math/atest-exp.c

   1 /* Copyright (C) 1997, 1998, 2000, 2006 Free Software Foundation, Inc.
   2    This file is part of the GNU C Library.
   3    Contributed by Geoffrey Keating <Geoff.Keating@anu.edu.au>, 1997.
   4
   5    The GNU C Library is free software; you can redistribute it and/or
   6    modify it under the terms of the GNU Lesser General Public
   7    License as published by the Free Software Foundation; either
   8    version 2.1 of the License, or (at your option) any later version.
   9
  10    The GNU C Library is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13    Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public
  16    License along with the GNU C Library; if not, write to the Free
  17    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  18    02111-1307 USA.  */
  19
  20 #include <stdio.h>
  21 #include <math.h>
  22 #include <gmp.h>
  23 #include <string.h>
  24 #include <limits.h>
  25 #include <assert.h>
  26
  27 #define PRINT_ERRORS 0
  28
  29 #define TOL 80
  30 #define N2 17
  31 #define FRAC (32*4)
  32
  33 #define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
  34 #define SZ (FRAC / mpbpl + 1)
  35 typedef mp_limb_t mp1[SZ], mp2[SZ * 2];
  36
  37 /* This string has 101 hex digits.  */
  38 static const char exp1[102] = "2" /* point */
  39 "b7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a7"
  40 "84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07";
  41 static const char hexdig[] = "0123456789abcdef";
  42
  43 static void
  44 print_mpn_hex (const mp_limb_t *x, unsigned size)
  45 {
  46    char value[size + 1];
  47    unsigned i;
  48    const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;
  49
  50    memset (value, '0', size);
  51
  52    for (i = 0; i < final ; i++)
  53      value[size - 1 - i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];
  54
  55    value[size] = '\0';
  56    fputs (value, stdout);
  57 }
  58
  59 static void
  60 exp_mpn (mp1 ex, mp1 x)
  61 {
  62    unsigned n;
  63    mp1 xp;
  64    mp2 tmp;
  65    mp_limb_t chk, round;
  66    mp1 tol;
  67
  68    memset (xp, 0, sizeof (mp1));
  69    memset (ex, 0, sizeof (mp1));
  70    xp[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
  71    memset (tol,0, sizeof (mp1));
  72    tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)1 << (FRAC - TOL) % mpbpl;
  73
  74    n = 0;
  75
  76    do
  77      {
  78        /* Calculate sum(x^n/n!) until the next term is sufficiently small.  */
  79
  80        mpn_mul_n (tmp, xp, x, SZ);
  81        assert (tmp[SZ * 2 - 1] == 0);
  82        if (n > 0)
  83          round = mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
  84        chk = mpn_add_n (ex, ex, xp, SZ);
  85        assert (chk == 0);
  86        n++;
  87        assert (n < 80); /* Catch too-high TOL.  */
  88      }
  89    while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0);
  90 }
  91
  92 static int
  93 mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE)
  94 {
  95    int i, j;
  96    for (i = SIZE - 1; i > 0; i--)
  97      if (SRC_PTR[i] != 0)
  98        break;
  99    for (j = mpbpl - 1; j >= 0; j--)
 100      if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
 101        break;
 102
 103    return i * mpbpl + j;
 104 }
 105
 106 int
 107 main (void)
 108 {
 109    mp1 ex, x, xt, e2, e3;
 110    int i;
 111    int errors = 0;
 112    int failures = 0;
 113    mp1 maxerror;
 114    int maxerror_s = 0;
 115    const double sf = pow (2, mpbpl);
 116
 117    /* assert (mpbpl == mp_bits_per_limb); */
 118    assert (FRAC / mpbpl * mpbpl == FRAC);
 119
 120    memset (maxerror, 0, sizeof (mp1));
 121    memset (xt, 0, sizeof (mp1));
 122    xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
 123
 124    for (i = 0; i < 1 << N2; i++)
 125    {
 126       int e2s, e3s, j;
 127       double de2;
 128
 129       mpn_mul_1 (x,xt,SZ,i);
 130       exp_mpn (ex, x);
 131       de2 = exp (i / (double) (1 << N2));
 132       for (j = SZ-1; j >= 0; j--)
 133         {
 134           e2[j] = (mp_limb_t) de2;
 135           de2 = (de2 - e2[j]) * sf;
 136         }
 137       if (mpn_cmp (ex,e2,SZ) >= 0)
 138         mpn_sub_n (e3,ex,e2,SZ);
 139       else
 140         mpn_sub_n (e3,e2,ex,SZ);
 141
 142       e2s = mpn_bitsize (e2,SZ);
 143       e3s = mpn_bitsize (e3,SZ);
 144       if (e3s >= 0 && e2s - e3s < 54)
 145         {
 146 #if PRINT_ERRORS
 147           printf ("%06x ", i * (0x100000 / (1 << N2)));
 148           print_mpn_hex (ex, (FRAC / 4) + 1);
 149           fputs ("\n       ",stdout);
 150           print_mpn_hex (e2, (FRAC / 4) + 1);
 151           printf ("\n %c     ",
 152                   e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
 153           print_mpn_hex (e3, (FRAC / 4) + 1);
 154           putchar ('\n');
 155 #endif
 156          errors += (e2s - e3s == 53);
 157          failures += (e2s - e3s < 53);
 158         }
 159       if (e3s >= maxerror_s
 160           && mpn_cmp (e3, maxerror, SZ) > 0)
 161         {
 162           memcpy (maxerror, e3, sizeof (mp1));
 163           maxerror_s = e3s;
 164         }
 165    }
 166
 167    /* Check exp_mpn against precomputed value of exp(1).  */
 168    memset (x, '\0', sizeof (mp1));
 169    x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
 170    exp_mpn (ex, x);
 171
 172    memset (e2, '\0', sizeof (mp1));
 173    for (i = -1; i < 100 && i < FRAC / 4; i++)
 174      e2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig,
 175                                                              exp1[i + 1])
 176                                                      - hexdig)
 177                                         << (FRAC - i * 4 - 4) % mpbpl);
 178
 179    if (mpn_cmp (ex, e2, SZ) >= 0)
 180      mpn_sub_n (e3, ex, e2, SZ);
 181    else
 182      mpn_sub_n (e3, e2, ex, SZ);
 183
 184    printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
 185            errors * 100.0 / (double) (1 << N2));
 186    fputs ("maximum error:   ", stdout);
 187    print_mpn_hex (maxerror, (FRAC / 4) + 1);
 188    fputs ("\nerror in exp(1): ", stdout);
 189    print_mpn_hex (e3, (FRAC / 4) + 1);
 190    putchar ('\n');
 191
 192    return failures == 0 ? 0 : 1;
 193 }