d03ab969 |
1 | /* -*-c-*- |
2 | * |
09d00c6b |
3 | * $Id: mp.h,v 1.14 2002/10/15 00:19:40 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 $ |
09d00c6b |
33 | * Revision 1.14 2002/10/15 00:19:40 mdw |
34 | * Bit setting and clearing functions. |
35 | * |
f09e814a |
36 | * Revision 1.13 2002/10/06 22:52:50 mdw |
37 | * Pile of changes for supporting two's complement properly. |
38 | * |
3bc0a0fe |
39 | * Revision 1.12 2001/06/16 12:57:43 mdw |
40 | * Move the @mpmont_factor@ structure and rename it now that it's used for |
41 | * Barrett simultaneous exponentiation too. |
42 | * |
0f32e0f8 |
43 | * Revision 1.11 2001/04/03 19:36:05 mdw |
44 | * Add some simple bitwise operations so that Perl can use them. |
45 | * |
740c9553 |
46 | * Revision 1.10 2000/10/08 12:03:16 mdw |
47 | * Provide @mp_eq@ and @MP_EQ@ for rapidly testing equality of two |
48 | * integers. |
49 | * |
5fbe3846 |
50 | * Revision 1.9 2000/07/29 17:03:31 mdw |
51 | * Add support for left-to-right bitscanning, for use in modular |
52 | * exponentiation. |
53 | * |
22a073c0 |
54 | * Revision 1.8 2000/06/22 19:02:01 mdw |
55 | * Add new functions. |
56 | * |
d34decd2 |
57 | * Revision 1.7 2000/06/17 11:45:09 mdw |
58 | * Major memory management overhaul. Added arena support. Use the secure |
59 | * arena for secret integers. Replace and improve the MP management macros |
60 | * (e.g., replace MP_MODIFY by MP_DEST). |
61 | * |
d9a8ae10 |
62 | * Revision 1.6 1999/12/10 23:19:46 mdw |
63 | * Minor bugfixes. New interface for suggested destinations. |
64 | * |
5b00a0ea |
65 | * Revision 1.5 1999/11/22 20:50:37 mdw |
66 | * Add support for computing Jacobi symbols. |
67 | * |
24e1e862 |
68 | * Revision 1.4 1999/11/21 22:13:02 mdw |
69 | * Add mp version of MPX_BITS. |
70 | * |
a790733d |
71 | * Revision 1.3 1999/11/19 13:19:14 mdw |
72 | * Fix const annotation. |
73 | * |
d3409d5e |
74 | * Revision 1.2 1999/11/17 18:02:16 mdw |
75 | * New multiprecision integer arithmetic suite. |
d03ab969 |
76 | * |
77 | */ |
78 | |
d9a8ae10 |
79 | #ifndef CATACOMB_MP_H |
80 | #define CATACOMB_MP_H |
d03ab969 |
81 | |
82 | #ifdef __cplusplus |
83 | extern "C" { |
84 | #endif |
85 | |
86 | /*----- Header files ------------------------------------------------------*/ |
87 | |
d3409d5e |
88 | #include <assert.h> |
d03ab969 |
89 | #include <string.h> |
90 | |
d3409d5e |
91 | #include <mLib/sub.h> |
92 | |
d9a8ae10 |
93 | #ifndef CATACOMB_MPW_H |
d3409d5e |
94 | # include "mpw.h" |
d03ab969 |
95 | #endif |
96 | |
d34decd2 |
97 | #ifndef CATACOMB_ARENA_H |
98 | # include "arena.h" |
99 | #endif |
100 | |
101 | #ifndef CATACOMB_MPARENA_H |
102 | # include "mparena.h" |
103 | #endif |
104 | |
d9a8ae10 |
105 | #ifndef CATACOMB_MPX_H |
d03ab969 |
106 | # include "mpx.h" |
107 | #endif |
108 | |
d03ab969 |
109 | /*----- Data structures ---------------------------------------------------*/ |
110 | |
3bc0a0fe |
111 | /* --- A multiprecision integer --- */ |
112 | |
d03ab969 |
113 | typedef struct mp { |
3bc0a0fe |
114 | mpw *v, *vl; /* Vector of digits, current limit */ |
115 | size_t sz; /* Size of digit buffer in words */ |
116 | mparena *a; /* Arena for buffer allocation */ |
117 | unsigned f; /* Flags (see below) */ |
118 | unsigned ref; /* Reference counter */ |
d03ab969 |
119 | } mp; |
120 | |
3bc0a0fe |
121 | #define MP_NEG 1u /* Negative (signed magnitude) */ |
122 | #define MP_BURN 2u /* Secret (viral flag) */ |
123 | #define MP_CONST 4u /* Uses strange memory allocation */ |
124 | #define MP_UNDEF 8u /* Contains nothing interesting */ |
125 | #define MP_DESTROYED 16u /* Has been destroyed */ |
126 | |
127 | /* --- A factor for simultaneous exponentation --- * |
128 | * |
129 | * Used by the Montgomery and Barrett exponentiators. |
130 | */ |
131 | |
132 | typedef struct mp_expfactor { |
133 | mp *base; |
134 | mp *exp; |
135 | } mp_expfactor; |
d03ab969 |
136 | |
d3409d5e |
137 | /*----- Useful constants --------------------------------------------------*/ |
d03ab969 |
138 | |
d3409d5e |
139 | extern mp mp_const[]; |
d03ab969 |
140 | |
d3409d5e |
141 | #define MP_ZERO (&mp_const[0]) |
142 | #define MP_ONE (&mp_const[1]) |
143 | #define MP_TWO (&mp_const[2]) |
144 | #define MP_THREE (&mp_const[3]) |
145 | #define MP_FOUR (&mp_const[4]) |
146 | #define MP_FIVE (&mp_const[5]) |
147 | #define MP_TEN (&mp_const[6]) |
d34decd2 |
148 | #define MP_256 (&mp_const[7]) |
149 | #define MP_MONE (&mp_const[8]) |
d03ab969 |
150 | |
d3409d5e |
151 | #define MP_NEW ((mp *)0) |
d34decd2 |
152 | #define MP_NEWSEC (&mp_const[9]) |
d03ab969 |
153 | |
d34decd2 |
154 | /*----- Trivial macros ----------------------------------------------------*/ |
d03ab969 |
155 | |
d34decd2 |
156 | /* --- @MP_LEN@ --- * |
d03ab969 |
157 | * |
d34decd2 |
158 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
159 | * |
d34decd2 |
160 | * Returns: Length of the integer, in words. |
d03ab969 |
161 | */ |
162 | |
d34decd2 |
163 | #define MP_LEN(m) ((m)->vl - ((m)->v)) |
d03ab969 |
164 | |
d34decd2 |
165 | /*----- Memory management and reference counting --------------------------*/ |
d3409d5e |
166 | |
d34decd2 |
167 | /* --- @mp_new@ --- * |
d03ab969 |
168 | * |
d34decd2 |
169 | * Arguments: @size_t sz@ = size of vector required |
170 | * @unsigned f@ = flags to set |
d03ab969 |
171 | * |
d34decd2 |
172 | * Returns: Pointer to a new MP structure. |
d03ab969 |
173 | * |
d34decd2 |
174 | * Use: Allocates a new multiprecision integer. The data space is |
175 | * allocated from either the standard global or secret arena, |
176 | * depending on the initial flags requested. |
d03ab969 |
177 | */ |
178 | |
d34decd2 |
179 | extern mp *mp_new(size_t /*sz*/, unsigned /*f*/); |
d03ab969 |
180 | |
d34decd2 |
181 | /* --- @mp_create@ --- * |
d03ab969 |
182 | * |
d34decd2 |
183 | * Arguments: @size_t sz@ = size of vector required |
d03ab969 |
184 | * |
d34decd2 |
185 | * Returns: Pointer to pristine new MP structure with enough memory |
186 | * bolted onto it. |
187 | * |
188 | * Use: Creates a new multiprecision integer with indeterminate |
189 | * contents. The integer has a single reference. |
d03ab969 |
190 | */ |
191 | |
d34decd2 |
192 | extern mp *mp_create(size_t /*sz*/); |
d3409d5e |
193 | |
d34decd2 |
194 | /* --- @mp_createsecure@ --- * |
d03ab969 |
195 | * |
d3409d5e |
196 | * Arguments: @size_t sz@ = size of vector required |
d03ab969 |
197 | * |
d3409d5e |
198 | * Returns: Pointer to pristine new MP structure with enough memory |
199 | * bolted onto it. |
d03ab969 |
200 | * |
d3409d5e |
201 | * Use: Creates a new multiprecision integer with indeterminate |
d34decd2 |
202 | * contents. The integer has a single reference. The integer's |
203 | * data space is allocated from the secure arena. Its burn flag |
204 | * is set. |
d03ab969 |
205 | */ |
206 | |
d34decd2 |
207 | extern mp *mp_createsecure(size_t /*sz*/); |
d03ab969 |
208 | |
d3409d5e |
209 | /* --- @mp_build@ --- * |
d03ab969 |
210 | * |
d3409d5e |
211 | * Arguments: @mp *m@ = pointer to an MP block to fill in |
212 | * @mpw *v@ = pointer to a word array |
213 | * @mpw *vl@ = pointer just past end of array |
d03ab969 |
214 | * |
215 | * Returns: --- |
216 | * |
d3409d5e |
217 | * Use: Creates a multiprecision integer representing some smallish |
218 | * number. You must provide storage for the number and dispose |
219 | * of it when you've finished with it. The number is marked as |
220 | * constant while it exists. |
d03ab969 |
221 | */ |
222 | |
d3409d5e |
223 | extern void mp_build(mp */*m*/, mpw */*v*/, mpw */*vl*/); |
d03ab969 |
224 | |
d3409d5e |
225 | /* --- @mp_destroy@ --- * |
d03ab969 |
226 | * |
d3409d5e |
227 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
228 | * |
229 | * Returns: --- |
230 | * |
d3409d5e |
231 | * Use: Destroys a multiprecision integer. The reference count isn't |
232 | * checked. Don't use this function if you don't know what |
233 | * you're doing: use @mp_drop@ instead. |
d03ab969 |
234 | */ |
235 | |
d3409d5e |
236 | extern void mp_destroy(mp */*m*/); |
d03ab969 |
237 | |
d3409d5e |
238 | /* --- @mp_copy@ --- * |
d03ab969 |
239 | * |
d3409d5e |
240 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
241 | * |
d3409d5e |
242 | * Returns: A copy of the given multiprecision integer. |
243 | * |
244 | * Use: Copies the given integer. In fact you just get another |
245 | * reference to the same old one again. |
d03ab969 |
246 | */ |
247 | |
d3409d5e |
248 | extern mp *mp_copy(mp */*m*/); |
d03ab969 |
249 | |
d3409d5e |
250 | #define MP_COPY(m) ((m)->ref++, (m)) |
251 | |
252 | /* --- @mp_drop@ --- * |
d03ab969 |
253 | * |
d3409d5e |
254 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
255 | * |
256 | * Returns: --- |
257 | * |
d3409d5e |
258 | * Use: Drops a reference to an integer which isn't wanted any more. |
259 | * If there are no more references, the integer is destroyed. |
d03ab969 |
260 | */ |
261 | |
d3409d5e |
262 | extern void mp_drop(mp */*m*/); |
d03ab969 |
263 | |
d3409d5e |
264 | #define MP_DROP(m) do { \ |
265 | mp *_mm = (m); \ |
d34decd2 |
266 | _mm->ref--; \ |
267 | if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \ |
d3409d5e |
268 | mp_destroy(_mm); \ |
269 | } while (0) |
270 | |
271 | /* --- @mp_split@ --- * |
d03ab969 |
272 | * |
d3409d5e |
273 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
274 | * |
d3409d5e |
275 | * Returns: A reference to the same integer, possibly with a different |
276 | * address. |
d03ab969 |
277 | * |
d3409d5e |
278 | * Use: Splits off a modifiable version of the integer referred to. |
d03ab969 |
279 | */ |
280 | |
d3409d5e |
281 | extern mp *mp_split(mp */*m*/); |
282 | |
283 | #define MP_SPLIT(m) do { \ |
d34decd2 |
284 | mp *_m = (m); \ |
285 | if ((_m->f & MP_CONST) || _m->ref > 1) { \ |
286 | size_t _len = MP_LEN(_m); \ |
287 | mp *_mm = mp_new(_len, _m->f); \ |
288 | if (!(_m->f & MP_UNDEF)) \ |
289 | memcpy(_mm->v, _m->v, MPWS(_len)); \ |
290 | _m->ref--; \ |
291 | _m = _mm; \ |
d3409d5e |
292 | } \ |
d34decd2 |
293 | (m) = _m; \ |
d3409d5e |
294 | } while (0) |
d03ab969 |
295 | |
d3409d5e |
296 | /* --- @mp_resize@ --- * |
d03ab969 |
297 | * |
d3409d5e |
298 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
299 | * @size_t sz@ = new size |
d03ab969 |
300 | * |
d3409d5e |
301 | * Returns: --- |
d03ab969 |
302 | * |
d3409d5e |
303 | * Use: Resizes the vector containing the integer's digits. The new |
304 | * size must be at least as large as the current integer's |
d34decd2 |
305 | * length. This isn't really intended for client use. |
d03ab969 |
306 | */ |
307 | |
d3409d5e |
308 | extern void mp_resize(mp */*m*/, size_t /*sz*/); |
309 | |
310 | #define MP_RESIZE(m, ssz) do { \ |
311 | mp *_m = (m); \ |
312 | size_t _sz = (ssz); \ |
d34decd2 |
313 | mparena *_a = (_m->f & MP_BURN) ? MPARENA_SECURE : MPARENA_GLOBAL; \ |
314 | mpw *_v; \ |
d3409d5e |
315 | size_t _len = MP_LEN(_m); \ |
d34decd2 |
316 | assert(((void)"can't make size less than length", _sz >= _len)); \ |
317 | _v = mpalloc(_a, _sz); \ |
d9a8ae10 |
318 | if (!(_m->f & MP_UNDEF)) \ |
319 | memcpy(_v, _m->v, MPWS(_len)); \ |
d3409d5e |
320 | if (_m->f & MP_BURN) \ |
321 | memset(_m->v, 0, MPWS(_m->sz)); \ |
d34decd2 |
322 | mpfree(_m->a, _m->v); \ |
323 | _m->a = _a; \ |
d3409d5e |
324 | _m->v = _v; \ |
325 | _m->vl = _v + _len; \ |
d3409d5e |
326 | } while (0) |
d03ab969 |
327 | |
d3409d5e |
328 | /* --- @mp_ensure@ --- * |
d03ab969 |
329 | * |
d3409d5e |
330 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
331 | * @size_t sz@ = required size |
d03ab969 |
332 | * |
333 | * Returns: --- |
334 | * |
d3409d5e |
335 | * Use: Ensures that the integer has enough space for @sz@ digits. |
336 | * The value is not changed. |
d03ab969 |
337 | */ |
338 | |
d3409d5e |
339 | extern void mp_ensure(mp */*m*/, size_t /*sz*/); |
340 | |
341 | #define MP_ENSURE(m, ssz) do { \ |
d34decd2 |
342 | mp *_m = (m); \ |
d3409d5e |
343 | size_t _ssz = (ssz); \ |
d34decd2 |
344 | size_t _len = MP_LEN(_m); \ |
345 | if (_ssz >= _len) { \ |
346 | if (_ssz > _m->sz) \ |
347 | mp_resize(_m, _ssz); \ |
348 | if (!(_m->f & MP_UNDEF) && _ssz > _len) \ |
349 | memset(_m->vl, 0, MPWS(_ssz - _len)); \ |
350 | _m->vl = _m->v + _ssz; \ |
351 | } \ |
d3409d5e |
352 | } while (0) |
d03ab969 |
353 | |
d34decd2 |
354 | /* --- @mp_dest@ --- * |
d03ab969 |
355 | * |
d34decd2 |
356 | * Arguments: @mp *m@ = a suggested destination integer |
357 | * @size_t sz@ = size required for result, in digits |
358 | * @unsigned f@ = various flags |
359 | * |
360 | * Returns: A pointer to an appropriate destination. |
361 | * |
362 | * Use: Converts a suggested destination into a real destination with |
363 | * the required properties. If the real destination is @d@, |
364 | * then the following properties will hold: |
365 | * |
366 | * * @d@ will have exactly one reference. |
d03ab969 |
367 | * |
d34decd2 |
368 | * * If @m@ is not @MP_NEW@, then the contents of @m@ will not |
369 | * change, unless @f@ has the @MP_UNDEF@ flag set. |
d03ab969 |
370 | * |
d34decd2 |
371 | * * If @m@ is not @MP_NEW@, then he reference count of @m@ on |
372 | * entry is equal to the sum of the counts of @d@ and @m@ on |
373 | * exit. |
374 | * |
375 | * * The size of @d@ will be at least @sz@. |
376 | * |
377 | * * If @f@ has the @MP_BURN@ flag set, then @d@ will be |
378 | * allocated from @MPARENA_SECURE@. |
379 | * |
380 | * Understanding this function is crucial to using Catacomb's |
381 | * multiprecision integer library effectively. |
d03ab969 |
382 | */ |
383 | |
d34decd2 |
384 | extern mp *mp_dest(mp */*m*/, size_t /*sz*/, unsigned /*f*/); |
d03ab969 |
385 | |
d34decd2 |
386 | #define MP_DEST(m, ssz, f) do { \ |
d3409d5e |
387 | mp *_m = (m); \ |
d34decd2 |
388 | size_t _ssz = (ssz); \ |
389 | unsigned _f = (f); \ |
390 | _m = mp_dest(_m, _ssz, _f); \ |
d3409d5e |
391 | (m) = _m; \ |
392 | } while (0) |
393 | |
394 | /*----- Size manipulation -------------------------------------------------*/ |
395 | |
396 | /* --- @mp_shrink@ --- * |
d03ab969 |
397 | * |
d3409d5e |
398 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
399 | * |
400 | * Returns: --- |
401 | * |
d3409d5e |
402 | * Use: Reduces the recorded length of an integer. This doesn't |
403 | * reduce the amount of memory used, although it can improve |
404 | * performance a bit. To reduce memory, use @mp_minimize@ |
405 | * instead. This can't change the value of an integer, and is |
406 | * therefore safe to use even when there are multiple |
407 | * references. |
d03ab969 |
408 | */ |
409 | |
d3409d5e |
410 | extern void mp_shrink(mp */*m*/); |
d03ab969 |
411 | |
d3409d5e |
412 | #define MP_SHRINK(m) do { \ |
413 | mp *_mm = (m); \ |
414 | MPX_SHRINK(_mm->v, _mm->vl); \ |
415 | if (!MP_LEN(_mm)) \ |
416 | _mm->f &= ~MP_NEG; \ |
417 | } while (0) |
418 | |
419 | /* --- @mp_minimize@ --- * |
d03ab969 |
420 | * |
d3409d5e |
421 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
422 | * |
423 | * Returns: --- |
424 | * |
d3409d5e |
425 | * Use: Reduces the amount of memory an integer uses. It's best to |
426 | * do this to numbers which aren't going to change in the |
427 | * future. |
d03ab969 |
428 | */ |
429 | |
d3409d5e |
430 | extern void mp_minimize(mp */*m*/); |
d03ab969 |
431 | |
d3409d5e |
432 | /*----- Bit scanning ------------------------------------------------------*/ |
d03ab969 |
433 | |
d9a8ae10 |
434 | #ifndef CATACOMB_MPSCAN_H |
d3409d5e |
435 | # include "mpscan.h" |
436 | #endif |
437 | |
438 | /* --- @mp_scan@ --- * |
d03ab969 |
439 | * |
d3409d5e |
440 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
441 | * @const mp *m@ = pointer to a multiprecision integer |
d03ab969 |
442 | * |
443 | * Returns: --- |
444 | * |
d3409d5e |
445 | * Use: Initializes a bitscanner on a multiprecision integer. |
d03ab969 |
446 | */ |
447 | |
d3409d5e |
448 | extern void mp_scan(mpscan */*sc*/, const mp */*m*/); |
449 | |
450 | #define MP_SCAN(sc, m) do { \ |
a790733d |
451 | const mp *_mm = (m); \ |
d3409d5e |
452 | mpscan *_sc = (sc); \ |
453 | MPSCAN_INITX(_sc, _mm->v, _mm->vl); \ |
454 | } while (0) |
455 | |
5fbe3846 |
456 | /* --- @mp_rscan@ --- * |
457 | * |
458 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
459 | * @const mp *m@ = pointer to a multiprecision integer |
460 | * |
461 | * Returns: --- |
462 | * |
463 | * Use: Initializes a reverse bitscanner on a multiprecision |
464 | * integer. |
465 | */ |
466 | |
467 | extern void mp_rscan(mpscan */*sc*/, const mp */*m*/); |
468 | |
469 | #define MP_RSCAN(sc, m) do { \ |
470 | const mp *_mm = (m); \ |
471 | mpscan *_sc = (sc); \ |
472 | MPSCAN_RINITX(_sc, _mm->v, _mm->vl); \ |
473 | } while (0) |
474 | |
d3409d5e |
475 | /* --- Other bitscanning aliases --- */ |
476 | |
477 | #define mp_step mpscan_step |
478 | #define mp_bit mpscan_bit |
5fbe3846 |
479 | #define mp_rstep mpscan_rstep |
480 | #define mp_rbit mpscan_rbit |
d3409d5e |
481 | |
482 | #define MP_STEP MPSCAN_STEP |
483 | #define MP_BIT MPSCAN_BIT |
5fbe3846 |
484 | #define MP_RSTEP MPSCAN_RSTEP |
485 | #define MP_RBIT MPSCAN_RBIT |
d3409d5e |
486 | |
487 | /*----- Loading and storing -----------------------------------------------*/ |
d03ab969 |
488 | |
d3409d5e |
489 | /* --- @mp_octets@ --- * |
d03ab969 |
490 | * |
d3409d5e |
491 | * Arguments: @const mp *m@ = a multiprecision integer |
d03ab969 |
492 | * |
d3409d5e |
493 | * Returns: The number of octets required to represent @m@. |
d03ab969 |
494 | * |
d3409d5e |
495 | * Use: Calculates the external storage required for a multiprecision |
496 | * integer. |
d03ab969 |
497 | */ |
498 | |
24e1e862 |
499 | extern size_t mp_octets(const mp */*m*/); |
500 | |
f09e814a |
501 | /* --- @mp_octets2c@ --- * |
502 | * |
503 | * Arguments: @const mp *m@ = a multiprecision integer |
504 | * |
505 | * Returns: The number of octets required to represent @m@. |
506 | * |
507 | * Use: Calculates the external storage required for a multiprecision |
508 | * integer represented as two's complement. |
509 | */ |
510 | |
511 | extern size_t mp_octets2c(const mp */*m*/); |
512 | |
24e1e862 |
513 | /* --- @mp_bits@ --- * |
514 | * |
515 | * Arguments: @const mp *m@ = a multiprecision integer |
516 | * |
517 | * Returns: The number of bits required to represent @m@. |
518 | * |
519 | * Use: Calculates the external storage required for a multiprecision |
520 | * integer. |
521 | */ |
522 | |
523 | extern unsigned long mp_bits(const mp */*m*/); |
d03ab969 |
524 | |
d3409d5e |
525 | /* --- @mp_loadl@ --- * |
d03ab969 |
526 | * |
d3409d5e |
527 | * Arguments: @mp *d@ = destination |
528 | * @const void *pv@ = pointer to source data |
529 | * @size_t sz@ = size of the source data |
d03ab969 |
530 | * |
d3409d5e |
531 | * Returns: Resulting multiprecision number. |
d03ab969 |
532 | * |
d3409d5e |
533 | * Use: Loads a multiprecision number from an array of octets. The |
534 | * first byte in the array is the least significant. More |
535 | * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$% |
536 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
d03ab969 |
537 | */ |
538 | |
d3409d5e |
539 | extern mp *mp_loadl(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d03ab969 |
540 | |
d3409d5e |
541 | /* --- @mp_storel@ --- * |
542 | * |
543 | * Arguments: @const mp *m@ = source |
544 | * @void *pv@ = pointer to output array |
545 | * @size_t sz@ = size of the output array |
546 | * |
547 | * Returns: --- |
548 | * |
549 | * Use: Stores a multiprecision number in an array of octets. The |
550 | * first byte in the array is the least significant. If the |
551 | * array is too small to represent the number, high-order bits |
552 | * are truncated; if the array is too large, high order bytes |
553 | * are filled with zeros. More formally, if the number is |
554 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
555 | * then the array is %$b_0, b_1, \ldots, b_{n-1}$%. |
556 | */ |
d03ab969 |
557 | |
d3409d5e |
558 | extern void mp_storel(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
d03ab969 |
559 | |
d3409d5e |
560 | /* --- @mp_loadb@ --- * |
d03ab969 |
561 | * |
d3409d5e |
562 | * Arguments: @mp *d@ = destination |
563 | * @const void *pv@ = pointer to source data |
564 | * @size_t sz@ = size of the source data |
d03ab969 |
565 | * |
d3409d5e |
566 | * Returns: Resulting multiprecision number. |
d03ab969 |
567 | * |
d3409d5e |
568 | * Use: Loads a multiprecision number from an array of octets. The |
569 | * last byte in the array is the least significant. More |
570 | * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$% |
571 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
d03ab969 |
572 | */ |
573 | |
d3409d5e |
574 | extern mp *mp_loadb(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d03ab969 |
575 | |
d3409d5e |
576 | /* --- @mp_storeb@ --- * |
d03ab969 |
577 | * |
d3409d5e |
578 | * Arguments: @const mp *m@ = source |
579 | * @void *pv@ = pointer to output array |
580 | * @size_t sz@ = size of the output array |
d03ab969 |
581 | * |
582 | * Returns: --- |
583 | * |
d3409d5e |
584 | * Use: Stores a multiprecision number in an array of octets. The |
585 | * last byte in the array is the least significant. If the |
586 | * array is too small to represent the number, high-order bits |
587 | * are truncated; if the array is too large, high order bytes |
588 | * are filled with zeros. More formally, if the number is |
589 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
590 | * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%. |
d03ab969 |
591 | */ |
592 | |
d3409d5e |
593 | extern void mp_storeb(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
d03ab969 |
594 | |
f09e814a |
595 | /* --- @mp_loadl2c@ --- * |
d03ab969 |
596 | * |
d3409d5e |
597 | * Arguments: @mp *d@ = destination |
f09e814a |
598 | * @const void *pv@ = pointer to source data |
599 | * @size_t sz@ = size of the source data |
600 | * |
601 | * Returns: Resulting multiprecision number. |
d03ab969 |
602 | * |
f09e814a |
603 | * Use: Loads a multiprecision number from an array of octets as |
604 | * two's complement. The first byte in the array is the least |
605 | * significant. |
d3409d5e |
606 | */ |
607 | |
f09e814a |
608 | extern mp *mp_loadl2c(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d3409d5e |
609 | |
f09e814a |
610 | /* --- @mp_storel2c@ --- * |
611 | * |
612 | * Arguments: @const mp *m@ = source |
613 | * @void *pv@ = pointer to output array |
614 | * @size_t sz@ = size of the output array |
615 | * |
616 | * Returns: --- |
617 | * |
618 | * Use: Stores a multiprecision number in an array of octets as two's |
619 | * complement. The first byte in the array is the least |
620 | * significant. If the array is too small to represent the |
621 | * number, high-order bits are truncated; if the array is too |
622 | * large, high order bytes are sign-extended. |
623 | */ |
624 | |
625 | extern void mp_storel2c(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
626 | |
627 | /* --- @mp_loadb2c@ --- * |
d3409d5e |
628 | * |
629 | * Arguments: @mp *d@ = destination |
f09e814a |
630 | * @const void *pv@ = pointer to source data |
631 | * @size_t sz@ = size of the source data |
d03ab969 |
632 | * |
f09e814a |
633 | * Returns: Resulting multiprecision number. |
634 | * |
635 | * Use: Loads a multiprecision number from an array of octets as |
636 | * two's complement. The last byte in the array is the least |
637 | * significant. |
d03ab969 |
638 | */ |
639 | |
f09e814a |
640 | extern mp *mp_loadb2c(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
641 | |
642 | /* --- @mp_storeb2c@ --- * |
643 | * |
644 | * Arguments: @const mp *m@ = source |
645 | * @void *pv@ = pointer to output array |
646 | * @size_t sz@ = size of the output array |
647 | * |
648 | * Returns: --- |
649 | * |
650 | * Use: Stores a multiprecision number in an array of octets, as |
651 | * two's complement. The last byte in the array is the least |
652 | * significant. If the array is too small to represent the |
653 | * number, high-order bits are truncated; if the array is too |
654 | * large, high order bytes are sign-extended. |
655 | */ |
656 | |
657 | extern void mp_storeb2c(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
658 | |
659 | /*----- Simple arithmetic -------------------------------------------------*/ |
d03ab969 |
660 | |
f09e814a |
661 | /* --- @mp_lsl@, @mp_lsr@ --- * |
d03ab969 |
662 | * |
d3409d5e |
663 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
664 | * @mp *a@ = source |
d3409d5e |
665 | * @size_t n@ = number of bits to move |
d03ab969 |
666 | * |
f09e814a |
667 | * Returns: Result, @a@ shifted left or right by @n@. |
d3409d5e |
668 | */ |
669 | |
d9a8ae10 |
670 | extern mp *mp_lsl(mp */*d*/, mp */*a*/, size_t /*n*/); |
f09e814a |
671 | extern mp *mp_lsr(mp */*d*/, mp */*a*/, size_t /*n*/); |
d3409d5e |
672 | |
f09e814a |
673 | /* --- @mp_lsl2c@, @mp_lsr2c@ --- * |
d3409d5e |
674 | * |
675 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
676 | * @mp *a@ = source |
d3409d5e |
677 | * @size_t n@ = number of bits to move |
d03ab969 |
678 | * |
f09e814a |
679 | * Returns: Result, @a@ shifted left or right by @n@. Handles the |
680 | * pretence of sign-extension for negative numbers. |
d03ab969 |
681 | */ |
682 | |
f09e814a |
683 | extern mp *mp_lsl2c(mp */*d*/, mp */*a*/, size_t /*n*/); |
684 | extern mp *mp_lsr2c(mp */*d*/, mp */*a*/, size_t /*n*/); |
685 | |
686 | /* --- @mp_testbit@ --- * |
687 | * |
688 | * Arguments: @mp *x@ = a large integer |
09d00c6b |
689 | * @unsigned long n@ = which bit to test |
f09e814a |
690 | * |
691 | * Returns: Nonzero if the bit is set, zero if not. |
692 | */ |
693 | |
09d00c6b |
694 | extern int mp_testbit(mp */*x*/, unsigned long /*n*/); |
f09e814a |
695 | |
696 | /* --- @mp_testbit2c@ --- * |
697 | * |
698 | * Arguments: @mp *x@ = a large integer |
09d00c6b |
699 | * @unsigned long n@ = which bit to test |
f09e814a |
700 | * |
701 | * Returns: Nonzero if the bit is set, zero if not. Fakes up two's |
702 | * complement representation. |
703 | */ |
704 | |
09d00c6b |
705 | extern int mp_testbit2c(mp */*x*/, unsigned long /*n*/); |
d03ab969 |
706 | |
740c9553 |
707 | /* --- @mp_eq@ --- * |
708 | * |
709 | * Arguments: @const mp *a, *b@ = two numbers |
710 | * |
711 | * Returns: Nonzero if the numbers are equal. |
712 | */ |
713 | |
714 | extern int mp_eq(const mp */*a*/, const mp */*b*/); |
715 | |
716 | #define MP_EQ(a, b) \ |
717 | ((((a)->f ^ (b)->f) & MP_NEG) == 0 && \ |
718 | mpx_ueq((a)->v, (a)->vl, (b)->v, (b)->vl)) |
719 | |
d3409d5e |
720 | /* --- @mp_cmp@ --- * |
d03ab969 |
721 | * |
d3409d5e |
722 | * Arguments: @const mp *a, *b@ = two numbers |
d03ab969 |
723 | * |
d3409d5e |
724 | * Returns: Less than, equal to or greater than zero, according to |
725 | * whether @a@ is less than, equal to or greater than @b@. |
726 | */ |
727 | |
728 | extern int mp_cmp(const mp */*a*/, const mp */*b*/); |
729 | |
730 | #define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0) |
731 | |
09d00c6b |
732 | /* --- @mp_setbit@, @mp_clearbit@ --- * |
733 | * |
734 | * Arguments: @mp *d@ = a destination |
735 | * @mp *x@ = a large integer |
736 | * @unsigned long n@ = which bit to modify |
737 | * |
738 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
739 | */ |
740 | |
741 | extern mp *mp_setbit(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
742 | extern mp *mp_clearbit(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
743 | |
744 | /* --- @mp_setbit2c@, @mp_clearbit2c@ --- * |
745 | * |
746 | * Arguments: @mp *d@ = a destination |
747 | * @mp *x@ = a large integer |
748 | * @unsigned long n@ = which bit to modify |
749 | * |
750 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
751 | * Fakes up two's complement representation. |
752 | */ |
753 | |
754 | extern mp *mp_setbit2c(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
755 | extern mp *mp_clearbit2c(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
756 | |
f09e814a |
757 | /* --- @mp_bitop@ --- * |
0f32e0f8 |
758 | * |
759 | * Arguments: @mp *d@ = destination |
760 | * @mp *a, *b@ = sources |
761 | * |
f09e814a |
762 | * Returns: The result of the given bitwise operation. These functions |
763 | * don't handle negative numbers at all sensibly. For that, use |
764 | * the @...2c@ variants. The functions are named after the |
765 | * truth tables they generate: |
766 | * |
767 | * a: 0011 |
768 | * b: 0101 |
769 | * @mpx_bitXXXX@ |
0f32e0f8 |
770 | */ |
771 | |
f09e814a |
772 | #define MP_BITDECL(string) \ |
773 | extern mp *mp_bit##string(mp */*d*/, mp */*a*/, mp */*b*/); |
774 | MPX_DOBIN(MP_BITDECL) |
775 | |
776 | /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- * |
777 | * |
778 | * Synonyms for the commonly-used functions. |
779 | */ |
780 | |
781 | #define mp_and mp_bit0001 |
782 | #define mp_or mp_bit0111 |
783 | #define mp_nand mp_bit1110 |
784 | #define mp_nor mp_bit1000 |
785 | #define mp_xor mp_bit0110 |
786 | |
787 | /* --- @mp_not@ --- * |
788 | * |
789 | * Arguments: @mp *d@ = destination |
790 | * @mp *a@ = source |
791 | * |
792 | * Returns: The bitwise complement of the source. |
793 | */ |
794 | |
0f32e0f8 |
795 | extern mp *mp_not(mp */*d*/, mp */*a*/); |
796 | |
f09e814a |
797 | /* --- @mp_bitop2c@ --- * |
798 | * |
799 | * Arguments: @mp *d@ = destination |
800 | * @mp *a, *b@ = sources |
801 | * |
802 | * Returns: The result of the given bitwise operation. Negative numbers |
803 | * are treated as two's complement, sign-extended infinitely to |
804 | * the left. The functions are named after the truth tables |
805 | * they generate: |
806 | * |
807 | * a: 0011 |
808 | * b: 0101 |
809 | * @mpx_bitXXXX@ |
810 | */ |
811 | |
812 | #define MP_BIT2CDECL(string) \ |
813 | extern mp *mp_bit##string##2c(mp */*d*/, mp */*a*/, mp */*b*/); |
814 | MPX_DOBIN(MP_BIT2CDECL) |
815 | |
816 | /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- * |
817 | * |
818 | * Synonyms for the commonly-used functions. |
819 | */ |
820 | |
821 | #define mp_and2c mp_bit00012c |
822 | #define mp_or2c mp_bit01112c |
823 | #define mp_nand2c mp_bit11102c |
824 | #define mp_nor2c mp_bit10002c |
825 | #define mp_xor2c mp_bit01102c |
826 | |
827 | /* --- @mp_not2c@ --- * |
828 | * |
829 | * Arguments: @mp *d@ = destination |
830 | * @mp *a@ = source |
831 | * |
832 | * Returns: The sign-extended complement of the argument. |
833 | */ |
834 | |
835 | extern mp *mp_not2c(mp */*d*/, mp */*a*/); |
836 | |
d3409d5e |
837 | /* --- @mp_add@ --- * |
d03ab969 |
838 | * |
d3409d5e |
839 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
840 | * @mp *a, *b@ = sources |
d3409d5e |
841 | * |
842 | * Returns: Result, @a@ added to @b@. |
d03ab969 |
843 | */ |
844 | |
d9a8ae10 |
845 | extern mp *mp_add(mp */*d*/, mp */*a*/, mp */*b*/); |
d03ab969 |
846 | |
d3409d5e |
847 | /* --- @mp_sub@ --- * |
848 | * |
849 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
850 | * @mp *a, *b@ = sources |
d3409d5e |
851 | * |
852 | * Returns: Result, @b@ subtracted from @a@. |
853 | */ |
d03ab969 |
854 | |
d9a8ae10 |
855 | extern mp *mp_sub(mp */*d*/, mp */*a*/, mp */*b*/); |
d3409d5e |
856 | |
857 | /* --- @mp_mul@ --- * |
d03ab969 |
858 | * |
d3409d5e |
859 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
860 | * @mp *a, *b@ = sources |
d03ab969 |
861 | * |
d3409d5e |
862 | * Returns: Result, @a@ multiplied by @b@. |
863 | */ |
864 | |
d9a8ae10 |
865 | extern mp *mp_mul(mp */*d*/, mp */*a*/, mp */*b*/); |
d3409d5e |
866 | |
867 | /* --- @mp_sqr@ --- * |
868 | * |
869 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
870 | * @mp *a@ = source |
d3409d5e |
871 | * |
872 | * Returns: Result, @a@ squared. |
873 | */ |
874 | |
d9a8ae10 |
875 | extern mp *mp_sqr(mp */*d*/, mp */*a*/); |
d3409d5e |
876 | |
877 | /* --- @mp_div@ --- * |
d03ab969 |
878 | * |
d3409d5e |
879 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
d9a8ae10 |
880 | * @mp *a, *b@ = sources |
d3409d5e |
881 | * |
882 | * Use: Calculates the quotient and remainder when @a@ is divided by |
883 | * @b@. |
d03ab969 |
884 | */ |
885 | |
d9a8ae10 |
886 | extern void mp_div(mp **/*qq*/, mp **/*rr*/, mp */*a*/, mp */*b*/); |
d3409d5e |
887 | |
22a073c0 |
888 | /* --- @mp_odd@ --- * |
889 | * |
890 | * Arguments: @mp *d@ = pointer to destination integer |
891 | * @mp *m@ = pointer to source integer |
892 | * @size_t *s@ = where to store the power of 2 |
893 | * |
894 | * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%. |
895 | * |
896 | * Use: Computes a power of two and an odd integer which, when |
897 | * multiplied, give a specified result. This sort of thing is |
898 | * useful in number theory quite often. |
899 | */ |
900 | |
901 | extern mp *mp_odd(mp */*d*/, mp */*m*/, size_t */*s*/); |
902 | |
d3409d5e |
903 | /*----- More advanced algorithms ------------------------------------------*/ |
d03ab969 |
904 | |
22a073c0 |
905 | /* --- @mp_sqrt@ --- * |
906 | * |
907 | * Arguments: @mp *d@ = pointer to destination integer |
908 | * @mp *a@ = (nonnegative) integer to take square root of |
909 | * |
910 | * Returns: The largest integer %$x$% such that %$x^2 \le a$%. |
911 | * |
912 | * Use: Computes integer square roots. |
913 | * |
914 | * The current implementation isn't very good: it uses the |
915 | * Newton-Raphson method to find an approximation to %$a$%. If |
916 | * there's any demand for a better version, I'll write one. |
917 | */ |
918 | |
919 | extern mp *mp_sqrt(mp */*d*/, mp */*a*/); |
920 | |
d3409d5e |
921 | /* --- @mp_gcd@ --- * |
d03ab969 |
922 | * |
d3409d5e |
923 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
924 | * @mp *a, *b@ = sources (must be nonzero) |
d03ab969 |
925 | * |
926 | * Returns: --- |
927 | * |
d3409d5e |
928 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
929 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
d9a8ae10 |
930 | * inverses. Neither @a@ nor @b@ may be zero. |
d03ab969 |
931 | */ |
932 | |
d3409d5e |
933 | extern void mp_gcd(mp **/*gcd*/, mp **/*xx*/, mp **/*yy*/, |
934 | mp */*a*/, mp */*b*/); |
935 | |
5b00a0ea |
936 | /* --- @mp_jacobi@ --- * |
937 | * |
938 | * Arguments: @mp *a@ = an integer less than @n@ |
939 | * @mp *n@ = an odd integer |
940 | * |
941 | * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%. |
942 | * |
943 | * Use: Computes the Jacobi symbol. If @n@ is prime, this is the |
944 | * Legendre symbol and is equal to 1 if and only if @a@ is a |
945 | * quadratic residue mod @n@. The result is zero if and only if |
946 | * @a@ and @n@ have a common factor greater than one. |
947 | */ |
948 | |
22a073c0 |
949 | extern int mp_jacobi(mp */*a*/, mp */*n*/); |
950 | |
951 | /* --- @mp_modsqrt@ --- * |
952 | * |
953 | * Arguments: @mp *d@ = destination integer |
954 | * @mp *a@ = source integer |
955 | * @mp *p@ = modulus (must be prime) |
956 | * |
957 | * Returns: If %$a$% is a quadratic residue, a square root of %$a$%; else |
958 | * a null pointer. |
959 | * |
960 | * Use: Returns an integer %$x$% such that %$x^2 \equiv a \pmod{p}$%, |
961 | * if one exists; else a null pointer. This function will not |
962 | * work if %$p$% is composite: you must factor the modulus, take |
963 | * a square root mod each factor, and recombine the results |
964 | * using the Chinese Remainder Theorem. |
965 | */ |
966 | |
967 | extern mp *mp_modsqrt(mp */*d*/, mp */*a*/, mp */*p*/); |
5b00a0ea |
968 | |
d3409d5e |
969 | /*----- Test harness support ----------------------------------------------*/ |
970 | |
971 | #include <mLib/testrig.h> |
972 | |
d9a8ae10 |
973 | #ifndef CATACOMB_MPTEXT_H |
d3409d5e |
974 | # include "mptext.h" |
975 | #endif |
976 | |
977 | extern const test_type type_mp; |
d03ab969 |
978 | |
979 | /*----- That's all, folks -------------------------------------------------*/ |
980 | |
981 | #ifdef __cplusplus |
982 | } |
983 | #endif |
984 | |
985 | #endif |