d03ab969 |
1 | /* -*-c-*- |
2 | * |
3cd24abb |
3 | * $Id: mp.h,v 1.16 2002/10/15 22:57:22 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 $ |
3cd24abb |
33 | * Revision 1.16 2002/10/15 22:57:22 mdw |
34 | * Handy new comparison macros. |
35 | * |
397041a9 |
36 | * Revision 1.15 2002/10/15 19:18:31 mdw |
37 | * New operation to negate numbers. |
38 | * |
09d00c6b |
39 | * Revision 1.14 2002/10/15 00:19:40 mdw |
40 | * Bit setting and clearing functions. |
41 | * |
f09e814a |
42 | * Revision 1.13 2002/10/06 22:52:50 mdw |
43 | * Pile of changes for supporting two's complement properly. |
44 | * |
3bc0a0fe |
45 | * Revision 1.12 2001/06/16 12:57:43 mdw |
46 | * Move the @mpmont_factor@ structure and rename it now that it's used for |
47 | * Barrett simultaneous exponentiation too. |
48 | * |
0f32e0f8 |
49 | * Revision 1.11 2001/04/03 19:36:05 mdw |
50 | * Add some simple bitwise operations so that Perl can use them. |
51 | * |
740c9553 |
52 | * Revision 1.10 2000/10/08 12:03:16 mdw |
53 | * Provide @mp_eq@ and @MP_EQ@ for rapidly testing equality of two |
54 | * integers. |
55 | * |
5fbe3846 |
56 | * Revision 1.9 2000/07/29 17:03:31 mdw |
57 | * Add support for left-to-right bitscanning, for use in modular |
58 | * exponentiation. |
59 | * |
22a073c0 |
60 | * Revision 1.8 2000/06/22 19:02:01 mdw |
61 | * Add new functions. |
62 | * |
d34decd2 |
63 | * Revision 1.7 2000/06/17 11:45:09 mdw |
64 | * Major memory management overhaul. Added arena support. Use the secure |
65 | * arena for secret integers. Replace and improve the MP management macros |
66 | * (e.g., replace MP_MODIFY by MP_DEST). |
67 | * |
d9a8ae10 |
68 | * Revision 1.6 1999/12/10 23:19:46 mdw |
69 | * Minor bugfixes. New interface for suggested destinations. |
70 | * |
5b00a0ea |
71 | * Revision 1.5 1999/11/22 20:50:37 mdw |
72 | * Add support for computing Jacobi symbols. |
73 | * |
24e1e862 |
74 | * Revision 1.4 1999/11/21 22:13:02 mdw |
75 | * Add mp version of MPX_BITS. |
76 | * |
a790733d |
77 | * Revision 1.3 1999/11/19 13:19:14 mdw |
78 | * Fix const annotation. |
79 | * |
d3409d5e |
80 | * Revision 1.2 1999/11/17 18:02:16 mdw |
81 | * New multiprecision integer arithmetic suite. |
d03ab969 |
82 | * |
83 | */ |
84 | |
d9a8ae10 |
85 | #ifndef CATACOMB_MP_H |
86 | #define CATACOMB_MP_H |
d03ab969 |
87 | |
88 | #ifdef __cplusplus |
89 | extern "C" { |
90 | #endif |
91 | |
92 | /*----- Header files ------------------------------------------------------*/ |
93 | |
d3409d5e |
94 | #include <assert.h> |
d03ab969 |
95 | #include <string.h> |
96 | |
d3409d5e |
97 | #include <mLib/sub.h> |
98 | |
d9a8ae10 |
99 | #ifndef CATACOMB_MPW_H |
d3409d5e |
100 | # include "mpw.h" |
d03ab969 |
101 | #endif |
102 | |
d34decd2 |
103 | #ifndef CATACOMB_ARENA_H |
104 | # include "arena.h" |
105 | #endif |
106 | |
107 | #ifndef CATACOMB_MPARENA_H |
108 | # include "mparena.h" |
109 | #endif |
110 | |
d9a8ae10 |
111 | #ifndef CATACOMB_MPX_H |
d03ab969 |
112 | # include "mpx.h" |
113 | #endif |
114 | |
d03ab969 |
115 | /*----- Data structures ---------------------------------------------------*/ |
116 | |
3bc0a0fe |
117 | /* --- A multiprecision integer --- */ |
118 | |
d03ab969 |
119 | typedef struct mp { |
3bc0a0fe |
120 | mpw *v, *vl; /* Vector of digits, current limit */ |
121 | size_t sz; /* Size of digit buffer in words */ |
122 | mparena *a; /* Arena for buffer allocation */ |
123 | unsigned f; /* Flags (see below) */ |
124 | unsigned ref; /* Reference counter */ |
d03ab969 |
125 | } mp; |
126 | |
3bc0a0fe |
127 | #define MP_NEG 1u /* Negative (signed magnitude) */ |
128 | #define MP_BURN 2u /* Secret (viral flag) */ |
129 | #define MP_CONST 4u /* Uses strange memory allocation */ |
130 | #define MP_UNDEF 8u /* Contains nothing interesting */ |
131 | #define MP_DESTROYED 16u /* Has been destroyed */ |
132 | |
133 | /* --- A factor for simultaneous exponentation --- * |
134 | * |
135 | * Used by the Montgomery and Barrett exponentiators. |
136 | */ |
137 | |
138 | typedef struct mp_expfactor { |
139 | mp *base; |
140 | mp *exp; |
141 | } mp_expfactor; |
d03ab969 |
142 | |
d3409d5e |
143 | /*----- Useful constants --------------------------------------------------*/ |
d03ab969 |
144 | |
d3409d5e |
145 | extern mp mp_const[]; |
d03ab969 |
146 | |
d3409d5e |
147 | #define MP_ZERO (&mp_const[0]) |
148 | #define MP_ONE (&mp_const[1]) |
149 | #define MP_TWO (&mp_const[2]) |
150 | #define MP_THREE (&mp_const[3]) |
151 | #define MP_FOUR (&mp_const[4]) |
152 | #define MP_FIVE (&mp_const[5]) |
153 | #define MP_TEN (&mp_const[6]) |
d34decd2 |
154 | #define MP_256 (&mp_const[7]) |
155 | #define MP_MONE (&mp_const[8]) |
d03ab969 |
156 | |
d3409d5e |
157 | #define MP_NEW ((mp *)0) |
d34decd2 |
158 | #define MP_NEWSEC (&mp_const[9]) |
d03ab969 |
159 | |
d34decd2 |
160 | /*----- Trivial macros ----------------------------------------------------*/ |
d03ab969 |
161 | |
d34decd2 |
162 | /* --- @MP_LEN@ --- * |
d03ab969 |
163 | * |
d34decd2 |
164 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
165 | * |
d34decd2 |
166 | * Returns: Length of the integer, in words. |
d03ab969 |
167 | */ |
168 | |
d34decd2 |
169 | #define MP_LEN(m) ((m)->vl - ((m)->v)) |
d03ab969 |
170 | |
d34decd2 |
171 | /*----- Memory management and reference counting --------------------------*/ |
d3409d5e |
172 | |
d34decd2 |
173 | /* --- @mp_new@ --- * |
d03ab969 |
174 | * |
d34decd2 |
175 | * Arguments: @size_t sz@ = size of vector required |
176 | * @unsigned f@ = flags to set |
d03ab969 |
177 | * |
d34decd2 |
178 | * Returns: Pointer to a new MP structure. |
d03ab969 |
179 | * |
d34decd2 |
180 | * Use: Allocates a new multiprecision integer. The data space is |
181 | * allocated from either the standard global or secret arena, |
182 | * depending on the initial flags requested. |
d03ab969 |
183 | */ |
184 | |
d34decd2 |
185 | extern mp *mp_new(size_t /*sz*/, unsigned /*f*/); |
d03ab969 |
186 | |
d34decd2 |
187 | /* --- @mp_create@ --- * |
d03ab969 |
188 | * |
d34decd2 |
189 | * Arguments: @size_t sz@ = size of vector required |
d03ab969 |
190 | * |
d34decd2 |
191 | * Returns: Pointer to pristine new MP structure with enough memory |
192 | * bolted onto it. |
193 | * |
194 | * Use: Creates a new multiprecision integer with indeterminate |
195 | * contents. The integer has a single reference. |
d03ab969 |
196 | */ |
197 | |
d34decd2 |
198 | extern mp *mp_create(size_t /*sz*/); |
d3409d5e |
199 | |
d34decd2 |
200 | /* --- @mp_createsecure@ --- * |
d03ab969 |
201 | * |
d3409d5e |
202 | * Arguments: @size_t sz@ = size of vector required |
d03ab969 |
203 | * |
d3409d5e |
204 | * Returns: Pointer to pristine new MP structure with enough memory |
205 | * bolted onto it. |
d03ab969 |
206 | * |
d3409d5e |
207 | * Use: Creates a new multiprecision integer with indeterminate |
d34decd2 |
208 | * contents. The integer has a single reference. The integer's |
209 | * data space is allocated from the secure arena. Its burn flag |
210 | * is set. |
d03ab969 |
211 | */ |
212 | |
d34decd2 |
213 | extern mp *mp_createsecure(size_t /*sz*/); |
d03ab969 |
214 | |
d3409d5e |
215 | /* --- @mp_build@ --- * |
d03ab969 |
216 | * |
d3409d5e |
217 | * Arguments: @mp *m@ = pointer to an MP block to fill in |
218 | * @mpw *v@ = pointer to a word array |
219 | * @mpw *vl@ = pointer just past end of array |
d03ab969 |
220 | * |
221 | * Returns: --- |
222 | * |
d3409d5e |
223 | * Use: Creates a multiprecision integer representing some smallish |
224 | * number. You must provide storage for the number and dispose |
225 | * of it when you've finished with it. The number is marked as |
226 | * constant while it exists. |
d03ab969 |
227 | */ |
228 | |
d3409d5e |
229 | extern void mp_build(mp */*m*/, mpw */*v*/, mpw */*vl*/); |
d03ab969 |
230 | |
d3409d5e |
231 | /* --- @mp_destroy@ --- * |
d03ab969 |
232 | * |
d3409d5e |
233 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
234 | * |
235 | * Returns: --- |
236 | * |
d3409d5e |
237 | * Use: Destroys a multiprecision integer. The reference count isn't |
238 | * checked. Don't use this function if you don't know what |
239 | * you're doing: use @mp_drop@ instead. |
d03ab969 |
240 | */ |
241 | |
d3409d5e |
242 | extern void mp_destroy(mp */*m*/); |
d03ab969 |
243 | |
d3409d5e |
244 | /* --- @mp_copy@ --- * |
d03ab969 |
245 | * |
d3409d5e |
246 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
247 | * |
d3409d5e |
248 | * Returns: A copy of the given multiprecision integer. |
249 | * |
250 | * Use: Copies the given integer. In fact you just get another |
251 | * reference to the same old one again. |
d03ab969 |
252 | */ |
253 | |
d3409d5e |
254 | extern mp *mp_copy(mp */*m*/); |
d03ab969 |
255 | |
d3409d5e |
256 | #define MP_COPY(m) ((m)->ref++, (m)) |
257 | |
258 | /* --- @mp_drop@ --- * |
d03ab969 |
259 | * |
d3409d5e |
260 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
261 | * |
262 | * Returns: --- |
263 | * |
d3409d5e |
264 | * Use: Drops a reference to an integer which isn't wanted any more. |
265 | * If there are no more references, the integer is destroyed. |
d03ab969 |
266 | */ |
267 | |
d3409d5e |
268 | extern void mp_drop(mp */*m*/); |
d03ab969 |
269 | |
d3409d5e |
270 | #define MP_DROP(m) do { \ |
271 | mp *_mm = (m); \ |
d34decd2 |
272 | _mm->ref--; \ |
273 | if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \ |
d3409d5e |
274 | mp_destroy(_mm); \ |
275 | } while (0) |
276 | |
277 | /* --- @mp_split@ --- * |
d03ab969 |
278 | * |
d3409d5e |
279 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
280 | * |
d3409d5e |
281 | * Returns: A reference to the same integer, possibly with a different |
282 | * address. |
d03ab969 |
283 | * |
d3409d5e |
284 | * Use: Splits off a modifiable version of the integer referred to. |
d03ab969 |
285 | */ |
286 | |
d3409d5e |
287 | extern mp *mp_split(mp */*m*/); |
288 | |
289 | #define MP_SPLIT(m) do { \ |
d34decd2 |
290 | mp *_m = (m); \ |
291 | if ((_m->f & MP_CONST) || _m->ref > 1) { \ |
292 | size_t _len = MP_LEN(_m); \ |
293 | mp *_mm = mp_new(_len, _m->f); \ |
294 | if (!(_m->f & MP_UNDEF)) \ |
295 | memcpy(_mm->v, _m->v, MPWS(_len)); \ |
296 | _m->ref--; \ |
297 | _m = _mm; \ |
d3409d5e |
298 | } \ |
d34decd2 |
299 | (m) = _m; \ |
d3409d5e |
300 | } while (0) |
d03ab969 |
301 | |
d3409d5e |
302 | /* --- @mp_resize@ --- * |
d03ab969 |
303 | * |
d3409d5e |
304 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
305 | * @size_t sz@ = new size |
d03ab969 |
306 | * |
d3409d5e |
307 | * Returns: --- |
d03ab969 |
308 | * |
d3409d5e |
309 | * Use: Resizes the vector containing the integer's digits. The new |
310 | * size must be at least as large as the current integer's |
d34decd2 |
311 | * length. This isn't really intended for client use. |
d03ab969 |
312 | */ |
313 | |
d3409d5e |
314 | extern void mp_resize(mp */*m*/, size_t /*sz*/); |
315 | |
316 | #define MP_RESIZE(m, ssz) do { \ |
317 | mp *_m = (m); \ |
318 | size_t _sz = (ssz); \ |
d34decd2 |
319 | mparena *_a = (_m->f & MP_BURN) ? MPARENA_SECURE : MPARENA_GLOBAL; \ |
320 | mpw *_v; \ |
d3409d5e |
321 | size_t _len = MP_LEN(_m); \ |
d34decd2 |
322 | assert(((void)"can't make size less than length", _sz >= _len)); \ |
323 | _v = mpalloc(_a, _sz); \ |
d9a8ae10 |
324 | if (!(_m->f & MP_UNDEF)) \ |
325 | memcpy(_v, _m->v, MPWS(_len)); \ |
d3409d5e |
326 | if (_m->f & MP_BURN) \ |
327 | memset(_m->v, 0, MPWS(_m->sz)); \ |
d34decd2 |
328 | mpfree(_m->a, _m->v); \ |
329 | _m->a = _a; \ |
d3409d5e |
330 | _m->v = _v; \ |
331 | _m->vl = _v + _len; \ |
d3409d5e |
332 | } while (0) |
d03ab969 |
333 | |
d3409d5e |
334 | /* --- @mp_ensure@ --- * |
d03ab969 |
335 | * |
d3409d5e |
336 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
337 | * @size_t sz@ = required size |
d03ab969 |
338 | * |
339 | * Returns: --- |
340 | * |
d3409d5e |
341 | * Use: Ensures that the integer has enough space for @sz@ digits. |
342 | * The value is not changed. |
d03ab969 |
343 | */ |
344 | |
d3409d5e |
345 | extern void mp_ensure(mp */*m*/, size_t /*sz*/); |
346 | |
347 | #define MP_ENSURE(m, ssz) do { \ |
d34decd2 |
348 | mp *_m = (m); \ |
d3409d5e |
349 | size_t _ssz = (ssz); \ |
d34decd2 |
350 | size_t _len = MP_LEN(_m); \ |
351 | if (_ssz >= _len) { \ |
352 | if (_ssz > _m->sz) \ |
353 | mp_resize(_m, _ssz); \ |
354 | if (!(_m->f & MP_UNDEF) && _ssz > _len) \ |
355 | memset(_m->vl, 0, MPWS(_ssz - _len)); \ |
356 | _m->vl = _m->v + _ssz; \ |
357 | } \ |
d3409d5e |
358 | } while (0) |
d03ab969 |
359 | |
d34decd2 |
360 | /* --- @mp_dest@ --- * |
d03ab969 |
361 | * |
d34decd2 |
362 | * Arguments: @mp *m@ = a suggested destination integer |
363 | * @size_t sz@ = size required for result, in digits |
364 | * @unsigned f@ = various flags |
365 | * |
366 | * Returns: A pointer to an appropriate destination. |
367 | * |
368 | * Use: Converts a suggested destination into a real destination with |
369 | * the required properties. If the real destination is @d@, |
370 | * then the following properties will hold: |
371 | * |
372 | * * @d@ will have exactly one reference. |
d03ab969 |
373 | * |
d34decd2 |
374 | * * If @m@ is not @MP_NEW@, then the contents of @m@ will not |
375 | * change, unless @f@ has the @MP_UNDEF@ flag set. |
d03ab969 |
376 | * |
d34decd2 |
377 | * * If @m@ is not @MP_NEW@, then he reference count of @m@ on |
378 | * entry is equal to the sum of the counts of @d@ and @m@ on |
379 | * exit. |
380 | * |
381 | * * The size of @d@ will be at least @sz@. |
382 | * |
383 | * * If @f@ has the @MP_BURN@ flag set, then @d@ will be |
384 | * allocated from @MPARENA_SECURE@. |
385 | * |
386 | * Understanding this function is crucial to using Catacomb's |
387 | * multiprecision integer library effectively. |
d03ab969 |
388 | */ |
389 | |
d34decd2 |
390 | extern mp *mp_dest(mp */*m*/, size_t /*sz*/, unsigned /*f*/); |
d03ab969 |
391 | |
d34decd2 |
392 | #define MP_DEST(m, ssz, f) do { \ |
d3409d5e |
393 | mp *_m = (m); \ |
d34decd2 |
394 | size_t _ssz = (ssz); \ |
395 | unsigned _f = (f); \ |
396 | _m = mp_dest(_m, _ssz, _f); \ |
d3409d5e |
397 | (m) = _m; \ |
398 | } while (0) |
399 | |
400 | /*----- Size manipulation -------------------------------------------------*/ |
401 | |
402 | /* --- @mp_shrink@ --- * |
d03ab969 |
403 | * |
d3409d5e |
404 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
405 | * |
406 | * Returns: --- |
407 | * |
d3409d5e |
408 | * Use: Reduces the recorded length of an integer. This doesn't |
409 | * reduce the amount of memory used, although it can improve |
410 | * performance a bit. To reduce memory, use @mp_minimize@ |
411 | * instead. This can't change the value of an integer, and is |
412 | * therefore safe to use even when there are multiple |
413 | * references. |
d03ab969 |
414 | */ |
415 | |
d3409d5e |
416 | extern void mp_shrink(mp */*m*/); |
d03ab969 |
417 | |
d3409d5e |
418 | #define MP_SHRINK(m) do { \ |
419 | mp *_mm = (m); \ |
420 | MPX_SHRINK(_mm->v, _mm->vl); \ |
421 | if (!MP_LEN(_mm)) \ |
422 | _mm->f &= ~MP_NEG; \ |
423 | } while (0) |
424 | |
425 | /* --- @mp_minimize@ --- * |
d03ab969 |
426 | * |
d3409d5e |
427 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
428 | * |
429 | * Returns: --- |
430 | * |
d3409d5e |
431 | * Use: Reduces the amount of memory an integer uses. It's best to |
432 | * do this to numbers which aren't going to change in the |
433 | * future. |
d03ab969 |
434 | */ |
435 | |
d3409d5e |
436 | extern void mp_minimize(mp */*m*/); |
d03ab969 |
437 | |
d3409d5e |
438 | /*----- Bit scanning ------------------------------------------------------*/ |
d03ab969 |
439 | |
d9a8ae10 |
440 | #ifndef CATACOMB_MPSCAN_H |
d3409d5e |
441 | # include "mpscan.h" |
442 | #endif |
443 | |
444 | /* --- @mp_scan@ --- * |
d03ab969 |
445 | * |
d3409d5e |
446 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
447 | * @const mp *m@ = pointer to a multiprecision integer |
d03ab969 |
448 | * |
449 | * Returns: --- |
450 | * |
d3409d5e |
451 | * Use: Initializes a bitscanner on a multiprecision integer. |
d03ab969 |
452 | */ |
453 | |
d3409d5e |
454 | extern void mp_scan(mpscan */*sc*/, const mp */*m*/); |
455 | |
456 | #define MP_SCAN(sc, m) do { \ |
a790733d |
457 | const mp *_mm = (m); \ |
d3409d5e |
458 | mpscan *_sc = (sc); \ |
459 | MPSCAN_INITX(_sc, _mm->v, _mm->vl); \ |
460 | } while (0) |
461 | |
5fbe3846 |
462 | /* --- @mp_rscan@ --- * |
463 | * |
464 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
465 | * @const mp *m@ = pointer to a multiprecision integer |
466 | * |
467 | * Returns: --- |
468 | * |
469 | * Use: Initializes a reverse bitscanner on a multiprecision |
470 | * integer. |
471 | */ |
472 | |
473 | extern void mp_rscan(mpscan */*sc*/, const mp */*m*/); |
474 | |
475 | #define MP_RSCAN(sc, m) do { \ |
476 | const mp *_mm = (m); \ |
477 | mpscan *_sc = (sc); \ |
478 | MPSCAN_RINITX(_sc, _mm->v, _mm->vl); \ |
479 | } while (0) |
480 | |
d3409d5e |
481 | /* --- Other bitscanning aliases --- */ |
482 | |
483 | #define mp_step mpscan_step |
484 | #define mp_bit mpscan_bit |
5fbe3846 |
485 | #define mp_rstep mpscan_rstep |
486 | #define mp_rbit mpscan_rbit |
d3409d5e |
487 | |
488 | #define MP_STEP MPSCAN_STEP |
489 | #define MP_BIT MPSCAN_BIT |
5fbe3846 |
490 | #define MP_RSTEP MPSCAN_RSTEP |
491 | #define MP_RBIT MPSCAN_RBIT |
d3409d5e |
492 | |
493 | /*----- Loading and storing -----------------------------------------------*/ |
d03ab969 |
494 | |
d3409d5e |
495 | /* --- @mp_octets@ --- * |
d03ab969 |
496 | * |
d3409d5e |
497 | * Arguments: @const mp *m@ = a multiprecision integer |
d03ab969 |
498 | * |
d3409d5e |
499 | * Returns: The number of octets required to represent @m@. |
d03ab969 |
500 | * |
d3409d5e |
501 | * Use: Calculates the external storage required for a multiprecision |
502 | * integer. |
d03ab969 |
503 | */ |
504 | |
24e1e862 |
505 | extern size_t mp_octets(const mp */*m*/); |
506 | |
f09e814a |
507 | /* --- @mp_octets2c@ --- * |
508 | * |
509 | * Arguments: @const mp *m@ = a multiprecision integer |
510 | * |
511 | * Returns: The number of octets required to represent @m@. |
512 | * |
513 | * Use: Calculates the external storage required for a multiprecision |
514 | * integer represented as two's complement. |
515 | */ |
516 | |
517 | extern size_t mp_octets2c(const mp */*m*/); |
518 | |
24e1e862 |
519 | /* --- @mp_bits@ --- * |
520 | * |
521 | * Arguments: @const mp *m@ = a multiprecision integer |
522 | * |
523 | * Returns: The number of bits required to represent @m@. |
524 | * |
525 | * Use: Calculates the external storage required for a multiprecision |
526 | * integer. |
527 | */ |
528 | |
529 | extern unsigned long mp_bits(const mp */*m*/); |
d03ab969 |
530 | |
d3409d5e |
531 | /* --- @mp_loadl@ --- * |
d03ab969 |
532 | * |
d3409d5e |
533 | * Arguments: @mp *d@ = destination |
534 | * @const void *pv@ = pointer to source data |
535 | * @size_t sz@ = size of the source data |
d03ab969 |
536 | * |
d3409d5e |
537 | * Returns: Resulting multiprecision number. |
d03ab969 |
538 | * |
d3409d5e |
539 | * Use: Loads a multiprecision number from an array of octets. The |
540 | * first byte in the array is the least significant. More |
541 | * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$% |
542 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
d03ab969 |
543 | */ |
544 | |
d3409d5e |
545 | extern mp *mp_loadl(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d03ab969 |
546 | |
d3409d5e |
547 | /* --- @mp_storel@ --- * |
548 | * |
549 | * Arguments: @const mp *m@ = source |
550 | * @void *pv@ = pointer to output array |
551 | * @size_t sz@ = size of the output array |
552 | * |
553 | * Returns: --- |
554 | * |
555 | * Use: Stores a multiprecision number in an array of octets. The |
556 | * first byte in the array is the least significant. If the |
557 | * array is too small to represent the number, high-order bits |
558 | * are truncated; if the array is too large, high order bytes |
559 | * are filled with zeros. More formally, if the number is |
560 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
561 | * then the array is %$b_0, b_1, \ldots, b_{n-1}$%. |
562 | */ |
d03ab969 |
563 | |
d3409d5e |
564 | extern void mp_storel(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
d03ab969 |
565 | |
d3409d5e |
566 | /* --- @mp_loadb@ --- * |
d03ab969 |
567 | * |
d3409d5e |
568 | * Arguments: @mp *d@ = destination |
569 | * @const void *pv@ = pointer to source data |
570 | * @size_t sz@ = size of the source data |
d03ab969 |
571 | * |
d3409d5e |
572 | * Returns: Resulting multiprecision number. |
d03ab969 |
573 | * |
d3409d5e |
574 | * Use: Loads a multiprecision number from an array of octets. The |
575 | * last byte in the array is the least significant. More |
576 | * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$% |
577 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
d03ab969 |
578 | */ |
579 | |
d3409d5e |
580 | extern mp *mp_loadb(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d03ab969 |
581 | |
d3409d5e |
582 | /* --- @mp_storeb@ --- * |
d03ab969 |
583 | * |
d3409d5e |
584 | * Arguments: @const mp *m@ = source |
585 | * @void *pv@ = pointer to output array |
586 | * @size_t sz@ = size of the output array |
d03ab969 |
587 | * |
588 | * Returns: --- |
589 | * |
d3409d5e |
590 | * Use: Stores a multiprecision number in an array of octets. The |
591 | * last byte in the array is the least significant. If the |
592 | * array is too small to represent the number, high-order bits |
593 | * are truncated; if the array is too large, high order bytes |
594 | * are filled with zeros. More formally, if the number is |
595 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
596 | * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%. |
d03ab969 |
597 | */ |
598 | |
d3409d5e |
599 | extern void mp_storeb(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
d03ab969 |
600 | |
f09e814a |
601 | /* --- @mp_loadl2c@ --- * |
d03ab969 |
602 | * |
d3409d5e |
603 | * Arguments: @mp *d@ = destination |
f09e814a |
604 | * @const void *pv@ = pointer to source data |
605 | * @size_t sz@ = size of the source data |
606 | * |
607 | * Returns: Resulting multiprecision number. |
d03ab969 |
608 | * |
f09e814a |
609 | * Use: Loads a multiprecision number from an array of octets as |
610 | * two's complement. The first byte in the array is the least |
611 | * significant. |
d3409d5e |
612 | */ |
613 | |
f09e814a |
614 | extern mp *mp_loadl2c(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d3409d5e |
615 | |
f09e814a |
616 | /* --- @mp_storel2c@ --- * |
617 | * |
618 | * Arguments: @const mp *m@ = source |
619 | * @void *pv@ = pointer to output array |
620 | * @size_t sz@ = size of the output array |
621 | * |
622 | * Returns: --- |
623 | * |
624 | * Use: Stores a multiprecision number in an array of octets as two's |
625 | * complement. The first byte in the array is the least |
626 | * significant. If the array is too small to represent the |
627 | * number, high-order bits are truncated; if the array is too |
628 | * large, high order bytes are sign-extended. |
629 | */ |
630 | |
631 | extern void mp_storel2c(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
632 | |
633 | /* --- @mp_loadb2c@ --- * |
d3409d5e |
634 | * |
635 | * Arguments: @mp *d@ = destination |
f09e814a |
636 | * @const void *pv@ = pointer to source data |
637 | * @size_t sz@ = size of the source data |
d03ab969 |
638 | * |
f09e814a |
639 | * Returns: Resulting multiprecision number. |
640 | * |
641 | * Use: Loads a multiprecision number from an array of octets as |
642 | * two's complement. The last byte in the array is the least |
643 | * significant. |
d03ab969 |
644 | */ |
645 | |
f09e814a |
646 | extern mp *mp_loadb2c(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
647 | |
648 | /* --- @mp_storeb2c@ --- * |
649 | * |
650 | * Arguments: @const mp *m@ = source |
651 | * @void *pv@ = pointer to output array |
652 | * @size_t sz@ = size of the output array |
653 | * |
654 | * Returns: --- |
655 | * |
656 | * Use: Stores a multiprecision number in an array of octets, as |
657 | * two's complement. The last byte in the array is the least |
658 | * significant. If the array is too small to represent the |
659 | * number, high-order bits are truncated; if the array is too |
660 | * large, high order bytes are sign-extended. |
661 | */ |
662 | |
663 | extern void mp_storeb2c(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
664 | |
397041a9 |
665 | /*----- Bit operations ----------------------------------------------------*/ |
d03ab969 |
666 | |
397041a9 |
667 | /* --- @mp_not@ --- * |
d03ab969 |
668 | * |
d3409d5e |
669 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
670 | * @mp *a@ = source |
d03ab969 |
671 | * |
397041a9 |
672 | * Returns: The bitwise complement of the source. |
673 | */ |
d3409d5e |
674 | |
397041a9 |
675 | extern mp *mp_not(mp */*d*/, mp */*a*/); |
d3409d5e |
676 | |
397041a9 |
677 | /* --- @mp_bitop@ --- * |
d3409d5e |
678 | * |
679 | * Arguments: @mp *d@ = destination |
397041a9 |
680 | * @mp *a, *b@ = sources |
d03ab969 |
681 | * |
397041a9 |
682 | * Returns: The result of the given bitwise operation. These functions |
683 | * don't handle negative numbers at all sensibly. For that, use |
684 | * the @...2c@ variants. The functions are named after the |
685 | * truth tables they generate: |
686 | * |
687 | * a: 0011 |
688 | * b: 0101 |
689 | * @mpx_bitXXXX@ |
d03ab969 |
690 | */ |
691 | |
397041a9 |
692 | #define MP_BITDECL(string) \ |
693 | extern mp *mp_bit##string(mp */*d*/, mp */*a*/, mp */*b*/); |
694 | MPX_DOBIN(MP_BITDECL) |
f09e814a |
695 | |
397041a9 |
696 | /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- * |
f09e814a |
697 | * |
397041a9 |
698 | * Synonyms for the commonly-used functions. |
f09e814a |
699 | */ |
700 | |
397041a9 |
701 | #define mp_and mp_bit0001 |
702 | #define mp_or mp_bit0111 |
703 | #define mp_nand mp_bit1110 |
704 | #define mp_nor mp_bit1000 |
705 | #define mp_xor mp_bit0110 |
f09e814a |
706 | |
397041a9 |
707 | /* --- @mp_testbit@ --- * |
f09e814a |
708 | * |
709 | * Arguments: @mp *x@ = a large integer |
09d00c6b |
710 | * @unsigned long n@ = which bit to test |
f09e814a |
711 | * |
397041a9 |
712 | * Returns: Nonzero if the bit is set, zero if not. |
d3409d5e |
713 | */ |
714 | |
397041a9 |
715 | extern int mp_testbit(mp */*x*/, unsigned long /*n*/); |
d3409d5e |
716 | |
09d00c6b |
717 | /* --- @mp_setbit@, @mp_clearbit@ --- * |
718 | * |
719 | * Arguments: @mp *d@ = a destination |
720 | * @mp *x@ = a large integer |
721 | * @unsigned long n@ = which bit to modify |
722 | * |
723 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
724 | */ |
725 | |
726 | extern mp *mp_setbit(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
727 | extern mp *mp_clearbit(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
728 | |
397041a9 |
729 | /* --- @mp_lsl@, @mp_lsr@ --- * |
0f32e0f8 |
730 | * |
731 | * Arguments: @mp *d@ = destination |
397041a9 |
732 | * @mp *a@ = source |
733 | * @size_t n@ = number of bits to move |
f09e814a |
734 | * |
397041a9 |
735 | * Returns: Result, @a@ shifted left or right by @n@. |
f09e814a |
736 | */ |
737 | |
397041a9 |
738 | extern mp *mp_lsl(mp */*d*/, mp */*a*/, size_t /*n*/); |
739 | extern mp *mp_lsr(mp */*d*/, mp */*a*/, size_t /*n*/); |
f09e814a |
740 | |
397041a9 |
741 | /* --- @mp_not2c@ --- * |
f09e814a |
742 | * |
743 | * Arguments: @mp *d@ = destination |
744 | * @mp *a@ = source |
745 | * |
397041a9 |
746 | * Returns: The sign-extended complement of the argument. |
747 | */ |
f09e814a |
748 | |
397041a9 |
749 | extern mp *mp_not2c(mp */*d*/, mp */*a*/); |
0f32e0f8 |
750 | |
f09e814a |
751 | /* --- @mp_bitop2c@ --- * |
752 | * |
753 | * Arguments: @mp *d@ = destination |
754 | * @mp *a, *b@ = sources |
755 | * |
756 | * Returns: The result of the given bitwise operation. Negative numbers |
757 | * are treated as two's complement, sign-extended infinitely to |
758 | * the left. The functions are named after the truth tables |
759 | * they generate: |
760 | * |
761 | * a: 0011 |
762 | * b: 0101 |
763 | * @mpx_bitXXXX@ |
764 | */ |
765 | |
766 | #define MP_BIT2CDECL(string) \ |
767 | extern mp *mp_bit##string##2c(mp */*d*/, mp */*a*/, mp */*b*/); |
768 | MPX_DOBIN(MP_BIT2CDECL) |
769 | |
770 | /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- * |
771 | * |
772 | * Synonyms for the commonly-used functions. |
773 | */ |
774 | |
775 | #define mp_and2c mp_bit00012c |
776 | #define mp_or2c mp_bit01112c |
777 | #define mp_nand2c mp_bit11102c |
778 | #define mp_nor2c mp_bit10002c |
779 | #define mp_xor2c mp_bit01102c |
780 | |
397041a9 |
781 | /* --- @mp_lsl2c@, @mp_lsr2c@ --- * |
f09e814a |
782 | * |
783 | * Arguments: @mp *d@ = destination |
784 | * @mp *a@ = source |
397041a9 |
785 | * @size_t n@ = number of bits to move |
f09e814a |
786 | * |
397041a9 |
787 | * Returns: Result, @a@ shifted left or right by @n@. Handles the |
788 | * pretence of sign-extension for negative numbers. |
f09e814a |
789 | */ |
790 | |
397041a9 |
791 | extern mp *mp_lsl2c(mp */*d*/, mp */*a*/, size_t /*n*/); |
792 | extern mp *mp_lsr2c(mp */*d*/, mp */*a*/, size_t /*n*/); |
793 | |
794 | /* --- @mp_testbit2c@ --- * |
795 | * |
796 | * Arguments: @mp *x@ = a large integer |
797 | * @unsigned long n@ = which bit to test |
798 | * |
799 | * Returns: Nonzero if the bit is set, zero if not. Fakes up two's |
800 | * complement representation. |
801 | */ |
802 | |
803 | extern int mp_testbit2c(mp */*x*/, unsigned long /*n*/); |
804 | |
805 | /* --- @mp_setbit2c@, @mp_clearbit2c@ --- * |
806 | * |
807 | * Arguments: @mp *d@ = a destination |
808 | * @mp *x@ = a large integer |
809 | * @unsigned long n@ = which bit to modify |
810 | * |
811 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
812 | * Fakes up two's complement representation. |
813 | */ |
814 | |
815 | extern mp *mp_setbit2c(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
816 | extern mp *mp_clearbit2c(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
817 | |
818 | /*----- Comparisons -------------------------------------------------------*/ |
819 | |
820 | /* --- @mp_eq@ --- * |
821 | * |
822 | * Arguments: @const mp *a, *b@ = two numbers |
823 | * |
824 | * Returns: Nonzero if the numbers are equal. |
825 | */ |
826 | |
827 | extern int mp_eq(const mp */*a*/, const mp */*b*/); |
828 | |
829 | #define MP_EQ(a, b) \ |
830 | ((((a)->f ^ (b)->f) & MP_NEG) == 0 && \ |
831 | mpx_ueq((a)->v, (a)->vl, (b)->v, (b)->vl)) |
832 | |
833 | /* --- @mp_cmp@ --- * |
834 | * |
835 | * Arguments: @const mp *a, *b@ = two numbers |
836 | * |
837 | * Returns: Less than, equal to or greater than zero, according to |
838 | * whether @a@ is less than, equal to or greater than @b@. |
839 | */ |
840 | |
841 | extern int mp_cmp(const mp */*a*/, const mp */*b*/); |
842 | |
843 | #define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0) |
844 | |
3cd24abb |
845 | /* --- Other handy macros --- */ |
846 | |
847 | #define MP_ISNEG(x) ((x)->f & MP_NEG) |
848 | #define MP_ISZERO(x) MP_EQ((x), MP_ZERO) |
849 | #define MP_ISPOS(x) (!MP_ISNEG(x) && !MP_ISZERO(x)) |
850 | |
397041a9 |
851 | /*----- Arithmetic operations ---------------------------------------------*/ |
852 | |
853 | /* --- @mp_neg@ --- * |
854 | * |
855 | * Arguments: @mp *d@ = destination |
856 | * @mp *a@ = argument |
857 | * |
858 | * Returns: The negation of the argument. |
859 | * |
860 | * Use: Negates its argument. |
861 | */ |
862 | |
863 | extern mp *mp_neg(mp */*d*/, mp */*a*/); |
f09e814a |
864 | |
d3409d5e |
865 | /* --- @mp_add@ --- * |
d03ab969 |
866 | * |
d3409d5e |
867 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
868 | * @mp *a, *b@ = sources |
d3409d5e |
869 | * |
870 | * Returns: Result, @a@ added to @b@. |
d03ab969 |
871 | */ |
872 | |
d9a8ae10 |
873 | extern mp *mp_add(mp */*d*/, mp */*a*/, mp */*b*/); |
d03ab969 |
874 | |
d3409d5e |
875 | /* --- @mp_sub@ --- * |
876 | * |
877 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
878 | * @mp *a, *b@ = sources |
d3409d5e |
879 | * |
880 | * Returns: Result, @b@ subtracted from @a@. |
881 | */ |
d03ab969 |
882 | |
d9a8ae10 |
883 | extern mp *mp_sub(mp */*d*/, mp */*a*/, mp */*b*/); |
d3409d5e |
884 | |
885 | /* --- @mp_mul@ --- * |
d03ab969 |
886 | * |
d3409d5e |
887 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
888 | * @mp *a, *b@ = sources |
d03ab969 |
889 | * |
d3409d5e |
890 | * Returns: Result, @a@ multiplied by @b@. |
891 | */ |
892 | |
d9a8ae10 |
893 | extern mp *mp_mul(mp */*d*/, mp */*a*/, mp */*b*/); |
d3409d5e |
894 | |
895 | /* --- @mp_sqr@ --- * |
896 | * |
897 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
898 | * @mp *a@ = source |
d3409d5e |
899 | * |
900 | * Returns: Result, @a@ squared. |
901 | */ |
902 | |
d9a8ae10 |
903 | extern mp *mp_sqr(mp */*d*/, mp */*a*/); |
d3409d5e |
904 | |
905 | /* --- @mp_div@ --- * |
d03ab969 |
906 | * |
d3409d5e |
907 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
d9a8ae10 |
908 | * @mp *a, *b@ = sources |
d3409d5e |
909 | * |
910 | * Use: Calculates the quotient and remainder when @a@ is divided by |
911 | * @b@. |
d03ab969 |
912 | */ |
913 | |
d9a8ae10 |
914 | extern void mp_div(mp **/*qq*/, mp **/*rr*/, mp */*a*/, mp */*b*/); |
d3409d5e |
915 | |
22a073c0 |
916 | /* --- @mp_odd@ --- * |
917 | * |
918 | * Arguments: @mp *d@ = pointer to destination integer |
919 | * @mp *m@ = pointer to source integer |
920 | * @size_t *s@ = where to store the power of 2 |
921 | * |
922 | * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%. |
923 | * |
924 | * Use: Computes a power of two and an odd integer which, when |
925 | * multiplied, give a specified result. This sort of thing is |
926 | * useful in number theory quite often. |
927 | */ |
928 | |
929 | extern mp *mp_odd(mp */*d*/, mp */*m*/, size_t */*s*/); |
930 | |
d3409d5e |
931 | /*----- More advanced algorithms ------------------------------------------*/ |
d03ab969 |
932 | |
22a073c0 |
933 | /* --- @mp_sqrt@ --- * |
934 | * |
935 | * Arguments: @mp *d@ = pointer to destination integer |
936 | * @mp *a@ = (nonnegative) integer to take square root of |
937 | * |
938 | * Returns: The largest integer %$x$% such that %$x^2 \le a$%. |
939 | * |
940 | * Use: Computes integer square roots. |
941 | * |
942 | * The current implementation isn't very good: it uses the |
943 | * Newton-Raphson method to find an approximation to %$a$%. If |
944 | * there's any demand for a better version, I'll write one. |
945 | */ |
946 | |
947 | extern mp *mp_sqrt(mp */*d*/, mp */*a*/); |
948 | |
d3409d5e |
949 | /* --- @mp_gcd@ --- * |
d03ab969 |
950 | * |
d3409d5e |
951 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
952 | * @mp *a, *b@ = sources (must be nonzero) |
d03ab969 |
953 | * |
954 | * Returns: --- |
955 | * |
d3409d5e |
956 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
957 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
d9a8ae10 |
958 | * inverses. Neither @a@ nor @b@ may be zero. |
d03ab969 |
959 | */ |
960 | |
d3409d5e |
961 | extern void mp_gcd(mp **/*gcd*/, mp **/*xx*/, mp **/*yy*/, |
962 | mp */*a*/, mp */*b*/); |
963 | |
5b00a0ea |
964 | /* --- @mp_jacobi@ --- * |
965 | * |
966 | * Arguments: @mp *a@ = an integer less than @n@ |
967 | * @mp *n@ = an odd integer |
968 | * |
969 | * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%. |
970 | * |
971 | * Use: Computes the Jacobi symbol. If @n@ is prime, this is the |
972 | * Legendre symbol and is equal to 1 if and only if @a@ is a |
973 | * quadratic residue mod @n@. The result is zero if and only if |
974 | * @a@ and @n@ have a common factor greater than one. |
975 | */ |
976 | |
22a073c0 |
977 | extern int mp_jacobi(mp */*a*/, mp */*n*/); |
978 | |
979 | /* --- @mp_modsqrt@ --- * |
980 | * |
981 | * Arguments: @mp *d@ = destination integer |
982 | * @mp *a@ = source integer |
983 | * @mp *p@ = modulus (must be prime) |
984 | * |
985 | * Returns: If %$a$% is a quadratic residue, a square root of %$a$%; else |
986 | * a null pointer. |
987 | * |
988 | * Use: Returns an integer %$x$% such that %$x^2 \equiv a \pmod{p}$%, |
989 | * if one exists; else a null pointer. This function will not |
990 | * work if %$p$% is composite: you must factor the modulus, take |
991 | * a square root mod each factor, and recombine the results |
992 | * using the Chinese Remainder Theorem. |
993 | */ |
994 | |
995 | extern mp *mp_modsqrt(mp */*d*/, mp */*a*/, mp */*p*/); |
5b00a0ea |
996 | |
d3409d5e |
997 | /*----- Test harness support ----------------------------------------------*/ |
998 | |
999 | #include <mLib/testrig.h> |
1000 | |
d9a8ae10 |
1001 | #ifndef CATACOMB_MPTEXT_H |
d3409d5e |
1002 | # include "mptext.h" |
1003 | #endif |
1004 | |
1005 | extern const test_type type_mp; |
d03ab969 |
1006 | |
1007 | /*----- That's all, folks -------------------------------------------------*/ |
1008 | |
1009 | #ifdef __cplusplus |
1010 | } |
1011 | #endif |
1012 | |
1013 | #endif |