math/atest-exp2.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 #include <stdlib.h>
  25
  26 #define PRINT_ERRORS 0
  27
  28 #define TOL 80
  29 #define N2 18
  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 #if BITS_PER_MP_LIMB == 64
  37 # define LIMB64(L, H) 0x ## H ## L
  38 #elif BITS_PER_MP_LIMB == 32
  39 # define LIMB64(L, H) 0x ## L, 0x ## H
  40 #else
  41 # error
  42 #endif
  43
  44 /* Once upon a time these constants were generated to 400 bits.
  45    We only need FRAC bits (128) at present, but we retain 384 bits
  46    in the text Just In Case.  */
  47 #define CONSTSZ(INT, F1, F2, F3, F4, F5, F6, F7, F8, F9, Fa, Fb, Fc) \
  48         LIMB64(F4, F3), LIMB64(F2, F1), INT
  49
  50 static const mp1 mp_exp1 = {
  51   CONSTSZ (2, b7e15162, 8aed2a6a, bf715880, 9cf4f3c7, 62e7160f, 38b4da56,
  52            a784d904, 5190cfef, 324e7738, 926cfbe5, f4bf8d8d, 8c31d763)
  53 };
  54
  55 static const mp1 mp_log2 = {
  56   CONSTSZ (0, b17217f7, d1cf79ab, c9e3b398, 03f2f6af, 40f34326, 7298b62d,
  57            8a0d175b, 8baafa2b, e7b87620, 6debac98, 559552fb, 4afa1b10)
  58 };
  59
  60 static void
  61 print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base)
  62 {
  63    static const char hexdig[16] = "0123456789abcdef";
  64    unsigned int i;
  65    mp1 tx;
  66
  67    memcpy (tx, x, sizeof (mp1));
  68    if (base == 16)
  69      fputs ("0x", stdout);
  70    assert (x[SZ-1] < base);
  71    fputc (hexdig[x[SZ - 1]], stdout);
  72    fputc ('.', stdout);
  73    for (i = 0; i < dp; i++)
  74      {
  75        tx[SZ - 1] = 0;
  76        mpn_mul_1 (tx, tx, SZ, base);
  77        assert (tx[SZ - 1] < base);
  78        fputc (hexdig[tx[SZ - 1]], stdout);
  79      }
  80 }
  81
  82 /* Compute e^x.  */
  83 static void
  84 exp_mpn (mp1 ex, mp1 x)
  85 {
  86    unsigned int n;
  87    mp1 xp;
  88    mp2 tmp;
  89    mp_limb_t chk __attribute__ ((unused));
  90    mp1 tol;
  91
  92    memset (xp, 0, sizeof (mp1));
  93    memset (ex, 0, sizeof (mp1));
  94    xp[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
  95    memset (tol, 0, sizeof (mp1));
  96    tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)1 << (FRAC - TOL) % mpbpl;
  97
  98    n = 0;
  99
 100    do
 101      {
 102        /* Calculate sum(x^n/n!) until the next term is sufficiently small.  */
 103
 104        mpn_mul_n (tmp, xp, x, SZ);
 105        assert(tmp[SZ * 2 - 1] == 0);
 106        if (n > 0)
 107          mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
 108        chk = mpn_add_n (ex, ex, xp, SZ);
 109        assert (chk == 0);
 110        ++n;
 111        assert (n < 80); /* Catch too-high TOL.  */
 112      }
 113    while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0);
 114 }
 115
 116 /* Calculate 2^x.  */
 117 static void
 118 exp2_mpn (mp1 ex, mp1 x)
 119 {
 120   mp2 tmp;
 121   mpn_mul_n (tmp, x, mp_log2, SZ);
 122   assert(tmp[SZ * 2 - 1] == 0);
 123   exp_mpn (ex, tmp + FRAC / mpbpl);
 124 }
 125
 126
 127 static int
 128 mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE)
 129 {
 130   int i, j;
 131   for (i = SIZE - 1; i > 0; --i)
 132     if (SRC_PTR[i] != 0)
 133       break;
 134   for (j = mpbpl - 1; j >= 0; --j)
 135     if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
 136       break;
 137
 138   return i * mpbpl + j;
 139 }
 140
 141 static int
 142 do_test (void)
 143 {
 144   mp1 ex, x, xt, e2, e3;
 145   int i;
 146   int errors = 0;
 147   int failures = 0;
 148   mp1 maxerror;
 149   int maxerror_s = 0;
 150   const double sf = pow (2, mpbpl);
 151
 152   /* assert(mpbpl == mp_bits_per_limb); */
 153   assert(FRAC / mpbpl * mpbpl == FRAC);
 154
 155   memset (maxerror, 0, sizeof (mp1));
 156   memset (xt, 0, sizeof (mp1));
 157   xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
 158
 159   for (i = 0; i < (1 << N2); ++i)
 160     {
 161       int e2s, e3s, j;
 162       double de2;
 163
 164       mpn_mul_1 (x, xt, SZ, i);
 165       exp2_mpn (ex, x);
 166       de2 = exp2 (i / (double) (1 << N2));
 167       for (j = SZ - 1; j >= 0; --j)
 168         {
 169           e2[j] = (mp_limb_t) de2;
 170           de2 = (de2 - e2[j]) * sf;
 171         }
 172       if (mpn_cmp (ex, e2, SZ) >= 0)
 173         mpn_sub_n (e3, ex, e2, SZ);
 174       else
 175         mpn_sub_n (e3, e2, ex, SZ);
 176
 177       e2s = mpn_bitsize (e2, SZ);
 178       e3s = mpn_bitsize (e3, SZ);
 179       if (e3s >= 0 && e2s - e3s < 54)
 180         {
 181 #if PRINT_ERRORS
 182           printf ("%06x ", i * (0x100000 / (1 << N2)));
 183           print_mpn_fp (ex, (FRAC / 4) + 1, 16);
 184           putchar ('\n');
 185           fputs ("       ",stdout);
 186           print_mpn_fp (e2, (FRAC / 4) + 1, 16);
 187           putchar ('\n');
 188           printf (" %c     ",
 189                   e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
 190           print_mpn_fp (e3, (FRAC / 4) + 1, 16);
 191           putchar ('\n');
 192 #endif
 193           errors += (e2s - e3s == 53);
 194           failures += (e2s - e3s < 53);
 195         }
 196       if (e3s >= maxerror_s
 197           && mpn_cmp (e3, maxerror, SZ) > 0)
 198         {
 199           memcpy (maxerror, e3, sizeof (mp1));
 200           maxerror_s = e3s;
 201         }
 202     }
 203
 204   /* Check exp_mpn against precomputed value of exp(1).  */
 205   memset (x, 0, sizeof (mp1));
 206   x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
 207   exp_mpn (ex, x);
 208   if (mpn_cmp (ex, mp_exp1, SZ) >= 0)
 209     mpn_sub_n (e3, ex, mp_exp1, SZ);
 210   else
 211     mpn_sub_n (e3, mp_exp1, ex, SZ);
 212
 213   printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
 214           errors * 100.0 / (double) (1 << N2));
 215   fputs ("maximum error:   ", stdout);
 216   print_mpn_fp (maxerror, (FRAC / 4) + 1, 16);
 217   putchar ('\n');
 218   fputs ("error in exp(1): ", stdout);
 219   print_mpn_fp (e3, (FRAC / 4) + 1, 16);
 220   putchar ('\n');
 221
 222   return failures == 0 ? 0 : 1;
 223 }
 224
 225 #define TIMEOUT 300
 226 #define TEST_FUNCTION do_test ()
 227 #include "../test-skeleton.c"