d03ab969 |
1 | /* -*-c-*- |
2 | * |
81578196 |
3 | * $Id: mp.h,v 1.17 2003/05/16 09:09:24 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 $ |
81578196 |
33 | * Revision 1.17 2003/05/16 09:09:24 mdw |
34 | * Fix @mp_lsl2c@. Turns out to be surprisingly tricky. |
35 | * |
3cd24abb |
36 | * Revision 1.16 2002/10/15 22:57:22 mdw |
37 | * Handy new comparison macros. |
38 | * |
397041a9 |
39 | * Revision 1.15 2002/10/15 19:18:31 mdw |
40 | * New operation to negate numbers. |
41 | * |
09d00c6b |
42 | * Revision 1.14 2002/10/15 00:19:40 mdw |
43 | * Bit setting and clearing functions. |
44 | * |
f09e814a |
45 | * Revision 1.13 2002/10/06 22:52:50 mdw |
46 | * Pile of changes for supporting two's complement properly. |
47 | * |
3bc0a0fe |
48 | * Revision 1.12 2001/06/16 12:57:43 mdw |
49 | * Move the @mpmont_factor@ structure and rename it now that it's used for |
50 | * Barrett simultaneous exponentiation too. |
51 | * |
0f32e0f8 |
52 | * Revision 1.11 2001/04/03 19:36:05 mdw |
53 | * Add some simple bitwise operations so that Perl can use them. |
54 | * |
740c9553 |
55 | * Revision 1.10 2000/10/08 12:03:16 mdw |
56 | * Provide @mp_eq@ and @MP_EQ@ for rapidly testing equality of two |
57 | * integers. |
58 | * |
5fbe3846 |
59 | * Revision 1.9 2000/07/29 17:03:31 mdw |
60 | * Add support for left-to-right bitscanning, for use in modular |
61 | * exponentiation. |
62 | * |
22a073c0 |
63 | * Revision 1.8 2000/06/22 19:02:01 mdw |
64 | * Add new functions. |
65 | * |
d34decd2 |
66 | * Revision 1.7 2000/06/17 11:45:09 mdw |
67 | * Major memory management overhaul. Added arena support. Use the secure |
68 | * arena for secret integers. Replace and improve the MP management macros |
69 | * (e.g., replace MP_MODIFY by MP_DEST). |
70 | * |
d9a8ae10 |
71 | * Revision 1.6 1999/12/10 23:19:46 mdw |
72 | * Minor bugfixes. New interface for suggested destinations. |
73 | * |
5b00a0ea |
74 | * Revision 1.5 1999/11/22 20:50:37 mdw |
75 | * Add support for computing Jacobi symbols. |
76 | * |
24e1e862 |
77 | * Revision 1.4 1999/11/21 22:13:02 mdw |
78 | * Add mp version of MPX_BITS. |
79 | * |
a790733d |
80 | * Revision 1.3 1999/11/19 13:19:14 mdw |
81 | * Fix const annotation. |
82 | * |
d3409d5e |
83 | * Revision 1.2 1999/11/17 18:02:16 mdw |
84 | * New multiprecision integer arithmetic suite. |
d03ab969 |
85 | * |
86 | */ |
87 | |
d9a8ae10 |
88 | #ifndef CATACOMB_MP_H |
89 | #define CATACOMB_MP_H |
d03ab969 |
90 | |
91 | #ifdef __cplusplus |
92 | extern "C" { |
93 | #endif |
94 | |
95 | /*----- Header files ------------------------------------------------------*/ |
96 | |
d3409d5e |
97 | #include <assert.h> |
d03ab969 |
98 | #include <string.h> |
99 | |
d3409d5e |
100 | #include <mLib/sub.h> |
101 | |
d9a8ae10 |
102 | #ifndef CATACOMB_MPW_H |
d3409d5e |
103 | # include "mpw.h" |
d03ab969 |
104 | #endif |
105 | |
d34decd2 |
106 | #ifndef CATACOMB_ARENA_H |
107 | # include "arena.h" |
108 | #endif |
109 | |
110 | #ifndef CATACOMB_MPARENA_H |
111 | # include "mparena.h" |
112 | #endif |
113 | |
d9a8ae10 |
114 | #ifndef CATACOMB_MPX_H |
d03ab969 |
115 | # include "mpx.h" |
116 | #endif |
117 | |
d03ab969 |
118 | /*----- Data structures ---------------------------------------------------*/ |
119 | |
3bc0a0fe |
120 | /* --- A multiprecision integer --- */ |
121 | |
d03ab969 |
122 | typedef struct mp { |
3bc0a0fe |
123 | mpw *v, *vl; /* Vector of digits, current limit */ |
124 | size_t sz; /* Size of digit buffer in words */ |
125 | mparena *a; /* Arena for buffer allocation */ |
126 | unsigned f; /* Flags (see below) */ |
127 | unsigned ref; /* Reference counter */ |
d03ab969 |
128 | } mp; |
129 | |
3bc0a0fe |
130 | #define MP_NEG 1u /* Negative (signed magnitude) */ |
131 | #define MP_BURN 2u /* Secret (viral flag) */ |
132 | #define MP_CONST 4u /* Uses strange memory allocation */ |
133 | #define MP_UNDEF 8u /* Contains nothing interesting */ |
134 | #define MP_DESTROYED 16u /* Has been destroyed */ |
135 | |
136 | /* --- A factor for simultaneous exponentation --- * |
137 | * |
138 | * Used by the Montgomery and Barrett exponentiators. |
139 | */ |
140 | |
141 | typedef struct mp_expfactor { |
142 | mp *base; |
143 | mp *exp; |
144 | } mp_expfactor; |
d03ab969 |
145 | |
d3409d5e |
146 | /*----- Useful constants --------------------------------------------------*/ |
d03ab969 |
147 | |
d3409d5e |
148 | extern mp mp_const[]; |
d03ab969 |
149 | |
d3409d5e |
150 | #define MP_ZERO (&mp_const[0]) |
151 | #define MP_ONE (&mp_const[1]) |
152 | #define MP_TWO (&mp_const[2]) |
153 | #define MP_THREE (&mp_const[3]) |
154 | #define MP_FOUR (&mp_const[4]) |
155 | #define MP_FIVE (&mp_const[5]) |
156 | #define MP_TEN (&mp_const[6]) |
d34decd2 |
157 | #define MP_256 (&mp_const[7]) |
158 | #define MP_MONE (&mp_const[8]) |
d03ab969 |
159 | |
d3409d5e |
160 | #define MP_NEW ((mp *)0) |
d34decd2 |
161 | #define MP_NEWSEC (&mp_const[9]) |
d03ab969 |
162 | |
d34decd2 |
163 | /*----- Trivial macros ----------------------------------------------------*/ |
d03ab969 |
164 | |
d34decd2 |
165 | /* --- @MP_LEN@ --- * |
d03ab969 |
166 | * |
d34decd2 |
167 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
168 | * |
d34decd2 |
169 | * Returns: Length of the integer, in words. |
d03ab969 |
170 | */ |
171 | |
d34decd2 |
172 | #define MP_LEN(m) ((m)->vl - ((m)->v)) |
d03ab969 |
173 | |
d34decd2 |
174 | /*----- Memory management and reference counting --------------------------*/ |
d3409d5e |
175 | |
d34decd2 |
176 | /* --- @mp_new@ --- * |
d03ab969 |
177 | * |
d34decd2 |
178 | * Arguments: @size_t sz@ = size of vector required |
179 | * @unsigned f@ = flags to set |
d03ab969 |
180 | * |
d34decd2 |
181 | * Returns: Pointer to a new MP structure. |
d03ab969 |
182 | * |
d34decd2 |
183 | * Use: Allocates a new multiprecision integer. The data space is |
184 | * allocated from either the standard global or secret arena, |
185 | * depending on the initial flags requested. |
d03ab969 |
186 | */ |
187 | |
d34decd2 |
188 | extern mp *mp_new(size_t /*sz*/, unsigned /*f*/); |
d03ab969 |
189 | |
d34decd2 |
190 | /* --- @mp_create@ --- * |
d03ab969 |
191 | * |
d34decd2 |
192 | * Arguments: @size_t sz@ = size of vector required |
d03ab969 |
193 | * |
d34decd2 |
194 | * Returns: Pointer to pristine new MP structure with enough memory |
195 | * bolted onto it. |
196 | * |
197 | * Use: Creates a new multiprecision integer with indeterminate |
198 | * contents. The integer has a single reference. |
d03ab969 |
199 | */ |
200 | |
d34decd2 |
201 | extern mp *mp_create(size_t /*sz*/); |
d3409d5e |
202 | |
d34decd2 |
203 | /* --- @mp_createsecure@ --- * |
d03ab969 |
204 | * |
d3409d5e |
205 | * Arguments: @size_t sz@ = size of vector required |
d03ab969 |
206 | * |
d3409d5e |
207 | * Returns: Pointer to pristine new MP structure with enough memory |
208 | * bolted onto it. |
d03ab969 |
209 | * |
d3409d5e |
210 | * Use: Creates a new multiprecision integer with indeterminate |
d34decd2 |
211 | * contents. The integer has a single reference. The integer's |
212 | * data space is allocated from the secure arena. Its burn flag |
213 | * is set. |
d03ab969 |
214 | */ |
215 | |
d34decd2 |
216 | extern mp *mp_createsecure(size_t /*sz*/); |
d03ab969 |
217 | |
d3409d5e |
218 | /* --- @mp_build@ --- * |
d03ab969 |
219 | * |
d3409d5e |
220 | * Arguments: @mp *m@ = pointer to an MP block to fill in |
221 | * @mpw *v@ = pointer to a word array |
222 | * @mpw *vl@ = pointer just past end of array |
d03ab969 |
223 | * |
224 | * Returns: --- |
225 | * |
d3409d5e |
226 | * Use: Creates a multiprecision integer representing some smallish |
227 | * number. You must provide storage for the number and dispose |
228 | * of it when you've finished with it. The number is marked as |
229 | * constant while it exists. |
d03ab969 |
230 | */ |
231 | |
d3409d5e |
232 | extern void mp_build(mp */*m*/, mpw */*v*/, mpw */*vl*/); |
d03ab969 |
233 | |
d3409d5e |
234 | /* --- @mp_destroy@ --- * |
d03ab969 |
235 | * |
d3409d5e |
236 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
237 | * |
238 | * Returns: --- |
239 | * |
d3409d5e |
240 | * Use: Destroys a multiprecision integer. The reference count isn't |
241 | * checked. Don't use this function if you don't know what |
242 | * you're doing: use @mp_drop@ instead. |
d03ab969 |
243 | */ |
244 | |
d3409d5e |
245 | extern void mp_destroy(mp */*m*/); |
d03ab969 |
246 | |
d3409d5e |
247 | /* --- @mp_copy@ --- * |
d03ab969 |
248 | * |
d3409d5e |
249 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
250 | * |
d3409d5e |
251 | * Returns: A copy of the given multiprecision integer. |
252 | * |
253 | * Use: Copies the given integer. In fact you just get another |
254 | * reference to the same old one again. |
d03ab969 |
255 | */ |
256 | |
d3409d5e |
257 | extern mp *mp_copy(mp */*m*/); |
d03ab969 |
258 | |
d3409d5e |
259 | #define MP_COPY(m) ((m)->ref++, (m)) |
260 | |
261 | /* --- @mp_drop@ --- * |
d03ab969 |
262 | * |
d3409d5e |
263 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
264 | * |
265 | * Returns: --- |
266 | * |
d3409d5e |
267 | * Use: Drops a reference to an integer which isn't wanted any more. |
268 | * If there are no more references, the integer is destroyed. |
d03ab969 |
269 | */ |
270 | |
d3409d5e |
271 | extern void mp_drop(mp */*m*/); |
d03ab969 |
272 | |
d3409d5e |
273 | #define MP_DROP(m) do { \ |
274 | mp *_mm = (m); \ |
d34decd2 |
275 | _mm->ref--; \ |
276 | if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \ |
d3409d5e |
277 | mp_destroy(_mm); \ |
278 | } while (0) |
279 | |
280 | /* --- @mp_split@ --- * |
d03ab969 |
281 | * |
d3409d5e |
282 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
283 | * |
d3409d5e |
284 | * Returns: A reference to the same integer, possibly with a different |
285 | * address. |
d03ab969 |
286 | * |
d3409d5e |
287 | * Use: Splits off a modifiable version of the integer referred to. |
d03ab969 |
288 | */ |
289 | |
d3409d5e |
290 | extern mp *mp_split(mp */*m*/); |
291 | |
292 | #define MP_SPLIT(m) do { \ |
d34decd2 |
293 | mp *_m = (m); \ |
294 | if ((_m->f & MP_CONST) || _m->ref > 1) { \ |
295 | size_t _len = MP_LEN(_m); \ |
296 | mp *_mm = mp_new(_len, _m->f); \ |
297 | if (!(_m->f & MP_UNDEF)) \ |
298 | memcpy(_mm->v, _m->v, MPWS(_len)); \ |
299 | _m->ref--; \ |
300 | _m = _mm; \ |
d3409d5e |
301 | } \ |
d34decd2 |
302 | (m) = _m; \ |
d3409d5e |
303 | } while (0) |
d03ab969 |
304 | |
d3409d5e |
305 | /* --- @mp_resize@ --- * |
d03ab969 |
306 | * |
d3409d5e |
307 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
308 | * @size_t sz@ = new size |
d03ab969 |
309 | * |
d3409d5e |
310 | * Returns: --- |
d03ab969 |
311 | * |
d3409d5e |
312 | * Use: Resizes the vector containing the integer's digits. The new |
313 | * size must be at least as large as the current integer's |
d34decd2 |
314 | * length. This isn't really intended for client use. |
d03ab969 |
315 | */ |
316 | |
d3409d5e |
317 | extern void mp_resize(mp */*m*/, size_t /*sz*/); |
318 | |
319 | #define MP_RESIZE(m, ssz) do { \ |
320 | mp *_m = (m); \ |
321 | size_t _sz = (ssz); \ |
d34decd2 |
322 | mparena *_a = (_m->f & MP_BURN) ? MPARENA_SECURE : MPARENA_GLOBAL; \ |
323 | mpw *_v; \ |
d3409d5e |
324 | size_t _len = MP_LEN(_m); \ |
d34decd2 |
325 | assert(((void)"can't make size less than length", _sz >= _len)); \ |
326 | _v = mpalloc(_a, _sz); \ |
d9a8ae10 |
327 | if (!(_m->f & MP_UNDEF)) \ |
328 | memcpy(_v, _m->v, MPWS(_len)); \ |
d3409d5e |
329 | if (_m->f & MP_BURN) \ |
330 | memset(_m->v, 0, MPWS(_m->sz)); \ |
d34decd2 |
331 | mpfree(_m->a, _m->v); \ |
332 | _m->a = _a; \ |
d3409d5e |
333 | _m->v = _v; \ |
334 | _m->vl = _v + _len; \ |
d3409d5e |
335 | } while (0) |
d03ab969 |
336 | |
d3409d5e |
337 | /* --- @mp_ensure@ --- * |
d03ab969 |
338 | * |
d3409d5e |
339 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
340 | * @size_t sz@ = required size |
d03ab969 |
341 | * |
342 | * Returns: --- |
343 | * |
d3409d5e |
344 | * Use: Ensures that the integer has enough space for @sz@ digits. |
345 | * The value is not changed. |
d03ab969 |
346 | */ |
347 | |
d3409d5e |
348 | extern void mp_ensure(mp */*m*/, size_t /*sz*/); |
349 | |
350 | #define MP_ENSURE(m, ssz) do { \ |
d34decd2 |
351 | mp *_m = (m); \ |
d3409d5e |
352 | size_t _ssz = (ssz); \ |
d34decd2 |
353 | size_t _len = MP_LEN(_m); \ |
354 | if (_ssz >= _len) { \ |
355 | if (_ssz > _m->sz) \ |
356 | mp_resize(_m, _ssz); \ |
357 | if (!(_m->f & MP_UNDEF) && _ssz > _len) \ |
358 | memset(_m->vl, 0, MPWS(_ssz - _len)); \ |
359 | _m->vl = _m->v + _ssz; \ |
360 | } \ |
d3409d5e |
361 | } while (0) |
d03ab969 |
362 | |
d34decd2 |
363 | /* --- @mp_dest@ --- * |
d03ab969 |
364 | * |
d34decd2 |
365 | * Arguments: @mp *m@ = a suggested destination integer |
366 | * @size_t sz@ = size required for result, in digits |
367 | * @unsigned f@ = various flags |
368 | * |
369 | * Returns: A pointer to an appropriate destination. |
370 | * |
371 | * Use: Converts a suggested destination into a real destination with |
372 | * the required properties. If the real destination is @d@, |
373 | * then the following properties will hold: |
374 | * |
375 | * * @d@ will have exactly one reference. |
d03ab969 |
376 | * |
d34decd2 |
377 | * * If @m@ is not @MP_NEW@, then the contents of @m@ will not |
378 | * change, unless @f@ has the @MP_UNDEF@ flag set. |
d03ab969 |
379 | * |
d34decd2 |
380 | * * If @m@ is not @MP_NEW@, then he reference count of @m@ on |
381 | * entry is equal to the sum of the counts of @d@ and @m@ on |
382 | * exit. |
383 | * |
384 | * * The size of @d@ will be at least @sz@. |
385 | * |
386 | * * If @f@ has the @MP_BURN@ flag set, then @d@ will be |
387 | * allocated from @MPARENA_SECURE@. |
388 | * |
389 | * Understanding this function is crucial to using Catacomb's |
390 | * multiprecision integer library effectively. |
d03ab969 |
391 | */ |
392 | |
d34decd2 |
393 | extern mp *mp_dest(mp */*m*/, size_t /*sz*/, unsigned /*f*/); |
d03ab969 |
394 | |
d34decd2 |
395 | #define MP_DEST(m, ssz, f) do { \ |
d3409d5e |
396 | mp *_m = (m); \ |
d34decd2 |
397 | size_t _ssz = (ssz); \ |
398 | unsigned _f = (f); \ |
399 | _m = mp_dest(_m, _ssz, _f); \ |
d3409d5e |
400 | (m) = _m; \ |
401 | } while (0) |
402 | |
403 | /*----- Size manipulation -------------------------------------------------*/ |
404 | |
405 | /* --- @mp_shrink@ --- * |
d03ab969 |
406 | * |
d3409d5e |
407 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
408 | * |
409 | * Returns: --- |
410 | * |
d3409d5e |
411 | * Use: Reduces the recorded length of an integer. This doesn't |
412 | * reduce the amount of memory used, although it can improve |
413 | * performance a bit. To reduce memory, use @mp_minimize@ |
414 | * instead. This can't change the value of an integer, and is |
415 | * therefore safe to use even when there are multiple |
416 | * references. |
d03ab969 |
417 | */ |
418 | |
d3409d5e |
419 | extern void mp_shrink(mp */*m*/); |
d03ab969 |
420 | |
d3409d5e |
421 | #define MP_SHRINK(m) do { \ |
422 | mp *_mm = (m); \ |
423 | MPX_SHRINK(_mm->v, _mm->vl); \ |
424 | if (!MP_LEN(_mm)) \ |
425 | _mm->f &= ~MP_NEG; \ |
426 | } while (0) |
427 | |
428 | /* --- @mp_minimize@ --- * |
d03ab969 |
429 | * |
d3409d5e |
430 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
431 | * |
432 | * Returns: --- |
433 | * |
d3409d5e |
434 | * Use: Reduces the amount of memory an integer uses. It's best to |
435 | * do this to numbers which aren't going to change in the |
436 | * future. |
d03ab969 |
437 | */ |
438 | |
d3409d5e |
439 | extern void mp_minimize(mp */*m*/); |
d03ab969 |
440 | |
d3409d5e |
441 | /*----- Bit scanning ------------------------------------------------------*/ |
d03ab969 |
442 | |
d9a8ae10 |
443 | #ifndef CATACOMB_MPSCAN_H |
d3409d5e |
444 | # include "mpscan.h" |
445 | #endif |
446 | |
447 | /* --- @mp_scan@ --- * |
d03ab969 |
448 | * |
d3409d5e |
449 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
450 | * @const mp *m@ = pointer to a multiprecision integer |
d03ab969 |
451 | * |
452 | * Returns: --- |
453 | * |
d3409d5e |
454 | * Use: Initializes a bitscanner on a multiprecision integer. |
d03ab969 |
455 | */ |
456 | |
d3409d5e |
457 | extern void mp_scan(mpscan */*sc*/, const mp */*m*/); |
458 | |
459 | #define MP_SCAN(sc, m) do { \ |
a790733d |
460 | const mp *_mm = (m); \ |
d3409d5e |
461 | mpscan *_sc = (sc); \ |
462 | MPSCAN_INITX(_sc, _mm->v, _mm->vl); \ |
463 | } while (0) |
464 | |
5fbe3846 |
465 | /* --- @mp_rscan@ --- * |
466 | * |
467 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
468 | * @const mp *m@ = pointer to a multiprecision integer |
469 | * |
470 | * Returns: --- |
471 | * |
472 | * Use: Initializes a reverse bitscanner on a multiprecision |
473 | * integer. |
474 | */ |
475 | |
476 | extern void mp_rscan(mpscan */*sc*/, const mp */*m*/); |
477 | |
478 | #define MP_RSCAN(sc, m) do { \ |
479 | const mp *_mm = (m); \ |
480 | mpscan *_sc = (sc); \ |
481 | MPSCAN_RINITX(_sc, _mm->v, _mm->vl); \ |
482 | } while (0) |
483 | |
d3409d5e |
484 | /* --- Other bitscanning aliases --- */ |
485 | |
486 | #define mp_step mpscan_step |
487 | #define mp_bit mpscan_bit |
5fbe3846 |
488 | #define mp_rstep mpscan_rstep |
489 | #define mp_rbit mpscan_rbit |
d3409d5e |
490 | |
491 | #define MP_STEP MPSCAN_STEP |
492 | #define MP_BIT MPSCAN_BIT |
5fbe3846 |
493 | #define MP_RSTEP MPSCAN_RSTEP |
494 | #define MP_RBIT MPSCAN_RBIT |
d3409d5e |
495 | |
496 | /*----- Loading and storing -----------------------------------------------*/ |
d03ab969 |
497 | |
d3409d5e |
498 | /* --- @mp_octets@ --- * |
d03ab969 |
499 | * |
d3409d5e |
500 | * Arguments: @const mp *m@ = a multiprecision integer |
d03ab969 |
501 | * |
d3409d5e |
502 | * Returns: The number of octets required to represent @m@. |
d03ab969 |
503 | * |
d3409d5e |
504 | * Use: Calculates the external storage required for a multiprecision |
505 | * integer. |
d03ab969 |
506 | */ |
507 | |
24e1e862 |
508 | extern size_t mp_octets(const mp */*m*/); |
509 | |
f09e814a |
510 | /* --- @mp_octets2c@ --- * |
511 | * |
512 | * Arguments: @const mp *m@ = a multiprecision integer |
513 | * |
514 | * Returns: The number of octets required to represent @m@. |
515 | * |
516 | * Use: Calculates the external storage required for a multiprecision |
517 | * integer represented as two's complement. |
518 | */ |
519 | |
520 | extern size_t mp_octets2c(const mp */*m*/); |
521 | |
24e1e862 |
522 | /* --- @mp_bits@ --- * |
523 | * |
524 | * Arguments: @const mp *m@ = a multiprecision integer |
525 | * |
526 | * Returns: The number of bits required to represent @m@. |
527 | * |
528 | * Use: Calculates the external storage required for a multiprecision |
529 | * integer. |
530 | */ |
531 | |
532 | extern unsigned long mp_bits(const mp */*m*/); |
d03ab969 |
533 | |
d3409d5e |
534 | /* --- @mp_loadl@ --- * |
d03ab969 |
535 | * |
d3409d5e |
536 | * Arguments: @mp *d@ = destination |
537 | * @const void *pv@ = pointer to source data |
538 | * @size_t sz@ = size of the source data |
d03ab969 |
539 | * |
d3409d5e |
540 | * Returns: Resulting multiprecision number. |
d03ab969 |
541 | * |
d3409d5e |
542 | * Use: Loads a multiprecision number from an array of octets. The |
543 | * first byte in the array is the least significant. More |
544 | * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$% |
545 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
d03ab969 |
546 | */ |
547 | |
d3409d5e |
548 | extern mp *mp_loadl(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d03ab969 |
549 | |
d3409d5e |
550 | /* --- @mp_storel@ --- * |
551 | * |
552 | * Arguments: @const mp *m@ = source |
553 | * @void *pv@ = pointer to output array |
554 | * @size_t sz@ = size of the output array |
555 | * |
556 | * Returns: --- |
557 | * |
558 | * Use: Stores a multiprecision number in an array of octets. The |
559 | * first byte in the array is the least significant. If the |
560 | * array is too small to represent the number, high-order bits |
561 | * are truncated; if the array is too large, high order bytes |
562 | * are filled with zeros. More formally, if the number is |
563 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
564 | * then the array is %$b_0, b_1, \ldots, b_{n-1}$%. |
565 | */ |
d03ab969 |
566 | |
d3409d5e |
567 | extern void mp_storel(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
d03ab969 |
568 | |
d3409d5e |
569 | /* --- @mp_loadb@ --- * |
d03ab969 |
570 | * |
d3409d5e |
571 | * Arguments: @mp *d@ = destination |
572 | * @const void *pv@ = pointer to source data |
573 | * @size_t sz@ = size of the source data |
d03ab969 |
574 | * |
d3409d5e |
575 | * Returns: Resulting multiprecision number. |
d03ab969 |
576 | * |
d3409d5e |
577 | * Use: Loads a multiprecision number from an array of octets. The |
578 | * last byte in the array is the least significant. More |
579 | * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$% |
580 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
d03ab969 |
581 | */ |
582 | |
d3409d5e |
583 | extern mp *mp_loadb(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d03ab969 |
584 | |
d3409d5e |
585 | /* --- @mp_storeb@ --- * |
d03ab969 |
586 | * |
d3409d5e |
587 | * Arguments: @const mp *m@ = source |
588 | * @void *pv@ = pointer to output array |
589 | * @size_t sz@ = size of the output array |
d03ab969 |
590 | * |
591 | * Returns: --- |
592 | * |
d3409d5e |
593 | * Use: Stores a multiprecision number in an array of octets. The |
594 | * last byte in the array is the least significant. If the |
595 | * array is too small to represent the number, high-order bits |
596 | * are truncated; if the array is too large, high order bytes |
597 | * are filled with zeros. More formally, if the number is |
598 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
599 | * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%. |
d03ab969 |
600 | */ |
601 | |
d3409d5e |
602 | extern void mp_storeb(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
d03ab969 |
603 | |
f09e814a |
604 | /* --- @mp_loadl2c@ --- * |
d03ab969 |
605 | * |
d3409d5e |
606 | * Arguments: @mp *d@ = destination |
f09e814a |
607 | * @const void *pv@ = pointer to source data |
608 | * @size_t sz@ = size of the source data |
609 | * |
610 | * Returns: Resulting multiprecision number. |
d03ab969 |
611 | * |
f09e814a |
612 | * Use: Loads a multiprecision number from an array of octets as |
613 | * two's complement. The first byte in the array is the least |
614 | * significant. |
d3409d5e |
615 | */ |
616 | |
f09e814a |
617 | extern mp *mp_loadl2c(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d3409d5e |
618 | |
f09e814a |
619 | /* --- @mp_storel2c@ --- * |
620 | * |
621 | * Arguments: @const mp *m@ = source |
622 | * @void *pv@ = pointer to output array |
623 | * @size_t sz@ = size of the output array |
624 | * |
625 | * Returns: --- |
626 | * |
627 | * Use: Stores a multiprecision number in an array of octets as two's |
628 | * complement. The first byte in the array is the least |
629 | * significant. If the array is too small to represent the |
630 | * number, high-order bits are truncated; if the array is too |
631 | * large, high order bytes are sign-extended. |
632 | */ |
633 | |
634 | extern void mp_storel2c(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
635 | |
636 | /* --- @mp_loadb2c@ --- * |
d3409d5e |
637 | * |
638 | * Arguments: @mp *d@ = destination |
f09e814a |
639 | * @const void *pv@ = pointer to source data |
640 | * @size_t sz@ = size of the source data |
d03ab969 |
641 | * |
f09e814a |
642 | * Returns: Resulting multiprecision number. |
643 | * |
644 | * Use: Loads a multiprecision number from an array of octets as |
645 | * two's complement. The last byte in the array is the least |
646 | * significant. |
d03ab969 |
647 | */ |
648 | |
f09e814a |
649 | extern mp *mp_loadb2c(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
650 | |
651 | /* --- @mp_storeb2c@ --- * |
652 | * |
653 | * Arguments: @const mp *m@ = source |
654 | * @void *pv@ = pointer to output array |
655 | * @size_t sz@ = size of the output array |
656 | * |
657 | * Returns: --- |
658 | * |
659 | * Use: Stores a multiprecision number in an array of octets, as |
660 | * two's complement. The last byte in the array is the least |
661 | * significant. If the array is too small to represent the |
662 | * number, high-order bits are truncated; if the array is too |
663 | * large, high order bytes are sign-extended. |
664 | */ |
665 | |
666 | extern void mp_storeb2c(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
667 | |
397041a9 |
668 | /*----- Bit operations ----------------------------------------------------*/ |
d03ab969 |
669 | |
397041a9 |
670 | /* --- @mp_not@ --- * |
d03ab969 |
671 | * |
d3409d5e |
672 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
673 | * @mp *a@ = source |
d03ab969 |
674 | * |
397041a9 |
675 | * Returns: The bitwise complement of the source. |
676 | */ |
d3409d5e |
677 | |
397041a9 |
678 | extern mp *mp_not(mp */*d*/, mp */*a*/); |
d3409d5e |
679 | |
397041a9 |
680 | /* --- @mp_bitop@ --- * |
d3409d5e |
681 | * |
682 | * Arguments: @mp *d@ = destination |
397041a9 |
683 | * @mp *a, *b@ = sources |
d03ab969 |
684 | * |
397041a9 |
685 | * Returns: The result of the given bitwise operation. These functions |
686 | * don't handle negative numbers at all sensibly. For that, use |
687 | * the @...2c@ variants. The functions are named after the |
688 | * truth tables they generate: |
689 | * |
690 | * a: 0011 |
691 | * b: 0101 |
692 | * @mpx_bitXXXX@ |
d03ab969 |
693 | */ |
694 | |
397041a9 |
695 | #define MP_BITDECL(string) \ |
696 | extern mp *mp_bit##string(mp */*d*/, mp */*a*/, mp */*b*/); |
697 | MPX_DOBIN(MP_BITDECL) |
f09e814a |
698 | |
397041a9 |
699 | /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- * |
f09e814a |
700 | * |
397041a9 |
701 | * Synonyms for the commonly-used functions. |
f09e814a |
702 | */ |
703 | |
397041a9 |
704 | #define mp_and mp_bit0001 |
705 | #define mp_or mp_bit0111 |
706 | #define mp_nand mp_bit1110 |
707 | #define mp_nor mp_bit1000 |
708 | #define mp_xor mp_bit0110 |
f09e814a |
709 | |
397041a9 |
710 | /* --- @mp_testbit@ --- * |
f09e814a |
711 | * |
712 | * Arguments: @mp *x@ = a large integer |
09d00c6b |
713 | * @unsigned long n@ = which bit to test |
f09e814a |
714 | * |
397041a9 |
715 | * Returns: Nonzero if the bit is set, zero if not. |
d3409d5e |
716 | */ |
717 | |
397041a9 |
718 | extern int mp_testbit(mp */*x*/, unsigned long /*n*/); |
d3409d5e |
719 | |
09d00c6b |
720 | /* --- @mp_setbit@, @mp_clearbit@ --- * |
721 | * |
722 | * Arguments: @mp *d@ = a destination |
723 | * @mp *x@ = a large integer |
724 | * @unsigned long n@ = which bit to modify |
725 | * |
726 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
727 | */ |
728 | |
729 | extern mp *mp_setbit(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
730 | extern mp *mp_clearbit(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
731 | |
81578196 |
732 | /* --- @mp_lsl@, @mp_lslc@, @mp_lsr@ --- * |
0f32e0f8 |
733 | * |
734 | * Arguments: @mp *d@ = destination |
397041a9 |
735 | * @mp *a@ = source |
736 | * @size_t n@ = number of bits to move |
f09e814a |
737 | * |
397041a9 |
738 | * Returns: Result, @a@ shifted left or right by @n@. |
81578196 |
739 | * |
740 | * Use: Bitwise shift operators. @mp_lslc@ fills the bits introduced |
741 | * on the right with ones instead of zeroes: it's used |
742 | * internally by @mp_lsl2c@, though it may be useful on its |
743 | * own. |
f09e814a |
744 | */ |
745 | |
397041a9 |
746 | extern mp *mp_lsl(mp */*d*/, mp */*a*/, size_t /*n*/); |
81578196 |
747 | extern mp *mp_lslc(mp */*d*/, mp */*a*/, size_t /*n*/); |
397041a9 |
748 | extern mp *mp_lsr(mp */*d*/, mp */*a*/, size_t /*n*/); |
f09e814a |
749 | |
397041a9 |
750 | /* --- @mp_not2c@ --- * |
f09e814a |
751 | * |
752 | * Arguments: @mp *d@ = destination |
753 | * @mp *a@ = source |
754 | * |
397041a9 |
755 | * Returns: The sign-extended complement of the argument. |
756 | */ |
f09e814a |
757 | |
397041a9 |
758 | extern mp *mp_not2c(mp */*d*/, mp */*a*/); |
0f32e0f8 |
759 | |
f09e814a |
760 | /* --- @mp_bitop2c@ --- * |
761 | * |
762 | * Arguments: @mp *d@ = destination |
763 | * @mp *a, *b@ = sources |
764 | * |
765 | * Returns: The result of the given bitwise operation. Negative numbers |
766 | * are treated as two's complement, sign-extended infinitely to |
767 | * the left. The functions are named after the truth tables |
768 | * they generate: |
769 | * |
770 | * a: 0011 |
771 | * b: 0101 |
772 | * @mpx_bitXXXX@ |
773 | */ |
774 | |
775 | #define MP_BIT2CDECL(string) \ |
776 | extern mp *mp_bit##string##2c(mp */*d*/, mp */*a*/, mp */*b*/); |
777 | MPX_DOBIN(MP_BIT2CDECL) |
778 | |
779 | /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- * |
780 | * |
781 | * Synonyms for the commonly-used functions. |
782 | */ |
783 | |
784 | #define mp_and2c mp_bit00012c |
785 | #define mp_or2c mp_bit01112c |
786 | #define mp_nand2c mp_bit11102c |
787 | #define mp_nor2c mp_bit10002c |
788 | #define mp_xor2c mp_bit01102c |
789 | |
397041a9 |
790 | /* --- @mp_lsl2c@, @mp_lsr2c@ --- * |
f09e814a |
791 | * |
792 | * Arguments: @mp *d@ = destination |
793 | * @mp *a@ = source |
397041a9 |
794 | * @size_t n@ = number of bits to move |
f09e814a |
795 | * |
397041a9 |
796 | * Returns: Result, @a@ shifted left or right by @n@. Handles the |
797 | * pretence of sign-extension for negative numbers. |
f09e814a |
798 | */ |
799 | |
397041a9 |
800 | extern mp *mp_lsl2c(mp */*d*/, mp */*a*/, size_t /*n*/); |
801 | extern mp *mp_lsr2c(mp */*d*/, mp */*a*/, size_t /*n*/); |
802 | |
803 | /* --- @mp_testbit2c@ --- * |
804 | * |
805 | * Arguments: @mp *x@ = a large integer |
806 | * @unsigned long n@ = which bit to test |
807 | * |
808 | * Returns: Nonzero if the bit is set, zero if not. Fakes up two's |
809 | * complement representation. |
810 | */ |
811 | |
812 | extern int mp_testbit2c(mp */*x*/, unsigned long /*n*/); |
813 | |
814 | /* --- @mp_setbit2c@, @mp_clearbit2c@ --- * |
815 | * |
816 | * Arguments: @mp *d@ = a destination |
817 | * @mp *x@ = a large integer |
818 | * @unsigned long n@ = which bit to modify |
819 | * |
820 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
821 | * Fakes up two's complement representation. |
822 | */ |
823 | |
824 | extern mp *mp_setbit2c(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
825 | extern mp *mp_clearbit2c(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
826 | |
827 | /*----- Comparisons -------------------------------------------------------*/ |
828 | |
829 | /* --- @mp_eq@ --- * |
830 | * |
831 | * Arguments: @const mp *a, *b@ = two numbers |
832 | * |
833 | * Returns: Nonzero if the numbers are equal. |
834 | */ |
835 | |
836 | extern int mp_eq(const mp */*a*/, const mp */*b*/); |
837 | |
838 | #define MP_EQ(a, b) \ |
839 | ((((a)->f ^ (b)->f) & MP_NEG) == 0 && \ |
840 | mpx_ueq((a)->v, (a)->vl, (b)->v, (b)->vl)) |
841 | |
842 | /* --- @mp_cmp@ --- * |
843 | * |
844 | * Arguments: @const mp *a, *b@ = two numbers |
845 | * |
846 | * Returns: Less than, equal to or greater than zero, according to |
847 | * whether @a@ is less than, equal to or greater than @b@. |
848 | */ |
849 | |
850 | extern int mp_cmp(const mp */*a*/, const mp */*b*/); |
851 | |
852 | #define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0) |
853 | |
3cd24abb |
854 | /* --- Other handy macros --- */ |
855 | |
856 | #define MP_ISNEG(x) ((x)->f & MP_NEG) |
857 | #define MP_ISZERO(x) MP_EQ((x), MP_ZERO) |
858 | #define MP_ISPOS(x) (!MP_ISNEG(x) && !MP_ISZERO(x)) |
859 | |
397041a9 |
860 | /*----- Arithmetic operations ---------------------------------------------*/ |
861 | |
862 | /* --- @mp_neg@ --- * |
863 | * |
864 | * Arguments: @mp *d@ = destination |
865 | * @mp *a@ = argument |
866 | * |
867 | * Returns: The negation of the argument. |
868 | * |
869 | * Use: Negates its argument. |
870 | */ |
871 | |
872 | extern mp *mp_neg(mp */*d*/, mp */*a*/); |
f09e814a |
873 | |
d3409d5e |
874 | /* --- @mp_add@ --- * |
d03ab969 |
875 | * |
d3409d5e |
876 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
877 | * @mp *a, *b@ = sources |
d3409d5e |
878 | * |
879 | * Returns: Result, @a@ added to @b@. |
d03ab969 |
880 | */ |
881 | |
d9a8ae10 |
882 | extern mp *mp_add(mp */*d*/, mp */*a*/, mp */*b*/); |
d03ab969 |
883 | |
d3409d5e |
884 | /* --- @mp_sub@ --- * |
885 | * |
886 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
887 | * @mp *a, *b@ = sources |
d3409d5e |
888 | * |
889 | * Returns: Result, @b@ subtracted from @a@. |
890 | */ |
d03ab969 |
891 | |
d9a8ae10 |
892 | extern mp *mp_sub(mp */*d*/, mp */*a*/, mp */*b*/); |
d3409d5e |
893 | |
894 | /* --- @mp_mul@ --- * |
d03ab969 |
895 | * |
d3409d5e |
896 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
897 | * @mp *a, *b@ = sources |
d03ab969 |
898 | * |
d3409d5e |
899 | * Returns: Result, @a@ multiplied by @b@. |
900 | */ |
901 | |
d9a8ae10 |
902 | extern mp *mp_mul(mp */*d*/, mp */*a*/, mp */*b*/); |
d3409d5e |
903 | |
904 | /* --- @mp_sqr@ --- * |
905 | * |
906 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
907 | * @mp *a@ = source |
d3409d5e |
908 | * |
909 | * Returns: Result, @a@ squared. |
910 | */ |
911 | |
d9a8ae10 |
912 | extern mp *mp_sqr(mp */*d*/, mp */*a*/); |
d3409d5e |
913 | |
914 | /* --- @mp_div@ --- * |
d03ab969 |
915 | * |
d3409d5e |
916 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
d9a8ae10 |
917 | * @mp *a, *b@ = sources |
d3409d5e |
918 | * |
919 | * Use: Calculates the quotient and remainder when @a@ is divided by |
920 | * @b@. |
d03ab969 |
921 | */ |
922 | |
d9a8ae10 |
923 | extern void mp_div(mp **/*qq*/, mp **/*rr*/, mp */*a*/, mp */*b*/); |
d3409d5e |
924 | |
22a073c0 |
925 | /* --- @mp_odd@ --- * |
926 | * |
927 | * Arguments: @mp *d@ = pointer to destination integer |
928 | * @mp *m@ = pointer to source integer |
929 | * @size_t *s@ = where to store the power of 2 |
930 | * |
931 | * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%. |
932 | * |
933 | * Use: Computes a power of two and an odd integer which, when |
934 | * multiplied, give a specified result. This sort of thing is |
935 | * useful in number theory quite often. |
936 | */ |
937 | |
938 | extern mp *mp_odd(mp */*d*/, mp */*m*/, size_t */*s*/); |
939 | |
d3409d5e |
940 | /*----- More advanced algorithms ------------------------------------------*/ |
d03ab969 |
941 | |
22a073c0 |
942 | /* --- @mp_sqrt@ --- * |
943 | * |
944 | * Arguments: @mp *d@ = pointer to destination integer |
945 | * @mp *a@ = (nonnegative) integer to take square root of |
946 | * |
947 | * Returns: The largest integer %$x$% such that %$x^2 \le a$%. |
948 | * |
949 | * Use: Computes integer square roots. |
950 | * |
951 | * The current implementation isn't very good: it uses the |
952 | * Newton-Raphson method to find an approximation to %$a$%. If |
953 | * there's any demand for a better version, I'll write one. |
954 | */ |
955 | |
956 | extern mp *mp_sqrt(mp */*d*/, mp */*a*/); |
957 | |
d3409d5e |
958 | /* --- @mp_gcd@ --- * |
d03ab969 |
959 | * |
d3409d5e |
960 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
961 | * @mp *a, *b@ = sources (must be nonzero) |
d03ab969 |
962 | * |
963 | * Returns: --- |
964 | * |
d3409d5e |
965 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
966 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
d9a8ae10 |
967 | * inverses. Neither @a@ nor @b@ may be zero. |
d03ab969 |
968 | */ |
969 | |
d3409d5e |
970 | extern void mp_gcd(mp **/*gcd*/, mp **/*xx*/, mp **/*yy*/, |
971 | mp */*a*/, mp */*b*/); |
972 | |
5b00a0ea |
973 | /* --- @mp_jacobi@ --- * |
974 | * |
975 | * Arguments: @mp *a@ = an integer less than @n@ |
976 | * @mp *n@ = an odd integer |
977 | * |
978 | * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%. |
979 | * |
980 | * Use: Computes the Jacobi symbol. If @n@ is prime, this is the |
981 | * Legendre symbol and is equal to 1 if and only if @a@ is a |
982 | * quadratic residue mod @n@. The result is zero if and only if |
983 | * @a@ and @n@ have a common factor greater than one. |
984 | */ |
985 | |
22a073c0 |
986 | extern int mp_jacobi(mp */*a*/, mp */*n*/); |
987 | |
988 | /* --- @mp_modsqrt@ --- * |
989 | * |
990 | * Arguments: @mp *d@ = destination integer |
991 | * @mp *a@ = source integer |
992 | * @mp *p@ = modulus (must be prime) |
993 | * |
994 | * Returns: If %$a$% is a quadratic residue, a square root of %$a$%; else |
995 | * a null pointer. |
996 | * |
997 | * Use: Returns an integer %$x$% such that %$x^2 \equiv a \pmod{p}$%, |
998 | * if one exists; else a null pointer. This function will not |
999 | * work if %$p$% is composite: you must factor the modulus, take |
1000 | * a square root mod each factor, and recombine the results |
1001 | * using the Chinese Remainder Theorem. |
1002 | */ |
1003 | |
1004 | extern mp *mp_modsqrt(mp */*d*/, mp */*a*/, mp */*p*/); |
5b00a0ea |
1005 | |
d3409d5e |
1006 | /*----- Test harness support ----------------------------------------------*/ |
1007 | |
1008 | #include <mLib/testrig.h> |
1009 | |
d9a8ae10 |
1010 | #ifndef CATACOMB_MPTEXT_H |
d3409d5e |
1011 | # include "mptext.h" |
1012 | #endif |
1013 | |
1014 | extern const test_type type_mp; |
d03ab969 |
1015 | |
1016 | /*----- That's all, folks -------------------------------------------------*/ |
1017 | |
1018 | #ifdef __cplusplus |
1019 | } |
1020 | #endif |
1021 | |
1022 | #endif |