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

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001-2013 Free Software Foundation, Inc.
   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 <math_private.h>
  36
  37 typedef unsigned int int4;
  38 typedef union {int4 i[4]; long double x; double d[2]; } mynumber;
  39
  40 static const  mynumber
  41   t512 = {{0x5ff00000, 0x00000000, 0x00000000, 0x00000000 }},  /* 2^512  */
  42   tm256 = {{0x2ff00000, 0x00000000, 0x00000000, 0x00000000 }};  /* 2^-256 */
  43 static const double
  44 two54 = 1.80143985094819840000e+16, /* 0x4350000000000000 */
  45 twom54 = 5.55111512312578270212e-17; /* 0x3C90000000000000 */
  46
  47 /*********************************************************************/
  48 /* An ultimate sqrt routine. Given an IEEE double machine number x   */
  49 /* it computes the correctly rounded (to nearest) value of square    */
  50 /* root of x.                                                        */
  51 /*********************************************************************/
  52 long double __ieee754_sqrtl(long double x)
  53 {
  54   static const long double big = 134217728.0, big1 = 134217729.0;
  55   long double t,s,i;
  56   mynumber a,c;
  57   int4 k, l, m;
  58   int n;
  59   double d;
  60
  61   a.x=x;
  62   k=a.i[0] & 0x7fffffff;
  63   /*----------------- 2^-1022  <= | x |< 2^1024  -----------------*/
  64   if (k>0x000fffff && k<0x7ff00000) {
  65     if (x < 0) return (big1-big1)/(big-big);
  66     l = (k&0x001fffff)|0x3fe00000;
  67     if (((a.i[2] & 0x7fffffff) | a.i[3]) != 0) {
  68       n = (int) ((l - k) * 2) >> 21;
  69       m = (a.i[2] >> 20) & 0x7ff;
  70       if (m == 0) {
  71         a.d[1] *= two54;
  72         m = ((a.i[2] >> 20) & 0x7ff) - 54;
  73       }
  74       m += n;
  75       if ((int) m > 0)
  76         a.i[2] = (a.i[2] & 0x800fffff) | (m << 20);
  77       else if ((int) m <= -54) {
  78         a.i[2] &= 0x80000000;
  79         a.i[3] = 0;
  80       } else {
  81         m += 54;
  82         a.i[2] = (a.i[2] & 0x800fffff) | (m << 20);
  83         a.d[1] *= twom54;
  84       }
  85     }
  86     a.i[0] = l;
  87     s = a.x;
  88     d = __ieee754_sqrt (a.d[0]);
  89     c.i[0] = 0x20000000+((k&0x7fe00000)>>1);
  90     c.i[1] = 0;
  91     c.i[2] = 0;
  92     c.i[3] = 0;
  93     i = d;
  94     t = 0.5L * (i + s / i);
  95     i = 0.5L * (t + s / t);
  96     return c.x * i;
  97   }
  98   else {
  99     if (k>=0x7ff00000) {
 100       if (a.i[0] == 0xfff00000 && a.i[1] == 0)
 101         return (big1-big1)/(big-big); /* sqrt (-Inf) = NaN.  */
 102       return x; /* sqrt (NaN) = NaN, sqrt (+Inf) = +Inf.  */
 103     }
 104     if (x == 0) return x;
 105     if (x < 0) return (big1-big1)/(big-big);
 106     return tm256.x*__ieee754_sqrtl(x*t512.x);
 107   }
 108 }
 109 strong_alias (__ieee754_sqrtl, __sqrtl_finite)