Back to index

glibc  2.9
e_sqrt.c
Go to the documentation of this file.
00001 /*
00002  * IBM Accurate Mathematical Library
00003  * written by International Business Machines Corp.
00004  * Copyright (C) 2001 Free Software Foundation
00005  *
00006  * This program is free software; you can redistribute it and/or modify
00007  * it under the terms of the GNU Lesser General Public License as published by
00008  * the Free Software Foundation; either version 2.1 of the License, or
00009  * (at your option) any later version.
00010  *
00011  * This program is distributed in the hope that it will be useful,
00012  * but WITHOUT ANY WARRANTY; without even the implied warranty of
00013  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
00014  * GNU Lesser General Public License for more details.
00015  *
00016  * You should have received a copy of the GNU Lesser General Public License
00017  * along with this program; if not, write to the Free Software
00018  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
00019  */
00020 /*********************************************************************/
00021 /* MODULE_NAME: uroot.c                                              */
00022 /*                                                                   */
00023 /* FUNCTION:    usqrt                                                */
00024 /*                                                                   */
00025 /* FILES NEEDED: dla.h endian.h mydefs.h uroot.h                     */
00026 /*               uroot.tbl                                           */
00027 /*                                                                   */
00028 /* An ultimate sqrt routine. Given an IEEE double machine number x   */
00029 /* it computes the correctly rounded (to nearest) value of square    */
00030 /* root of x.                                                        */
00031 /* Assumption: Machine arithmetic operations are performed in        */
00032 /* round to nearest mode of IEEE 754 standard.                       */
00033 /*                                                                   */
00034 /*********************************************************************/
00035 
00036 #include "endian.h"
00037 #include "mydefs.h"
00038 #include "dla.h"
00039 #include "MathLib.h"
00040 #include "root.tbl"
00041 #include "math_private.h"
00042 
00043 /*********************************************************************/
00044 /* An ultimate sqrt routine. Given an IEEE double machine number x   */
00045 /* it computes the correctly rounded (to nearest) value of square    */
00046 /* root of x.                                                        */
00047 /*********************************************************************/
00048 double __ieee754_sqrt(double x) {
00049 #include "uroot.h"
00050   static const double
00051     rt0 = 9.99999999859990725855365213134618E-01,
00052     rt1 = 4.99999999495955425917856814202739E-01,
00053     rt2 = 3.75017500867345182581453026130850E-01,
00054     rt3 = 3.12523626554518656309172508769531E-01;
00055   static const double big =  134217728.0;
00056   double y,t,del,res,res1,hy,z,zz,p,hx,tx,ty,s;
00057   mynumber a,c={{0,0}};
00058   int4 k;
00059 
00060   a.x=x;
00061   k=a.i[HIGH_HALF];
00062   a.i[HIGH_HALF]=(k&0x001fffff)|0x3fe00000;
00063   t=inroot[(k&0x001fffff)>>14];
00064   s=a.x;
00065   /*----------------- 2^-1022  <= | x |< 2^1024  -----------------*/
00066   if (k>0x000fffff && k<0x7ff00000) {
00067     y=1.0-t*(t*s);
00068     t=t*(rt0+y*(rt1+y*(rt2+y*rt3)));
00069     c.i[HIGH_HALF]=0x20000000+((k&0x7fe00000)>>1);
00070     y=t*s;
00071     hy=(y+big)-big;
00072     del=0.5*t*((s-hy*hy)-(y-hy)*(y+hy));
00073     res=y+del;
00074     if (res == (res+1.002*((y-res)+del))) return res*c.x;
00075     else {
00076       res1=res+1.5*((y-res)+del);
00077       EMULV(res,res1,z,zz,p,hx,tx,hy,ty);  /* (z+zz)=res*res1 */
00078       return ((((z-s)+zz)<0)?max(res,res1):min(res,res1))*c.x;
00079     }
00080   }
00081   else {
00082     if ((k & 0x7ff00000) == 0x7ff00000)
00083       return x*x+x;  /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
00084     if (x==0) return x;     /* sqrt(+0)=+0, sqrt(-0)=-0 */
00085     if (k<0) return (x-x)/(x-x); /* sqrt(-ve)=sNaN */
00086     return tm256.x*__ieee754_sqrt(x*t512.x);
00087   }
00088 }