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110 lines
4.1 KiB
C
110 lines
4.1 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, 2004, 2006 Free Software Foundation
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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, write to the Free Software
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
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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 unsigned int int4;
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typedef union {int4 i[4]; long double x; double d[2]; } mynumber;
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static const mynumber
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t512 = {{0x5ff00000, 0x00000000, 0x00000000, 0x00000000 }}, /* 2^512 */
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tm256 = {{0x2ff00000, 0x00000000, 0x00000000, 0x00000000 }}; /* 2^-256 */
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static const double
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two54 = 1.80143985094819840000e+16, /* 0x4350000000000000 */
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twom54 = 5.55111512312578270212e-17; /* 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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int4 k, l, m;
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int n;
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double d;
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a.x=x;
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k=a.i[0] & 0x7fffffff;
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/*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
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if (k>0x000fffff && k<0x7ff00000) {
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if (x < 0) return (big1-big1)/(big-big);
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l = (k&0x001fffff)|0x3fe00000;
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if (((a.i[2] & 0x7fffffff) | a.i[3]) != 0) {
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n = (int) ((l - k) * 2) >> 21;
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m = (a.i[2] >> 20) & 0x7ff;
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if (m == 0) {
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a.d[1] *= two54;
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m = ((a.i[2] >> 20) & 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[2] = (a.i[2] & 0x800fffff) | (m << 20);
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else if (m <= -54) {
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a.i[2] &= 0x80000000;
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a.i[3] = 0;
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} else {
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m += 54;
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a.i[2] = (a.i[2] & 0x800fffff) | (m << 20);
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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] = 0x20000000+((k&0x7fe00000)>>1);
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c.i[1] = 0;
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c.i[2] = 0;
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c.i[3] = 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>=0x7ff00000) {
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if (a.i[0] == 0xfff00000 && a.i[1] == 0)
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return (big1-big1)/(big-big); /* sqrt (-Inf) = NaN. */
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return x; /* sqrt (NaN) = NaN, sqrt (+Inf) = +Inf. */
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}
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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.x*__ieee754_sqrtl(x*t512.x);
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}
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}
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