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/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2020 Free Software Foundation, Inc.
*
* This program 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.
*
* This program 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 this program; if not, see <https://www.gnu.org/licenses/>.
*/
/*********************************************************************/
/* MODULE_NAME: uroot.c */
/* */
/* FUNCTION: usqrt */
/* */
/* FILES NEEDED: dla.h endian.h mydefs.h uroot.h */
/* uroot.tbl */
/* */
/* An ultimate sqrt routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of square */
/* root of x. */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
/*********************************************************************/
#include <math_private.h>
#include <libm-alias-finite.h>
typedef union {int64_t i[2]; long double x; double d[2]; } mynumber;
static const double
t512 = 0x1p512,
tm256 = 0x1p-256,
two54 = 0x1p54, /* 0x4350000000000000 */
twom54 = 0x1p-54; /* 0x3C90000000000000 */
/*********************************************************************/
/* An ultimate sqrt routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of square */
/* root of x. */
/*********************************************************************/
long double __ieee754_sqrtl(long double x)
{
static const long double big = 134217728.0, big1 = 134217729.0;
long double t,s,i;
mynumber a,c;
uint64_t k, l;
int64_t m, n;
double d;
a.x=x;
k=a.i[0] & INT64_C(0x7fffffffffffffff);
/*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
if (k>INT64_C(0x000fffff00000000) && k<INT64_C(0x7ff0000000000000)) {
if (x < 0) return (big1-big1)/(big-big);
l = (k&INT64_C(0x001fffffffffffff))|INT64_C(0x3fe0000000000000);
if ((a.i[1] & INT64_C(0x7fffffffffffffff)) != 0) {
n = (int64_t) ((l - k) * 2) >> 53;
m = (a.i[1] >> 52) & 0x7ff;
if (m == 0) {
a.d[1] *= two54;
m = ((a.i[1] >> 52) & 0x7ff) - 54;
}
m += n;
if (m > 0)
a.i[1] = (a.i[1] & INT64_C(0x800fffffffffffff)) | (m << 52);
else if (m <= -54) {
a.i[1] &= INT64_C(0x8000000000000000);
} else {
m += 54;
a.i[1] = (a.i[1] & INT64_C(0x800fffffffffffff)) | (m << 52);
a.d[1] *= twom54;
}
}
a.i[0] = l;
s = a.x;
d = __ieee754_sqrt (a.d[0]);
c.i[0] = INT64_C(0x2000000000000000)+((k&INT64_C(0x7fe0000000000000))>>1);
c.i[1] = 0;
i = d;
t = 0.5L * (i + s / i);
i = 0.5L * (t + s / t);
return c.x * i;
}
else {
if (k>=INT64_C(0x7ff0000000000000))
/* sqrt (-Inf) = NaN, sqrt (NaN) = NaN, sqrt (+Inf) = +Inf. */
return x * x + x;
if (x == 0) return x;
if (x < 0) return (big1-big1)/(big-big);
return tm256*__ieee754_sqrtl(x*t512);
}
}
libm_alias_finite (__ieee754_sqrtl, __sqrtl)
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