d03ab969 |
1 | /* -*-c-*- |
2 | * |
f40868de |
3 | * $Id: mpx.c,v 1.19 2004/04/03 03:29:40 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 $ |
f40868de |
33 | * Revision 1.19 2004/04/03 03:29:40 mdw |
34 | * Fix overrun in @mpx_lsr@. |
35 | * |
34e4f738 |
36 | * Revision 1.18 2004/04/01 12:50:09 mdw |
37 | * Add cyclic group abstraction, with test code. Separate off exponentation |
38 | * functions for better static linking. Fix a buttload of bugs on the way. |
39 | * Generally ensure that negative exponents do inversion correctly. Add |
40 | * table of standard prime-field subgroups. (Binary field subgroups are |
41 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
42 | * |
f46efa79 |
43 | * Revision 1.17 2004/03/27 00:04:46 mdw |
44 | * Implement efficient reduction for pleasant-looking primes. |
45 | * |
81578196 |
46 | * Revision 1.16 2003/05/16 09:09:24 mdw |
47 | * Fix @mp_lsl2c@. Turns out to be surprisingly tricky. |
48 | * |
2bd53494 |
49 | * Revision 1.15 2002/10/20 01:12:31 mdw |
50 | * Two's complement I/O fixes. |
51 | * |
4f29a732 |
52 | * Revision 1.14 2002/10/19 18:55:08 mdw |
53 | * Fix overflows in shift primitives. |
54 | * |
75263f25 |
55 | * Revision 1.13 2002/10/19 17:56:50 mdw |
56 | * Fix bit operations. Test them (a bit) better. |
57 | * |
f09e814a |
58 | * Revision 1.12 2002/10/06 22:52:50 mdw |
59 | * Pile of changes for supporting two's complement properly. |
60 | * |
0f32e0f8 |
61 | * Revision 1.11 2001/04/03 19:36:05 mdw |
62 | * Add some simple bitwise operations so that Perl can use them. |
63 | * |
1a05a8ef |
64 | * Revision 1.10 2000/10/08 12:06:12 mdw |
65 | * Provide @mpx_ueq@ for rapidly testing equality of two integers. |
66 | * |
99b30c23 |
67 | * Revision 1.9 2000/06/26 07:52:50 mdw |
68 | * Portability fix for the bug fix. |
69 | * |
ce76ff16 |
70 | * Revision 1.8 2000/06/25 12:59:02 mdw |
71 | * (mpx_udiv): Fix bug in quotient digit estimation. |
72 | * |
698bd937 |
73 | * Revision 1.7 1999/12/22 15:49:07 mdw |
74 | * New function for division by a small integer. |
75 | * |
42684bdb |
76 | * Revision 1.6 1999/11/20 22:43:44 mdw |
77 | * Integrate testing for MPX routines. |
78 | * |
dd517851 |
79 | * Revision 1.5 1999/11/20 22:23:27 mdw |
80 | * Add function versions of some low-level macros with wider use. |
81 | * |
f45a00c6 |
82 | * Revision 1.4 1999/11/17 18:04:09 mdw |
83 | * Add two's-complement functionality. Improve mpx_udiv a little by |
84 | * performing the multiplication of the divisor by q with the subtraction |
85 | * from r. |
86 | * |
501da53c |
87 | * Revision 1.3 1999/11/13 01:57:31 mdw |
88 | * Remove stray debugging code. |
89 | * |
c8a2f9ef |
90 | * Revision 1.2 1999/11/13 01:50:59 mdw |
91 | * Multiprecision routines finished and tested. |
92 | * |
d03ab969 |
93 | * Revision 1.1 1999/09/03 08:41:12 mdw |
94 | * Initial import. |
95 | * |
96 | */ |
97 | |
98 | /*----- Header files ------------------------------------------------------*/ |
99 | |
c8a2f9ef |
100 | #include <assert.h> |
d03ab969 |
101 | #include <stdio.h> |
102 | #include <stdlib.h> |
103 | #include <string.h> |
104 | |
105 | #include <mLib/bits.h> |
106 | |
107 | #include "mptypes.h" |
108 | #include "mpx.h" |
75263f25 |
109 | #include "bitops.h" |
d03ab969 |
110 | |
111 | /*----- Loading and storing -----------------------------------------------*/ |
112 | |
113 | /* --- @mpx_storel@ --- * |
114 | * |
115 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
c8a2f9ef |
116 | * @void *pp@ = pointer to octet array |
d03ab969 |
117 | * @size_t sz@ = size of octet array |
118 | * |
119 | * Returns: --- |
120 | * |
121 | * Use: Stores an MP in an octet array, least significant octet |
122 | * first. High-end octets are silently discarded if there |
123 | * isn't enough space for them. |
124 | */ |
125 | |
c8a2f9ef |
126 | void mpx_storel(const mpw *v, const mpw *vl, void *pp, size_t sz) |
d03ab969 |
127 | { |
128 | mpw n, w = 0; |
c8a2f9ef |
129 | octet *p = pp, *q = p + sz; |
d03ab969 |
130 | unsigned bits = 0; |
131 | |
132 | while (p < q) { |
133 | if (bits < 8) { |
134 | if (v >= vl) { |
135 | *p++ = U8(w); |
136 | break; |
137 | } |
138 | n = *v++; |
139 | *p++ = U8(w | n << bits); |
140 | w = n >> (8 - bits); |
141 | bits += MPW_BITS - 8; |
142 | } else { |
143 | *p++ = U8(w); |
144 | w >>= 8; |
145 | bits -= 8; |
146 | } |
147 | } |
148 | memset(p, 0, q - p); |
149 | } |
150 | |
151 | /* --- @mpx_loadl@ --- * |
152 | * |
153 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
c8a2f9ef |
154 | * @const void *pp@ = pointer to octet array |
d03ab969 |
155 | * @size_t sz@ = size of octet array |
156 | * |
157 | * Returns: --- |
158 | * |
159 | * Use: Loads an MP in an octet array, least significant octet |
160 | * first. High-end octets are ignored if there isn't enough |
161 | * space for them. |
162 | */ |
163 | |
c8a2f9ef |
164 | void mpx_loadl(mpw *v, mpw *vl, const void *pp, size_t sz) |
d03ab969 |
165 | { |
166 | unsigned n; |
c8a2f9ef |
167 | mpw w = 0; |
168 | const octet *p = pp, *q = p + sz; |
d03ab969 |
169 | unsigned bits = 0; |
170 | |
171 | if (v >= vl) |
172 | return; |
173 | while (p < q) { |
174 | n = U8(*p++); |
175 | w |= n << bits; |
176 | bits += 8; |
177 | if (bits >= MPW_BITS) { |
178 | *v++ = MPW(w); |
179 | w = n >> (MPW_BITS - bits + 8); |
180 | bits -= MPW_BITS; |
181 | if (v >= vl) |
182 | return; |
183 | } |
184 | } |
185 | *v++ = w; |
186 | MPX_ZERO(v, vl); |
187 | } |
188 | |
189 | /* --- @mpx_storeb@ --- * |
190 | * |
191 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
c8a2f9ef |
192 | * @void *pp@ = pointer to octet array |
d03ab969 |
193 | * @size_t sz@ = size of octet array |
194 | * |
195 | * Returns: --- |
196 | * |
197 | * Use: Stores an MP in an octet array, most significant octet |
198 | * first. High-end octets are silently discarded if there |
199 | * isn't enough space for them. |
200 | */ |
201 | |
c8a2f9ef |
202 | void mpx_storeb(const mpw *v, const mpw *vl, void *pp, size_t sz) |
d03ab969 |
203 | { |
204 | mpw n, w = 0; |
c8a2f9ef |
205 | octet *p = pp, *q = p + sz; |
d03ab969 |
206 | unsigned bits = 0; |
207 | |
208 | while (q > p) { |
209 | if (bits < 8) { |
210 | if (v >= vl) { |
211 | *--q = U8(w); |
212 | break; |
213 | } |
214 | n = *v++; |
215 | *--q = U8(w | n << bits); |
216 | w = n >> (8 - bits); |
217 | bits += MPW_BITS - 8; |
218 | } else { |
219 | *--q = U8(w); |
220 | w >>= 8; |
221 | bits -= 8; |
222 | } |
223 | } |
224 | memset(p, 0, q - p); |
225 | } |
226 | |
227 | /* --- @mpx_loadb@ --- * |
228 | * |
229 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
c8a2f9ef |
230 | * @const void *pp@ = pointer to octet array |
d03ab969 |
231 | * @size_t sz@ = size of octet array |
232 | * |
233 | * Returns: --- |
234 | * |
235 | * Use: Loads an MP in an octet array, most significant octet |
236 | * first. High-end octets are ignored if there isn't enough |
237 | * space for them. |
238 | */ |
239 | |
c8a2f9ef |
240 | void mpx_loadb(mpw *v, mpw *vl, const void *pp, size_t sz) |
d03ab969 |
241 | { |
242 | unsigned n; |
c8a2f9ef |
243 | mpw w = 0; |
244 | const octet *p = pp, *q = p + sz; |
d03ab969 |
245 | unsigned bits = 0; |
246 | |
247 | if (v >= vl) |
248 | return; |
249 | while (q > p) { |
250 | n = U8(*--q); |
251 | w |= n << bits; |
252 | bits += 8; |
253 | if (bits >= MPW_BITS) { |
254 | *v++ = MPW(w); |
255 | w = n >> (MPW_BITS - bits + 8); |
256 | bits -= MPW_BITS; |
257 | if (v >= vl) |
258 | return; |
259 | } |
260 | } |
261 | *v++ = w; |
262 | MPX_ZERO(v, vl); |
263 | } |
264 | |
f09e814a |
265 | /* --- @mpx_storel2cn@ --- * |
266 | * |
267 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
268 | * @void *pp@ = pointer to octet array |
269 | * @size_t sz@ = size of octet array |
270 | * |
271 | * Returns: --- |
272 | * |
273 | * Use: Stores a negative MP in an octet array, least significant |
274 | * octet first, as two's complement. High-end octets are |
275 | * silently discarded if there isn't enough space for them. |
276 | * This obviously makes the output bad. |
277 | */ |
278 | |
279 | void mpx_storel2cn(const mpw *v, const mpw *vl, void *pp, size_t sz) |
280 | { |
281 | unsigned c = 1; |
282 | unsigned b = 0; |
283 | mpw n, w = 0; |
284 | octet *p = pp, *q = p + sz; |
285 | unsigned bits = 0; |
286 | |
287 | while (p < q) { |
288 | if (bits < 8) { |
289 | if (v >= vl) { |
290 | b = w; |
291 | break; |
292 | } |
293 | n = *v++; |
294 | b = w | n << bits; |
295 | w = n >> (8 - bits); |
296 | bits += MPW_BITS - 8; |
297 | } else { |
298 | b = w; |
299 | w >>= 8; |
300 | bits -= 8; |
301 | } |
302 | b = U8(~b + c); |
2bd53494 |
303 | c = c && !b; |
f09e814a |
304 | *p++ = b; |
305 | } |
306 | while (p < q) { |
307 | b = U8(~b + c); |
2bd53494 |
308 | c = c && !b; |
f09e814a |
309 | *p++ = b; |
310 | b = 0; |
311 | } |
312 | } |
313 | |
314 | /* --- @mpx_loadl2cn@ --- * |
315 | * |
316 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
317 | * @const void *pp@ = pointer to octet array |
318 | * @size_t sz@ = size of octet array |
319 | * |
320 | * Returns: --- |
321 | * |
322 | * Use: Loads a negative MP in an octet array, least significant |
323 | * octet first, as two's complement. High-end octets are |
324 | * ignored if there isn't enough space for them. This probably |
325 | * means you made the wrong choice coming here. |
326 | */ |
327 | |
328 | void mpx_loadl2cn(mpw *v, mpw *vl, const void *pp, size_t sz) |
329 | { |
330 | unsigned n; |
331 | unsigned c = 1; |
332 | mpw w = 0; |
333 | const octet *p = pp, *q = p + sz; |
334 | unsigned bits = 0; |
335 | |
336 | if (v >= vl) |
337 | return; |
338 | while (p < q) { |
339 | n = U8(~(*p++) + c); |
2bd53494 |
340 | c = c && !n; |
f09e814a |
341 | w |= n << bits; |
342 | bits += 8; |
343 | if (bits >= MPW_BITS) { |
344 | *v++ = MPW(w); |
345 | w = n >> (MPW_BITS - bits + 8); |
346 | bits -= MPW_BITS; |
347 | if (v >= vl) |
348 | return; |
349 | } |
350 | } |
351 | *v++ = w; |
352 | MPX_ZERO(v, vl); |
353 | } |
354 | |
355 | /* --- @mpx_storeb2cn@ --- * |
356 | * |
357 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
358 | * @void *pp@ = pointer to octet array |
359 | * @size_t sz@ = size of octet array |
360 | * |
361 | * Returns: --- |
362 | * |
363 | * Use: Stores a negative MP in an octet array, most significant |
364 | * octet first, as two's complement. High-end octets are |
365 | * silently discarded if there isn't enough space for them, |
366 | * which probably isn't what you meant. |
367 | */ |
368 | |
369 | void mpx_storeb2cn(const mpw *v, const mpw *vl, void *pp, size_t sz) |
370 | { |
371 | mpw n, w = 0; |
372 | unsigned b = 0; |
373 | unsigned c = 1; |
374 | octet *p = pp, *q = p + sz; |
375 | unsigned bits = 0; |
376 | |
377 | while (q > p) { |
378 | if (bits < 8) { |
379 | if (v >= vl) { |
380 | b = w; |
381 | break; |
382 | } |
383 | n = *v++; |
384 | b = w | n << bits; |
385 | w = n >> (8 - bits); |
386 | bits += MPW_BITS - 8; |
387 | } else { |
388 | b = w; |
389 | w >>= 8; |
390 | bits -= 8; |
391 | } |
392 | b = U8(~b + c); |
2bd53494 |
393 | c = c && !b; |
f09e814a |
394 | *--q = b; |
395 | } |
396 | while (q > p) { |
397 | b = ~b + c; |
2bd53494 |
398 | c = c && !(b & 0xff); |
f09e814a |
399 | *--q = b; |
400 | b = 0; |
401 | } |
402 | } |
403 | |
404 | /* --- @mpx_loadb2cn@ --- * |
405 | * |
406 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
407 | * @const void *pp@ = pointer to octet array |
408 | * @size_t sz@ = size of octet array |
409 | * |
410 | * Returns: --- |
411 | * |
412 | * Use: Loads a negative MP in an octet array, most significant octet |
413 | * first as two's complement. High-end octets are ignored if |
414 | * there isn't enough space for them. This probably means you |
415 | * chose this function wrongly. |
416 | */ |
417 | |
418 | void mpx_loadb2cn(mpw *v, mpw *vl, const void *pp, size_t sz) |
419 | { |
420 | unsigned n; |
421 | unsigned c = 1; |
422 | mpw w = 0; |
423 | const octet *p = pp, *q = p + sz; |
424 | unsigned bits = 0; |
425 | |
426 | if (v >= vl) |
427 | return; |
428 | while (q > p) { |
429 | n = U8(~(*--q) + c); |
2bd53494 |
430 | c = c && !n; |
f09e814a |
431 | w |= n << bits; |
432 | bits += 8; |
433 | if (bits >= MPW_BITS) { |
434 | *v++ = MPW(w); |
435 | w = n >> (MPW_BITS - bits + 8); |
436 | bits -= MPW_BITS; |
437 | if (v >= vl) |
438 | return; |
439 | } |
440 | } |
441 | *v++ = w; |
442 | MPX_ZERO(v, vl); |
443 | } |
444 | |
d03ab969 |
445 | /*----- Logical shifting --------------------------------------------------*/ |
446 | |
447 | /* --- @mpx_lsl@ --- * |
448 | * |
449 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
450 | * @const mpw *av, *avl@ = source vector base and limit |
451 | * @size_t n@ = number of bit positions to shift by |
452 | * |
453 | * Returns: --- |
454 | * |
455 | * Use: Performs a logical shift left operation on an integer. |
456 | */ |
457 | |
458 | void mpx_lsl(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
459 | { |
460 | size_t nw; |
461 | unsigned nb; |
462 | |
463 | /* --- Trivial special case --- */ |
464 | |
465 | if (n == 0) |
466 | MPX_COPY(dv, dvl, av, avl); |
467 | |
468 | /* --- Single bit shifting --- */ |
469 | |
470 | else if (n == 1) { |
471 | mpw w = 0; |
472 | while (av < avl) { |
473 | mpw t; |
474 | if (dv >= dvl) |
475 | goto done; |
476 | t = *av++; |
477 | *dv++ = MPW((t << 1) | w); |
478 | w = t >> (MPW_BITS - 1); |
479 | } |
480 | if (dv >= dvl) |
481 | goto done; |
482 | *dv++ = MPW(w); |
483 | MPX_ZERO(dv, dvl); |
c8a2f9ef |
484 | goto done; |
d03ab969 |
485 | } |
486 | |
487 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
488 | |
489 | nw = n / MPW_BITS; |
490 | nb = n % MPW_BITS; |
491 | |
492 | /* --- Handle a shift by a multiple of the word size --- */ |
493 | |
494 | if (nb == 0) { |
4f29a732 |
495 | if (nw >= dvl - dv) |
496 | MPX_ZERO(dv, dvl); |
497 | else { |
498 | MPX_COPY(dv + nw, dvl, av, avl); |
499 | memset(dv, 0, MPWS(nw)); |
500 | } |
d03ab969 |
501 | } |
502 | |
c8a2f9ef |
503 | /* --- And finally the difficult case --- * |
504 | * |
505 | * This is a little convoluted, because I have to start from the end and |
506 | * work backwards to avoid overwriting the source, if they're both the same |
507 | * block of memory. |
508 | */ |
d03ab969 |
509 | |
510 | else { |
511 | mpw w; |
512 | size_t nr = MPW_BITS - nb; |
c8a2f9ef |
513 | size_t dvn = dvl - dv; |
514 | size_t avn = avl - av; |
d03ab969 |
515 | |
c8a2f9ef |
516 | if (dvn <= nw) { |
d03ab969 |
517 | MPX_ZERO(dv, dvl); |
518 | goto done; |
519 | } |
d03ab969 |
520 | |
c8a2f9ef |
521 | if (dvn > avn + nw) { |
522 | size_t off = avn + nw + 1; |
523 | MPX_ZERO(dv + off, dvl); |
524 | dvl = dv + off; |
525 | w = 0; |
526 | } else { |
527 | avl = av + dvn - nw; |
528 | w = *--avl << nb; |
d03ab969 |
529 | } |
530 | |
c8a2f9ef |
531 | while (avl > av) { |
532 | mpw t = *--avl; |
533 | *--dvl = (t >> nr) | w; |
534 | w = t << nb; |
d03ab969 |
535 | } |
c8a2f9ef |
536 | |
537 | *--dvl = w; |
538 | MPX_ZERO(dv, dvl); |
d03ab969 |
539 | } |
540 | |
541 | done:; |
542 | } |
543 | |
81578196 |
544 | /* --- @mpx_lslc@ --- * |
545 | * |
546 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
547 | * @const mpw *av, *avl@ = source vector base and limit |
548 | * @size_t n@ = number of bit positions to shift by |
549 | * |
550 | * Returns: --- |
551 | * |
552 | * Use: Performs a logical shift left operation on an integer, only |
553 | * it fills in the bits with ones instead of zeroes. |
554 | */ |
555 | |
556 | void mpx_lslc(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
557 | { |
558 | size_t nw; |
559 | unsigned nb; |
560 | |
561 | /* --- Trivial special case --- */ |
562 | |
563 | if (n == 0) |
564 | MPX_COPY(dv, dvl, av, avl); |
565 | |
566 | /* --- Single bit shifting --- */ |
567 | |
568 | else if (n == 1) { |
569 | mpw w = 1; |
570 | while (av < avl) { |
571 | mpw t; |
572 | if (dv >= dvl) |
573 | goto done; |
574 | t = *av++; |
575 | *dv++ = MPW((t << 1) | w); |
576 | w = t >> (MPW_BITS - 1); |
577 | } |
578 | if (dv >= dvl) |
579 | goto done; |
580 | *dv++ = MPW(w); |
581 | MPX_ZERO(dv, dvl); |
582 | goto done; |
583 | } |
584 | |
585 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
586 | |
587 | nw = n / MPW_BITS; |
588 | nb = n % MPW_BITS; |
589 | |
590 | /* --- Handle a shift by a multiple of the word size --- */ |
591 | |
592 | if (nb == 0) { |
593 | if (nw >= dvl - dv) |
594 | MPX_ONE(dv, dvl); |
595 | else { |
596 | MPX_COPY(dv + nw, dvl, av, avl); |
597 | MPX_ONE(dv, dv + nw); |
598 | } |
599 | } |
600 | |
601 | /* --- And finally the difficult case --- * |
602 | * |
603 | * This is a little convoluted, because I have to start from the end and |
604 | * work backwards to avoid overwriting the source, if they're both the same |
605 | * block of memory. |
606 | */ |
607 | |
608 | else { |
609 | mpw w; |
610 | size_t nr = MPW_BITS - nb; |
611 | size_t dvn = dvl - dv; |
612 | size_t avn = avl - av; |
613 | |
614 | if (dvn <= nw) { |
615 | MPX_ONE(dv, dvl); |
616 | goto done; |
617 | } |
618 | |
619 | if (dvn > avn + nw) { |
620 | size_t off = avn + nw + 1; |
621 | MPX_ZERO(dv + off, dvl); |
622 | dvl = dv + off; |
623 | w = 0; |
624 | } else { |
625 | avl = av + dvn - nw; |
626 | w = *--avl << nb; |
627 | } |
628 | |
629 | while (avl > av) { |
630 | mpw t = *--avl; |
631 | *--dvl = (t >> nr) | w; |
632 | w = t << nb; |
633 | } |
634 | |
635 | *--dvl = (MPW_MAX >> nr) | w; |
636 | MPX_ONE(dv, dvl); |
637 | } |
638 | |
639 | done:; |
640 | } |
641 | |
d03ab969 |
642 | /* --- @mpx_lsr@ --- * |
643 | * |
644 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
645 | * @const mpw *av, *avl@ = source vector base and limit |
646 | * @size_t n@ = number of bit positions to shift by |
647 | * |
648 | * Returns: --- |
649 | * |
650 | * Use: Performs a logical shift right operation on an integer. |
651 | */ |
652 | |
653 | void mpx_lsr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
654 | { |
655 | size_t nw; |
656 | unsigned nb; |
657 | |
658 | /* --- Trivial special case --- */ |
659 | |
660 | if (n == 0) |
661 | MPX_COPY(dv, dvl, av, avl); |
662 | |
663 | /* --- Single bit shifting --- */ |
664 | |
665 | else if (n == 1) { |
f40868de |
666 | mpw w = av < avl ? *av++ >> 1 : 0; |
d03ab969 |
667 | while (av < avl) { |
668 | mpw t; |
669 | if (dv >= dvl) |
670 | goto done; |
671 | t = *av++; |
672 | *dv++ = MPW((t << (MPW_BITS - 1)) | w); |
673 | w = t >> 1; |
674 | } |
675 | if (dv >= dvl) |
676 | goto done; |
677 | *dv++ = MPW(w); |
678 | MPX_ZERO(dv, dvl); |
c8a2f9ef |
679 | goto done; |
d03ab969 |
680 | } |
681 | |
682 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
683 | |
684 | nw = n / MPW_BITS; |
685 | nb = n % MPW_BITS; |
686 | |
687 | /* --- Handle a shift by a multiple of the word size --- */ |
688 | |
4f29a732 |
689 | if (nb == 0) { |
690 | if (nw >= avl - av) |
691 | MPX_ZERO(dv, dvl); |
692 | else |
693 | MPX_COPY(dv, dvl, av + nw, avl); |
694 | } |
d03ab969 |
695 | |
696 | /* --- And finally the difficult case --- */ |
697 | |
698 | else { |
699 | mpw w; |
700 | size_t nr = MPW_BITS - nb; |
701 | |
702 | av += nw; |
4f29a732 |
703 | w = av < avl ? *av++ : 0; |
d03ab969 |
704 | while (av < avl) { |
705 | mpw t; |
706 | if (dv >= dvl) |
707 | goto done; |
708 | t = *av++; |
709 | *dv++ = MPW((w >> nb) | (t << nr)); |
710 | w = t; |
711 | } |
712 | if (dv < dvl) { |
713 | *dv++ = MPW(w >> nb); |
714 | MPX_ZERO(dv, dvl); |
715 | } |
716 | } |
717 | |
718 | done:; |
719 | } |
720 | |
0f32e0f8 |
721 | /*----- Bitwise operations ------------------------------------------------*/ |
722 | |
f09e814a |
723 | /* --- @mpx_bitop@ --- * |
0f32e0f8 |
724 | * |
725 | * Arguments: @mpw *dv, *dvl@ = destination vector |
726 | * @const mpw *av, *avl@ = first source vector |
727 | * @const mpw *bv, *bvl@ = second source vector |
728 | * |
729 | * Returns: --- |
730 | * |
f09e814a |
731 | * Use; Provides the dyadic boolean functions. |
0f32e0f8 |
732 | */ |
733 | |
f09e814a |
734 | #define MPX_BITBINOP(string) \ |
0f32e0f8 |
735 | \ |
f09e814a |
736 | void mpx_bit##string(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, \ |
737 | const mpw *bv, const mpw *bvl) \ |
0f32e0f8 |
738 | { \ |
739 | MPX_SHRINK(av, avl); \ |
740 | MPX_SHRINK(bv, bvl); \ |
741 | \ |
742 | while (dv < dvl) { \ |
743 | mpw a, b; \ |
744 | a = (av < avl) ? *av++ : 0; \ |
745 | b = (bv < bvl) ? *bv++ : 0; \ |
75263f25 |
746 | *dv++ = B##string(a, b); \ |
0f32e0f8 |
747 | } \ |
748 | } |
749 | |
f09e814a |
750 | MPX_DOBIN(MPX_BITBINOP) |
0f32e0f8 |
751 | |
752 | void mpx_not(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl) |
753 | { |
754 | MPX_SHRINK(av, avl); |
755 | |
756 | while (dv < dvl) { |
757 | mpw a; |
758 | a = (av < avl) ? *av++ : 0; |
759 | *dv++ = ~a; |
760 | } |
761 | } |
762 | |
d03ab969 |
763 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
764 | |
f45a00c6 |
765 | /* --- @mpx_2c@ --- * |
766 | * |
767 | * Arguments: @mpw *dv, *dvl@ = destination vector |
768 | * @const mpw *v, *vl@ = source vector |
769 | * |
770 | * Returns: --- |
771 | * |
772 | * Use: Calculates the two's complement of @v@. |
773 | */ |
774 | |
775 | void mpx_2c(mpw *dv, mpw *dvl, const mpw *v, const mpw *vl) |
776 | { |
777 | mpw c = 0; |
778 | while (dv < dvl && v < vl) |
779 | *dv++ = c = MPW(~*v++); |
780 | if (dv < dvl) { |
781 | if (c > MPW_MAX / 2) |
782 | c = MPW(~0); |
783 | while (dv < dvl) |
784 | *dv++ = c; |
785 | } |
786 | MPX_UADDN(dv, dvl, 1); |
787 | } |
788 | |
1a05a8ef |
789 | /* --- @mpx_ueq@ --- * |
790 | * |
791 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
792 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
793 | * |
794 | * Returns: Nonzero if the two vectors are equal. |
795 | * |
796 | * Use: Performs an unsigned integer test for equality. |
797 | */ |
798 | |
799 | int mpx_ueq(const mpw *av, const mpw *avl, const mpw *bv, const mpw *bvl) |
800 | { |
801 | MPX_SHRINK(av, avl); |
802 | MPX_SHRINK(bv, bvl); |
803 | if (avl - av != bvl - bv) |
804 | return (0); |
805 | while (av < avl) { |
806 | if (*av++ != *bv++) |
807 | return (0); |
808 | } |
809 | return (1); |
810 | } |
811 | |
d03ab969 |
812 | /* --- @mpx_ucmp@ --- * |
813 | * |
814 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
815 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
816 | * |
817 | * Returns: Less than, equal to, or greater than zero depending on |
818 | * whether @a@ is less than, equal to or greater than @b@, |
819 | * respectively. |
820 | * |
821 | * Use: Performs an unsigned integer comparison. |
822 | */ |
823 | |
824 | int mpx_ucmp(const mpw *av, const mpw *avl, const mpw *bv, const mpw *bvl) |
825 | { |
826 | MPX_SHRINK(av, avl); |
827 | MPX_SHRINK(bv, bvl); |
828 | |
829 | if (avl - av > bvl - bv) |
830 | return (+1); |
831 | else if (avl - av < bvl - bv) |
832 | return (-1); |
833 | else while (avl > av) { |
834 | mpw a = *--avl, b = *--bvl; |
835 | if (a > b) |
836 | return (+1); |
837 | else if (a < b) |
838 | return (-1); |
839 | } |
840 | return (0); |
841 | } |
1a05a8ef |
842 | |
d03ab969 |
843 | /* --- @mpx_uadd@ --- * |
844 | * |
845 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
846 | * @const mpw *av, *avl@ = first addend vector base and limit |
847 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
848 | * |
849 | * Returns: --- |
850 | * |
851 | * Use: Performs unsigned integer addition. If the result overflows |
852 | * the destination vector, high-order bits are discarded. This |
853 | * means that two's complement addition happens more or less for |
854 | * free, although that's more a side-effect than anything else. |
855 | * The result vector may be equal to either or both source |
856 | * vectors, but may not otherwise overlap them. |
857 | */ |
858 | |
859 | void mpx_uadd(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
860 | const mpw *bv, const mpw *bvl) |
861 | { |
862 | mpw c = 0; |
863 | |
864 | while (av < avl || bv < bvl) { |
865 | mpw a, b; |
866 | mpd x; |
867 | if (dv >= dvl) |
868 | return; |
869 | a = (av < avl) ? *av++ : 0; |
870 | b = (bv < bvl) ? *bv++ : 0; |
871 | x = (mpd)a + (mpd)b + c; |
872 | *dv++ = MPW(x); |
873 | c = x >> MPW_BITS; |
874 | } |
875 | if (dv < dvl) { |
876 | *dv++ = c; |
877 | MPX_ZERO(dv, dvl); |
878 | } |
879 | } |
880 | |
dd517851 |
881 | /* --- @mpx_uaddn@ --- * |
882 | * |
883 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
884 | * @mpw n@ = other addend |
885 | * |
886 | * Returns: --- |
887 | * |
888 | * Use: Adds a small integer to a multiprecision number. |
889 | */ |
890 | |
891 | void mpx_uaddn(mpw *dv, mpw *dvl, mpw n) { MPX_UADDN(dv, dvl, n); } |
892 | |
f46efa79 |
893 | /* --- @mpx_uaddnlsl@ --- * |
894 | * |
895 | * Arguments: @mpw *dv, *dvl@ = destination and first argument vector |
896 | * @mpw a@ = second argument |
897 | * @unsigned o@ = offset in bits |
898 | * |
899 | * Returns: --- |
900 | * |
901 | * Use: Computes %$d + 2^o a$%. If the result overflows then |
902 | * high-order bits are discarded, as usual. We must have |
903 | * @0 < o < MPW_BITS@. |
904 | */ |
905 | |
906 | void mpx_uaddnlsl(mpw *dv, mpw *dvl, mpw a, unsigned o) |
907 | { |
908 | mpd x = (mpd)a << o; |
909 | |
910 | while (x && dv < dvl) { |
911 | x += *dv; |
912 | *dv++ = MPW(x); |
913 | x >>= MPW_BITS; |
914 | } |
915 | } |
916 | |
d03ab969 |
917 | /* --- @mpx_usub@ --- * |
918 | * |
919 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
920 | * @const mpw *av, *avl@ = first argument vector base and limit |
921 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
922 | * |
923 | * Returns: --- |
924 | * |
925 | * Use: Performs unsigned integer subtraction. If the result |
926 | * overflows the destination vector, high-order bits are |
927 | * discarded. This means that two's complement subtraction |
928 | * happens more or less for free, althuogh that's more a side- |
929 | * effect than anything else. The result vector may be equal to |
930 | * either or both source vectors, but may not otherwise overlap |
931 | * them. |
932 | */ |
933 | |
934 | void mpx_usub(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
935 | const mpw *bv, const mpw *bvl) |
936 | { |
937 | mpw c = 0; |
938 | |
939 | while (av < avl || bv < bvl) { |
940 | mpw a, b; |
941 | mpd x; |
942 | if (dv >= dvl) |
943 | return; |
944 | a = (av < avl) ? *av++ : 0; |
945 | b = (bv < bvl) ? *bv++ : 0; |
c8a2f9ef |
946 | x = (mpd)a - (mpd)b - c; |
d03ab969 |
947 | *dv++ = MPW(x); |
c8a2f9ef |
948 | if (x >> MPW_BITS) |
949 | c = 1; |
950 | else |
951 | c = 0; |
d03ab969 |
952 | } |
c8a2f9ef |
953 | if (c) |
954 | c = MPW_MAX; |
d03ab969 |
955 | while (dv < dvl) |
c8a2f9ef |
956 | *dv++ = c; |
d03ab969 |
957 | } |
958 | |
dd517851 |
959 | /* --- @mpx_usubn@ --- * |
960 | * |
961 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
962 | * @n@ = subtrahend |
963 | * |
964 | * Returns: --- |
965 | * |
966 | * Use: Subtracts a small integer from a multiprecision number. |
967 | */ |
968 | |
969 | void mpx_usubn(mpw *dv, mpw *dvl, mpw n) { MPX_USUBN(dv, dvl, n); } |
970 | |
f46efa79 |
971 | /* --- @mpx_uaddnlsl@ --- * |
972 | * |
973 | * Arguments: @mpw *dv, *dvl@ = destination and first argument vector |
974 | * @mpw a@ = second argument |
975 | * @unsigned o@ = offset in bits |
976 | * |
977 | * Returns: --- |
978 | * |
979 | * Use: Computes %$d + 2^o a$%. If the result overflows then |
980 | * high-order bits are discarded, as usual. We must have |
981 | * @0 < o < MPW_BITS@. |
982 | */ |
983 | |
984 | void mpx_usubnlsl(mpw *dv, mpw *dvl, mpw a, unsigned o) |
985 | { |
986 | mpw b = a >> (MPW_BITS - o); |
987 | a <<= o; |
988 | |
989 | if (dv < dvl) { |
990 | mpd x = (mpd)*dv - (mpd)a; |
991 | *dv++ = MPW(x); |
992 | if (x >> MPW_BITS) |
993 | b++; |
994 | MPX_USUBN(dv, dvl, b); |
995 | } |
996 | } |
997 | |
d03ab969 |
998 | /* --- @mpx_umul@ --- * |
999 | * |
1000 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
1001 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
1002 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
1003 | * |
1004 | * Returns: --- |
1005 | * |
1006 | * Use: Performs unsigned integer multiplication. If the result |
1007 | * overflows the desination vector, high-order bits are |
1008 | * discarded. The result vector may not overlap the argument |
1009 | * vectors in any way. |
1010 | */ |
1011 | |
1012 | void mpx_umul(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
1013 | const mpw *bv, const mpw *bvl) |
1014 | { |
1015 | /* --- This is probably worthwhile on a multiply --- */ |
1016 | |
1017 | MPX_SHRINK(av, avl); |
1018 | MPX_SHRINK(bv, bvl); |
1019 | |
1020 | /* --- Deal with a multiply by zero --- */ |
1021 | |
1022 | if (bv == bvl) { |
c8a2f9ef |
1023 | MPX_ZERO(dv, dvl); |
d03ab969 |
1024 | return; |
1025 | } |
1026 | |
1027 | /* --- Do the initial multiply and initialize the accumulator --- */ |
1028 | |
1029 | MPX_UMULN(dv, dvl, av, avl, *bv++); |
1030 | |
1031 | /* --- Do the remaining multiply/accumulates --- */ |
1032 | |
c8a2f9ef |
1033 | while (dv < dvl && bv < bvl) { |
d03ab969 |
1034 | mpw m = *bv++; |
c8a2f9ef |
1035 | mpw c = 0; |
d03ab969 |
1036 | const mpw *avv = av; |
1037 | mpw *dvv = ++dv; |
1038 | |
1039 | while (avv < avl) { |
1040 | mpd x; |
1041 | if (dvv >= dvl) |
1042 | goto next; |
c8a2f9ef |
1043 | x = (mpd)*dvv + (mpd)m * (mpd)*avv++ + c; |
1044 | *dvv++ = MPW(x); |
d03ab969 |
1045 | c = x >> MPW_BITS; |
1046 | } |
c8a2f9ef |
1047 | MPX_UADDN(dvv, dvl, c); |
d03ab969 |
1048 | next:; |
1049 | } |
1050 | } |
1051 | |
dd517851 |
1052 | /* --- @mpx_umuln@ --- * |
1053 | * |
1054 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
1055 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
1056 | * @mpw m@ = multiplier |
1057 | * |
1058 | * Returns: --- |
1059 | * |
1060 | * Use: Multiplies a multiprecision integer by a single-word value. |
1061 | * The destination and source may be equal. The destination |
1062 | * is completely cleared after use. |
1063 | */ |
1064 | |
1065 | void mpx_umuln(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, mpw m) |
1066 | { |
1067 | MPX_UMULN(dv, dvl, av, avl, m); |
1068 | } |
1069 | |
1070 | /* --- @mpx_umlan@ --- * |
1071 | * |
1072 | * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit |
1073 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
1074 | * @mpw m@ = multiplier |
1075 | * |
1076 | * Returns: --- |
1077 | * |
1078 | * Use: Multiplies a multiprecision integer by a single-word value |
1079 | * and adds the result to an accumulator. |
1080 | */ |
1081 | |
1082 | void mpx_umlan(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, mpw m) |
1083 | { |
1084 | MPX_UMLAN(dv, dvl, av, avl, m); |
1085 | } |
1086 | |
c8a2f9ef |
1087 | /* --- @mpx_usqr@ --- * |
1088 | * |
1089 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
1090 | * @const mpw *av, *av@ = source vector base and limit |
1091 | * |
1092 | * Returns: --- |
1093 | * |
1094 | * Use: Performs unsigned integer squaring. The result vector must |
1095 | * not overlap the source vector in any way. |
1096 | */ |
1097 | |
1098 | void mpx_usqr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl) |
1099 | { |
1100 | MPX_ZERO(dv, dvl); |
1101 | |
1102 | /* --- Main loop --- */ |
1103 | |
1104 | while (av < avl) { |
1105 | const mpw *avv = av; |
1106 | mpw *dvv = dv; |
1107 | mpw a = *av; |
1108 | mpd c; |
1109 | |
1110 | /* --- Stop if I've run out of destination --- */ |
1111 | |
1112 | if (dvv >= dvl) |
1113 | break; |
1114 | |
1115 | /* --- Work out the square at this point in the proceedings --- */ |
1116 | |
1117 | { |
c8a2f9ef |
1118 | mpd x = (mpd)a * (mpd)a + *dvv; |
1119 | *dvv++ = MPW(x); |
1120 | c = MPW(x >> MPW_BITS); |
1121 | } |
1122 | |
1123 | /* --- Now fix up the rest of the vector upwards --- */ |
1124 | |
1125 | avv++; |
1126 | while (dvv < dvl && avv < avl) { |
c8a2f9ef |
1127 | mpd x = (mpd)a * (mpd)*avv++; |
1128 | mpd y = ((x << 1) & MPW_MAX) + c + *dvv; |
1129 | c = (x >> (MPW_BITS - 1)) + (y >> MPW_BITS); |
1130 | *dvv++ = MPW(y); |
1131 | } |
1132 | while (dvv < dvl && c) { |
1133 | mpd x = c + *dvv; |
1134 | *dvv++ = MPW(x); |
1135 | c = x >> MPW_BITS; |
1136 | } |
1137 | |
1138 | /* --- Get ready for the next round --- */ |
1139 | |
1140 | av++; |
1141 | dv += 2; |
1142 | } |
1143 | } |
1144 | |
d03ab969 |
1145 | /* --- @mpx_udiv@ --- * |
1146 | * |
1147 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
1148 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
1149 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
c8a2f9ef |
1150 | * @mpw *sv, *svl@ = scratch workspace |
d03ab969 |
1151 | * |
1152 | * Returns: --- |
1153 | * |
1154 | * Use: Performs unsigned integer division. If the result overflows |
1155 | * the quotient vector, high-order bits are discarded. (Clearly |
1156 | * the remainder vector can't overflow.) The various vectors |
1157 | * may not overlap in any way. Yes, I know it's a bit odd |
1158 | * requiring the dividend to be in the result position but it |
1159 | * does make some sense really. The remainder must have |
c8a2f9ef |
1160 | * headroom for at least two extra words. The scratch space |
f45a00c6 |
1161 | * must be at least one word larger than the divisor. |
d03ab969 |
1162 | */ |
1163 | |
1164 | void mpx_udiv(mpw *qv, mpw *qvl, mpw *rv, mpw *rvl, |
c8a2f9ef |
1165 | const mpw *dv, const mpw *dvl, |
1166 | mpw *sv, mpw *svl) |
d03ab969 |
1167 | { |
d03ab969 |
1168 | unsigned norm = 0; |
1169 | size_t scale; |
1170 | mpw d, dd; |
1171 | |
1172 | /* --- Initialize the quotient --- */ |
1173 | |
1174 | MPX_ZERO(qv, qvl); |
1175 | |
c8a2f9ef |
1176 | /* --- Perform some sanity checks --- */ |
1177 | |
1178 | MPX_SHRINK(dv, dvl); |
1179 | assert(((void)"division by zero in mpx_udiv", dv < dvl)); |
1180 | |
d03ab969 |
1181 | /* --- Normalize the divisor --- * |
1182 | * |
1183 | * The algorithm requires that the divisor be at least two digits long. |
1184 | * This is easy to fix. |
1185 | */ |
1186 | |
c8a2f9ef |
1187 | { |
1188 | unsigned b; |
d03ab969 |
1189 | |
c8a2f9ef |
1190 | d = dvl[-1]; |
1191 | for (b = MPW_BITS / 2; b; b >>= 1) { |
34e4f738 |
1192 | if (d <= (MPW_MAX >> b)) { |
c8a2f9ef |
1193 | d <<= b; |
1194 | norm += b; |
1195 | } |
1196 | } |
1197 | if (dv + 1 == dvl) |
1198 | norm += MPW_BITS; |
d03ab969 |
1199 | } |
d03ab969 |
1200 | |
1201 | /* --- Normalize the dividend/remainder to match --- */ |
1202 | |
c8a2f9ef |
1203 | if (norm) { |
c8a2f9ef |
1204 | mpx_lsl(rv, rvl, rv, rvl, norm); |
f45a00c6 |
1205 | mpx_lsl(sv, svl, dv, dvl, norm); |
c8a2f9ef |
1206 | dv = sv; |
f45a00c6 |
1207 | dvl = svl; |
c8a2f9ef |
1208 | MPX_SHRINK(dv, dvl); |
1209 | } |
1210 | |
d03ab969 |
1211 | MPX_SHRINK(rv, rvl); |
c8a2f9ef |
1212 | d = dvl[-1]; |
1213 | dd = dvl[-2]; |
d03ab969 |
1214 | |
1215 | /* --- Work out the relative scales --- */ |
1216 | |
1217 | { |
1218 | size_t rvn = rvl - rv; |
c8a2f9ef |
1219 | size_t dvn = dvl - dv; |
d03ab969 |
1220 | |
1221 | /* --- If the divisor is clearly larger, notice this --- */ |
1222 | |
1223 | if (dvn > rvn) { |
1224 | mpx_lsr(rv, rvl, rv, rvl, norm); |
1225 | return; |
1226 | } |
1227 | |
1228 | scale = rvn - dvn; |
1229 | } |
1230 | |
1231 | /* --- Calculate the most significant quotient digit --- * |
1232 | * |
1233 | * Because the divisor has its top bit set, this can only happen once. The |
1234 | * pointer arithmetic is a little contorted, to make sure that the |
1235 | * behaviour is defined. |
1236 | */ |
1237 | |
1238 | if (MPX_UCMP(rv + scale, rvl, >=, dv, dvl)) { |
1239 | mpx_usub(rv + scale, rvl, rv + scale, rvl, dv, dvl); |
1240 | if (qvl - qv > scale) |
1241 | qv[scale] = 1; |
1242 | } |
1243 | |
1244 | /* --- Now for the main loop --- */ |
1245 | |
1246 | { |
c8a2f9ef |
1247 | mpw *rvv = rvl - 2; |
d03ab969 |
1248 | |
1249 | while (scale) { |
c8a2f9ef |
1250 | mpw q; |
1251 | mpd rh; |
d03ab969 |
1252 | |
1253 | /* --- Get an estimate for the next quotient digit --- */ |
1254 | |
c8a2f9ef |
1255 | mpw r = rvv[1]; |
1256 | mpw rr = rvv[0]; |
1257 | mpw rrr = *--rvv; |
1258 | |
1259 | scale--; |
1260 | rh = ((mpd)r << MPW_BITS) | rr; |
d03ab969 |
1261 | if (r == d) |
1262 | q = MPW_MAX; |
c8a2f9ef |
1263 | else |
1264 | q = MPW(rh / d); |
d03ab969 |
1265 | |
1266 | /* --- Refine the estimate --- */ |
1267 | |
1268 | { |
1269 | mpd yh = (mpd)d * q; |
ce76ff16 |
1270 | mpd yy = (mpd)dd * q; |
1271 | mpw yl; |
c8a2f9ef |
1272 | |
ce76ff16 |
1273 | if (yy > MPW_MAX) |
1274 | yh += yy >> MPW_BITS; |
1275 | yl = MPW(yy); |
c8a2f9ef |
1276 | |
1277 | while (yh > rh || (yh == rh && yl > rrr)) { |
1278 | q--; |
1279 | yh -= d; |
ce76ff16 |
1280 | if (yl < dd) |
1281 | yh--; |
99b30c23 |
1282 | yl = MPW(yl - dd); |
c8a2f9ef |
1283 | } |
1284 | } |
1285 | |
1286 | /* --- Remove a chunk from the dividend --- */ |
1287 | |
1288 | { |
1289 | mpw *svv; |
1290 | const mpw *dvv; |
f45a00c6 |
1291 | mpw mc = 0, sc = 0; |
c8a2f9ef |
1292 | |
f45a00c6 |
1293 | /* --- Calculate the size of the chunk --- * |
1294 | * |
1295 | * This does the whole job of calculating @r >> scale - qd@. |
1296 | */ |
c8a2f9ef |
1297 | |
f45a00c6 |
1298 | for (svv = rv + scale, dvv = dv; |
1299 | dvv < dvl && svv < rvl; |
1300 | svv++, dvv++) { |
1301 | mpd x = (mpd)*dvv * (mpd)q + mc; |
1302 | mc = x >> MPW_BITS; |
1303 | x = (mpd)*svv - MPW(x) - sc; |
c8a2f9ef |
1304 | *svv = MPW(x); |
f45a00c6 |
1305 | if (x >> MPW_BITS) |
1306 | sc = 1; |
1307 | else |
1308 | sc = 0; |
1309 | } |
1310 | |
1311 | if (svv < rvl) { |
1312 | mpd x = (mpd)*svv - mc - sc; |
1313 | *svv++ = MPW(x); |
1314 | if (x >> MPW_BITS) |
1315 | sc = MPW_MAX; |
1316 | else |
1317 | sc = 0; |
1318 | while (svv < rvl) |
1319 | *svv++ = sc; |
c8a2f9ef |
1320 | } |
c8a2f9ef |
1321 | |
f45a00c6 |
1322 | /* --- Fix if the quotient was too large --- * |
c8a2f9ef |
1323 | * |
f45a00c6 |
1324 | * This doesn't seem to happen very often. |
c8a2f9ef |
1325 | */ |
1326 | |
c8a2f9ef |
1327 | if (rvl[-1] > MPW_MAX / 2) { |
1328 | mpx_uadd(rv + scale, rvl, rv + scale, rvl, dv, dvl); |
1329 | q--; |
1330 | } |
1331 | } |
1332 | |
1333 | /* --- Done for another iteration --- */ |
1334 | |
1335 | if (qvl - qv > scale) |
1336 | qv[scale] = q; |
1337 | r = rr; |
1338 | rr = rrr; |
1339 | } |
1340 | } |
1341 | |
1342 | /* --- Now fiddle with unnormalizing and things --- */ |
1343 | |
1344 | mpx_lsr(rv, rvl, rv, rvl, norm); |
d03ab969 |
1345 | } |
1346 | |
698bd937 |
1347 | /* --- @mpx_udivn@ --- * |
1348 | * |
1349 | * Arguments: @mpw *qv, *qvl@ = storage for the quotient (may overlap |
1350 | * dividend) |
1351 | * @const mpw *rv, *rvl@ = dividend |
1352 | * @mpw d@ = single-precision divisor |
1353 | * |
1354 | * Returns: Remainder after divison. |
1355 | * |
1356 | * Use: Performs a single-precision division operation. |
1357 | */ |
1358 | |
1359 | mpw mpx_udivn(mpw *qv, mpw *qvl, const mpw *rv, const mpw *rvl, mpw d) |
1360 | { |
1361 | size_t i; |
1362 | size_t ql = qvl - qv; |
1363 | mpd r = 0; |
1364 | |
1365 | i = rvl - rv; |
1366 | while (i > 0) { |
1367 | i--; |
1368 | r = (r << MPW_BITS) | rv[i]; |
1369 | if (i < ql) |
1370 | qv[i] = r / d; |
1371 | r %= d; |
1372 | } |
1373 | return (MPW(r)); |
1374 | } |
1375 | |
42684bdb |
1376 | /*----- Test rig ----------------------------------------------------------*/ |
1377 | |
1378 | #ifdef TEST_RIG |
1379 | |
1380 | #include <mLib/alloc.h> |
1381 | #include <mLib/dstr.h> |
1382 | #include <mLib/quis.h> |
1383 | #include <mLib/testrig.h> |
1384 | |
1385 | #include "mpscan.h" |
1386 | |
1387 | #define ALLOC(v, vl, sz) do { \ |
1388 | size_t _sz = (sz); \ |
1389 | mpw *_vv = xmalloc(MPWS(_sz)); \ |
1390 | mpw *_vvl = _vv + _sz; \ |
1391 | (v) = _vv; \ |
1392 | (vl) = _vvl; \ |
1393 | } while (0) |
1394 | |
1395 | #define LOAD(v, vl, d) do { \ |
1396 | const dstr *_d = (d); \ |
1397 | mpw *_v, *_vl; \ |
1398 | ALLOC(_v, _vl, MPW_RQ(_d->len)); \ |
1399 | mpx_loadb(_v, _vl, _d->buf, _d->len); \ |
1400 | (v) = _v; \ |
1401 | (vl) = _vl; \ |
1402 | } while (0) |
1403 | |
1404 | #define MAX(x, y) ((x) > (y) ? (x) : (y)) |
1405 | |
1406 | static void dumpbits(const char *msg, const void *pp, size_t sz) |
1407 | { |
1408 | const octet *p = pp; |
1409 | fputs(msg, stderr); |
1410 | for (; sz; sz--) |
1411 | fprintf(stderr, " %02x", *p++); |
1412 | fputc('\n', stderr); |
1413 | } |
1414 | |
1415 | static void dumpmp(const char *msg, const mpw *v, const mpw *vl) |
1416 | { |
1417 | fputs(msg, stderr); |
1418 | MPX_SHRINK(v, vl); |
1419 | while (v < vl) |
1420 | fprintf(stderr, " %08lx", (unsigned long)*--vl); |
1421 | fputc('\n', stderr); |
1422 | } |
1423 | |
1424 | static int chkscan(const mpw *v, const mpw *vl, |
1425 | const void *pp, size_t sz, int step) |
1426 | { |
1427 | mpscan mps; |
1428 | const octet *p = pp; |
1429 | unsigned bit = 0; |
1430 | int ok = 1; |
1431 | |
1432 | mpscan_initx(&mps, v, vl); |
1433 | while (sz) { |
1434 | unsigned x = *p; |
1435 | int i; |
1436 | p += step; |
1437 | for (i = 0; i < 8 && MPSCAN_STEP(&mps); i++) { |
1438 | if (MPSCAN_BIT(&mps) != (x & 1)) { |
1439 | fprintf(stderr, |
1440 | "\n*** error, step %i, bit %u, expected %u, found %u\n", |
1441 | step, bit, x & 1, MPSCAN_BIT(&mps)); |
1442 | ok = 0; |
1443 | } |
1444 | x >>= 1; |
1445 | bit++; |
1446 | } |
1447 | sz--; |
1448 | } |
1449 | |
1450 | return (ok); |
1451 | } |
1452 | |
1453 | static int loadstore(dstr *v) |
1454 | { |
1455 | dstr d = DSTR_INIT; |
1456 | size_t sz = MPW_RQ(v->len) * 2, diff; |
1457 | mpw *m, *ml; |
1458 | int ok = 1; |
1459 | |
1460 | dstr_ensure(&d, v->len); |
1461 | m = xmalloc(MPWS(sz)); |
1462 | |
1463 | for (diff = 0; diff < sz; diff += 5) { |
1464 | size_t oct; |
1465 | |
1466 | ml = m + sz - diff; |
1467 | |
1468 | mpx_loadl(m, ml, v->buf, v->len); |
1469 | if (!chkscan(m, ml, v->buf, v->len, +1)) |
1470 | ok = 0; |
1471 | MPX_OCTETS(oct, m, ml); |
1472 | mpx_storel(m, ml, d.buf, d.sz); |
1473 | if (memcmp(d.buf, v->buf, oct) != 0) { |
1474 | dumpbits("\n*** storel failed", d.buf, d.sz); |
1475 | ok = 0; |
1476 | } |
1477 | |
1478 | mpx_loadb(m, ml, v->buf, v->len); |
1479 | if (!chkscan(m, ml, v->buf + v->len - 1, v->len, -1)) |
1480 | ok = 0; |
1481 | MPX_OCTETS(oct, m, ml); |
1482 | mpx_storeb(m, ml, d.buf, d.sz); |
1483 | if (memcmp(d.buf + d.sz - oct, v->buf + v->len - oct, oct) != 0) { |
1484 | dumpbits("\n*** storeb failed", d.buf, d.sz); |
1485 | ok = 0; |
1486 | } |
1487 | } |
1488 | |
1489 | if (!ok) |
1490 | dumpbits("input data", v->buf, v->len); |
1491 | |
1492 | free(m); |
1493 | dstr_destroy(&d); |
1494 | return (ok); |
1495 | } |
1496 | |
f09e814a |
1497 | static int twocl(dstr *v) |
1498 | { |
1499 | dstr d = DSTR_INIT; |
1500 | mpw *m, *ml; |
1501 | size_t sz; |
1502 | int ok = 1; |
1503 | |
1504 | sz = v[0].len; if (v[1].len > sz) sz = v[1].len; |
1505 | dstr_ensure(&d, sz); |
1506 | |
1507 | sz = MPW_RQ(sz); |
1508 | m = xmalloc(MPWS(sz)); |
1509 | ml = m + sz; |
1510 | |
1511 | mpx_loadl(m, ml, v[0].buf, v[0].len); |
1512 | mpx_storel2cn(m, ml, d.buf, v[1].len); |
1513 | if (memcmp(d.buf, v[1].buf, v[1].len)) { |
1514 | dumpbits("\n*** storel2cn failed", d.buf, v[1].len); |
1515 | ok = 0; |
1516 | } |
1517 | |
1518 | mpx_loadl2cn(m, ml, v[1].buf, v[1].len); |
1519 | mpx_storel(m, ml, d.buf, v[0].len); |
1520 | if (memcmp(d.buf, v[0].buf, v[0].len)) { |
1521 | dumpbits("\n*** loadl2cn failed", d.buf, v[0].len); |
1522 | ok = 0; |
1523 | } |
1524 | |
1525 | if (!ok) { |
1526 | dumpbits("pos", v[0].buf, v[0].len); |
1527 | dumpbits("neg", v[1].buf, v[1].len); |
1528 | } |
1529 | |
1530 | free(m); |
1531 | dstr_destroy(&d); |
1532 | |
1533 | return (ok); |
1534 | } |
1535 | |
1536 | static int twocb(dstr *v) |
1537 | { |
1538 | dstr d = DSTR_INIT; |
1539 | mpw *m, *ml; |
1540 | size_t sz; |
1541 | int ok = 1; |
1542 | |
1543 | sz = v[0].len; if (v[1].len > sz) sz = v[1].len; |
1544 | dstr_ensure(&d, sz); |
1545 | |
1546 | sz = MPW_RQ(sz); |
1547 | m = xmalloc(MPWS(sz)); |
1548 | ml = m + sz; |
1549 | |
1550 | mpx_loadb(m, ml, v[0].buf, v[0].len); |
1551 | mpx_storeb2cn(m, ml, d.buf, v[1].len); |
1552 | if (memcmp(d.buf, v[1].buf, v[1].len)) { |
1553 | dumpbits("\n*** storeb2cn failed", d.buf, v[1].len); |
1554 | ok = 0; |
1555 | } |
1556 | |
1557 | mpx_loadb2cn(m, ml, v[1].buf, v[1].len); |
1558 | mpx_storeb(m, ml, d.buf, v[0].len); |
1559 | if (memcmp(d.buf, v[0].buf, v[0].len)) { |
1560 | dumpbits("\n*** loadb2cn failed", d.buf, v[0].len); |
1561 | ok = 0; |
1562 | } |
1563 | |
1564 | if (!ok) { |
1565 | dumpbits("pos", v[0].buf, v[0].len); |
1566 | dumpbits("neg", v[1].buf, v[1].len); |
1567 | } |
1568 | |
1569 | free(m); |
1570 | dstr_destroy(&d); |
1571 | |
1572 | return (ok); |
1573 | } |
1574 | |
42684bdb |
1575 | static int lsl(dstr *v) |
1576 | { |
1577 | mpw *a, *al; |
1578 | int n = *(int *)v[1].buf; |
1579 | mpw *c, *cl; |
1580 | mpw *d, *dl; |
1581 | int ok = 1; |
1582 | |
1583 | LOAD(a, al, &v[0]); |
1584 | LOAD(c, cl, &v[2]); |
1585 | ALLOC(d, dl, al - a + (n + MPW_BITS - 1) / MPW_BITS); |
1586 | |
1587 | mpx_lsl(d, dl, a, al, n); |
1a05a8ef |
1588 | if (!mpx_ueq(d, dl, c, cl)) { |
42684bdb |
1589 | fprintf(stderr, "\n*** lsl(%i) failed\n", n); |
1590 | dumpmp(" a", a, al); |
1591 | dumpmp("expected", c, cl); |
1592 | dumpmp(" result", d, dl); |
1593 | ok = 0; |
1594 | } |
1595 | |
1596 | free(a); free(c); free(d); |
1597 | return (ok); |
1598 | } |
1599 | |
81578196 |
1600 | static int lslc(dstr *v) |
1601 | { |
1602 | mpw *a, *al; |
1603 | int n = *(int *)v[1].buf; |
1604 | mpw *c, *cl; |
1605 | mpw *d, *dl; |
1606 | int ok = 1; |
1607 | |
1608 | LOAD(a, al, &v[0]); |
1609 | LOAD(c, cl, &v[2]); |
1610 | ALLOC(d, dl, al - a + (n + MPW_BITS - 1) / MPW_BITS); |
1611 | |
1612 | mpx_lslc(d, dl, a, al, n); |
1613 | if (!mpx_ueq(d, dl, c, cl)) { |
1614 | fprintf(stderr, "\n*** lslc(%i) failed\n", n); |
1615 | dumpmp(" a", a, al); |
1616 | dumpmp("expected", c, cl); |
1617 | dumpmp(" result", d, dl); |
1618 | ok = 0; |
1619 | } |
1620 | |
1621 | free(a); free(c); free(d); |
1622 | return (ok); |
1623 | } |
1624 | |
42684bdb |
1625 | static int lsr(dstr *v) |
1626 | { |
1627 | mpw *a, *al; |
1628 | int n = *(int *)v[1].buf; |
1629 | mpw *c, *cl; |
1630 | mpw *d, *dl; |
1631 | int ok = 1; |
1632 | |
1633 | LOAD(a, al, &v[0]); |
1634 | LOAD(c, cl, &v[2]); |
1635 | ALLOC(d, dl, al - a + (n + MPW_BITS - 1) / MPW_BITS + 1); |
1636 | |
1637 | mpx_lsr(d, dl, a, al, n); |
1a05a8ef |
1638 | if (!mpx_ueq(d, dl, c, cl)) { |
42684bdb |
1639 | fprintf(stderr, "\n*** lsr(%i) failed\n", n); |
1640 | dumpmp(" a", a, al); |
1641 | dumpmp("expected", c, cl); |
1642 | dumpmp(" result", d, dl); |
1643 | ok = 0; |
1644 | } |
1645 | |
1646 | free(a); free(c); free(d); |
1647 | return (ok); |
1648 | } |
1649 | |
1650 | static int uadd(dstr *v) |
1651 | { |
1652 | mpw *a, *al; |
1653 | mpw *b, *bl; |
1654 | mpw *c, *cl; |
1655 | mpw *d, *dl; |
1656 | int ok = 1; |
1657 | |
1658 | LOAD(a, al, &v[0]); |
1659 | LOAD(b, bl, &v[1]); |
1660 | LOAD(c, cl, &v[2]); |
1661 | ALLOC(d, dl, MAX(al - a, bl - b) + 1); |
1662 | |
1663 | mpx_uadd(d, dl, a, al, b, bl); |
1a05a8ef |
1664 | if (!mpx_ueq(d, dl, c, cl)) { |
42684bdb |
1665 | fprintf(stderr, "\n*** uadd failed\n"); |
1666 | dumpmp(" a", a, al); |
1667 | dumpmp(" b", b, bl); |
1668 | dumpmp("expected", c, cl); |
1669 | dumpmp(" result", d, dl); |
1670 | ok = 0; |
1671 | } |
1672 | |
1673 | free(a); free(b); free(c); free(d); |
1674 | return (ok); |
1675 | } |
1676 | |
1677 | static int usub(dstr *v) |
1678 | { |
1679 | mpw *a, *al; |
1680 | mpw *b, *bl; |
1681 | mpw *c, *cl; |
1682 | mpw *d, *dl; |
1683 | int ok = 1; |
1684 | |
1685 | LOAD(a, al, &v[0]); |
1686 | LOAD(b, bl, &v[1]); |
1687 | LOAD(c, cl, &v[2]); |
1688 | ALLOC(d, dl, al - a); |
1689 | |
1690 | mpx_usub(d, dl, a, al, b, bl); |
1a05a8ef |
1691 | if (!mpx_ueq(d, dl, c, cl)) { |
42684bdb |
1692 | fprintf(stderr, "\n*** usub failed\n"); |
1693 | dumpmp(" a", a, al); |
1694 | dumpmp(" b", b, bl); |
1695 | dumpmp("expected", c, cl); |
1696 | dumpmp(" result", d, dl); |
1697 | ok = 0; |
1698 | } |
1699 | |
1700 | free(a); free(b); free(c); free(d); |
1701 | return (ok); |
1702 | } |
1703 | |
1704 | static int umul(dstr *v) |
1705 | { |
1706 | mpw *a, *al; |
1707 | mpw *b, *bl; |
1708 | mpw *c, *cl; |
1709 | mpw *d, *dl; |
1710 | int ok = 1; |
1711 | |
1712 | LOAD(a, al, &v[0]); |
1713 | LOAD(b, bl, &v[1]); |
1714 | LOAD(c, cl, &v[2]); |
1715 | ALLOC(d, dl, (al - a) + (bl - b)); |
1716 | |
1717 | mpx_umul(d, dl, a, al, b, bl); |
1a05a8ef |
1718 | if (!mpx_ueq(d, dl, c, cl)) { |
42684bdb |
1719 | fprintf(stderr, "\n*** umul failed\n"); |
1720 | dumpmp(" a", a, al); |
1721 | dumpmp(" b", b, bl); |
1722 | dumpmp("expected", c, cl); |
1723 | dumpmp(" result", d, dl); |
1724 | ok = 0; |
1725 | } |
1726 | |
1727 | free(a); free(b); free(c); free(d); |
1728 | return (ok); |
1729 | } |
1730 | |
1731 | static int usqr(dstr *v) |
1732 | { |
1733 | mpw *a, *al; |
1734 | mpw *c, *cl; |
1735 | mpw *d, *dl; |
1736 | int ok = 1; |
1737 | |
1738 | LOAD(a, al, &v[0]); |
1739 | LOAD(c, cl, &v[1]); |
1740 | ALLOC(d, dl, 2 * (al - a)); |
1741 | |
1742 | mpx_usqr(d, dl, a, al); |
1a05a8ef |
1743 | if (!mpx_ueq(d, dl, c, cl)) { |
42684bdb |
1744 | fprintf(stderr, "\n*** usqr failed\n"); |
1745 | dumpmp(" a", a, al); |
1746 | dumpmp("expected", c, cl); |
1747 | dumpmp(" result", d, dl); |
1748 | ok = 0; |
1749 | } |
1750 | |
1751 | free(a); free(c); free(d); |
1752 | return (ok); |
1753 | } |
1754 | |
1755 | static int udiv(dstr *v) |
1756 | { |
1757 | mpw *a, *al; |
1758 | mpw *b, *bl; |
1759 | mpw *q, *ql; |
1760 | mpw *r, *rl; |
1761 | mpw *qq, *qql; |
1762 | mpw *s, *sl; |
1763 | int ok = 1; |
1764 | |
1765 | ALLOC(a, al, MPW_RQ(v[0].len) + 2); mpx_loadb(a, al, v[0].buf, v[0].len); |
1766 | LOAD(b, bl, &v[1]); |
1767 | LOAD(q, ql, &v[2]); |
1768 | LOAD(r, rl, &v[3]); |
1769 | ALLOC(qq, qql, al - a); |
1770 | ALLOC(s, sl, (bl - b) + 1); |
1771 | |
1772 | mpx_udiv(qq, qql, a, al, b, bl, s, sl); |
1a05a8ef |
1773 | if (!mpx_ueq(qq, qql, q, ql) || |
1774 | !mpx_ueq(a, al, r, rl)) { |
42684bdb |
1775 | fprintf(stderr, "\n*** udiv failed\n"); |
1776 | dumpmp(" divisor", b, bl); |
1777 | dumpmp("expect r", r, rl); |
1778 | dumpmp("result r", a, al); |
1779 | dumpmp("expect q", q, ql); |
1780 | dumpmp("result q", qq, qql); |
1781 | ok = 0; |
1782 | } |
1783 | |
1784 | free(a); free(b); free(r); free(q); free(s); free(qq); |
1785 | return (ok); |
1786 | } |
1787 | |
1788 | static test_chunk defs[] = { |
1789 | { "load-store", loadstore, { &type_hex, 0 } }, |
f09e814a |
1790 | { "2cl", twocl, { &type_hex, &type_hex, } }, |
1791 | { "2cb", twocb, { &type_hex, &type_hex, } }, |
42684bdb |
1792 | { "lsl", lsl, { &type_hex, &type_int, &type_hex, 0 } }, |
81578196 |
1793 | { "lslc", lslc, { &type_hex, &type_int, &type_hex, 0 } }, |
42684bdb |
1794 | { "lsr", lsr, { &type_hex, &type_int, &type_hex, 0 } }, |
1795 | { "uadd", uadd, { &type_hex, &type_hex, &type_hex, 0 } }, |
1796 | { "usub", usub, { &type_hex, &type_hex, &type_hex, 0 } }, |
1797 | { "umul", umul, { &type_hex, &type_hex, &type_hex, 0 } }, |
1798 | { "usqr", usqr, { &type_hex, &type_hex, 0 } }, |
1799 | { "udiv", udiv, { &type_hex, &type_hex, &type_hex, &type_hex, 0 } }, |
1800 | { 0, 0, { 0 } } |
1801 | }; |
1802 | |
1803 | int main(int argc, char *argv[]) |
1804 | { |
1805 | test_run(argc, argv, defs, SRCDIR"/tests/mpx"); |
1806 | return (0); |
1807 | } |
1808 | |
42684bdb |
1809 | #endif |
1810 | |
d03ab969 |
1811 | /*----- That's all, folks -------------------------------------------------*/ |