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Diffstat (limited to 'sysdeps/ieee754/dbl-64/e_acos.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_acos.c | 144 |
1 files changed, 144 insertions, 0 deletions
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); + } +} |