sysdeps/ieee754/dbl-64/halfulp.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001, 2005, 2011 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, see <http://www.gnu.org/licenses/>.
  18  */
  19 /************************************************************************/
  20 /*                                                                      */
  21 /* MODULE_NAME:halfulp.c                                                */
  22 /*                                                                      */
  23 /*  FUNCTIONS:halfulp                                                   */
  24 /*  FILES NEEDED: mydefs.h dla.h endian.h                               */
  25 /*                uroot.c                                               */
  26 /*                                                                      */
  27 /*Routine halfulp(double x, double y) computes x^y where result does    */
  28 /*not need rounding. If the result is closer to 0 than can be           */
  29 /*represented it returns 0.                                             */
  30 /*     In the following cases the function does not compute anything    */
  31 /*and returns a negative number:                                        */
  32 /*1. if the result needs rounding,                                      */
  33 /*2. if y is outside the interval [0,  2^20-1],                         */
  34 /*3. if x can be represented by  x=2**n for some integer n.             */
  35 /************************************************************************/
  36
  37 #include "endian.h"
  38 #include "mydefs.h"
  39 #include <dla.h>
  40 #include "math_private.h"
  41
  42 #ifndef SECTION
  43 # define SECTION
  44 #endif
  45
  46 static const int4 tab54[32] = {
  47    262143, 11585, 1782, 511, 210, 107, 63, 42,
  48        30,    22,   17,  14,  12,  10,  9,  7,
  49         7,     6,    5,   5,   5,   4,  4,  4,
  50         3,     3,    3,   3,   3,   3,  3,  3 };
  51
  52
  53 double
  54 SECTION
  55 __halfulp(double x, double y)
  56 {
  57   mynumber v;
  58   double z,u,uu;
  59 #ifndef DLA_FMS
  60   double j1,j2,j3,j4,j5;
  61 #endif
  62   int4 k,l,m,n;
  63   if (y <= 0) {               /*if power is negative or zero */
  64     v.x = y;
  65     if (v.i[LOW_HALF] != 0) return -10.0;
  66     v.x = x;
  67     if (v.i[LOW_HALF] != 0) return -10.0;
  68     if ((v.i[HIGH_HALF]&0x000fffff) != 0) return -10;   /* if x =2 ^ n */
  69     k = ((v.i[HIGH_HALF]&0x7fffffff)>>20)-1023;         /* find this n */
  70     z = (double) k;
  71     return (z*y == -1075.0)?0: -10.0;
  72   }
  73                               /* if y > 0  */
  74   v.x = y;
  75     if (v.i[LOW_HALF] != 0) return -10.0;
  76
  77   v.x=x;
  78                               /*  case where x = 2**n for some integer n */
  79   if (((v.i[HIGH_HALF]&0x000fffff)|v.i[LOW_HALF]) == 0) {
  80     k=(v.i[HIGH_HALF]>>20)-1023;
  81     return (((double) k)*y == -1075.0)?0:-10.0;
  82   }
  83
  84   v.x = y;
  85   k = v.i[HIGH_HALF];
  86   m = k<<12;
  87   l = 0;
  88   while (m)
  89     {m = m<<1; l++; }
  90   n = (k&0x000fffff)|0x00100000;
  91   n = n>>(20-l);                       /*   n is the odd integer of y    */
  92   k = ((k>>20) -1023)-l;               /*   y = n*2**k                   */
  93   if (k>5) return -10.0;
  94   if (k>0) for (;k>0;k--) n *= 2;
  95   if (n > 34) return -10.0;
  96   k = -k;
  97   if (k>5) return -10.0;
  98
  99                             /*   now treat x        */
 100   while (k>0) {
 101     z = __ieee754_sqrt(x);
 102     EMULV(z,z,u,uu,j1,j2,j3,j4,j5);
 103     if (((u-x)+uu) != 0) break;
 104     x = z;
 105     k--;
 106  }
 107   if (k) return -10.0;
 108
 109   /* it is impossible that n == 2,  so the mantissa of x must be short  */
 110
 111   v.x = x;
 112   if (v.i[LOW_HALF]) return -10.0;
 113   k = v.i[HIGH_HALF];
 114   m = k<<12;
 115   l = 0;
 116   while (m) {m = m<<1; l++; }
 117   m = (k&0x000fffff)|0x00100000;
 118   m = m>>(20-l);                       /*   m is the odd integer of x    */
 119
 120             /*   now check whether the length of m**n is at most 54 bits */
 121
 122   if  (m > tab54[n-3]) return -10.0;
 123
 124              /* yes, it is - now compute x**n by simple multiplications  */
 125
 126   u = x;
 127   for (k=1;k<n;k++) u = u*x;
 128   return u;
 129 }