mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-27 15:30:07 +00:00
89 lines
3.7 KiB
C
89 lines
3.7 KiB
C
/*
|
|
* IBM Accurate Mathematical Library
|
|
* written by International Business Machines Corp.
|
|
* Copyright (C) 2001-2013 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: 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 "endian.h"
|
|
#include "mydefs.h"
|
|
#include <dla.h>
|
|
#include "MathLib.h"
|
|
#include "root.tbl"
|
|
#include <math_private.h>
|
|
|
|
/*********************************************************************/
|
|
/* An ultimate sqrt routine. Given an IEEE double machine number x */
|
|
/* it computes the correctly rounded (to nearest) value of square */
|
|
/* root of x. */
|
|
/*********************************************************************/
|
|
double __ieee754_sqrt(double x) {
|
|
#include "uroot.h"
|
|
static const double
|
|
rt0 = 9.99999999859990725855365213134618E-01,
|
|
rt1 = 4.99999999495955425917856814202739E-01,
|
|
rt2 = 3.75017500867345182581453026130850E-01,
|
|
rt3 = 3.12523626554518656309172508769531E-01;
|
|
static const double big = 134217728.0;
|
|
double y,t,del,res,res1,hy,z,zz,p,hx,tx,ty,s;
|
|
mynumber a,c={{0,0}};
|
|
int4 k;
|
|
|
|
a.x=x;
|
|
k=a.i[HIGH_HALF];
|
|
a.i[HIGH_HALF]=(k&0x001fffff)|0x3fe00000;
|
|
t=inroot[(k&0x001fffff)>>14];
|
|
s=a.x;
|
|
/*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
|
|
if (k>0x000fffff && k<0x7ff00000) {
|
|
y=1.0-t*(t*s);
|
|
t=t*(rt0+y*(rt1+y*(rt2+y*rt3)));
|
|
c.i[HIGH_HALF]=0x20000000+((k&0x7fe00000)>>1);
|
|
y=t*s;
|
|
hy=(y+big)-big;
|
|
del=0.5*t*((s-hy*hy)-(y-hy)*(y+hy));
|
|
res=y+del;
|
|
if (res == (res+1.002*((y-res)+del))) return res*c.x;
|
|
else {
|
|
res1=res+1.5*((y-res)+del);
|
|
EMULV(res,res1,z,zz,p,hx,tx,hy,ty); /* (z+zz)=res*res1 */
|
|
return ((((z-s)+zz)<0)?max(res,res1):min(res,res1))*c.x;
|
|
}
|
|
}
|
|
else {
|
|
if ((k & 0x7ff00000) == 0x7ff00000)
|
|
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
|
|
if (x==0) return x; /* sqrt(+0)=+0, sqrt(-0)=-0 */
|
|
if (k<0) return (x-x)/(x-x); /* sqrt(-ve)=sNaN */
|
|
return tm256.x*__ieee754_sqrt(x*t512.x);
|
|
}
|
|
}
|
|
strong_alias (__ieee754_sqrt, __sqrt_finite)
|