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