1 | /* Copyright (C) 1997-2022 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 N 0 |
28 | #define N2 20 |
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 | /* These strings have exactly 100 hex digits in them. */ |
36 | static const char sin1[101] = |
37 | "d76aa47848677020c6e9e909c50f3c3289e511132f518b4def" |
38 | "b6ca5fd6c649bdfb0bd9ff1edcd4577655b5826a3d3b50c264" ; |
39 | static const char cos1[101] = |
40 | "8a51407da8345c91c2466d976871bd29a2373a894f96c3b7f2" |
41 | "300240b760e6fa96a94430a52d0e9e43f3450e3b8ff99bc934" ; |
42 | static const char hexdig[] = "0123456789abcdef" ; |
43 | |
44 | static void |
45 | print_mpn_hex (const mp_limb_t *x, unsigned size) |
46 | { |
47 | char value[size + 1]; |
48 | unsigned i; |
49 | const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size; |
50 | |
51 | memset (s: value, c: '0', n: size); |
52 | |
53 | for (i = 0; i < final ; i++) |
54 | value[size-1-i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf]; |
55 | |
56 | value[size] = '\0'; |
57 | fputs (s: value, stdout); |
58 | } |
59 | |
60 | static void |
61 | sincosx_mpn (mp1 si, mp1 co, mp1 xx, mp1 ix) |
62 | { |
63 | int i; |
64 | mp2 s[4], c[4]; |
65 | mp1 tmp, x; |
66 | |
67 | if (ix == NULL) |
68 | { |
69 | memset (s: si, c: 0, n: sizeof (mp1)); |
70 | memset (s: co, c: 0, n: sizeof (mp1)); |
71 | co[SZ-1] = 1; |
72 | memcpy (dest: x, src: xx, n: sizeof (mp1)); |
73 | } |
74 | else |
75 | mpn_sub_n (x, xx, ix, SZ); |
76 | |
77 | for (i = 0; i < 1 << N; i++) |
78 | { |
79 | #define add_shift_mulh(d,x,s1,s2,sh,n) \ |
80 | do { \ |
81 | if (s2 != NULL) { \ |
82 | if (sh > 0) { \ |
83 | assert (sh < mpbpl); \ |
84 | mpn_lshift (tmp, s1, SZ, sh); \ |
85 | if (n) \ |
86 | mpn_sub_n (tmp,tmp,s2+FRAC/mpbpl,SZ); \ |
87 | else \ |
88 | mpn_add_n (tmp,tmp,s2+FRAC/mpbpl,SZ); \ |
89 | } else { \ |
90 | if (n) \ |
91 | mpn_sub_n (tmp,s1,s2+FRAC/mpbpl,SZ); \ |
92 | else \ |
93 | mpn_add_n (tmp,s1,s2+FRAC/mpbpl,SZ); \ |
94 | } \ |
95 | mpn_mul_n(d,tmp,x,SZ); \ |
96 | } else \ |
97 | mpn_mul_n(d,s1,x,SZ); \ |
98 | assert(N+sh < mpbpl); \ |
99 | if (N+sh > 0) mpn_rshift(d,d,2*SZ,N+sh); \ |
100 | } while(0) |
101 | #define summ(d,ss,s,n) \ |
102 | do { \ |
103 | mpn_add_n(tmp,s[1]+FRAC/mpbpl,s[2]+FRAC/mpbpl,SZ); \ |
104 | mpn_lshift(tmp,tmp,SZ,1); \ |
105 | mpn_add_n(tmp,tmp,s[0]+FRAC/mpbpl,SZ); \ |
106 | mpn_add_n(tmp,tmp,s[3]+FRAC/mpbpl,SZ); \ |
107 | mpn_divmod_1(tmp,tmp,SZ,6); \ |
108 | if (n) \ |
109 | mpn_sub_n (d,ss,tmp,SZ); \ |
110 | else \ |
111 | mpn_add_n (d,ss,tmp,SZ); \ |
112 | } while (0) |
113 | |
114 | add_shift_mulh (s[0], x, co, NULL, 0, 0); /* s0 = h * c; */ |
115 | add_shift_mulh (c[0], x, si, NULL, 0, 0); /* c0 = h * s; */ |
116 | add_shift_mulh (s[1], x, co, c[0], 1, 1); /* s1 = h * (c - c0/2); */ |
117 | add_shift_mulh (c[1], x, si, s[0], 1, 0); /* c1 = h * (s + s0/2); */ |
118 | add_shift_mulh (s[2], x, co, c[1], 1, 1); /* s2 = h * (c - c1/2); */ |
119 | add_shift_mulh (c[2], x, si, s[1], 1, 0); /* c2 = h * (s + s1/2); */ |
120 | add_shift_mulh (s[3], x, co, c[2], 0, 1); /* s3 = h * (c - c2); */ |
121 | add_shift_mulh (c[3], x, si, s[2], 0, 0); /* c3 = h * (s + s2); */ |
122 | summ (si, si, s, 0); /* s = s + (s0+2*s1+2*s2+s3)/6; */ |
123 | summ (co, co, c, 1); /* c = c - (c0+2*c1+2*c2+c3)/6; */ |
124 | } |
125 | #undef add_shift_mulh |
126 | #undef summ |
127 | } |
128 | |
129 | static int |
130 | mpn_bitsize (const mp_limb_t *SRC_PTR, mp_size_t SIZE) |
131 | { |
132 | int i, j; |
133 | for (i = SIZE - 1; i > 0; i--) |
134 | if (SRC_PTR[i] != 0) |
135 | break; |
136 | for (j = mpbpl - 1; j >= 0; j--) |
137 | if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0) |
138 | break; |
139 | |
140 | return i * mpbpl + j; |
141 | } |
142 | |
143 | static int |
144 | do_test (void) |
145 | { |
146 | mp1 si, co, x, ox, xt, s2, c2, s3, c3; |
147 | int i; |
148 | int sin_errors = 0, cos_errors = 0; |
149 | int sin_failures = 0, cos_failures = 0; |
150 | mp1 sin_maxerror, cos_maxerror; |
151 | int sin_maxerror_s = 0, cos_maxerror_s = 0; |
152 | const double sf = pow (x: 2, mpbpl); |
153 | |
154 | /* assert(mpbpl == mp_bits_per_limb); */ |
155 | assert(FRAC / mpbpl * mpbpl == FRAC); |
156 | |
157 | memset (s: sin_maxerror, c: 0, n: sizeof (mp1)); |
158 | memset (s: cos_maxerror, c: 0, n: sizeof (mp1)); |
159 | memset (s: xt, c: 0, n: sizeof (mp1)); |
160 | xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl; |
161 | |
162 | for (i = 0; i < 1 << N2; i++) |
163 | { |
164 | int s2s, s3s, c2s, c3s, j; |
165 | double ds2,dc2; |
166 | |
167 | mpn_mul_1 (x, xt, SZ, i); |
168 | sincosx_mpn (si, co, xx: x, ix: i == 0 ? NULL : ox); |
169 | memcpy (dest: ox, src: x, n: sizeof (mp1)); |
170 | ds2 = sin (x: i / (double) (1 << N2)); |
171 | dc2 = cos (x: i / (double) (1 << N2)); |
172 | for (j = SZ-1; j >= 0; j--) |
173 | { |
174 | s2[j] = (mp_limb_t) ds2; |
175 | ds2 = (ds2 - s2[j]) * sf; |
176 | c2[j] = (mp_limb_t) dc2; |
177 | dc2 = (dc2 - c2[j]) * sf; |
178 | } |
179 | if (mpn_cmp (si, s2, SZ) >= 0) |
180 | mpn_sub_n (s3, si, s2, SZ); |
181 | else |
182 | mpn_sub_n (s3, s2, si, SZ); |
183 | if (mpn_cmp (co, c2, SZ) >= 0) |
184 | mpn_sub_n (c3, co, c2, SZ); |
185 | else |
186 | mpn_sub_n (c3, c2, co, SZ); |
187 | |
188 | s2s = mpn_bitsize (SRC_PTR: s2, SZ); |
189 | s3s = mpn_bitsize (SRC_PTR: s3, SZ); |
190 | c2s = mpn_bitsize (SRC_PTR: c2, SZ); |
191 | c3s = mpn_bitsize (SRC_PTR: c3, SZ); |
192 | if ((s3s >= 0 && s2s - s3s < 54) |
193 | || (c3s >= 0 && c2s - c3s < 54) |
194 | || 0) |
195 | { |
196 | #if PRINT_ERRORS |
197 | printf ("%06x " , i * (0x100000 / (1 << N2))); |
198 | print_mpn_hex(si, (FRAC / 4) + 1); |
199 | putchar (' '); |
200 | print_mpn_hex (co, (FRAC / 4) + 1); |
201 | putchar ('\n'); |
202 | fputs (" " , stdout); |
203 | print_mpn_hex (s2, (FRAC / 4) + 1); |
204 | putchar (' '); |
205 | print_mpn_hex (c2, (FRAC / 4) + 1); |
206 | putchar ('\n'); |
207 | printf (" %c%c " , |
208 | s3s >= 0 && s2s-s3s < 54 ? s2s - s3s == 53 ? 'e' : 'F' : 'P', |
209 | c3s >= 0 && c2s-c3s < 54 ? c2s - c3s == 53 ? 'e' : 'F' : 'P'); |
210 | print_mpn_hex (s3, (FRAC / 4) + 1); |
211 | putchar (' '); |
212 | print_mpn_hex (c3, (FRAC / 4) + 1); |
213 | putchar ('\n'); |
214 | #endif |
215 | sin_errors += s2s - s3s == 53; |
216 | cos_errors += c2s - c3s == 53; |
217 | sin_failures += s2s - s3s < 53; |
218 | cos_failures += c2s - c3s < 53; |
219 | } |
220 | if (s3s >= sin_maxerror_s |
221 | && mpn_cmp (s3, sin_maxerror, SZ) > 0) |
222 | { |
223 | memcpy (dest: sin_maxerror, src: s3, n: sizeof (mp1)); |
224 | sin_maxerror_s = s3s; |
225 | } |
226 | if (c3s >= cos_maxerror_s |
227 | && mpn_cmp (c3, cos_maxerror, SZ) > 0) |
228 | { |
229 | memcpy (dest: cos_maxerror, src: c3, n: sizeof (mp1)); |
230 | cos_maxerror_s = c3s; |
231 | } |
232 | } |
233 | |
234 | /* Check Range-Kutta against precomputed values of sin(1) and cos(1). */ |
235 | memset (s: x, c: 0, n: sizeof (mp1)); |
236 | x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl; |
237 | sincosx_mpn (si, co, xx: x, ix: ox); |
238 | |
239 | memset (s: s2, c: 0, n: sizeof (mp1)); |
240 | memset (s: c2, c: 0, n: sizeof (mp1)); |
241 | for (i = 0; i < 100 && i < FRAC / 4; i++) |
242 | { |
243 | s2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (s: hexdig, c: sin1[i]) |
244 | - hexdig) |
245 | << (FRAC - i * 4 - 4) % mpbpl); |
246 | c2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (s: hexdig, c: cos1[i]) |
247 | - hexdig) |
248 | << (FRAC - i * 4 - 4) % mpbpl); |
249 | } |
250 | |
251 | if (mpn_cmp (si, s2, SZ) >= 0) |
252 | mpn_sub_n (s3, si, s2, SZ); |
253 | else |
254 | mpn_sub_n (s3, s2, si, SZ); |
255 | if (mpn_cmp (co, c2, SZ) >= 0) |
256 | mpn_sub_n (c3, co, c2, SZ); |
257 | else |
258 | mpn_sub_n (c3, c2, co, SZ); |
259 | |
260 | printf (format: "sin:\n" ); |
261 | printf (format: "%d failures; %d errors; error rate %0.2f%%\n" , |
262 | sin_failures, sin_errors, sin_errors * 100.0 / (double) (1 << N2)); |
263 | fputs (s: "maximum error: " , stdout); |
264 | print_mpn_hex (x: sin_maxerror, size: (FRAC / 4) + 1); |
265 | fputs (s: "\nerror in sin(1): " , stdout); |
266 | print_mpn_hex (x: s3, size: (FRAC / 4) + 1); |
267 | |
268 | fputs (s: "\n\ncos:\n" , stdout); |
269 | printf (format: "%d failures; %d errors; error rate %0.2f%%\n" , |
270 | cos_failures, cos_errors, cos_errors * 100.0 / (double) (1 << N2)); |
271 | fputs (s: "maximum error: " , stdout); |
272 | print_mpn_hex (x: cos_maxerror, size: (FRAC / 4) + 1); |
273 | fputs (s: "\nerror in cos(1): " , stdout); |
274 | print_mpn_hex (x: c3, size: (FRAC / 4) + 1); |
275 | putchar (c: '\n'); |
276 | |
277 | return (sin_failures == 0 && cos_failures == 0) ? 0 : 1; |
278 | } |
279 | |
280 | #define TIMEOUT 600 |
281 | #define TEST_FUNCTION do_test () |
282 | #include "../test-skeleton.c" |
283 | |