sysdeps/ieee754/dbl-64/e_sqrt.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001 Free Software Foundation
   5  *
   6  * This program is free software; you can redistribute it and/or modify
   7  * it under the terms of the GNU Lesser General Public License as published by
   8  * the Free Software Foundation; either version 2.1 of the License, or
   9  * (at your option) any later version.
  10  *
  11  * This program is distributed in the hope that it will be useful,
  12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14  * GNU Lesser General Public License for more details.
  15  *
  16  * You should have received a copy of the GNU Lesser General Public License
  17  * along with this program; if not, write to the Free Software
  18  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
  19  */
  20 /*********************************************************************/
  21 /* MODULE_NAME: uroot.c                                              */
  22 /*                                                                   */
  23 /* FUNCTION:    usqrt                                                */
  24 /*                                                                   */
  25 /* FILES NEEDED: dla.h endian.h mydefs.h uroot.h                     */
  26 /*               uroot.tbl                                           */
  27 /*                                                                   */
  28 /* An ultimate sqrt routine. Given an IEEE double machine number x   */
  29 /* it computes the correctly rounded (to nearest) value of square    */
  30 /* root of x.                                                        */
  31 /* Assumption: Machine arithmetic operations are performed in        */
  32 /* round to nearest mode of IEEE 754 standard.                       */
  33 /*                                                                   */
  34 /*********************************************************************/
  35
  36 #include "endian.h"
  37 #include "mydefs.h"
  38 #include "dla.h"
  39 #include "MathLib.h"
  40 #include "root.tbl"
  41 #include "math_private.h"
  42
  43 /*********************************************************************/
  44 /* An ultimate sqrt routine. Given an IEEE double machine number x   */
  45 /* it computes the correctly rounded (to nearest) value of square    */
  46 /* root of x.                                                        */
  47 /*********************************************************************/
  48 double __ieee754_sqrt(double x) {
  49 #include "uroot.h"
  50   static const double
  51     rt0 = 9.99999999859990725855365213134618E-01,
  52     rt1 = 4.99999999495955425917856814202739E-01,
  53     rt2 = 3.75017500867345182581453026130850E-01,
  54     rt3 = 3.12523626554518656309172508769531E-01;
  55   static const double big =  134217728.0;
  56   double y,t,del,res,res1,hy,z,zz,p,hx,tx,ty,s;
  57   mynumber a,c={{0,0}};
  58   int4 k;
  59
  60   a.x=x;
  61   k=a.i[HIGH_HALF];
  62   a.i[HIGH_HALF]=(k&0x001fffff)|0x3fe00000;
  63   t=inroot[(k&0x001fffff)>>14];
  64   s=a.x;
  65   /*----------------- 2^-1022  <= | x |< 2^1024  -----------------*/
  66   if (k>0x000fffff && k<0x7ff00000) {
  67     y=1.0-t*(t*s);
  68     t=t*(rt0+y*(rt1+y*(rt2+y*rt3)));
  69     c.i[HIGH_HALF]=0x20000000+((k&0x7fe00000)>>1);
  70     y=t*s;
  71     hy=(y+big)-big;
  72     del=0.5*t*((s-hy*hy)-(y-hy)*(y+hy));
  73     res=y+del;
  74     if (res == (res+1.002*((y-res)+del))) return res*c.x;
  75     else {
  76       res1=res+1.5*((y-res)+del);
  77       EMULV(res,res1,z,zz,p,hx,tx,hy,ty);  /* (z+zz)=res*res1 */
  78       return ((((z-s)+zz)<0)?max(res,res1):min(res,res1))*c.x;
  79     }
  80   }
  81   else {
  82     if ((k & 0x7ff00000) == 0x7ff00000)
  83       return x*x+x;     /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
  84     if (x==0) return x; /* sqrt(+0)=+0, sqrt(-0)=-0 */
  85     if (k<0) return (x-x)/(x-x); /* sqrt(-ve)=sNaN */
  86     return tm256.x*__ieee754_sqrt(x*t512.x);
  87   }
  88 }