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