about summary refs log tree commit diff
path: root/math/atest-exp.c
blob: 158be4231ac79a53095ecf928de58c00af718f45 (plain) (blame)
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
/* Copyright (C) 1997, 1998, 2000 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 Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 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
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; 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>

#define PRINT_ERRORS 0

#define TOL 80
#define N2 17
#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 hexdig[] = "0123456789abcdef";

static void
print_mpn_hex (const mp_limb_t *x, unsigned size)
{
   char value[size + 1];
   unsigned i;
   const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;

   memset (value, '0', size);

   for (i = 0; i < final ; i++)
     value[size - 1 - i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];

   value[size] = '\0';
   fputs (value, stdout);
}

static void
exp_mpn (mp1 ex, mp1 x)
{
   unsigned 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] = (mp_limb_t)1 << FRAC % mpbpl;
   memset (tol,0, sizeof (mp1));
   tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)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);
}

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] & (mp_limb_t)1 << j) != 0)
       break;

   return i * mpbpl + 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] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;

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

      mpn_mul_1 (x,xt,SZ,i);
      exp_mpn (ex, x);
      de2 = exp (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 >= 0 && e2s - e3s < 54)
	{
#if PRINT_ERRORS
	  printf ("%06x ", i * (0x100000 / (1 << N2)));
	  print_mpn_hex (ex, (FRAC / 4) + 1);
	  fputs ("\n       ",stdout);
	  print_mpn_hex (e2, (FRAC / 4) + 1);
	  printf ("\n %c     ",
		  e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
	  print_mpn_hex (e3, (FRAC / 4) + 1);
	  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] = (mp_limb_t)1 << FRAC % mpbpl;
   exp_mpn (ex, x);

   memset (e2, '\0', sizeof (mp1));
   for (i = -1; i < 100 && i < FRAC / 4; i++)
     e2[(FRAC - i * 4 - 4) / mpbpl] |= ((strchr (hexdig, exp1[i + 1]) - hexdig)
					<< (FRAC - i * 4 - 4) % mpbpl);

   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_hex (maxerror, (FRAC / 4) + 1);
   fputs ("\nerror in exp(1): ", stdout);
   print_mpn_hex (e3, (FRAC / 4) + 1);
   putchar ('\n');

   return failures == 0 ? 0 : 1;
}