sysdeps/ieee754/dbl-64/e_sqrt.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001, 2011 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, see <http://www.gnu.org/licenses/>.
  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 #include <math_private.h>
  41
  42 /*********************************************************************/
  43 /* An ultimate sqrt routine. Given an IEEE double machine number x   */
  44 /* it computes the correctly rounded (to nearest) value of square    */
  45 /* root of x.                                                        */
  46 /*********************************************************************/
  47 double __ieee754_sqrt(double x) {
  48 #include "uroot.h"
  49   static const double
  50     rt0 = 9.99999999859990725855365213134618E-01,
  51     rt1 = 4.99999999495955425917856814202739E-01,
  52     rt2 = 3.75017500867345182581453026130850E-01,
  53     rt3 = 3.12523626554518656309172508769531E-01;
  54   static const double big =  134217728.0;
  55   double y,t,del,res,res1,hy,z,zz,p,hx,tx,ty,s;
  56   mynumber a,c={{0,0}};
  57   int4 k;
  58
  59   a.x=x;
  60   k=a.i[HIGH_HALF];
  61   a.i[HIGH_HALF]=(k&0x001fffff)|0x3fe00000;
  62   t=inroot[(k&0x001fffff)>>14];
  63   s=a.x;
  64   /*----------------- 2^-1022  <= | x |< 2^1024  -----------------*/
  65   if (k>0x000fffff && k<0x7ff00000) {
  66     y=1.0-t*(t*s);
  67     t=t*(rt0+y*(rt1+y*(rt2+y*rt3)));
  68     c.i[HIGH_HALF]=0x20000000+((k&0x7fe00000)>>1);
  69     y=t*s;
  70     hy=(y+big)-big;
  71     del=0.5*t*((s-hy*hy)-(y-hy)*(y+hy));
  72     res=y+del;
  73     if (res == (res+1.002*((y-res)+del))) return res*c.x;
  74     else {
  75       res1=res+1.5*((y-res)+del);
  76       EMULV(res,res1,z,zz,p,hx,tx,hy,ty);  /* (z+zz)=res*res1 */
  77       return ((((z-s)+zz)<0)?max(res,res1):min(res,res1))*c.x;
  78     }
  79   }
  80   else {
  81     if ((k & 0x7ff00000) == 0x7ff00000)
  82       return x*x+x;     /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
  83     if (x==0) return x; /* sqrt(+0)=+0, sqrt(-0)=-0 */
  84     if (k<0) return (x-x)/(x-x); /* sqrt(-ve)=sNaN */
  85     return tm256.x*__ieee754_sqrt(x*t512.x);
  86   }
  87 }
  88 strong_alias (__ieee754_sqrt, __sqrt_finite)