1 /* Copyright (C) 1997-2023 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"