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