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1 | /* Copyright (C) 1997 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 Library General Public License as | |
7 | published by the Free Software Foundation; either version 2 of the | |
8 | 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 | Library General Public License for more details. | |
14 | ||
15 | You should have received a copy of the GNU Library General Public | |
16 | License along with the GNU C Library; see the file COPYING.LIB. If not, | |
17 | write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, | |
18 | Boston, MA 02111-1307, USA. */ | |
19 | ||
20 | #include <stdio.h> | |
21 | #include <math.h> | |
a2b08ee5 | 22 | #include <stdlib/gmp.h> |
650425ce UD |
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 | 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 | 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] |= (strchr (hexdig, str[i + 1]) - hexdig | |
77 | << (FRAC - i * 4 - 4) % mpbpl); | |
78 | } | |
79 | ||
80 | static mp_limb_t *get_log2(void) __attribute__((const)); | |
81 | static mp_limb_t * | |
82 | get_log2(void) | |
83 | { | |
84 | static mp1 log2_m; | |
85 | static int log2_m_inited = 0; | |
86 | static const char log2[102] = "0" /* point */ | |
87 | "b17217f7d1cf79abc9e3b39803f2f6af40f343267298b62d8a" | |
88 | "0d175b8baafa2be7b876206debac98559552fb4afa1b10ed2e"; | |
89 | ||
90 | if (!log2_m_inited) | |
91 | { | |
92 | read_mpn_hex (log2_m, log2); | |
93 | log2_m_inited = 1; | |
94 | } | |
95 | return log2_m; | |
96 | } | |
97 | ||
98 | /* Compute e^x. */ | |
99 | void | |
100 | exp_mpn (mp1 ex, mp1 x) | |
101 | { | |
102 | unsigned int n; | |
103 | mp1 xp; | |
104 | mp2 tmp; | |
105 | mp_limb_t chk, round; | |
106 | mp1 tol; | |
107 | ||
108 | memset (xp, 0, sizeof (mp1)); | |
109 | memset (ex, 0, sizeof (mp1)); | |
110 | xp[FRAC / mpbpl] = 1 << FRAC % mpbpl; | |
111 | memset (tol, 0, sizeof (mp1)); | |
112 | tol[(FRAC - TOL) / mpbpl] = 1 << (FRAC - TOL) % mpbpl; | |
113 | ||
114 | n = 0; | |
115 | ||
116 | do | |
117 | { | |
118 | /* Calculate sum(x^n/n!) until the next term is sufficiently small. */ | |
119 | ||
120 | mpn_mul_n (tmp, xp, x, SZ); | |
121 | assert(tmp[SZ * 2 - 1] == 0); | |
122 | if (n > 0) | |
123 | round = mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n); | |
124 | chk = mpn_add_n (ex, ex, xp, SZ); | |
125 | assert (chk == 0); | |
126 | ++n; | |
127 | assert (n < 80); /* Catch too-high TOL. */ | |
128 | } | |
129 | while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0); | |
130 | } | |
131 | ||
132 | /* Calculate 2^x. */ | |
133 | void | |
134 | exp2_mpn (mp1 ex, mp1 x) | |
135 | { | |
136 | mp2 tmp; | |
137 | mpn_mul_n (tmp, x, get_log2 (), SZ); | |
138 | assert(tmp[SZ * 2 - 1] == 0); | |
139 | exp_mpn (ex, tmp + FRAC / mpbpl); | |
140 | } | |
141 | ||
142 | ||
143 | static int | |
144 | mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE) | |
145 | { | |
146 | int i, j; | |
147 | for (i = SIZE - 1; i > 0; --i) | |
148 | if (SRC_PTR[i] != 0) | |
149 | break; | |
150 | for (j = mpbpl - 1; j > 0; --j) | |
151 | if ((SRC_PTR[i] & 1 << j) != 0) | |
152 | break; | |
153 | ||
154 | return i * 32 + j; | |
155 | } | |
156 | ||
157 | int | |
158 | main (void) | |
159 | { | |
160 | mp1 ex, x, xt, e2, e3; | |
161 | int i; | |
162 | int errors = 0; | |
163 | int failures = 0; | |
164 | mp1 maxerror; | |
165 | int maxerror_s = 0; | |
166 | const double sf = pow (2, mpbpl); | |
167 | ||
168 | /* assert(mpbpl == mp_bits_per_limb); */ | |
169 | assert(FRAC / mpbpl * mpbpl == FRAC); | |
170 | ||
171 | memset (maxerror, 0, sizeof (mp1)); | |
172 | memset (xt, 0, sizeof (mp1)); | |
173 | xt[(FRAC - N2) / mpbpl] = 1 << (FRAC - N2) % mpbpl; | |
174 | ||
175 | for (i = 0; i < (1 << N2); ++i) | |
176 | { | |
177 | int e2s, e3s, j; | |
178 | double de2; | |
179 | ||
180 | mpn_mul_1 (x, xt, SZ, i); | |
181 | exp2_mpn (ex, x); | |
182 | de2 = exp2 (i / (double) (1 << N2)); | |
183 | for (j = SZ - 1; j >= 0; --j) | |
184 | { | |
185 | e2[j] = (mp_limb_t) de2; | |
186 | de2 = (de2 - e2[j]) * sf; | |
187 | } | |
188 | if (mpn_cmp (ex, e2, SZ) >= 0) | |
189 | mpn_sub_n (e3, ex, e2, SZ); | |
190 | else | |
191 | mpn_sub_n (e3, e2, ex, SZ); | |
192 | ||
193 | e2s = mpn_bitsize (e2, SZ); | |
194 | e3s = mpn_bitsize (e3, SZ); | |
195 | if (e3s > 1 && e2s - e3s < 54) | |
196 | { | |
197 | #if PRINT_ERRORS | |
198 | printf ("%06x ", i * (0x100000 / (1 << N2))); | |
199 | print_mpn_fp (ex, (FRAC / 4) + 1, 16); | |
200 | putchar ('\n'); | |
201 | fputs (" ",stdout); | |
202 | print_mpn_fp (e2, (FRAC / 4) + 1, 16); | |
203 | putchar ('\n'); | |
204 | printf (" %c ", | |
205 | e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P'); | |
206 | print_mpn_fp (e3, (FRAC / 4) + 1, 16); | |
207 | putchar ('\n'); | |
208 | #endif | |
209 | errors += (e2s - e3s == 53); | |
210 | failures += (e2s - e3s < 53); | |
211 | } | |
212 | if (e3s >= maxerror_s | |
213 | && mpn_cmp (e3, maxerror, SZ) > 0) | |
214 | { | |
215 | memcpy (maxerror, e3, sizeof (mp1)); | |
216 | maxerror_s = e3s; | |
217 | } | |
218 | } | |
219 | ||
220 | /* Check exp_mpn against precomputed value of exp(1). */ | |
221 | memset (x, 0, sizeof (mp1)); | |
222 | x[FRAC / mpbpl] = 1 << FRAC % mpbpl; | |
223 | exp_mpn (ex, x); | |
224 | read_mpn_hex (e2, exp1); | |
225 | if (mpn_cmp (ex, e2, SZ) >= 0) | |
226 | mpn_sub_n (e3, ex, e2, SZ); | |
227 | else | |
228 | mpn_sub_n (e3, e2, ex, SZ); | |
229 | ||
230 | printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors, | |
231 | errors * 100.0 / (double) (1 << N2)); | |
232 | fputs ("maximum error: ", stdout); | |
233 | print_mpn_fp (maxerror, (FRAC / 4) + 1, 16); | |
234 | putchar ('\n'); | |
235 | fputs ("error in exp(1): ", stdout); | |
236 | print_mpn_fp (e3, (FRAC / 4) + 1, 16); | |
237 | putchar ('\n'); | |
238 | ||
239 | return failures == 0 ? 0 : 1; | |
240 | } |