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Diffstat (limited to 'sysdeps/ieee754/ldbl-128ibm/e_hypotl.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-128ibm/e_hypotl.c | 131 |
1 files changed, 131 insertions, 0 deletions
diff --git a/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c b/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c new file mode 100644 index 0000000..4330f28 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c @@ -0,0 +1,131 @@ +/* @(#)e_hypotl.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_hypotl.c,v 1.9 1995/05/12 04:57:27 jtc Exp $"; +#endif + +/* __ieee754_hypotl(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrtl(2)/2 ulp, than + * sqrtl(z) has error less than 1 ulp (exercise). + * + * So, compute sqrtl(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 53 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 53 bits cleared, t2 = 2x-t1, + * y1= y with lower 53 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypotl(x,y) is INF if x or y is +INF or -INF; else + * hypotl(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypotl(x,y) returns sqrtl(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include "math.h" +#include "math_private.h" + +static const long double two600 = 0x1.0p+600L; +static const long double two1022 = 0x1.0p+1022L; + +#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,kld; + int64_t j,k,ha,hb; + + GET_LDOUBLE_MSW64(ha,x); + ha &= 0x7fffffffffffffffLL; + GET_LDOUBLE_MSW64(hb,y); + hb &= 0x7fffffffffffffffLL; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + a = fabsl(a); /* a <- |a| */ + b = fabsl(b); /* b <- |b| */ + if((ha-hb)>0x3c0000000000000LL) {return a+b;} /* x/y > 2**60 */ + k=0; + kld = 1.0L; + if(ha > 0x5f30000000000000LL) { /* a>2**500 */ + if(ha >= 0x7ff0000000000000LL) { /* Inf or NaN */ + u_int64_t low; + w = a+b; /* for sNaN */ + GET_LDOUBLE_LSW64(low,a); + if(((ha&0xfffffffffffffLL)|(low&0x7fffffffffffffffLL))==0) + w = a; + GET_LDOUBLE_LSW64(low,b); + if(((hb^0x7ff0000000000000LL)|(low&0x7fffffffffffffffLL))==0) + w = b; + return w; + } + /* scale a and b by 2**-600 */ + ha -= 0x2580000000000000LL; hb -= 0x2580000000000000LL; k += 600; + a /= two600; + b /= two600; + k += 600; + kld = two600; + } + if(hb < 0x20b0000000000000LL) { /* b < 2**-500 */ + if(hb <= 0x000fffffffffffffLL) { /* subnormal b or 0 */ + u_int64_t low; + GET_LDOUBLE_LSW64(low,b); + if((hb|(low&0x7fffffffffffffffLL))==0) return a; + t1=two1022; /* t1=2^1022 */ + b *= t1; + a *= t1; + k -= 1022; + kld = kld / two1022; + } else { /* scale a and b by 2^600 */ + ha += 0x2580000000000000LL; /* a *= 2^600 */ + hb += 0x2580000000000000LL; /* b *= 2^600 */ + k -= 600; + a *= two600; + b *= two600; + kld = kld / two600; + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + SET_LDOUBLE_WORDS64(t1,ha,0); + t2 = a-t1; + w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + SET_LDOUBLE_WORDS64(y1,hb,0); + y2 = b - y1; + SET_LDOUBLE_WORDS64(t1,ha+0x0010000000000000LL,0); + t2 = a - t1; + w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) + return w*kld; + else + return w; +} |