sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001, 2004, 2006 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 <math_private.h>
  37
  38 typedef unsigned int int4;
  39 typedef union {int4 i[4]; long double x; double d[2]; } mynumber;
  40
  41 static const  mynumber
  42   t512 = {{0x5ff00000, 0x00000000, 0x00000000, 0x00000000 }},  /* 2^512  */
  43   tm256 = {{0x2ff00000, 0x00000000, 0x00000000, 0x00000000 }};  /* 2^-256 */
  44 static const double
  45 two54 = 1.80143985094819840000e+16, /* 0x4350000000000000 */
  46 twom54 = 5.55111512312578270212e-17; /* 0x3C90000000000000 */
  47
  48 /*********************************************************************/
  49 /* An ultimate sqrt routine. Given an IEEE double machine number x   */
  50 /* it computes the correctly rounded (to nearest) value of square    */
  51 /* root of x.                                                        */
  52 /*********************************************************************/
  53 long double __ieee754_sqrtl(long double x)
  54 {
  55   static const long double big = 134217728.0, big1 = 134217729.0;
  56   long double t,s,i;
  57   mynumber a,c;
  58   int4 k, l, m;
  59   int n;
  60   double d;
  61
  62   a.x=x;
  63   k=a.i[0] & 0x7fffffff;
  64   /*----------------- 2^-1022  <= | x |< 2^1024  -----------------*/
  65   if (k>0x000fffff && k<0x7ff00000) {
  66     if (x < 0) return (big1-big1)/(big-big);
  67     l = (k&0x001fffff)|0x3fe00000;
  68     if (((a.i[2] & 0x7fffffff) | a.i[3]) != 0) {
  69       n = (int) ((l - k) * 2) >> 21;
  70       m = (a.i[2] >> 20) & 0x7ff;
  71       if (m == 0) {
  72         a.d[1] *= two54;
  73         m = ((a.i[2] >> 20) & 0x7ff) - 54;
  74       }
  75       m += n;
  76       if (m > 0)
  77         a.i[2] = (a.i[2] & 0x800fffff) | (m << 20);
  78       else if (m <= -54) {
  79         a.i[2] &= 0x80000000;
  80         a.i[3] = 0;
  81       } else {
  82         m += 54;
  83         a.i[2] = (a.i[2] & 0x800fffff) | (m << 20);
  84         a.d[1] *= twom54;
  85       }
  86     }
  87     a.i[0] = l;
  88     s = a.x;
  89     d = __ieee754_sqrt (a.d[0]);
  90     c.i[0] = 0x20000000+((k&0x7fe00000)>>1);
  91     c.i[1] = 0;
  92     c.i[2] = 0;
  93     c.i[3] = 0;
  94     i = d;
  95     t = 0.5L * (i + s / i);
  96     i = 0.5L * (t + s / t);
  97     return c.x * i;
  98   }
  99   else {
 100     if (k>=0x7ff00000) {
 101       if (a.i[0] == 0xfff00000 && a.i[1] == 0)
 102         return (big1-big1)/(big-big); /* sqrt (-Inf) = NaN.  */
 103       return x; /* sqrt (NaN) = NaN, sqrt (+Inf) = +Inf.  */
 104     }
 105     if (x == 0) return x;
 106     if (x < 0) return (big1-big1)/(big-big);
 107     return tm256.x*__ieee754_sqrtl(x*t512.x);
 108   }
 109 }