d03ab969 |
1 | /* -*-c-*- |
2 | * |
3 | * $Id: mpx.c,v 1.1 1999/09/03 08:41:12 mdw Exp $ |
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.c,v $ |
33 | * Revision 1.1 1999/09/03 08:41:12 mdw |
34 | * Initial import. |
35 | * |
36 | */ |
37 | |
38 | /*----- Header files ------------------------------------------------------*/ |
39 | |
40 | #include <stdio.h> |
41 | #include <stdlib.h> |
42 | #include <string.h> |
43 | |
44 | #include <mLib/bits.h> |
45 | |
46 | #include "mptypes.h" |
47 | #include "mpx.h" |
48 | |
49 | /*----- Loading and storing -----------------------------------------------*/ |
50 | |
51 | /* --- @mpx_storel@ --- * |
52 | * |
53 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
54 | * @octet *p@ = pointer to octet array |
55 | * @size_t sz@ = size of octet array |
56 | * |
57 | * Returns: --- |
58 | * |
59 | * Use: Stores an MP in an octet array, least significant octet |
60 | * first. High-end octets are silently discarded if there |
61 | * isn't enough space for them. |
62 | */ |
63 | |
64 | void mpx_storel(const mpw *v, const mpw *vl, octet *p, size_t sz) |
65 | { |
66 | mpw n, w = 0; |
67 | octet *q = p + sz; |
68 | unsigned bits = 0; |
69 | |
70 | while (p < q) { |
71 | if (bits < 8) { |
72 | if (v >= vl) { |
73 | *p++ = U8(w); |
74 | break; |
75 | } |
76 | n = *v++; |
77 | *p++ = U8(w | n << bits); |
78 | w = n >> (8 - bits); |
79 | bits += MPW_BITS - 8; |
80 | } else { |
81 | *p++ = U8(w); |
82 | w >>= 8; |
83 | bits -= 8; |
84 | } |
85 | } |
86 | memset(p, 0, q - p); |
87 | } |
88 | |
89 | /* --- @mpx_loadl@ --- * |
90 | * |
91 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
92 | * @const octet *p@ = pointer to octet array |
93 | * @size_t sz@ = size of octet array |
94 | * |
95 | * Returns: --- |
96 | * |
97 | * Use: Loads an MP in an octet array, least significant octet |
98 | * first. High-end octets are ignored if there isn't enough |
99 | * space for them. |
100 | */ |
101 | |
102 | void mpx_loadl(mpw *v, const mpw *vl, const octet *p, size_t sz) |
103 | { |
104 | unsigned n; |
105 | const octet *q = p + sz; |
106 | unsigned bits = 0; |
107 | |
108 | if (v >= vl) |
109 | return; |
110 | while (p < q) { |
111 | n = U8(*p++); |
112 | w |= n << bits; |
113 | bits += 8; |
114 | if (bits >= MPW_BITS) { |
115 | *v++ = MPW(w); |
116 | w = n >> (MPW_BITS - bits + 8); |
117 | bits -= MPW_BITS; |
118 | if (v >= vl) |
119 | return; |
120 | } |
121 | } |
122 | *v++ = w; |
123 | MPX_ZERO(v, vl); |
124 | } |
125 | |
126 | /* --- @mpx_storeb@ --- * |
127 | * |
128 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
129 | * @octet *p@ = pointer to octet array |
130 | * @size_t sz@ = size of octet array |
131 | * |
132 | * Returns: --- |
133 | * |
134 | * Use: Stores an MP in an octet array, most significant octet |
135 | * first. High-end octets are silently discarded if there |
136 | * isn't enough space for them. |
137 | */ |
138 | |
139 | void mpx_storeb(const mpw *v, const mpw *vl, octet *p, size_t sz); |
140 | { |
141 | mpw n, w = 0; |
142 | octet *q = p + sz; |
143 | unsigned bits = 0; |
144 | |
145 | while (q > p) { |
146 | if (bits < 8) { |
147 | if (v >= vl) { |
148 | *--q = U8(w); |
149 | break; |
150 | } |
151 | n = *v++; |
152 | *--q = U8(w | n << bits); |
153 | w = n >> (8 - bits); |
154 | bits += MPW_BITS - 8; |
155 | } else { |
156 | *--q = U8(w); |
157 | w >>= 8; |
158 | bits -= 8; |
159 | } |
160 | } |
161 | memset(p, 0, q - p); |
162 | } |
163 | |
164 | /* --- @mpx_loadb@ --- * |
165 | * |
166 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
167 | * @const octet *p@ = pointer to octet array |
168 | * @size_t sz@ = size of octet array |
169 | * |
170 | * Returns: --- |
171 | * |
172 | * Use: Loads an MP in an octet array, most significant octet |
173 | * first. High-end octets are ignored if there isn't enough |
174 | * space for them. |
175 | */ |
176 | |
177 | void mpx_loadb(mpw *v, const mpw *vl, const octet *p, size_t sz) |
178 | { |
179 | unsigned n; |
180 | const octet *q = p + sz; |
181 | unsigned bits = 0; |
182 | |
183 | if (v >= vl) |
184 | return; |
185 | while (q > p) { |
186 | n = U8(*--q); |
187 | w |= n << bits; |
188 | bits += 8; |
189 | if (bits >= MPW_BITS) { |
190 | *v++ = MPW(w); |
191 | w = n >> (MPW_BITS - bits + 8); |
192 | bits -= MPW_BITS; |
193 | if (v >= vl) |
194 | return; |
195 | } |
196 | } |
197 | *v++ = w; |
198 | MPX_ZERO(v, vl); |
199 | } |
200 | |
201 | /*----- Logical shifting --------------------------------------------------*/ |
202 | |
203 | /* --- @mpx_lsl@ --- * |
204 | * |
205 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
206 | * @const mpw *av, *avl@ = source vector base and limit |
207 | * @size_t n@ = number of bit positions to shift by |
208 | * |
209 | * Returns: --- |
210 | * |
211 | * Use: Performs a logical shift left operation on an integer. |
212 | */ |
213 | |
214 | void mpx_lsl(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
215 | { |
216 | size_t nw; |
217 | unsigned nb; |
218 | |
219 | /* --- Trivial special case --- */ |
220 | |
221 | if (n == 0) |
222 | MPX_COPY(dv, dvl, av, avl); |
223 | |
224 | /* --- Single bit shifting --- */ |
225 | |
226 | else if (n == 1) { |
227 | mpw w = 0; |
228 | while (av < avl) { |
229 | mpw t; |
230 | if (dv >= dvl) |
231 | goto done; |
232 | t = *av++; |
233 | *dv++ = MPW((t << 1) | w); |
234 | w = t >> (MPW_BITS - 1); |
235 | } |
236 | if (dv >= dvl) |
237 | goto done; |
238 | *dv++ = MPW(w); |
239 | MPX_ZERO(dv, dvl); |
240 | } |
241 | |
242 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
243 | |
244 | nw = n / MPW_BITS; |
245 | nb = n % MPW_BITS; |
246 | |
247 | /* --- Handle a shift by a multiple of the word size --- */ |
248 | |
249 | if (nb == 0) { |
250 | MPX_COPY(dv + nw, dvl, av, avl); |
251 | memset(dv, 0, MPWS(nw)); |
252 | } |
253 | |
254 | /* --- And finally the difficult case --- */ |
255 | |
256 | else { |
257 | mpw w; |
258 | size_t nr = MPW_BITS - nb; |
259 | |
260 | if (dv + nw >= dvl) { |
261 | MPX_ZERO(dv, dvl); |
262 | goto done; |
263 | } |
264 | memset(dv, 0, MPWS(nw)); |
265 | dv += nw; |
266 | w = *av++; |
267 | |
268 | while (av < avl) { |
269 | mpw t; |
270 | if (dv >= dvl) |
271 | goto done; |
272 | t = *av++; |
273 | *dv++ = MPW((w >> nr) | (t << nb)); |
274 | w = t; |
275 | } |
276 | |
277 | if (dv < dvl) { |
278 | *dv++ = MPW(w >> nr); |
279 | MPX_ZERO(dv, dvl); |
280 | } |
281 | } |
282 | |
283 | done:; |
284 | } |
285 | |
286 | /* --- @mpx_lsr@ --- * |
287 | * |
288 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
289 | * @const mpw *av, *avl@ = source vector base and limit |
290 | * @size_t n@ = number of bit positions to shift by |
291 | * |
292 | * Returns: --- |
293 | * |
294 | * Use: Performs a logical shift right operation on an integer. |
295 | */ |
296 | |
297 | void mpx_lsr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
298 | { |
299 | size_t nw; |
300 | unsigned nb; |
301 | |
302 | /* --- Trivial special case --- */ |
303 | |
304 | if (n == 0) |
305 | MPX_COPY(dv, dvl, av, avl); |
306 | |
307 | /* --- Single bit shifting --- */ |
308 | |
309 | else if (n == 1) { |
310 | mpw w = *av++ >> 1; |
311 | while (av < avl) { |
312 | mpw t; |
313 | if (dv >= dvl) |
314 | goto done; |
315 | t = *av++; |
316 | *dv++ = MPW((t << (MPW_BITS - 1)) | w); |
317 | w = t >> 1; |
318 | } |
319 | if (dv >= dvl) |
320 | goto done; |
321 | *dv++ = MPW(w); |
322 | MPX_ZERO(dv, dvl); |
323 | } |
324 | |
325 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
326 | |
327 | nw = n / MPW_BITS; |
328 | nb = n % MPW_BITS; |
329 | |
330 | /* --- Handle a shift by a multiple of the word size --- */ |
331 | |
332 | if (nb == 0) |
333 | MPX_COPY(dv, dvl, av + nw, avl); |
334 | |
335 | /* --- And finally the difficult case --- */ |
336 | |
337 | else { |
338 | mpw w; |
339 | size_t nr = MPW_BITS - nb; |
340 | |
341 | av += nw; |
342 | w = *av++; |
343 | while (av < avl) { |
344 | mpw t; |
345 | if (dv >= dvl) |
346 | goto done; |
347 | t = *av++; |
348 | *dv++ = MPW((w >> nb) | (t << nr)); |
349 | w = t; |
350 | } |
351 | if (dv < dvl) { |
352 | *dv++ = MPW(w >> nb); |
353 | MPX_ZERO(dv, dvl); |
354 | } |
355 | } |
356 | |
357 | done:; |
358 | } |
359 | |
360 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
361 | |
362 | /* --- @mpx_ucmp@ --- * |
363 | * |
364 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
365 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
366 | * |
367 | * Returns: Less than, equal to, or greater than zero depending on |
368 | * whether @a@ is less than, equal to or greater than @b@, |
369 | * respectively. |
370 | * |
371 | * Use: Performs an unsigned integer comparison. |
372 | */ |
373 | |
374 | int mpx_ucmp(const mpw *av, const mpw *avl, const mpw *bv, const mpw *bvl) |
375 | { |
376 | MPX_SHRINK(av, avl); |
377 | MPX_SHRINK(bv, bvl); |
378 | |
379 | if (avl - av > bvl - bv) |
380 | return (+1); |
381 | else if (avl - av < bvl - bv) |
382 | return (-1); |
383 | else while (avl > av) { |
384 | mpw a = *--avl, b = *--bvl; |
385 | if (a > b) |
386 | return (+1); |
387 | else if (a < b) |
388 | return (-1); |
389 | } |
390 | return (0); |
391 | } |
392 | |
393 | /* --- @mpx_uadd@ --- * |
394 | * |
395 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
396 | * @const mpw *av, *avl@ = first addend vector base and limit |
397 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
398 | * |
399 | * Returns: --- |
400 | * |
401 | * Use: Performs unsigned integer addition. If the result overflows |
402 | * the destination vector, high-order bits are discarded. This |
403 | * means that two's complement addition happens more or less for |
404 | * free, although that's more a side-effect than anything else. |
405 | * The result vector may be equal to either or both source |
406 | * vectors, but may not otherwise overlap them. |
407 | */ |
408 | |
409 | void mpx_uadd(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
410 | const mpw *bv, const mpw *bvl) |
411 | { |
412 | mpw c = 0; |
413 | |
414 | while (av < avl || bv < bvl) { |
415 | mpw a, b; |
416 | mpd x; |
417 | if (dv >= dvl) |
418 | return; |
419 | a = (av < avl) ? *av++ : 0; |
420 | b = (bv < bvl) ? *bv++ : 0; |
421 | x = (mpd)a + (mpd)b + c; |
422 | *dv++ = MPW(x); |
423 | c = x >> MPW_BITS; |
424 | } |
425 | if (dv < dvl) { |
426 | *dv++ = c; |
427 | MPX_ZERO(dv, dvl); |
428 | } |
429 | } |
430 | |
431 | /* --- @mpx_usub@ --- * |
432 | * |
433 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
434 | * @const mpw *av, *avl@ = first argument vector base and limit |
435 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
436 | * |
437 | * Returns: --- |
438 | * |
439 | * Use: Performs unsigned integer subtraction. If the result |
440 | * overflows the destination vector, high-order bits are |
441 | * discarded. This means that two's complement subtraction |
442 | * happens more or less for free, althuogh that's more a side- |
443 | * effect than anything else. The result vector may be equal to |
444 | * either or both source vectors, but may not otherwise overlap |
445 | * them. |
446 | */ |
447 | |
448 | void mpx_usub(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
449 | const mpw *bv, const mpw *bvl) |
450 | { |
451 | mpw c = 0; |
452 | |
453 | while (av < avl || bv < bvl) { |
454 | mpw a, b; |
455 | mpd x; |
456 | if (dv >= dvl) |
457 | return; |
458 | a = (av < avl) ? *av++ : 0; |
459 | b = (bv < bvl) ? *bv++ : 0; |
460 | x = (mpd)a - (mpd)b + c; |
461 | *dv++ = MPW(x); |
462 | if (c >> MPW_BITS) |
463 | c = MPW(~0u); |
464 | } |
465 | c = c ? ~0u : 0; |
466 | while (dv < dvl) |
467 | *dv++ = c |
468 | } |
469 | |
470 | /* --- @mpx_umul@ --- * |
471 | * |
472 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
473 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
474 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
475 | * |
476 | * Returns: --- |
477 | * |
478 | * Use: Performs unsigned integer multiplication. If the result |
479 | * overflows the desination vector, high-order bits are |
480 | * discarded. The result vector may not overlap the argument |
481 | * vectors in any way. |
482 | */ |
483 | |
484 | void mpx_umul(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
485 | const mpw *bv, const mpw *bvl) |
486 | { |
487 | /* --- This is probably worthwhile on a multiply --- */ |
488 | |
489 | MPX_SHRINK(av, avl); |
490 | MPX_SHRINK(bv, bvl); |
491 | |
492 | /* --- Deal with a multiply by zero --- */ |
493 | |
494 | if (bv == bvl) { |
495 | MPX_COPY(dv, dvl, bv, bvl); |
496 | return; |
497 | } |
498 | |
499 | /* --- Do the initial multiply and initialize the accumulator --- */ |
500 | |
501 | MPX_UMULN(dv, dvl, av, avl, *bv++); |
502 | |
503 | /* --- Do the remaining multiply/accumulates --- */ |
504 | |
505 | while (bv < bvl) { |
506 | mpw m = *bv++; |
507 | mpw c = ; |
508 | const mpw *avv = av; |
509 | mpw *dvv = ++dv; |
510 | |
511 | while (avv < avl) { |
512 | mpd x; |
513 | if (dvv >= dvl) |
514 | goto next; |
515 | x = *dvv + m * *av++ + c; |
516 | *dv++ = MPW(x); |
517 | c = x >> MPW_BITS; |
518 | } |
519 | if (dvv < dvl) |
520 | *dvv++ = MPW(c); |
521 | next:; |
522 | } |
523 | } |
524 | |
525 | /* --- @mpx_udiv@ --- * |
526 | * |
527 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
528 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
529 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
530 | * |
531 | * Returns: --- |
532 | * |
533 | * Use: Performs unsigned integer division. If the result overflows |
534 | * the quotient vector, high-order bits are discarded. (Clearly |
535 | * the remainder vector can't overflow.) The various vectors |
536 | * may not overlap in any way. Yes, I know it's a bit odd |
537 | * requiring the dividend to be in the result position but it |
538 | * does make some sense really. The remainder must have |
539 | * headroom for at least two extra words. |
540 | */ |
541 | |
542 | void mpx_udiv(mpw *qv, mpw *qvl, mpw *rv, mpw *rvl, |
543 | const mpw *dv, const mpw *dvl) |
544 | { |
545 | mpw spare[2]; |
546 | unsigned norm = 0; |
547 | size_t scale; |
548 | mpw d, dd; |
549 | |
550 | /* --- Initialize the quotient --- */ |
551 | |
552 | MPX_ZERO(qv, qvl); |
553 | |
554 | /* --- Normalize the divisor --- * |
555 | * |
556 | * The algorithm requires that the divisor be at least two digits long. |
557 | * This is easy to fix. |
558 | */ |
559 | |
560 | MPX_SHRINK(dv, dvl); |
561 | |
562 | assert(((void)"division by zero in mpx_udiv", dv < dvl)); |
563 | |
564 | d = dvl[-1]; |
565 | if (dv + 1 == dvl) { |
566 | spare[0] = 0; |
567 | spare[1] = d; |
568 | dv = spare; |
569 | dvl = spare + 2; |
570 | norm += MPW_BITS; |
571 | } |
572 | |
573 | while (d < MPW_MAX / 2) { |
574 | d <<= 1; |
575 | norm += 1; |
576 | } |
577 | dd = dvl[-2]; |
578 | |
579 | /* --- Normalize the dividend/remainder to match --- */ |
580 | |
581 | mpx_lsl(rv, rvl, rv, rvl, norm); |
582 | MPX_SHRINK(rv, rvl); |
583 | |
584 | /* --- Work out the relative scales --- */ |
585 | |
586 | { |
587 | size_t rvn = rvl - rv; |
588 | size_t dvn = dvn - dv; |
589 | |
590 | /* --- If the divisor is clearly larger, notice this --- */ |
591 | |
592 | if (dvn > rvn) { |
593 | mpx_lsr(rv, rvl, rv, rvl, norm); |
594 | return; |
595 | } |
596 | |
597 | scale = rvn - dvn; |
598 | } |
599 | |
600 | /* --- Calculate the most significant quotient digit --- * |
601 | * |
602 | * Because the divisor has its top bit set, this can only happen once. The |
603 | * pointer arithmetic is a little contorted, to make sure that the |
604 | * behaviour is defined. |
605 | */ |
606 | |
607 | if (MPX_UCMP(rv + scale, rvl, >=, dv, dvl)) { |
608 | mpx_usub(rv + scale, rvl, rv + scale, rvl, dv, dvl); |
609 | if (qvl - qv > scale) |
610 | qv[scale] = 1; |
611 | } |
612 | |
613 | /* --- Now for the main loop --- */ |
614 | |
615 | { |
616 | mpw *rvv; |
617 | mpw r; |
618 | |
619 | scale--; |
620 | rvv = rvl - 2; |
621 | r = rvv[1]; |
622 | |
623 | while (scale) { |
624 | mpw q, rr; |
625 | |
626 | /* --- Get an estimate for the next quotient digit --- */ |
627 | |
628 | rr = *rvv--; |
629 | if (r == d) |
630 | q = MPW_MAX; |
631 | else { |
632 | mpd rx = (r << MPW_BITS) | rr; |
633 | q = MPW(rx / d); |
634 | } |
635 | |
636 | /* --- Refine the estimate --- */ |
637 | |
638 | { |
639 | mpd yh = (mpd)d * q; |
640 | mpd yl = (mpd)dd * q; |
641 | |
642 | } |
643 | |
644 | /*----- That's all, folks -------------------------------------------------*/ |