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