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 #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"