math/atest-exp2.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 #include <stdlib.h>
  27
  28 #define PRINT_ERRORS 0
  29
  30 #define TOL 80
  31 #define N2 18
  32 #define FRAC (32*4)
  33
  34 #define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
  35 #define SZ (FRAC / mpbpl + 1)
  36 typedef mp_limb_t mp1[SZ], mp2[SZ * 2];
  37
  38 /* This string has 101 hex digits.  */
  39 static const char exp1[102] = "2" /* point */
  40 "b7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a7"
  41 "84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07";
  42 static const char exp_m1[102] = "0" /* point */
  43 "5e2d58d8b3bcdf1abadec7829054f90dda9805aab56c773330"
  44 "24b9d0a507daedb16400bf472b4215b8245b669d90d27a5aea";
  45
  46 static const char hexdig[] = "0123456789abcdef";
  47
  48 static void
  49 print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base)
  50 {
  51    unsigned int i;
  52    mp1 tx;
  53
  54    memcpy (tx, x, sizeof (mp1));
  55    if (base == 16)
  56      fputs ("0x", stdout);
  57    assert (x[SZ-1] < base);
  58    fputc (hexdig[x[SZ - 1]], stdout);
  59    fputc ('.', stdout);
  60    for (i = 0; i < dp; i++)
  61      {
  62        tx[SZ - 1] = 0;
  63        mpn_mul_1 (tx, tx, SZ, base);
  64        assert (tx[SZ - 1] < base);
  65        fputc (hexdig[tx[SZ - 1]], stdout);
  66      }
  67 }
  68
  69 static void
  70 read_mpn_hex(mp_limb_t *x, const char *str)
  71 {
  72   int i;
  73
  74   memset (x, 0, sizeof (mp1));
  75   for (i = -1; i < 100 && i < FRAC / 4; ++i)
  76     x[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, str[i + 1])
  77                                                    - hexdig)
  78                                       << (FRAC - i * 4 - 4) % mpbpl);
  79 }
  80
  81 static mp_limb_t *get_log2(void) __attribute__((const));
  82 static mp_limb_t *
  83 get_log2(void)
  84 {
  85   static mp1 log2_m;
  86   static int log2_m_inited = 0;
  87   static const char log2[102] = "0" /* point */
  88     "b17217f7d1cf79abc9e3b39803f2f6af40f343267298b62d8a"
  89     "0d175b8baafa2be7b876206debac98559552fb4afa1b10ed2e";
  90
  91   if (!log2_m_inited)
  92     {
  93       read_mpn_hex (log2_m, log2);
  94       log2_m_inited = 1;
  95     }
  96   return log2_m;
  97 }
  98
  99 /* Compute e^x.  */
 100 static void
 101 exp_mpn (mp1 ex, mp1 x)
 102 {
 103    unsigned int n;
 104    mp1 xp;
 105    mp2 tmp;
 106    mp_limb_t chk, round;
 107    mp1 tol;
 108
 109    memset (xp, 0, sizeof (mp1));
 110    memset (ex, 0, sizeof (mp1));
 111    xp[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
 112    memset (tol, 0, sizeof (mp1));
 113    tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)1 << (FRAC - TOL) % mpbpl;
 114
 115    n = 0;
 116
 117    do
 118      {
 119        /* Calculate sum(x^n/n!) until the next term is sufficiently small.  */
 120
 121        mpn_mul_n (tmp, xp, x, SZ);
 122        assert(tmp[SZ * 2 - 1] == 0);
 123        if (n > 0)
 124          round = mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
 125        chk = mpn_add_n (ex, ex, xp, SZ);
 126        assert (chk == 0);
 127        ++n;
 128        assert (n < 80); /* Catch too-high TOL.  */
 129      }
 130    while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0);
 131 }
 132
 133 /* Calculate 2^x.  */
 134 static void
 135 exp2_mpn (mp1 ex, mp1 x)
 136 {
 137   mp2 tmp;
 138   mpn_mul_n (tmp, x, get_log2 (), SZ);
 139   assert(tmp[SZ * 2 - 1] == 0);
 140   exp_mpn (ex, tmp + FRAC / mpbpl);
 141 }
 142
 143
 144 static int
 145 mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE)
 146 {
 147   int i, j;
 148   for (i = SIZE - 1; i > 0; --i)
 149     if (SRC_PTR[i] != 0)
 150       break;
 151   for (j = mpbpl - 1; j >= 0; --j)
 152     if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
 153       break;
 154
 155   return i * mpbpl + j;
 156 }
 157
 158 int
 159 main (void)
 160 {
 161   mp1 ex, x, xt, e2, e3;
 162   int i;
 163   int errors = 0;
 164   int failures = 0;
 165   mp1 maxerror;
 166   int maxerror_s = 0;
 167   const double sf = pow (2, mpbpl);
 168
 169   /* assert(mpbpl == mp_bits_per_limb); */
 170   assert(FRAC / mpbpl * mpbpl == FRAC);
 171
 172   memset (maxerror, 0, sizeof (mp1));
 173   memset (xt, 0, sizeof (mp1));
 174   xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
 175
 176   for (i = 0; i < (1 << N2); ++i)
 177     {
 178       int e2s, e3s, j;
 179       double de2;
 180
 181       mpn_mul_1 (x, xt, SZ, i);
 182       exp2_mpn (ex, x);
 183       de2 = exp2 (i / (double) (1 << N2));
 184       for (j = SZ - 1; j >= 0; --j)
 185         {
 186           e2[j] = (mp_limb_t) de2;
 187           de2 = (de2 - e2[j]) * sf;
 188         }
 189       if (mpn_cmp (ex, e2, SZ) >= 0)
 190         mpn_sub_n (e3, ex, e2, SZ);
 191       else
 192         mpn_sub_n (e3, e2, ex, SZ);
 193
 194       e2s = mpn_bitsize (e2, SZ);
 195       e3s = mpn_bitsize (e3, SZ);
 196       if (e3s >= 0 && e2s - e3s < 54)
 197         {
 198 #if PRINT_ERRORS
 199           printf ("%06x ", i * (0x100000 / (1 << N2)));
 200           print_mpn_fp (ex, (FRAC / 4) + 1, 16);
 201           putchar ('\n');
 202           fputs ("       ",stdout);
 203           print_mpn_fp (e2, (FRAC / 4) + 1, 16);
 204           putchar ('\n');
 205           printf (" %c     ",
 206                   e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
 207           print_mpn_fp (e3, (FRAC / 4) + 1, 16);
 208           putchar ('\n');
 209 #endif
 210           errors += (e2s - e3s == 53);
 211           failures += (e2s - e3s < 53);
 212         }
 213       if (e3s >= maxerror_s
 214           && mpn_cmp (e3, maxerror, SZ) > 0)
 215         {
 216           memcpy (maxerror, e3, sizeof (mp1));
 217           maxerror_s = e3s;
 218         }
 219     }
 220
 221   /* Check exp_mpn against precomputed value of exp(1).  */
 222   memset (x, 0, sizeof (mp1));
 223   x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
 224   exp_mpn (ex, x);
 225   read_mpn_hex (e2, exp1);
 226   if (mpn_cmp (ex, e2, SZ) >= 0)
 227     mpn_sub_n (e3, ex, e2, SZ);
 228   else
 229     mpn_sub_n (e3, e2, ex, SZ);
 230
 231   printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
 232           errors * 100.0 / (double) (1 << N2));
 233   fputs ("maximum error:   ", stdout);
 234   print_mpn_fp (maxerror, (FRAC / 4) + 1, 16);
 235   putchar ('\n');
 236   fputs ("error in exp(1): ", stdout);
 237   print_mpn_fp (e3, (FRAC / 4) + 1, 16);
 238   putchar ('\n');
 239
 240   return failures == 0 ? 0 : 1;
 241 }