mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-26 23:10:06 +00:00
112 lines
3.9 KiB
C
112 lines
3.9 KiB
C
/*
|
|
* IBM Accurate Mathematical Library
|
|
* written by International Business Machines Corp.
|
|
* Copyright (C) 2001-2015 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 <http://www.gnu.org/licenses/>.
|
|
*/
|
|
/****************************************************************************/
|
|
/* MODULE_NAME:mpsqrt.c */
|
|
/* */
|
|
/* FUNCTION:mpsqrt */
|
|
/* fastiroot */
|
|
/* */
|
|
/* FILES NEEDED:endian.h mpa.h mpsqrt.h */
|
|
/* mpa.c */
|
|
/* Multi-Precision square root function subroutine for precision p >= 4. */
|
|
/* The relative error is bounded by 3.501*r**(1-p), where r=2**24. */
|
|
/* */
|
|
/****************************************************************************/
|
|
#include "endian.h"
|
|
#include "mpa.h"
|
|
|
|
#ifndef SECTION
|
|
# define SECTION
|
|
#endif
|
|
|
|
#include "mpsqrt.h"
|
|
|
|
/****************************************************************************/
|
|
/* Multi-Precision square root function subroutine for precision p >= 4. */
|
|
/* The relative error is bounded by 3.501*r**(1-p), where r=2**24. */
|
|
/* Routine receives two pointers to Multi Precision numbers: */
|
|
/* x (left argument) and y (next argument). Routine also receives precision */
|
|
/* p as integer. Routine computes sqrt(*x) and stores result in *y */
|
|
/****************************************************************************/
|
|
|
|
static double fastiroot (double);
|
|
|
|
void
|
|
SECTION
|
|
__mpsqrt (mp_no *x, mp_no *y, int p)
|
|
{
|
|
int i, m, ey;
|
|
double dx, dy;
|
|
static const mp_no mphalf = {0, {1.0, HALFRAD}};
|
|
static const mp_no mp3halfs = {1, {1.0, 1.0, HALFRAD}};
|
|
mp_no mpxn, mpz, mpu, mpt1, mpt2;
|
|
|
|
ey = EX / 2;
|
|
__cpy (x, &mpxn, p);
|
|
mpxn.e -= (ey + ey);
|
|
__mp_dbl (&mpxn, &dx, p);
|
|
dy = fastiroot (dx);
|
|
__dbl_mp (dy, &mpu, p);
|
|
__mul (&mpxn, &mphalf, &mpz, p);
|
|
|
|
m = __mpsqrt_mp[p];
|
|
for (i = 0; i < m; i++)
|
|
{
|
|
__sqr (&mpu, &mpt1, p);
|
|
__mul (&mpt1, &mpz, &mpt2, p);
|
|
__sub (&mp3halfs, &mpt2, &mpt1, p);
|
|
__mul (&mpu, &mpt1, &mpt2, p);
|
|
__cpy (&mpt2, &mpu, p);
|
|
}
|
|
__mul (&mpxn, &mpu, y, p);
|
|
EY += ey;
|
|
}
|
|
|
|
/***********************************************************/
|
|
/* Compute a double precision approximation for 1/sqrt(x) */
|
|
/* with the relative error bounded by 2**-51. */
|
|
/***********************************************************/
|
|
static double
|
|
SECTION
|
|
fastiroot (double x)
|
|
{
|
|
union
|
|
{
|
|
int i[2];
|
|
double d;
|
|
} p, q;
|
|
double y, z, t;
|
|
int n;
|
|
static const double c0 = 0.99674, c1 = -0.53380;
|
|
static const double c2 = 0.45472, c3 = -0.21553;
|
|
|
|
p.d = x;
|
|
p.i[HIGH_HALF] = (p.i[HIGH_HALF] & 0x3FFFFFFF) | 0x3FE00000;
|
|
q.d = x;
|
|
y = p.d;
|
|
z = y - 1.0;
|
|
n = (q.i[HIGH_HALF] - p.i[HIGH_HALF]) >> 1;
|
|
z = ((c3 * z + c2) * z + c1) * z + c0; /* 2**-7 */
|
|
z = z * (1.5 - 0.5 * y * z * z); /* 2**-14 */
|
|
p.d = z * (1.5 - 0.5 * y * z * z); /* 2**-28 */
|
|
p.i[HIGH_HALF] -= n;
|
|
t = x * p.d;
|
|
return p.d * (1.5 - 0.5 * p.d * t);
|
|
}
|