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