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102 lines
4.0 KiB
C
102 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) 2001-2013 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 <http://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 "endian.h"
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#include "mydefs.h"
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#include <dla.h>
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#include "MathLib.h"
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#include "root.tbl"
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#include <math_private.h>
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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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double __ieee754_sqrt(double x) {
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#include "uroot.h"
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static const double
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rt0 = 9.99999999859990725855365213134618E-01,
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rt1 = 4.99999999495955425917856814202739E-01,
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rt2 = 3.75017500867345182581453026130850E-01,
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rt3 = 3.12523626554518656309172508769531E-01;
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static const double big = 134217728.0;
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double y,t,del,res,res1,hy,z,zz,p,hx,tx,ty,s;
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mynumber a,c={{0,0}};
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int4 k;
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a.x=x;
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k=a.i[HIGH_HALF];
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a.i[HIGH_HALF]=(k&0x001fffff)|0x3fe00000;
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t=inroot[(k&0x001fffff)>>14];
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s=a.x;
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/*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
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if (k>0x000fffff && k<0x7ff00000) {
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fenv_t env;
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libc_feholdexcept (&env);
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double ret;
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y=1.0-t*(t*s);
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t=t*(rt0+y*(rt1+y*(rt2+y*rt3)));
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c.i[HIGH_HALF]=0x20000000+((k&0x7fe00000)>>1);
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y=t*s;
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hy=(y+big)-big;
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del=0.5*t*((s-hy*hy)-(y-hy)*(y+hy));
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res=y+del;
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if (res == (res+1.002*((y-res)+del))) ret = res*c.x;
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else {
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res1=res+1.5*((y-res)+del);
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EMULV(res,res1,z,zz,p,hx,tx,hy,ty); /* (z+zz)=res*res1 */
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ret = ((((z-s)+zz)<0)?max(res,res1):min(res,res1))*c.x;
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}
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math_force_eval (ret);
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libc_fesetenv (&env);
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if (x / ret != ret)
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{
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double force_inexact = 1.0 / 3.0;
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math_force_eval (force_inexact);
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}
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/* Otherwise (x / ret == ret), either the square root was exact or
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the division was inexact. */
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return ret;
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}
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else {
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if ((k & 0x7ff00000) == 0x7ff00000)
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return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
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if (x==0) return x; /* sqrt(+0)=+0, sqrt(-0)=-0 */
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if (k<0) return (x-x)/(x-x); /* sqrt(-ve)=sNaN */
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return tm256.x*__ieee754_sqrt(x*t512.x);
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}
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}
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strong_alias (__ieee754_sqrt, __sqrt_finite)
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