d03ab969 |
1 | /* -*-c-*- |
2 | * |
52cdaca9 |
3 | * $Id: mpx.h,v 1.11 2000/10/08 15:48:35 mdw Exp $ |
d03ab969 |
4 | * |
5 | * Low level multiprecision arithmetic |
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: mpx.h,v $ |
52cdaca9 |
33 | * Revision 1.11 2000/10/08 15:48:35 mdw |
34 | * Rename Karatsuba constants now that we have @gfx_kmul@ too. |
35 | * |
1a05a8ef |
36 | * Revision 1.10 2000/10/08 12:06:12 mdw |
37 | * Provide @mpx_ueq@ for rapidly testing equality of two integers. |
38 | * |
698bd937 |
39 | * Revision 1.9 1999/12/22 15:49:07 mdw |
40 | * New function for division by a small integer. |
41 | * |
5bf74dea |
42 | * Revision 1.8 1999/12/11 10:57:43 mdw |
43 | * Karatsuba squaring algorithm. |
44 | * |
652a6acf |
45 | * Revision 1.7 1999/12/11 01:51:28 mdw |
46 | * Change Karatsuba parameters slightly. |
47 | * |
a86e33af |
48 | * Revision 1.6 1999/12/10 23:23:51 mdw |
49 | * Karatsuba-Ofman multiplication algorithm. |
50 | * |
dd517851 |
51 | * Revision 1.5 1999/11/20 22:23:27 mdw |
52 | * Add function versions of some low-level macros with wider use. |
53 | * |
7c13f461 |
54 | * Revision 1.4 1999/11/17 18:04:43 mdw |
55 | * Add two's complement support. Fix a bug in MPX_UMLAN. |
56 | * |
3c9ede17 |
57 | * Revision 1.3 1999/11/13 01:51:29 mdw |
58 | * Minor interface changes. Should be stable now. |
59 | * |
b9b1c853 |
60 | * Revision 1.2 1999/11/11 17:47:55 mdw |
61 | * Minor changes for different `mptypes.h' format. |
62 | * |
d03ab969 |
63 | * Revision 1.1 1999/09/03 08:41:12 mdw |
64 | * Initial import. |
65 | * |
66 | */ |
67 | |
a86e33af |
68 | #ifndef CATACOMB_MPX_H |
69 | #define CATACOMB_MPX_H |
d03ab969 |
70 | |
71 | #ifdef __cplusplus |
72 | extern "C" { |
73 | #endif |
74 | |
75 | /*----- The idea ----------------------------------------------------------* |
76 | * |
77 | * This file provides functions and macros which work on vectors of words as |
78 | * unsigned multiprecision integers. The interface works in terms of base |
79 | * and limit pointers (i.e., a pointer to the start of a vector, and a |
80 | * pointer just past its end) rather than base pointer and length, because |
81 | * that requires more arithmetic and state to work on. |
82 | * |
83 | * The interfaces are slightly bizarre in other ways. Try to use the |
84 | * higher-level functions where you can: they're rather better designed to |
85 | * actually be friendly and useful. |
86 | */ |
87 | |
88 | /*----- Header files ------------------------------------------------------*/ |
89 | |
90 | #include <string.h> |
91 | |
a86e33af |
92 | #ifndef CATACOMB_MPW_H |
3c9ede17 |
93 | # include "mpw.h" |
d03ab969 |
94 | #endif |
95 | |
96 | /*----- General manipulation ----------------------------------------------*/ |
97 | |
98 | /* --- @MPX_SHRINK@ --- * |
99 | * |
100 | * Arguments: @const mpw *v@ = pointer to vector of words |
101 | * @const mpw *vl@ = (updated) current limit of vector |
102 | * |
103 | * Use: Shrinks down the limit of a multiprecision integer vector. |
104 | */ |
105 | |
106 | #define MPX_SHRINK(v, vl) do { \ |
3c9ede17 |
107 | const mpw *_vv = (v), *_vvl = (vl); \ |
108 | while (_vvl > _vv && !_vvl[-1]) \ |
109 | _vvl--; \ |
110 | (vl) = (mpw *)_vvl; \ |
d03ab969 |
111 | } while (0) |
112 | |
113 | /* --- @MPX_BITS@ --- * |
114 | * |
115 | * Arguments: @unsigned long b@ = result variable |
116 | * @const mpw *v@ = pointer to array of words |
117 | * @const mpw *vl@ = limit of vector (from @MPX_SHRINK@) |
118 | * |
119 | * Use: Calculates the number of bits in a multiprecision value. |
120 | */ |
121 | |
122 | #define MPX_BITS(b, v, vl) do { \ |
123 | const mpw *_v = (v), *_vl = (vl); \ |
3c9ede17 |
124 | MPX_SHRINK(_v, _vl); \ |
d03ab969 |
125 | if (_v == _vl) \ |
126 | (b) = 0; \ |
127 | else { \ |
128 | unsigned long _b = MPW_BITS * (_vl - _v - 1) + 1; \ |
129 | mpw _w = _vl[-1]; \ |
130 | unsigned _k = MPW_BITS / 2; \ |
131 | while (_k) { \ |
132 | if (_w >> _k) { \ |
133 | _w >>= _k; \ |
134 | _b += _k; \ |
135 | } \ |
136 | _k >>= 1; \ |
137 | } \ |
138 | (b) = _b; \ |
139 | } \ |
140 | } while (0) |
141 | |
142 | /* --- @MPX_OCTETS@ --- * |
143 | * |
144 | * Arguments: @size_t o@ = result variable |
3c9ede17 |
145 | * @const mpw *v, *vl@ = pointer to array of words |
d03ab969 |
146 | * |
147 | * Use: Calculates the number of octets in a multiprecision value. |
148 | */ |
149 | |
3c9ede17 |
150 | #define MPX_OCTETS(o, v, vl) do { \ |
d03ab969 |
151 | const mpw *_v = (v), *_vl = (vl); \ |
3c9ede17 |
152 | MPX_SHRINK(_v, _vl); \ |
d03ab969 |
153 | if (_v == _vl) \ |
154 | (o) = 0; \ |
155 | else { \ |
3c9ede17 |
156 | size_t _o = (MPW_BITS / 8) * (_vl - _v - 1); \ |
d03ab969 |
157 | mpw _w = _vl[-1]; \ |
158 | unsigned _k = MPW_BITS / 2; \ |
3c9ede17 |
159 | while (_k >= 8) { \ |
d03ab969 |
160 | if (_w >> _k) { \ |
161 | _w >>= _k; \ |
3c9ede17 |
162 | _o += _k >> 3; \ |
d03ab969 |
163 | } \ |
164 | _k >>= 1; \ |
165 | } \ |
166 | if (_w) \ |
167 | _o++; \ |
168 | (o) = _o; \ |
169 | } \ |
170 | } while (0) |
171 | |
172 | /* --- @MPX_COPY@ --- * |
173 | * |
174 | * Arguments: @dv, dvl@ = destination vector base and limit |
175 | * @av, avl@ = source vector base and limit |
176 | * |
177 | * Use: Copies a multiprecision integer. |
178 | */ |
179 | |
3c9ede17 |
180 | #define MPX_COPY(dv, dvl, av, avl) do { \ |
181 | mpw *_dv = (dv), *_dvl = (dvl); \ |
182 | size_t _dn = _dvl - _dv; \ |
183 | const mpw *_av = (av), *_avl = (avl); \ |
184 | size_t _an = _avl - _av; \ |
d03ab969 |
185 | if (_av == _dv) { \ |
186 | if (_dvl > _avl) \ |
3c9ede17 |
187 | memset(_dv, 0, MPWS(_dn - _an)); \ |
d03ab969 |
188 | } else if (_an >= _dn) \ |
189 | memmove(_dv, _av, MPWS(_dn)); \ |
190 | else { \ |
191 | memmove(_dv, _av, MPWS(_an)); \ |
192 | memset(_dv + _an, 0, MPWS(_dn - _an)); \ |
193 | } \ |
194 | } while (0) |
195 | |
196 | /* --- @MPX_ZERO@ --- * |
197 | * |
198 | * Arguments: @v, vl@ = base and limit of vector to clear |
199 | * |
200 | * Use: Zeroes the area between the two vector pointers. |
201 | */ |
202 | |
3c9ede17 |
203 | #define MPX_ZERO(v, vl) do { \ |
d03ab969 |
204 | mpw *_v = (v), *_vl = (vl); \ |
3c9ede17 |
205 | if (_v < _vl) \ |
206 | memset(_v, 0, MPWS(_vl - _v)); \ |
d03ab969 |
207 | } while (0) |
208 | |
209 | /*----- Loading and storing -----------------------------------------------*/ |
210 | |
211 | /* --- @mpx_storel@ --- * |
212 | * |
213 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
3c9ede17 |
214 | * @void *p@ = pointer to octet array |
d03ab969 |
215 | * @size_t sz@ = size of octet array |
216 | * |
217 | * Returns: --- |
218 | * |
219 | * Use: Stores an MP in an octet array, least significant octet |
220 | * first. High-end octets are silently discarded if there |
221 | * isn't enough space for them. |
222 | */ |
223 | |
224 | extern void mpx_storel(const mpw */*v*/, const mpw */*vl*/, |
3c9ede17 |
225 | void */*p*/, size_t /*sz*/); |
d03ab969 |
226 | |
227 | /* --- @mpx_loadl@ --- * |
228 | * |
229 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
3c9ede17 |
230 | * @const void *p@ = pointer to octet array |
d03ab969 |
231 | * @size_t sz@ = size of octet array |
232 | * |
233 | * Returns: --- |
234 | * |
235 | * Use: Loads an MP in an octet array, least significant octet |
236 | * first. High-end octets are ignored if there isn't enough |
237 | * space for them. |
238 | */ |
239 | |
240 | extern void mpx_loadl(mpw */*v*/, mpw */*vl*/, |
3c9ede17 |
241 | const void */*p*/, size_t /*sz*/); |
d03ab969 |
242 | |
243 | /* --- @mpx_storeb@ --- * |
244 | * |
245 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
3c9ede17 |
246 | * @void *p@ = pointer to octet array |
d03ab969 |
247 | * @size_t sz@ = size of octet array |
248 | * |
249 | * Returns: --- |
250 | * |
251 | * Use: Stores an MP in an octet array, most significant octet |
252 | * first. High-end octets are silently discarded if there |
253 | * isn't enough space for them. |
254 | */ |
255 | |
256 | extern void mpx_storeb(const mpw */*v*/, const mpw */*vl*/, |
3c9ede17 |
257 | void */*p*/, size_t /*sz*/); |
d03ab969 |
258 | |
259 | /* --- @mpx_loadb@ --- * |
260 | * |
261 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
3c9ede17 |
262 | * @const void *p@ = pointer to octet array |
d03ab969 |
263 | * @size_t sz@ = size of octet array |
264 | * |
265 | * Returns: --- |
266 | * |
267 | * Use: Loads an MP in an octet array, most significant octet |
268 | * first. High-end octets are ignored if there isn't enough |
269 | * space for them. |
270 | */ |
271 | |
272 | extern void mpx_loadb(mpw */*v*/, mpw */*vl*/, |
3c9ede17 |
273 | const void */*p*/, size_t /*sz*/); |
d03ab969 |
274 | |
275 | /*----- Logical shifting --------------------------------------------------*/ |
276 | |
277 | /* --- @mpx_lsl@ --- * |
278 | * |
279 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
280 | * @const mpw *av, *avl@ = source vector base and limit |
281 | * @size_t n@ = number of bit positions to shift by |
282 | * |
283 | * Returns: --- |
284 | * |
285 | * Use: Performs a logical shift left operation on an integer. |
286 | */ |
287 | |
288 | extern void mpx_lsl(mpw */*dv*/, mpw */*dvl*/, |
289 | const mpw */*av*/, const mpw */*avl*/, |
290 | size_t /*n*/); |
291 | |
292 | /* --- @mpx_lsr@ --- * |
293 | * |
294 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
295 | * @const mpw *av, *avl@ = source vector base and limit |
296 | * @size_t n@ = number of bit positions to shift by |
297 | * |
298 | * Returns: --- |
299 | * |
300 | * Use: Performs a logical shift right operation on an integer. |
301 | */ |
302 | |
303 | extern void mpx_lsr(mpw */*dv*/, mpw */*dvl*/, |
304 | const mpw */*av*/, const mpw */*avl*/, |
305 | size_t /*n*/); |
306 | |
307 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
308 | |
7c13f461 |
309 | /* --- @mpx_2c@ --- * |
310 | * |
311 | * Arguments: @mpw *dv, *dvl@ = destination vector |
312 | * @const mpw *v, *vl@ = source vector |
313 | * |
314 | * Returns: --- |
315 | * |
316 | * Use: Calculates the two's complement of @v@. |
317 | */ |
318 | |
319 | extern void mpx_2c(mpw */*dv*/, mpw */*dvl*/, |
320 | const mpw */*v*/, const mpw */*vl*/); |
321 | |
1a05a8ef |
322 | /* --- @mpx_ueq@ --- * |
323 | * |
324 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
325 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
326 | * |
327 | * Returns: Nonzero if the two vectors are equal. |
328 | * |
329 | * Use: Performs an unsigned integer test for equality. |
330 | */ |
331 | |
332 | extern int mpx_ueq(const mpw */*av*/, const mpw */*avl*/, |
333 | const mpw */*bv*/, const mpw */*bvl*/); |
334 | |
d03ab969 |
335 | /* --- @mpx_ucmp@ --- * |
336 | * |
337 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
338 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
339 | * |
340 | * Returns: Less than, equal to, or greater than zero depending on |
341 | * whether @a@ is less than, equal to or greater than @b@, |
342 | * respectively. |
343 | * |
344 | * Use: Performs an unsigned integer comparison. |
345 | */ |
346 | |
347 | #define MPX_UCMP(av, avl, op, dv, dvl) \ |
348 | (mpx_ucmp((av), (avl), (dv), (dvl)) op 0) |
349 | |
350 | extern int mpx_ucmp(const mpw */*av*/, const mpw */*avl*/, |
351 | const mpw */*bv*/, const mpw */*bvl*/); |
352 | |
353 | /* --- @mpx_uadd@ --- * |
354 | * |
355 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
356 | * @const mpw *av, *avl@ = first addend vector base and limit |
357 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
358 | * |
359 | * Returns: --- |
360 | * |
361 | * Use: Performs unsigned integer addition. If the result overflows |
362 | * the destination vector, high-order bits are discarded. This |
363 | * means that two's complement addition happens more or less for |
364 | * free, although that's more a side-effect than anything else. |
365 | * The result vector may be equal to either or both source |
366 | * vectors, but may not otherwise overlap them. |
367 | */ |
368 | |
369 | extern void mpx_uadd(mpw */*dv*/, mpw */*dvl*/, |
370 | const mpw */*av*/, const mpw */*avl*/, |
371 | const mpw */*bv*/, const mpw */*bvl*/); |
372 | |
dd517851 |
373 | /* --- @mpx_uaddn@ --- * |
374 | * |
375 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
376 | * @mpw n@ = other addend |
3c9ede17 |
377 | * |
dd517851 |
378 | * Returns: --- |
3c9ede17 |
379 | * |
380 | * Use: Adds a small integer to a multiprecision number. |
381 | */ |
382 | |
383 | #define MPX_UADDN(dv, dvl, n) do { \ |
384 | mpw *_ddv = (dv), *_ddvl = (dvl); \ |
385 | mpw _c = (n); \ |
386 | \ |
387 | while (_c && _ddv < _ddvl) { \ |
388 | mpd _x = (mpd)*_ddv + (mpd)_c; \ |
389 | *_ddv++ = MPW(_x); \ |
390 | _c = _x >> MPW_BITS; \ |
391 | } \ |
392 | } while (0) |
393 | |
dd517851 |
394 | extern void mpx_uaddn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/); |
395 | |
d03ab969 |
396 | /* --- @mpx_usub@ --- * |
397 | * |
398 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
399 | * @const mpw *av, *avl@ = first argument vector base and limit |
400 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
401 | * |
402 | * Returns: --- |
403 | * |
404 | * Use: Performs unsigned integer subtraction. If the result |
405 | * overflows the destination vector, high-order bits are |
406 | * discarded. This means that two's complement subtraction |
3c9ede17 |
407 | * happens more or less for free, although that's more a side- |
d03ab969 |
408 | * effect than anything else. The result vector may be equal to |
409 | * either or both source vectors, but may not otherwise overlap |
410 | * them. |
411 | */ |
412 | |
413 | extern void mpx_usub(mpw */*dv*/, mpw */*dvl*/, |
414 | const mpw */*av*/, const mpw */*avl*/, |
415 | const mpw */*bv*/, const mpw */*bvl*/); |
416 | |
dd517851 |
417 | /* --- @mpx_usubn@ --- * |
3c9ede17 |
418 | * |
dd517851 |
419 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
420 | * @n@ = subtrahend |
421 | * |
422 | * Returns: --- |
3c9ede17 |
423 | * |
424 | * Use: Subtracts a small integer from a multiprecision number. |
425 | */ |
426 | |
427 | #define MPX_USUBN(dv, dvl, n) do { \ |
428 | mpw *_ddv = (dv), *_ddvl = (dvl); \ |
429 | mpw _c = (n); \ |
430 | \ |
431 | while (_ddv < _ddvl) { \ |
432 | mpd _x = (mpd)*_ddv - (mpd)_c; \ |
433 | *_ddv++ = MPW(_x); \ |
434 | if (_x >> MPW_BITS) \ |
435 | _c = 1; \ |
436 | else \ |
437 | break; \ |
438 | } \ |
439 | } while (0) |
440 | |
dd517851 |
441 | extern void mpx_usubn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/); |
442 | |
3c9ede17 |
443 | /* --- @mpx_umul@ --- * |
444 | * |
445 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
446 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
447 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
448 | * |
449 | * Returns: --- |
450 | * |
451 | * Use: Performs unsigned integer multiplication. If the result |
452 | * overflows the desination vector, high-order bits are |
453 | * discarded. The result vector may not overlap the argument |
454 | * vectors in any way. |
455 | */ |
456 | |
457 | extern void mpx_umul(mpw */*dv*/, mpw */*dvl*/, |
458 | const mpw */*av*/, const mpw */*avl*/, |
459 | const mpw */*bv*/, const mpw */*bvl*/); |
460 | |
dd517851 |
461 | /* --- @mpx_umuln@ --- * |
d03ab969 |
462 | * |
dd517851 |
463 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
464 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
465 | * @mpw m@ = multiplier |
466 | * |
467 | * Returns: --- |
d03ab969 |
468 | * |
469 | * Use: Multiplies a multiprecision integer by a single-word value. |
470 | * The destination and source may be equal. The destination |
471 | * is completely cleared after use. |
472 | */ |
473 | |
474 | #define MPX_UMULN(dv, dvl, av, avl, m) do { \ |
475 | mpw *_dv = (dv), *_dvl = (dvl); \ |
476 | const mpw *_av = (av), *_avl = (avl); \ |
477 | mpw _c = 0; \ |
478 | mpd _m = (m); \ |
479 | \ |
480 | while (_av < _avl) { \ |
481 | mpd _x; \ |
482 | if (_dv >= _dvl) \ |
483 | break; \ |
3c9ede17 |
484 | _x = (mpd)_m * (mpd)*_av++ + _c; \ |
d03ab969 |
485 | *_dv++ = MPW(_x); \ |
486 | _c = _x >> MPW_BITS; \ |
487 | } \ |
488 | if (_dv < _dvl) { \ |
489 | *_dv++ = MPW(_c); \ |
490 | MPX_ZERO(_dv, _dvl); \ |
491 | } \ |
492 | } while (0) |
493 | |
dd517851 |
494 | extern void mpx_umuln(mpw */*dv*/, mpw */*dvl*/, |
495 | const mpw */*av*/, const mpw */*avl*/, mpw m); |
496 | |
497 | /* --- @mpx_umlan@ --- * |
d03ab969 |
498 | * |
dd517851 |
499 | * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit |
500 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
501 | * @mpw m@ = multiplier |
502 | * |
503 | * Returns: --- |
d03ab969 |
504 | * |
505 | * Use: Multiplies a multiprecision integer by a single-word value |
506 | * and adds the result to an accumulator. |
507 | */ |
508 | |
509 | #define MPX_UMLAN(dv, dvl, av, avl, m) do { \ |
510 | mpw *_dv = (dv), *_dvl = (dvl); \ |
511 | const mpw *_av = (av), *_avl = (avl); \ |
7c13f461 |
512 | mpw _cc = 0; \ |
d03ab969 |
513 | mpd _m = (m); \ |
514 | \ |
5bf74dea |
515 | while (_dv < _dvl && _av < _avl) { \ |
d03ab969 |
516 | mpd _x; \ |
7c13f461 |
517 | _x = (mpd)*_dv + (mpd)_m * (mpd)*_av++ + _cc; \ |
d03ab969 |
518 | *_dv++ = MPW(_x); \ |
7c13f461 |
519 | _cc = _x >> MPW_BITS; \ |
d03ab969 |
520 | } \ |
7c13f461 |
521 | MPX_UADDN(_dv, _dvl, _cc); \ |
d03ab969 |
522 | } while (0) |
523 | |
dd517851 |
524 | extern void mpx_umlan(mpw */*dv*/, mpw */*dvl*/, |
525 | const mpw */*av*/, const mpw */*avl*/, mpw m); |
526 | |
3c9ede17 |
527 | /* --- @mpx_usqr@ --- * |
d03ab969 |
528 | * |
529 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
3c9ede17 |
530 | * @const mpw *av, *av@ = source vector base and limit |
d03ab969 |
531 | * |
532 | * Returns: --- |
533 | * |
3c9ede17 |
534 | * Use: Performs unsigned integer squaring. The result vector must |
535 | * not overlap the source vector in any way. |
d03ab969 |
536 | */ |
537 | |
3c9ede17 |
538 | extern void mpx_usqr(mpw */*dv*/, mpw */*dvl*/, |
539 | const mpw */*av*/, const mpw */*avl*/); |
d03ab969 |
540 | |
5bf74dea |
541 | /* --- @mpx_udiv@ --- * |
542 | * |
543 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
544 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
545 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
546 | * @mpw *sv, *svl@ = scratch workspace |
547 | * |
548 | * Returns: --- |
549 | * |
550 | * Use: Performs unsigned integer division. If the result overflows |
551 | * the quotient vector, high-order bits are discarded. (Clearly |
552 | * the remainder vector can't overflow.) The various vectors |
553 | * may not overlap in any way. Yes, I know it's a bit odd |
554 | * requiring the dividend to be in the result position but it |
555 | * does make some sense really. The remainder must have |
556 | * headroom for at least two extra words. The scratch space |
557 | * must be at least one word larger than the divisor. |
558 | */ |
559 | |
560 | extern void mpx_udiv(mpw */*qv*/, mpw */*qvl*/, mpw */*rv*/, mpw */*rvl*/, |
561 | const mpw */*dv*/, const mpw */*dvl*/, |
562 | mpw */*sv*/, mpw */*svl*/); |
563 | |
698bd937 |
564 | /* --- @mpx_udivn@ --- * |
565 | * |
566 | * Arguments: @mpw *qv, *qvl@ = storage for the quotient (may overlap |
567 | * dividend) |
568 | * @const mpw *rv, *rvl@ = dividend |
569 | * @mpw d@ = single-precision divisor |
570 | * |
571 | * Returns: Remainder after divison. |
572 | * |
573 | * Use: Performs a single-precision division operation. |
574 | */ |
575 | |
576 | extern mpw mpx_udivn(mpw */*qv*/, mpw */*qvl*/, |
577 | const mpw */*rv*/, const mpw */*rvl*/, mpw /*d*/); |
578 | |
5bf74dea |
579 | /*----- Karatsuba multiplication algorithms -------------------------------*/ |
580 | |
52cdaca9 |
581 | /* --- @MPK_THRESH@ --- * |
5bf74dea |
582 | * |
583 | * This is the limiting length for using Karatsuba algorithms. It's best to |
584 | * use the simpler classical multiplication method on numbers smaller than |
585 | * this. |
586 | */ |
587 | |
52cdaca9 |
588 | #define MPK_THRESH 16 |
5bf74dea |
589 | |
52cdaca9 |
590 | /* --- @MPK_SLOP@ --- * |
5bf74dea |
591 | * |
592 | * The extra number of words required as scratch space by the Karatsuba |
593 | * routines. This is a (generous) guess, since the actual amount of space |
594 | * required is proportional to the recursion depth. |
595 | */ |
596 | |
52cdaca9 |
597 | #define MPK_SLOP 64 |
5bf74dea |
598 | |
a86e33af |
599 | /* --- @mpx_kmul@ --- * |
600 | * |
601 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer |
602 | * @const mpw *av, *avl@ = pointer to first argument |
603 | * @const mpw *bv, *bvl@ = pointer to second argument |
604 | * @mpw *sv, *svl@ = pointer to scratch workspace |
605 | * |
606 | * Returns: --- |
607 | * |
608 | * Use: Multiplies two multiprecision integers using Karatsuba's |
609 | * algorithm. This is rather faster than traditional long |
610 | * multiplication (e.g., @mpx_umul@) on large numbers, although |
611 | * more expensive on small ones. |
612 | * |
613 | * The destination and scratch buffers must be twice as large as |
5bf74dea |
614 | * the larger argument. The scratch space must be twice as |
615 | * large as the larger argument, plus the magic number |
52cdaca9 |
616 | * @MPK_SLOP@. |
a86e33af |
617 | */ |
618 | |
a86e33af |
619 | extern void mpx_kmul(mpw */*dv*/, mpw */*dvl*/, |
620 | const mpw */*av*/, const mpw */*avl*/, |
621 | const mpw */*bv*/, const mpw */*bvl*/, |
622 | mpw */*sv*/, mpw */*svl*/); |
623 | |
5bf74dea |
624 | /* --- @mpx_ksqr@ --- * |
d03ab969 |
625 | * |
5bf74dea |
626 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer |
627 | * @const mpw *av, *avl@ = pointer to first argument |
628 | * @mpw *sv, *svl@ = pointer to scratch workspace |
d03ab969 |
629 | * |
630 | * Returns: --- |
631 | * |
5bf74dea |
632 | * Use: Squares a multiprecision integers using something similar to |
633 | * Karatsuba's multiplication algorithm. This is rather faster |
634 | * than traditional long multiplication (e.g., @mpx_umul@) on |
635 | * large numbers, although more expensive on small ones, and |
636 | * rather simpler than full-blown Karatsuba multiplication. |
637 | * |
638 | * The destination must be twice as large as the argument. The |
639 | * scratch space must be twice as large as the argument, plus |
52cdaca9 |
640 | * the magic number @MPK_SLOP@. |
d03ab969 |
641 | */ |
642 | |
5bf74dea |
643 | extern void mpx_ksqr(mpw */*dv*/, mpw */*dvl*/, |
644 | const mpw */*av*/, const mpw */*avl*/, |
3c9ede17 |
645 | mpw */*sv*/, mpw */*svl*/); |
d03ab969 |
646 | |
647 | /*----- That's all, folks -------------------------------------------------*/ |
648 | |
649 | #ifdef __cplusplus |
650 | } |
651 | #endif |
652 | |
653 | #endif |