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