d03ab969 |
1 | /* -*-c-*- |
2 | * |
652a6acf |
3 | * $Id: mpx.h,v 1.7 1999/12/11 01:51:28 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 $ |
652a6acf |
33 | * Revision 1.7 1999/12/11 01:51:28 mdw |
34 | * Change Karatsuba parameters slightly. |
35 | * |
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36 | * Revision 1.6 1999/12/10 23:23:51 mdw |
37 | * Karatsuba-Ofman multiplication algorithm. |
38 | * |
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39 | * Revision 1.5 1999/11/20 22:23:27 mdw |
40 | * Add function versions of some low-level macros with wider use. |
41 | * |
7c13f461 |
42 | * Revision 1.4 1999/11/17 18:04:43 mdw |
43 | * Add two's complement support. Fix a bug in MPX_UMLAN. |
44 | * |
3c9ede17 |
45 | * Revision 1.3 1999/11/13 01:51:29 mdw |
46 | * Minor interface changes. Should be stable now. |
47 | * |
b9b1c853 |
48 | * Revision 1.2 1999/11/11 17:47:55 mdw |
49 | * Minor changes for different `mptypes.h' format. |
50 | * |
d03ab969 |
51 | * Revision 1.1 1999/09/03 08:41:12 mdw |
52 | * Initial import. |
53 | * |
54 | */ |
55 | |
a86e33af |
56 | #ifndef CATACOMB_MPX_H |
57 | #define CATACOMB_MPX_H |
d03ab969 |
58 | |
59 | #ifdef __cplusplus |
60 | extern "C" { |
61 | #endif |
62 | |
63 | /*----- The idea ----------------------------------------------------------* |
64 | * |
65 | * This file provides functions and macros which work on vectors of words as |
66 | * unsigned multiprecision integers. The interface works in terms of base |
67 | * and limit pointers (i.e., a pointer to the start of a vector, and a |
68 | * pointer just past its end) rather than base pointer and length, because |
69 | * that requires more arithmetic and state to work on. |
70 | * |
71 | * The interfaces are slightly bizarre in other ways. Try to use the |
72 | * higher-level functions where you can: they're rather better designed to |
73 | * actually be friendly and useful. |
74 | */ |
75 | |
76 | /*----- Header files ------------------------------------------------------*/ |
77 | |
78 | #include <string.h> |
79 | |
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80 | #ifndef CATACOMB_MPW_H |
3c9ede17 |
81 | # include "mpw.h" |
d03ab969 |
82 | #endif |
83 | |
84 | /*----- General manipulation ----------------------------------------------*/ |
85 | |
86 | /* --- @MPX_SHRINK@ --- * |
87 | * |
88 | * Arguments: @const mpw *v@ = pointer to vector of words |
89 | * @const mpw *vl@ = (updated) current limit of vector |
90 | * |
91 | * Use: Shrinks down the limit of a multiprecision integer vector. |
92 | */ |
93 | |
94 | #define MPX_SHRINK(v, vl) do { \ |
3c9ede17 |
95 | const mpw *_vv = (v), *_vvl = (vl); \ |
96 | while (_vvl > _vv && !_vvl[-1]) \ |
97 | _vvl--; \ |
98 | (vl) = (mpw *)_vvl; \ |
d03ab969 |
99 | } while (0) |
100 | |
101 | /* --- @MPX_BITS@ --- * |
102 | * |
103 | * Arguments: @unsigned long b@ = result variable |
104 | * @const mpw *v@ = pointer to array of words |
105 | * @const mpw *vl@ = limit of vector (from @MPX_SHRINK@) |
106 | * |
107 | * Use: Calculates the number of bits in a multiprecision value. |
108 | */ |
109 | |
110 | #define MPX_BITS(b, v, vl) do { \ |
111 | const mpw *_v = (v), *_vl = (vl); \ |
3c9ede17 |
112 | MPX_SHRINK(_v, _vl); \ |
d03ab969 |
113 | if (_v == _vl) \ |
114 | (b) = 0; \ |
115 | else { \ |
116 | unsigned long _b = MPW_BITS * (_vl - _v - 1) + 1; \ |
117 | mpw _w = _vl[-1]; \ |
118 | unsigned _k = MPW_BITS / 2; \ |
119 | while (_k) { \ |
120 | if (_w >> _k) { \ |
121 | _w >>= _k; \ |
122 | _b += _k; \ |
123 | } \ |
124 | _k >>= 1; \ |
125 | } \ |
126 | (b) = _b; \ |
127 | } \ |
128 | } while (0) |
129 | |
130 | /* --- @MPX_OCTETS@ --- * |
131 | * |
132 | * Arguments: @size_t o@ = result variable |
3c9ede17 |
133 | * @const mpw *v, *vl@ = pointer to array of words |
d03ab969 |
134 | * |
135 | * Use: Calculates the number of octets in a multiprecision value. |
136 | */ |
137 | |
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138 | #define MPX_OCTETS(o, v, vl) do { \ |
d03ab969 |
139 | const mpw *_v = (v), *_vl = (vl); \ |
3c9ede17 |
140 | MPX_SHRINK(_v, _vl); \ |
d03ab969 |
141 | if (_v == _vl) \ |
142 | (o) = 0; \ |
143 | else { \ |
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144 | size_t _o = (MPW_BITS / 8) * (_vl - _v - 1); \ |
d03ab969 |
145 | mpw _w = _vl[-1]; \ |
146 | unsigned _k = MPW_BITS / 2; \ |
3c9ede17 |
147 | while (_k >= 8) { \ |
d03ab969 |
148 | if (_w >> _k) { \ |
149 | _w >>= _k; \ |
3c9ede17 |
150 | _o += _k >> 3; \ |
d03ab969 |
151 | } \ |
152 | _k >>= 1; \ |
153 | } \ |
154 | if (_w) \ |
155 | _o++; \ |
156 | (o) = _o; \ |
157 | } \ |
158 | } while (0) |
159 | |
160 | /* --- @MPX_COPY@ --- * |
161 | * |
162 | * Arguments: @dv, dvl@ = destination vector base and limit |
163 | * @av, avl@ = source vector base and limit |
164 | * |
165 | * Use: Copies a multiprecision integer. |
166 | */ |
167 | |
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168 | #define MPX_COPY(dv, dvl, av, avl) do { \ |
169 | mpw *_dv = (dv), *_dvl = (dvl); \ |
170 | size_t _dn = _dvl - _dv; \ |
171 | const mpw *_av = (av), *_avl = (avl); \ |
172 | size_t _an = _avl - _av; \ |
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173 | if (_av == _dv) { \ |
174 | if (_dvl > _avl) \ |
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175 | memset(_dv, 0, MPWS(_dn - _an)); \ |
d03ab969 |
176 | } else if (_an >= _dn) \ |
177 | memmove(_dv, _av, MPWS(_dn)); \ |
178 | else { \ |
179 | memmove(_dv, _av, MPWS(_an)); \ |
180 | memset(_dv + _an, 0, MPWS(_dn - _an)); \ |
181 | } \ |
182 | } while (0) |
183 | |
184 | /* --- @MPX_ZERO@ --- * |
185 | * |
186 | * Arguments: @v, vl@ = base and limit of vector to clear |
187 | * |
188 | * Use: Zeroes the area between the two vector pointers. |
189 | */ |
190 | |
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191 | #define MPX_ZERO(v, vl) do { \ |
d03ab969 |
192 | mpw *_v = (v), *_vl = (vl); \ |
3c9ede17 |
193 | if (_v < _vl) \ |
194 | memset(_v, 0, MPWS(_vl - _v)); \ |
d03ab969 |
195 | } while (0) |
196 | |
197 | /*----- Loading and storing -----------------------------------------------*/ |
198 | |
199 | /* --- @mpx_storel@ --- * |
200 | * |
201 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
3c9ede17 |
202 | * @void *p@ = pointer to octet array |
d03ab969 |
203 | * @size_t sz@ = size of octet array |
204 | * |
205 | * Returns: --- |
206 | * |
207 | * Use: Stores an MP in an octet array, least significant octet |
208 | * first. High-end octets are silently discarded if there |
209 | * isn't enough space for them. |
210 | */ |
211 | |
212 | extern void mpx_storel(const mpw */*v*/, const mpw */*vl*/, |
3c9ede17 |
213 | void */*p*/, size_t /*sz*/); |
d03ab969 |
214 | |
215 | /* --- @mpx_loadl@ --- * |
216 | * |
217 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
3c9ede17 |
218 | * @const void *p@ = pointer to octet array |
d03ab969 |
219 | * @size_t sz@ = size of octet array |
220 | * |
221 | * Returns: --- |
222 | * |
223 | * Use: Loads an MP in an octet array, least significant octet |
224 | * first. High-end octets are ignored if there isn't enough |
225 | * space for them. |
226 | */ |
227 | |
228 | extern void mpx_loadl(mpw */*v*/, mpw */*vl*/, |
3c9ede17 |
229 | const void */*p*/, size_t /*sz*/); |
d03ab969 |
230 | |
231 | /* --- @mpx_storeb@ --- * |
232 | * |
233 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
3c9ede17 |
234 | * @void *p@ = pointer to octet array |
d03ab969 |
235 | * @size_t sz@ = size of octet array |
236 | * |
237 | * Returns: --- |
238 | * |
239 | * Use: Stores an MP in an octet array, most significant octet |
240 | * first. High-end octets are silently discarded if there |
241 | * isn't enough space for them. |
242 | */ |
243 | |
244 | extern void mpx_storeb(const mpw */*v*/, const mpw */*vl*/, |
3c9ede17 |
245 | void */*p*/, size_t /*sz*/); |
d03ab969 |
246 | |
247 | /* --- @mpx_loadb@ --- * |
248 | * |
249 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
3c9ede17 |
250 | * @const void *p@ = pointer to octet array |
d03ab969 |
251 | * @size_t sz@ = size of octet array |
252 | * |
253 | * Returns: --- |
254 | * |
255 | * Use: Loads an MP in an octet array, most significant octet |
256 | * first. High-end octets are ignored if there isn't enough |
257 | * space for them. |
258 | */ |
259 | |
260 | extern void mpx_loadb(mpw */*v*/, mpw */*vl*/, |
3c9ede17 |
261 | const void */*p*/, size_t /*sz*/); |
d03ab969 |
262 | |
263 | /*----- Logical shifting --------------------------------------------------*/ |
264 | |
265 | /* --- @mpx_lsl@ --- * |
266 | * |
267 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
268 | * @const mpw *av, *avl@ = source vector base and limit |
269 | * @size_t n@ = number of bit positions to shift by |
270 | * |
271 | * Returns: --- |
272 | * |
273 | * Use: Performs a logical shift left operation on an integer. |
274 | */ |
275 | |
276 | extern void mpx_lsl(mpw */*dv*/, mpw */*dvl*/, |
277 | const mpw */*av*/, const mpw */*avl*/, |
278 | size_t /*n*/); |
279 | |
280 | /* --- @mpx_lsr@ --- * |
281 | * |
282 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
283 | * @const mpw *av, *avl@ = source vector base and limit |
284 | * @size_t n@ = number of bit positions to shift by |
285 | * |
286 | * Returns: --- |
287 | * |
288 | * Use: Performs a logical shift right operation on an integer. |
289 | */ |
290 | |
291 | extern void mpx_lsr(mpw */*dv*/, mpw */*dvl*/, |
292 | const mpw */*av*/, const mpw */*avl*/, |
293 | size_t /*n*/); |
294 | |
295 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
296 | |
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297 | /* --- @mpx_2c@ --- * |
298 | * |
299 | * Arguments: @mpw *dv, *dvl@ = destination vector |
300 | * @const mpw *v, *vl@ = source vector |
301 | * |
302 | * Returns: --- |
303 | * |
304 | * Use: Calculates the two's complement of @v@. |
305 | */ |
306 | |
307 | extern void mpx_2c(mpw */*dv*/, mpw */*dvl*/, |
308 | const mpw */*v*/, const mpw */*vl*/); |
309 | |
d03ab969 |
310 | /* --- @mpx_ucmp@ --- * |
311 | * |
312 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
313 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
314 | * |
315 | * Returns: Less than, equal to, or greater than zero depending on |
316 | * whether @a@ is less than, equal to or greater than @b@, |
317 | * respectively. |
318 | * |
319 | * Use: Performs an unsigned integer comparison. |
320 | */ |
321 | |
322 | #define MPX_UCMP(av, avl, op, dv, dvl) \ |
323 | (mpx_ucmp((av), (avl), (dv), (dvl)) op 0) |
324 | |
325 | extern int mpx_ucmp(const mpw */*av*/, const mpw */*avl*/, |
326 | const mpw */*bv*/, const mpw */*bvl*/); |
327 | |
328 | /* --- @mpx_uadd@ --- * |
329 | * |
330 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
331 | * @const mpw *av, *avl@ = first addend vector base and limit |
332 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
333 | * |
334 | * Returns: --- |
335 | * |
336 | * Use: Performs unsigned integer addition. If the result overflows |
337 | * the destination vector, high-order bits are discarded. This |
338 | * means that two's complement addition happens more or less for |
339 | * free, although that's more a side-effect than anything else. |
340 | * The result vector may be equal to either or both source |
341 | * vectors, but may not otherwise overlap them. |
342 | */ |
343 | |
344 | extern void mpx_uadd(mpw */*dv*/, mpw */*dvl*/, |
345 | const mpw */*av*/, const mpw */*avl*/, |
346 | const mpw */*bv*/, const mpw */*bvl*/); |
347 | |
dd517851 |
348 | /* --- @mpx_uaddn@ --- * |
349 | * |
350 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
351 | * @mpw n@ = other addend |
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352 | * |
dd517851 |
353 | * Returns: --- |
3c9ede17 |
354 | * |
355 | * Use: Adds a small integer to a multiprecision number. |
356 | */ |
357 | |
358 | #define MPX_UADDN(dv, dvl, n) do { \ |
359 | mpw *_ddv = (dv), *_ddvl = (dvl); \ |
360 | mpw _c = (n); \ |
361 | \ |
362 | while (_c && _ddv < _ddvl) { \ |
363 | mpd _x = (mpd)*_ddv + (mpd)_c; \ |
364 | *_ddv++ = MPW(_x); \ |
365 | _c = _x >> MPW_BITS; \ |
366 | } \ |
367 | } while (0) |
368 | |
dd517851 |
369 | extern void mpx_uaddn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/); |
370 | |
d03ab969 |
371 | /* --- @mpx_usub@ --- * |
372 | * |
373 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
374 | * @const mpw *av, *avl@ = first argument vector base and limit |
375 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
376 | * |
377 | * Returns: --- |
378 | * |
379 | * Use: Performs unsigned integer subtraction. If the result |
380 | * overflows the destination vector, high-order bits are |
381 | * discarded. This means that two's complement subtraction |
3c9ede17 |
382 | * happens more or less for free, although that's more a side- |
d03ab969 |
383 | * effect than anything else. The result vector may be equal to |
384 | * either or both source vectors, but may not otherwise overlap |
385 | * them. |
386 | */ |
387 | |
388 | extern void mpx_usub(mpw */*dv*/, mpw */*dvl*/, |
389 | const mpw */*av*/, const mpw */*avl*/, |
390 | const mpw */*bv*/, const mpw */*bvl*/); |
391 | |
dd517851 |
392 | /* --- @mpx_usubn@ --- * |
3c9ede17 |
393 | * |
dd517851 |
394 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
395 | * @n@ = subtrahend |
396 | * |
397 | * Returns: --- |
3c9ede17 |
398 | * |
399 | * Use: Subtracts a small integer from a multiprecision number. |
400 | */ |
401 | |
402 | #define MPX_USUBN(dv, dvl, n) do { \ |
403 | mpw *_ddv = (dv), *_ddvl = (dvl); \ |
404 | mpw _c = (n); \ |
405 | \ |
406 | while (_ddv < _ddvl) { \ |
407 | mpd _x = (mpd)*_ddv - (mpd)_c; \ |
408 | *_ddv++ = MPW(_x); \ |
409 | if (_x >> MPW_BITS) \ |
410 | _c = 1; \ |
411 | else \ |
412 | break; \ |
413 | } \ |
414 | } while (0) |
415 | |
dd517851 |
416 | extern void mpx_usubn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/); |
417 | |
3c9ede17 |
418 | /* --- @mpx_umul@ --- * |
419 | * |
420 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
421 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
422 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
423 | * |
424 | * Returns: --- |
425 | * |
426 | * Use: Performs unsigned integer multiplication. If the result |
427 | * overflows the desination vector, high-order bits are |
428 | * discarded. The result vector may not overlap the argument |
429 | * vectors in any way. |
430 | */ |
431 | |
432 | extern void mpx_umul(mpw */*dv*/, mpw */*dvl*/, |
433 | const mpw */*av*/, const mpw */*avl*/, |
434 | const mpw */*bv*/, const mpw */*bvl*/); |
435 | |
dd517851 |
436 | /* --- @mpx_umuln@ --- * |
d03ab969 |
437 | * |
dd517851 |
438 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
439 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
440 | * @mpw m@ = multiplier |
441 | * |
442 | * Returns: --- |
d03ab969 |
443 | * |
444 | * Use: Multiplies a multiprecision integer by a single-word value. |
445 | * The destination and source may be equal. The destination |
446 | * is completely cleared after use. |
447 | */ |
448 | |
449 | #define MPX_UMULN(dv, dvl, av, avl, m) do { \ |
450 | mpw *_dv = (dv), *_dvl = (dvl); \ |
451 | const mpw *_av = (av), *_avl = (avl); \ |
452 | mpw _c = 0; \ |
453 | mpd _m = (m); \ |
454 | \ |
455 | while (_av < _avl) { \ |
456 | mpd _x; \ |
457 | if (_dv >= _dvl) \ |
458 | break; \ |
3c9ede17 |
459 | _x = (mpd)_m * (mpd)*_av++ + _c; \ |
d03ab969 |
460 | *_dv++ = MPW(_x); \ |
461 | _c = _x >> MPW_BITS; \ |
462 | } \ |
463 | if (_dv < _dvl) { \ |
464 | *_dv++ = MPW(_c); \ |
465 | MPX_ZERO(_dv, _dvl); \ |
466 | } \ |
467 | } while (0) |
468 | |
dd517851 |
469 | extern void mpx_umuln(mpw */*dv*/, mpw */*dvl*/, |
470 | const mpw */*av*/, const mpw */*avl*/, mpw m); |
471 | |
472 | /* --- @mpx_umlan@ --- * |
d03ab969 |
473 | * |
dd517851 |
474 | * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit |
475 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
476 | * @mpw m@ = multiplier |
477 | * |
478 | * Returns: --- |
d03ab969 |
479 | * |
480 | * Use: Multiplies a multiprecision integer by a single-word value |
481 | * and adds the result to an accumulator. |
482 | */ |
483 | |
484 | #define MPX_UMLAN(dv, dvl, av, avl, m) do { \ |
485 | mpw *_dv = (dv), *_dvl = (dvl); \ |
486 | const mpw *_av = (av), *_avl = (avl); \ |
7c13f461 |
487 | mpw _cc = 0; \ |
d03ab969 |
488 | mpd _m = (m); \ |
489 | \ |
490 | while (_av < _avl) { \ |
491 | mpd _x; \ |
492 | if (_dv >= _dvl) \ |
493 | break; \ |
7c13f461 |
494 | _x = (mpd)*_dv + (mpd)_m * (mpd)*_av++ + _cc; \ |
d03ab969 |
495 | *_dv++ = MPW(_x); \ |
7c13f461 |
496 | _cc = _x >> MPW_BITS; \ |
d03ab969 |
497 | } \ |
7c13f461 |
498 | MPX_UADDN(_dv, _dvl, _cc); \ |
d03ab969 |
499 | } while (0) |
500 | |
dd517851 |
501 | extern void mpx_umlan(mpw */*dv*/, mpw */*dvl*/, |
502 | const mpw */*av*/, const mpw */*avl*/, mpw m); |
503 | |
3c9ede17 |
504 | /* --- @mpx_usqr@ --- * |
d03ab969 |
505 | * |
506 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
3c9ede17 |
507 | * @const mpw *av, *av@ = source vector base and limit |
d03ab969 |
508 | * |
509 | * Returns: --- |
510 | * |
3c9ede17 |
511 | * Use: Performs unsigned integer squaring. The result vector must |
512 | * not overlap the source vector in any way. |
d03ab969 |
513 | */ |
514 | |
3c9ede17 |
515 | extern void mpx_usqr(mpw */*dv*/, mpw */*dvl*/, |
516 | const mpw */*av*/, const mpw */*avl*/); |
d03ab969 |
517 | |
a86e33af |
518 | /* --- @mpx_kmul@ --- * |
519 | * |
520 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer |
521 | * @const mpw *av, *avl@ = pointer to first argument |
522 | * @const mpw *bv, *bvl@ = pointer to second argument |
523 | * @mpw *sv, *svl@ = pointer to scratch workspace |
524 | * |
525 | * Returns: --- |
526 | * |
527 | * Use: Multiplies two multiprecision integers using Karatsuba's |
528 | * algorithm. This is rather faster than traditional long |
529 | * multiplication (e.g., @mpx_umul@) on large numbers, although |
530 | * more expensive on small ones. |
531 | * |
532 | * The destination and scratch buffers must be twice as large as |
533 | * the larger argument. |
534 | */ |
535 | |
652a6acf |
536 | #define KARATSUBA_CUTOFF 20 |
a86e33af |
537 | #define KARATSUBA_SLOP 32 |
538 | |
539 | extern void mpx_kmul(mpw */*dv*/, mpw */*dvl*/, |
540 | const mpw */*av*/, const mpw */*avl*/, |
541 | const mpw */*bv*/, const mpw */*bvl*/, |
542 | mpw */*sv*/, mpw */*svl*/); |
543 | |
d03ab969 |
544 | /* --- @mpx_udiv@ --- * |
545 | * |
546 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
547 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
548 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
3c9ede17 |
549 | * @mpw *sv, *svl@ = scratch workspace |
d03ab969 |
550 | * |
551 | * Returns: --- |
552 | * |
553 | * Use: Performs unsigned integer division. If the result overflows |
554 | * the quotient vector, high-order bits are discarded. (Clearly |
555 | * the remainder vector can't overflow.) The various vectors |
556 | * may not overlap in any way. Yes, I know it's a bit odd |
557 | * requiring the dividend to be in the result position but it |
3c9ede17 |
558 | * does make some sense really. The remainder must have |
559 | * headroom for at least two extra words. The scratch space |
7c13f461 |
560 | * must be at least one word larger than the divisor. |
d03ab969 |
561 | */ |
562 | |
563 | extern void mpx_udiv(mpw */*qv*/, mpw */*qvl*/, mpw */*rv*/, mpw */*rvl*/, |
3c9ede17 |
564 | const mpw */*dv*/, const mpw */*dvl*/, |
565 | mpw */*sv*/, mpw */*svl*/); |
d03ab969 |
566 | |
567 | /*----- That's all, folks -------------------------------------------------*/ |
568 | |
569 | #ifdef __cplusplus |
570 | } |
571 | #endif |
572 | |
573 | #endif |