sysdeps/ieee754/dbl-64/e_sqrt.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * Copyright (c) International Business Machines Corp., 2001
   4  *
   5  * This program is free software; you can redistribute it and/or modify
   6  * it under the terms of the GNU Lesser General Public License as published by
   7  * the Free Software Foundation; either version 2 of the License, or
   8  * (at your option) any later version.
   9  *
  10  * This program is distributed in the hope that it will be useful,
  11  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  12  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  13  * GNU General Public License for more details.
  14  *
  15  * You should have received a copy of the GNU Lesser General Public License
  16  * along with this program; if not, write to the Free Software
  17  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
  18  */
  19 /*********************************************************************/
  20 /* MODULE_NAME: uroot.c                                              */
  21 /*                                                                   */
  22 /* FUNCTION:    usqrt                                                */
  23 /*                                                                   */
  24 /* FILES NEEDED: dla.h endian.h mydefs.h uroot.h                     */
  25 /*               uroot.tbl                                           */
  26 /*                                                                   */
  27 /* An ultimate sqrt routine. Given an IEEE double machine number x   */
  28 /* it computes the correctly rounded (to nearest) value of square    */
  29 /* root of x.                                                        */
  30 /* Assumption: Machine arithmetic operations are performed in        */
  31 /* round to nearest mode of IEEE 754 standard.                       */
  32 /*                                                                   */
  33 /*********************************************************************/
  34
  35 #include "endian.h"
  36 #include "mydefs.h"
  37 #include "dla.h"
  38 #include "MathLib.h"
  39 #include "root.tbl"
  40
  41 /*********************************************************************/
  42 /* An ultimate aqrt routine. Given an IEEE double machine number x   */
  43 /* it computes the correctly rounded (to nearest) value of square    */
  44 /* root of x.                                                        */
  45 /*********************************************************************/
  46 double __ieee754_sqrt(double x) {
  47 #include "uroot.h"
  48   static const double
  49     rt0 = 9.99999999859990725855365213134618E-01,
  50     rt1 = 4.99999999495955425917856814202739E-01,
  51     rt2 = 3.75017500867345182581453026130850E-01,
  52     rt3 = 3.12523626554518656309172508769531E-01;
  53   static const double big =  134217728.0, big1 =  134217729.0;
  54   double y,t,del,res,res1,hy,z,zz,p,hx,tx,ty,s;
  55   mynumber a,c={{0,0}};
  56   int4 k;
  57
  58   a.x=x;
  59   k=a.i[HIGH_HALF];
  60   a.i[HIGH_HALF]=(k&0x001fffff)|0x3fe00000;
  61   t=inroot[(k&0x001fffff)>>14];
  62   s=a.x;
  63   /*----------------- 2^-1022  <= | x |< 2^1024  -----------------*/
  64   if (k>0x000fffff && k<0x7ff00000) {
  65     y=1.0-t*(t*s);
  66     t=t*(rt0+y*(rt1+y*(rt2+y*rt3)));
  67     c.i[HIGH_HALF]=0x20000000+((k&0x7fe00000)>>1);
  68     y=t*s;
  69     hy=(y+big)-big;
  70     del=0.5*t*((s-hy*hy)-(y-hy)*(y+hy));
  71     res=y+del;
  72     if (res == (res+1.002*((y-res)+del))) return res*c.x;
  73     else {
  74       res1=res+1.5*((y-res)+del);
  75       EMULV(res,res1,z,zz,p,hx,tx,hy,ty);  /* (z+zz)=res*res1 */
  76       return ((((z-s)+zz)<0)?max(res,res1):min(res,res1))*c.x;
  77     }
  78   }
  79   else {
  80     if (k>0x7ff00000)            /* x -> infinity */
  81        return (big1-big1)/(big-big);
  82       if (k<0x00100000) {        /* x -> -infinity */
  83       if (x==0) return x;
  84       if (k<0) return (big1-big1)/(big-big);
  85       else return tm256.x*__ieee754_sqrt(x*t512.x);
  86     }
  87     else return (a.i[LOW_HALF]==0)?x:(big1-big1)/(big-big);
  88   }
  89 }