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