (__truncl, truncl) diff --git a/sysdeps/ieee754/ldbl-128/strtold.c b/sysdeps/ieee754/ldbl-128/strtold.c new file mode 100644 index 0000000..32049fc --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/strtold.c @@ -0,0 +1,42 @@ +/* Copyright (C) 1999 Free Software Foundation, Inc. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +/* The actual implementation for all floating point sizes is in strtod.c. + These macros tell it to produce the `long double' version, `strtold'. */ + +# define FLOAT long double +# define FLT LDBL +# ifdef USE_IN_EXTENDED_LOCALE_MODEL +# define STRTOF __strtold_l +# else +# define STRTOF strtold +# endif +# define MPN2FLOAT __mpn_construct_long_double +# define FLOAT_HUGE_VAL HUGE_VALL +# define SET_MANTISSA(flt, mant) \ + do { union ieee854_long_double u; \ + u.d = (flt); \ + u.ieee.mantissa0 = 0x8000; \ + u.ieee.mantissa1 = 0; \ + u.ieee.mantissa2 = ((mant) >> 32); \ + u.ieee.mantissa3 = (mant) & 0xffffffff; \ + (flt) = u.d; \ + } while (0) + +# include "strtod.c" diff --git a/sysdeps/ieee754/ldbl-96/e_acoshl.c b/sysdeps/ieee754/ldbl-96/e_acoshl.c new file mode 100644 index 0000000..a60704a --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/e_acoshl.c @@ -0,0 +1,72 @@ +/* e_acoshl.c -- long double version of e_acosh.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* __ieee754_acoshl(x) + * Method : + * Based on + * acoshl(x) = logl [ x + sqrtl(x*x-1) ] + * we have + * acoshl(x) := logl(x)+ln2, if x is large; else + * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else + * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acoshl(x) is NaN with signal if x<1. + * acoshl(NaN) is NaN without signal. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +one = 1.0, +ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */ + +#ifdef __STDC__ + long double __ieee754_acoshl(long double x) +#else + long double __ieee754_acoshl(x) + long double x; +#endif +{ + long double t; + u_int32_t se,i0,i1; + GET_LDOUBLE_WORDS(se,i0,i1,x); + if(se<0x3fff || se & 0x8000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(se >=0x401b) { /* x > 2**28 */ + if(se >=0x7fff) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */ + } else if(((se-0x3fff)|i0|i1)==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (se > 0x4000) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one))); + } else { /* 1<x<2 */ + t = x-one; + return __log1pl(t+__sqrtl(2.0*t+t*t)); + } +} diff --git a/sysdeps/ieee754/ldbl-96/e_atan2l.c b/sysdeps/ieee754/ldbl-96/e_atan2l.c new file mode 100644 index 0000000..aff7a3d --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/e_atan2l.c @@ -0,0 +1,136 @@ +/* e_atan2l.c -- long double version of e_atan2.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* __ieee754_atan2l(y,x) + * Method : + * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). + * 2. Reduce x to positive by (if x and y are unexceptional): + * ARG (x+iy) = arctan(y/x) ... if x > 0, + * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * + * Special cases: + * + * ATAN2((anything), NaN ) is NaN; + * ATAN2(NAN , (anything) ) is NaN; + * ATAN2(+-0, +(anything but NaN)) is +-0 ; + * ATAN2(+-0, -(anything but NaN)) is +-pi ; + * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; + * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; + * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; + * ATAN2(+-INF,+INF ) is +-pi/4 ; + * ATAN2(+-INF,-INF ) is +-3pi/4; + * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +tiny = 1.0e-4900L, +zero = 0.0, +pi_o_4 = 7.85398163397448309628202E-01L, /* 0x3FFE, 0xC90FDAA2, 0x2168C235 */ +pi_o_2 = 1.5707963267948966192564E+00L, /* 0x3FFF, 0xC90FDAA2, 0x2168C235 */ +pi = 3.14159265358979323851281E+00L, /* 0x4000, 0xC90FDAA2, 0x2168C235 */ +pi_lo = -5.01655761266833202345176e-20L;/* 0xBFBE, 0xECE675D1, 0xFC8F8CBB */ + +#ifdef __STDC__ + long double __ieee754_atan2l(long double y, long double x) +#else + long double __ieee754_atan2l(y,x) + long double y,x; +#endif +{ + long double z; + int32_t k,m,hx,hy,ix,iy; + u_int32_t sx,sy,lx,ly; + + GET_LDOUBLE_WORDS(sx,hx,lx,x); + ix = sx&0x7fff; + lx |= hx & 0x7fffffff; + GET_LDOUBLE_WORDS(sy,hy,ly,y); + iy = sy&0x7fff; + ly |= hy & 0x7fffffff; + if(((2*ix|((lx|-lx)>>31))>0xfffe)|| + ((2*iy|((ly|-ly)>>31))>0xfffe)) /* x or y is NaN */ + return x+y; + if((sx-0x3fff|lx)==0) return __atanl(y); /* x=1.0 */ + m = ((sy>>15)&1)|((sx>>14)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if((iy|ly)==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if((ix|lx)==0) return (sy>=0x8000)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7fff) { + if(iy==0x7fff) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7fff) return (sy>=0x8000)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = sy-sx; + if(k > 70) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**70 */ + else if(sx>=0x8000&&k<-70) z=0.0; /* |y|/x < -2**70 */ + else z=__atanl(fabsl(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: { + u_int32_t sz; + GET_LDOUBLE_EXP(sz,z); + SET_LDOUBLE_EXP(z,sz ^ 0x8000); + } + return z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} diff --git a/sysdeps/ieee754/ldbl-96/e_atanhl.c b/sysdeps/ieee754/ldbl-96/e_atanhl.c new file mode 100644 index 0000000..fdcd1e9 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/e_atanhl.c @@ -0,0 +1,79 @@ +/* s_atanhl.c -- long double version of s_atan.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* __ieee754_atanhl(x) + * Method : + * 1.Reduced x to positive by atanh(-x) = -atanh(x) + * 2.For x>=0.5 + * 1 2x x + * atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * For x<0.5 + * atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x)) + * + * Special cases: + * atanhl(x) is NaN if |x| > 1 with signal; + * atanhl(NaN) is that NaN with no signal; + * atanhl(+-1) is +-INF with signal. + * + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double one = 1.0, huge = 1e4900L; +#else +static long double one = 1.0, huge = 1e4900L; +#endif + +#ifdef __STDC__ +static const long double zero = 0.0; +#else +static double long zero = 0.0; +#endif + +#ifdef __STDC__ + long double __ieee754_atanhl(long double x) +#else + long double __ieee754_atanhl(x) + long double x; +#endif +{ + long double t; + int32_t ix; + u_int32_t se,i0,i1; + GET_LDOUBLE_WORDS(se,i0,i1,x); + ix = se&0x7fff; + if ((ix+((((i0&0x7fffffff)|i1)|(-((i0&0x7fffffff)|i1)))>>31))>0x3fff) + /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3fff) + return x/zero; + if(ix<0x3fe3&&(huge+x)>zero) return x; /* x<2**-28 */ + SET_LDOUBLE_EXP(x,ix); + if(ix<0x3ffe) { /* x < 0.5 */ + t = x+x; + t = 0.5*__log1pl(t+t*x/(one-x)); + } else + t = 0.5*__log1pl((x+x)/(one-x)); + if(se<=0x7fff) return t; else return -t; +} diff --git a/sysdeps/ieee754/ldbl-96/e_coshl.c b/sysdeps/ieee754/ldbl-96/e_coshl.c new file mode 100644 index 0000000..6af846c --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/e_coshl.c @@ -0,0 +1,94 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $"; +#endif + +/* __ieee754_coshl(x) + * Method : + * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (coshl(x) = coshl(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : coshl(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : coshl(x) := ------------------- + * 2 + * 22 <= x <= lnovft : coshl(x) := expl(x)/2 + * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2) + * ln2ovft < x : coshl(x) := huge*huge (overflow) + * + * Special cases: + * coshl(x) is |x| if x is +INF, -INF, or NaN. + * only coshl(0)=1 is exact for finite x. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double one = 1.0, half=0.5, huge = 1.0e4900L; +#else +static long double one = 1.0, half=0.5, huge = 1.0e4900L; +#endif + +#ifdef __STDC__ + long double __ieee754_coshl(long double x) +#else + long double __ieee754_coshl(x) + long double x; +#endif +{ + long double t,w; + int32_t ex; + u_int32_t mx,lx; + + /* High word of |x|. */ + GET_LDOUBLE_WORDS(ex,mx,lx,x); + ex &= 0x7fff; + + /* x is INF or NaN */ + if(ex==0x7fff) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ + if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) { + t = __expm1l(fabsl(x)); + w = one+t; + if (ex<0x3fbc) return w; /* cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) { + t = __ieee754_expl(fabsl(x)); + return half*t+half/t; + } + + /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */ + if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u)) + return half*__ieee754_expl(fabsl(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ex < 0x400d + || (ex == 0x400d && (mx < 0xb170b513u + || (mx == 0xb170b513u && lx < 0xa1dfd60cu)))) + { + w = __ieee754_expl(half*fabsl(x)); + t = half*w; + return t*w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} diff --git a/sysdeps/ieee754/ldbl-96/e_gammal_r.c b/sysdeps/ieee754/ldbl-96/e_gammal_r.c new file mode 100644 index 0000000..1049924 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/e_gammal_r.c @@ -0,0 +1,50 @@ +/* Implementation of gamma function according to ISO C. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> +#include <math_private.h> + + +long double +__ieee754_gammal_r (long double x, int *signgamp) +{ + /* We don't have a real gamma implementation now. We'll use lgamma + and the exp function. But due to the required boundary + conditions we must check some values separately. */ + u_int32_t es, hx, lx; + + GET_LDOUBLE_WORDS (es, hx, lx, x); + + if (((es & 0x7fff) | hx | lx) == 0) + { + /* Return value for x == 0 is NaN with invalid exception. */ + *signgamp = 0; + return x / x; + } + if ((hx & 0x8000) != 0 && (hx & 0x7fff) != 0x7fff && __rintl (x) == x) + { + /* Return value for integer x < 0 is NaN with invalid exception. */ + *signgamp = 0; + return (x - x) / (x - x); + } + + /* XXX FIXME. */ + return __ieee754_expl (__ieee754_lgammal_r (x, signgamp)); +} diff --git a/sysdeps/ieee754/ldbl-96/e_hypotl.c b/sysdeps/ieee754/ldbl-96/e_hypotl.c new file mode 100644 index 0000000..1a40c55 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/e_hypotl.c @@ -0,0 +1,133 @@ +/* e_hypotl.c -- long double version of e_hypot.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* __ieee754_hypotl(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 32 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, + * y1= y with lower 32 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __ieee754_hypotl(long double x, long double y) +#else + long double __ieee754_hypotl(x,y) + long double x, y; +#endif +{ + long double a,b,t1,t2,y1,y2,w; + u_int32_t j,k,ea,eb; + + GET_LDOUBLE_EXP(ea,x); + ea &= 0x7fff; + GET_LDOUBLE_EXP(eb,y); + eb &= 0x7fff; + if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;} + SET_LDOUBLE_EXP(a,ea); /* a <- |a| */ + SET_LDOUBLE_EXP(b,eb); /* b <- |b| */ + if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */ + k=0; + if(ea > 0x5f3f) { /* a>2**8000 */ + if(ea == 0x7fff) { /* Inf or NaN */ + u_int32_t exp,high,low; + w = a+b; /* for sNaN */ + GET_LDOUBLE_WORDS(exp,high,low,a); + if(((high&0x7fffffff)|low)==0) w = a; + GET_LDOUBLE_WORDS(exp,high,low,b); + if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b; + return w; + } + /* scale a and b by 2**-9600 */ + ea -= 0x2580; eb -= 0x2580; k += 9600; + SET_LDOUBLE_EXP(a,ea); + SET_LDOUBLE_EXP(b,eb); + } + if(eb < 0x20bf) { /* b < 2**-8000 */ + if(eb == 0) { /* subnormal b or 0 */ + u_int32_t exp,high,low; + GET_LDOUBLE_WORDS(exp,high,low,b); + if((high|low)==0) return a; + SET_LDOUBLE_WORDS(t1, 0x7ffd, 0, 0); /* t1=2^16382 */ + b *= t1; + a *= t1; + k -= 16382; + } else { /* scale a and b by 2^9600 */ + ea += 0x2580; /* a *= 2^9600 */ + eb += 0x2580; /* b *= 2^9600 */ + k -= 9600; + SET_LDOUBLE_EXP(a,ea); + SET_LDOUBLE_EXP(b,eb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + u_int32_t high; + GET_LDOUBLE_MSW(high,a); + SET_LDOUBLE_WORDS(t1,ea,high,0); + t2 = a-t1; + w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + u_int32_t high; + GET_LDOUBLE_MSW(high,b); + a = a+a; + SET_LDOUBLE_WORDS(y1,eb,high,0); + y2 = b - y1; + GET_LDOUBLE_MSW(high,a); + SET_LDOUBLE_WORDS(t1,ea+1,high,0); + t2 = a - t1; + w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + u_int32_t exp; + t1 = 1.0; + GET_LDOUBLE_EXP(exp,t1); + SET_LDOUBLE_EXP(t1,exp+k); + return t1*w; + } else return w; +} diff --git a/sysdeps/ieee754/ldbl-96/e_remainderl.c b/sysdeps/ieee754/ldbl-96/e_remainderl.c new file mode 100644 index 0000000..e721a6e --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/e_remainderl.c @@ -0,0 +1,83 @@ +/* e_remainderl.c -- long double version of e_remainder.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* __ieee754_remainderl(x,p) + * Return : + * returns x REM p = x - [x/p]*p as if in infinite + * precise arithmetic, where [x/p] is the (infinite bit) + * integer nearest x/p (in half way case choose the even one). + * Method : + * Based on fmod() return x-[x/p]chopped*p exactlp. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double zero = 0.0; +#else +static long double zero = 0.0; +#endif + + +#ifdef __STDC__ + long double __ieee754_remainderl(long double x, long double p) +#else + long double __ieee754_remainderl(x,p) + long double x,p; +#endif +{ + u_int32_t sx,sex,sep,x0,x1,p0,p1; + long double p_half; + + GET_LDOUBLE_WORDS(sex,x0,x1,x); + GET_LDOUBLE_WORDS(sep,p0,p1,p); + sx = sex&0x8000; + sep &= 0x7fff; + sex &= 0x7fff; + + /* purge off exception values */ + if((sep|p0|p1)==0) return (x*p)/(x*p); /* p = 0 */ + if((sex==0x7fff)|| /* x not finite */ + ((sep==0x7fff)&& /* p is NaN */ + ((p0|p1)!=0))) + return (x*p)/(x*p); + + + if (sep<0x7ffe) x = __ieee754_fmodl(x,p+p); /* now x < 2p */ + if (((sex-sep)|(x0-p0)|(x1-p1))==0) return zero*x; + x = fabsl(x); + p = fabsl(p); + if (sep<0x0002) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = 0.5*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_LDOUBLE_EXP(sex,x); + SET_LDOUBLE_EXP(x,sex^sx); + return x; +} diff --git a/sysdeps/ieee754/ldbl-96/e_sinhl.c b/sysdeps/ieee754/ldbl-96/e_sinhl.c new file mode 100644 index 0000000..4f9cfe2 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/e_sinhl.c @@ -0,0 +1,91 @@ +/* e_asinhl.c -- long double version of e_asinh.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* __ieee754_sinhl(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x) + * 2 + * + * 25 <= x <= lnovft : sinhl(x) := expl(x)/2 + * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2) + * ln2ovft < x : sinhl(x) := x*shuge (overflow) + * + * Special cases: + * sinhl(x) is |x| if x is +INF, -INF, or NaN. + * only sinhl(0)=0 is exact for finite x. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double one = 1.0, shuge = 1.0e4931L; +#else +static long double one = 1.0, shuge = 1.0e4931L; +#endif + +#ifdef __STDC__ + long double __ieee754_sinhl(long double x) +#else + long double __ieee754_sinhl(x) + long double x; +#endif +{ + long double t,w,h; + u_int32_t jx,ix,i0,i1; + + /* Words of |x|. */ + GET_LDOUBLE_WORDS(jx,i0,i1,x); + ix = jx&0x7fff; + + /* x is INF or NaN */ + if(ix==0x7fff) return x+x; + + h = 0.5; + if (jx & 0x8000) h = -h; + /* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x|<25 */ + if (ix<0x3fe3) /* |x|<2**-28 */ + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + t = __expm1l(fabsl(x)); + if(ix<0x3fff) return h*(2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7)) + return h*__ieee754_expl(fabsl(x)); + + /* |x| in [log(maxdouble), overflowthreshold] */ + if (ix<0x400c || (ix == 0x400c && (i0 < 0xb174ddc0 + || (i0 == 0xb174ddc0 + && i1 <= 0x31aec0ea)))) { + w = __ieee754_expl(0.5*fabsl(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthreshold, sinhl(x) overflow */ + return x*shuge; +} diff --git a/sysdeps/ieee754/ldbl2mpn.c b/sysdeps/ieee754/ldbl-96/ldbl2mpn.c index e95895c..78e0b70 100644 --- a/sysdeps/ieee754/ldbl2mpn.c +++ b/sysdeps/ieee754/ldbl-96/ldbl2mpn.c @@ -24,8 +24,6 @@ #include <math.h> #include <stdlib.h> -#ifndef __NO_LONG_DOUBLE_MATH - /* Convert a `long double' in IEEE854 standard double-precision format to a multi-precision integer representing the significand scaled up by its number of bits (64 for long double) and an integral power of two @@ -95,5 +93,3 @@ __mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size, return N; } - -#endif /* __NO_LONG_DOUBLE_MATH */ diff --git a/sysdeps/ieee754/ldbl-96/math_ldbl.h b/sysdeps/ieee754/ldbl-96/math_ldbl.h new file mode 100644 index 0000000..dccc4a1 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/math_ldbl.h @@ -0,0 +1,98 @@ +#ifndef _MATH_PRIVATE_H_ +#error "Never use <math_ldbl.h> directly; include <math_private.h> instead." +#endif + +/* A union which permits us to convert between a long double and + three 32 bit ints. */ + +#if __FLOAT_WORD_ORDER == BIG_ENDIAN + +typedef union +{ + long double value; + struct + { + unsigned int sign_exponent:16; + unsigned int empty:16; + u_int32_t msw; + u_int32_t lsw; + } parts; +} ieee_long_double_shape_type; + +#endif + +#if __FLOAT_WORD_ORDER == LITTLE_ENDIAN + +typedef union +{ + long double value; + struct + { + u_int32_t lsw; + u_int32_t msw; + unsigned int sign_exponent:16; + unsigned int empty:16; + } parts; +} ieee_long_double_shape_type; + +#endif + +/* Get three 32 bit ints from a double. */ + +#define GET_LDOUBLE_WORDS(exp,ix0,ix1,d) \ +do { \ + ieee_long_double_shape_type ew_u; \ + ew_u.value = (d); \ + (exp) = ew_u.parts.sign_exponent; \ + (ix0) = ew_u.parts.msw; \ + (ix1) = ew_u.parts.lsw; \ +} while (0) + +/* Set a double from two 32 bit ints. */ + +#define SET_LDOUBLE_WORDS(d,exp,ix0,ix1) \ +do { \ + ieee_long_double_shape_type iw_u; \ + iw_u.parts.sign_exponent = (exp); \ + iw_u.parts.msw = (ix0); \ + iw_u.parts.lsw = (ix1); \ + (d) = iw_u.value; \ +} while (0) + +/* Get the more significant 32 bits of a long double mantissa. */ + +#define GET_LDOUBLE_MSW(v,d) \ +do { \ + ieee_long_double_shape_type sh_u; \ + sh_u.value = (d); \ + (v) = sh_u.parts.msw; \ +} while (0) + +/* Set the more significant 32 bits of a long double mantissa from an int. */ + +#define SET_LDOUBLE_MSW(d,v) \ +do { \ + ieee_long_double_shape_type sh_u; \ + sh_u.value = (d); \ + sh_u.parts.msw = (v); \ + (d) = sh_u.value; \ +} while (0) + +/* Get int from the exponent of a long double. */ + +#define GET_LDOUBLE_EXP(exp,d) \ +do { \ + ieee_long_double_shape_type ge_u; \ + ge_u.value = (d); \ + (exp) = ge_u.parts.sign_exponent; \ +} while (0) + +/* Set exponent of a long double from an int. */ + +#define SET_LDOUBLE_EXP(d,exp) \ +do { \ + ieee_long_double_shape_type se_u; \ + se_u.value = (d); \ + se_u.parts.sign_exponent = (exp); \ + (d) = se_u.value; \ +} while (0) diff --git a/sysdeps/ieee754/mpn2ldbl.c b/sysdeps/ieee754/ldbl-96/mpn2ldbl.c index 7802355..1f049ba 100644 --- a/sysdeps/ieee754/mpn2ldbl.c +++ b/sysdeps/ieee754/ldbl-96/mpn2ldbl.c @@ -22,8 +22,6 @@ #include <float.h> #include <math.h> -#ifndef __NO_LONG_DOUBLE_MATH - /* Convert a multi-precision integer of the needed number of bits (64 for long double) and an integral power of two to a `long double' in IEEE854 extended-precision format. */ @@ -47,5 +45,3 @@ __mpn_construct_long_double (mp_srcptr frac_ptr, int expt, int sign) return u.d; } - -#endif /* __NO_LONG_DOUBLE_MATH */ diff --git a/sysdeps/ieee754/ldbl-96/printf_fphex.c b/sysdeps/ieee754/ldbl-96/printf_fphex.c new file mode 100644 index 0000000..8dfa387 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/printf_fphex.c @@ -0,0 +1,61 @@ +#ifndef LONG_DOUBLE_DENORM_BIAS +# define LONG_DOUBLE_DENORM_BIAS (IEEE854_LONG_DOUBLE_BIAS - 1) +#endif + +#define PRINT_FPHEX_LONG_DOUBLE \ +do { \ + /* The "strange" 80 bit format on ix86 and m68k has an explicit \ + leading digit in the 64 bit mantissa. */ \ + unsigned long long int num; \ + \ + assert (sizeof (long double) == 12); \ + \ + num = (((unsigned long long int) fpnum.ldbl.ieee.mantissa0) << 32 \ + | fpnum.ldbl.ieee.mantissa1); \ + \ + zero_mantissa = num == 0; \ + \ + if (sizeof (unsigned long int) > 6) \ + numstr = _itoa_word (num, numbuf + sizeof numbuf, 16, \ + info->spec == 'A'); \ + else \ + numstr = _itoa (num, numbuf + sizeof numbuf, 16, info->spec == 'A'); \ + \ + /* Fill with zeroes. */ \ + while (numstr > numbuf + (sizeof numbuf - 64 / 4)) \ + *--numstr = '0'; \ + \ + /* We use a full nibble for the leading digit. */ \ + leading = *numstr++; \ + \ + /* We have 3 bits from the mantissa in the leading nibble. \ + Therefore we are here using `IEEE854_LONG_DOUBLE_BIAS + 3'. */ \ + exponent = fpnum.ldbl.ieee.exponent; \ + \ + if (exponent == 0) \ + { \ + if (zero_mantissa) \ + expnegative = 0; \ + else \ + { \ + /* This is a denormalized number. */ \ + expnegative = 1; \ + /* This is a hook for the m68k long double format, where the \ + exponent bias is the same for normalized and denormalized \ + numbers. */ \ + exponent = LONG_DOUBLE_DENORM_BIAS + 3; \ + } \ + } \ + else if (exponent >= IEEE854_LONG_DOUBLE_BIAS + 3) \ + { \ + expnegative = 0; \ + exponent -= IEEE854_LONG_DOUBLE_BIAS + 3; \ + } \ + else \ + { \ + expnegative = 1; \ + exponent = -(exponent - (IEEE854_LONG_DOUBLE_BIAS + 3)); \ + } \ +} while (0) + +#include <sysdeps/generic/printf_fphex.c> diff --git a/sysdeps/ieee754/ldbl-96/s_asinhl.c b/sysdeps/ieee754/ldbl-96/s_asinhl.c new file mode 100644 index 0000000..6eb434c --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_asinhl.c @@ -0,0 +1,70 @@ +/* s_asinhl.c -- long double version of s_asinh.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* asinhl(x) + * Method : + * Based on + * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ] + * we have + * asinhl(x) := x if 1+x*x=1, + * := signl(x)*(logl(x)+ln2)) for large |x|, else + * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else + * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2))) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +one = 1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */ +ln2 = 6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */ +huge= 1.000000000000000000e+4900L; + +#ifdef __STDC__ + long double __asinhl(long double x) +#else + long double __asinhl(x) + long double x; +#endif +{ + long double t,w; + int32_t hx,ix; + GET_LDOUBLE_EXP(hx,x); + ix = hx&0x7fff; + if(ix==0x7fff) return x+x; /* x is inf or NaN */ + if(ix< 0x3fde) { /* |x|<2**-34 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x4020) { /* |x| > 2**34 */ + w = __ieee754_logl(fabsl(x))+ln2; + } else if (ix>0x4000) { /* 2**34 > |x| > 2.0 */ + t = fabsl(x); + w = __ieee754_logl(2.0*t+one/(__ieee754_sqrtl(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =__log1pl(fabsl(x)+t/(one+__ieee754_sqrtl(one+t))); + } + if(hx&0x8000) return -w; else return w; +} +weak_alias (__asinhl, asinhl) diff --git a/sysdeps/ieee754/ldbl-96/s_cbrtl.c b/sysdeps/ieee754/ldbl-96/s_cbrtl.c new file mode 100644 index 0000000..1d021b7 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_cbrtl.c @@ -0,0 +1,78 @@ +/* Compute cubic root of double value. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Dirk Alboth <dirka@uni-paderborn.de> and + Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include "math.h" +#include "math_private.h" + + +#define CBRT2 1.2599210498948731648 /* 2^(1/3) */ +#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */ + +/* We don't use long double values here since U need not be computed + with full precision. */ +static const double factor[5] = +{ + 1.0 / SQR_CBRT2, + 1.0 / CBRT2, + 1.0, + CBRT2, + SQR_CBRT2 +}; + + +long double +__cbrtl (long double x) +{ + long double xm, ym, u, t2; + int xe; + + /* Reduce X. XM now is an range 1.0 to 0.5. */ + xm = __frexpl (fabs (x), &xe); + + /* If X is not finite or is null return it (with raising exceptions + if necessary. + Note: *Our* version of `frexp' sets XE to zero if the argument is + Inf or NaN. This is not portable but faster. */ + if (xe == 0 && fpclassify (x) <= FP_ZERO) + return x + x; + + u = (0.338058687610520237 + + (1.67595307700780102 + + (-2.82414939754975962 + + (4.09559907378707839 + + (-4.11151425200350531 + + (2.65298938441952296 + + (-0.988553671195413709 + + 0.161617097923756032 * xm) + * xm) + * xm) + * xm) + * xm) + * xm) + *xm); + + t2 = u * u * u; + + ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3]; + + return __ldexpl (x > 0.0 ? ym : -ym, xe / 3); +} +weak_alias (__cbrtl, cbrtl) diff --git a/sysdeps/ieee754/ldbl-96/s_ceill.c b/sysdeps/ieee754/ldbl-96/s_ceill.c new file mode 100644 index 0000000..d53f395 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_ceill.c @@ -0,0 +1,89 @@ +/* s_ceill.c -- long double version of s_ceil.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * ceill(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to ceil(x). + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double huge = 1.0e4930; +#else +static long double huge = 1.0e4930; +#endif + +#ifdef __STDC__ + long double __ceill(long double x) +#else + long double __ceill(x) + long double x; +#endif +{ + int32_t i1,j0; + u_int32_t i,j,se,i0,sx; + GET_LDOUBLE_WORDS(se,i0,i1,x); + sx = (se>>15)&1; + j0 = (se&0x7fff)-0x3fff; + if(j0<31) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(sx) {se=0x8000;i0=0;i1=0;} + else if((i0|i1)!=0) { se=0x3fff;i0=0;i1=0;} + } + } else { + i = (0x7fffffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(sx==0) { + if (j0>0) i0 += (0x80000000)>>j0; + else ++se; + } + i0 &= (~i); i1=0; + } + } + } else if (j0>62) { + if(j0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-31); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(sx==0) { + if(j0==31) i0+=1; + else { + j = i1 + (1<<(63-j0)); + if(j<i1) i0+=1; /* got a carry */ + i1 = j; + } + } + i1 &= (~i); + } + } + SET_LDOUBLE_WORDS(x,se,i0,i1); + return x; +} +weak_alias (__ceill, ceill) diff --git a/sysdeps/ieee754/ldbl-96/s_copysignl.c b/sysdeps/ieee754/ldbl-96/s_copysignl.c new file mode 100644 index 0000000..9976575 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_copysignl.c @@ -0,0 +1,43 @@ +/* s_copysignl.c -- long double version of s_copysign.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * copysignl(long double x, long double y) + * copysignl(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __copysignl(long double x, long double y) +#else + long double __copysignl(x,y) + long double x,y; +#endif +{ + u_int32_t es1,es2; + GET_LDOUBLE_EXP(es1,x); + GET_LDOUBLE_EXP(es2,y); + SET_LDOUBLE_EXP(x,(es1&0x7fff)|(es2&0x8000)); + return x; +} +weak_alias (__copysignl, copysignl) diff --git a/sysdeps/ieee754/ldbl-96/s_cosl.c b/sysdeps/ieee754/ldbl-96/s_cosl.c new file mode 100644 index 0000000..9765f7f --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_cosl.c @@ -0,0 +1,88 @@ +/* s_cosl.c -- long double version of s_cos.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* cosl(x) + * Return cosine function of x. + * + * kernel function: + * __kernel_sinl ... sine function on [-pi/4,pi/4] + * __kernel_cosl ... cosine function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __cosl(long double x) +#else + long double __cosl(x) + long double x; +#endif +{ + long double y[2],z=0.0; + int32_t n, se, i0, i1; + + /* High word of x. */ + GET_LDOUBLE_WORDS(se,i0,i1,x); + + /* |x| ~< pi/4 */ + se &= 0x7fff; + if(se < 0x3ffe || (se == 0x3ffe && i0 <= 0xc90fdaa2)) + return __kernel_cosl(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (se==0x7fff) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + switch(n&3) { + case 0: return __kernel_cosl(y[0],y[1]); + case 1: return -__kernel_sinl(y[0],y[1],1); + case 2: return -__kernel_cosl(y[0],y[1]); + default: + return __kernel_sinl(y[0],y[1],1); + } + } +} +weak_alias (__cosl, cosl) diff --git a/sysdeps/ieee754/ldbl-96/s_fabsl.c b/sysdeps/ieee754/ldbl-96/s_fabsl.c new file mode 100644 index 0000000..f717050 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_fabsl.c @@ -0,0 +1,40 @@ +/* s_fabsl.c -- long double version of s_fabs.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * fabsl(x) returns the absolute value of x. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __fabsl(long double x) +#else + long double __fabsl(x) + long double x; +#endif +{ + u_int32_t exp; + GET_LDOUBLE_EXP(exp,x); + SET_LDOUBLE_EXP(x,exp&0x7fff); + return x; +} +weak_alias (__fabsl, fabsl) diff --git a/sysdeps/ieee754/ldbl-96/s_finitel.c b/sysdeps/ieee754/ldbl-96/s_finitel.c new file mode 100644 index 0000000..6e444e9 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_finitel.c @@ -0,0 +1,40 @@ +/* s_finitel.c -- long double version of s_finite.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * finitel(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int __finitel(long double x) +#else + int __finitel(x) + long double x; +#endif +{ + int32_t exp; + GET_LDOUBLE_EXP(exp,x); + return (int)((u_int32_t)((exp&0x7fff)-0x7fff)>>31); +} +weak_alias (__finitel, finitel) diff --git a/sysdeps/ieee754/ldbl-96/s_floorl.c b/sysdeps/ieee754/ldbl-96/s_floorl.c new file mode 100644 index 0000000..fb0c37e --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_floorl.c @@ -0,0 +1,90 @@ +/* s_floorl.c -- long double version of s_floor.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * floorl(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floor(x). + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double huge = 1.0e4930; +#else +static long double huge = 1.0e4930; +#endif + +#ifdef __STDC__ + long double __floorl(long double x) +#else + long double __floorl(x) + long double x; +#endif +{ + int32_t i1,j0; + u_int32_t i,j,se,i0,sx; + GET_LDOUBLE_WORDS(se,i0,i1,x); + sx = (se>>15)&1; + j0 = (se&0x7fff)-0x3fff; + if(j0<31) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(sx==0) {se=0;i0=i1=0;} + else if(((se&0x7fff)|i0|i1)!=0) + { se=0xbfff;i0=i1=0;} + } + } else { + i = (0x7fffffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(sx) { + if (j0>0) i0 += (0x80000000)>>j0; + else ++se; + } + i0 &= (~i); i1=0; + } + } + } else if (j0>62) { + if(j0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-31); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(sx) { + if(j0==31) i0+=1; + else { + j = i1+(1<<(63-j0)); + if(j<i1) i0 +=1 ; /* got a carry */ + i1=j; + } + } + i1 &= (~i); + } + } + SET_LDOUBLE_WORDS(x,se,i0,i1); + return x; +} +weak_alias (__floorl, floorl) diff --git a/sysdeps/ieee754/ldbl-96/s_fpclassifyl.c b/sysdeps/ieee754/ldbl-96/s_fpclassifyl.c new file mode 100644 index 0000000..4df0b44 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_fpclassifyl.c @@ -0,0 +1,44 @@ +/* Return classification value corresponding to argument. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + Fixed by Andreas Schwab <schwab@issan.informatik.uni-dortmund.de>. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +int +__fpclassifyl (long double x) +{ + u_int32_t ex, hx, lx, m; + int retval = FP_NORMAL; + + GET_LDOUBLE_WORDS (ex, hx, lx, x); + m = (hx & 0x7fffffff) | lx; + ex &= 0x7fff; + if ((ex | m) == 0) + retval = FP_ZERO; + else if (ex == 0 && (hx & 0x80000000) == 0) + retval = FP_SUBNORMAL; + else if (ex == 0x7fff) + retval = m != 0 ? FP_NAN : FP_INFINITE; + + return retval; +} diff --git a/sysdeps/ieee754/ldbl-96/s_frexpl.c b/sysdeps/ieee754/ldbl-96/s_frexpl.c new file mode 100644 index 0000000..7a49bc3 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_frexpl.c @@ -0,0 +1,69 @@ +/* s_frexpl.c -- long double version of s_frexp.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * for non-zero x + * x = frexpl(arg,&exp); + * return a long double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexpl(arg,&exp) returns arg + * with *exp=0. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +#if LDBL_MANT_DIG == 64 +two65 = 3.68934881474191032320e+19L; /* 0x4040, 0x80000000, 0x00000000 */ +#else +# error "Cannot handle this MANT_DIG" +#endif + + +#ifdef __STDC__ + long double __frexpl(long double x, int *eptr) +#else + long double __frexpl(x, eptr) + long double x; int *eptr; +#endif +{ + u_int32_t se, hx, ix, lx; + GET_LDOUBLE_WORDS(se,hx,lx,x); + ix = 0x7fff&se; + *eptr = 0; + if(ix==0x7fff||((ix|hx|lx)==0)) return x; /* 0,inf,nan */ + if (ix==0x0000) { /* subnormal */ + x *= two65; + GET_LDOUBLE_EXP(se,x); + ix = se&0x7fff; + *eptr = -65; + } + *eptr += ix-16382; + se = (se & 0x8000) | 0x3ffe; + SET_LDOUBLE_EXP(x,se); + return x; +} +weak_alias (__frexpl, frexpl) diff --git a/sysdeps/ieee754/ldbl-96/s_ilogbl.c b/sysdeps/ieee754/ldbl-96/s_ilogbl.c new file mode 100644 index 0000000..d44229d --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_ilogbl.c @@ -0,0 +1,56 @@ +/* s_ilogbl.c -- long double version of s_ilogb.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* ilogbl(long double x) + * return the binary exponent of non-zero x + * ilogbl(0) = 0x80000001 + * ilogbl(inf/NaN) = 0x7fffffff (no signal is raised) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int __ilogbl(long double x) +#else + int __ilogbl(x) + long double x; +#endif +{ + int32_t es,hx,lx,ix; + + GET_LDOUBLE_EXP(es,x); + es &= 0x7fff; + if(es==0) { + GET_LDOUBLE_WORDS(es,hx,lx,x); + if((hx|lx)==0) + return FP_ILOGB0; /* ilogbl(0) = FP_ILOGB0 */ + else /* subnormal x */ + if(hx==0) { + for (ix = -16415; lx>0; lx<<=1) ix -=1; + } else { + for (ix = -16383; hx>0; hx<<=1) ix -=1; + } + return ix; + } + else if (es<0x7fff) return es-0x3fff; + else return FP_ILOGBNAN; +} +weak_alias (__ilogbl, ilogbl) diff --git a/sysdeps/ieee754/ldbl-96/s_isinfl.c b/sysdeps/ieee754/ldbl-96/s_isinfl.c new file mode 100644 index 0000000..6f7c07c --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_isinfl.c @@ -0,0 +1,29 @@ +/* + * Written by J.T. Conklin <jtc@netbsd.org>. + * Change for long double by Ulrich Drepper <drepper@cygnus.com>. + * Public domain. + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * isinfl(x) returns 1 if x is inf, -1 if x is -inf, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +int +__isinfl (long double x) +{ + int32_t se,hx,lx; + GET_LDOUBLE_WORDS(se,hx,lx,x); + lx |= (hx & 0x7fffffff) | ((se & 0x7fff) ^ 0x7fff); + lx |= -lx; + se &= 0x8000; + return ~(lx >> 31) & (1 - (se >> 14)); +} +weak_alias (__isinfl, isinfl) diff --git a/sysdeps/ieee754/ldbl-96/s_isnanl.c b/sysdeps/ieee754/ldbl-96/s_isnanl.c new file mode 100644 index 0000000..0a7ff38 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_isnanl.c @@ -0,0 +1,44 @@ +/* s_isnanl.c -- long double version of s_isnan.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * isnanl(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int __isnanl(long double x) +#else + int __isnanl(x) + long double x; +#endif +{ + int32_t se,hx,lx; + GET_LDOUBLE_WORDS(se,hx,lx,x); + se = (se & 0x7fff) << 1; + lx |= hx & 0x7fffffff; + se |= (u_int32_t)(lx|(-lx))>>31; + se = 0xfffe - se; + return (int)(((u_int32_t)(se))>>31); +} +weak_alias (__isnanl, isnanl) diff --git a/sysdeps/ieee754/ldbl-96/s_llrintl.c b/sysdeps/ieee754/ldbl-96/s_llrintl.c new file mode 100644 index 0000000..2aeaa1e --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_llrintl.c @@ -0,0 +1,77 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + +static const long double two63[2] = +{ + 9.223372036854775808000000e+18, /* 0x403E, 0x00000000, 0x00000000 */ + -9.223372036854775808000000e+18 /* 0xC03E, 0x00000000, 0x00000000 */ +}; + + +long long int +__llrintl (long double x) +{ + int32_t se,j0; + u_int32_t i0, i1; + long long int result; + volatile long double w; + long double t; + int sx; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + + sx = (se >> 15) & 1; + j0 = (se & 0x7fff) - 0x3fff; + + if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 < -1) + return 0; + else if (j0 >= 63) + result = (((long long int) i0 << 32) | i1) << (j0 - 63); + else + { + w = two63[sx] + x; + t = w - two63[sx]; + GET_LDOUBLE_WORDS (se, i0, i1, t); + j0 = (se & 0x7fff) - 0x3fff; + + if (j0 < 31) + result = i0 >> (31 - j0); + else + result = ((long long int) i0 << (j0 - 31)) | (i1 >> (63 - j0)); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__llrintl, llrintl) diff --git a/sysdeps/ieee754/ldbl-96/s_llroundl.c b/sysdeps/ieee754/ldbl-96/s_llroundl.c new file mode 100644 index 0000000..4a537c8 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_llroundl.c @@ -0,0 +1,81 @@ +/* Round long double value to long long int. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +long long int +__llroundl (long double x) +{ + int32_t j0; + u_int32_t se, i1, i0; + long long int result; + int sign; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + j0 = (se & 0x7fff) - 0x3fff; + sign = (se & 0x8000) != 0 ? -1 : 1; + + if (j0 < 31) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else + { + u_int32_t j = i0 + (0x40000000 >> j0); + if (j < i0) + { + j >>= 1; + j |= 0x80000000; + ++j0; + } + + result = j >> (31 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long long int)) - 1) + { + if (j0 >= 63) + result = (((long long int) i0 << 32) | i1) << (j0 - 63); + else + { + u_int32_t j = i1 + (0x80000000 >> (j0 - 31)); + if (j < i1) + ++i0; + + if (j0 == 31) + result = (long long int) i0; + else + result = ((long long int) i0 << (j0 - 31)) | (j >> (63 - j0)); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long long int) x; + } + + return sign * result; +} + +weak_alias (__llroundl, llroundl) diff --git a/sysdeps/ieee754/ldbl-96/s_logbl.c b/sysdeps/ieee754/ldbl-96/s_logbl.c new file mode 100644 index 0000000..2cd9d10 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_logbl.c @@ -0,0 +1,47 @@ +/* s_logbl.c -- long double version of s_logb.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * long double logbl(x) + * IEEE 754 logb. Included to pass IEEE test suite. Not recommend. + * Use ilogb instead. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __logbl(long double x) +#else + long double __logbl(x) + long double x; +#endif +{ + int32_t es,lx,ix; + GET_LDOUBLE_WORDS(es,ix,lx,x); + es &= 0x7fff; /* exponent */ + if((es|ix|lx)==0) return -1.0/fabs(x); + if(es==0x7fff) return x*x; + if(es==0) /* IEEE 754 logb */ + return -16382.0; + else + return (long double) (es-0x3fff); +} +weak_alias (__logbl, logbl) diff --git a/sysdeps/ieee754/ldbl-96/s_lrintl.c b/sysdeps/ieee754/ldbl-96/s_lrintl.c new file mode 100644 index 0000000..673cf3d --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_lrintl.c @@ -0,0 +1,86 @@ +/* Round argument to nearest integral value according to current rounding + direction. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + +static const long double two63[2] = +{ + 9.223372036854775808000000e+18, /* 0x403E, 0x00000000, 0x00000000 */ + -9.223372036854775808000000e+18 /* 0xC03E, 0x00000000, 0x00000000 */ +}; + + +long int +__lrintl (long double x) +{ + int32_t se,j0; + u_int32_t i0, i1; + long int result; + volatile long double w; + long double t; + int sx; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + + sx = (se >> 15) & 1; + j0 = (se & 0x7fff) - 0x3fff; + + if (j0 < 31) + { + if (j0 < -1) + return 0; + else + { + w = two63[sx] + x; + t = w - two63[sx]; + GET_LDOUBLE_WORDS (se, i0, i1, t); + j0 = (se & 0x7fff) - 0x3fff; + + result = i0 >> (31 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 >= 63) + result = ((long int) i0 << (j0 - 31)) | (i1 << (j0 - 63)); + else + { + w = two63[sx] + x; + t = w - two63[sx]; + GET_LDOUBLE_WORDS (se, i0, i1, t); + j0 = (se & 0x7fff) - 0x3fff; + + result = ((long int) i0 << (j0 - 31)) | (i1 >> (63 - j0)); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long int) x; + } + + return sx ? -result : result; +} + +weak_alias (__lrintl, lrintl) diff --git a/sysdeps/ieee754/ldbl-96/s_lroundl.c b/sysdeps/ieee754/ldbl-96/s_lroundl.c new file mode 100644 index 0000000..3bdac83 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_lroundl.c @@ -0,0 +1,78 @@ +/* Round long double value to long int. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +long int +__lroundl (long double x) +{ + int32_t j0; + u_int32_t se, i1, i0; + long int result; + int sign; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + j0 = (se & 0x7fff) - 0x3fff; + sign = (se & 0x8000) != 0 ? -1 : 1; + + if (j0 < 31) + { + if (j0 < 0) + return j0 < -1 ? 0 : sign; + else + { + u_int32_t j = i0 + (0x40000000 >> j0); + if (j < i0) + { + j >>= 1; + j |= 0x80000000; + ++j0; + } + + result = j >> (31 - j0); + } + } + else if (j0 < (int32_t) (8 * sizeof (long int)) - 1) + { + if (j0 >= 63) + result = ((long int) i0 << (j0 - 31)) | (i1 << (j0 - 63)); + else + { + u_int32_t j = i1 + (0x80000000 >> (j0 - 31)); + if (j < i1) + ++i0; + + result = ((long int) i0 << (j0 - 31)) | (j >> (63 - j0)); + } + } + else + { + /* The number is too large. It is left implementation defined + what happens. */ + return (long int) x; + } + + return sign * result; +} + +weak_alias (__lroundl, lroundl) diff --git a/sysdeps/ieee754/ldbl-96/s_modfl.c b/sysdeps/ieee754/ldbl-96/s_modfl.c new file mode 100644 index 0000000..fb1b3ac --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_modfl.c @@ -0,0 +1,85 @@ +/* s_modfl.c -- long double version of s_modf.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * modfl(long double x, long double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double one = 1.0; +#else +static long double one = 1.0; +#endif + +#ifdef __STDC__ + long double __modfl(long double x, long double *iptr) +#else + long double __modfl(x, iptr) + long double x,*iptr; +#endif +{ + int32_t i0,i1,j0; + u_int32_t i,se; + GET_LDOUBLE_WORDS(se,i0,i1,x); + j0 = (se&0x7fff)-0x3fff; /* exponent of x */ + if(j0<32) { /* integer part in high x */ + if(j0<0) { /* |x|<1 */ + SET_LDOUBLE_WORDS(*iptr,se&0x8000,0,0); /* *iptr = +-0 */ + return x; + } else { + i = (0x7fffffff)>>j0; + if(((i0&i)|i1)==0) { /* x is integral */ + *iptr = x; + SET_LDOUBLE_WORDS(x,se&0x8000,0,0); /* return +-0 */ + return x; + } else { + SET_LDOUBLE_WORDS(*iptr,se,i0&(~i),0); + return x - *iptr; + } + } + } else if (j0>63) { /* no fraction part */ + *iptr = x*one; + /* We must handle NaNs separately. */ + if (j0 == 0x4000 && ((i0 & 0x7fffffff) | i1)) + return x*one; + SET_LDOUBLE_WORDS(x,se&0x8000,0,0); /* return +-0 */ + return x; + } else { /* fraction part in low x */ + i = ((u_int32_t)(0xffffffff))>>(j0-32); + if((i1&i)==0) { /* x is integral */ + *iptr = x; + SET_LDOUBLE_WORDS(x,se&0x8000,0,0); /* return +-0 */ + return x; + } else { + SET_LDOUBLE_WORDS(*iptr,se,i0,i1&(~i)); + return x - *iptr; + } + } +} +weak_alias (__modfl, modfl) diff --git a/sysdeps/ieee754/ldbl-96/s_nearbyintl.c b/sysdeps/ieee754/ldbl-96/s_nearbyintl.c new file mode 100644 index 0000000..92c3ebf --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_nearbyintl.c @@ -0,0 +1,95 @@ +/* s_rintl.c -- long double version of s_rint.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ +/* Adapted for use as nearbyint by Ulrich Drepper <drepper@cygnus.com>. */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * rintl(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rintl(x). + */ + +#include <fenv.h> +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +TWO63[2]={ + 9.223372036854775808000000e+18, /* 0x403E, 0x00000000, 0x00000000 */ + -9.223372036854775808000000e+18 /* 0xC03E, 0x00000000, 0x00000000 */ +}; + +#ifdef __STDC__ + long double __nearbyintl(long double x) +#else + long double __nearbyintl(x) + long double x; +#endif +{ + fenv_t env; + int32_t se,j0,sx; + u_int32_t i,i0,i1; + long double w,t; + GET_LDOUBLE_WORDS(se,i0,i1,x); + sx = (se>>15)&1; + j0 = (se&0x7fff)-0x3fff; + if(j0<31) { + if(j0<0) { + if(((se&0x7fff)|i0|i1)==0) return x; + i1 |= i0; + i0 &= 0xe0000000; + i0 |= (i1|-i1)&0x80000000; + SET_LDOUBLE_MSW(x,i0); + feholdexcept (&env); + w = TWO63[sx]+x; + t = w-TWO63[sx]; + fesetenv (&env); + GET_LDOUBLE_EXP(i0,t); + SET_LDOUBLE_EXP(t,(i0&0x7fff)|(sx<<15)); + return t; + } else { + i = (0x7fffffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + i>>=1; + if(((i0&i)|i1)!=0) { + if (j0==30) i1 = 0x40000000; else + i0 = (i0&(~i))|((0x20000000)>>j0); + } + } + } else if (j0>62) { + if(j0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-31); + if((i1&i)==0) return x; /* x is integral */ + i>>=1; + if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-31)); + } + SET_LDOUBLE_WORDS(x,se,i0,i1); + feholdexcept (&env); + w = TWO63[sx]+x; + t = w-TWO63[sx]; + fesetenv (&env); + return t; +} +weak_alias (__nearbyintl, nearbyintl) diff --git a/sysdeps/ieee754/ldbl-96/s_nextafterl.c b/sysdeps/ieee754/ldbl-96/s_nextafterl.c new file mode 100644 index 0000000..aea57e3 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_nextafterl.c @@ -0,0 +1,101 @@ +/* s_nextafterl.c -- long double version of s_nextafter.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* IEEE functions + * nextafterl(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __nextafterl(long double x, long double y) +#else + long double __nextafterl(x,y) + long double x,y; +#endif +{ + int32_t hx,hy,ix,iy; + u_int32_t lx,ly,esx,esy; + + GET_LDOUBLE_WORDS(esx,hx,lx,x); + GET_LDOUBLE_WORDS(esy,hy,ly,y); + ix = esx&0x7fff; /* |x| */ + iy = esy&0x7fff; /* |y| */ + + if(((ix==0x7fff)&&((hx|lx)|-(hx|lx))!=0) || /* x is nan */ + ((iy==0x7fff)&&((hy|ly)|-(hy|ly))!=0)) /* y is nan */ + return x+y; + if(x==y) return y; /* x=y, return y */ + if((ix|hx|lx)==0) { /* x == 0 */ + SET_LDOUBLE_WORDS(x,esx&0x8000,0,1);/* return +-minsubnormal */ + y = x*x; + if(y==x) return y; else return x; /* raise underflow flag */ + } + if(esx<0x8000) { /* x > 0 */ + if(ix>iy||((ix==iy) && (hx>hy||((hx==hy)&&(lx>ly))))) { + /* x > y, x -= ulp */ + if(lx==0) { + if (hx==0) esx -= 1; + hx -= 1; + } + lx -= 1; + } else { /* x < y, x += ulp */ + lx += 1; + if(lx==0) { + hx += 1; + if (hx==0) + esx += 1; + } + } + } else { /* x < 0 */ + if(esy>=0||(ix>iy||((ix==iy)&&(hx>hy||((hx==hy)&&(lx>ly)))))){ + /* x < y, x -= ulp */ + if(lx==0) { + if (hx==0) esx -= 1; + hx -= 1; + } + lx -= 1; + } else { /* x > y, x += ulp */ + lx += 1; + if(lx==0) { + hx += 1; + if (hx==0) esx += 1; + } + } + } + esy = esx&0x7fff; + if(esy==0x7fff) return x+x; /* overflow */ + if(esy==0) { /* underflow */ + y = x*x; + if(y!=x) { /* raise underflow flag */ + SET_LDOUBLE_WORDS(y,esx,hx,lx); + return y; + } + } + SET_LDOUBLE_WORDS(x,esx,hx,lx); + return x; +} +weak_alias (__nextafterl, nextafterl) +strong_alias (__nextafterl, __nexttowardl) +weak_alias (__nextafterl, nexttowardl) diff --git a/sysdeps/ieee754/ldbl-96/s_nexttoward.c b/sysdeps/ieee754/ldbl-96/s_nexttoward.c new file mode 100644 index 0000000..debbb86 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_nexttoward.c @@ -0,0 +1,98 @@ +/* s_nexttoward.c + * Conversion from s_nextafter.c by Ulrich Drepper, Cygnus Support, + * drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* IEEE functions + * nextafterx(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double __nexttoward(double x, long double y) +#else + double __nexttoward(x,y) + double x; + long double y; +#endif +{ + int32_t hx,ix,iy; + u_int32_t lx,hy,ly,esy; + + EXTRACT_WORDS(hx,lx,x); + GET_LDOUBLE_WORDS(esy,hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = esy&0x7fff; /* |y| */ + + if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ + ((iy>=0x7fff)&&((hy|ly)|-(hy|ly))!=0)) /* y is nan */ + return x+y; + if((long double) x==y) return x; /* x=y, return x */ + if((ix|lx)==0) { /* x == 0 */ + double x2; + INSERT_WORDS(x,esy&0x8000?0x80000000:0,1);/* return +-minsub */ + x2 = x*x; + if(x2==x) return x2; else return x; /* raise underflow flag */ + } + if(hx>=0) { /* x > 0 */ + if (esy>=0x8000||((ix>>20)&0x7ff)>iy-0x3c00 + || (((ix>>20)&0x7ff)==iy-0x3c00 + && (((hx<<11)|(lx>>21))>(hy&0x7fffffff) + || (((hx<<11)|(lx>>21))==(hy&0x7fffffff) + && (lx<<11)>ly)))) { /* x > y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x < y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } else { /* x < 0 */ + if (esy<0x8000||((ix>>20)&0x7ff)>iy-0x3c00 + || (((ix>>20)&0x7ff)==iy-0x3c00 + && (((hx<<11)|(lx>>21))>(hy&0x7fffffff) + || (((hx<<11)|(lx>>21))==(hy&0x7fffffff) + && (lx<<11)>ly)))) {/* x < y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x > y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } + hy = hx&0x7ff00000; + if(hy>=0x7ff00000) return x+x; /* overflow */ + if(hy<0x00100000) { /* underflow */ + double x2 = x*x; + if(x2!=x) { /* raise underflow flag */ + INSERT_WORDS(x2,hx,lx); + return x2; + } + } + INSERT_WORDS(x,hx,lx); + return x; +} +weak_alias (__nexttoward, nexttoward) +#ifdef NO_LONG_DOUBLE +strong_alias (__nexttoward, __nexttowardl) +weak_alias (__nexttoward, nexttowardl) +#endif diff --git a/sysdeps/ieee754/ldbl-96/s_nexttowardf.c b/sysdeps/ieee754/ldbl-96/s_nexttowardf.c new file mode 100644 index 0000000..b7e9f00 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_nexttowardf.c @@ -0,0 +1,78 @@ +/* s_nexttowardf.c -- float version of s_nextafter.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + float __nexttowardf(float x, long double y) +#else + float __nexttowardf(x,y) + float x; + long double y; +#endif +{ + int32_t hx,ix,iy; + u_int32_t hy,ly,esy; + + GET_FLOAT_WORD(hx,x); + GET_LDOUBLE_WORDS(esy,hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = esy&0x7fff; /* |y| */ + + if((ix>0x7f800000) || /* x is nan */ + (iy>=0x7fff&&((hy|ly)|-(hy|ly))!=0)) /* y is nan */ + return x+y; + if((long double) x==y) return y; /* x=y, return y */ + if(ix==0) { /* x == 0 */ + float x2; + SET_FLOAT_WORD(x,(esy&0x8000?0x80000000:0)|1);/* return +-minsub*/ + x2 = x*x; + if(x2==x) return x2; else return x; /* raise underflow flag */ + } + if(hx>=0) { /* x > 0 */ + if(esy>=0x8000||((ix>>23)&0xff)>iy-0x3f80 + || (((ix>>23)&0xff)==iy-0x3f80 + && ((ix&0x7fffff)<<8)>(hy&0x7fffffff))) {/* x > y, x -= ulp */ + hx -= 1; + } else { /* x < y, x += ulp */ + hx += 1; + } + } else { /* x < 0 */ + if(esy<0x8000||((ix>>23)&0xff)>iy-0x3f80 + || (((ix>>23)&0xff)==iy-0x3f80 + && ((ix&0x7fffff)<<8)>(hy&0x7fffffff))) {/* x < y, x -= ulp */ + hx -= 1; + } else { /* x > y, x += ulp */ + hx += 1; + } + } + hy = hx&0x7f800000; + if(hy>=0x7f800000) return x+x; /* overflow */ + if(hy<0x00800000) { /* underflow */ + float x2 = x*x; + if(x2!=x) { /* raise underflow flag */ + SET_FLOAT_WORD(x2,hx); + return x2; + } + } + SET_FLOAT_WORD(x,hx); + return x; +} +weak_alias (__nexttowardf, nexttowardf) diff --git a/sysdeps/ieee754/ldbl-96/s_remquol.c b/sysdeps/ieee754/ldbl-96/s_remquol.c new file mode 100644 index 0000000..88ff298 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_remquol.c @@ -0,0 +1,109 @@ +/* Compute remainder and a congruent to the quotient. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +static const long double zero = 0.0; + + +long double +__remquol (long double x, long double p, int *quo) +{ + int32_t ex,ep,hx,hp; + u_int32_t sx,lx,lp; + int cquo,qs; + + GET_LDOUBLE_WORDS (ex, hx, lx, x); + GET_LDOUBLE_WORDS (ep, hp, lp, p); + sx = ex & 0x8000; + qs = (sx ^ (ep & 0x8000)) >> 15; + ep &= 0x7fff; + ex &= 0x7fff; + + /* Purge off exception values. */ + if ((ep | hp | lp) == 0) + return (x * p) / (x * p); /* p = 0 */ + if ((ex == 0x7fff) /* x not finite */ + || ((ep == 0x7fff) /* p is NaN */ + && ((hp | lp) != 0))) + return (x * p) / (x * p); + + if (ep <= 0x7ffb) + x = __ieee754_fmodl (x, 8 * p); /* now x < 8p */ + + if (((ex - ep) | (hx - hp) | (lx - lp)) == 0) + { + *quo = qs ? -1 : 1; + return zero * x; + } + + x = fabsl (x); + p = fabsl (p); + cquo = 0; + + if (x >= 4 * p) + { + x -= 4 * p; + cquo += 4; + } + if (x >= 2 * p) + { + x -= 2 * p; + cquo += 2; + } + + if (ep < 0x0002) + { + if (x + x > p) + { + x -= p; + ++cquo; + if (x + x >= p) + { + x -= p; + ++cquo; + } + } + } + else + { + long double p_half = 0.5 * p; + if (x > p_half) + { + x -= p; + ++cquo; + if (x >= p_half) + { + x -= p; + ++cquo; + } + } + } + + *quo = qs ? -cquo : cquo; + + if (sx) + x = -x; + return x; +} +weak_alias (__remquol, remquol) diff --git a/sysdeps/ieee754/ldbl-96/s_rintl.c b/sysdeps/ieee754/ldbl-96/s_rintl.c new file mode 100644 index 0000000..9d4777d --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_rintl.c @@ -0,0 +1,91 @@ +/* s_rintl.c -- long double version of s_rint.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * rintl(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rintl(x). + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +TWO63[2]={ + 9.223372036854775808000000e+18, /* 0x403E, 0x00000000, 0x00000000 */ + -9.223372036854775808000000e+18 /* 0xC03E, 0x00000000, 0x00000000 */ +}; + +#ifdef __STDC__ + long double __rintl(long double x) +#else + long double __rintl(x) + long double x; +#endif +{ + int32_t se,j0,sx; + u_int32_t i,i0,i1; + long double w,t; + GET_LDOUBLE_WORDS(se,i0,i1,x); + sx = (se>>15)&1; + j0 = (se&0x7fff)-0x3fff; + if(j0<31) { + if(j0<0) { + if(((se&0x7fff)|i0|i1)==0) return x; + i1 |= i0; + i0 &= 0xe0000000; + i0 |= (i1|-i1)&0x80000000; + SET_LDOUBLE_MSW(x,i0); + w = TWO63[sx]+x; + t = w-TWO63[sx]; + GET_LDOUBLE_EXP(i0,t); + SET_LDOUBLE_EXP(t,(i0&0x7fff)|(sx<<15)); + return t; + } else { + i = (0x7fffffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + i>>=1; + if(((i0&i)|i1)!=0) { + if(j0==30) i1 = 0x40000000; else + i0 = (i0&(~i))|((0x20000000)>>j0); + } + } + } else if (j0>62) { + if(j0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-31); + if((i1&i)==0) return x; /* x is integral */ + i>>=1; + if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-31)); + } + SET_LDOUBLE_WORDS(x,se,i0,i1); + w = TWO63[sx]+x; + return w-TWO63[sx]; +} +weak_alias (__rintl, rintl) diff --git a/sysdeps/ieee754/ldbl-96/s_roundl.c b/sysdeps/ieee754/ldbl-96/s_roundl.c new file mode 100644 index 0000000..d7482b9 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_roundl.c @@ -0,0 +1,106 @@ +/* Round long double to integer away from zero. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +static const long double huge = 1.0e4930; + + +long double +__roundl (long double x) +{ + int32_t j0; + u_int32_t se, i1, i0; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + j0 = (se & 0x7fff) - 0x3fff; + if (j0 < 31) + { + if (j0 < 0) + { + if (huge + x > 0.0) + { + se &= 0x8000; + i0 = i1 = 0; + if (j0 == -1) + { + se |= 0x3fff; + i0 = 0x80000000; + } + } + } + else + { + u_int32_t i = 0x7fffffff >> j0; + if (((i0 & i) | i1) == 0) + /* X is integral. */ + return x; + if (huge + x > 0.0) + { + /* Raise inexact if x != 0. */ + u_int32_t j = i0 + (0x40000000 >> j0); + if (j < i0) + se += 1; + i0 = (j & ~i) | 0x80000000; + i1 = 0; + } + } + } + else if (j0 > 62) + { + if (j0 == 0x4000) + /* Inf or NaN. */ + return x + x; + else + return x; + } + else + { + u_int32_t i = 0xffffffff >> (j0 - 31); + if ((i1 & i) == 0) + /* X is integral. */ + return x; + + if (huge + x > 0.0) + { + /* Raise inexact if x != 0. */ + u_int32_t j = i1 + (1 << (62 - j0)); + if (j < i1) + { + u_int32_t k = i0 + 1; + if (k < i0) + { + se += 1; + k |= 0x80000000; + } + i0 = k; + } + i1 = j; + } + i1 &= ~i; + } + + SET_LDOUBLE_WORDS (x, se, i0, i1); + return x; +} +weak_alias (__roundl, roundl) diff --git a/sysdeps/ieee754/ldbl-96/s_scalblnl.c b/sysdeps/ieee754/ldbl-96/s_scalblnl.c new file mode 100644 index 0000000..8e556fa --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_scalblnl.c @@ -0,0 +1,71 @@ +/* s_scalbnl.c -- long double version of s_scalbn.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * scalbnl (long double x, int n) + * scalbnl(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +two63 = 4.50359962737049600000e+15, +twom63 = 1.08420217248550443400e-19, +huge = 1.0e+4900L, +tiny = 1.0e-4900L; + +#ifdef __STDC__ + long double __scalblnl (long double x, long int n) +#else + long double __scalblnl (x,n) + long double x; long int n; +#endif +{ + int32_t k,es,hx,lx; + GET_LDOUBLE_WORDS(es,hx,lx,x); + k = es&0x7fff; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ + x *= two63; + GET_LDOUBLE_EXP(es,x); + k = (hx&0x7fff) - 63; + } + if (k==0x7fff) return x+x; /* NaN or Inf */ + k = k+n; + if (n> 50000 || k > 0x7ffe) + return huge*__copysignl(huge,x); /* overflow */ + if (n< -50000) + return tiny*__copysignl(tiny,x); + if (k > 0) /* normal result */ + {SET_LDOUBLE_EXP(x,(es&0x8000)|k); return x;} + if (k <= -63) + return tiny*__copysignl(tiny,x); /*underflow*/ + k += 63; /* subnormal result */ + SET_LDOUBLE_EXP(x,(es&0x8000)|k); + return x*twom63; +} +weak_alias (__scalblnl, scalblnl) diff --git a/sysdeps/ieee754/ldbl-96/s_scalbnl.c b/sysdeps/ieee754/ldbl-96/s_scalbnl.c new file mode 100644 index 0000000..34c52e7 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_scalbnl.c @@ -0,0 +1,71 @@ +/* s_scalbnl.c -- long double version of s_scalbn.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * scalbnl (long double x, int n) + * scalbnl(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +two63 = 4.50359962737049600000e+15, +twom63 = 1.08420217248550443400e-19, +huge = 1.0e+4900L, +tiny = 1.0e-4900L; + +#ifdef __STDC__ + long double __scalbnl (long double x, int n) +#else + long double __scalbnl (x,n) + long double x; int n; +#endif +{ + int32_t k,es,hx,lx; + GET_LDOUBLE_WORDS(es,hx,lx,x); + k = es&0x7fff; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ + x *= two63; + GET_LDOUBLE_EXP(es,x); + k = (hx&0x7fff) - 63; + } + if (k==0x7fff) return x+x; /* NaN or Inf */ + k = k+n; + if (n> 50000 || k > 0x7ffe) + return huge*__copysignl(huge,x); /* overflow */ + if (n< -50000) + return tiny*__copysignl(tiny,x); + if (k > 0) /* normal result */ + {SET_LDOUBLE_EXP(x,(es&0x8000)|k); return x;} + if (k <= -63) + return tiny*__copysignl(tiny,x); /*underflow*/ + k += 63; /* subnormal result */ + SET_LDOUBLE_EXP(x,(es&0x8000)|k); + return x*twom63; +} +weak_alias (__scalbnl, scalbnl) diff --git a/sysdeps/ieee754/ldbl-96/s_signbitl.c b/sysdeps/ieee754/ldbl-96/s_signbitl.c new file mode 100644 index 0000000..b12fdef --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_signbitl.c @@ -0,0 +1,32 @@ +/* Return nonzero value if number is negative. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + +int +__signbitl (long double x) +{ + int32_t e; + + GET_LDOUBLE_EXP (e, x); + return e & 0x8000; +} diff --git a/sysdeps/ieee754/ldbl-96/s_sincosl.c b/sysdeps/ieee754/ldbl-96/s_sincosl.c new file mode 100644 index 0000000..78c78d5 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_sincosl.c @@ -0,0 +1,74 @@ +/* Compute sine and cosine of argument. + Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +void +__sincosl (long double x, long double *sinx, long double *cosx) +{ + int32_t se, i0, i1; + + /* High word of x. */ + GET_LDOUBLE_WORDS (se, i0, i1, x); + + /* |x| ~< pi/4 */ + se &= 0x7fff; + if (se < 0x3ffe || (se == 0x3ffe && i0 <= 0xc90fdaa2)) + { + *sinx = __kernel_sinl (x, 0.0, 0); + *cosx = __kernel_cosl (x, 0.0); + } + else if (se == 0x7fff) + { + /* sin(Inf or NaN) is NaN */ + *sinx = *cosx = x - x; + } + else + { + /* Argument reduction needed. */ + long double y[2]; + int n; + + n = __ieee754_rem_pio2l (x, y); + switch (n & 3) + { + case 0: + *sinx = __kernel_sinl (y[0], y[1], 1); + *cosx = __kernel_cosl (y[0], y[1]); + break; + case 1: + *sinx = __kernel_cosl (y[0], y[1]); + *cosx = -__kernel_sinl (y[0], y[1], 1); + break; + case 2: + *sinx = -__kernel_sinl (y[0], y[1], 1); + *cosx = -__kernel_cosl (y[0], y[1]); + break; + default: + *sinx = -__kernel_cosl (y[0], y[1]); + *cosx = __kernel_sinl (y[0], y[1], 1); + break; + } + } +} +weak_alias (__sincosl, sincosl) diff --git a/sysdeps/ieee754/ldbl-96/s_sinl.c b/sysdeps/ieee754/ldbl-96/s_sinl.c new file mode 100644 index 0000000..4fd4880 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_sinl.c @@ -0,0 +1,88 @@ +/* s_sinl.c -- long double version of s_sin.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* sinl(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sinl ... sine function on [-pi/4,pi/4] + * __kernel_cosl ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __sinl(long double x) +#else + long double __sinl(x) + long double x; +#endif +{ + long double y[2],z=0.0; + int32_t n, se, i0, i1; + + /* High word of x. */ + GET_LDOUBLE_WORDS(se,i0,i1,x); + + /* |x| ~< pi/4 */ + se &= 0x7fff; + if(se < 0x3ffe || (se == 0x3ffe && i0 <= 0xc90fdaa2)) + return __kernel_sinl(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (se==0x7fff) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + switch(n&3) { + case 0: return __kernel_sinl(y[0],y[1],1); + case 1: return __kernel_cosl(y[0],y[1]); + case 2: return -__kernel_sinl(y[0],y[1],1); + default: + return -__kernel_cosl(y[0],y[1]); + } + } +} +weak_alias (__sinl, sinl) diff --git a/sysdeps/ieee754/ldbl-96/s_tanhl.c b/sysdeps/ieee754/ldbl-96/s_tanhl.c new file mode 100644 index 0000000..1e3dc3b --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_tanhl.c @@ -0,0 +1,95 @@ +/* s_tanhl.c -- long double version of s_tanh.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* tanhl(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanhl(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x). + * 2. 0 <= x <= 2**-55 : tanhl(x) := x*(one+x) + * -t + * 2**-55 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x) + * t + 2 + * 2 + * 1 <= x <= 23.0 : tanhl(x) := 1- ----- ; t=expm1l(2x) + * t + 2 + * 23.0 < x <= INF : tanhl(x) := 1. + * + * Special cases: + * tanhl(NaN) is NaN; + * only tanhl(0)=0 is exact for finite argument. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double one=1.0, two=2.0, tiny = 1.0e-4900L; +#else +static long double one=1.0, two=2.0, tiny = 1.0e-4900L; +#endif + +#ifdef __STDC__ + long double __tanhl(long double x) +#else + long double __tanhl(x) + long double x; +#endif +{ + long double t,z; + int32_t se; + u_int32_t j0,j1,ix; + + /* High word of |x|. */ + GET_LDOUBLE_WORDS(se,j0,j1,x); + ix = se&0x7fff; + + /* x is INF or NaN */ + if(ix==0x7fff) { + /* for NaN it's not important which branch: tanhl(NaN) = NaN */ + if (se&0x8000) return one/x-one; /* tanhl(-inf)= -1; */ + else return one/x+one; /* tanhl(+inf)=+1 */ + } + + /* |x| < 23 */ + if (ix < 0x4003 || (ix == 0x4003 && j0 < 0xb8000000u)) {/* |x|<23 */ + if ((ix|j0|j1) == 0) + return x; /* x == +- 0 */ + if (ix<0x3fc8) /* |x|<2**-55 */ + return x*(one+x); /* tanh(small) = small */ + if (ix>=0x3fff) { /* |x|>=1 */ + t = __expm1l(two*fabsl(x)); + z = one - two/(t+two); + } else { + t = __expm1l(-two*fabsl(x)); + z= -t/(t+two); + } + /* |x| > 23, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (se>0x7fff)? -z: z; +} +weak_alias (__tanhl, tanhl) diff --git a/sysdeps/ieee754/ldbl-96/s_tanl.c b/sysdeps/ieee754/ldbl-96/s_tanl.c new file mode 100644 index 0000000..97a0b27 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_tanl.c @@ -0,0 +1,81 @@ +/* s_tanl.c -- long double version of s_tan.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* tanl(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tanl ... tangent function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + long double __tanl(long double x) +#else + long double __tanl(x) + long double x; +#endif +{ + long double y[2],z=0.0; + int32_t n, se; + + /* High word of x. */ + GET_LDOUBLE_EXP(se,x); + + /* |x| ~< pi/4 */ + se &= 0x7fff; + if(se <= 0x3ffe) return __kernel_tanl(x,z,1); + + /* tan(Inf or NaN) is NaN */ + else if (se==0x7fff) return x-x; /* NaN */ + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2l(x,y); + return __kernel_tanl(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} +weak_alias (__tanl, tanl) diff --git a/sysdeps/ieee754/ldbl-96/s_truncl.c b/sysdeps/ieee754/ldbl-96/s_truncl.c new file mode 100644 index 0000000..59c3b9c --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/s_truncl.c @@ -0,0 +1,57 @@ +/* Truncate argument to nearest integral value not larger than the argument. + Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +#include "math_private.h" + + +long double +__truncl (long double x) +{ + int32_t i0, j0; + u_int32_t se, i1; + int sx; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + sx = se & 0x8000; + j0 = (se & 0x7fff) - 0x3fff; + if (j0 < 31) + { + if (j0 < 0) + /* The magnitude of the number is < 1 so the result is +-0. */ + SET_LDOUBLE_WORDS (x, sx, 0, 0); + else + SET_LDOUBLE_WORDS (x, se, i0 & ~(0x7fffffff >> j0), 0); + } + else if (j0 > 63) + { + if (j0 == 0x4000) + /* x is inf or NaN. */ + return x + x; + } + else + { + SET_LDOUBLE_WORDS (x, se, i0, i1 & ~(0xffffffffu >> (j0 - 31))); + } + + return x; +} +weak_alias (__truncl, truncl) diff --git a/sysdeps/ieee754/ldbl-96/strtold.c b/sysdeps/ieee754/ldbl-96/strtold.c new file mode 100644 index 0000000..cabb787 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/strtold.c @@ -0,0 +1,42 @@ +/* Copyright (C) 1999 Free Software Foundation, Inc. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <math.h> + +/* The actual implementation for all floating point sizes is in strtod.c. + These macros tell it to produce the `long double' version, `strtold'. */ + +# define FLOAT long double +# define FLT LDBL +# ifdef USE_IN_EXTENDED_LOCALE_MODEL +# define STRTOF __strtold_l +# else +# define STRTOF strtold +# endif +# define MPN2FLOAT __mpn_construct_long_double +# define FLOAT_HUGE_VAL HUGE_VALL +# define SET_MANTISSA(flt, mant) \ + do { union ieee854_long_double u; \ + u.d = (flt); \ + if ((mant & 0x7fffffffffffffffULL) == 0) \ + mant = 0x4000000000000000ULL; \ + u.ieee.mantissa0 = (((mant) >> 32) & 0x7fffffff) | 0x80000000; \ + u.ieee.mantissa1 = (mant) & 0xffffffff; \ + (flt) = u.d; \ + } while (0) + +# include "strtod.c" diff --git a/sysdeps/ieee754/ldbl-96/w_expl.c b/sysdeps/ieee754/ldbl-96/w_expl.c new file mode 100644 index 0000000..b8152ce --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/w_expl.c @@ -0,0 +1,60 @@ +/* w_expl.c -- long double version of w_exp.c. + * Conversion to long double by Ulrich Drepper, + * Cygnus Support, drepper@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: $"; +#endif + +/* + * wrapper expl(x) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif +o_threshold= 1.135652340629414394949193107797076489134e4, + /* 0x400C, 0xB17217F7, 0xD1CF79AC */ +u_threshold= -1.140019167866942050398521670162263001513e4; + /* 0x400C, 0xB220C447, 0x69C201E8 */ + +#ifdef __STDC__ + long double __expl(long double x) /* wrapper exp */ +#else + long double __expl(x) /* wrapper exp */ + long double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_expl(x); +#else + long double z; + z = __ieee754_expl(x); + if(_LIB_VERSION == _IEEE_) return z; + if(__finitel(x)) { + if(x>o_threshold) + return __kernel_standard(x,x,206); /* exp overflow */ + else if(x<u_threshold) + return __kernel_standard(x,x,207); /* exp underflow */ + } + return z; +#endif +} +weak_alias (__expl, expl) diff --git a/sysdeps/ieee754/s_lib_version.c b/sysdeps/ieee754/s_lib_version.c new file mode 100644 index 0000000..121bdaa --- /dev/null +++ b/sysdeps/ieee754/s_lib_version.c @@ -0,0 +1,40 @@ +/* @(#)s_lib_ver.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_lib_version.c,v 1.6 1995/05/10 20:47:44 jtc Exp $"; +#endif + +/* + * MACRO for standards + */ + +#include "math.h" +#include "math_private.h" + +/* + * define and initialize _LIB_VERSION + */ +#ifdef _POSIX_MODE +_LIB_VERSION_TYPE _LIB_VERSION = _POSIX_; +#else +#ifdef _XOPEN_MODE +_LIB_VERSION_TYPE _LIB_VERSION = _XOPEN_; +#else +#ifdef _SVID3_MODE +_LIB_VERSION_TYPE _LIB_VERSION = _SVID_; +#else /* default _IEEE_MODE */ +_LIB_VERSION_TYPE _LIB_VERSION = _IEEE_; +#endif +#endif +#endif + diff --git a/sysdeps/ieee754/s_matherr.c b/sysdeps/ieee754/s_matherr.c new file mode 100644 index 0000000..1ad3eb3 --- /dev/null +++ b/sysdeps/ieee754/s_matherr.c @@ -0,0 +1,35 @@ +/* @(#)s_matherr.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_matherr.c,v 1.6 1995/05/10 20:47:53 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int + weak_function + __matherr(struct exception *x) +#else + int + weak_function + __matherr(x) + struct exception *x; +#endif +{ + int n=0; + if(x->arg1!=x->arg1) return 0; + return n; +} +weak_alias (__matherr, matherr) diff --git a/sysdeps/ieee754/s_signgam.c b/sysdeps/ieee754/s_signgam.c new file mode 100644 index 0000000..021b0ff --- /dev/null +++ b/sysdeps/ieee754/s_signgam.c @@ -0,0 +1,3 @@ +#include "math.h" +#include "math_private.h" +int signgam; |