d03ab969 |
1 | /* -*-c-*- |
2 | * |
740c9553 |
3 | * $Id: mp.h,v 1.10 2000/10/08 12:03:16 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 $ |
740c9553 |
33 | * Revision 1.10 2000/10/08 12:03:16 mdw |
34 | * Provide @mp_eq@ and @MP_EQ@ for rapidly testing equality of two |
35 | * integers. |
36 | * |
5fbe3846 |
37 | * Revision 1.9 2000/07/29 17:03:31 mdw |
38 | * Add support for left-to-right bitscanning, for use in modular |
39 | * exponentiation. |
40 | * |
22a073c0 |
41 | * Revision 1.8 2000/06/22 19:02:01 mdw |
42 | * Add new functions. |
43 | * |
d34decd2 |
44 | * Revision 1.7 2000/06/17 11:45:09 mdw |
45 | * Major memory management overhaul. Added arena support. Use the secure |
46 | * arena for secret integers. Replace and improve the MP management macros |
47 | * (e.g., replace MP_MODIFY by MP_DEST). |
48 | * |
d9a8ae10 |
49 | * Revision 1.6 1999/12/10 23:19:46 mdw |
50 | * Minor bugfixes. New interface for suggested destinations. |
51 | * |
5b00a0ea |
52 | * Revision 1.5 1999/11/22 20:50:37 mdw |
53 | * Add support for computing Jacobi symbols. |
54 | * |
24e1e862 |
55 | * Revision 1.4 1999/11/21 22:13:02 mdw |
56 | * Add mp version of MPX_BITS. |
57 | * |
a790733d |
58 | * Revision 1.3 1999/11/19 13:19:14 mdw |
59 | * Fix const annotation. |
60 | * |
d3409d5e |
61 | * Revision 1.2 1999/11/17 18:02:16 mdw |
62 | * New multiprecision integer arithmetic suite. |
d03ab969 |
63 | * |
64 | */ |
65 | |
d9a8ae10 |
66 | #ifndef CATACOMB_MP_H |
67 | #define CATACOMB_MP_H |
d03ab969 |
68 | |
69 | #ifdef __cplusplus |
70 | extern "C" { |
71 | #endif |
72 | |
73 | /*----- Header files ------------------------------------------------------*/ |
74 | |
d3409d5e |
75 | #include <assert.h> |
d03ab969 |
76 | #include <string.h> |
77 | |
d3409d5e |
78 | #include <mLib/sub.h> |
79 | |
d9a8ae10 |
80 | #ifndef CATACOMB_MPW_H |
d3409d5e |
81 | # include "mpw.h" |
d03ab969 |
82 | #endif |
83 | |
d34decd2 |
84 | #ifndef CATACOMB_ARENA_H |
85 | # include "arena.h" |
86 | #endif |
87 | |
88 | #ifndef CATACOMB_MPARENA_H |
89 | # include "mparena.h" |
90 | #endif |
91 | |
d9a8ae10 |
92 | #ifndef CATACOMB_MPX_H |
d03ab969 |
93 | # include "mpx.h" |
94 | #endif |
95 | |
d03ab969 |
96 | /*----- Data structures ---------------------------------------------------*/ |
97 | |
98 | typedef struct mp { |
d3409d5e |
99 | mpw *v, *vl; |
100 | size_t sz; |
d34decd2 |
101 | mparena *a; |
d3409d5e |
102 | unsigned f; |
103 | unsigned ref; |
d03ab969 |
104 | } mp; |
105 | |
d3409d5e |
106 | #define MP_NEG 1u |
107 | #define MP_BURN 2u |
108 | #define MP_CONST 4u |
109 | #define MP_UNDEF 8u |
d9a8ae10 |
110 | #define MP_DESTROYED 16u |
d03ab969 |
111 | |
d3409d5e |
112 | /*----- Useful constants --------------------------------------------------*/ |
d03ab969 |
113 | |
d3409d5e |
114 | extern mp mp_const[]; |
d03ab969 |
115 | |
d3409d5e |
116 | #define MP_ZERO (&mp_const[0]) |
117 | #define MP_ONE (&mp_const[1]) |
118 | #define MP_TWO (&mp_const[2]) |
119 | #define MP_THREE (&mp_const[3]) |
120 | #define MP_FOUR (&mp_const[4]) |
121 | #define MP_FIVE (&mp_const[5]) |
122 | #define MP_TEN (&mp_const[6]) |
d34decd2 |
123 | #define MP_256 (&mp_const[7]) |
124 | #define MP_MONE (&mp_const[8]) |
d03ab969 |
125 | |
d3409d5e |
126 | #define MP_NEW ((mp *)0) |
d34decd2 |
127 | #define MP_NEWSEC (&mp_const[9]) |
d03ab969 |
128 | |
d34decd2 |
129 | /*----- Trivial macros ----------------------------------------------------*/ |
d03ab969 |
130 | |
d34decd2 |
131 | /* --- @MP_LEN@ --- * |
d03ab969 |
132 | * |
d34decd2 |
133 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
134 | * |
d34decd2 |
135 | * Returns: Length of the integer, in words. |
d03ab969 |
136 | */ |
137 | |
d34decd2 |
138 | #define MP_LEN(m) ((m)->vl - ((m)->v)) |
d03ab969 |
139 | |
d34decd2 |
140 | /*----- Memory management and reference counting --------------------------*/ |
d3409d5e |
141 | |
d34decd2 |
142 | /* --- @mp_new@ --- * |
d03ab969 |
143 | * |
d34decd2 |
144 | * Arguments: @size_t sz@ = size of vector required |
145 | * @unsigned f@ = flags to set |
d03ab969 |
146 | * |
d34decd2 |
147 | * Returns: Pointer to a new MP structure. |
d03ab969 |
148 | * |
d34decd2 |
149 | * Use: Allocates a new multiprecision integer. The data space is |
150 | * allocated from either the standard global or secret arena, |
151 | * depending on the initial flags requested. |
d03ab969 |
152 | */ |
153 | |
d34decd2 |
154 | extern mp *mp_new(size_t /*sz*/, unsigned /*f*/); |
d03ab969 |
155 | |
d34decd2 |
156 | /* --- @mp_create@ --- * |
d03ab969 |
157 | * |
d34decd2 |
158 | * Arguments: @size_t sz@ = size of vector required |
d03ab969 |
159 | * |
d34decd2 |
160 | * Returns: Pointer to pristine new MP structure with enough memory |
161 | * bolted onto it. |
162 | * |
163 | * Use: Creates a new multiprecision integer with indeterminate |
164 | * contents. The integer has a single reference. |
d03ab969 |
165 | */ |
166 | |
d34decd2 |
167 | extern mp *mp_create(size_t /*sz*/); |
d3409d5e |
168 | |
d34decd2 |
169 | /* --- @mp_createsecure@ --- * |
d03ab969 |
170 | * |
d3409d5e |
171 | * Arguments: @size_t sz@ = size of vector required |
d03ab969 |
172 | * |
d3409d5e |
173 | * Returns: Pointer to pristine new MP structure with enough memory |
174 | * bolted onto it. |
d03ab969 |
175 | * |
d3409d5e |
176 | * Use: Creates a new multiprecision integer with indeterminate |
d34decd2 |
177 | * contents. The integer has a single reference. The integer's |
178 | * data space is allocated from the secure arena. Its burn flag |
179 | * is set. |
d03ab969 |
180 | */ |
181 | |
d34decd2 |
182 | extern mp *mp_createsecure(size_t /*sz*/); |
d03ab969 |
183 | |
d3409d5e |
184 | /* --- @mp_build@ --- * |
d03ab969 |
185 | * |
d3409d5e |
186 | * Arguments: @mp *m@ = pointer to an MP block to fill in |
187 | * @mpw *v@ = pointer to a word array |
188 | * @mpw *vl@ = pointer just past end of array |
d03ab969 |
189 | * |
190 | * Returns: --- |
191 | * |
d3409d5e |
192 | * Use: Creates a multiprecision integer representing some smallish |
193 | * number. You must provide storage for the number and dispose |
194 | * of it when you've finished with it. The number is marked as |
195 | * constant while it exists. |
d03ab969 |
196 | */ |
197 | |
d3409d5e |
198 | extern void mp_build(mp */*m*/, mpw */*v*/, mpw */*vl*/); |
d03ab969 |
199 | |
d3409d5e |
200 | /* --- @mp_destroy@ --- * |
d03ab969 |
201 | * |
d3409d5e |
202 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
203 | * |
204 | * Returns: --- |
205 | * |
d3409d5e |
206 | * Use: Destroys a multiprecision integer. The reference count isn't |
207 | * checked. Don't use this function if you don't know what |
208 | * you're doing: use @mp_drop@ instead. |
d03ab969 |
209 | */ |
210 | |
d3409d5e |
211 | extern void mp_destroy(mp */*m*/); |
d03ab969 |
212 | |
d3409d5e |
213 | /* --- @mp_copy@ --- * |
d03ab969 |
214 | * |
d3409d5e |
215 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
216 | * |
d3409d5e |
217 | * Returns: A copy of the given multiprecision integer. |
218 | * |
219 | * Use: Copies the given integer. In fact you just get another |
220 | * reference to the same old one again. |
d03ab969 |
221 | */ |
222 | |
d3409d5e |
223 | extern mp *mp_copy(mp */*m*/); |
d03ab969 |
224 | |
d3409d5e |
225 | #define MP_COPY(m) ((m)->ref++, (m)) |
226 | |
227 | /* --- @mp_drop@ --- * |
d03ab969 |
228 | * |
d3409d5e |
229 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
230 | * |
231 | * Returns: --- |
232 | * |
d3409d5e |
233 | * Use: Drops a reference to an integer which isn't wanted any more. |
234 | * If there are no more references, the integer is destroyed. |
d03ab969 |
235 | */ |
236 | |
d3409d5e |
237 | extern void mp_drop(mp */*m*/); |
d03ab969 |
238 | |
d3409d5e |
239 | #define MP_DROP(m) do { \ |
240 | mp *_mm = (m); \ |
d34decd2 |
241 | _mm->ref--; \ |
242 | if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \ |
d3409d5e |
243 | mp_destroy(_mm); \ |
244 | } while (0) |
245 | |
246 | /* --- @mp_split@ --- * |
d03ab969 |
247 | * |
d3409d5e |
248 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
249 | * |
d3409d5e |
250 | * Returns: A reference to the same integer, possibly with a different |
251 | * address. |
d03ab969 |
252 | * |
d3409d5e |
253 | * Use: Splits off a modifiable version of the integer referred to. |
d03ab969 |
254 | */ |
255 | |
d3409d5e |
256 | extern mp *mp_split(mp */*m*/); |
257 | |
258 | #define MP_SPLIT(m) do { \ |
d34decd2 |
259 | mp *_m = (m); \ |
260 | if ((_m->f & MP_CONST) || _m->ref > 1) { \ |
261 | size_t _len = MP_LEN(_m); \ |
262 | mp *_mm = mp_new(_len, _m->f); \ |
263 | if (!(_m->f & MP_UNDEF)) \ |
264 | memcpy(_mm->v, _m->v, MPWS(_len)); \ |
265 | _m->ref--; \ |
266 | _m = _mm; \ |
d3409d5e |
267 | } \ |
d34decd2 |
268 | (m) = _m; \ |
d3409d5e |
269 | } while (0) |
d03ab969 |
270 | |
d3409d5e |
271 | /* --- @mp_resize@ --- * |
d03ab969 |
272 | * |
d3409d5e |
273 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
274 | * @size_t sz@ = new size |
d03ab969 |
275 | * |
d3409d5e |
276 | * Returns: --- |
d03ab969 |
277 | * |
d3409d5e |
278 | * Use: Resizes the vector containing the integer's digits. The new |
279 | * size must be at least as large as the current integer's |
d34decd2 |
280 | * length. This isn't really intended for client use. |
d03ab969 |
281 | */ |
282 | |
d3409d5e |
283 | extern void mp_resize(mp */*m*/, size_t /*sz*/); |
284 | |
285 | #define MP_RESIZE(m, ssz) do { \ |
286 | mp *_m = (m); \ |
287 | size_t _sz = (ssz); \ |
d34decd2 |
288 | mparena *_a = (_m->f & MP_BURN) ? MPARENA_SECURE : MPARENA_GLOBAL; \ |
289 | mpw *_v; \ |
d3409d5e |
290 | size_t _len = MP_LEN(_m); \ |
d34decd2 |
291 | assert(((void)"can't make size less than length", _sz >= _len)); \ |
292 | _v = mpalloc(_a, _sz); \ |
d9a8ae10 |
293 | if (!(_m->f & MP_UNDEF)) \ |
294 | memcpy(_v, _m->v, MPWS(_len)); \ |
d3409d5e |
295 | if (_m->f & MP_BURN) \ |
296 | memset(_m->v, 0, MPWS(_m->sz)); \ |
d34decd2 |
297 | mpfree(_m->a, _m->v); \ |
298 | _m->a = _a; \ |
d3409d5e |
299 | _m->v = _v; \ |
300 | _m->vl = _v + _len; \ |
d3409d5e |
301 | } while (0) |
d03ab969 |
302 | |
d3409d5e |
303 | /* --- @mp_ensure@ --- * |
d03ab969 |
304 | * |
d3409d5e |
305 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
306 | * @size_t sz@ = required size |
d03ab969 |
307 | * |
308 | * Returns: --- |
309 | * |
d3409d5e |
310 | * Use: Ensures that the integer has enough space for @sz@ digits. |
311 | * The value is not changed. |
d03ab969 |
312 | */ |
313 | |
d3409d5e |
314 | extern void mp_ensure(mp */*m*/, size_t /*sz*/); |
315 | |
316 | #define MP_ENSURE(m, ssz) do { \ |
d34decd2 |
317 | mp *_m = (m); \ |
d3409d5e |
318 | size_t _ssz = (ssz); \ |
d34decd2 |
319 | size_t _len = MP_LEN(_m); \ |
320 | if (_ssz >= _len) { \ |
321 | if (_ssz > _m->sz) \ |
322 | mp_resize(_m, _ssz); \ |
323 | if (!(_m->f & MP_UNDEF) && _ssz > _len) \ |
324 | memset(_m->vl, 0, MPWS(_ssz - _len)); \ |
325 | _m->vl = _m->v + _ssz; \ |
326 | } \ |
d3409d5e |
327 | } while (0) |
d03ab969 |
328 | |
d34decd2 |
329 | /* --- @mp_dest@ --- * |
d03ab969 |
330 | * |
d34decd2 |
331 | * Arguments: @mp *m@ = a suggested destination integer |
332 | * @size_t sz@ = size required for result, in digits |
333 | * @unsigned f@ = various flags |
334 | * |
335 | * Returns: A pointer to an appropriate destination. |
336 | * |
337 | * Use: Converts a suggested destination into a real destination with |
338 | * the required properties. If the real destination is @d@, |
339 | * then the following properties will hold: |
340 | * |
341 | * * @d@ will have exactly one reference. |
d03ab969 |
342 | * |
d34decd2 |
343 | * * If @m@ is not @MP_NEW@, then the contents of @m@ will not |
344 | * change, unless @f@ has the @MP_UNDEF@ flag set. |
d03ab969 |
345 | * |
d34decd2 |
346 | * * If @m@ is not @MP_NEW@, then he reference count of @m@ on |
347 | * entry is equal to the sum of the counts of @d@ and @m@ on |
348 | * exit. |
349 | * |
350 | * * The size of @d@ will be at least @sz@. |
351 | * |
352 | * * If @f@ has the @MP_BURN@ flag set, then @d@ will be |
353 | * allocated from @MPARENA_SECURE@. |
354 | * |
355 | * Understanding this function is crucial to using Catacomb's |
356 | * multiprecision integer library effectively. |
d03ab969 |
357 | */ |
358 | |
d34decd2 |
359 | extern mp *mp_dest(mp */*m*/, size_t /*sz*/, unsigned /*f*/); |
d03ab969 |
360 | |
d34decd2 |
361 | #define MP_DEST(m, ssz, f) do { \ |
d3409d5e |
362 | mp *_m = (m); \ |
d34decd2 |
363 | size_t _ssz = (ssz); \ |
364 | unsigned _f = (f); \ |
365 | _m = mp_dest(_m, _ssz, _f); \ |
d3409d5e |
366 | (m) = _m; \ |
367 | } while (0) |
368 | |
369 | /*----- Size manipulation -------------------------------------------------*/ |
370 | |
371 | /* --- @mp_shrink@ --- * |
d03ab969 |
372 | * |
d3409d5e |
373 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
374 | * |
375 | * Returns: --- |
376 | * |
d3409d5e |
377 | * Use: Reduces the recorded length of an integer. This doesn't |
378 | * reduce the amount of memory used, although it can improve |
379 | * performance a bit. To reduce memory, use @mp_minimize@ |
380 | * instead. This can't change the value of an integer, and is |
381 | * therefore safe to use even when there are multiple |
382 | * references. |
d03ab969 |
383 | */ |
384 | |
d3409d5e |
385 | extern void mp_shrink(mp */*m*/); |
d03ab969 |
386 | |
d3409d5e |
387 | #define MP_SHRINK(m) do { \ |
388 | mp *_mm = (m); \ |
389 | MPX_SHRINK(_mm->v, _mm->vl); \ |
390 | if (!MP_LEN(_mm)) \ |
391 | _mm->f &= ~MP_NEG; \ |
392 | } while (0) |
393 | |
394 | /* --- @mp_minimize@ --- * |
d03ab969 |
395 | * |
d3409d5e |
396 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
397 | * |
398 | * Returns: --- |
399 | * |
d3409d5e |
400 | * Use: Reduces the amount of memory an integer uses. It's best to |
401 | * do this to numbers which aren't going to change in the |
402 | * future. |
d03ab969 |
403 | */ |
404 | |
d3409d5e |
405 | extern void mp_minimize(mp */*m*/); |
d03ab969 |
406 | |
d3409d5e |
407 | /*----- Bit scanning ------------------------------------------------------*/ |
d03ab969 |
408 | |
d9a8ae10 |
409 | #ifndef CATACOMB_MPSCAN_H |
d3409d5e |
410 | # include "mpscan.h" |
411 | #endif |
412 | |
413 | /* --- @mp_scan@ --- * |
d03ab969 |
414 | * |
d3409d5e |
415 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
416 | * @const mp *m@ = pointer to a multiprecision integer |
d03ab969 |
417 | * |
418 | * Returns: --- |
419 | * |
d3409d5e |
420 | * Use: Initializes a bitscanner on a multiprecision integer. |
d03ab969 |
421 | */ |
422 | |
d3409d5e |
423 | extern void mp_scan(mpscan */*sc*/, const mp */*m*/); |
424 | |
425 | #define MP_SCAN(sc, m) do { \ |
a790733d |
426 | const mp *_mm = (m); \ |
d3409d5e |
427 | mpscan *_sc = (sc); \ |
428 | MPSCAN_INITX(_sc, _mm->v, _mm->vl); \ |
429 | } while (0) |
430 | |
5fbe3846 |
431 | /* --- @mp_rscan@ --- * |
432 | * |
433 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
434 | * @const mp *m@ = pointer to a multiprecision integer |
435 | * |
436 | * Returns: --- |
437 | * |
438 | * Use: Initializes a reverse bitscanner on a multiprecision |
439 | * integer. |
440 | */ |
441 | |
442 | extern void mp_rscan(mpscan */*sc*/, const mp */*m*/); |
443 | |
444 | #define MP_RSCAN(sc, m) do { \ |
445 | const mp *_mm = (m); \ |
446 | mpscan *_sc = (sc); \ |
447 | MPSCAN_RINITX(_sc, _mm->v, _mm->vl); \ |
448 | } while (0) |
449 | |
d3409d5e |
450 | /* --- Other bitscanning aliases --- */ |
451 | |
452 | #define mp_step mpscan_step |
453 | #define mp_bit mpscan_bit |
5fbe3846 |
454 | #define mp_rstep mpscan_rstep |
455 | #define mp_rbit mpscan_rbit |
d3409d5e |
456 | |
457 | #define MP_STEP MPSCAN_STEP |
458 | #define MP_BIT MPSCAN_BIT |
5fbe3846 |
459 | #define MP_RSTEP MPSCAN_RSTEP |
460 | #define MP_RBIT MPSCAN_RBIT |
d3409d5e |
461 | |
462 | /*----- Loading and storing -----------------------------------------------*/ |
d03ab969 |
463 | |
d3409d5e |
464 | /* --- @mp_octets@ --- * |
d03ab969 |
465 | * |
d3409d5e |
466 | * Arguments: @const mp *m@ = a multiprecision integer |
d03ab969 |
467 | * |
d3409d5e |
468 | * Returns: The number of octets required to represent @m@. |
d03ab969 |
469 | * |
d3409d5e |
470 | * Use: Calculates the external storage required for a multiprecision |
471 | * integer. |
d03ab969 |
472 | */ |
473 | |
24e1e862 |
474 | extern size_t mp_octets(const mp */*m*/); |
475 | |
476 | /* --- @mp_bits@ --- * |
477 | * |
478 | * Arguments: @const mp *m@ = a multiprecision integer |
479 | * |
480 | * Returns: The number of bits required to represent @m@. |
481 | * |
482 | * Use: Calculates the external storage required for a multiprecision |
483 | * integer. |
484 | */ |
485 | |
486 | extern unsigned long mp_bits(const mp */*m*/); |
d03ab969 |
487 | |
d3409d5e |
488 | /* --- @mp_loadl@ --- * |
d03ab969 |
489 | * |
d3409d5e |
490 | * Arguments: @mp *d@ = destination |
491 | * @const void *pv@ = pointer to source data |
492 | * @size_t sz@ = size of the source data |
d03ab969 |
493 | * |
d3409d5e |
494 | * Returns: Resulting multiprecision number. |
d03ab969 |
495 | * |
d3409d5e |
496 | * Use: Loads a multiprecision number from an array of octets. The |
497 | * first byte in the array is the least significant. More |
498 | * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$% |
499 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
d03ab969 |
500 | */ |
501 | |
d3409d5e |
502 | extern mp *mp_loadl(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d03ab969 |
503 | |
d3409d5e |
504 | /* --- @mp_storel@ --- * |
505 | * |
506 | * Arguments: @const mp *m@ = source |
507 | * @void *pv@ = pointer to output array |
508 | * @size_t sz@ = size of the output array |
509 | * |
510 | * Returns: --- |
511 | * |
512 | * Use: Stores a multiprecision number in an array of octets. The |
513 | * first byte in the array is the least significant. If the |
514 | * array is too small to represent the number, high-order bits |
515 | * are truncated; if the array is too large, high order bytes |
516 | * are filled with zeros. More formally, if the number is |
517 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
518 | * then the array is %$b_0, b_1, \ldots, b_{n-1}$%. |
519 | */ |
d03ab969 |
520 | |
d3409d5e |
521 | extern void mp_storel(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
d03ab969 |
522 | |
d3409d5e |
523 | /* --- @mp_loadb@ --- * |
d03ab969 |
524 | * |
d3409d5e |
525 | * Arguments: @mp *d@ = destination |
526 | * @const void *pv@ = pointer to source data |
527 | * @size_t sz@ = size of the source data |
d03ab969 |
528 | * |
d3409d5e |
529 | * Returns: Resulting multiprecision number. |
d03ab969 |
530 | * |
d3409d5e |
531 | * Use: Loads a multiprecision number from an array of octets. The |
532 | * last byte in the array is the least significant. More |
533 | * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$% |
534 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
d03ab969 |
535 | */ |
536 | |
d3409d5e |
537 | extern mp *mp_loadb(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d03ab969 |
538 | |
d3409d5e |
539 | /* --- @mp_storeb@ --- * |
d03ab969 |
540 | * |
d3409d5e |
541 | * Arguments: @const mp *m@ = source |
542 | * @void *pv@ = pointer to output array |
543 | * @size_t sz@ = size of the output array |
d03ab969 |
544 | * |
545 | * Returns: --- |
546 | * |
d3409d5e |
547 | * Use: Stores a multiprecision number in an array of octets. The |
548 | * last byte in the array is the least significant. If the |
549 | * array is too small to represent the number, high-order bits |
550 | * are truncated; if the array is too large, high order bytes |
551 | * are filled with zeros. More formally, if the number is |
552 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
553 | * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%. |
d03ab969 |
554 | */ |
555 | |
d3409d5e |
556 | extern void mp_storeb(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
d03ab969 |
557 | |
d3409d5e |
558 | /*----- Simple arithmetic -------------------------------------------------*/ |
d03ab969 |
559 | |
d3409d5e |
560 | /* --- @mp_2c@ --- * |
d03ab969 |
561 | * |
d3409d5e |
562 | * Arguments: @mp *d@ = destination |
563 | * @mp *a@ = source |
d03ab969 |
564 | * |
d3409d5e |
565 | * Returns: Result, @a@ converted to two's complement notation. |
566 | */ |
567 | |
568 | extern mp *mp_2c(mp */*d*/, mp */*a*/); |
569 | |
570 | /* --- @mp_sm@ --- * |
571 | * |
572 | * Arguments: @mp *d@ = destination |
573 | * @mp *a@ = source |
d03ab969 |
574 | * |
d3409d5e |
575 | * Returns: Result, @a@ converted to the native signed-magnitude |
576 | * notation. |
d03ab969 |
577 | */ |
578 | |
d3409d5e |
579 | extern mp *mp_sm(mp */*d*/, mp */*a*/); |
d03ab969 |
580 | |
d3409d5e |
581 | /* --- @mp_lsl@ --- * |
d03ab969 |
582 | * |
d3409d5e |
583 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
584 | * @mp *a@ = source |
d3409d5e |
585 | * @size_t n@ = number of bits to move |
d03ab969 |
586 | * |
d3409d5e |
587 | * Returns: Result, @a@ shifted left by @n@. |
588 | */ |
589 | |
d9a8ae10 |
590 | extern mp *mp_lsl(mp */*d*/, mp */*a*/, size_t /*n*/); |
d3409d5e |
591 | |
592 | /* --- @mp_lsr@ --- * |
593 | * |
594 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
595 | * @mp *a@ = source |
d3409d5e |
596 | * @size_t n@ = number of bits to move |
d03ab969 |
597 | * |
d3409d5e |
598 | * Returns: Result, @a@ shifted left by @n@. |
d03ab969 |
599 | */ |
600 | |
d9a8ae10 |
601 | extern mp *mp_lsr(mp */*d*/, mp */*a*/, size_t /*n*/); |
d03ab969 |
602 | |
740c9553 |
603 | /* --- @mp_eq@ --- * |
604 | * |
605 | * Arguments: @const mp *a, *b@ = two numbers |
606 | * |
607 | * Returns: Nonzero if the numbers are equal. |
608 | */ |
609 | |
610 | extern int mp_eq(const mp */*a*/, const mp */*b*/); |
611 | |
612 | #define MP_EQ(a, b) \ |
613 | ((((a)->f ^ (b)->f) & MP_NEG) == 0 && \ |
614 | mpx_ueq((a)->v, (a)->vl, (b)->v, (b)->vl)) |
615 | |
d3409d5e |
616 | /* --- @mp_cmp@ --- * |
d03ab969 |
617 | * |
d3409d5e |
618 | * Arguments: @const mp *a, *b@ = two numbers |
d03ab969 |
619 | * |
d3409d5e |
620 | * Returns: Less than, equal to or greater than zero, according to |
621 | * whether @a@ is less than, equal to or greater than @b@. |
622 | */ |
623 | |
624 | extern int mp_cmp(const mp */*a*/, const mp */*b*/); |
625 | |
626 | #define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0) |
627 | |
628 | /* --- @mp_add@ --- * |
d03ab969 |
629 | * |
d3409d5e |
630 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
631 | * @mp *a, *b@ = sources |
d3409d5e |
632 | * |
633 | * Returns: Result, @a@ added to @b@. |
d03ab969 |
634 | */ |
635 | |
d9a8ae10 |
636 | extern mp *mp_add(mp */*d*/, mp */*a*/, mp */*b*/); |
d03ab969 |
637 | |
d3409d5e |
638 | /* --- @mp_sub@ --- * |
639 | * |
640 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
641 | * @mp *a, *b@ = sources |
d3409d5e |
642 | * |
643 | * Returns: Result, @b@ subtracted from @a@. |
644 | */ |
d03ab969 |
645 | |
d9a8ae10 |
646 | extern mp *mp_sub(mp */*d*/, mp */*a*/, mp */*b*/); |
d3409d5e |
647 | |
648 | /* --- @mp_mul@ --- * |
d03ab969 |
649 | * |
d3409d5e |
650 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
651 | * @mp *a, *b@ = sources |
d03ab969 |
652 | * |
d3409d5e |
653 | * Returns: Result, @a@ multiplied by @b@. |
654 | */ |
655 | |
d9a8ae10 |
656 | extern mp *mp_mul(mp */*d*/, mp */*a*/, mp */*b*/); |
d3409d5e |
657 | |
658 | /* --- @mp_sqr@ --- * |
659 | * |
660 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
661 | * @mp *a@ = source |
d3409d5e |
662 | * |
663 | * Returns: Result, @a@ squared. |
664 | */ |
665 | |
d9a8ae10 |
666 | extern mp *mp_sqr(mp */*d*/, mp */*a*/); |
d3409d5e |
667 | |
668 | /* --- @mp_div@ --- * |
d03ab969 |
669 | * |
d3409d5e |
670 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
d9a8ae10 |
671 | * @mp *a, *b@ = sources |
d3409d5e |
672 | * |
673 | * Use: Calculates the quotient and remainder when @a@ is divided by |
674 | * @b@. |
d03ab969 |
675 | */ |
676 | |
d9a8ae10 |
677 | extern void mp_div(mp **/*qq*/, mp **/*rr*/, mp */*a*/, mp */*b*/); |
d3409d5e |
678 | |
22a073c0 |
679 | /* --- @mp_odd@ --- * |
680 | * |
681 | * Arguments: @mp *d@ = pointer to destination integer |
682 | * @mp *m@ = pointer to source integer |
683 | * @size_t *s@ = where to store the power of 2 |
684 | * |
685 | * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%. |
686 | * |
687 | * Use: Computes a power of two and an odd integer which, when |
688 | * multiplied, give a specified result. This sort of thing is |
689 | * useful in number theory quite often. |
690 | */ |
691 | |
692 | extern mp *mp_odd(mp */*d*/, mp */*m*/, size_t */*s*/); |
693 | |
d3409d5e |
694 | /*----- More advanced algorithms ------------------------------------------*/ |
d03ab969 |
695 | |
22a073c0 |
696 | /* --- @mp_sqrt@ --- * |
697 | * |
698 | * Arguments: @mp *d@ = pointer to destination integer |
699 | * @mp *a@ = (nonnegative) integer to take square root of |
700 | * |
701 | * Returns: The largest integer %$x$% such that %$x^2 \le a$%. |
702 | * |
703 | * Use: Computes integer square roots. |
704 | * |
705 | * The current implementation isn't very good: it uses the |
706 | * Newton-Raphson method to find an approximation to %$a$%. If |
707 | * there's any demand for a better version, I'll write one. |
708 | */ |
709 | |
710 | extern mp *mp_sqrt(mp */*d*/, mp */*a*/); |
711 | |
d3409d5e |
712 | /* --- @mp_gcd@ --- * |
d03ab969 |
713 | * |
d3409d5e |
714 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
715 | * @mp *a, *b@ = sources (must be nonzero) |
d03ab969 |
716 | * |
717 | * Returns: --- |
718 | * |
d3409d5e |
719 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
720 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
d9a8ae10 |
721 | * inverses. Neither @a@ nor @b@ may be zero. |
d03ab969 |
722 | */ |
723 | |
d3409d5e |
724 | extern void mp_gcd(mp **/*gcd*/, mp **/*xx*/, mp **/*yy*/, |
725 | mp */*a*/, mp */*b*/); |
726 | |
5b00a0ea |
727 | /* --- @mp_jacobi@ --- * |
728 | * |
729 | * Arguments: @mp *a@ = an integer less than @n@ |
730 | * @mp *n@ = an odd integer |
731 | * |
732 | * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%. |
733 | * |
734 | * Use: Computes the Jacobi symbol. If @n@ is prime, this is the |
735 | * Legendre symbol and is equal to 1 if and only if @a@ is a |
736 | * quadratic residue mod @n@. The result is zero if and only if |
737 | * @a@ and @n@ have a common factor greater than one. |
738 | */ |
739 | |
22a073c0 |
740 | extern int mp_jacobi(mp */*a*/, mp */*n*/); |
741 | |
742 | /* --- @mp_modsqrt@ --- * |
743 | * |
744 | * Arguments: @mp *d@ = destination integer |
745 | * @mp *a@ = source integer |
746 | * @mp *p@ = modulus (must be prime) |
747 | * |
748 | * Returns: If %$a$% is a quadratic residue, a square root of %$a$%; else |
749 | * a null pointer. |
750 | * |
751 | * Use: Returns an integer %$x$% such that %$x^2 \equiv a \pmod{p}$%, |
752 | * if one exists; else a null pointer. This function will not |
753 | * work if %$p$% is composite: you must factor the modulus, take |
754 | * a square root mod each factor, and recombine the results |
755 | * using the Chinese Remainder Theorem. |
756 | */ |
757 | |
758 | extern mp *mp_modsqrt(mp */*d*/, mp */*a*/, mp */*p*/); |
5b00a0ea |
759 | |
d3409d5e |
760 | /*----- Test harness support ----------------------------------------------*/ |
761 | |
762 | #include <mLib/testrig.h> |
763 | |
d9a8ae10 |
764 | #ifndef CATACOMB_MPTEXT_H |
d3409d5e |
765 | # include "mptext.h" |
766 | #endif |
767 | |
768 | extern const test_type type_mp; |
d03ab969 |
769 | |
770 | /*----- That's all, folks -------------------------------------------------*/ |
771 | |
772 | #ifdef __cplusplus |
773 | } |
774 | #endif |
775 | |
776 | #endif |