d03ab969 |
1 | /* -*-c-*- |
2 | * |
d34decd2 |
3 | * $Id: mp.h,v 1.7 2000/06/17 11:45:09 mdw Exp $ |
d03ab969 |
4 | * |
d3409d5e |
5 | * Simple multiprecision arithmetic |
d03ab969 |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: mp.h,v $ |
d34decd2 |
33 | * Revision 1.7 2000/06/17 11:45:09 mdw |
34 | * Major memory management overhaul. Added arena support. Use the secure |
35 | * arena for secret integers. Replace and improve the MP management macros |
36 | * (e.g., replace MP_MODIFY by MP_DEST). |
37 | * |
d9a8ae10 |
38 | * Revision 1.6 1999/12/10 23:19:46 mdw |
39 | * Minor bugfixes. New interface for suggested destinations. |
40 | * |
5b00a0ea |
41 | * Revision 1.5 1999/11/22 20:50:37 mdw |
42 | * Add support for computing Jacobi symbols. |
43 | * |
24e1e862 |
44 | * Revision 1.4 1999/11/21 22:13:02 mdw |
45 | * Add mp version of MPX_BITS. |
46 | * |
a790733d |
47 | * Revision 1.3 1999/11/19 13:19:14 mdw |
48 | * Fix const annotation. |
49 | * |
d3409d5e |
50 | * Revision 1.2 1999/11/17 18:02:16 mdw |
51 | * New multiprecision integer arithmetic suite. |
d03ab969 |
52 | * |
53 | */ |
54 | |
d9a8ae10 |
55 | #ifndef CATACOMB_MP_H |
56 | #define CATACOMB_MP_H |
d03ab969 |
57 | |
58 | #ifdef __cplusplus |
59 | extern "C" { |
60 | #endif |
61 | |
62 | /*----- Header files ------------------------------------------------------*/ |
63 | |
d3409d5e |
64 | #include <assert.h> |
d03ab969 |
65 | #include <string.h> |
66 | |
d3409d5e |
67 | #include <mLib/sub.h> |
68 | |
d9a8ae10 |
69 | #ifndef CATACOMB_MPW_H |
d3409d5e |
70 | # include "mpw.h" |
d03ab969 |
71 | #endif |
72 | |
d34decd2 |
73 | #ifndef CATACOMB_ARENA_H |
74 | # include "arena.h" |
75 | #endif |
76 | |
77 | #ifndef CATACOMB_MPARENA_H |
78 | # include "mparena.h" |
79 | #endif |
80 | |
d9a8ae10 |
81 | #ifndef CATACOMB_MPX_H |
d03ab969 |
82 | # include "mpx.h" |
83 | #endif |
84 | |
d03ab969 |
85 | /*----- Data structures ---------------------------------------------------*/ |
86 | |
87 | typedef struct mp { |
d3409d5e |
88 | mpw *v, *vl; |
89 | size_t sz; |
d34decd2 |
90 | mparena *a; |
d3409d5e |
91 | unsigned f; |
92 | unsigned ref; |
d03ab969 |
93 | } mp; |
94 | |
d3409d5e |
95 | #define MP_NEG 1u |
96 | #define MP_BURN 2u |
97 | #define MP_CONST 4u |
98 | #define MP_UNDEF 8u |
d9a8ae10 |
99 | #define MP_DESTROYED 16u |
d03ab969 |
100 | |
d3409d5e |
101 | /*----- Useful constants --------------------------------------------------*/ |
d03ab969 |
102 | |
d3409d5e |
103 | extern mp mp_const[]; |
d03ab969 |
104 | |
d3409d5e |
105 | #define MP_ZERO (&mp_const[0]) |
106 | #define MP_ONE (&mp_const[1]) |
107 | #define MP_TWO (&mp_const[2]) |
108 | #define MP_THREE (&mp_const[3]) |
109 | #define MP_FOUR (&mp_const[4]) |
110 | #define MP_FIVE (&mp_const[5]) |
111 | #define MP_TEN (&mp_const[6]) |
d34decd2 |
112 | #define MP_256 (&mp_const[7]) |
113 | #define MP_MONE (&mp_const[8]) |
d03ab969 |
114 | |
d3409d5e |
115 | #define MP_NEW ((mp *)0) |
d34decd2 |
116 | #define MP_NEWSEC (&mp_const[9]) |
d03ab969 |
117 | |
d34decd2 |
118 | /*----- Trivial macros ----------------------------------------------------*/ |
d03ab969 |
119 | |
d34decd2 |
120 | /* --- @MP_LEN@ --- * |
d03ab969 |
121 | * |
d34decd2 |
122 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
123 | * |
d34decd2 |
124 | * Returns: Length of the integer, in words. |
d03ab969 |
125 | */ |
126 | |
d34decd2 |
127 | #define MP_LEN(m) ((m)->vl - ((m)->v)) |
d03ab969 |
128 | |
d34decd2 |
129 | /*----- Memory management and reference counting --------------------------*/ |
d3409d5e |
130 | |
d34decd2 |
131 | /* --- @mp_new@ --- * |
d03ab969 |
132 | * |
d34decd2 |
133 | * Arguments: @size_t sz@ = size of vector required |
134 | * @unsigned f@ = flags to set |
d03ab969 |
135 | * |
d34decd2 |
136 | * Returns: Pointer to a new MP structure. |
d03ab969 |
137 | * |
d34decd2 |
138 | * Use: Allocates a new multiprecision integer. The data space is |
139 | * allocated from either the standard global or secret arena, |
140 | * depending on the initial flags requested. |
d03ab969 |
141 | */ |
142 | |
d34decd2 |
143 | extern mp *mp_new(size_t /*sz*/, unsigned /*f*/); |
d03ab969 |
144 | |
d34decd2 |
145 | /* --- @mp_create@ --- * |
d03ab969 |
146 | * |
d34decd2 |
147 | * Arguments: @size_t sz@ = size of vector required |
d03ab969 |
148 | * |
d34decd2 |
149 | * Returns: Pointer to pristine new MP structure with enough memory |
150 | * bolted onto it. |
151 | * |
152 | * Use: Creates a new multiprecision integer with indeterminate |
153 | * contents. The integer has a single reference. |
d03ab969 |
154 | */ |
155 | |
d34decd2 |
156 | extern mp *mp_create(size_t /*sz*/); |
d3409d5e |
157 | |
d34decd2 |
158 | /* --- @mp_createsecure@ --- * |
d03ab969 |
159 | * |
d3409d5e |
160 | * Arguments: @size_t sz@ = size of vector required |
d03ab969 |
161 | * |
d3409d5e |
162 | * Returns: Pointer to pristine new MP structure with enough memory |
163 | * bolted onto it. |
d03ab969 |
164 | * |
d3409d5e |
165 | * Use: Creates a new multiprecision integer with indeterminate |
d34decd2 |
166 | * contents. The integer has a single reference. The integer's |
167 | * data space is allocated from the secure arena. Its burn flag |
168 | * is set. |
d03ab969 |
169 | */ |
170 | |
d34decd2 |
171 | extern mp *mp_createsecure(size_t /*sz*/); |
d03ab969 |
172 | |
d3409d5e |
173 | /* --- @mp_build@ --- * |
d03ab969 |
174 | * |
d3409d5e |
175 | * Arguments: @mp *m@ = pointer to an MP block to fill in |
176 | * @mpw *v@ = pointer to a word array |
177 | * @mpw *vl@ = pointer just past end of array |
d03ab969 |
178 | * |
179 | * Returns: --- |
180 | * |
d3409d5e |
181 | * Use: Creates a multiprecision integer representing some smallish |
182 | * number. You must provide storage for the number and dispose |
183 | * of it when you've finished with it. The number is marked as |
184 | * constant while it exists. |
d03ab969 |
185 | */ |
186 | |
d3409d5e |
187 | extern void mp_build(mp */*m*/, mpw */*v*/, mpw */*vl*/); |
d03ab969 |
188 | |
d3409d5e |
189 | /* --- @mp_destroy@ --- * |
d03ab969 |
190 | * |
d3409d5e |
191 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
192 | * |
193 | * Returns: --- |
194 | * |
d3409d5e |
195 | * Use: Destroys a multiprecision integer. The reference count isn't |
196 | * checked. Don't use this function if you don't know what |
197 | * you're doing: use @mp_drop@ instead. |
d03ab969 |
198 | */ |
199 | |
d3409d5e |
200 | extern void mp_destroy(mp */*m*/); |
d03ab969 |
201 | |
d3409d5e |
202 | /* --- @mp_copy@ --- * |
d03ab969 |
203 | * |
d3409d5e |
204 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
205 | * |
d3409d5e |
206 | * Returns: A copy of the given multiprecision integer. |
207 | * |
208 | * Use: Copies the given integer. In fact you just get another |
209 | * reference to the same old one again. |
d03ab969 |
210 | */ |
211 | |
d3409d5e |
212 | extern mp *mp_copy(mp */*m*/); |
d03ab969 |
213 | |
d3409d5e |
214 | #define MP_COPY(m) ((m)->ref++, (m)) |
215 | |
216 | /* --- @mp_drop@ --- * |
d03ab969 |
217 | * |
d3409d5e |
218 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
219 | * |
220 | * Returns: --- |
221 | * |
d3409d5e |
222 | * Use: Drops a reference to an integer which isn't wanted any more. |
223 | * If there are no more references, the integer is destroyed. |
d03ab969 |
224 | */ |
225 | |
d3409d5e |
226 | extern void mp_drop(mp */*m*/); |
d03ab969 |
227 | |
d3409d5e |
228 | #define MP_DROP(m) do { \ |
229 | mp *_mm = (m); \ |
d34decd2 |
230 | _mm->ref--; \ |
231 | if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \ |
d3409d5e |
232 | mp_destroy(_mm); \ |
233 | } while (0) |
234 | |
235 | /* --- @mp_split@ --- * |
d03ab969 |
236 | * |
d3409d5e |
237 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
238 | * |
d3409d5e |
239 | * Returns: A reference to the same integer, possibly with a different |
240 | * address. |
d03ab969 |
241 | * |
d3409d5e |
242 | * Use: Splits off a modifiable version of the integer referred to. |
d03ab969 |
243 | */ |
244 | |
d3409d5e |
245 | extern mp *mp_split(mp */*m*/); |
246 | |
247 | #define MP_SPLIT(m) do { \ |
d34decd2 |
248 | mp *_m = (m); \ |
249 | if ((_m->f & MP_CONST) || _m->ref > 1) { \ |
250 | size_t _len = MP_LEN(_m); \ |
251 | mp *_mm = mp_new(_len, _m->f); \ |
252 | if (!(_m->f & MP_UNDEF)) \ |
253 | memcpy(_mm->v, _m->v, MPWS(_len)); \ |
254 | _m->ref--; \ |
255 | _m = _mm; \ |
d3409d5e |
256 | } \ |
d34decd2 |
257 | (m) = _m; \ |
d3409d5e |
258 | } while (0) |
d03ab969 |
259 | |
d3409d5e |
260 | /* --- @mp_resize@ --- * |
d03ab969 |
261 | * |
d3409d5e |
262 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
263 | * @size_t sz@ = new size |
d03ab969 |
264 | * |
d3409d5e |
265 | * Returns: --- |
d03ab969 |
266 | * |
d3409d5e |
267 | * Use: Resizes the vector containing the integer's digits. The new |
268 | * size must be at least as large as the current integer's |
d34decd2 |
269 | * length. This isn't really intended for client use. |
d03ab969 |
270 | */ |
271 | |
d3409d5e |
272 | extern void mp_resize(mp */*m*/, size_t /*sz*/); |
273 | |
274 | #define MP_RESIZE(m, ssz) do { \ |
275 | mp *_m = (m); \ |
276 | size_t _sz = (ssz); \ |
d34decd2 |
277 | mparena *_a = (_m->f & MP_BURN) ? MPARENA_SECURE : MPARENA_GLOBAL; \ |
278 | mpw *_v; \ |
d3409d5e |
279 | size_t _len = MP_LEN(_m); \ |
d34decd2 |
280 | assert(((void)"can't make size less than length", _sz >= _len)); \ |
281 | _v = mpalloc(_a, _sz); \ |
d9a8ae10 |
282 | if (!(_m->f & MP_UNDEF)) \ |
283 | memcpy(_v, _m->v, MPWS(_len)); \ |
d3409d5e |
284 | if (_m->f & MP_BURN) \ |
285 | memset(_m->v, 0, MPWS(_m->sz)); \ |
d34decd2 |
286 | mpfree(_m->a, _m->v); \ |
287 | _m->a = _a; \ |
d3409d5e |
288 | _m->v = _v; \ |
289 | _m->vl = _v + _len; \ |
d3409d5e |
290 | } while (0) |
d03ab969 |
291 | |
d3409d5e |
292 | /* --- @mp_ensure@ --- * |
d03ab969 |
293 | * |
d3409d5e |
294 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
295 | * @size_t sz@ = required size |
d03ab969 |
296 | * |
297 | * Returns: --- |
298 | * |
d3409d5e |
299 | * Use: Ensures that the integer has enough space for @sz@ digits. |
300 | * The value is not changed. |
d03ab969 |
301 | */ |
302 | |
d3409d5e |
303 | extern void mp_ensure(mp */*m*/, size_t /*sz*/); |
304 | |
305 | #define MP_ENSURE(m, ssz) do { \ |
d34decd2 |
306 | mp *_m = (m); \ |
d3409d5e |
307 | size_t _ssz = (ssz); \ |
d34decd2 |
308 | size_t _len = MP_LEN(_m); \ |
309 | if (_ssz >= _len) { \ |
310 | if (_ssz > _m->sz) \ |
311 | mp_resize(_m, _ssz); \ |
312 | if (!(_m->f & MP_UNDEF) && _ssz > _len) \ |
313 | memset(_m->vl, 0, MPWS(_ssz - _len)); \ |
314 | _m->vl = _m->v + _ssz; \ |
315 | } \ |
d3409d5e |
316 | } while (0) |
d03ab969 |
317 | |
d34decd2 |
318 | /* --- @mp_dest@ --- * |
d03ab969 |
319 | * |
d34decd2 |
320 | * Arguments: @mp *m@ = a suggested destination integer |
321 | * @size_t sz@ = size required for result, in digits |
322 | * @unsigned f@ = various flags |
323 | * |
324 | * Returns: A pointer to an appropriate destination. |
325 | * |
326 | * Use: Converts a suggested destination into a real destination with |
327 | * the required properties. If the real destination is @d@, |
328 | * then the following properties will hold: |
329 | * |
330 | * * @d@ will have exactly one reference. |
d03ab969 |
331 | * |
d34decd2 |
332 | * * If @m@ is not @MP_NEW@, then the contents of @m@ will not |
333 | * change, unless @f@ has the @MP_UNDEF@ flag set. |
d03ab969 |
334 | * |
d34decd2 |
335 | * * If @m@ is not @MP_NEW@, then he reference count of @m@ on |
336 | * entry is equal to the sum of the counts of @d@ and @m@ on |
337 | * exit. |
338 | * |
339 | * * The size of @d@ will be at least @sz@. |
340 | * |
341 | * * If @f@ has the @MP_BURN@ flag set, then @d@ will be |
342 | * allocated from @MPARENA_SECURE@. |
343 | * |
344 | * Understanding this function is crucial to using Catacomb's |
345 | * multiprecision integer library effectively. |
d03ab969 |
346 | */ |
347 | |
d34decd2 |
348 | extern mp *mp_dest(mp */*m*/, size_t /*sz*/, unsigned /*f*/); |
d03ab969 |
349 | |
d34decd2 |
350 | #define MP_DEST(m, ssz, f) do { \ |
d3409d5e |
351 | mp *_m = (m); \ |
d34decd2 |
352 | size_t _ssz = (ssz); \ |
353 | unsigned _f = (f); \ |
354 | _m = mp_dest(_m, _ssz, _f); \ |
d3409d5e |
355 | (m) = _m; \ |
356 | } while (0) |
357 | |
358 | /*----- Size manipulation -------------------------------------------------*/ |
359 | |
360 | /* --- @mp_shrink@ --- * |
d03ab969 |
361 | * |
d3409d5e |
362 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
363 | * |
364 | * Returns: --- |
365 | * |
d3409d5e |
366 | * Use: Reduces the recorded length of an integer. This doesn't |
367 | * reduce the amount of memory used, although it can improve |
368 | * performance a bit. To reduce memory, use @mp_minimize@ |
369 | * instead. This can't change the value of an integer, and is |
370 | * therefore safe to use even when there are multiple |
371 | * references. |
d03ab969 |
372 | */ |
373 | |
d3409d5e |
374 | extern void mp_shrink(mp */*m*/); |
d03ab969 |
375 | |
d3409d5e |
376 | #define MP_SHRINK(m) do { \ |
377 | mp *_mm = (m); \ |
378 | MPX_SHRINK(_mm->v, _mm->vl); \ |
379 | if (!MP_LEN(_mm)) \ |
380 | _mm->f &= ~MP_NEG; \ |
381 | } while (0) |
382 | |
383 | /* --- @mp_minimize@ --- * |
d03ab969 |
384 | * |
d3409d5e |
385 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
386 | * |
387 | * Returns: --- |
388 | * |
d3409d5e |
389 | * Use: Reduces the amount of memory an integer uses. It's best to |
390 | * do this to numbers which aren't going to change in the |
391 | * future. |
d03ab969 |
392 | */ |
393 | |
d3409d5e |
394 | extern void mp_minimize(mp */*m*/); |
d03ab969 |
395 | |
d3409d5e |
396 | /*----- Bit scanning ------------------------------------------------------*/ |
d03ab969 |
397 | |
d9a8ae10 |
398 | #ifndef CATACOMB_MPSCAN_H |
d3409d5e |
399 | # include "mpscan.h" |
400 | #endif |
401 | |
402 | /* --- @mp_scan@ --- * |
d03ab969 |
403 | * |
d3409d5e |
404 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
405 | * @const mp *m@ = pointer to a multiprecision integer |
d03ab969 |
406 | * |
407 | * Returns: --- |
408 | * |
d3409d5e |
409 | * Use: Initializes a bitscanner on a multiprecision integer. |
d03ab969 |
410 | */ |
411 | |
d3409d5e |
412 | extern void mp_scan(mpscan */*sc*/, const mp */*m*/); |
413 | |
414 | #define MP_SCAN(sc, m) do { \ |
a790733d |
415 | const mp *_mm = (m); \ |
d3409d5e |
416 | mpscan *_sc = (sc); \ |
417 | MPSCAN_INITX(_sc, _mm->v, _mm->vl); \ |
418 | } while (0) |
419 | |
420 | /* --- Other bitscanning aliases --- */ |
421 | |
422 | #define mp_step mpscan_step |
423 | #define mp_bit mpscan_bit |
424 | |
425 | #define MP_STEP MPSCAN_STEP |
426 | #define MP_BIT MPSCAN_BIT |
427 | |
428 | /*----- Loading and storing -----------------------------------------------*/ |
d03ab969 |
429 | |
d3409d5e |
430 | /* --- @mp_octets@ --- * |
d03ab969 |
431 | * |
d3409d5e |
432 | * Arguments: @const mp *m@ = a multiprecision integer |
d03ab969 |
433 | * |
d3409d5e |
434 | * Returns: The number of octets required to represent @m@. |
d03ab969 |
435 | * |
d3409d5e |
436 | * Use: Calculates the external storage required for a multiprecision |
437 | * integer. |
d03ab969 |
438 | */ |
439 | |
24e1e862 |
440 | extern size_t mp_octets(const mp */*m*/); |
441 | |
442 | /* --- @mp_bits@ --- * |
443 | * |
444 | * Arguments: @const mp *m@ = a multiprecision integer |
445 | * |
446 | * Returns: The number of bits required to represent @m@. |
447 | * |
448 | * Use: Calculates the external storage required for a multiprecision |
449 | * integer. |
450 | */ |
451 | |
452 | extern unsigned long mp_bits(const mp */*m*/); |
d03ab969 |
453 | |
d3409d5e |
454 | /* --- @mp_loadl@ --- * |
d03ab969 |
455 | * |
d3409d5e |
456 | * Arguments: @mp *d@ = destination |
457 | * @const void *pv@ = pointer to source data |
458 | * @size_t sz@ = size of the source data |
d03ab969 |
459 | * |
d3409d5e |
460 | * Returns: Resulting multiprecision number. |
d03ab969 |
461 | * |
d3409d5e |
462 | * Use: Loads a multiprecision number from an array of octets. The |
463 | * first byte in the array is the least significant. More |
464 | * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$% |
465 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
d03ab969 |
466 | */ |
467 | |
d3409d5e |
468 | extern mp *mp_loadl(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d03ab969 |
469 | |
d3409d5e |
470 | /* --- @mp_storel@ --- * |
471 | * |
472 | * Arguments: @const mp *m@ = source |
473 | * @void *pv@ = pointer to output array |
474 | * @size_t sz@ = size of the output array |
475 | * |
476 | * Returns: --- |
477 | * |
478 | * Use: Stores a multiprecision number in an array of octets. The |
479 | * first byte in the array is the least significant. If the |
480 | * array is too small to represent the number, high-order bits |
481 | * are truncated; if the array is too large, high order bytes |
482 | * are filled with zeros. More formally, if the number is |
483 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
484 | * then the array is %$b_0, b_1, \ldots, b_{n-1}$%. |
485 | */ |
d03ab969 |
486 | |
d3409d5e |
487 | extern void mp_storel(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
d03ab969 |
488 | |
d3409d5e |
489 | /* --- @mp_loadb@ --- * |
d03ab969 |
490 | * |
d3409d5e |
491 | * Arguments: @mp *d@ = destination |
492 | * @const void *pv@ = pointer to source data |
493 | * @size_t sz@ = size of the source data |
d03ab969 |
494 | * |
d3409d5e |
495 | * Returns: Resulting multiprecision number. |
d03ab969 |
496 | * |
d3409d5e |
497 | * Use: Loads a multiprecision number from an array of octets. The |
498 | * last byte in the array is the least significant. More |
499 | * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$% |
500 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
d03ab969 |
501 | */ |
502 | |
d3409d5e |
503 | extern mp *mp_loadb(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d03ab969 |
504 | |
d3409d5e |
505 | /* --- @mp_storeb@ --- * |
d03ab969 |
506 | * |
d3409d5e |
507 | * Arguments: @const mp *m@ = source |
508 | * @void *pv@ = pointer to output array |
509 | * @size_t sz@ = size of the output array |
d03ab969 |
510 | * |
511 | * Returns: --- |
512 | * |
d3409d5e |
513 | * Use: Stores a multiprecision number in an array of octets. The |
514 | * last byte in the array is the least significant. If the |
515 | * array is too small to represent the number, high-order bits |
516 | * are truncated; if the array is too large, high order bytes |
517 | * are filled with zeros. More formally, if the number is |
518 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
519 | * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%. |
d03ab969 |
520 | */ |
521 | |
d3409d5e |
522 | extern void mp_storeb(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
d03ab969 |
523 | |
d3409d5e |
524 | /*----- Simple arithmetic -------------------------------------------------*/ |
d03ab969 |
525 | |
d3409d5e |
526 | /* --- @mp_2c@ --- * |
d03ab969 |
527 | * |
d3409d5e |
528 | * Arguments: @mp *d@ = destination |
529 | * @mp *a@ = source |
d03ab969 |
530 | * |
d3409d5e |
531 | * Returns: Result, @a@ converted to two's complement notation. |
532 | */ |
533 | |
534 | extern mp *mp_2c(mp */*d*/, mp */*a*/); |
535 | |
536 | /* --- @mp_sm@ --- * |
537 | * |
538 | * Arguments: @mp *d@ = destination |
539 | * @mp *a@ = source |
d03ab969 |
540 | * |
d3409d5e |
541 | * Returns: Result, @a@ converted to the native signed-magnitude |
542 | * notation. |
d03ab969 |
543 | */ |
544 | |
d3409d5e |
545 | extern mp *mp_sm(mp */*d*/, mp */*a*/); |
d03ab969 |
546 | |
d3409d5e |
547 | /* --- @mp_lsl@ --- * |
d03ab969 |
548 | * |
d3409d5e |
549 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
550 | * @mp *a@ = source |
d3409d5e |
551 | * @size_t n@ = number of bits to move |
d03ab969 |
552 | * |
d3409d5e |
553 | * Returns: Result, @a@ shifted left by @n@. |
554 | */ |
555 | |
d9a8ae10 |
556 | extern mp *mp_lsl(mp */*d*/, mp */*a*/, size_t /*n*/); |
d3409d5e |
557 | |
558 | /* --- @mp_lsr@ --- * |
559 | * |
560 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
561 | * @mp *a@ = source |
d3409d5e |
562 | * @size_t n@ = number of bits to move |
d03ab969 |
563 | * |
d3409d5e |
564 | * Returns: Result, @a@ shifted left by @n@. |
d03ab969 |
565 | */ |
566 | |
d9a8ae10 |
567 | extern mp *mp_lsr(mp */*d*/, mp */*a*/, size_t /*n*/); |
d03ab969 |
568 | |
d3409d5e |
569 | /* --- @mp_cmp@ --- * |
d03ab969 |
570 | * |
d3409d5e |
571 | * Arguments: @const mp *a, *b@ = two numbers |
d03ab969 |
572 | * |
d3409d5e |
573 | * Returns: Less than, equal to or greater than zero, according to |
574 | * whether @a@ is less than, equal to or greater than @b@. |
575 | */ |
576 | |
577 | extern int mp_cmp(const mp */*a*/, const mp */*b*/); |
578 | |
579 | #define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0) |
580 | |
581 | /* --- @mp_add@ --- * |
d03ab969 |
582 | * |
d3409d5e |
583 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
584 | * @mp *a, *b@ = sources |
d3409d5e |
585 | * |
586 | * Returns: Result, @a@ added to @b@. |
d03ab969 |
587 | */ |
588 | |
d9a8ae10 |
589 | extern mp *mp_add(mp */*d*/, mp */*a*/, mp */*b*/); |
d03ab969 |
590 | |
d3409d5e |
591 | /* --- @mp_sub@ --- * |
592 | * |
593 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
594 | * @mp *a, *b@ = sources |
d3409d5e |
595 | * |
596 | * Returns: Result, @b@ subtracted from @a@. |
597 | */ |
d03ab969 |
598 | |
d9a8ae10 |
599 | extern mp *mp_sub(mp */*d*/, mp */*a*/, mp */*b*/); |
d3409d5e |
600 | |
601 | /* --- @mp_mul@ --- * |
d03ab969 |
602 | * |
d3409d5e |
603 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
604 | * @mp *a, *b@ = sources |
d03ab969 |
605 | * |
d3409d5e |
606 | * Returns: Result, @a@ multiplied by @b@. |
607 | */ |
608 | |
d9a8ae10 |
609 | extern mp *mp_mul(mp */*d*/, mp */*a*/, mp */*b*/); |
d3409d5e |
610 | |
611 | /* --- @mp_sqr@ --- * |
612 | * |
613 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
614 | * @mp *a@ = source |
d3409d5e |
615 | * |
616 | * Returns: Result, @a@ squared. |
617 | */ |
618 | |
d9a8ae10 |
619 | extern mp *mp_sqr(mp */*d*/, mp */*a*/); |
d3409d5e |
620 | |
621 | /* --- @mp_div@ --- * |
d03ab969 |
622 | * |
d3409d5e |
623 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
d9a8ae10 |
624 | * @mp *a, *b@ = sources |
d3409d5e |
625 | * |
626 | * Use: Calculates the quotient and remainder when @a@ is divided by |
627 | * @b@. |
d03ab969 |
628 | */ |
629 | |
d9a8ae10 |
630 | extern void mp_div(mp **/*qq*/, mp **/*rr*/, mp */*a*/, mp */*b*/); |
d3409d5e |
631 | |
632 | /*----- More advanced algorithms ------------------------------------------*/ |
d03ab969 |
633 | |
d3409d5e |
634 | /* --- @mp_gcd@ --- * |
d03ab969 |
635 | * |
d3409d5e |
636 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
637 | * @mp *a, *b@ = sources (must be nonzero) |
d03ab969 |
638 | * |
639 | * Returns: --- |
640 | * |
d3409d5e |
641 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
642 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
d9a8ae10 |
643 | * inverses. Neither @a@ nor @b@ may be zero. |
d03ab969 |
644 | */ |
645 | |
d3409d5e |
646 | extern void mp_gcd(mp **/*gcd*/, mp **/*xx*/, mp **/*yy*/, |
647 | mp */*a*/, mp */*b*/); |
648 | |
5b00a0ea |
649 | /* --- @mp_jacobi@ --- * |
650 | * |
651 | * Arguments: @mp *a@ = an integer less than @n@ |
652 | * @mp *n@ = an odd integer |
653 | * |
654 | * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%. |
655 | * |
656 | * Use: Computes the Jacobi symbol. If @n@ is prime, this is the |
657 | * Legendre symbol and is equal to 1 if and only if @a@ is a |
658 | * quadratic residue mod @n@. The result is zero if and only if |
659 | * @a@ and @n@ have a common factor greater than one. |
660 | */ |
661 | |
662 | int mp_jacobi(mp */*a*/, mp */*n*/); |
663 | |
d3409d5e |
664 | /*----- Test harness support ----------------------------------------------*/ |
665 | |
666 | #include <mLib/testrig.h> |
667 | |
d9a8ae10 |
668 | #ifndef CATACOMB_MPTEXT_H |
d3409d5e |
669 | # include "mptext.h" |
670 | #endif |
671 | |
672 | extern const test_type type_mp; |
d03ab969 |
673 | |
674 | /*----- That's all, folks -------------------------------------------------*/ |
675 | |
676 | #ifdef __cplusplus |
677 | } |
678 | #endif |
679 | |
680 | #endif |