math/atest-exp.c

   1 /* Copyright (C) 1997-2022 Free Software Foundation, Inc.
   2    This file is part of the GNU C Library.
   3
   4    The GNU C Library is free software; you can redistribute it and/or
   5    modify it under the terms of the GNU Lesser General Public
   6    License as published by the Free Software Foundation; either
   7    version 2.1 of the License, or (at your option) any later version.
   8
   9    The GNU C Library is distributed in the hope that it will be useful,
  10    but WITHOUT ANY WARRANTY; without even the implied warranty of
  11    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  12    Lesser General Public License for more details.
  13
  14    You should have received a copy of the GNU Lesser General Public
  15    License along with the GNU C Library; if not, see
  16    <https://www.gnu.org/licenses/>.  */
  17
  18 #include <stdio.h>
  19 #include <math.h>
  20 #include <gmp.h>
  21 #include <string.h>
  22 #include <limits.h>
  23 #include <assert.h>
  24
  25 #define PRINT_ERRORS 0
  26
  27 #define TOL 80
  28 #define N2 17
  29 #define FRAC (32*4)
  30
  31 #define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
  32 #define SZ (FRAC / mpbpl + 1)
  33 typedef mp_limb_t mp1[SZ], mp2[SZ * 2];
  34
  35 /* This string has 101 hex digits.  */
  36 static const char exp1[102] = "2" /* point */
  37 "b7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a7"
  38 "84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07";
  39 static const char hexdig[] = "0123456789abcdef";
  40
  41 static void
  42 print_mpn_hex (const mp_limb_t *x, unsigned size)
  43 {
  44    char value[size + 1];
  45    unsigned i;
  46    const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;
  47
  48    memset (value, '0', size);
  49
  50    for (i = 0; i < final ; i++)
  51      value[size - 1 - i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];
  52
  53    value[size] = '\0';
  54    fputs (value, stdout);
  55 }
  56
  57 static void
  58 exp_mpn (mp1 ex, mp1 x)
  59 {
  60    unsigned n;
  61    mp1 xp;
  62    mp2 tmp;
  63    mp_limb_t chk __attribute__ ((unused));
  64    mp1 tol;
  65
  66    memset (xp, 0, sizeof (mp1));
  67    memset (ex, 0, sizeof (mp1));
  68    xp[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
  69    memset (tol,0, sizeof (mp1));
  70    tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)1 << (FRAC - TOL) % mpbpl;
  71
  72    n = 0;
  73
  74    do
  75      {
  76        /* Calculate sum(x^n/n!) until the next term is sufficiently small.  */
  77
  78        mpn_mul_n (tmp, xp, x, SZ);
  79        assert (tmp[SZ * 2 - 1] == 0);
  80        if (n > 0)
  81          mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
  82        chk = mpn_add_n (ex, ex, xp, SZ);
  83        assert (chk == 0);
  84        n++;
  85        assert (n < 80); /* Catch too-high TOL.  */
  86      }
  87    while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0);
  88 }
  89
  90 static int
  91 mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE)
  92 {
  93    int i, j;
  94    for (i = SIZE - 1; i > 0; i--)
  95      if (SRC_PTR[i] != 0)
  96        break;
  97    for (j = mpbpl - 1; j >= 0; j--)
  98      if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
  99        break;
 100
 101    return i * mpbpl + j;
 102 }
 103
 104 static int
 105 do_test (void)
 106 {
 107    mp1 ex, x, xt, e2, e3;
 108    int i;
 109    int errors = 0;
 110    int failures = 0;
 111    mp1 maxerror;
 112    int maxerror_s = 0;
 113    const double sf = pow (2, mpbpl);
 114
 115    /* assert (mpbpl == mp_bits_per_limb); */
 116    assert (FRAC / mpbpl * mpbpl == FRAC);
 117
 118    memset (maxerror, 0, sizeof (mp1));
 119    memset (xt, 0, sizeof (mp1));
 120    xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
 121
 122    for (i = 0; i < 1 << N2; i++)
 123    {
 124       int e2s, e3s, j;
 125       double de2;
 126
 127       mpn_mul_1 (x,xt,SZ,i);
 128       exp_mpn (ex, x);
 129       de2 = exp (i / (double) (1 << N2));
 130       for (j = SZ-1; j >= 0; j--)
 131         {
 132           e2[j] = (mp_limb_t) de2;
 133           de2 = (de2 - e2[j]) * sf;
 134         }
 135       if (mpn_cmp (ex,e2,SZ) >= 0)
 136         mpn_sub_n (e3,ex,e2,SZ);
 137       else
 138         mpn_sub_n (e3,e2,ex,SZ);
 139
 140       e2s = mpn_bitsize (e2,SZ);
 141       e3s = mpn_bitsize (e3,SZ);
 142       if (e3s >= 0 && e2s - e3s < 54)
 143         {
 144 #if PRINT_ERRORS
 145           printf ("%06x ", i * (0x100000 / (1 << N2)));
 146           print_mpn_hex (ex, (FRAC / 4) + 1);
 147           fputs ("\n       ",stdout);
 148           print_mpn_hex (e2, (FRAC / 4) + 1);
 149           printf ("\n %c     ",
 150                   e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
 151           print_mpn_hex (e3, (FRAC / 4) + 1);
 152           putchar ('\n');
 153 #endif
 154          errors += (e2s - e3s == 53);
 155          failures += (e2s - e3s < 53);
 156         }
 157       if (e3s >= maxerror_s
 158           && mpn_cmp (e3, maxerror, SZ) > 0)
 159         {
 160           memcpy (maxerror, e3, sizeof (mp1));
 161           maxerror_s = e3s;
 162         }
 163    }
 164
 165    /* Check exp_mpn against precomputed value of exp(1).  */
 166    memset (x, '\0', sizeof (mp1));
 167    x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
 168    exp_mpn (ex, x);
 169
 170    memset (e2, '\0', sizeof (mp1));
 171    for (i = -1; i < 100 && i < FRAC / 4; i++)
 172      e2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig,
 173                                                              exp1[i + 1])
 174                                                      - hexdig)
 175                                         << (FRAC - i * 4 - 4) % mpbpl);
 176
 177    if (mpn_cmp (ex, e2, SZ) >= 0)
 178      mpn_sub_n (e3, ex, e2, SZ);
 179    else
 180      mpn_sub_n (e3, e2, ex, SZ);
 181
 182    printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
 183            errors * 100.0 / (double) (1 << N2));
 184    fputs ("maximum error:   ", stdout);
 185    print_mpn_hex (maxerror, (FRAC / 4) + 1);
 186    fputs ("\nerror in exp(1): ", stdout);
 187    print_mpn_hex (e3, (FRAC / 4) + 1);
 188    putchar ('\n');
 189
 190    return failures == 0 ? 0 : 1;
 191 }
 192
 193 #define TIMEOUT 200
 194 #define TEST_FUNCTION do_test ()
 195 #include "../test-skeleton.c"