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f46efa79 | 1 | /* -*-c-*- |
2 | * | |
f46efa79 | 3 | * Efficient reduction modulo nice primes |
4 | * | |
5 | * (c) 2004 Straylight/Edgeware | |
6 | */ | |
7 | ||
45c0fd36 | 8 | /*----- Licensing notice --------------------------------------------------* |
f46efa79 | 9 | * |
10 | * This file is part of Catacomb. | |
11 | * | |
12 | * Catacomb is free software; you can redistribute it and/or modify | |
13 | * it under the terms of the GNU Library General Public License as | |
14 | * published by the Free Software Foundation; either version 2 of the | |
15 | * License, or (at your option) any later version. | |
45c0fd36 | 16 | * |
f46efa79 | 17 | * Catacomb is distributed in the hope that it will be useful, |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
20 | * GNU Library General Public License for more details. | |
45c0fd36 | 21 | * |
f46efa79 | 22 | * You should have received a copy of the GNU Library General Public |
23 | * License along with Catacomb; if not, write to the Free | |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, | |
25 | * MA 02111-1307, USA. | |
26 | */ | |
27 | ||
f46efa79 | 28 | /*----- Header files ------------------------------------------------------*/ |
29 | ||
30 | #include <mLib/darray.h> | |
31 | #include <mLib/macros.h> | |
32 | ||
33 | #include "mp.h" | |
34 | #include "mpreduce.h" | |
35 | #include "mpreduce-exp.h" | |
36 | ||
37 | /*----- Data structures ---------------------------------------------------*/ | |
38 | ||
39 | DA_DECL(instr_v, mpreduce_instr); | |
40 | ||
21f82da4 MW |
41 | /*----- Theory ------------------------------------------------------------* |
42 | * | |
43 | * We're given a modulus %$p = 2^n - d$%, where %$d < 2^n$%, and some %$x$%, | |
44 | * and we want to compute %$x \bmod p$%. We work in base %$2^w$%, for some | |
45 | * appropriate %$w$%. The important observation is that | |
46 | * %$d \equiv 2^n \pmod p$%. | |
47 | * | |
48 | * Suppose %$x = x' + z 2^k$%, where %$k \ge n$%; then | |
49 | * %$x \equiv x' + d z 2^{k-n} \pmod p$%. We can use this to trim the | |
50 | * representation of %$x$%; each time, we reduce %$x$% by a mutliple of | |
51 | * %$2^{k-n} p$%. We can do this in two passes: firstly by taking whole | |
52 | * words off the top, and then (if necessary) by trimming the top word. | |
53 | * Finally, if %$p \le x < 2^n$% then %$0 \le x - p < p$% and we're done. | |
54 | * | |
55 | * A common trick, apparently, is to choose %$d$% such that it has a very | |
56 | * sparse non-adjacent form, and, moreover, that this form is nicely aligned | |
57 | * with common word sizes. (That is, write %$d = \sum_{0\le i<m} d_i 2^i$%, | |
58 | * with %$d_i \in \{ -1, 0, +1 \}$% and most %$d_i = 0$%.) Then adding | |
59 | * %$z d$% is a matter of adding and subtracting appropriately shifted copies | |
60 | * of %$z$%. | |
61 | * | |
62 | * Most libraries come with hardwired code for doing this for a few | |
63 | * well-known values of %$p$%. We take a different approach, for two | |
64 | * reasons. | |
65 | * | |
66 | * * Firstly, it privileges built-in numbers over user-selected ones, even | |
67 | * if the latter have the right (or better) properties. | |
68 | * | |
69 | * * Secondly, writing appropriately optimized reduction functions when we | |
70 | * don't know the exact characteristics of the target machine is rather | |
71 | * difficult. | |
72 | * | |
73 | * Our solution, then, is to `compile' the value %$p$% at runtime, into a | |
74 | * sequence of simple instructions for doing the reduction. | |
75 | */ | |
76 | ||
f46efa79 | 77 | /*----- Main code ---------------------------------------------------------*/ |
78 | ||
79 | /* --- @mpreduce_create@ --- * | |
80 | * | |
81 | * Arguments: @gfreduce *r@ = structure to fill in | |
82 | * @mp *x@ = an integer | |
83 | * | |
f4535c64 | 84 | * Returns: Zero if successful; nonzero on failure. |
f46efa79 | 85 | * |
86 | * Use: Initializes a context structure for reduction. | |
87 | */ | |
88 | ||
f4535c64 | 89 | int mpreduce_create(mpreduce *r, mp *p) |
f46efa79 | 90 | { |
91 | mpscan sc; | |
92 | enum { Z = 0, Z1 = 2, X = 4, X0 = 6 }; | |
93 | unsigned st = Z; | |
94 | instr_v iv = DA_INIT; | |
95 | unsigned long d, i; | |
96 | unsigned op; | |
c29970a7 | 97 | size_t w, b, bb; |
f46efa79 | 98 | |
99 | /* --- Fill in the easy stuff --- */ | |
100 | ||
f4535c64 | 101 | if (!MP_POSP(p)) |
102 | return (-1); | |
f46efa79 | 103 | d = mp_bits(p); |
104 | r->lim = d/MPW_BITS; | |
105 | r->s = d%MPW_BITS; | |
106 | if (r->s) | |
107 | r->lim++; | |
108 | r->p = mp_copy(p); | |
109 | ||
110 | /* --- Stash a new instruction --- */ | |
111 | ||
112 | #define INSTR(op_, argx_, argy_) do { \ | |
113 | DA_ENSURE(&iv, 1); \ | |
114 | DA(&iv)[DA_LEN(&iv)].op = (op_); \ | |
115 | DA(&iv)[DA_LEN(&iv)].argx = (argx_); \ | |
116 | DA(&iv)[DA_LEN(&iv)].argy = (argy_); \ | |
117 | DA_EXTEND(&iv, 1); \ | |
118 | } while (0) | |
119 | ||
120 | /* --- Main loop --- * | |
121 | * | |
122 | * A simple state machine decomposes @p@ conveniently into positive and | |
21f82da4 MW |
123 | * negative powers of 2. |
124 | * | |
125 | * Here's the relevant theory. The important observation is that | |
126 | * %$2^i = 2^{i+1} - 2^i$%, and hence | |
127 | * | |
128 | * * %$\sum_{a\le i<b} 2^i = 2^b - 2^a$%, and | |
129 | * | |
130 | * * %$2^c - 2^{b+1} + 2^b - 2^a = 2^c - 2^b - 2^a$%. | |
131 | * | |
132 | * The first of these gives us a way of combining a run of several one | |
133 | * bits, and the second gives us a way of handling a single-bit | |
134 | * interruption in such a run. | |
135 | * | |
136 | * We start with a number %$p = \sum_{0\le i<n} p_i 2^i$%, and scan | |
137 | * right-to-left using a simple state-machine keeping (approximate) track | |
138 | * of the two previous bits. The @Z@ states denote that we're in a string | |
139 | * of zeros; @Z1@ means that we just saw a 1 bit after a sequence of zeros. | |
140 | * Similarly, the @X@ states denote that we're in a string of ones; and | |
141 | * @X0@ means that we just saw a zero bit after a sequence of ones. The | |
142 | * state machine lets us delay decisions about what to do when we've seen a | |
143 | * change to the status quo (a one after a run of zeros, or vice-versa) | |
144 | * until we've seen the next bit, so we can tell whether this is an | |
145 | * isolated bit or the start of a new sequence. | |
146 | * | |
147 | * More formally: we define two functions %$Z^b_i$% and %$X^b_i$% as | |
148 | * follows. | |
149 | * | |
150 | * * %$Z^0_i(S, 0) = S$% | |
151 | * * %$Z^0_i(S, n) = Z^0_{i+1}(S, n)$% | |
152 | * * %$Z^0_i(S, n + 2^i) = Z^1_{i+1}(S, n)$% | |
153 | * * %$Z^1_i(S, n) = Z^0_{i+1}(S \cup \{ 2^{i-1} \}, n)$% | |
154 | * * %$Z^1_i(S, n + 2^i) = X^1_{i+1}(S \cup \{ -2^{i-1} \}, n)$% | |
155 | * * %$X^0_i(S, n) = Z^0_{i+1}(S, \{ 2^{i-1} \})$% | |
156 | * * %$X^0_i(S, n + 2^i) = X^1_{i+1}(S \cup \{ -2^{i-1} \}, n)$% | |
157 | * * %$X^1_i(S, n) = X^0_{i+1}(S, n)$% | |
158 | * * %$X^1_i(S, n + 2^i) = X^1_{i+1}(S, n)$% | |
159 | * | |
160 | * The reader may verify (by induction on %$n$%) that the following | |
161 | * properties hold. | |
162 | * | |
163 | * * %$Z^0_0(\emptyset, n)$% is well-defined for all %$n \ge 0$% | |
164 | * * %$\sum Z^b_i(S, n) = \sum S + n + b 2^{i-1}$% | |
165 | * * %$\sum X^b_i(S, n) = \sum S + n + (b + 1) 2^{i-1}$% | |
166 | * | |
167 | * From these, of course, we can deduce %$\sum Z^0_0(\emptyset, n) = n$%. | |
168 | * | |
169 | * We apply the above recurrence to build a simple instruction sequence for | |
170 | * adding an appropriate multiple of %$d$% to a given number. Suppose that | |
171 | * %$2^{w(N-1)} \le 2^{n-1} \le p < 2^n \le 2^{wN}$%. The machine which | |
172 | * interprets these instructions does so in the context of a | |
173 | * single-precision multiplicand @z@ and a pointer @v@ to the | |
174 | * %%\emph{most}%% significant word of an %$N + 1$%-word integer, and the | |
175 | * instruction sequence should add %$z d$% to this integer. | |
176 | * | |
177 | * The available instructions are named @MPRI_{ADD,SUB}{,LSL}@; they add | |
178 | * (or subtract) %$z$% (shifted left by some amount, in the @LSL@ variants) | |
179 | * to some word earlier than @v@. The relevant quantities are encoded in | |
180 | * the instruction's immediate operands. | |
f46efa79 | 181 | */ |
182 | ||
c29970a7 | 183 | bb = MPW_BITS - (d + 1)%MPW_BITS; |
bccb92dd | 184 | for (i = 0, mp_scan(&sc, p); i < d && mp_step(&sc); i++) { |
f46efa79 | 185 | switch (st | mp_bit(&sc)) { |
186 | case Z | 1: st = Z1; break; | |
45c0fd36 MW |
187 | case Z1 | 0: st = Z; op = MPRI_SUB; goto instr; |
188 | case Z1 | 1: st = X; op = MPRI_ADD; goto instr; | |
f46efa79 | 189 | case X | 0: st = X0; break; |
45c0fd36 MW |
190 | case X0 | 1: st = X; op = MPRI_ADD; goto instr; |
191 | case X0 | 0: st = Z; op = MPRI_SUB; goto instr; | |
f46efa79 | 192 | instr: |
193 | w = (d - i)/MPW_BITS + 1; | |
c29970a7 | 194 | b = (bb + i)%MPW_BITS; |
f46efa79 | 195 | INSTR(op | !!b, w, b); |
196 | } | |
197 | } | |
21f82da4 MW |
198 | |
199 | /* --- This doesn't always work --- * | |
200 | * | |
201 | * If %$d \ge 2^{n-1}$% then the above recurrence will output a subtraction | |
202 | * as the final instruction, which may sometimes underflow. (It interprets | |
203 | * such numbers as being in the form %$2^{n-1} + d$%.) This is clearly | |
204 | * bad, so detect the situation and fail gracefully. | |
205 | */ | |
206 | ||
cd9aae84 | 207 | if (DA_LEN(&iv) && (DA(&iv)[DA_LEN(&iv) - 1].op & ~1u) == MPRI_SUB) { |
f4535c64 | 208 | mp_drop(r->p); |
209 | DA_DESTROY(&iv); | |
210 | return (-1); | |
f46efa79 | 211 | } |
212 | ||
213 | #undef INSTR | |
214 | ||
21f82da4 MW |
215 | /* --- Wrap up --- * |
216 | * | |
217 | * Store the generated instruction sequence in our context structure. If | |
218 | * %$p$%'s bit length %$n$% is a multiple of the word size %$w$% then | |
219 | * there's nothing much else to do here. Otherwise, we have an additional | |
220 | * job. | |
221 | * | |
222 | * The reduction operation has three phases. The first trims entire words | |
223 | * from the argument, and the instruction sequence constructed above does | |
224 | * this well; the second phase reduces an integer which has the same number | |
225 | * of words as %$p$%, but strictly more bits. (The third phase is a single | |
226 | * conditional subtraction of %$p$%, in case the argument is the same bit | |
227 | * length as %$p$% but greater; this doesn't concern us here.) To handle | |
228 | * the second phase, we create another copy of the instruction stream, with | |
229 | * all of the target shifts adjusted upwards by %$s = n \bmod w$%. | |
230 | * | |
231 | * In this case, we are acting on an %$(N - 1)$%-word operand, and so | |
232 | * (given the remarks above) must check that this is still valid, but a | |
233 | * moment's reflection shows that this must be fine: the most distant | |
234 | * target must be the bit %$s$% from the top of the least-significant word; | |
235 | * but since we shift all of the targets up by %$s$%, this now addresses | |
236 | * the bottom bit of the next most significant word, and there is no | |
237 | * underflow. | |
238 | */ | |
f46efa79 | 239 | |
240 | r->in = DA_LEN(&iv); | |
cd9aae84 MW |
241 | if (!r->in) |
242 | r->iv = 0; | |
243 | else if (!r->s) { | |
f46efa79 | 244 | r->iv = xmalloc(r->in * sizeof(mpreduce_instr)); |
245 | memcpy(r->iv, DA(&iv), r->in * sizeof(mpreduce_instr)); | |
246 | } else { | |
247 | r->iv = xmalloc(r->in * 2 * sizeof(mpreduce_instr)); | |
248 | for (i = 0; i < r->in; i++) { | |
249 | r->iv[i] = DA(&iv)[i]; | |
250 | op = r->iv[i].op & ~1u; | |
251 | w = r->iv[i].argx; | |
252 | b = r->iv[i].argy; | |
253 | b += r->s; | |
254 | if (b >= MPW_BITS) { | |
255 | b -= MPW_BITS; | |
256 | w--; | |
257 | } | |
258 | if (b) op |= 1; | |
259 | r->iv[i + r->in].op = op; | |
260 | r->iv[i + r->in].argx = w; | |
261 | r->iv[i + r->in].argy = b; | |
262 | } | |
263 | } | |
f4535c64 | 264 | DA_DESTROY(&iv); |
c29970a7 | 265 | |
f4535c64 | 266 | return (0); |
f46efa79 | 267 | } |
268 | ||
269 | /* --- @mpreduce_destroy@ --- * | |
270 | * | |
271 | * Arguments: @mpreduce *r@ = structure to free | |
272 | * | |
273 | * Returns: --- | |
274 | * | |
275 | * Use: Reclaims the resources from a reduction context. | |
276 | */ | |
277 | ||
278 | void mpreduce_destroy(mpreduce *r) | |
279 | { | |
280 | mp_drop(r->p); | |
cd9aae84 | 281 | if (r->iv) xfree(r->iv); |
f46efa79 | 282 | } |
283 | ||
284 | /* --- @mpreduce_dump@ --- * | |
285 | * | |
286 | * Arguments: @mpreduce *r@ = structure to dump | |
287 | * @FILE *fp@ = file to dump on | |
288 | * | |
289 | * Returns: --- | |
290 | * | |
291 | * Use: Dumps a reduction context. | |
292 | */ | |
293 | ||
294 | void mpreduce_dump(mpreduce *r, FILE *fp) | |
295 | { | |
296 | size_t i; | |
297 | static const char *opname[] = { "add", "addshift", "sub", "subshift" }; | |
298 | ||
299 | fprintf(fp, "mod = "); mp_writefile(r->p, fp, 16); | |
300 | fprintf(fp, "\n lim = %lu; s = %d\n", (unsigned long)r->lim, r->s); | |
301 | for (i = 0; i < r->in; i++) { | |
302 | assert(r->iv[i].op < N(opname)); | |
303 | fprintf(fp, " %s %lu %lu\n", | |
304 | opname[r->iv[i].op], | |
305 | (unsigned long)r->iv[i].argx, | |
306 | (unsigned long)r->iv[i].argy); | |
307 | } | |
308 | if (r->s) { | |
309 | fprintf(fp, "tail end charlie\n"); | |
310 | for (i = r->in; i < 2 * r->in; i++) { | |
311 | assert(r->iv[i].op < N(opname)); | |
312 | fprintf(fp, " %s %lu %lu\n", | |
313 | opname[r->iv[i].op], | |
314 | (unsigned long)r->iv[i].argx, | |
315 | (unsigned long)r->iv[i].argy); | |
316 | } | |
317 | } | |
318 | } | |
319 | ||
320 | /* --- @mpreduce_do@ --- * | |
321 | * | |
322 | * Arguments: @mpreduce *r@ = reduction context | |
323 | * @mp *d@ = destination | |
324 | * @mp *x@ = source | |
325 | * | |
326 | * Returns: Destination, @x@ reduced modulo the reduction poly. | |
327 | */ | |
328 | ||
329 | static void run(const mpreduce_instr *i, const mpreduce_instr *il, | |
330 | mpw *v, mpw z) | |
331 | { | |
332 | for (; i < il; i++) { | |
f46efa79 | 333 | switch (i->op) { |
334 | case MPRI_ADD: MPX_UADDN(v - i->argx, v + 1, z); break; | |
335 | case MPRI_ADDLSL: mpx_uaddnlsl(v - i->argx, v + 1, z, i->argy); break; | |
336 | case MPRI_SUB: MPX_USUBN(v - i->argx, v + 1, z); break; | |
337 | case MPRI_SUBLSL: mpx_usubnlsl(v - i->argx, v + 1, z, i->argy); break; | |
338 | default: | |
339 | abort(); | |
340 | } | |
f46efa79 | 341 | } |
342 | } | |
343 | ||
344 | mp *mpreduce_do(mpreduce *r, mp *d, mp *x) | |
345 | { | |
346 | mpw *v, *vl; | |
347 | const mpreduce_instr *il; | |
348 | mpw z; | |
349 | ||
f46efa79 | 350 | /* --- If source is negative, divide --- */ |
351 | ||
a69a3efd | 352 | if (MP_NEGP(x)) { |
f46efa79 | 353 | mp_div(0, &d, x, r->p); |
354 | return (d); | |
355 | } | |
356 | ||
357 | /* --- Try to reuse the source's space --- */ | |
358 | ||
359 | MP_COPY(x); | |
360 | if (d) MP_DROP(d); | |
361 | MP_DEST(x, MP_LEN(x), x->f); | |
362 | ||
21f82da4 | 363 | /* --- Stage one: trim excess words from the most significant end --- */ |
f46efa79 | 364 | |
f46efa79 | 365 | il = r->iv + r->in; |
366 | if (MP_LEN(x) >= r->lim) { | |
367 | v = x->v + r->lim; | |
368 | vl = x->vl; | |
369 | while (vl-- > v) { | |
370 | while (*vl) { | |
371 | z = *vl; | |
372 | *vl = 0; | |
373 | run(r->iv, il, vl, z); | |
f46efa79 | 374 | } |
375 | } | |
21f82da4 MW |
376 | |
377 | /* --- Stage two: trim excess bits from the most significant word --- */ | |
378 | ||
f46efa79 | 379 | if (r->s) { |
380 | while (*vl >> r->s) { | |
381 | z = *vl >> r->s; | |
382 | *vl &= ((1 << r->s) - 1); | |
383 | run(r->iv + r->in, il + r->in, vl, z); | |
f46efa79 | 384 | } |
385 | } | |
386 | } | |
387 | ||
21f82da4 | 388 | /* --- Stage three: conditional subtraction --- */ |
f46efa79 | 389 | |
390 | MP_SHRINK(x); | |
391 | if (MP_CMP(x, >=, r->p)) | |
392 | x = mp_sub(x, x, r->p); | |
393 | ||
394 | /* --- Done --- */ | |
395 | ||
f46efa79 | 396 | return (x); |
397 | } | |
398 | ||
399 | /* --- @mpreduce_exp@ --- * | |
400 | * | |
401 | * Arguments: @mpreduce *mr@ = pointer to reduction context | |
45c0fd36 MW |
402 | * @mp *d@ = fake destination |
403 | * @mp *a@ = base | |
404 | * @mp *e@ = exponent | |
f46efa79 | 405 | * |
45c0fd36 | 406 | * Returns: Result, %$a^e \bmod m$%. |
f46efa79 | 407 | */ |
408 | ||
409 | mp *mpreduce_exp(mpreduce *mr, mp *d, mp *a, mp *e) | |
410 | { | |
411 | mp *x = MP_ONE; | |
412 | mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW; | |
413 | ||
414 | MP_SHRINK(e); | |
a69a3efd | 415 | MP_COPY(a); |
416 | if (MP_ZEROP(e)) | |
f46efa79 | 417 | ; |
a69a3efd | 418 | else { |
419 | if (MP_NEGP(e)) | |
420 | a = mp_modinv(a, a, mr->p); | |
421 | if (MP_LEN(e) < EXP_THRESH) | |
422 | EXP_SIMPLE(x, a, e); | |
423 | else | |
424 | EXP_WINDOW(x, a, e); | |
425 | } | |
426 | mp_drop(a); | |
f46efa79 | 427 | mp_drop(d); |
428 | mp_drop(spare); | |
429 | return (x); | |
430 | } | |
431 | ||
432 | /*----- Test rig ----------------------------------------------------------*/ | |
433 | ||
434 | ||
435 | #ifdef TEST_RIG | |
436 | ||
437 | #define MP(x) mp_readstring(MP_NEW, #x, 0, 0) | |
438 | ||
439 | static int vreduce(dstr *v) | |
440 | { | |
441 | mp *d = *(mp **)v[0].buf; | |
442 | mp *n = *(mp **)v[1].buf; | |
443 | mp *r = *(mp **)v[2].buf; | |
444 | mp *c; | |
445 | int ok = 1; | |
446 | mpreduce rr; | |
447 | ||
448 | mpreduce_create(&rr, d); | |
449 | c = mpreduce_do(&rr, MP_NEW, n); | |
450 | if (!MP_EQ(c, r)) { | |
451 | fprintf(stderr, "\n*** reduction failed\n*** "); | |
452 | mpreduce_dump(&rr, stderr); | |
453 | fprintf(stderr, "\n*** n = "); mp_writefile(n, stderr, 10); | |
454 | fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 10); | |
455 | fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 10); | |
456 | fprintf(stderr, "\n"); | |
457 | ok = 0; | |
458 | } | |
459 | mpreduce_destroy(&rr); | |
460 | mp_drop(n); mp_drop(d); mp_drop(r); mp_drop(c); | |
461 | assert(mparena_count(MPARENA_GLOBAL) == 0); | |
462 | return (ok); | |
463 | } | |
464 | ||
465 | static int vmodexp(dstr *v) | |
466 | { | |
467 | mp *p = *(mp **)v[0].buf; | |
468 | mp *g = *(mp **)v[1].buf; | |
469 | mp *x = *(mp **)v[2].buf; | |
470 | mp *r = *(mp **)v[3].buf; | |
471 | mp *c; | |
472 | int ok = 1; | |
473 | mpreduce rr; | |
474 | ||
475 | mpreduce_create(&rr, p); | |
476 | c = mpreduce_exp(&rr, MP_NEW, g, x); | |
477 | if (!MP_EQ(c, r)) { | |
478 | fprintf(stderr, "\n*** modexp failed\n*** "); | |
479 | fprintf(stderr, "\n*** p = "); mp_writefile(p, stderr, 10); | |
480 | fprintf(stderr, "\n*** g = "); mp_writefile(g, stderr, 10); | |
481 | fprintf(stderr, "\n*** x = "); mp_writefile(x, stderr, 10); | |
482 | fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 10); | |
483 | fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 10); | |
484 | fprintf(stderr, "\n"); | |
485 | ok = 0; | |
486 | } | |
487 | mpreduce_destroy(&rr); | |
488 | mp_drop(p); mp_drop(g); mp_drop(r); mp_drop(x); mp_drop(c); | |
489 | assert(mparena_count(MPARENA_GLOBAL) == 0); | |
490 | return (ok); | |
491 | } | |
492 | ||
493 | static test_chunk defs[] = { | |
494 | { "reduce", vreduce, { &type_mp, &type_mp, &type_mp, 0 } }, | |
495 | { "modexp", vmodexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, | |
496 | { 0, 0, { 0 } } | |
497 | }; | |
498 | ||
499 | int main(int argc, char *argv[]) | |
500 | { | |
0f00dc4c | 501 | test_run(argc, argv, defs, SRCDIR"/t/mpreduce"); |
f46efa79 | 502 | return (0); |
503 | } | |
504 | ||
505 | #endif | |
506 | ||
507 | /*----- That's all, folks -------------------------------------------------*/ |