summaryrefslogtreecommitdiff
path: root/math/atest-exp2.c
blob: 95e72aa5075b7e40368da88422c2a586fb39f12a (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
/* Copyright (C) 1997 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Geoffrey Keating <Geoff.Keating@anu.edu.au>, 1997.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Library General Public License as
   published by the Free Software Foundation; either version 2 of the
   License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Library General Public License for more details.

   You should have received a copy of the GNU Library General Public
   License along with the GNU C Library; see the file COPYING.LIB.  If not,
   write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
   Boston, MA 02111-1307, USA.  */

#include <stdio.h>
#include <math.h>
#include <gmp.h>
#include <string.h>
#include <limits.h>
#include <assert.h>
#include <stdlib.h>

#define PRINT_ERRORS 0

#define TOL 80
#define N2 18
#define FRAC (32*4)

#define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
#define SZ (FRAC / mpbpl + 1)
typedef mp_limb_t mp1[SZ], mp2[SZ * 2];

/* This string has 101 hex digits.  */
static const char exp1[102] = "2" /* point */
"b7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a7"
"84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07";
static const char exp_m1[102] = "0" /* point */
"5e2d58d8b3bcdf1abadec7829054f90dda9805aab56c773330"
"24b9d0a507daedb16400bf472b4215b8245b669d90d27a5aea";

static const char hexdig[] = "0123456789abcdef";

void
print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base)
{
   unsigned int i;
   mp1 tx;

   memcpy (tx, x, sizeof (mp1));
   if (base == 16)
     fputs ("0x", stdout);
   assert (x[SZ-1] < base);
   fputc (hexdig[x[SZ - 1]], stdout);
   fputc ('.', stdout);
   for (i = 0; i < dp; i++)
     {
       tx[SZ - 1] = 0;
       mpn_mul_1 (tx, tx, SZ, base);
       assert (tx[SZ - 1] < base);
       fputc (hexdig[tx[SZ - 1]], stdout);
     }
}

void
read_mpn_hex(mp_limb_t *x, const char *str)
{
  int i;

  memset (x, 0, sizeof (mp1));
  for (i = -1; i < 100 && i < FRAC / 4; ++i)
    x[(FRAC - i * 4 - 4) / mpbpl] |= (strchr (hexdig, str[i + 1]) - hexdig
				      << (FRAC - i * 4 - 4) % mpbpl);
}

static mp_limb_t *get_log2(void) __attribute__((const));
static mp_limb_t *
get_log2(void)
{
  static mp1 log2_m;
  static int log2_m_inited = 0;
  static const char log2[102] = "0" /* point */
    "b17217f7d1cf79abc9e3b39803f2f6af40f343267298b62d8a"
    "0d175b8baafa2be7b876206debac98559552fb4afa1b10ed2e";

  if (!log2_m_inited)
    {
      read_mpn_hex (log2_m, log2);
      log2_m_inited = 1;
    }
  return log2_m;
}

/* Compute e^x.  */
void
exp_mpn (mp1 ex, mp1 x)
{
   unsigned int n;
   mp1 xp;
   mp2 tmp;
   mp_limb_t chk, round;
   mp1 tol;

   memset (xp, 0, sizeof (mp1));
   memset (ex, 0, sizeof (mp1));
   xp[FRAC / mpbpl] = 1 << FRAC % mpbpl;
   memset (tol, 0, sizeof (mp1));
   tol[(FRAC - TOL) / mpbpl] = 1 << (FRAC - TOL) % mpbpl;

   n = 0;

   do
     {
       /* Calculate sum(x^n/n!) until the next term is sufficiently small.  */

       mpn_mul_n (tmp, xp, x, SZ);
       assert(tmp[SZ * 2 - 1] == 0);
       if (n > 0)
	 round = mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
       chk = mpn_add_n (ex, ex, xp, SZ);
       assert (chk == 0);
       ++n;
       assert (n < 80); /* Catch too-high TOL.  */
     }
   while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0);
}

/* Calculate 2^x.  */
void
exp2_mpn (mp1 ex, mp1 x)
{
  mp2 tmp;
  mpn_mul_n (tmp, x, get_log2 (), SZ);
  assert(tmp[SZ * 2 - 1] == 0);
  exp_mpn (ex, tmp + FRAC / mpbpl);
}


static int
mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE)
{
  int i, j;
  for (i = SIZE - 1; i > 0; --i)
    if (SRC_PTR[i] != 0)
      break;
  for (j = mpbpl - 1; j > 0; --j)
    if ((SRC_PTR[i] & 1 << j) != 0)
      break;

  return i * 32 + j;
}

int
main (void)
{
  mp1 ex, x, xt, e2, e3;
  int i;
  int errors = 0;
  int failures = 0;
  mp1 maxerror;
  int maxerror_s = 0;
  const double sf = pow (2, mpbpl);

  /* assert(mpbpl == mp_bits_per_limb); */
  assert(FRAC / mpbpl * mpbpl == FRAC);

  memset (maxerror, 0, sizeof (mp1));
  memset (xt, 0, sizeof (mp1));
  xt[(FRAC - N2) / mpbpl] = 1 << (FRAC - N2) % mpbpl;

  for (i = 0; i < (1 << N2); ++i)
    {
      int e2s, e3s, j;
      double de2;

      mpn_mul_1 (x, xt, SZ, i);
      exp2_mpn (ex, x);
      de2 = exp2 (i / (double) (1 << N2));
      for (j = SZ - 1; j >= 0; --j)
	{
	  e2[j] = (mp_limb_t) de2;
	  de2 = (de2 - e2[j]) * sf;
	}
      if (mpn_cmp (ex, e2, SZ) >= 0)
	mpn_sub_n (e3, ex, e2, SZ);
      else
	mpn_sub_n (e3, e2, ex, SZ);

      e2s = mpn_bitsize (e2, SZ);
      e3s = mpn_bitsize (e3, SZ);
      if (e3s > 1 && e2s - e3s < 54)
	{
#if PRINT_ERRORS
	  printf ("%06x ", i * (0x100000 / (1 << N2)));
	  print_mpn_fp (ex, (FRAC / 4) + 1, 16);
	  putchar ('\n');
	  fputs ("       ",stdout);
	  print_mpn_fp (e2, (FRAC / 4) + 1, 16);
	  putchar ('\n');
	  printf (" %c     ",
		  e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
	  print_mpn_fp (e3, (FRAC / 4) + 1, 16);
	  putchar ('\n');
#endif
	  errors += (e2s - e3s == 53);
	  failures += (e2s - e3s < 53);
	}
      if (e3s >= maxerror_s
	  && mpn_cmp (e3, maxerror, SZ) > 0)
	{
	  memcpy (maxerror, e3, sizeof (mp1));
	  maxerror_s = e3s;
	}
    }

  /* Check exp_mpn against precomputed value of exp(1).  */
  memset (x, 0, sizeof (mp1));
  x[FRAC / mpbpl] = 1 << FRAC % mpbpl;
  exp_mpn (ex, x);
  read_mpn_hex (e2, exp1);
  if (mpn_cmp (ex, e2, SZ) >= 0)
    mpn_sub_n (e3, ex, e2, SZ);
  else
    mpn_sub_n (e3, e2, ex, SZ);

  printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
	  errors * 100.0 / (double) (1 << N2));
  fputs ("maximum error:   ", stdout);
  print_mpn_fp (maxerror, (FRAC / 4) + 1, 16);
  putchar ('\n');
  fputs ("error in exp(1): ", stdout);
  print_mpn_fp (e3, (FRAC / 4) + 1, 16);
  putchar ('\n');

  return failures == 0 ? 0 : 1;
}