sysdeps/ieee754/dbl-64/e_sqrt.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001-2016 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                             */
  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   static const double
  51     rt0 = 9.99999999859990725855365213134618E-01,
  52     rt1 = 4.99999999495955425917856814202739E-01,
  53     rt2 = 3.75017500867345182581453026130850E-01,
  54     rt3 = 3.12523626554518656309172508769531E-01;
  55   static const double big = 134217728.0;
  56   double y, t, del, res, res1, hy, z, zz, p, hx, tx, ty, s;
  57   mynumber a, c = { { 0, 0 } };
  58   int4 k;
  59
  60   a.x = x;
  61   k = a.i[HIGH_HALF];
  62   a.i[HIGH_HALF] = (k & 0x001fffff) | 0x3fe00000;
  63   t = inroot[(k & 0x001fffff) >> 14];
  64   s = a.x;
  65   /*----------------- 2^-1022  <= | x |< 2^1024  -----------------*/
  66   if (k > 0x000fffff && k < 0x7ff00000)
  67     {
  68       int rm = __fegetround ();
  69       fenv_t env;
  70       libc_feholdexcept_setround (&env, FE_TONEAREST);
  71       double ret;
  72       y = 1.0 - t * (t * s);
  73       t = t * (rt0 + y * (rt1 + y * (rt2 + y * rt3)));
  74       c.i[HIGH_HALF] = 0x20000000 + ((k & 0x7fe00000) >> 1);
  75       y = t * s;
  76       hy = (y + big) - big;
  77       del = 0.5 * t * ((s - hy * hy) - (y - hy) * (y + hy));
  78       res = y + del;
  79       if (res == (res + 1.002 * ((y - res) + del)))
  80         ret = res * c.x;
  81       else
  82         {
  83           res1 = res + 1.5 * ((y - res) + del);
  84           EMULV (res, res1, z, zz, p, hx, tx, hy, ty); /* (z+zz)=res*res1 */
  85           res = ((((z - s) + zz) < 0) ? max (res, res1) :
  86                                         min (res, res1));
  87           ret = res * c.x;
  88         }
  89       math_force_eval (ret);
  90       libc_fesetenv (&env);
  91       double dret = x / ret;
  92       if (dret != ret)
  93         {
  94           double force_inexact = 1.0 / 3.0;
  95           math_force_eval (force_inexact);
  96           /* The square root is inexact, ret is the round-to-nearest
  97              value which may need adjusting for other rounding
  98              modes.  */
  99           switch (rm)
 100             {
 101 #ifdef FE_UPWARD
 102             case FE_UPWARD:
 103               if (dret > ret)
 104                 ret = (res + 0x1p-1022) * c.x;
 105               break;
 106 #endif
 107
 108 #ifdef FE_DOWNWARD
 109             case FE_DOWNWARD:
 110 #endif
 111 #ifdef FE_TOWARDZERO
 112             case FE_TOWARDZERO:
 113 #endif
 114 #if defined FE_DOWNWARD || defined FE_TOWARDZERO
 115               if (dret < ret)
 116                 ret = (res - 0x1p-1022) * c.x;
 117               break;
 118 #endif
 119
 120             default:
 121               break;
 122             }
 123         }
 124       /* Otherwise (x / ret == ret), either the square root was exact or
 125          the division was inexact.  */
 126       return ret;
 127     }
 128   else
 129     {
 130       if ((k & 0x7ff00000) == 0x7ff00000)
 131         return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
 132       if (x == 0)
 133         return x;       /* sqrt(+0)=+0, sqrt(-0)=-0 */
 134       if (k < 0)
 135         return (x - x) / (x - x); /* sqrt(-ve)=sNaN */
 136       return 0x1p-256 * __ieee754_sqrt (x * 0x1p512);
 137     }
 138 }
 139 strong_alias (__ieee754_sqrt, __sqrt_finite)