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