d03ab969 |
1 | /* -*-c-*- |
2 | * |
3bc0a0fe |
3 | * $Id: mp.h,v 1.12 2001/06/16 12:57:43 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 $ |
3bc0a0fe |
33 | * Revision 1.12 2001/06/16 12:57:43 mdw |
34 | * Move the @mpmont_factor@ structure and rename it now that it's used for |
35 | * Barrett simultaneous exponentiation too. |
36 | * |
0f32e0f8 |
37 | * Revision 1.11 2001/04/03 19:36:05 mdw |
38 | * Add some simple bitwise operations so that Perl can use them. |
39 | * |
740c9553 |
40 | * Revision 1.10 2000/10/08 12:03:16 mdw |
41 | * Provide @mp_eq@ and @MP_EQ@ for rapidly testing equality of two |
42 | * integers. |
43 | * |
5fbe3846 |
44 | * Revision 1.9 2000/07/29 17:03:31 mdw |
45 | * Add support for left-to-right bitscanning, for use in modular |
46 | * exponentiation. |
47 | * |
22a073c0 |
48 | * Revision 1.8 2000/06/22 19:02:01 mdw |
49 | * Add new functions. |
50 | * |
d34decd2 |
51 | * Revision 1.7 2000/06/17 11:45:09 mdw |
52 | * Major memory management overhaul. Added arena support. Use the secure |
53 | * arena for secret integers. Replace and improve the MP management macros |
54 | * (e.g., replace MP_MODIFY by MP_DEST). |
55 | * |
d9a8ae10 |
56 | * Revision 1.6 1999/12/10 23:19:46 mdw |
57 | * Minor bugfixes. New interface for suggested destinations. |
58 | * |
5b00a0ea |
59 | * Revision 1.5 1999/11/22 20:50:37 mdw |
60 | * Add support for computing Jacobi symbols. |
61 | * |
24e1e862 |
62 | * Revision 1.4 1999/11/21 22:13:02 mdw |
63 | * Add mp version of MPX_BITS. |
64 | * |
a790733d |
65 | * Revision 1.3 1999/11/19 13:19:14 mdw |
66 | * Fix const annotation. |
67 | * |
d3409d5e |
68 | * Revision 1.2 1999/11/17 18:02:16 mdw |
69 | * New multiprecision integer arithmetic suite. |
d03ab969 |
70 | * |
71 | */ |
72 | |
d9a8ae10 |
73 | #ifndef CATACOMB_MP_H |
74 | #define CATACOMB_MP_H |
d03ab969 |
75 | |
76 | #ifdef __cplusplus |
77 | extern "C" { |
78 | #endif |
79 | |
80 | /*----- Header files ------------------------------------------------------*/ |
81 | |
d3409d5e |
82 | #include <assert.h> |
d03ab969 |
83 | #include <string.h> |
84 | |
d3409d5e |
85 | #include <mLib/sub.h> |
86 | |
d9a8ae10 |
87 | #ifndef CATACOMB_MPW_H |
d3409d5e |
88 | # include "mpw.h" |
d03ab969 |
89 | #endif |
90 | |
d34decd2 |
91 | #ifndef CATACOMB_ARENA_H |
92 | # include "arena.h" |
93 | #endif |
94 | |
95 | #ifndef CATACOMB_MPARENA_H |
96 | # include "mparena.h" |
97 | #endif |
98 | |
d9a8ae10 |
99 | #ifndef CATACOMB_MPX_H |
d03ab969 |
100 | # include "mpx.h" |
101 | #endif |
102 | |
d03ab969 |
103 | /*----- Data structures ---------------------------------------------------*/ |
104 | |
3bc0a0fe |
105 | /* --- A multiprecision integer --- */ |
106 | |
d03ab969 |
107 | typedef struct mp { |
3bc0a0fe |
108 | mpw *v, *vl; /* Vector of digits, current limit */ |
109 | size_t sz; /* Size of digit buffer in words */ |
110 | mparena *a; /* Arena for buffer allocation */ |
111 | unsigned f; /* Flags (see below) */ |
112 | unsigned ref; /* Reference counter */ |
d03ab969 |
113 | } mp; |
114 | |
3bc0a0fe |
115 | #define MP_NEG 1u /* Negative (signed magnitude) */ |
116 | #define MP_BURN 2u /* Secret (viral flag) */ |
117 | #define MP_CONST 4u /* Uses strange memory allocation */ |
118 | #define MP_UNDEF 8u /* Contains nothing interesting */ |
119 | #define MP_DESTROYED 16u /* Has been destroyed */ |
120 | |
121 | /* --- A factor for simultaneous exponentation --- * |
122 | * |
123 | * Used by the Montgomery and Barrett exponentiators. |
124 | */ |
125 | |
126 | typedef struct mp_expfactor { |
127 | mp *base; |
128 | mp *exp; |
129 | } mp_expfactor; |
d03ab969 |
130 | |
d3409d5e |
131 | /*----- Useful constants --------------------------------------------------*/ |
d03ab969 |
132 | |
d3409d5e |
133 | extern mp mp_const[]; |
d03ab969 |
134 | |
d3409d5e |
135 | #define MP_ZERO (&mp_const[0]) |
136 | #define MP_ONE (&mp_const[1]) |
137 | #define MP_TWO (&mp_const[2]) |
138 | #define MP_THREE (&mp_const[3]) |
139 | #define MP_FOUR (&mp_const[4]) |
140 | #define MP_FIVE (&mp_const[5]) |
141 | #define MP_TEN (&mp_const[6]) |
d34decd2 |
142 | #define MP_256 (&mp_const[7]) |
143 | #define MP_MONE (&mp_const[8]) |
d03ab969 |
144 | |
d3409d5e |
145 | #define MP_NEW ((mp *)0) |
d34decd2 |
146 | #define MP_NEWSEC (&mp_const[9]) |
d03ab969 |
147 | |
d34decd2 |
148 | /*----- Trivial macros ----------------------------------------------------*/ |
d03ab969 |
149 | |
d34decd2 |
150 | /* --- @MP_LEN@ --- * |
d03ab969 |
151 | * |
d34decd2 |
152 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
153 | * |
d34decd2 |
154 | * Returns: Length of the integer, in words. |
d03ab969 |
155 | */ |
156 | |
d34decd2 |
157 | #define MP_LEN(m) ((m)->vl - ((m)->v)) |
d03ab969 |
158 | |
d34decd2 |
159 | /*----- Memory management and reference counting --------------------------*/ |
d3409d5e |
160 | |
d34decd2 |
161 | /* --- @mp_new@ --- * |
d03ab969 |
162 | * |
d34decd2 |
163 | * Arguments: @size_t sz@ = size of vector required |
164 | * @unsigned f@ = flags to set |
d03ab969 |
165 | * |
d34decd2 |
166 | * Returns: Pointer to a new MP structure. |
d03ab969 |
167 | * |
d34decd2 |
168 | * Use: Allocates a new multiprecision integer. The data space is |
169 | * allocated from either the standard global or secret arena, |
170 | * depending on the initial flags requested. |
d03ab969 |
171 | */ |
172 | |
d34decd2 |
173 | extern mp *mp_new(size_t /*sz*/, unsigned /*f*/); |
d03ab969 |
174 | |
d34decd2 |
175 | /* --- @mp_create@ --- * |
d03ab969 |
176 | * |
d34decd2 |
177 | * Arguments: @size_t sz@ = size of vector required |
d03ab969 |
178 | * |
d34decd2 |
179 | * Returns: Pointer to pristine new MP structure with enough memory |
180 | * bolted onto it. |
181 | * |
182 | * Use: Creates a new multiprecision integer with indeterminate |
183 | * contents. The integer has a single reference. |
d03ab969 |
184 | */ |
185 | |
d34decd2 |
186 | extern mp *mp_create(size_t /*sz*/); |
d3409d5e |
187 | |
d34decd2 |
188 | /* --- @mp_createsecure@ --- * |
d03ab969 |
189 | * |
d3409d5e |
190 | * Arguments: @size_t sz@ = size of vector required |
d03ab969 |
191 | * |
d3409d5e |
192 | * Returns: Pointer to pristine new MP structure with enough memory |
193 | * bolted onto it. |
d03ab969 |
194 | * |
d3409d5e |
195 | * Use: Creates a new multiprecision integer with indeterminate |
d34decd2 |
196 | * contents. The integer has a single reference. The integer's |
197 | * data space is allocated from the secure arena. Its burn flag |
198 | * is set. |
d03ab969 |
199 | */ |
200 | |
d34decd2 |
201 | extern mp *mp_createsecure(size_t /*sz*/); |
d03ab969 |
202 | |
d3409d5e |
203 | /* --- @mp_build@ --- * |
d03ab969 |
204 | * |
d3409d5e |
205 | * Arguments: @mp *m@ = pointer to an MP block to fill in |
206 | * @mpw *v@ = pointer to a word array |
207 | * @mpw *vl@ = pointer just past end of array |
d03ab969 |
208 | * |
209 | * Returns: --- |
210 | * |
d3409d5e |
211 | * Use: Creates a multiprecision integer representing some smallish |
212 | * number. You must provide storage for the number and dispose |
213 | * of it when you've finished with it. The number is marked as |
214 | * constant while it exists. |
d03ab969 |
215 | */ |
216 | |
d3409d5e |
217 | extern void mp_build(mp */*m*/, mpw */*v*/, mpw */*vl*/); |
d03ab969 |
218 | |
d3409d5e |
219 | /* --- @mp_destroy@ --- * |
d03ab969 |
220 | * |
d3409d5e |
221 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
222 | * |
223 | * Returns: --- |
224 | * |
d3409d5e |
225 | * Use: Destroys a multiprecision integer. The reference count isn't |
226 | * checked. Don't use this function if you don't know what |
227 | * you're doing: use @mp_drop@ instead. |
d03ab969 |
228 | */ |
229 | |
d3409d5e |
230 | extern void mp_destroy(mp */*m*/); |
d03ab969 |
231 | |
d3409d5e |
232 | /* --- @mp_copy@ --- * |
d03ab969 |
233 | * |
d3409d5e |
234 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
235 | * |
d3409d5e |
236 | * Returns: A copy of the given multiprecision integer. |
237 | * |
238 | * Use: Copies the given integer. In fact you just get another |
239 | * reference to the same old one again. |
d03ab969 |
240 | */ |
241 | |
d3409d5e |
242 | extern mp *mp_copy(mp */*m*/); |
d03ab969 |
243 | |
d3409d5e |
244 | #define MP_COPY(m) ((m)->ref++, (m)) |
245 | |
246 | /* --- @mp_drop@ --- * |
d03ab969 |
247 | * |
d3409d5e |
248 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
249 | * |
250 | * Returns: --- |
251 | * |
d3409d5e |
252 | * Use: Drops a reference to an integer which isn't wanted any more. |
253 | * If there are no more references, the integer is destroyed. |
d03ab969 |
254 | */ |
255 | |
d3409d5e |
256 | extern void mp_drop(mp */*m*/); |
d03ab969 |
257 | |
d3409d5e |
258 | #define MP_DROP(m) do { \ |
259 | mp *_mm = (m); \ |
d34decd2 |
260 | _mm->ref--; \ |
261 | if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \ |
d3409d5e |
262 | mp_destroy(_mm); \ |
263 | } while (0) |
264 | |
265 | /* --- @mp_split@ --- * |
d03ab969 |
266 | * |
d3409d5e |
267 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
268 | * |
d3409d5e |
269 | * Returns: A reference to the same integer, possibly with a different |
270 | * address. |
d03ab969 |
271 | * |
d3409d5e |
272 | * Use: Splits off a modifiable version of the integer referred to. |
d03ab969 |
273 | */ |
274 | |
d3409d5e |
275 | extern mp *mp_split(mp */*m*/); |
276 | |
277 | #define MP_SPLIT(m) do { \ |
d34decd2 |
278 | mp *_m = (m); \ |
279 | if ((_m->f & MP_CONST) || _m->ref > 1) { \ |
280 | size_t _len = MP_LEN(_m); \ |
281 | mp *_mm = mp_new(_len, _m->f); \ |
282 | if (!(_m->f & MP_UNDEF)) \ |
283 | memcpy(_mm->v, _m->v, MPWS(_len)); \ |
284 | _m->ref--; \ |
285 | _m = _mm; \ |
d3409d5e |
286 | } \ |
d34decd2 |
287 | (m) = _m; \ |
d3409d5e |
288 | } while (0) |
d03ab969 |
289 | |
d3409d5e |
290 | /* --- @mp_resize@ --- * |
d03ab969 |
291 | * |
d3409d5e |
292 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
293 | * @size_t sz@ = new size |
d03ab969 |
294 | * |
d3409d5e |
295 | * Returns: --- |
d03ab969 |
296 | * |
d3409d5e |
297 | * Use: Resizes the vector containing the integer's digits. The new |
298 | * size must be at least as large as the current integer's |
d34decd2 |
299 | * length. This isn't really intended for client use. |
d03ab969 |
300 | */ |
301 | |
d3409d5e |
302 | extern void mp_resize(mp */*m*/, size_t /*sz*/); |
303 | |
304 | #define MP_RESIZE(m, ssz) do { \ |
305 | mp *_m = (m); \ |
306 | size_t _sz = (ssz); \ |
d34decd2 |
307 | mparena *_a = (_m->f & MP_BURN) ? MPARENA_SECURE : MPARENA_GLOBAL; \ |
308 | mpw *_v; \ |
d3409d5e |
309 | size_t _len = MP_LEN(_m); \ |
d34decd2 |
310 | assert(((void)"can't make size less than length", _sz >= _len)); \ |
311 | _v = mpalloc(_a, _sz); \ |
d9a8ae10 |
312 | if (!(_m->f & MP_UNDEF)) \ |
313 | memcpy(_v, _m->v, MPWS(_len)); \ |
d3409d5e |
314 | if (_m->f & MP_BURN) \ |
315 | memset(_m->v, 0, MPWS(_m->sz)); \ |
d34decd2 |
316 | mpfree(_m->a, _m->v); \ |
317 | _m->a = _a; \ |
d3409d5e |
318 | _m->v = _v; \ |
319 | _m->vl = _v + _len; \ |
d3409d5e |
320 | } while (0) |
d03ab969 |
321 | |
d3409d5e |
322 | /* --- @mp_ensure@ --- * |
d03ab969 |
323 | * |
d3409d5e |
324 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
325 | * @size_t sz@ = required size |
d03ab969 |
326 | * |
327 | * Returns: --- |
328 | * |
d3409d5e |
329 | * Use: Ensures that the integer has enough space for @sz@ digits. |
330 | * The value is not changed. |
d03ab969 |
331 | */ |
332 | |
d3409d5e |
333 | extern void mp_ensure(mp */*m*/, size_t /*sz*/); |
334 | |
335 | #define MP_ENSURE(m, ssz) do { \ |
d34decd2 |
336 | mp *_m = (m); \ |
d3409d5e |
337 | size_t _ssz = (ssz); \ |
d34decd2 |
338 | size_t _len = MP_LEN(_m); \ |
339 | if (_ssz >= _len) { \ |
340 | if (_ssz > _m->sz) \ |
341 | mp_resize(_m, _ssz); \ |
342 | if (!(_m->f & MP_UNDEF) && _ssz > _len) \ |
343 | memset(_m->vl, 0, MPWS(_ssz - _len)); \ |
344 | _m->vl = _m->v + _ssz; \ |
345 | } \ |
d3409d5e |
346 | } while (0) |
d03ab969 |
347 | |
d34decd2 |
348 | /* --- @mp_dest@ --- * |
d03ab969 |
349 | * |
d34decd2 |
350 | * Arguments: @mp *m@ = a suggested destination integer |
351 | * @size_t sz@ = size required for result, in digits |
352 | * @unsigned f@ = various flags |
353 | * |
354 | * Returns: A pointer to an appropriate destination. |
355 | * |
356 | * Use: Converts a suggested destination into a real destination with |
357 | * the required properties. If the real destination is @d@, |
358 | * then the following properties will hold: |
359 | * |
360 | * * @d@ will have exactly one reference. |
d03ab969 |
361 | * |
d34decd2 |
362 | * * If @m@ is not @MP_NEW@, then the contents of @m@ will not |
363 | * change, unless @f@ has the @MP_UNDEF@ flag set. |
d03ab969 |
364 | * |
d34decd2 |
365 | * * If @m@ is not @MP_NEW@, then he reference count of @m@ on |
366 | * entry is equal to the sum of the counts of @d@ and @m@ on |
367 | * exit. |
368 | * |
369 | * * The size of @d@ will be at least @sz@. |
370 | * |
371 | * * If @f@ has the @MP_BURN@ flag set, then @d@ will be |
372 | * allocated from @MPARENA_SECURE@. |
373 | * |
374 | * Understanding this function is crucial to using Catacomb's |
375 | * multiprecision integer library effectively. |
d03ab969 |
376 | */ |
377 | |
d34decd2 |
378 | extern mp *mp_dest(mp */*m*/, size_t /*sz*/, unsigned /*f*/); |
d03ab969 |
379 | |
d34decd2 |
380 | #define MP_DEST(m, ssz, f) do { \ |
d3409d5e |
381 | mp *_m = (m); \ |
d34decd2 |
382 | size_t _ssz = (ssz); \ |
383 | unsigned _f = (f); \ |
384 | _m = mp_dest(_m, _ssz, _f); \ |
d3409d5e |
385 | (m) = _m; \ |
386 | } while (0) |
387 | |
388 | /*----- Size manipulation -------------------------------------------------*/ |
389 | |
390 | /* --- @mp_shrink@ --- * |
d03ab969 |
391 | * |
d3409d5e |
392 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
393 | * |
394 | * Returns: --- |
395 | * |
d3409d5e |
396 | * Use: Reduces the recorded length of an integer. This doesn't |
397 | * reduce the amount of memory used, although it can improve |
398 | * performance a bit. To reduce memory, use @mp_minimize@ |
399 | * instead. This can't change the value of an integer, and is |
400 | * therefore safe to use even when there are multiple |
401 | * references. |
d03ab969 |
402 | */ |
403 | |
d3409d5e |
404 | extern void mp_shrink(mp */*m*/); |
d03ab969 |
405 | |
d3409d5e |
406 | #define MP_SHRINK(m) do { \ |
407 | mp *_mm = (m); \ |
408 | MPX_SHRINK(_mm->v, _mm->vl); \ |
409 | if (!MP_LEN(_mm)) \ |
410 | _mm->f &= ~MP_NEG; \ |
411 | } while (0) |
412 | |
413 | /* --- @mp_minimize@ --- * |
d03ab969 |
414 | * |
d3409d5e |
415 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
416 | * |
417 | * Returns: --- |
418 | * |
d3409d5e |
419 | * Use: Reduces the amount of memory an integer uses. It's best to |
420 | * do this to numbers which aren't going to change in the |
421 | * future. |
d03ab969 |
422 | */ |
423 | |
d3409d5e |
424 | extern void mp_minimize(mp */*m*/); |
d03ab969 |
425 | |
d3409d5e |
426 | /*----- Bit scanning ------------------------------------------------------*/ |
d03ab969 |
427 | |
d9a8ae10 |
428 | #ifndef CATACOMB_MPSCAN_H |
d3409d5e |
429 | # include "mpscan.h" |
430 | #endif |
431 | |
432 | /* --- @mp_scan@ --- * |
d03ab969 |
433 | * |
d3409d5e |
434 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
435 | * @const mp *m@ = pointer to a multiprecision integer |
d03ab969 |
436 | * |
437 | * Returns: --- |
438 | * |
d3409d5e |
439 | * Use: Initializes a bitscanner on a multiprecision integer. |
d03ab969 |
440 | */ |
441 | |
d3409d5e |
442 | extern void mp_scan(mpscan */*sc*/, const mp */*m*/); |
443 | |
444 | #define MP_SCAN(sc, m) do { \ |
a790733d |
445 | const mp *_mm = (m); \ |
d3409d5e |
446 | mpscan *_sc = (sc); \ |
447 | MPSCAN_INITX(_sc, _mm->v, _mm->vl); \ |
448 | } while (0) |
449 | |
5fbe3846 |
450 | /* --- @mp_rscan@ --- * |
451 | * |
452 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
453 | * @const mp *m@ = pointer to a multiprecision integer |
454 | * |
455 | * Returns: --- |
456 | * |
457 | * Use: Initializes a reverse bitscanner on a multiprecision |
458 | * integer. |
459 | */ |
460 | |
461 | extern void mp_rscan(mpscan */*sc*/, const mp */*m*/); |
462 | |
463 | #define MP_RSCAN(sc, m) do { \ |
464 | const mp *_mm = (m); \ |
465 | mpscan *_sc = (sc); \ |
466 | MPSCAN_RINITX(_sc, _mm->v, _mm->vl); \ |
467 | } while (0) |
468 | |
d3409d5e |
469 | /* --- Other bitscanning aliases --- */ |
470 | |
471 | #define mp_step mpscan_step |
472 | #define mp_bit mpscan_bit |
5fbe3846 |
473 | #define mp_rstep mpscan_rstep |
474 | #define mp_rbit mpscan_rbit |
d3409d5e |
475 | |
476 | #define MP_STEP MPSCAN_STEP |
477 | #define MP_BIT MPSCAN_BIT |
5fbe3846 |
478 | #define MP_RSTEP MPSCAN_RSTEP |
479 | #define MP_RBIT MPSCAN_RBIT |
d3409d5e |
480 | |
481 | /*----- Loading and storing -----------------------------------------------*/ |
d03ab969 |
482 | |
d3409d5e |
483 | /* --- @mp_octets@ --- * |
d03ab969 |
484 | * |
d3409d5e |
485 | * Arguments: @const mp *m@ = a multiprecision integer |
d03ab969 |
486 | * |
d3409d5e |
487 | * Returns: The number of octets required to represent @m@. |
d03ab969 |
488 | * |
d3409d5e |
489 | * Use: Calculates the external storage required for a multiprecision |
490 | * integer. |
d03ab969 |
491 | */ |
492 | |
24e1e862 |
493 | extern size_t mp_octets(const mp */*m*/); |
494 | |
495 | /* --- @mp_bits@ --- * |
496 | * |
497 | * Arguments: @const mp *m@ = a multiprecision integer |
498 | * |
499 | * Returns: The number of bits required to represent @m@. |
500 | * |
501 | * Use: Calculates the external storage required for a multiprecision |
502 | * integer. |
503 | */ |
504 | |
505 | extern unsigned long mp_bits(const mp */*m*/); |
d03ab969 |
506 | |
d3409d5e |
507 | /* --- @mp_loadl@ --- * |
d03ab969 |
508 | * |
d3409d5e |
509 | * Arguments: @mp *d@ = destination |
510 | * @const void *pv@ = pointer to source data |
511 | * @size_t sz@ = size of the source data |
d03ab969 |
512 | * |
d3409d5e |
513 | * Returns: Resulting multiprecision number. |
d03ab969 |
514 | * |
d3409d5e |
515 | * Use: Loads a multiprecision number from an array of octets. The |
516 | * first byte in the array is the least significant. More |
517 | * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$% |
518 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
d03ab969 |
519 | */ |
520 | |
d3409d5e |
521 | extern mp *mp_loadl(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d03ab969 |
522 | |
d3409d5e |
523 | /* --- @mp_storel@ --- * |
524 | * |
525 | * Arguments: @const mp *m@ = source |
526 | * @void *pv@ = pointer to output array |
527 | * @size_t sz@ = size of the output array |
528 | * |
529 | * Returns: --- |
530 | * |
531 | * Use: Stores a multiprecision number in an array of octets. The |
532 | * first byte in the array is the least significant. If the |
533 | * array is too small to represent the number, high-order bits |
534 | * are truncated; if the array is too large, high order bytes |
535 | * are filled with zeros. More formally, if the number is |
536 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
537 | * then the array is %$b_0, b_1, \ldots, b_{n-1}$%. |
538 | */ |
d03ab969 |
539 | |
d3409d5e |
540 | extern void mp_storel(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
d03ab969 |
541 | |
d3409d5e |
542 | /* --- @mp_loadb@ --- * |
d03ab969 |
543 | * |
d3409d5e |
544 | * Arguments: @mp *d@ = destination |
545 | * @const void *pv@ = pointer to source data |
546 | * @size_t sz@ = size of the source data |
d03ab969 |
547 | * |
d3409d5e |
548 | * Returns: Resulting multiprecision number. |
d03ab969 |
549 | * |
d3409d5e |
550 | * Use: Loads a multiprecision number from an array of octets. The |
551 | * last byte in the array is the least significant. More |
552 | * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$% |
553 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
d03ab969 |
554 | */ |
555 | |
d3409d5e |
556 | extern mp *mp_loadb(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d03ab969 |
557 | |
d3409d5e |
558 | /* --- @mp_storeb@ --- * |
d03ab969 |
559 | * |
d3409d5e |
560 | * Arguments: @const mp *m@ = source |
561 | * @void *pv@ = pointer to output array |
562 | * @size_t sz@ = size of the output array |
d03ab969 |
563 | * |
564 | * Returns: --- |
565 | * |
d3409d5e |
566 | * Use: Stores a multiprecision number in an array of octets. The |
567 | * last byte in the array is the least significant. If the |
568 | * array is too small to represent the number, high-order bits |
569 | * are truncated; if the array is too large, high order bytes |
570 | * are filled with zeros. More formally, if the number is |
571 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
572 | * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%. |
d03ab969 |
573 | */ |
574 | |
d3409d5e |
575 | extern void mp_storeb(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
d03ab969 |
576 | |
d3409d5e |
577 | /*----- Simple arithmetic -------------------------------------------------*/ |
d03ab969 |
578 | |
d3409d5e |
579 | /* --- @mp_2c@ --- * |
d03ab969 |
580 | * |
d3409d5e |
581 | * Arguments: @mp *d@ = destination |
582 | * @mp *a@ = source |
d03ab969 |
583 | * |
d3409d5e |
584 | * Returns: Result, @a@ converted to two's complement notation. |
585 | */ |
586 | |
587 | extern mp *mp_2c(mp */*d*/, mp */*a*/); |
588 | |
589 | /* --- @mp_sm@ --- * |
590 | * |
591 | * Arguments: @mp *d@ = destination |
592 | * @mp *a@ = source |
d03ab969 |
593 | * |
d3409d5e |
594 | * Returns: Result, @a@ converted to the native signed-magnitude |
595 | * notation. |
d03ab969 |
596 | */ |
597 | |
d3409d5e |
598 | extern mp *mp_sm(mp */*d*/, mp */*a*/); |
d03ab969 |
599 | |
d3409d5e |
600 | /* --- @mp_lsl@ --- * |
d03ab969 |
601 | * |
d3409d5e |
602 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
603 | * @mp *a@ = source |
d3409d5e |
604 | * @size_t n@ = number of bits to move |
d03ab969 |
605 | * |
d3409d5e |
606 | * Returns: Result, @a@ shifted left by @n@. |
607 | */ |
608 | |
d9a8ae10 |
609 | extern mp *mp_lsl(mp */*d*/, mp */*a*/, size_t /*n*/); |
d3409d5e |
610 | |
611 | /* --- @mp_lsr@ --- * |
612 | * |
613 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
614 | * @mp *a@ = source |
d3409d5e |
615 | * @size_t n@ = number of bits to move |
d03ab969 |
616 | * |
d3409d5e |
617 | * Returns: Result, @a@ shifted left by @n@. |
d03ab969 |
618 | */ |
619 | |
d9a8ae10 |
620 | extern mp *mp_lsr(mp */*d*/, mp */*a*/, size_t /*n*/); |
d03ab969 |
621 | |
740c9553 |
622 | /* --- @mp_eq@ --- * |
623 | * |
624 | * Arguments: @const mp *a, *b@ = two numbers |
625 | * |
626 | * Returns: Nonzero if the numbers are equal. |
627 | */ |
628 | |
629 | extern int mp_eq(const mp */*a*/, const mp */*b*/); |
630 | |
631 | #define MP_EQ(a, b) \ |
632 | ((((a)->f ^ (b)->f) & MP_NEG) == 0 && \ |
633 | mpx_ueq((a)->v, (a)->vl, (b)->v, (b)->vl)) |
634 | |
d3409d5e |
635 | /* --- @mp_cmp@ --- * |
d03ab969 |
636 | * |
d3409d5e |
637 | * Arguments: @const mp *a, *b@ = two numbers |
d03ab969 |
638 | * |
d3409d5e |
639 | * Returns: Less than, equal to or greater than zero, according to |
640 | * whether @a@ is less than, equal to or greater than @b@. |
641 | */ |
642 | |
643 | extern int mp_cmp(const mp */*a*/, const mp */*b*/); |
644 | |
645 | #define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0) |
646 | |
0f32e0f8 |
647 | /* --- @mpx_and@, @mpx_or@, @mpx_xor@, @mpx_not@ --- * |
648 | * |
649 | * Arguments: @mp *d@ = destination |
650 | * @mp *a, *b@ = sources |
651 | * |
652 | * Returns: The result of the obvious bitwise operation. |
653 | */ |
654 | |
655 | extern mp *mp_and(mp */*d*/, mp */*a*/, mp */*b*/); |
656 | extern mp *mp_or(mp */*d*/, mp */*a*/, mp */*b*/); |
657 | extern mp *mp_xor(mp */*d*/, mp */*a*/, mp */*b*/); |
658 | extern mp *mp_not(mp */*d*/, mp */*a*/); |
659 | |
d3409d5e |
660 | /* --- @mp_add@ --- * |
d03ab969 |
661 | * |
d3409d5e |
662 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
663 | * @mp *a, *b@ = sources |
d3409d5e |
664 | * |
665 | * Returns: Result, @a@ added to @b@. |
d03ab969 |
666 | */ |
667 | |
d9a8ae10 |
668 | extern mp *mp_add(mp */*d*/, mp */*a*/, mp */*b*/); |
d03ab969 |
669 | |
d3409d5e |
670 | /* --- @mp_sub@ --- * |
671 | * |
672 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
673 | * @mp *a, *b@ = sources |
d3409d5e |
674 | * |
675 | * Returns: Result, @b@ subtracted from @a@. |
676 | */ |
d03ab969 |
677 | |
d9a8ae10 |
678 | extern mp *mp_sub(mp */*d*/, mp */*a*/, mp */*b*/); |
d3409d5e |
679 | |
680 | /* --- @mp_mul@ --- * |
d03ab969 |
681 | * |
d3409d5e |
682 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
683 | * @mp *a, *b@ = sources |
d03ab969 |
684 | * |
d3409d5e |
685 | * Returns: Result, @a@ multiplied by @b@. |
686 | */ |
687 | |
d9a8ae10 |
688 | extern mp *mp_mul(mp */*d*/, mp */*a*/, mp */*b*/); |
d3409d5e |
689 | |
690 | /* --- @mp_sqr@ --- * |
691 | * |
692 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
693 | * @mp *a@ = source |
d3409d5e |
694 | * |
695 | * Returns: Result, @a@ squared. |
696 | */ |
697 | |
d9a8ae10 |
698 | extern mp *mp_sqr(mp */*d*/, mp */*a*/); |
d3409d5e |
699 | |
700 | /* --- @mp_div@ --- * |
d03ab969 |
701 | * |
d3409d5e |
702 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
d9a8ae10 |
703 | * @mp *a, *b@ = sources |
d3409d5e |
704 | * |
705 | * Use: Calculates the quotient and remainder when @a@ is divided by |
706 | * @b@. |
d03ab969 |
707 | */ |
708 | |
d9a8ae10 |
709 | extern void mp_div(mp **/*qq*/, mp **/*rr*/, mp */*a*/, mp */*b*/); |
d3409d5e |
710 | |
22a073c0 |
711 | /* --- @mp_odd@ --- * |
712 | * |
713 | * Arguments: @mp *d@ = pointer to destination integer |
714 | * @mp *m@ = pointer to source integer |
715 | * @size_t *s@ = where to store the power of 2 |
716 | * |
717 | * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%. |
718 | * |
719 | * Use: Computes a power of two and an odd integer which, when |
720 | * multiplied, give a specified result. This sort of thing is |
721 | * useful in number theory quite often. |
722 | */ |
723 | |
724 | extern mp *mp_odd(mp */*d*/, mp */*m*/, size_t */*s*/); |
725 | |
d3409d5e |
726 | /*----- More advanced algorithms ------------------------------------------*/ |
d03ab969 |
727 | |
22a073c0 |
728 | /* --- @mp_sqrt@ --- * |
729 | * |
730 | * Arguments: @mp *d@ = pointer to destination integer |
731 | * @mp *a@ = (nonnegative) integer to take square root of |
732 | * |
733 | * Returns: The largest integer %$x$% such that %$x^2 \le a$%. |
734 | * |
735 | * Use: Computes integer square roots. |
736 | * |
737 | * The current implementation isn't very good: it uses the |
738 | * Newton-Raphson method to find an approximation to %$a$%. If |
739 | * there's any demand for a better version, I'll write one. |
740 | */ |
741 | |
742 | extern mp *mp_sqrt(mp */*d*/, mp */*a*/); |
743 | |
d3409d5e |
744 | /* --- @mp_gcd@ --- * |
d03ab969 |
745 | * |
d3409d5e |
746 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
747 | * @mp *a, *b@ = sources (must be nonzero) |
d03ab969 |
748 | * |
749 | * Returns: --- |
750 | * |
d3409d5e |
751 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
752 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
d9a8ae10 |
753 | * inverses. Neither @a@ nor @b@ may be zero. |
d03ab969 |
754 | */ |
755 | |
d3409d5e |
756 | extern void mp_gcd(mp **/*gcd*/, mp **/*xx*/, mp **/*yy*/, |
757 | mp */*a*/, mp */*b*/); |
758 | |
5b00a0ea |
759 | /* --- @mp_jacobi@ --- * |
760 | * |
761 | * Arguments: @mp *a@ = an integer less than @n@ |
762 | * @mp *n@ = an odd integer |
763 | * |
764 | * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%. |
765 | * |
766 | * Use: Computes the Jacobi symbol. If @n@ is prime, this is the |
767 | * Legendre symbol and is equal to 1 if and only if @a@ is a |
768 | * quadratic residue mod @n@. The result is zero if and only if |
769 | * @a@ and @n@ have a common factor greater than one. |
770 | */ |
771 | |
22a073c0 |
772 | extern int mp_jacobi(mp */*a*/, mp */*n*/); |
773 | |
774 | /* --- @mp_modsqrt@ --- * |
775 | * |
776 | * Arguments: @mp *d@ = destination integer |
777 | * @mp *a@ = source integer |
778 | * @mp *p@ = modulus (must be prime) |
779 | * |
780 | * Returns: If %$a$% is a quadratic residue, a square root of %$a$%; else |
781 | * a null pointer. |
782 | * |
783 | * Use: Returns an integer %$x$% such that %$x^2 \equiv a \pmod{p}$%, |
784 | * if one exists; else a null pointer. This function will not |
785 | * work if %$p$% is composite: you must factor the modulus, take |
786 | * a square root mod each factor, and recombine the results |
787 | * using the Chinese Remainder Theorem. |
788 | */ |
789 | |
790 | extern mp *mp_modsqrt(mp */*d*/, mp */*a*/, mp */*p*/); |
5b00a0ea |
791 | |
d3409d5e |
792 | /*----- Test harness support ----------------------------------------------*/ |
793 | |
794 | #include <mLib/testrig.h> |
795 | |
d9a8ae10 |
796 | #ifndef CATACOMB_MPTEXT_H |
d3409d5e |
797 | # include "mptext.h" |
798 | #endif |
799 | |
800 | extern const test_type type_mp; |
d03ab969 |
801 | |
802 | /*----- That's all, folks -------------------------------------------------*/ |
803 | |
804 | #ifdef __cplusplus |
805 | } |
806 | #endif |
807 | |
808 | #endif |