diff options
Diffstat (limited to 'sysdeps')
| -rw-r--r-- | sysdeps/ieee754/ldbl-96/e_hypotl.c | 231 |
1 files changed, 98 insertions, 133 deletions
diff --git a/sysdeps/ieee754/ldbl-96/e_hypotl.c b/sysdeps/ieee754/ldbl-96/e_hypotl.c index 44e7235..0f9b814 100644 --- a/sysdeps/ieee754/ldbl-96/e_hypotl.c +++ b/sysdeps/ieee754/ldbl-96/e_hypotl.c @@ -1,142 +1,107 @@ -/* e_hypotl.c -- long double version of e_hypot.c. - */ - -/* - * ==================================================== - * 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_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) - */ +/* Euclidean distance function. Long Double/Binary96 version. + Copyright (C) 2021 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 Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 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 + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <https://www.gnu.org/licenses/>. */ + +/* This implementation is based on 'An Improved Algorithm for hypot(a,b)' by + Carlos F. Borges [1] using the MyHypot3 with the following changes: + + - Handle qNaN and sNaN. + - Tune the 'widely varying operands' to avoid spurious underflow + due the multiplication and fix the return value for upwards + rounding mode. + - Handle required underflow exception for subnormal results. + + [1] https://arxiv.org/pdf/1904.09481.pdf */ #include <math.h> #include <math_private.h> #include <math-underflow.h> #include <libm-alias-finite.h> -long double __ieee754_hypotl(long double x, long double y) +#define SCALE 0x8p-8257L +#define LARGE_VAL 0xb.504f333f9de6484p+8188L +#define TINY_VAL 0x8p-8194L +#define EPS 0x8p-68L + +/* Hypot kernel. The inputs must be adjusted so that ax >= ay >= 0 + and squaring ax, ay and (ax - ay) does not overflow or underflow. */ +static inline long double +kernel (long double ax, long double ay) { - long double a,b,t1,t2,y1,y2,w; - uint32_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(__builtin_expect(ea > 0x5f3f,0)) { /* a>2**8000 */ - if(ea == 0x7fff) { /* Inf or NaN */ - uint32_t exp __attribute__ ((unused)); - uint32_t high,low; - w = a+b; /* for sNaN */ - if (issignaling (a) || issignaling (b)) - return w; - 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(__builtin_expect(eb < 0x20bf, 0)) { /* b < 2**-8000 */ - if(eb == 0) { /* subnormal b or 0 */ - uint32_t exp __attribute__ ((unused)); - uint32_t high,low; - GET_LDOUBLE_WORDS(exp,high,low,b); - if((high|low)==0) return a; - SET_LDOUBLE_WORDS(t1, 0x7ffd, 0x80000000, 0); /* t1=2^16382 */ - b *= t1; - a *= t1; - k -= 16382; - GET_LDOUBLE_EXP (ea, a); - GET_LDOUBLE_EXP (eb, b); - if (eb > ea) - { - t1 = a; - a = b; - b = t1; - j = ea; - ea = eb; - eb = j; - } - } 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) { - uint32_t high; - GET_LDOUBLE_MSW(high,a); - SET_LDOUBLE_WORDS(t1,ea,high,0); - t2 = a-t1; - w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1))); - } else { - uint32_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 = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b))); - } - if(k!=0) { - uint32_t exp; - t1 = 1.0; - GET_LDOUBLE_EXP(exp,t1); - SET_LDOUBLE_EXP(t1,exp+k); - w *= t1; - math_check_force_underflow_nonneg (w); - return w; - } else return w; + long double t1, t2; + long double h = sqrtl (ax * ax + ay * ay); + if (h <= 2.0L * ay) + { + long double delta = h - ay; + t1 = ax * (2.0L * delta - ax); + t2 = (delta - 2.0L * (ax - ay)) * delta; + } + else + { + long double delta = h - ax; + t1 = 2.0L * delta * (ax - 2.0L * ay); + t2 = (4.0L * delta - ay) * ay + delta * delta; + } + + h -= (t1 + t2) / (2.0L * h); + return h; +} + +long double +__ieee754_hypotl (long double x, long double y) +{ + if (!isfinite(x) || !isfinite(y)) + { + if ((isinf (x) || isinf (y)) + && !issignaling (x) && !issignaling (y)) + return INFINITY; + return x + y; + } + + x = fabsl (x); + y = fabsl (y); + + long double ax = x < y ? y : x; + long double ay = x < y ? x : y; + + /* If ax is huge, scale both inputs down. */ + if (__glibc_unlikely (ax > LARGE_VAL)) + { + if (__glibc_unlikely (ay <= ax * EPS)) + return ax + ay; + + return kernel (ax * SCALE, ay * SCALE) / SCALE; + } + + /* If ay is tiny, scale both inputs up. */ + if (__glibc_unlikely (ay < TINY_VAL)) + { + if (__glibc_unlikely (ax >= ay / EPS)) + return ax + ay; + + ax = kernel (ax / SCALE, ay / SCALE) * SCALE; + math_check_force_underflow_nonneg (ax); + return ax; + } + + /* Common case: ax is not huge and ay is not tiny. */ + if (__glibc_unlikely (ay <= ax * EPS)) + return ax + ay; + + return kernel (ax, ay); } libm_alias_finite (__ieee754_hypotl, __hypotl) |