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d03ab969 | 1 | /* -*-c-*- |
2 | * | |
b817bfc6 | 3 | * $Id: mpx.h,v 1.18 2004/04/08 01:36:15 mdw Exp $ |
d03ab969 | 4 | * |
5 | * Low level multiprecision arithmetic | |
6 | * | |
7 | * (c) 1999 Straylight/Edgeware | |
8 | */ | |
9 | ||
45c0fd36 | 10 | /*----- Licensing notice --------------------------------------------------* |
d03ab969 | 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. | |
45c0fd36 | 18 | * |
d03ab969 | 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. | |
45c0fd36 | 23 | * |
d03ab969 | 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 | ||
a86e33af | 30 | #ifndef CATACOMB_MPX_H |
31 | #define CATACOMB_MPX_H | |
d03ab969 | 32 | |
33 | #ifdef __cplusplus | |
34 | extern "C" { | |
35 | #endif | |
36 | ||
37 | /*----- The idea ----------------------------------------------------------* | |
38 | * | |
39 | * This file provides functions and macros which work on vectors of words as | |
40 | * unsigned multiprecision integers. The interface works in terms of base | |
41 | * and limit pointers (i.e., a pointer to the start of a vector, and a | |
42 | * pointer just past its end) rather than base pointer and length, because | |
43 | * that requires more arithmetic and state to work on. | |
44 | * | |
45 | * The interfaces are slightly bizarre in other ways. Try to use the | |
46 | * higher-level functions where you can: they're rather better designed to | |
47 | * actually be friendly and useful. | |
48 | */ | |
49 | ||
50 | /*----- Header files ------------------------------------------------------*/ | |
51 | ||
52 | #include <string.h> | |
53 | ||
a86e33af | 54 | #ifndef CATACOMB_MPW_H |
3c9ede17 | 55 | # include "mpw.h" |
d03ab969 | 56 | #endif |
57 | ||
58 | /*----- General manipulation ----------------------------------------------*/ | |
59 | ||
60 | /* --- @MPX_SHRINK@ --- * | |
61 | * | |
62 | * Arguments: @const mpw *v@ = pointer to vector of words | |
63 | * @const mpw *vl@ = (updated) current limit of vector | |
64 | * | |
65 | * Use: Shrinks down the limit of a multiprecision integer vector. | |
66 | */ | |
67 | ||
68 | #define MPX_SHRINK(v, vl) do { \ | |
3c9ede17 | 69 | const mpw *_vv = (v), *_vvl = (vl); \ |
70 | while (_vvl > _vv && !_vvl[-1]) \ | |
71 | _vvl--; \ | |
72 | (vl) = (mpw *)_vvl; \ | |
d03ab969 | 73 | } while (0) |
74 | ||
75 | /* --- @MPX_BITS@ --- * | |
76 | * | |
77 | * Arguments: @unsigned long b@ = result variable | |
78 | * @const mpw *v@ = pointer to array of words | |
79 | * @const mpw *vl@ = limit of vector (from @MPX_SHRINK@) | |
80 | * | |
81 | * Use: Calculates the number of bits in a multiprecision value. | |
82 | */ | |
83 | ||
84 | #define MPX_BITS(b, v, vl) do { \ | |
85 | const mpw *_v = (v), *_vl = (vl); \ | |
3c9ede17 | 86 | MPX_SHRINK(_v, _vl); \ |
d03ab969 | 87 | if (_v == _vl) \ |
88 | (b) = 0; \ | |
89 | else { \ | |
45c0fd36 | 90 | unsigned long _b = MPW_BITS * (_vl - _v - 1) + 1; \ |
d03ab969 | 91 | mpw _w = _vl[-1]; \ |
c29970a7 | 92 | unsigned _k = MPW_P2; \ |
d03ab969 | 93 | while (_k) { \ |
94 | if (_w >> _k) { \ | |
95 | _w >>= _k; \ | |
96 | _b += _k; \ | |
97 | } \ | |
98 | _k >>= 1; \ | |
99 | } \ | |
100 | (b) = _b; \ | |
101 | } \ | |
102 | } while (0) | |
103 | ||
104 | /* --- @MPX_OCTETS@ --- * | |
105 | * | |
106 | * Arguments: @size_t o@ = result variable | |
3c9ede17 | 107 | * @const mpw *v, *vl@ = pointer to array of words |
d03ab969 | 108 | * |
109 | * Use: Calculates the number of octets in a multiprecision value. | |
110 | */ | |
111 | ||
3c9ede17 | 112 | #define MPX_OCTETS(o, v, vl) do { \ |
f09e814a | 113 | unsigned long _bb; \ |
114 | MPX_BITS(_bb, (v), (vl)); \ | |
115 | (o) = (_bb + 7) >> 3; \ | |
116 | } while (0) | |
117 | ||
118 | /* --- @MPX_OCTETS2C@ --- * | |
119 | * | |
120 | * Arguments: @size_t o@ = result variable | |
121 | * @const mpw *v, *vl@ = pointer to array of words | |
122 | * | |
123 | * Use: Calculates the number of octets in a multiprecision value, if | |
124 | * you represent it as two's complement. | |
125 | */ | |
126 | ||
127 | #define MPX_OCTETS2C(o, v, vl) do { \ | |
128 | unsigned long _bb; \ | |
129 | MPX_BITS(_bb, (v), (vl)); \ | |
130 | (o) = (_bb >> 3) + 1; \ | |
d03ab969 | 131 | } while (0) |
132 | ||
133 | /* --- @MPX_COPY@ --- * | |
134 | * | |
135 | * Arguments: @dv, dvl@ = destination vector base and limit | |
136 | * @av, avl@ = source vector base and limit | |
137 | * | |
138 | * Use: Copies a multiprecision integer. | |
139 | */ | |
140 | ||
3c9ede17 | 141 | #define MPX_COPY(dv, dvl, av, avl) do { \ |
142 | mpw *_dv = (dv), *_dvl = (dvl); \ | |
143 | size_t _dn = _dvl - _dv; \ | |
144 | const mpw *_av = (av), *_avl = (avl); \ | |
145 | size_t _an = _avl - _av; \ | |
d03ab969 | 146 | if (_av == _dv) { \ |
147 | if (_dvl > _avl) \ | |
3c9ede17 | 148 | memset(_dv, 0, MPWS(_dn - _an)); \ |
d03ab969 | 149 | } else if (_an >= _dn) \ |
150 | memmove(_dv, _av, MPWS(_dn)); \ | |
151 | else { \ | |
152 | memmove(_dv, _av, MPWS(_an)); \ | |
153 | memset(_dv + _an, 0, MPWS(_dn - _an)); \ | |
154 | } \ | |
155 | } while (0) | |
156 | ||
157 | /* --- @MPX_ZERO@ --- * | |
158 | * | |
159 | * Arguments: @v, vl@ = base and limit of vector to clear | |
160 | * | |
161 | * Use: Zeroes the area between the two vector pointers. | |
162 | */ | |
163 | ||
3c9ede17 | 164 | #define MPX_ZERO(v, vl) do { \ |
d03ab969 | 165 | mpw *_v = (v), *_vl = (vl); \ |
3c9ede17 | 166 | if (_v < _vl) \ |
167 | memset(_v, 0, MPWS(_vl - _v)); \ | |
d03ab969 | 168 | } while (0) |
169 | ||
81578196 | 170 | /* --- @MPX_ONE@ --- * |
171 | * | |
172 | * Arguments: @v, vl@ = base and limit of vector to clear | |
173 | * | |
174 | * Use: Fills the area between the two vector pointers with ones. | |
175 | */ | |
176 | ||
177 | #define MPX_ONE(v, vl) do { \ | |
178 | mpw * _v = (v); \ | |
179 | const mpw *_vl = (vl); \ | |
180 | while (_v < _vl) \ | |
181 | *_v++ = MPW_MAX; \ | |
182 | } while (0) | |
183 | ||
d03ab969 | 184 | /*----- Loading and storing -----------------------------------------------*/ |
185 | ||
186 | /* --- @mpx_storel@ --- * | |
187 | * | |
188 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector | |
3c9ede17 | 189 | * @void *p@ = pointer to octet array |
d03ab969 | 190 | * @size_t sz@ = size of octet array |
191 | * | |
192 | * Returns: --- | |
193 | * | |
194 | * Use: Stores an MP in an octet array, least significant octet | |
195 | * first. High-end octets are silently discarded if there | |
196 | * isn't enough space for them. | |
197 | */ | |
198 | ||
199 | extern void mpx_storel(const mpw */*v*/, const mpw */*vl*/, | |
3c9ede17 | 200 | void */*p*/, size_t /*sz*/); |
d03ab969 | 201 | |
202 | /* --- @mpx_loadl@ --- * | |
203 | * | |
204 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector | |
3c9ede17 | 205 | * @const void *p@ = pointer to octet array |
d03ab969 | 206 | * @size_t sz@ = size of octet array |
207 | * | |
208 | * Returns: --- | |
209 | * | |
210 | * Use: Loads an MP in an octet array, least significant octet | |
211 | * first. High-end octets are ignored if there isn't enough | |
212 | * space for them. | |
213 | */ | |
214 | ||
215 | extern void mpx_loadl(mpw */*v*/, mpw */*vl*/, | |
3c9ede17 | 216 | const void */*p*/, size_t /*sz*/); |
d03ab969 | 217 | |
218 | /* --- @mpx_storeb@ --- * | |
219 | * | |
220 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector | |
3c9ede17 | 221 | * @void *p@ = pointer to octet array |
d03ab969 | 222 | * @size_t sz@ = size of octet array |
223 | * | |
224 | * Returns: --- | |
225 | * | |
226 | * Use: Stores an MP in an octet array, most significant octet | |
227 | * first. High-end octets are silently discarded if there | |
228 | * isn't enough space for them. | |
229 | */ | |
230 | ||
231 | extern void mpx_storeb(const mpw */*v*/, const mpw */*vl*/, | |
3c9ede17 | 232 | void */*p*/, size_t /*sz*/); |
d03ab969 | 233 | |
234 | /* --- @mpx_loadb@ --- * | |
235 | * | |
236 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector | |
3c9ede17 | 237 | * @const void *p@ = pointer to octet array |
d03ab969 | 238 | * @size_t sz@ = size of octet array |
239 | * | |
240 | * Returns: --- | |
241 | * | |
242 | * Use: Loads an MP in an octet array, most significant octet | |
243 | * first. High-end octets are ignored if there isn't enough | |
244 | * space for them. | |
245 | */ | |
246 | ||
247 | extern void mpx_loadb(mpw */*v*/, mpw */*vl*/, | |
3c9ede17 | 248 | const void */*p*/, size_t /*sz*/); |
d03ab969 | 249 | |
f09e814a | 250 | /* --- @mpx_storel2cn@ --- * |
251 | * | |
252 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector | |
253 | * @void *pp@ = pointer to octet array | |
254 | * @size_t sz@ = size of octet array | |
255 | * | |
256 | * Returns: --- | |
257 | * | |
258 | * Use: Stores a negative MP in an octet array, least significant | |
259 | * octet first, as two's complement. High-end octets are | |
260 | * silently discarded if there isn't enough space for them. | |
261 | * This obviously makes the output bad. | |
262 | */ | |
263 | ||
264 | extern void mpx_storel2cn(const mpw */*v*/, const mpw */*vl*/, | |
265 | void */*p*/, size_t /*sz*/); | |
266 | ||
267 | /* --- @mpx_loadl2cn@ --- * | |
268 | * | |
269 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector | |
270 | * @const void *pp@ = pointer to octet array | |
271 | * @size_t sz@ = size of octet array | |
272 | * | |
273 | * Returns: --- | |
274 | * | |
275 | * Use: Loads a negative MP in an octet array, least significant | |
276 | * octet first, as two's complement. High-end octets are | |
277 | * ignored if there isn't enough space for them. This probably | |
278 | * means you made the wrong choice coming here. | |
279 | */ | |
280 | ||
281 | extern void mpx_loadl2cn(mpw */*v*/, mpw */*vl*/, | |
282 | const void */*p*/, size_t /*sz*/); | |
283 | ||
284 | /* --- @mpx_storeb2cn@ --- * | |
285 | * | |
286 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector | |
287 | * @void *pp@ = pointer to octet array | |
288 | * @size_t sz@ = size of octet array | |
289 | * | |
290 | * Returns: --- | |
291 | * | |
292 | * Use: Stores a negative MP in an octet array, most significant | |
293 | * octet first, as two's complement. High-end octets are | |
294 | * silently discarded if there isn't enough space for them, | |
295 | * which probably isn't what you meant. | |
296 | */ | |
297 | ||
298 | extern void mpx_storeb2cn(const mpw */*v*/, const mpw */*vl*/, | |
299 | void */*p*/, size_t /*sz*/); | |
300 | ||
301 | /* --- @mpx_loadb2cn@ --- * | |
302 | * | |
303 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector | |
304 | * @const void *pp@ = pointer to octet array | |
305 | * @size_t sz@ = size of octet array | |
306 | * | |
307 | * Returns: --- | |
308 | * | |
309 | * Use: Loads a negative MP in an octet array, most significant octet | |
310 | * first as two's complement. High-end octets are ignored if | |
311 | * there isn't enough space for them. This probably means you | |
312 | * chose this function wrongly. | |
313 | */ | |
314 | ||
315 | extern void mpx_loadb2cn(mpw */*v*/, mpw */*vl*/, | |
316 | const void */*p*/, size_t /*sz*/); | |
317 | ||
318 | ||
d03ab969 | 319 | /*----- Logical shifting --------------------------------------------------*/ |
320 | ||
321 | /* --- @mpx_lsl@ --- * | |
322 | * | |
323 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
324 | * @const mpw *av, *avl@ = source vector base and limit | |
325 | * @size_t n@ = number of bit positions to shift by | |
326 | * | |
327 | * Returns: --- | |
328 | * | |
329 | * Use: Performs a logical shift left operation on an integer. | |
330 | */ | |
331 | ||
332 | extern void mpx_lsl(mpw */*dv*/, mpw */*dvl*/, | |
333 | const mpw */*av*/, const mpw */*avl*/, | |
334 | size_t /*n*/); | |
335 | ||
81578196 | 336 | /* --- @mpx_lslc@ --- * |
337 | * | |
338 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
339 | * @const mpw *av, *avl@ = source vector base and limit | |
340 | * @size_t n@ = number of bit positions to shift by | |
341 | * | |
342 | * Returns: --- | |
343 | * | |
344 | * Use: Performs a logical shift left operation on an integer, only | |
345 | * it fills in the bits with ones instead of zeroes. | |
346 | */ | |
347 | ||
348 | extern void mpx_lslc(mpw */*dv*/, mpw */*dvl*/, | |
349 | const mpw */*av*/, const mpw */*avl*/, | |
350 | size_t /*n*/); | |
351 | ||
d03ab969 | 352 | /* --- @mpx_lsr@ --- * |
353 | * | |
354 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
355 | * @const mpw *av, *avl@ = source vector base and limit | |
356 | * @size_t n@ = number of bit positions to shift by | |
357 | * | |
358 | * Returns: --- | |
359 | * | |
360 | * Use: Performs a logical shift right operation on an integer. | |
361 | */ | |
362 | ||
363 | extern void mpx_lsr(mpw */*dv*/, mpw */*dvl*/, | |
364 | const mpw */*av*/, const mpw */*avl*/, | |
365 | size_t /*n*/); | |
366 | ||
0f32e0f8 | 367 | /*----- Bitwise operations ------------------------------------------------*/ |
368 | ||
f09e814a | 369 | /* --- @mpx_bitop@ --- * |
0f32e0f8 | 370 | * |
371 | * Arguments: @mpw *dv, *dvl@ = destination vector | |
372 | * @const mpw *av, *avl@ = first source vector | |
373 | * @const mpw *bv, *bvl@ = second source vector | |
374 | * | |
375 | * Returns: --- | |
376 | * | |
f09e814a | 377 | * Use: Provide the dyadic boolean functions. The functions are |
378 | * named after the truth table they generate: | |
379 | * | |
380 | * a: 0011 | |
381 | * b: 0101 | |
382 | * @mpx_bitXXXX@ | |
0f32e0f8 | 383 | */ |
384 | ||
f09e814a | 385 | #define MPX_DOBIN(what) \ |
386 | what(0000) what(0001) what(0010) what(0011) \ | |
387 | what(0100) what(0101) what(0110) what(0111) \ | |
388 | what(1000) what(1001) what(1010) what(1011) \ | |
389 | what(1100) what(1101) what(1110) what(1111) | |
0f32e0f8 | 390 | |
f09e814a | 391 | #define MPX_BITDECL(string) \ |
392 | extern void mpx_bit##string(mpw */*dv*/, mpw */*dvl*/, \ | |
393 | const mpw */*av*/, const mpw */*avl*/, \ | |
394 | const mpw */*bv*/, const mpw */*bvl*/); | |
395 | MPX_DOBIN(MPX_BITDECL) | |
0f32e0f8 | 396 | |
f09e814a | 397 | /* --- @mpx_[n]and@, @mpx_[n]or@, @mpx_xor@ --- * |
398 | * | |
399 | * Synonyms for the commonly-used functions above. | |
400 | */ | |
401 | ||
45c0fd36 MW |
402 | #define mpx_and mpx_bit0001 |
403 | #define mpx_or mpx_bit0111 | |
f09e814a | 404 | #define mpx_nand mpx_bit1110 |
45c0fd36 MW |
405 | #define mpx_nor mpx_bit1000 |
406 | #define mpx_xor mpx_bit0110 | |
f09e814a | 407 | |
408 | /* --- @mpx_not@ --- * | |
409 | * | |
410 | * Arguments: @mpw *dv, *dvl@ = destination vector | |
411 | * @const mpw *av, *avl@ = first source vector | |
412 | * | |
413 | * Returns: --- | |
414 | * | |
415 | * Use; Bitwise NOT. | |
416 | */ | |
0f32e0f8 | 417 | |
418 | extern void mpx_not(mpw */*dv*/, mpw */*dvl*/, | |
419 | const mpw */*av*/, const mpw */*avl*/); | |
420 | ||
d03ab969 | 421 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
422 | ||
7c13f461 | 423 | /* --- @mpx_2c@ --- * |
424 | * | |
425 | * Arguments: @mpw *dv, *dvl@ = destination vector | |
426 | * @const mpw *v, *vl@ = source vector | |
427 | * | |
428 | * Returns: --- | |
429 | * | |
430 | * Use: Calculates the two's complement of @v@. | |
431 | */ | |
432 | ||
433 | extern void mpx_2c(mpw */*dv*/, mpw */*dvl*/, | |
434 | const mpw */*v*/, const mpw */*vl*/); | |
435 | ||
1a05a8ef | 436 | /* --- @mpx_ueq@ --- * |
437 | * | |
438 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit | |
439 | * @const mpw *bv, *bvl@ = second argument vector base and limit | |
440 | * | |
441 | * Returns: Nonzero if the two vectors are equal. | |
442 | * | |
443 | * Use: Performs an unsigned integer test for equality. | |
444 | */ | |
445 | ||
446 | extern int mpx_ueq(const mpw */*av*/, const mpw */*avl*/, | |
447 | const mpw */*bv*/, const mpw */*bvl*/); | |
448 | ||
d03ab969 | 449 | /* --- @mpx_ucmp@ --- * |
450 | * | |
451 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit | |
452 | * @const mpw *bv, *bvl@ = second argument vector base and limit | |
453 | * | |
454 | * Returns: Less than, equal to, or greater than zero depending on | |
455 | * whether @a@ is less than, equal to or greater than @b@, | |
456 | * respectively. | |
457 | * | |
458 | * Use: Performs an unsigned integer comparison. | |
459 | */ | |
460 | ||
461 | #define MPX_UCMP(av, avl, op, dv, dvl) \ | |
462 | (mpx_ucmp((av), (avl), (dv), (dvl)) op 0) | |
463 | ||
464 | extern int mpx_ucmp(const mpw */*av*/, const mpw */*avl*/, | |
465 | const mpw */*bv*/, const mpw */*bvl*/); | |
466 | ||
467 | /* --- @mpx_uadd@ --- * | |
468 | * | |
469 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
470 | * @const mpw *av, *avl@ = first addend vector base and limit | |
471 | * @const mpw *bv, *bvl@ = second addend vector base and limit | |
472 | * | |
473 | * Returns: --- | |
474 | * | |
475 | * Use: Performs unsigned integer addition. If the result overflows | |
476 | * the destination vector, high-order bits are discarded. This | |
477 | * means that two's complement addition happens more or less for | |
478 | * free, although that's more a side-effect than anything else. | |
479 | * The result vector may be equal to either or both source | |
480 | * vectors, but may not otherwise overlap them. | |
481 | */ | |
482 | ||
483 | extern void mpx_uadd(mpw */*dv*/, mpw */*dvl*/, | |
484 | const mpw */*av*/, const mpw */*avl*/, | |
485 | const mpw */*bv*/, const mpw */*bvl*/); | |
486 | ||
dd517851 | 487 | /* --- @mpx_uaddn@ --- * |
488 | * | |
489 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit | |
490 | * @mpw n@ = other addend | |
3c9ede17 | 491 | * |
dd517851 | 492 | * Returns: --- |
3c9ede17 | 493 | * |
494 | * Use: Adds a small integer to a multiprecision number. | |
495 | */ | |
496 | ||
497 | #define MPX_UADDN(dv, dvl, n) do { \ | |
498 | mpw *_ddv = (dv), *_ddvl = (dvl); \ | |
499 | mpw _c = (n); \ | |
500 | \ | |
501 | while (_c && _ddv < _ddvl) { \ | |
502 | mpd _x = (mpd)*_ddv + (mpd)_c; \ | |
503 | *_ddv++ = MPW(_x); \ | |
504 | _c = _x >> MPW_BITS; \ | |
505 | } \ | |
506 | } while (0) | |
507 | ||
dd517851 | 508 | extern void mpx_uaddn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/); |
509 | ||
f46efa79 | 510 | /* --- @mpx_uaddnlsl@ --- * |
511 | * | |
512 | * Arguments: @mpw *dv, *dvl@ = destination and first argument vector | |
513 | * @mpw a@ = second argument | |
514 | * @unsigned o@ = offset in bits | |
515 | * | |
516 | * Returns: --- | |
517 | * | |
518 | * Use: Computes %$d + 2^o a$%. If the result overflows then | |
519 | * high-order bits are discarded, as usual. We must have | |
520 | * @0 < o < MPW_BITS@. | |
521 | */ | |
522 | ||
523 | extern void mpx_uaddnlsl(mpw */*dv*/, mpw */*dvl*/, | |
524 | mpw /*a*/, unsigned /*o*/); | |
525 | ||
d03ab969 | 526 | /* --- @mpx_usub@ --- * |
527 | * | |
528 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
529 | * @const mpw *av, *avl@ = first argument vector base and limit | |
530 | * @const mpw *bv, *bvl@ = second argument vector base and limit | |
531 | * | |
532 | * Returns: --- | |
533 | * | |
534 | * Use: Performs unsigned integer subtraction. If the result | |
535 | * overflows the destination vector, high-order bits are | |
536 | * discarded. This means that two's complement subtraction | |
3c9ede17 | 537 | * happens more or less for free, although that's more a side- |
d03ab969 | 538 | * effect than anything else. The result vector may be equal to |
539 | * either or both source vectors, but may not otherwise overlap | |
540 | * them. | |
541 | */ | |
542 | ||
543 | extern void mpx_usub(mpw */*dv*/, mpw */*dvl*/, | |
544 | const mpw */*av*/, const mpw */*avl*/, | |
545 | const mpw */*bv*/, const mpw */*bvl*/); | |
546 | ||
dd517851 | 547 | /* --- @mpx_usubn@ --- * |
3c9ede17 | 548 | * |
dd517851 | 549 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
550 | * @n@ = subtrahend | |
551 | * | |
552 | * Returns: --- | |
3c9ede17 | 553 | * |
554 | * Use: Subtracts a small integer from a multiprecision number. | |
555 | */ | |
556 | ||
557 | #define MPX_USUBN(dv, dvl, n) do { \ | |
558 | mpw *_ddv = (dv), *_ddvl = (dvl); \ | |
559 | mpw _c = (n); \ | |
560 | \ | |
561 | while (_ddv < _ddvl) { \ | |
562 | mpd _x = (mpd)*_ddv - (mpd)_c; \ | |
563 | *_ddv++ = MPW(_x); \ | |
564 | if (_x >> MPW_BITS) \ | |
565 | _c = 1; \ | |
566 | else \ | |
567 | break; \ | |
568 | } \ | |
569 | } while (0) | |
570 | ||
dd517851 | 571 | extern void mpx_usubn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/); |
572 | ||
f46efa79 | 573 | /* --- @mpx_usubnlsl@ --- * |
574 | * | |
575 | * Arguments: @mpw *dv, *dvl@ = destination and first argument vector | |
576 | * @mpw a@ = second argument | |
577 | * @unsigned o@ = offset in bits | |
578 | * | |
579 | * Returns: --- | |
580 | * | |
581 | * Use: Computes %$d - 2^o a$%. If the result overflows then | |
582 | * high-order bits are discarded, as usual, so you get two's | |
583 | * complement. Which might be what you wanted... We must have | |
584 | * @0 < o < MPW_BITS@. | |
585 | */ | |
586 | ||
587 | extern void mpx_usubnlsl(mpw */*dv*/, mpw */*dvl*/, | |
588 | mpw /*a*/, unsigned /*o*/); | |
589 | ||
3c9ede17 | 590 | /* --- @mpx_umul@ --- * |
591 | * | |
592 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
593 | * @const mpw *av, *avl@ = multiplicand vector base and limit | |
594 | * @const mpw *bv, *bvl@ = multiplier vector base and limit | |
595 | * | |
596 | * Returns: --- | |
597 | * | |
598 | * Use: Performs unsigned integer multiplication. If the result | |
599 | * overflows the desination vector, high-order bits are | |
600 | * discarded. The result vector may not overlap the argument | |
601 | * vectors in any way. | |
602 | */ | |
603 | ||
604 | extern void mpx_umul(mpw */*dv*/, mpw */*dvl*/, | |
605 | const mpw */*av*/, const mpw */*avl*/, | |
606 | const mpw */*bv*/, const mpw */*bvl*/); | |
607 | ||
dd517851 | 608 | /* --- @mpx_umuln@ --- * |
d03ab969 | 609 | * |
dd517851 | 610 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
611 | * @const mpw *av, *avl@ = multiplicand vector base and limit | |
612 | * @mpw m@ = multiplier | |
613 | * | |
614 | * Returns: --- | |
d03ab969 | 615 | * |
616 | * Use: Multiplies a multiprecision integer by a single-word value. | |
617 | * The destination and source may be equal. The destination | |
618 | * is completely cleared after use. | |
619 | */ | |
620 | ||
621 | #define MPX_UMULN(dv, dvl, av, avl, m) do { \ | |
622 | mpw *_dv = (dv), *_dvl = (dvl); \ | |
623 | const mpw *_av = (av), *_avl = (avl); \ | |
624 | mpw _c = 0; \ | |
625 | mpd _m = (m); \ | |
626 | \ | |
627 | while (_av < _avl) { \ | |
628 | mpd _x; \ | |
629 | if (_dv >= _dvl) \ | |
630 | break; \ | |
3c9ede17 | 631 | _x = (mpd)_m * (mpd)*_av++ + _c; \ |
d03ab969 | 632 | *_dv++ = MPW(_x); \ |
633 | _c = _x >> MPW_BITS; \ | |
634 | } \ | |
635 | if (_dv < _dvl) { \ | |
636 | *_dv++ = MPW(_c); \ | |
637 | MPX_ZERO(_dv, _dvl); \ | |
638 | } \ | |
639 | } while (0) | |
640 | ||
dd517851 | 641 | extern void mpx_umuln(mpw */*dv*/, mpw */*dvl*/, |
642 | const mpw */*av*/, const mpw */*avl*/, mpw m); | |
643 | ||
644 | /* --- @mpx_umlan@ --- * | |
d03ab969 | 645 | * |
dd517851 | 646 | * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit |
647 | * @const mpw *av, *avl@ = multiplicand vector base and limit | |
648 | * @mpw m@ = multiplier | |
649 | * | |
650 | * Returns: --- | |
d03ab969 | 651 | * |
652 | * Use: Multiplies a multiprecision integer by a single-word value | |
653 | * and adds the result to an accumulator. | |
654 | */ | |
655 | ||
656 | #define MPX_UMLAN(dv, dvl, av, avl, m) do { \ | |
657 | mpw *_dv = (dv), *_dvl = (dvl); \ | |
658 | const mpw *_av = (av), *_avl = (avl); \ | |
7c13f461 | 659 | mpw _cc = 0; \ |
d03ab969 | 660 | mpd _m = (m); \ |
661 | \ | |
5bf74dea | 662 | while (_dv < _dvl && _av < _avl) { \ |
d03ab969 | 663 | mpd _x; \ |
7c13f461 | 664 | _x = (mpd)*_dv + (mpd)_m * (mpd)*_av++ + _cc; \ |
d03ab969 | 665 | *_dv++ = MPW(_x); \ |
7c13f461 | 666 | _cc = _x >> MPW_BITS; \ |
d03ab969 | 667 | } \ |
7c13f461 | 668 | MPX_UADDN(_dv, _dvl, _cc); \ |
d03ab969 | 669 | } while (0) |
670 | ||
dd517851 | 671 | extern void mpx_umlan(mpw */*dv*/, mpw */*dvl*/, |
672 | const mpw */*av*/, const mpw */*avl*/, mpw m); | |
673 | ||
3c9ede17 | 674 | /* --- @mpx_usqr@ --- * |
d03ab969 | 675 | * |
676 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
3c9ede17 | 677 | * @const mpw *av, *av@ = source vector base and limit |
d03ab969 | 678 | * |
679 | * Returns: --- | |
680 | * | |
3c9ede17 | 681 | * Use: Performs unsigned integer squaring. The result vector must |
682 | * not overlap the source vector in any way. | |
d03ab969 | 683 | */ |
684 | ||
3c9ede17 | 685 | extern void mpx_usqr(mpw */*dv*/, mpw */*dvl*/, |
686 | const mpw */*av*/, const mpw */*avl*/); | |
d03ab969 | 687 | |
5bf74dea | 688 | /* --- @mpx_udiv@ --- * |
689 | * | |
690 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit | |
691 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit | |
692 | * @const mpw *dv, *dvl@ = divisor vector base and limit | |
45c0fd36 | 693 | * @mpw *sv, *svl@ = scratch workspace |
5bf74dea | 694 | * |
695 | * Returns: --- | |
696 | * | |
697 | * Use: Performs unsigned integer division. If the result overflows | |
698 | * the quotient vector, high-order bits are discarded. (Clearly | |
699 | * the remainder vector can't overflow.) The various vectors | |
700 | * may not overlap in any way. Yes, I know it's a bit odd | |
701 | * requiring the dividend to be in the result position but it | |
702 | * does make some sense really. The remainder must have | |
703 | * headroom for at least two extra words. The scratch space | |
704 | * must be at least one word larger than the divisor. | |
705 | */ | |
706 | ||
707 | extern void mpx_udiv(mpw */*qv*/, mpw */*qvl*/, mpw */*rv*/, mpw */*rvl*/, | |
708 | const mpw */*dv*/, const mpw */*dvl*/, | |
709 | mpw */*sv*/, mpw */*svl*/); | |
710 | ||
698bd937 | 711 | /* --- @mpx_udivn@ --- * |
712 | * | |
713 | * Arguments: @mpw *qv, *qvl@ = storage for the quotient (may overlap | |
714 | * dividend) | |
715 | * @const mpw *rv, *rvl@ = dividend | |
716 | * @mpw d@ = single-precision divisor | |
717 | * | |
718 | * Returns: Remainder after divison. | |
719 | * | |
720 | * Use: Performs a single-precision division operation. | |
721 | */ | |
722 | ||
723 | extern mpw mpx_udivn(mpw */*qv*/, mpw */*qvl*/, | |
724 | const mpw */*rv*/, const mpw */*rvl*/, mpw /*d*/); | |
725 | ||
5bf74dea | 726 | /*----- Karatsuba multiplication algorithms -------------------------------*/ |
727 | ||
52cdaca9 | 728 | /* --- @MPK_THRESH@ --- * |
5bf74dea | 729 | * |
730 | * This is the limiting length for using Karatsuba algorithms. It's best to | |
731 | * use the simpler classical multiplication method on numbers smaller than | |
dd22938e | 732 | * this. It is unsafe to make this constant less than four (i.e., the |
733 | * algorithms will fail). | |
5bf74dea | 734 | */ |
735 | ||
52cdaca9 | 736 | #define MPK_THRESH 16 |
5bf74dea | 737 | |
a86e33af | 738 | /* --- @mpx_kmul@ --- * |
739 | * | |
740 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer | |
741 | * @const mpw *av, *avl@ = pointer to first argument | |
742 | * @const mpw *bv, *bvl@ = pointer to second argument | |
743 | * @mpw *sv, *svl@ = pointer to scratch workspace | |
744 | * | |
745 | * Returns: --- | |
746 | * | |
747 | * Use: Multiplies two multiprecision integers using Karatsuba's | |
748 | * algorithm. This is rather faster than traditional long | |
749 | * multiplication (e.g., @mpx_umul@) on large numbers, although | |
750 | * more expensive on small ones. | |
751 | * | |
dd22938e | 752 | * The destination must be three times as large as the larger |
753 | * argument. The scratch space must be five times as large as | |
754 | * the larger argument. | |
a86e33af | 755 | */ |
756 | ||
a86e33af | 757 | extern void mpx_kmul(mpw */*dv*/, mpw */*dvl*/, |
758 | const mpw */*av*/, const mpw */*avl*/, | |
759 | const mpw */*bv*/, const mpw */*bvl*/, | |
760 | mpw */*sv*/, mpw */*svl*/); | |
761 | ||
5bf74dea | 762 | /* --- @mpx_ksqr@ --- * |
d03ab969 | 763 | * |
5bf74dea | 764 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer |
765 | * @const mpw *av, *avl@ = pointer to first argument | |
766 | * @mpw *sv, *svl@ = pointer to scratch workspace | |
d03ab969 | 767 | * |
768 | * Returns: --- | |
769 | * | |
5bf74dea | 770 | * Use: Squares a multiprecision integers using something similar to |
771 | * Karatsuba's multiplication algorithm. This is rather faster | |
772 | * than traditional long multiplication (e.g., @mpx_umul@) on | |
773 | * large numbers, although more expensive on small ones, and | |
774 | * rather simpler than full-blown Karatsuba multiplication. | |
775 | * | |
dd22938e | 776 | * The destination must be three times as large as the larger |
777 | * argument. The scratch space must be five times as large as | |
778 | * the larger argument. | |
d03ab969 | 779 | */ |
780 | ||
5bf74dea | 781 | extern void mpx_ksqr(mpw */*dv*/, mpw */*dvl*/, |
782 | const mpw */*av*/, const mpw */*avl*/, | |
3c9ede17 | 783 | mpw */*sv*/, mpw */*svl*/); |
d03ab969 | 784 | |
785 | /*----- That's all, folks -------------------------------------------------*/ | |
786 | ||
787 | #ifdef __cplusplus | |
788 | } | |
789 | #endif | |
790 | ||
791 | #endif |