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1 | /* -*-c-*- |
2 | * |
5bf74dea |
3 | * $Id: mpx.h,v 1.8 1999/12/11 10:57:43 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 $ |
5bf74dea |
33 | * Revision 1.8 1999/12/11 10:57:43 mdw |
34 | * Karatsuba squaring algorithm. |
35 | * |
652a6acf |
36 | * Revision 1.7 1999/12/11 01:51:28 mdw |
37 | * Change Karatsuba parameters slightly. |
38 | * |
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39 | * Revision 1.6 1999/12/10 23:23:51 mdw |
40 | * Karatsuba-Ofman multiplication algorithm. |
41 | * |
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42 | * Revision 1.5 1999/11/20 22:23:27 mdw |
43 | * Add function versions of some low-level macros with wider use. |
44 | * |
7c13f461 |
45 | * Revision 1.4 1999/11/17 18:04:43 mdw |
46 | * Add two's complement support. Fix a bug in MPX_UMLAN. |
47 | * |
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48 | * Revision 1.3 1999/11/13 01:51:29 mdw |
49 | * Minor interface changes. Should be stable now. |
50 | * |
b9b1c853 |
51 | * Revision 1.2 1999/11/11 17:47:55 mdw |
52 | * Minor changes for different `mptypes.h' format. |
53 | * |
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54 | * Revision 1.1 1999/09/03 08:41:12 mdw |
55 | * Initial import. |
56 | * |
57 | */ |
58 | |
a86e33af |
59 | #ifndef CATACOMB_MPX_H |
60 | #define CATACOMB_MPX_H |
d03ab969 |
61 | |
62 | #ifdef __cplusplus |
63 | extern "C" { |
64 | #endif |
65 | |
66 | /*----- The idea ----------------------------------------------------------* |
67 | * |
68 | * This file provides functions and macros which work on vectors of words as |
69 | * unsigned multiprecision integers. The interface works in terms of base |
70 | * and limit pointers (i.e., a pointer to the start of a vector, and a |
71 | * pointer just past its end) rather than base pointer and length, because |
72 | * that requires more arithmetic and state to work on. |
73 | * |
74 | * The interfaces are slightly bizarre in other ways. Try to use the |
75 | * higher-level functions where you can: they're rather better designed to |
76 | * actually be friendly and useful. |
77 | */ |
78 | |
79 | /*----- Header files ------------------------------------------------------*/ |
80 | |
81 | #include <string.h> |
82 | |
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83 | #ifndef CATACOMB_MPW_H |
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84 | # include "mpw.h" |
d03ab969 |
85 | #endif |
86 | |
87 | /*----- General manipulation ----------------------------------------------*/ |
88 | |
89 | /* --- @MPX_SHRINK@ --- * |
90 | * |
91 | * Arguments: @const mpw *v@ = pointer to vector of words |
92 | * @const mpw *vl@ = (updated) current limit of vector |
93 | * |
94 | * Use: Shrinks down the limit of a multiprecision integer vector. |
95 | */ |
96 | |
97 | #define MPX_SHRINK(v, vl) do { \ |
3c9ede17 |
98 | const mpw *_vv = (v), *_vvl = (vl); \ |
99 | while (_vvl > _vv && !_vvl[-1]) \ |
100 | _vvl--; \ |
101 | (vl) = (mpw *)_vvl; \ |
d03ab969 |
102 | } while (0) |
103 | |
104 | /* --- @MPX_BITS@ --- * |
105 | * |
106 | * Arguments: @unsigned long b@ = result variable |
107 | * @const mpw *v@ = pointer to array of words |
108 | * @const mpw *vl@ = limit of vector (from @MPX_SHRINK@) |
109 | * |
110 | * Use: Calculates the number of bits in a multiprecision value. |
111 | */ |
112 | |
113 | #define MPX_BITS(b, v, vl) do { \ |
114 | const mpw *_v = (v), *_vl = (vl); \ |
3c9ede17 |
115 | MPX_SHRINK(_v, _vl); \ |
d03ab969 |
116 | if (_v == _vl) \ |
117 | (b) = 0; \ |
118 | else { \ |
119 | unsigned long _b = MPW_BITS * (_vl - _v - 1) + 1; \ |
120 | mpw _w = _vl[-1]; \ |
121 | unsigned _k = MPW_BITS / 2; \ |
122 | while (_k) { \ |
123 | if (_w >> _k) { \ |
124 | _w >>= _k; \ |
125 | _b += _k; \ |
126 | } \ |
127 | _k >>= 1; \ |
128 | } \ |
129 | (b) = _b; \ |
130 | } \ |
131 | } while (0) |
132 | |
133 | /* --- @MPX_OCTETS@ --- * |
134 | * |
135 | * Arguments: @size_t o@ = result variable |
3c9ede17 |
136 | * @const mpw *v, *vl@ = pointer to array of words |
d03ab969 |
137 | * |
138 | * Use: Calculates the number of octets in a multiprecision value. |
139 | */ |
140 | |
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141 | #define MPX_OCTETS(o, v, vl) do { \ |
d03ab969 |
142 | const mpw *_v = (v), *_vl = (vl); \ |
3c9ede17 |
143 | MPX_SHRINK(_v, _vl); \ |
d03ab969 |
144 | if (_v == _vl) \ |
145 | (o) = 0; \ |
146 | else { \ |
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147 | size_t _o = (MPW_BITS / 8) * (_vl - _v - 1); \ |
d03ab969 |
148 | mpw _w = _vl[-1]; \ |
149 | unsigned _k = MPW_BITS / 2; \ |
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150 | while (_k >= 8) { \ |
d03ab969 |
151 | if (_w >> _k) { \ |
152 | _w >>= _k; \ |
3c9ede17 |
153 | _o += _k >> 3; \ |
d03ab969 |
154 | } \ |
155 | _k >>= 1; \ |
156 | } \ |
157 | if (_w) \ |
158 | _o++; \ |
159 | (o) = _o; \ |
160 | } \ |
161 | } while (0) |
162 | |
163 | /* --- @MPX_COPY@ --- * |
164 | * |
165 | * Arguments: @dv, dvl@ = destination vector base and limit |
166 | * @av, avl@ = source vector base and limit |
167 | * |
168 | * Use: Copies a multiprecision integer. |
169 | */ |
170 | |
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171 | #define MPX_COPY(dv, dvl, av, avl) do { \ |
172 | mpw *_dv = (dv), *_dvl = (dvl); \ |
173 | size_t _dn = _dvl - _dv; \ |
174 | const mpw *_av = (av), *_avl = (avl); \ |
175 | size_t _an = _avl - _av; \ |
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176 | if (_av == _dv) { \ |
177 | if (_dvl > _avl) \ |
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178 | memset(_dv, 0, MPWS(_dn - _an)); \ |
d03ab969 |
179 | } else if (_an >= _dn) \ |
180 | memmove(_dv, _av, MPWS(_dn)); \ |
181 | else { \ |
182 | memmove(_dv, _av, MPWS(_an)); \ |
183 | memset(_dv + _an, 0, MPWS(_dn - _an)); \ |
184 | } \ |
185 | } while (0) |
186 | |
187 | /* --- @MPX_ZERO@ --- * |
188 | * |
189 | * Arguments: @v, vl@ = base and limit of vector to clear |
190 | * |
191 | * Use: Zeroes the area between the two vector pointers. |
192 | */ |
193 | |
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194 | #define MPX_ZERO(v, vl) do { \ |
d03ab969 |
195 | mpw *_v = (v), *_vl = (vl); \ |
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196 | if (_v < _vl) \ |
197 | memset(_v, 0, MPWS(_vl - _v)); \ |
d03ab969 |
198 | } while (0) |
199 | |
200 | /*----- Loading and storing -----------------------------------------------*/ |
201 | |
202 | /* --- @mpx_storel@ --- * |
203 | * |
204 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
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205 | * @void *p@ = pointer to octet array |
d03ab969 |
206 | * @size_t sz@ = size of octet array |
207 | * |
208 | * Returns: --- |
209 | * |
210 | * Use: Stores an MP in an octet array, least significant octet |
211 | * first. High-end octets are silently discarded if there |
212 | * isn't enough space for them. |
213 | */ |
214 | |
215 | extern void mpx_storel(const mpw */*v*/, const mpw */*vl*/, |
3c9ede17 |
216 | void */*p*/, size_t /*sz*/); |
d03ab969 |
217 | |
218 | /* --- @mpx_loadl@ --- * |
219 | * |
220 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
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221 | * @const void *p@ = pointer to octet array |
d03ab969 |
222 | * @size_t sz@ = size of octet array |
223 | * |
224 | * Returns: --- |
225 | * |
226 | * Use: Loads an MP in an octet array, least significant octet |
227 | * first. High-end octets are ignored if there isn't enough |
228 | * space for them. |
229 | */ |
230 | |
231 | extern void mpx_loadl(mpw */*v*/, mpw */*vl*/, |
3c9ede17 |
232 | const void */*p*/, size_t /*sz*/); |
d03ab969 |
233 | |
234 | /* --- @mpx_storeb@ --- * |
235 | * |
236 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
3c9ede17 |
237 | * @void *p@ = pointer to octet array |
d03ab969 |
238 | * @size_t sz@ = size of octet array |
239 | * |
240 | * Returns: --- |
241 | * |
242 | * Use: Stores an MP in an octet array, most significant octet |
243 | * first. High-end octets are silently discarded if there |
244 | * isn't enough space for them. |
245 | */ |
246 | |
247 | extern void mpx_storeb(const mpw */*v*/, const mpw */*vl*/, |
3c9ede17 |
248 | void */*p*/, size_t /*sz*/); |
d03ab969 |
249 | |
250 | /* --- @mpx_loadb@ --- * |
251 | * |
252 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
3c9ede17 |
253 | * @const void *p@ = pointer to octet array |
d03ab969 |
254 | * @size_t sz@ = size of octet array |
255 | * |
256 | * Returns: --- |
257 | * |
258 | * Use: Loads an MP in an octet array, most significant octet |
259 | * first. High-end octets are ignored if there isn't enough |
260 | * space for them. |
261 | */ |
262 | |
263 | extern void mpx_loadb(mpw */*v*/, mpw */*vl*/, |
3c9ede17 |
264 | const void */*p*/, size_t /*sz*/); |
d03ab969 |
265 | |
266 | /*----- Logical shifting --------------------------------------------------*/ |
267 | |
268 | /* --- @mpx_lsl@ --- * |
269 | * |
270 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
271 | * @const mpw *av, *avl@ = source vector base and limit |
272 | * @size_t n@ = number of bit positions to shift by |
273 | * |
274 | * Returns: --- |
275 | * |
276 | * Use: Performs a logical shift left operation on an integer. |
277 | */ |
278 | |
279 | extern void mpx_lsl(mpw */*dv*/, mpw */*dvl*/, |
280 | const mpw */*av*/, const mpw */*avl*/, |
281 | size_t /*n*/); |
282 | |
283 | /* --- @mpx_lsr@ --- * |
284 | * |
285 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
286 | * @const mpw *av, *avl@ = source vector base and limit |
287 | * @size_t n@ = number of bit positions to shift by |
288 | * |
289 | * Returns: --- |
290 | * |
291 | * Use: Performs a logical shift right operation on an integer. |
292 | */ |
293 | |
294 | extern void mpx_lsr(mpw */*dv*/, mpw */*dvl*/, |
295 | const mpw */*av*/, const mpw */*avl*/, |
296 | size_t /*n*/); |
297 | |
298 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
299 | |
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300 | /* --- @mpx_2c@ --- * |
301 | * |
302 | * Arguments: @mpw *dv, *dvl@ = destination vector |
303 | * @const mpw *v, *vl@ = source vector |
304 | * |
305 | * Returns: --- |
306 | * |
307 | * Use: Calculates the two's complement of @v@. |
308 | */ |
309 | |
310 | extern void mpx_2c(mpw */*dv*/, mpw */*dvl*/, |
311 | const mpw */*v*/, const mpw */*vl*/); |
312 | |
d03ab969 |
313 | /* --- @mpx_ucmp@ --- * |
314 | * |
315 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
316 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
317 | * |
318 | * Returns: Less than, equal to, or greater than zero depending on |
319 | * whether @a@ is less than, equal to or greater than @b@, |
320 | * respectively. |
321 | * |
322 | * Use: Performs an unsigned integer comparison. |
323 | */ |
324 | |
325 | #define MPX_UCMP(av, avl, op, dv, dvl) \ |
326 | (mpx_ucmp((av), (avl), (dv), (dvl)) op 0) |
327 | |
328 | extern int mpx_ucmp(const mpw */*av*/, const mpw */*avl*/, |
329 | const mpw */*bv*/, const mpw */*bvl*/); |
330 | |
331 | /* --- @mpx_uadd@ --- * |
332 | * |
333 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
334 | * @const mpw *av, *avl@ = first addend vector base and limit |
335 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
336 | * |
337 | * Returns: --- |
338 | * |
339 | * Use: Performs unsigned integer addition. If the result overflows |
340 | * the destination vector, high-order bits are discarded. This |
341 | * means that two's complement addition happens more or less for |
342 | * free, although that's more a side-effect than anything else. |
343 | * The result vector may be equal to either or both source |
344 | * vectors, but may not otherwise overlap them. |
345 | */ |
346 | |
347 | extern void mpx_uadd(mpw */*dv*/, mpw */*dvl*/, |
348 | const mpw */*av*/, const mpw */*avl*/, |
349 | const mpw */*bv*/, const mpw */*bvl*/); |
350 | |
dd517851 |
351 | /* --- @mpx_uaddn@ --- * |
352 | * |
353 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
354 | * @mpw n@ = other addend |
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355 | * |
dd517851 |
356 | * Returns: --- |
3c9ede17 |
357 | * |
358 | * Use: Adds a small integer to a multiprecision number. |
359 | */ |
360 | |
361 | #define MPX_UADDN(dv, dvl, n) do { \ |
362 | mpw *_ddv = (dv), *_ddvl = (dvl); \ |
363 | mpw _c = (n); \ |
364 | \ |
365 | while (_c && _ddv < _ddvl) { \ |
366 | mpd _x = (mpd)*_ddv + (mpd)_c; \ |
367 | *_ddv++ = MPW(_x); \ |
368 | _c = _x >> MPW_BITS; \ |
369 | } \ |
370 | } while (0) |
371 | |
dd517851 |
372 | extern void mpx_uaddn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/); |
373 | |
d03ab969 |
374 | /* --- @mpx_usub@ --- * |
375 | * |
376 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
377 | * @const mpw *av, *avl@ = first argument vector base and limit |
378 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
379 | * |
380 | * Returns: --- |
381 | * |
382 | * Use: Performs unsigned integer subtraction. If the result |
383 | * overflows the destination vector, high-order bits are |
384 | * discarded. This means that two's complement subtraction |
3c9ede17 |
385 | * happens more or less for free, although that's more a side- |
d03ab969 |
386 | * effect than anything else. The result vector may be equal to |
387 | * either or both source vectors, but may not otherwise overlap |
388 | * them. |
389 | */ |
390 | |
391 | extern void mpx_usub(mpw */*dv*/, mpw */*dvl*/, |
392 | const mpw */*av*/, const mpw */*avl*/, |
393 | const mpw */*bv*/, const mpw */*bvl*/); |
394 | |
dd517851 |
395 | /* --- @mpx_usubn@ --- * |
3c9ede17 |
396 | * |
dd517851 |
397 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
398 | * @n@ = subtrahend |
399 | * |
400 | * Returns: --- |
3c9ede17 |
401 | * |
402 | * Use: Subtracts a small integer from a multiprecision number. |
403 | */ |
404 | |
405 | #define MPX_USUBN(dv, dvl, n) do { \ |
406 | mpw *_ddv = (dv), *_ddvl = (dvl); \ |
407 | mpw _c = (n); \ |
408 | \ |
409 | while (_ddv < _ddvl) { \ |
410 | mpd _x = (mpd)*_ddv - (mpd)_c; \ |
411 | *_ddv++ = MPW(_x); \ |
412 | if (_x >> MPW_BITS) \ |
413 | _c = 1; \ |
414 | else \ |
415 | break; \ |
416 | } \ |
417 | } while (0) |
418 | |
dd517851 |
419 | extern void mpx_usubn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/); |
420 | |
3c9ede17 |
421 | /* --- @mpx_umul@ --- * |
422 | * |
423 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
424 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
425 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
426 | * |
427 | * Returns: --- |
428 | * |
429 | * Use: Performs unsigned integer multiplication. If the result |
430 | * overflows the desination vector, high-order bits are |
431 | * discarded. The result vector may not overlap the argument |
432 | * vectors in any way. |
433 | */ |
434 | |
435 | extern void mpx_umul(mpw */*dv*/, mpw */*dvl*/, |
436 | const mpw */*av*/, const mpw */*avl*/, |
437 | const mpw */*bv*/, const mpw */*bvl*/); |
438 | |
dd517851 |
439 | /* --- @mpx_umuln@ --- * |
d03ab969 |
440 | * |
dd517851 |
441 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
442 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
443 | * @mpw m@ = multiplier |
444 | * |
445 | * Returns: --- |
d03ab969 |
446 | * |
447 | * Use: Multiplies a multiprecision integer by a single-word value. |
448 | * The destination and source may be equal. The destination |
449 | * is completely cleared after use. |
450 | */ |
451 | |
452 | #define MPX_UMULN(dv, dvl, av, avl, m) do { \ |
453 | mpw *_dv = (dv), *_dvl = (dvl); \ |
454 | const mpw *_av = (av), *_avl = (avl); \ |
455 | mpw _c = 0; \ |
456 | mpd _m = (m); \ |
457 | \ |
458 | while (_av < _avl) { \ |
459 | mpd _x; \ |
460 | if (_dv >= _dvl) \ |
461 | break; \ |
3c9ede17 |
462 | _x = (mpd)_m * (mpd)*_av++ + _c; \ |
d03ab969 |
463 | *_dv++ = MPW(_x); \ |
464 | _c = _x >> MPW_BITS; \ |
465 | } \ |
466 | if (_dv < _dvl) { \ |
467 | *_dv++ = MPW(_c); \ |
468 | MPX_ZERO(_dv, _dvl); \ |
469 | } \ |
470 | } while (0) |
471 | |
dd517851 |
472 | extern void mpx_umuln(mpw */*dv*/, mpw */*dvl*/, |
473 | const mpw */*av*/, const mpw */*avl*/, mpw m); |
474 | |
475 | /* --- @mpx_umlan@ --- * |
d03ab969 |
476 | * |
dd517851 |
477 | * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit |
478 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
479 | * @mpw m@ = multiplier |
480 | * |
481 | * Returns: --- |
d03ab969 |
482 | * |
483 | * Use: Multiplies a multiprecision integer by a single-word value |
484 | * and adds the result to an accumulator. |
485 | */ |
486 | |
487 | #define MPX_UMLAN(dv, dvl, av, avl, m) do { \ |
488 | mpw *_dv = (dv), *_dvl = (dvl); \ |
489 | const mpw *_av = (av), *_avl = (avl); \ |
7c13f461 |
490 | mpw _cc = 0; \ |
d03ab969 |
491 | mpd _m = (m); \ |
492 | \ |
5bf74dea |
493 | while (_dv < _dvl && _av < _avl) { \ |
d03ab969 |
494 | mpd _x; \ |
7c13f461 |
495 | _x = (mpd)*_dv + (mpd)_m * (mpd)*_av++ + _cc; \ |
d03ab969 |
496 | *_dv++ = MPW(_x); \ |
7c13f461 |
497 | _cc = _x >> MPW_BITS; \ |
d03ab969 |
498 | } \ |
7c13f461 |
499 | MPX_UADDN(_dv, _dvl, _cc); \ |
d03ab969 |
500 | } while (0) |
501 | |
dd517851 |
502 | extern void mpx_umlan(mpw */*dv*/, mpw */*dvl*/, |
503 | const mpw */*av*/, const mpw */*avl*/, mpw m); |
504 | |
3c9ede17 |
505 | /* --- @mpx_usqr@ --- * |
d03ab969 |
506 | * |
507 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
3c9ede17 |
508 | * @const mpw *av, *av@ = source vector base and limit |
d03ab969 |
509 | * |
510 | * Returns: --- |
511 | * |
3c9ede17 |
512 | * Use: Performs unsigned integer squaring. The result vector must |
513 | * not overlap the source vector in any way. |
d03ab969 |
514 | */ |
515 | |
3c9ede17 |
516 | extern void mpx_usqr(mpw */*dv*/, mpw */*dvl*/, |
517 | const mpw */*av*/, const mpw */*avl*/); |
d03ab969 |
518 | |
5bf74dea |
519 | /* --- @mpx_udiv@ --- * |
520 | * |
521 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
522 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
523 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
524 | * @mpw *sv, *svl@ = scratch workspace |
525 | * |
526 | * Returns: --- |
527 | * |
528 | * Use: Performs unsigned integer division. If the result overflows |
529 | * the quotient vector, high-order bits are discarded. (Clearly |
530 | * the remainder vector can't overflow.) The various vectors |
531 | * may not overlap in any way. Yes, I know it's a bit odd |
532 | * requiring the dividend to be in the result position but it |
533 | * does make some sense really. The remainder must have |
534 | * headroom for at least two extra words. The scratch space |
535 | * must be at least one word larger than the divisor. |
536 | */ |
537 | |
538 | extern void mpx_udiv(mpw */*qv*/, mpw */*qvl*/, mpw */*rv*/, mpw */*rvl*/, |
539 | const mpw */*dv*/, const mpw */*dvl*/, |
540 | mpw */*sv*/, mpw */*svl*/); |
541 | |
542 | /*----- Karatsuba multiplication algorithms -------------------------------*/ |
543 | |
544 | /* --- @KARATSUBA_CUTOFF@ --- * |
545 | * |
546 | * This is the limiting length for using Karatsuba algorithms. It's best to |
547 | * use the simpler classical multiplication method on numbers smaller than |
548 | * this. |
549 | */ |
550 | |
551 | #define KARATSUBA_CUTOFF 16 |
552 | |
553 | /* --- @KARATSUBA_SLOP@ --- * |
554 | * |
555 | * The extra number of words required as scratch space by the Karatsuba |
556 | * routines. This is a (generous) guess, since the actual amount of space |
557 | * required is proportional to the recursion depth. |
558 | */ |
559 | |
560 | #define KARATSUBA_SLOP 32 |
561 | |
a86e33af |
562 | /* --- @mpx_kmul@ --- * |
563 | * |
564 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer |
565 | * @const mpw *av, *avl@ = pointer to first argument |
566 | * @const mpw *bv, *bvl@ = pointer to second argument |
567 | * @mpw *sv, *svl@ = pointer to scratch workspace |
568 | * |
569 | * Returns: --- |
570 | * |
571 | * Use: Multiplies two multiprecision integers using Karatsuba's |
572 | * algorithm. This is rather faster than traditional long |
573 | * multiplication (e.g., @mpx_umul@) on large numbers, although |
574 | * more expensive on small ones. |
575 | * |
576 | * The destination and scratch buffers must be twice as large as |
5bf74dea |
577 | * the larger argument. The scratch space must be twice as |
578 | * large as the larger argument, plus the magic number |
579 | * @KARATSUBA_SLOP@. |
a86e33af |
580 | */ |
581 | |
a86e33af |
582 | extern void mpx_kmul(mpw */*dv*/, mpw */*dvl*/, |
583 | const mpw */*av*/, const mpw */*avl*/, |
584 | const mpw */*bv*/, const mpw */*bvl*/, |
585 | mpw */*sv*/, mpw */*svl*/); |
586 | |
5bf74dea |
587 | /* --- @mpx_ksqr@ --- * |
d03ab969 |
588 | * |
5bf74dea |
589 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer |
590 | * @const mpw *av, *avl@ = pointer to first argument |
591 | * @mpw *sv, *svl@ = pointer to scratch workspace |
d03ab969 |
592 | * |
593 | * Returns: --- |
594 | * |
5bf74dea |
595 | * Use: Squares a multiprecision integers using something similar to |
596 | * Karatsuba's multiplication algorithm. This is rather faster |
597 | * than traditional long multiplication (e.g., @mpx_umul@) on |
598 | * large numbers, although more expensive on small ones, and |
599 | * rather simpler than full-blown Karatsuba multiplication. |
600 | * |
601 | * The destination must be twice as large as the argument. The |
602 | * scratch space must be twice as large as the argument, plus |
603 | * the magic number @KARATSUBA_SLOP@. |
d03ab969 |
604 | */ |
605 | |
5bf74dea |
606 | extern void mpx_ksqr(mpw */*dv*/, mpw */*dvl*/, |
607 | const mpw */*av*/, const mpw */*avl*/, |
3c9ede17 |
608 | mpw */*sv*/, mpw */*svl*/); |
d03ab969 |
609 | |
610 | /*----- That's all, folks -------------------------------------------------*/ |
611 | |
612 | #ifdef __cplusplus |
613 | } |
614 | #endif |
615 | |
616 | #endif |