d03ab969 |
1 | /* -*-c-*- |
2 | * |
42684bdb |
3 | * $Id: mpx.c,v 1.6 1999/11/20 22:43:44 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.c,v $ |
42684bdb |
33 | * Revision 1.6 1999/11/20 22:43:44 mdw |
34 | * Integrate testing for MPX routines. |
35 | * |
dd517851 |
36 | * Revision 1.5 1999/11/20 22:23:27 mdw |
37 | * Add function versions of some low-level macros with wider use. |
38 | * |
f45a00c6 |
39 | * Revision 1.4 1999/11/17 18:04:09 mdw |
40 | * Add two's-complement functionality. Improve mpx_udiv a little by |
41 | * performing the multiplication of the divisor by q with the subtraction |
42 | * from r. |
43 | * |
501da53c |
44 | * Revision 1.3 1999/11/13 01:57:31 mdw |
45 | * Remove stray debugging code. |
46 | * |
c8a2f9ef |
47 | * Revision 1.2 1999/11/13 01:50:59 mdw |
48 | * Multiprecision routines finished and tested. |
49 | * |
d03ab969 |
50 | * Revision 1.1 1999/09/03 08:41:12 mdw |
51 | * Initial import. |
52 | * |
53 | */ |
54 | |
55 | /*----- Header files ------------------------------------------------------*/ |
56 | |
c8a2f9ef |
57 | #include <assert.h> |
d03ab969 |
58 | #include <stdio.h> |
59 | #include <stdlib.h> |
60 | #include <string.h> |
61 | |
62 | #include <mLib/bits.h> |
63 | |
64 | #include "mptypes.h" |
65 | #include "mpx.h" |
66 | |
67 | /*----- Loading and storing -----------------------------------------------*/ |
68 | |
69 | /* --- @mpx_storel@ --- * |
70 | * |
71 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
c8a2f9ef |
72 | * @void *pp@ = pointer to octet array |
d03ab969 |
73 | * @size_t sz@ = size of octet array |
74 | * |
75 | * Returns: --- |
76 | * |
77 | * Use: Stores an MP in an octet array, least significant octet |
78 | * first. High-end octets are silently discarded if there |
79 | * isn't enough space for them. |
80 | */ |
81 | |
c8a2f9ef |
82 | void mpx_storel(const mpw *v, const mpw *vl, void *pp, size_t sz) |
d03ab969 |
83 | { |
84 | mpw n, w = 0; |
c8a2f9ef |
85 | octet *p = pp, *q = p + sz; |
d03ab969 |
86 | unsigned bits = 0; |
87 | |
88 | while (p < q) { |
89 | if (bits < 8) { |
90 | if (v >= vl) { |
91 | *p++ = U8(w); |
92 | break; |
93 | } |
94 | n = *v++; |
95 | *p++ = U8(w | n << bits); |
96 | w = n >> (8 - bits); |
97 | bits += MPW_BITS - 8; |
98 | } else { |
99 | *p++ = U8(w); |
100 | w >>= 8; |
101 | bits -= 8; |
102 | } |
103 | } |
104 | memset(p, 0, q - p); |
105 | } |
106 | |
107 | /* --- @mpx_loadl@ --- * |
108 | * |
109 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
c8a2f9ef |
110 | * @const void *pp@ = pointer to octet array |
d03ab969 |
111 | * @size_t sz@ = size of octet array |
112 | * |
113 | * Returns: --- |
114 | * |
115 | * Use: Loads an MP in an octet array, least significant octet |
116 | * first. High-end octets are ignored if there isn't enough |
117 | * space for them. |
118 | */ |
119 | |
c8a2f9ef |
120 | void mpx_loadl(mpw *v, mpw *vl, const void *pp, size_t sz) |
d03ab969 |
121 | { |
122 | unsigned n; |
c8a2f9ef |
123 | mpw w = 0; |
124 | const octet *p = pp, *q = p + sz; |
d03ab969 |
125 | unsigned bits = 0; |
126 | |
127 | if (v >= vl) |
128 | return; |
129 | while (p < q) { |
130 | n = U8(*p++); |
131 | w |= n << bits; |
132 | bits += 8; |
133 | if (bits >= MPW_BITS) { |
134 | *v++ = MPW(w); |
135 | w = n >> (MPW_BITS - bits + 8); |
136 | bits -= MPW_BITS; |
137 | if (v >= vl) |
138 | return; |
139 | } |
140 | } |
141 | *v++ = w; |
142 | MPX_ZERO(v, vl); |
143 | } |
144 | |
145 | /* --- @mpx_storeb@ --- * |
146 | * |
147 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
c8a2f9ef |
148 | * @void *pp@ = pointer to octet array |
d03ab969 |
149 | * @size_t sz@ = size of octet array |
150 | * |
151 | * Returns: --- |
152 | * |
153 | * Use: Stores an MP in an octet array, most significant octet |
154 | * first. High-end octets are silently discarded if there |
155 | * isn't enough space for them. |
156 | */ |
157 | |
c8a2f9ef |
158 | void mpx_storeb(const mpw *v, const mpw *vl, void *pp, size_t sz) |
d03ab969 |
159 | { |
160 | mpw n, w = 0; |
c8a2f9ef |
161 | octet *p = pp, *q = p + sz; |
d03ab969 |
162 | unsigned bits = 0; |
163 | |
164 | while (q > p) { |
165 | if (bits < 8) { |
166 | if (v >= vl) { |
167 | *--q = U8(w); |
168 | break; |
169 | } |
170 | n = *v++; |
171 | *--q = U8(w | n << bits); |
172 | w = n >> (8 - bits); |
173 | bits += MPW_BITS - 8; |
174 | } else { |
175 | *--q = U8(w); |
176 | w >>= 8; |
177 | bits -= 8; |
178 | } |
179 | } |
180 | memset(p, 0, q - p); |
181 | } |
182 | |
183 | /* --- @mpx_loadb@ --- * |
184 | * |
185 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
c8a2f9ef |
186 | * @const void *pp@ = pointer to octet array |
d03ab969 |
187 | * @size_t sz@ = size of octet array |
188 | * |
189 | * Returns: --- |
190 | * |
191 | * Use: Loads an MP in an octet array, most significant octet |
192 | * first. High-end octets are ignored if there isn't enough |
193 | * space for them. |
194 | */ |
195 | |
c8a2f9ef |
196 | void mpx_loadb(mpw *v, mpw *vl, const void *pp, size_t sz) |
d03ab969 |
197 | { |
198 | unsigned n; |
c8a2f9ef |
199 | mpw w = 0; |
200 | const octet *p = pp, *q = p + sz; |
d03ab969 |
201 | unsigned bits = 0; |
202 | |
203 | if (v >= vl) |
204 | return; |
205 | while (q > p) { |
206 | n = U8(*--q); |
207 | w |= n << bits; |
208 | bits += 8; |
209 | if (bits >= MPW_BITS) { |
210 | *v++ = MPW(w); |
211 | w = n >> (MPW_BITS - bits + 8); |
212 | bits -= MPW_BITS; |
213 | if (v >= vl) |
214 | return; |
215 | } |
216 | } |
217 | *v++ = w; |
218 | MPX_ZERO(v, vl); |
219 | } |
220 | |
221 | /*----- Logical shifting --------------------------------------------------*/ |
222 | |
223 | /* --- @mpx_lsl@ --- * |
224 | * |
225 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
226 | * @const mpw *av, *avl@ = source vector base and limit |
227 | * @size_t n@ = number of bit positions to shift by |
228 | * |
229 | * Returns: --- |
230 | * |
231 | * Use: Performs a logical shift left operation on an integer. |
232 | */ |
233 | |
234 | void mpx_lsl(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
235 | { |
236 | size_t nw; |
237 | unsigned nb; |
238 | |
239 | /* --- Trivial special case --- */ |
240 | |
241 | if (n == 0) |
242 | MPX_COPY(dv, dvl, av, avl); |
243 | |
244 | /* --- Single bit shifting --- */ |
245 | |
246 | else if (n == 1) { |
247 | mpw w = 0; |
248 | while (av < avl) { |
249 | mpw t; |
250 | if (dv >= dvl) |
251 | goto done; |
252 | t = *av++; |
253 | *dv++ = MPW((t << 1) | w); |
254 | w = t >> (MPW_BITS - 1); |
255 | } |
256 | if (dv >= dvl) |
257 | goto done; |
258 | *dv++ = MPW(w); |
259 | MPX_ZERO(dv, dvl); |
c8a2f9ef |
260 | goto done; |
d03ab969 |
261 | } |
262 | |
263 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
264 | |
265 | nw = n / MPW_BITS; |
266 | nb = n % MPW_BITS; |
267 | |
268 | /* --- Handle a shift by a multiple of the word size --- */ |
269 | |
270 | if (nb == 0) { |
271 | MPX_COPY(dv + nw, dvl, av, avl); |
272 | memset(dv, 0, MPWS(nw)); |
273 | } |
274 | |
c8a2f9ef |
275 | /* --- And finally the difficult case --- * |
276 | * |
277 | * This is a little convoluted, because I have to start from the end and |
278 | * work backwards to avoid overwriting the source, if they're both the same |
279 | * block of memory. |
280 | */ |
d03ab969 |
281 | |
282 | else { |
283 | mpw w; |
284 | size_t nr = MPW_BITS - nb; |
c8a2f9ef |
285 | size_t dvn = dvl - dv; |
286 | size_t avn = avl - av; |
d03ab969 |
287 | |
c8a2f9ef |
288 | if (dvn <= nw) { |
d03ab969 |
289 | MPX_ZERO(dv, dvl); |
290 | goto done; |
291 | } |
d03ab969 |
292 | |
c8a2f9ef |
293 | if (dvn > avn + nw) { |
294 | size_t off = avn + nw + 1; |
295 | MPX_ZERO(dv + off, dvl); |
296 | dvl = dv + off; |
297 | w = 0; |
298 | } else { |
299 | avl = av + dvn - nw; |
300 | w = *--avl << nb; |
d03ab969 |
301 | } |
302 | |
c8a2f9ef |
303 | while (avl > av) { |
304 | mpw t = *--avl; |
305 | *--dvl = (t >> nr) | w; |
306 | w = t << nb; |
d03ab969 |
307 | } |
c8a2f9ef |
308 | |
309 | *--dvl = w; |
310 | MPX_ZERO(dv, dvl); |
d03ab969 |
311 | } |
312 | |
313 | done:; |
314 | } |
315 | |
316 | /* --- @mpx_lsr@ --- * |
317 | * |
318 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
319 | * @const mpw *av, *avl@ = source vector base and limit |
320 | * @size_t n@ = number of bit positions to shift by |
321 | * |
322 | * Returns: --- |
323 | * |
324 | * Use: Performs a logical shift right operation on an integer. |
325 | */ |
326 | |
327 | void mpx_lsr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
328 | { |
329 | size_t nw; |
330 | unsigned nb; |
331 | |
332 | /* --- Trivial special case --- */ |
333 | |
334 | if (n == 0) |
335 | MPX_COPY(dv, dvl, av, avl); |
336 | |
337 | /* --- Single bit shifting --- */ |
338 | |
339 | else if (n == 1) { |
340 | mpw w = *av++ >> 1; |
341 | while (av < avl) { |
342 | mpw t; |
343 | if (dv >= dvl) |
344 | goto done; |
345 | t = *av++; |
346 | *dv++ = MPW((t << (MPW_BITS - 1)) | w); |
347 | w = t >> 1; |
348 | } |
349 | if (dv >= dvl) |
350 | goto done; |
351 | *dv++ = MPW(w); |
352 | MPX_ZERO(dv, dvl); |
c8a2f9ef |
353 | goto done; |
d03ab969 |
354 | } |
355 | |
356 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
357 | |
358 | nw = n / MPW_BITS; |
359 | nb = n % MPW_BITS; |
360 | |
361 | /* --- Handle a shift by a multiple of the word size --- */ |
362 | |
363 | if (nb == 0) |
364 | MPX_COPY(dv, dvl, av + nw, avl); |
365 | |
366 | /* --- And finally the difficult case --- */ |
367 | |
368 | else { |
369 | mpw w; |
370 | size_t nr = MPW_BITS - nb; |
371 | |
372 | av += nw; |
373 | w = *av++; |
374 | while (av < avl) { |
375 | mpw t; |
376 | if (dv >= dvl) |
377 | goto done; |
378 | t = *av++; |
379 | *dv++ = MPW((w >> nb) | (t << nr)); |
380 | w = t; |
381 | } |
382 | if (dv < dvl) { |
383 | *dv++ = MPW(w >> nb); |
384 | MPX_ZERO(dv, dvl); |
385 | } |
386 | } |
387 | |
388 | done:; |
389 | } |
390 | |
391 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
392 | |
f45a00c6 |
393 | /* --- @mpx_2c@ --- * |
394 | * |
395 | * Arguments: @mpw *dv, *dvl@ = destination vector |
396 | * @const mpw *v, *vl@ = source vector |
397 | * |
398 | * Returns: --- |
399 | * |
400 | * Use: Calculates the two's complement of @v@. |
401 | */ |
402 | |
403 | void mpx_2c(mpw *dv, mpw *dvl, const mpw *v, const mpw *vl) |
404 | { |
405 | mpw c = 0; |
406 | while (dv < dvl && v < vl) |
407 | *dv++ = c = MPW(~*v++); |
408 | if (dv < dvl) { |
409 | if (c > MPW_MAX / 2) |
410 | c = MPW(~0); |
411 | while (dv < dvl) |
412 | *dv++ = c; |
413 | } |
414 | MPX_UADDN(dv, dvl, 1); |
415 | } |
416 | |
d03ab969 |
417 | /* --- @mpx_ucmp@ --- * |
418 | * |
419 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
420 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
421 | * |
422 | * Returns: Less than, equal to, or greater than zero depending on |
423 | * whether @a@ is less than, equal to or greater than @b@, |
424 | * respectively. |
425 | * |
426 | * Use: Performs an unsigned integer comparison. |
427 | */ |
428 | |
429 | int mpx_ucmp(const mpw *av, const mpw *avl, const mpw *bv, const mpw *bvl) |
430 | { |
431 | MPX_SHRINK(av, avl); |
432 | MPX_SHRINK(bv, bvl); |
433 | |
434 | if (avl - av > bvl - bv) |
435 | return (+1); |
436 | else if (avl - av < bvl - bv) |
437 | return (-1); |
438 | else while (avl > av) { |
439 | mpw a = *--avl, b = *--bvl; |
440 | if (a > b) |
441 | return (+1); |
442 | else if (a < b) |
443 | return (-1); |
444 | } |
445 | return (0); |
446 | } |
447 | |
448 | /* --- @mpx_uadd@ --- * |
449 | * |
450 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
451 | * @const mpw *av, *avl@ = first addend vector base and limit |
452 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
453 | * |
454 | * Returns: --- |
455 | * |
456 | * Use: Performs unsigned integer addition. If the result overflows |
457 | * the destination vector, high-order bits are discarded. This |
458 | * means that two's complement addition happens more or less for |
459 | * free, although that's more a side-effect than anything else. |
460 | * The result vector may be equal to either or both source |
461 | * vectors, but may not otherwise overlap them. |
462 | */ |
463 | |
464 | void mpx_uadd(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
465 | const mpw *bv, const mpw *bvl) |
466 | { |
467 | mpw c = 0; |
468 | |
469 | while (av < avl || bv < bvl) { |
470 | mpw a, b; |
471 | mpd x; |
472 | if (dv >= dvl) |
473 | return; |
474 | a = (av < avl) ? *av++ : 0; |
475 | b = (bv < bvl) ? *bv++ : 0; |
476 | x = (mpd)a + (mpd)b + c; |
477 | *dv++ = MPW(x); |
478 | c = x >> MPW_BITS; |
479 | } |
480 | if (dv < dvl) { |
481 | *dv++ = c; |
482 | MPX_ZERO(dv, dvl); |
483 | } |
484 | } |
485 | |
dd517851 |
486 | /* --- @mpx_uaddn@ --- * |
487 | * |
488 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
489 | * @mpw n@ = other addend |
490 | * |
491 | * Returns: --- |
492 | * |
493 | * Use: Adds a small integer to a multiprecision number. |
494 | */ |
495 | |
496 | void mpx_uaddn(mpw *dv, mpw *dvl, mpw n) { MPX_UADDN(dv, dvl, n); } |
497 | |
d03ab969 |
498 | /* --- @mpx_usub@ --- * |
499 | * |
500 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
501 | * @const mpw *av, *avl@ = first argument vector base and limit |
502 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
503 | * |
504 | * Returns: --- |
505 | * |
506 | * Use: Performs unsigned integer subtraction. If the result |
507 | * overflows the destination vector, high-order bits are |
508 | * discarded. This means that two's complement subtraction |
509 | * happens more or less for free, althuogh that's more a side- |
510 | * effect than anything else. The result vector may be equal to |
511 | * either or both source vectors, but may not otherwise overlap |
512 | * them. |
513 | */ |
514 | |
515 | void mpx_usub(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
516 | const mpw *bv, const mpw *bvl) |
517 | { |
518 | mpw c = 0; |
519 | |
520 | while (av < avl || bv < bvl) { |
521 | mpw a, b; |
522 | mpd x; |
523 | if (dv >= dvl) |
524 | return; |
525 | a = (av < avl) ? *av++ : 0; |
526 | b = (bv < bvl) ? *bv++ : 0; |
c8a2f9ef |
527 | x = (mpd)a - (mpd)b - c; |
d03ab969 |
528 | *dv++ = MPW(x); |
c8a2f9ef |
529 | if (x >> MPW_BITS) |
530 | c = 1; |
531 | else |
532 | c = 0; |
d03ab969 |
533 | } |
c8a2f9ef |
534 | if (c) |
535 | c = MPW_MAX; |
d03ab969 |
536 | while (dv < dvl) |
c8a2f9ef |
537 | *dv++ = c; |
d03ab969 |
538 | } |
539 | |
dd517851 |
540 | /* --- @mpx_usubn@ --- * |
541 | * |
542 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
543 | * @n@ = subtrahend |
544 | * |
545 | * Returns: --- |
546 | * |
547 | * Use: Subtracts a small integer from a multiprecision number. |
548 | */ |
549 | |
550 | void mpx_usubn(mpw *dv, mpw *dvl, mpw n) { MPX_USUBN(dv, dvl, n); } |
551 | |
d03ab969 |
552 | /* --- @mpx_umul@ --- * |
553 | * |
554 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
555 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
556 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
557 | * |
558 | * Returns: --- |
559 | * |
560 | * Use: Performs unsigned integer multiplication. If the result |
561 | * overflows the desination vector, high-order bits are |
562 | * discarded. The result vector may not overlap the argument |
563 | * vectors in any way. |
564 | */ |
565 | |
566 | void mpx_umul(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
567 | const mpw *bv, const mpw *bvl) |
568 | { |
569 | /* --- This is probably worthwhile on a multiply --- */ |
570 | |
571 | MPX_SHRINK(av, avl); |
572 | MPX_SHRINK(bv, bvl); |
573 | |
574 | /* --- Deal with a multiply by zero --- */ |
575 | |
576 | if (bv == bvl) { |
c8a2f9ef |
577 | MPX_ZERO(dv, dvl); |
d03ab969 |
578 | return; |
579 | } |
580 | |
581 | /* --- Do the initial multiply and initialize the accumulator --- */ |
582 | |
583 | MPX_UMULN(dv, dvl, av, avl, *bv++); |
584 | |
585 | /* --- Do the remaining multiply/accumulates --- */ |
586 | |
c8a2f9ef |
587 | while (dv < dvl && bv < bvl) { |
d03ab969 |
588 | mpw m = *bv++; |
c8a2f9ef |
589 | mpw c = 0; |
d03ab969 |
590 | const mpw *avv = av; |
591 | mpw *dvv = ++dv; |
592 | |
593 | while (avv < avl) { |
594 | mpd x; |
595 | if (dvv >= dvl) |
596 | goto next; |
c8a2f9ef |
597 | x = (mpd)*dvv + (mpd)m * (mpd)*avv++ + c; |
598 | *dvv++ = MPW(x); |
d03ab969 |
599 | c = x >> MPW_BITS; |
600 | } |
c8a2f9ef |
601 | MPX_UADDN(dvv, dvl, c); |
d03ab969 |
602 | next:; |
603 | } |
604 | } |
605 | |
dd517851 |
606 | /* --- @mpx_umuln@ --- * |
607 | * |
608 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
609 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
610 | * @mpw m@ = multiplier |
611 | * |
612 | * Returns: --- |
613 | * |
614 | * Use: Multiplies a multiprecision integer by a single-word value. |
615 | * The destination and source may be equal. The destination |
616 | * is completely cleared after use. |
617 | */ |
618 | |
619 | void mpx_umuln(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, mpw m) |
620 | { |
621 | MPX_UMULN(dv, dvl, av, avl, m); |
622 | } |
623 | |
624 | /* --- @mpx_umlan@ --- * |
625 | * |
626 | * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit |
627 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
628 | * @mpw m@ = multiplier |
629 | * |
630 | * Returns: --- |
631 | * |
632 | * Use: Multiplies a multiprecision integer by a single-word value |
633 | * and adds the result to an accumulator. |
634 | */ |
635 | |
636 | void mpx_umlan(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, mpw m) |
637 | { |
638 | MPX_UMLAN(dv, dvl, av, avl, m); |
639 | } |
640 | |
c8a2f9ef |
641 | /* --- @mpx_usqr@ --- * |
642 | * |
643 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
644 | * @const mpw *av, *av@ = source vector base and limit |
645 | * |
646 | * Returns: --- |
647 | * |
648 | * Use: Performs unsigned integer squaring. The result vector must |
649 | * not overlap the source vector in any way. |
650 | */ |
651 | |
652 | void mpx_usqr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl) |
653 | { |
654 | MPX_ZERO(dv, dvl); |
655 | |
656 | /* --- Main loop --- */ |
657 | |
658 | while (av < avl) { |
659 | const mpw *avv = av; |
660 | mpw *dvv = dv; |
661 | mpw a = *av; |
662 | mpd c; |
663 | |
664 | /* --- Stop if I've run out of destination --- */ |
665 | |
666 | if (dvv >= dvl) |
667 | break; |
668 | |
669 | /* --- Work out the square at this point in the proceedings --- */ |
670 | |
671 | { |
c8a2f9ef |
672 | mpd x = (mpd)a * (mpd)a + *dvv; |
673 | *dvv++ = MPW(x); |
674 | c = MPW(x >> MPW_BITS); |
675 | } |
676 | |
677 | /* --- Now fix up the rest of the vector upwards --- */ |
678 | |
679 | avv++; |
680 | while (dvv < dvl && avv < avl) { |
c8a2f9ef |
681 | mpd x = (mpd)a * (mpd)*avv++; |
682 | mpd y = ((x << 1) & MPW_MAX) + c + *dvv; |
683 | c = (x >> (MPW_BITS - 1)) + (y >> MPW_BITS); |
684 | *dvv++ = MPW(y); |
685 | } |
686 | while (dvv < dvl && c) { |
687 | mpd x = c + *dvv; |
688 | *dvv++ = MPW(x); |
689 | c = x >> MPW_BITS; |
690 | } |
691 | |
692 | /* --- Get ready for the next round --- */ |
693 | |
694 | av++; |
695 | dv += 2; |
696 | } |
697 | } |
698 | |
d03ab969 |
699 | /* --- @mpx_udiv@ --- * |
700 | * |
701 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
702 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
703 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
c8a2f9ef |
704 | * @mpw *sv, *svl@ = scratch workspace |
d03ab969 |
705 | * |
706 | * Returns: --- |
707 | * |
708 | * Use: Performs unsigned integer division. If the result overflows |
709 | * the quotient vector, high-order bits are discarded. (Clearly |
710 | * the remainder vector can't overflow.) The various vectors |
711 | * may not overlap in any way. Yes, I know it's a bit odd |
712 | * requiring the dividend to be in the result position but it |
713 | * does make some sense really. The remainder must have |
c8a2f9ef |
714 | * headroom for at least two extra words. The scratch space |
f45a00c6 |
715 | * must be at least one word larger than the divisor. |
d03ab969 |
716 | */ |
717 | |
718 | void mpx_udiv(mpw *qv, mpw *qvl, mpw *rv, mpw *rvl, |
c8a2f9ef |
719 | const mpw *dv, const mpw *dvl, |
720 | mpw *sv, mpw *svl) |
d03ab969 |
721 | { |
d03ab969 |
722 | unsigned norm = 0; |
723 | size_t scale; |
724 | mpw d, dd; |
725 | |
726 | /* --- Initialize the quotient --- */ |
727 | |
728 | MPX_ZERO(qv, qvl); |
729 | |
c8a2f9ef |
730 | /* --- Perform some sanity checks --- */ |
731 | |
732 | MPX_SHRINK(dv, dvl); |
733 | assert(((void)"division by zero in mpx_udiv", dv < dvl)); |
734 | |
d03ab969 |
735 | /* --- Normalize the divisor --- * |
736 | * |
737 | * The algorithm requires that the divisor be at least two digits long. |
738 | * This is easy to fix. |
739 | */ |
740 | |
c8a2f9ef |
741 | { |
742 | unsigned b; |
d03ab969 |
743 | |
c8a2f9ef |
744 | d = dvl[-1]; |
745 | for (b = MPW_BITS / 2; b; b >>= 1) { |
746 | if (d < (MPW_MAX >> b)) { |
747 | d <<= b; |
748 | norm += b; |
749 | } |
750 | } |
751 | if (dv + 1 == dvl) |
752 | norm += MPW_BITS; |
d03ab969 |
753 | } |
d03ab969 |
754 | |
755 | /* --- Normalize the dividend/remainder to match --- */ |
756 | |
c8a2f9ef |
757 | if (norm) { |
c8a2f9ef |
758 | mpx_lsl(rv, rvl, rv, rvl, norm); |
f45a00c6 |
759 | mpx_lsl(sv, svl, dv, dvl, norm); |
c8a2f9ef |
760 | dv = sv; |
f45a00c6 |
761 | dvl = svl; |
c8a2f9ef |
762 | MPX_SHRINK(dv, dvl); |
763 | } |
764 | |
d03ab969 |
765 | MPX_SHRINK(rv, rvl); |
c8a2f9ef |
766 | d = dvl[-1]; |
767 | dd = dvl[-2]; |
d03ab969 |
768 | |
769 | /* --- Work out the relative scales --- */ |
770 | |
771 | { |
772 | size_t rvn = rvl - rv; |
c8a2f9ef |
773 | size_t dvn = dvl - dv; |
d03ab969 |
774 | |
775 | /* --- If the divisor is clearly larger, notice this --- */ |
776 | |
777 | if (dvn > rvn) { |
778 | mpx_lsr(rv, rvl, rv, rvl, norm); |
779 | return; |
780 | } |
781 | |
782 | scale = rvn - dvn; |
783 | } |
784 | |
785 | /* --- Calculate the most significant quotient digit --- * |
786 | * |
787 | * Because the divisor has its top bit set, this can only happen once. The |
788 | * pointer arithmetic is a little contorted, to make sure that the |
789 | * behaviour is defined. |
790 | */ |
791 | |
792 | if (MPX_UCMP(rv + scale, rvl, >=, dv, dvl)) { |
793 | mpx_usub(rv + scale, rvl, rv + scale, rvl, dv, dvl); |
794 | if (qvl - qv > scale) |
795 | qv[scale] = 1; |
796 | } |
797 | |
798 | /* --- Now for the main loop --- */ |
799 | |
800 | { |
c8a2f9ef |
801 | mpw *rvv = rvl - 2; |
d03ab969 |
802 | |
803 | while (scale) { |
c8a2f9ef |
804 | mpw q; |
805 | mpd rh; |
d03ab969 |
806 | |
807 | /* --- Get an estimate for the next quotient digit --- */ |
808 | |
c8a2f9ef |
809 | mpw r = rvv[1]; |
810 | mpw rr = rvv[0]; |
811 | mpw rrr = *--rvv; |
812 | |
813 | scale--; |
814 | rh = ((mpd)r << MPW_BITS) | rr; |
d03ab969 |
815 | if (r == d) |
816 | q = MPW_MAX; |
c8a2f9ef |
817 | else |
818 | q = MPW(rh / d); |
d03ab969 |
819 | |
820 | /* --- Refine the estimate --- */ |
821 | |
822 | { |
823 | mpd yh = (mpd)d * q; |
824 | mpd yl = (mpd)dd * q; |
c8a2f9ef |
825 | |
826 | if (yl > MPW_MAX) { |
827 | yh += yl >> MPW_BITS; |
828 | yl &= MPW_MAX; |
829 | } |
830 | |
831 | while (yh > rh || (yh == rh && yl > rrr)) { |
832 | q--; |
833 | yh -= d; |
834 | if (yl < dd) { |
835 | yh++; |
836 | yl += MPW_MAX; |
837 | } |
838 | yl -= dd; |
839 | } |
840 | } |
841 | |
842 | /* --- Remove a chunk from the dividend --- */ |
843 | |
844 | { |
845 | mpw *svv; |
846 | const mpw *dvv; |
f45a00c6 |
847 | mpw mc = 0, sc = 0; |
c8a2f9ef |
848 | |
f45a00c6 |
849 | /* --- Calculate the size of the chunk --- * |
850 | * |
851 | * This does the whole job of calculating @r >> scale - qd@. |
852 | */ |
c8a2f9ef |
853 | |
f45a00c6 |
854 | for (svv = rv + scale, dvv = dv; |
855 | dvv < dvl && svv < rvl; |
856 | svv++, dvv++) { |
857 | mpd x = (mpd)*dvv * (mpd)q + mc; |
858 | mc = x >> MPW_BITS; |
859 | x = (mpd)*svv - MPW(x) - sc; |
c8a2f9ef |
860 | *svv = MPW(x); |
f45a00c6 |
861 | if (x >> MPW_BITS) |
862 | sc = 1; |
863 | else |
864 | sc = 0; |
865 | } |
866 | |
867 | if (svv < rvl) { |
868 | mpd x = (mpd)*svv - mc - sc; |
869 | *svv++ = MPW(x); |
870 | if (x >> MPW_BITS) |
871 | sc = MPW_MAX; |
872 | else |
873 | sc = 0; |
874 | while (svv < rvl) |
875 | *svv++ = sc; |
c8a2f9ef |
876 | } |
c8a2f9ef |
877 | |
f45a00c6 |
878 | /* --- Fix if the quotient was too large --- * |
c8a2f9ef |
879 | * |
f45a00c6 |
880 | * This doesn't seem to happen very often. |
c8a2f9ef |
881 | */ |
882 | |
c8a2f9ef |
883 | if (rvl[-1] > MPW_MAX / 2) { |
884 | mpx_uadd(rv + scale, rvl, rv + scale, rvl, dv, dvl); |
885 | q--; |
886 | } |
887 | } |
888 | |
889 | /* --- Done for another iteration --- */ |
890 | |
891 | if (qvl - qv > scale) |
892 | qv[scale] = q; |
893 | r = rr; |
894 | rr = rrr; |
895 | } |
896 | } |
897 | |
898 | /* --- Now fiddle with unnormalizing and things --- */ |
899 | |
900 | mpx_lsr(rv, rvl, rv, rvl, norm); |
d03ab969 |
901 | } |
902 | |
42684bdb |
903 | /*----- Test rig ----------------------------------------------------------*/ |
904 | |
905 | #ifdef TEST_RIG |
906 | |
907 | #include <mLib/alloc.h> |
908 | #include <mLib/dstr.h> |
909 | #include <mLib/quis.h> |
910 | #include <mLib/testrig.h> |
911 | |
912 | #include "mpscan.h" |
913 | |
914 | #define ALLOC(v, vl, sz) do { \ |
915 | size_t _sz = (sz); \ |
916 | mpw *_vv = xmalloc(MPWS(_sz)); \ |
917 | mpw *_vvl = _vv + _sz; \ |
918 | (v) = _vv; \ |
919 | (vl) = _vvl; \ |
920 | } while (0) |
921 | |
922 | #define LOAD(v, vl, d) do { \ |
923 | const dstr *_d = (d); \ |
924 | mpw *_v, *_vl; \ |
925 | ALLOC(_v, _vl, MPW_RQ(_d->len)); \ |
926 | mpx_loadb(_v, _vl, _d->buf, _d->len); \ |
927 | (v) = _v; \ |
928 | (vl) = _vl; \ |
929 | } while (0) |
930 | |
931 | #define MAX(x, y) ((x) > (y) ? (x) : (y)) |
932 | |
933 | static void dumpbits(const char *msg, const void *pp, size_t sz) |
934 | { |
935 | const octet *p = pp; |
936 | fputs(msg, stderr); |
937 | for (; sz; sz--) |
938 | fprintf(stderr, " %02x", *p++); |
939 | fputc('\n', stderr); |
940 | } |
941 | |
942 | static void dumpmp(const char *msg, const mpw *v, const mpw *vl) |
943 | { |
944 | fputs(msg, stderr); |
945 | MPX_SHRINK(v, vl); |
946 | while (v < vl) |
947 | fprintf(stderr, " %08lx", (unsigned long)*--vl); |
948 | fputc('\n', stderr); |
949 | } |
950 | |
951 | static int chkscan(const mpw *v, const mpw *vl, |
952 | const void *pp, size_t sz, int step) |
953 | { |
954 | mpscan mps; |
955 | const octet *p = pp; |
956 | unsigned bit = 0; |
957 | int ok = 1; |
958 | |
959 | mpscan_initx(&mps, v, vl); |
960 | while (sz) { |
961 | unsigned x = *p; |
962 | int i; |
963 | p += step; |
964 | for (i = 0; i < 8 && MPSCAN_STEP(&mps); i++) { |
965 | if (MPSCAN_BIT(&mps) != (x & 1)) { |
966 | fprintf(stderr, |
967 | "\n*** error, step %i, bit %u, expected %u, found %u\n", |
968 | step, bit, x & 1, MPSCAN_BIT(&mps)); |
969 | ok = 0; |
970 | } |
971 | x >>= 1; |
972 | bit++; |
973 | } |
974 | sz--; |
975 | } |
976 | |
977 | return (ok); |
978 | } |
979 | |
980 | static int loadstore(dstr *v) |
981 | { |
982 | dstr d = DSTR_INIT; |
983 | size_t sz = MPW_RQ(v->len) * 2, diff; |
984 | mpw *m, *ml; |
985 | int ok = 1; |
986 | |
987 | dstr_ensure(&d, v->len); |
988 | m = xmalloc(MPWS(sz)); |
989 | |
990 | for (diff = 0; diff < sz; diff += 5) { |
991 | size_t oct; |
992 | |
993 | ml = m + sz - diff; |
994 | |
995 | mpx_loadl(m, ml, v->buf, v->len); |
996 | if (!chkscan(m, ml, v->buf, v->len, +1)) |
997 | ok = 0; |
998 | MPX_OCTETS(oct, m, ml); |
999 | mpx_storel(m, ml, d.buf, d.sz); |
1000 | if (memcmp(d.buf, v->buf, oct) != 0) { |
1001 | dumpbits("\n*** storel failed", d.buf, d.sz); |
1002 | ok = 0; |
1003 | } |
1004 | |
1005 | mpx_loadb(m, ml, v->buf, v->len); |
1006 | if (!chkscan(m, ml, v->buf + v->len - 1, v->len, -1)) |
1007 | ok = 0; |
1008 | MPX_OCTETS(oct, m, ml); |
1009 | mpx_storeb(m, ml, d.buf, d.sz); |
1010 | if (memcmp(d.buf + d.sz - oct, v->buf + v->len - oct, oct) != 0) { |
1011 | dumpbits("\n*** storeb failed", d.buf, d.sz); |
1012 | ok = 0; |
1013 | } |
1014 | } |
1015 | |
1016 | if (!ok) |
1017 | dumpbits("input data", v->buf, v->len); |
1018 | |
1019 | free(m); |
1020 | dstr_destroy(&d); |
1021 | return (ok); |
1022 | } |
1023 | |
1024 | static int lsl(dstr *v) |
1025 | { |
1026 | mpw *a, *al; |
1027 | int n = *(int *)v[1].buf; |
1028 | mpw *c, *cl; |
1029 | mpw *d, *dl; |
1030 | int ok = 1; |
1031 | |
1032 | LOAD(a, al, &v[0]); |
1033 | LOAD(c, cl, &v[2]); |
1034 | ALLOC(d, dl, al - a + (n + MPW_BITS - 1) / MPW_BITS); |
1035 | |
1036 | mpx_lsl(d, dl, a, al, n); |
1037 | if (MPX_UCMP(d, dl, !=, c, cl)) { |
1038 | fprintf(stderr, "\n*** lsl(%i) failed\n", n); |
1039 | dumpmp(" a", a, al); |
1040 | dumpmp("expected", c, cl); |
1041 | dumpmp(" result", d, dl); |
1042 | ok = 0; |
1043 | } |
1044 | |
1045 | free(a); free(c); free(d); |
1046 | return (ok); |
1047 | } |
1048 | |
1049 | static int lsr(dstr *v) |
1050 | { |
1051 | mpw *a, *al; |
1052 | int n = *(int *)v[1].buf; |
1053 | mpw *c, *cl; |
1054 | mpw *d, *dl; |
1055 | int ok = 1; |
1056 | |
1057 | LOAD(a, al, &v[0]); |
1058 | LOAD(c, cl, &v[2]); |
1059 | ALLOC(d, dl, al - a + (n + MPW_BITS - 1) / MPW_BITS + 1); |
1060 | |
1061 | mpx_lsr(d, dl, a, al, n); |
1062 | if (MPX_UCMP(d, dl, !=, c, cl)) { |
1063 | fprintf(stderr, "\n*** lsr(%i) failed\n", n); |
1064 | dumpmp(" a", a, al); |
1065 | dumpmp("expected", c, cl); |
1066 | dumpmp(" result", d, dl); |
1067 | ok = 0; |
1068 | } |
1069 | |
1070 | free(a); free(c); free(d); |
1071 | return (ok); |
1072 | } |
1073 | |
1074 | static int uadd(dstr *v) |
1075 | { |
1076 | mpw *a, *al; |
1077 | mpw *b, *bl; |
1078 | mpw *c, *cl; |
1079 | mpw *d, *dl; |
1080 | int ok = 1; |
1081 | |
1082 | LOAD(a, al, &v[0]); |
1083 | LOAD(b, bl, &v[1]); |
1084 | LOAD(c, cl, &v[2]); |
1085 | ALLOC(d, dl, MAX(al - a, bl - b) + 1); |
1086 | |
1087 | mpx_uadd(d, dl, a, al, b, bl); |
1088 | if (MPX_UCMP(d, dl, !=, c, cl)) { |
1089 | fprintf(stderr, "\n*** uadd failed\n"); |
1090 | dumpmp(" a", a, al); |
1091 | dumpmp(" b", b, bl); |
1092 | dumpmp("expected", c, cl); |
1093 | dumpmp(" result", d, dl); |
1094 | ok = 0; |
1095 | } |
1096 | |
1097 | free(a); free(b); free(c); free(d); |
1098 | return (ok); |
1099 | } |
1100 | |
1101 | static int usub(dstr *v) |
1102 | { |
1103 | mpw *a, *al; |
1104 | mpw *b, *bl; |
1105 | mpw *c, *cl; |
1106 | mpw *d, *dl; |
1107 | int ok = 1; |
1108 | |
1109 | LOAD(a, al, &v[0]); |
1110 | LOAD(b, bl, &v[1]); |
1111 | LOAD(c, cl, &v[2]); |
1112 | ALLOC(d, dl, al - a); |
1113 | |
1114 | mpx_usub(d, dl, a, al, b, bl); |
1115 | if (MPX_UCMP(d, dl, !=, c, cl)) { |
1116 | fprintf(stderr, "\n*** usub failed\n"); |
1117 | dumpmp(" a", a, al); |
1118 | dumpmp(" b", b, bl); |
1119 | dumpmp("expected", c, cl); |
1120 | dumpmp(" result", d, dl); |
1121 | ok = 0; |
1122 | } |
1123 | |
1124 | free(a); free(b); free(c); free(d); |
1125 | return (ok); |
1126 | } |
1127 | |
1128 | static int umul(dstr *v) |
1129 | { |
1130 | mpw *a, *al; |
1131 | mpw *b, *bl; |
1132 | mpw *c, *cl; |
1133 | mpw *d, *dl; |
1134 | int ok = 1; |
1135 | |
1136 | LOAD(a, al, &v[0]); |
1137 | LOAD(b, bl, &v[1]); |
1138 | LOAD(c, cl, &v[2]); |
1139 | ALLOC(d, dl, (al - a) + (bl - b)); |
1140 | |
1141 | mpx_umul(d, dl, a, al, b, bl); |
1142 | if (MPX_UCMP(d, dl, !=, c, cl)) { |
1143 | fprintf(stderr, "\n*** umul failed\n"); |
1144 | dumpmp(" a", a, al); |
1145 | dumpmp(" b", b, bl); |
1146 | dumpmp("expected", c, cl); |
1147 | dumpmp(" result", d, dl); |
1148 | ok = 0; |
1149 | } |
1150 | |
1151 | free(a); free(b); free(c); free(d); |
1152 | return (ok); |
1153 | } |
1154 | |
1155 | static int usqr(dstr *v) |
1156 | { |
1157 | mpw *a, *al; |
1158 | mpw *c, *cl; |
1159 | mpw *d, *dl; |
1160 | int ok = 1; |
1161 | |
1162 | LOAD(a, al, &v[0]); |
1163 | LOAD(c, cl, &v[1]); |
1164 | ALLOC(d, dl, 2 * (al - a)); |
1165 | |
1166 | mpx_usqr(d, dl, a, al); |
1167 | if (MPX_UCMP(d, dl, !=, c, cl)) { |
1168 | fprintf(stderr, "\n*** usqr failed\n"); |
1169 | dumpmp(" a", a, al); |
1170 | dumpmp("expected", c, cl); |
1171 | dumpmp(" result", d, dl); |
1172 | ok = 0; |
1173 | } |
1174 | |
1175 | free(a); free(c); free(d); |
1176 | return (ok); |
1177 | } |
1178 | |
1179 | static int udiv(dstr *v) |
1180 | { |
1181 | mpw *a, *al; |
1182 | mpw *b, *bl; |
1183 | mpw *q, *ql; |
1184 | mpw *r, *rl; |
1185 | mpw *qq, *qql; |
1186 | mpw *s, *sl; |
1187 | int ok = 1; |
1188 | |
1189 | ALLOC(a, al, MPW_RQ(v[0].len) + 2); mpx_loadb(a, al, v[0].buf, v[0].len); |
1190 | LOAD(b, bl, &v[1]); |
1191 | LOAD(q, ql, &v[2]); |
1192 | LOAD(r, rl, &v[3]); |
1193 | ALLOC(qq, qql, al - a); |
1194 | ALLOC(s, sl, (bl - b) + 1); |
1195 | |
1196 | mpx_udiv(qq, qql, a, al, b, bl, s, sl); |
1197 | if (MPX_UCMP(qq, qql, !=, q, ql) || |
1198 | MPX_UCMP(a, al, !=, r, rl)) { |
1199 | fprintf(stderr, "\n*** udiv failed\n"); |
1200 | dumpmp(" divisor", b, bl); |
1201 | dumpmp("expect r", r, rl); |
1202 | dumpmp("result r", a, al); |
1203 | dumpmp("expect q", q, ql); |
1204 | dumpmp("result q", qq, qql); |
1205 | ok = 0; |
1206 | } |
1207 | |
1208 | free(a); free(b); free(r); free(q); free(s); free(qq); |
1209 | return (ok); |
1210 | } |
1211 | |
1212 | static test_chunk defs[] = { |
1213 | { "load-store", loadstore, { &type_hex, 0 } }, |
1214 | { "lsl", lsl, { &type_hex, &type_int, &type_hex, 0 } }, |
1215 | { "lsr", lsr, { &type_hex, &type_int, &type_hex, 0 } }, |
1216 | { "uadd", uadd, { &type_hex, &type_hex, &type_hex, 0 } }, |
1217 | { "usub", usub, { &type_hex, &type_hex, &type_hex, 0 } }, |
1218 | { "umul", umul, { &type_hex, &type_hex, &type_hex, 0 } }, |
1219 | { "usqr", usqr, { &type_hex, &type_hex, 0 } }, |
1220 | { "udiv", udiv, { &type_hex, &type_hex, &type_hex, &type_hex, 0 } }, |
1221 | { 0, 0, { 0 } } |
1222 | }; |
1223 | |
1224 | int main(int argc, char *argv[]) |
1225 | { |
1226 | test_run(argc, argv, defs, SRCDIR"/tests/mpx"); |
1227 | return (0); |
1228 | } |
1229 | |
1230 | |
1231 | #endif |
1232 | |
d03ab969 |
1233 | /*----- That's all, folks -------------------------------------------------*/ |