sysdeps/ieee754/dbl-64/e_sqrt.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001-2014 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 "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
  48 __ieee754_sqrt (double x)
  49 {
  50 #include "uroot.h"
  51   static const double
  52     rt0 = 9.99999999859990725855365213134618E-01,
  53     rt1 = 4.99999999495955425917856814202739E-01,
  54     rt2 = 3.75017500867345182581453026130850E-01,
  55     rt3 = 3.12523626554518656309172508769531E-01;
  56   static const double big = 134217728.0;
  57   double y, t, del, res, res1, hy, z, zz, p, hx, tx, ty, s;
  58   mynumber a, c = { { 0, 0 } };
  59   int4 k;
  60
  61   a.x = x;
  62   k = a.i[HIGH_HALF];
  63   a.i[HIGH_HALF] = (k & 0x001fffff) | 0x3fe00000;
  64   t = inroot[(k & 0x001fffff) >> 14];
  65   s = a.x;
  66   /*----------------- 2^-1022  <= | x |< 2^1024  -----------------*/
  67   if (k > 0x000fffff && k < 0x7ff00000)
  68     {
  69       int rm = fegetround ();
  70       fenv_t env;
  71       libc_feholdexcept_setround (&env, FE_TONEAREST);
  72       double ret;
  73       y = 1.0 - t * (t * s);
  74       t = t * (rt0 + y * (rt1 + y * (rt2 + y * rt3)));
  75       c.i[HIGH_HALF] = 0x20000000 + ((k & 0x7fe00000) >> 1);
  76       y = t * s;
  77       hy = (y + big) - big;
  78       del = 0.5 * t * ((s - hy * hy) - (y - hy) * (y + hy));
  79       res = y + del;
  80       if (res == (res + 1.002 * ((y - res) + del)))
  81         ret = res * c.x;
  82       else
  83         {
  84           res1 = res + 1.5 * ((y - res) + del);
  85           EMULV (res, res1, z, zz, p, hx, tx, hy, ty); /* (z+zz)=res*res1 */
  86           res = ((((z - s) + zz) < 0) ? max (res, res1) :
  87                                         min (res, res1));
  88           ret = res * c.x;
  89         }
  90       math_force_eval (ret);
  91       libc_fesetenv (&env);
  92       double dret = x / ret;
  93       if (dret != ret)
  94         {
  95           double force_inexact = 1.0 / 3.0;
  96           math_force_eval (force_inexact);
  97           /* The square root is inexact, ret is the round-to-nearest
  98              value which may need adjusting for other rounding
  99              modes.  */
 100           switch (rm)
 101             {
 102 #ifdef FE_UPWARD
 103             case FE_UPWARD:
 104               if (dret > ret)
 105                 ret = (res + 0x1p-1022) * c.x;
 106               break;
 107 #endif
 108
 109 #ifdef FE_DOWNWARD
 110             case FE_DOWNWARD:
 111 #endif
 112 #ifdef FE_TOWARDZERO
 113             case FE_TOWARDZERO:
 114 #endif
 115 #if defined FE_DOWNWARD || defined FE_TOWARDZERO
 116               if (dret < ret)
 117                 ret = (res - 0x1p-1022) * c.x;
 118               break;
 119 #endif
 120
 121             default:
 122               break;
 123             }
 124         }
 125       /* Otherwise (x / ret == ret), either the square root was exact or
 126          the division was inexact.  */
 127       return ret;
 128     }
 129   else
 130     {
 131       if ((k & 0x7ff00000) == 0x7ff00000)
 132         return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
 133       if (x == 0)
 134         return x;       /* sqrt(+0)=+0, sqrt(-0)=-0 */
 135       if (k < 0)
 136         return (x - x) / (x - x); /* sqrt(-ve)=sNaN */
 137       return tm256.x * __ieee754_sqrt (x * t512.x);
 138     }
 139 }
 140 strong_alias (__ieee754_sqrt, __sqrt_finite)