math/atest-exp.c

   1 /* Copyright (C) 1997-2013 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, see
  17    <http://www.gnu.org/licenses/>.  */
  18
  19 #include <stdio.h>
  20 #include <math.h>
  21 #include <gmp.h>
  22 #include <string.h>
  23 #include <limits.h>
  24 #include <assert.h>
  25
  26 #define PRINT_ERRORS 0
  27
  28 #define TOL 80
  29 #define N2 17
  30 #define FRAC (32*4)
  31
  32 #define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
  33 #define SZ (FRAC / mpbpl + 1)
  34 typedef mp_limb_t mp1[SZ], mp2[SZ * 2];
  35
  36 /* This string has 101 hex digits.  */
  37 static const char exp1[102] = "2" /* point */
  38 "b7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a7"
  39 "84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07";
  40 static const char hexdig[] = "0123456789abcdef";
  41
  42 static void
  43 print_mpn_hex (const mp_limb_t *x, unsigned size)
  44 {
  45    char value[size + 1];
  46    unsigned i;
  47    const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;
  48
  49    memset (value, '0', size);
  50
  51    for (i = 0; i < final ; i++)
  52      value[size - 1 - i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];
  53
  54    value[size] = '\0';
  55    fputs (value, stdout);
  56 }
  57
  58 static void
  59 exp_mpn (mp1 ex, mp1 x)
  60 {
  61    unsigned n;
  62    mp1 xp;
  63    mp2 tmp;
  64    mp_limb_t chk;
  65    mp1 tol;
  66
  67    memset (xp, 0, sizeof (mp1));
  68    memset (ex, 0, sizeof (mp1));
  69    xp[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
  70    memset (tol,0, sizeof (mp1));
  71    tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)1 << (FRAC - TOL) % mpbpl;
  72
  73    n = 0;
  74
  75    do
  76      {
  77        /* Calculate sum(x^n/n!) until the next term is sufficiently small.  */
  78
  79        mpn_mul_n (tmp, xp, x, SZ);
  80        assert (tmp[SZ * 2 - 1] == 0);
  81        if (n > 0)
  82          mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
  83        chk = mpn_add_n (ex, ex, xp, SZ);
  84        assert (chk == 0);
  85        n++;
  86        assert (n < 80); /* Catch too-high TOL.  */
  87      }
  88    while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0);
  89 }
  90
  91 static int
  92 mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE)
  93 {
  94    int i, j;
  95    for (i = SIZE - 1; i > 0; i--)
  96      if (SRC_PTR[i] != 0)
  97        break;
  98    for (j = mpbpl - 1; j >= 0; j--)
  99      if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
 100        break;
 101
 102    return i * mpbpl + j;
 103 }
 104
 105 int
 106 main (void)
 107 {
 108    mp1 ex, x, xt, e2, e3;
 109    int i;
 110    int errors = 0;
 111    int failures = 0;
 112    mp1 maxerror;
 113    int maxerror_s = 0;
 114    const double sf = pow (2, mpbpl);
 115
 116    /* assert (mpbpl == mp_bits_per_limb); */
 117    assert (FRAC / mpbpl * mpbpl == FRAC);
 118
 119    memset (maxerror, 0, sizeof (mp1));
 120    memset (xt, 0, sizeof (mp1));
 121    xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
 122
 123    for (i = 0; i < 1 << N2; i++)
 124    {
 125       int e2s, e3s, j;
 126       double de2;
 127
 128       mpn_mul_1 (x,xt,SZ,i);
 129       exp_mpn (ex, x);
 130       de2 = exp (i / (double) (1 << N2));
 131       for (j = SZ-1; j >= 0; j--)
 132         {
 133           e2[j] = (mp_limb_t) de2;
 134           de2 = (de2 - e2[j]) * sf;
 135         }
 136       if (mpn_cmp (ex,e2,SZ) >= 0)
 137         mpn_sub_n (e3,ex,e2,SZ);
 138       else
 139         mpn_sub_n (e3,e2,ex,SZ);
 140
 141       e2s = mpn_bitsize (e2,SZ);
 142       e3s = mpn_bitsize (e3,SZ);
 143       if (e3s >= 0 && e2s - e3s < 54)
 144         {
 145 #if PRINT_ERRORS
 146           printf ("%06x ", i * (0x100000 / (1 << N2)));
 147           print_mpn_hex (ex, (FRAC / 4) + 1);
 148           fputs ("\n       ",stdout);
 149           print_mpn_hex (e2, (FRAC / 4) + 1);
 150           printf ("\n %c     ",
 151                   e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
 152           print_mpn_hex (e3, (FRAC / 4) + 1);
 153           putchar ('\n');
 154 #endif
 155          errors += (e2s - e3s == 53);
 156          failures += (e2s - e3s < 53);
 157         }
 158       if (e3s >= maxerror_s
 159           && mpn_cmp (e3, maxerror, SZ) > 0)
 160         {
 161           memcpy (maxerror, e3, sizeof (mp1));
 162           maxerror_s = e3s;
 163         }
 164    }
 165
 166    /* Check exp_mpn against precomputed value of exp(1).  */
 167    memset (x, '\0', sizeof (mp1));
 168    x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
 169    exp_mpn (ex, x);
 170
 171    memset (e2, '\0', sizeof (mp1));
 172    for (i = -1; i < 100 && i < FRAC / 4; i++)
 173      e2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig,
 174                                                              exp1[i + 1])
 175                                                      - hexdig)
 176                                         << (FRAC - i * 4 - 4) % mpbpl);
 177
 178    if (mpn_cmp (ex, e2, SZ) >= 0)
 179      mpn_sub_n (e3, ex, e2, SZ);
 180    else
 181      mpn_sub_n (e3, e2, ex, SZ);
 182
 183    printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
 184            errors * 100.0 / (double) (1 << N2));
 185    fputs ("maximum error:   ", stdout);
 186    print_mpn_hex (maxerror, (FRAC / 4) + 1);
 187    fputs ("\nerror in exp(1): ", stdout);
 188    print_mpn_hex (e3, (FRAC / 4) + 1);
 189    putchar ('\n');
 190
 191    return failures == 0 ? 0 : 1;
 192 }