diff options
Diffstat (limited to 'sysdeps')
| -rw-r--r-- | sysdeps/ieee754/ldbl-128/e_hypotl.c | 226 |
1 files changed, 96 insertions, 130 deletions
diff --git a/sysdeps/ieee754/ldbl-128/e_hypotl.c b/sysdeps/ieee754/ldbl-128/e_hypotl.c index cd4fdbc4a6..43affd9167 100644 --- a/sysdeps/ieee754/ldbl-128/e_hypotl.c +++ b/sysdeps/ieee754/ldbl-128/e_hypotl.c @@ -1,141 +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 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 64 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 64 bits cleared, t2 = 2x-t1, - * y1= y with lower 64 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) - */ +/* Euclidean distance function. Long Double/Binary128 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> +#define SCALE L(0x1p-8303) +#define LARGE_VAL L(0x1.6a09e667f3bcc908b2fb1366ea95p+8191) +#define TINY_VAL L(0x1p-8191) +#define EPS L(0x1p-114) + +/* 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 _Float128 +kernel (_Float128 ax, _Float128 ay) +{ + _Float128 t1, t2; + _Float128 h = sqrtl (ax * ax + ay * ay); + if (h <= L(2.0) * ay) + { + _Float128 delta = h - ay; + t1 = ax * (L(2.0) * delta - ax); + t2 = (delta - L(2.0) * (ax - ay)) * delta; + } + else + { + _Float128 delta = h - ax; + t1 = L(2.0) * delta * (ax - L(2.0) * ay); + t2 = (L(4.0) * delta - ay) * ay + delta * delta; + } + + h -= (t1 + t2) / (L(2.0) * h); + return h; +} + _Float128 __ieee754_hypotl(_Float128 x, _Float128 y) { - _Float128 a,b,t1,t2,y1,y2,w; - 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;} - SET_LDOUBLE_MSW64(a,ha); /* a <- |a| */ - SET_LDOUBLE_MSW64(b,hb); /* b <- |b| */ - if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */ - k=0; - if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */ - if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */ - uint64_t low; - w = a+b; /* for sNaN */ - if (issignaling (a) || issignaling (b)) - return w; - GET_LDOUBLE_LSW64(low,a); - if(((ha&0xffffffffffffLL)|low)==0) w = a; - GET_LDOUBLE_LSW64(low,b); - if(((hb^0x7fff000000000000LL)|low)==0) w = b; - return w; - } - /* scale a and b by 2**-9600 */ - ha -= 0x2580000000000000LL; - hb -= 0x2580000000000000LL; k += 9600; - SET_LDOUBLE_MSW64(a,ha); - SET_LDOUBLE_MSW64(b,hb); - } - if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */ - if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */ - uint64_t low; - GET_LDOUBLE_LSW64(low,b); - if((hb|low)==0) return a; - t1=0; - SET_LDOUBLE_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */ - b *= t1; - a *= t1; - k -= 16382; - GET_LDOUBLE_MSW64 (ha, a); - GET_LDOUBLE_MSW64 (hb, b); - if (hb > ha) - { - t1 = a; - a = b; - b = t1; - j = ha; - ha = hb; - hb = j; - } - } else { /* scale a and b by 2^9600 */ - ha += 0x2580000000000000LL; /* a *= 2^9600 */ - hb += 0x2580000000000000LL; /* b *= 2^9600 */ - k -= 9600; - SET_LDOUBLE_MSW64(a,ha); - SET_LDOUBLE_MSW64(b,hb); - } - } - /* medium size a and b */ - w = a-b; - if (w>b) { - t1 = 0; - SET_LDOUBLE_MSW64(t1,ha); - t2 = a-t1; - w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1))); - } else { - a = a+a; - y1 = 0; - SET_LDOUBLE_MSW64(y1,hb); - y2 = b - y1; - t1 = 0; - SET_LDOUBLE_MSW64(t1,ha+0x0001000000000000LL); - t2 = a - t1; - w = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b))); - } - if(k!=0) { - uint64_t high; - t1 = 1; - GET_LDOUBLE_MSW64(high,t1); - SET_LDOUBLE_MSW64(t1,high+(k<<48)); - w *= t1; - math_check_force_underflow_nonneg (w); - return w; - } else return w; + 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); + + _Float128 ax = x < y ? y : x; + _Float128 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) |