sysdeps/ieee754/dbl-64/e_sqrt.c

/*
 * IBM Accurate Mathematical Library
 * written by International Business Machines Corp.
 * Copyright (C) 2001 Free Software Foundation
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation; either version 2.1 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
 */
/*********************************************************************/
/* MODULE_NAME: uroot.c                                              */
/*                                                                   */
/* FUNCTION:    usqrt                                                */
/*                                                                   */
/* FILES NEEDED: dla.h endian.h mydefs.h uroot.h                     */
/*               uroot.tbl                                           */
/*                                                                   */
/* An ultimate sqrt routine. Given an IEEE double machine number x   */
/* it computes the correctly rounded (to nearest) value of square    */
/* root of x.                                                        */
/* Assumption: Machine arithmetic operations are performed in        */
/* round to nearest mode of IEEE 754 standard.                       */
/*                                                                   */
/*********************************************************************/

#include "endian.h"
#include "mydefs.h"
#include "dla.h"
#include "MathLib.h"
#include "root.tbl"
#include "math_private.h"

/*********************************************************************/
/* An ultimate sqrt routine. Given an IEEE double machine number x   */
/* it computes the correctly rounded (to nearest) value of square    */
/* root of x.                                                        */
/*********************************************************************/
double __ieee754_sqrt(double x) {
#include "uroot.h"
  static const double
    rt0 = 9.99999999859990725855365213134618E-01,
    rt1 = 4.99999999495955425917856814202739E-01,
    rt2 = 3.75017500867345182581453026130850E-01,
    rt3 = 3.12523626554518656309172508769531E-01;
  static const double big =  134217728.0;
  double y,t,del,res,res1,hy,z,zz,p,hx,tx,ty,s;
  mynumber a,c={{0,0}};
  int4 k;

  a.x=x;
  k=a.i[HIGH_HALF];
  a.i[HIGH_HALF]=(k&0x001fffff)|0x3fe00000;
  t=inroot[(k&0x001fffff)>>14];
  s=a.x;
  /*----------------- 2^-1022  <= | x |< 2^1024  -----------------*/
  if (k>0x000fffff && k<0x7ff00000) {
    y=1.0-t*(t*s);
    t=t*(rt0+y*(rt1+y*(rt2+y*rt3)));
    c.i[HIGH_HALF]=0x20000000+((k&0x7fe00000)>>1);
    y=t*s;
    hy=(y+big)-big;
    del=0.5*t*((s-hy*hy)-(y-hy)*(y+hy));
    res=y+del;
    if (res == (res+1.002*((y-res)+del))) return res*c.x;
    else {
      res1=res+1.5*((y-res)+del);
      EMULV(res,res1,z,zz,p,hx,tx,hy,ty);  /* (z+zz)=res*res1 */
      return ((((z-s)+zz)<0)?max(res,res1):min(res,res1))*c.x;
    }
  }
  else {
    if ((k & 0x7ff00000) == 0x7ff00000)
      return x*x+x;	/* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
    if (x==0) return x;	/* sqrt(+0)=+0, sqrt(-0)=-0 */
    if (k<0) return (x-x)/(x-x); /* sqrt(-ve)=sNaN */
    return tm256.x*__ieee754_sqrt(x*t512.x);
  }
}