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103 lines
4.0 KiB
C
103 lines
4.0 KiB
C
/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001-2020 Free Software Foundation, Inc.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, see <https://www.gnu.org/licenses/>.
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*/
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/*********************************************************************/
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/* MODULE_NAME: uroot.c */
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/* */
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/* FUNCTION: usqrt */
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/* */
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/* FILES NEEDED: dla.h endian.h mydefs.h uroot.h */
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/* uroot.tbl */
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/* */
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/* An ultimate sqrt routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of square */
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/* root of x. */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/* */
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/*********************************************************************/
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#include <math_private.h>
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typedef union {int64_t i[2]; long double x; double d[2]; } mynumber;
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static const double
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t512 = 0x1p512,
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tm256 = 0x1p-256,
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two54 = 0x1p54, /* 0x4350000000000000 */
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twom54 = 0x1p-54; /* 0x3C90000000000000 */
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/*********************************************************************/
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/* An ultimate sqrt routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of square */
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/* root of x. */
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/*********************************************************************/
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long double __ieee754_sqrtl(long double x)
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{
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static const long double big = 134217728.0, big1 = 134217729.0;
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long double t,s,i;
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mynumber a,c;
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uint64_t k, l;
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int64_t m, n;
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double d;
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a.x=x;
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k=a.i[0] & INT64_C(0x7fffffffffffffff);
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/*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
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if (k>INT64_C(0x000fffff00000000) && k<INT64_C(0x7ff0000000000000)) {
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if (x < 0) return (big1-big1)/(big-big);
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l = (k&INT64_C(0x001fffffffffffff))|INT64_C(0x3fe0000000000000);
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if ((a.i[1] & INT64_C(0x7fffffffffffffff)) != 0) {
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n = (int64_t) ((l - k) * 2) >> 53;
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m = (a.i[1] >> 52) & 0x7ff;
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if (m == 0) {
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a.d[1] *= two54;
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m = ((a.i[1] >> 52) & 0x7ff) - 54;
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}
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m += n;
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if (m > 0)
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a.i[1] = (a.i[1] & INT64_C(0x800fffffffffffff)) | (m << 52);
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else if (m <= -54) {
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a.i[1] &= INT64_C(0x8000000000000000);
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} else {
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m += 54;
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a.i[1] = (a.i[1] & INT64_C(0x800fffffffffffff)) | (m << 52);
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a.d[1] *= twom54;
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}
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}
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a.i[0] = l;
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s = a.x;
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d = __ieee754_sqrt (a.d[0]);
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c.i[0] = INT64_C(0x2000000000000000)+((k&INT64_C(0x7fe0000000000000))>>1);
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c.i[1] = 0;
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i = d;
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t = 0.5L * (i + s / i);
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i = 0.5L * (t + s / t);
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return c.x * i;
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}
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else {
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if (k>=INT64_C(0x7ff0000000000000))
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/* sqrt (-Inf) = NaN, sqrt (NaN) = NaN, sqrt (+Inf) = +Inf. */
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return x * x + x;
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if (x == 0) return x;
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if (x < 0) return (big1-big1)/(big-big);
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return tm256*__ieee754_sqrtl(x*t512);
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}
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}
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strong_alias (__ieee754_sqrtl, __sqrtl_finite)
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