Commit | Line | Data |
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d03ab969 | 1 | /* -*-c-*- |
2 | * | |
d03ab969 | 3 | * Low-level multiprecision arithmetic |
4 | * | |
5 | * (c) 1999 Straylight/Edgeware | |
6 | */ | |
7 | ||
45c0fd36 | 8 | /*----- Licensing notice --------------------------------------------------* |
d03ab969 | 9 | * |
10 | * This file is part of Catacomb. | |
11 | * | |
12 | * Catacomb is free software; you can redistribute it and/or modify | |
13 | * it under the terms of the GNU Library General Public License as | |
14 | * published by the Free Software Foundation; either version 2 of the | |
15 | * License, or (at your option) any later version. | |
45c0fd36 | 16 | * |
d03ab969 | 17 | * Catacomb is distributed in the hope that it will be useful, |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
20 | * GNU Library General Public License for more details. | |
45c0fd36 | 21 | * |
d03ab969 | 22 | * You should have received a copy of the GNU Library General Public |
23 | * License along with Catacomb; if not, write to the Free | |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, | |
25 | * MA 02111-1307, USA. | |
26 | */ | |
27 | ||
d03ab969 | 28 | /*----- Header files ------------------------------------------------------*/ |
29 | ||
c8a2f9ef | 30 | #include <assert.h> |
d03ab969 | 31 | #include <stdio.h> |
32 | #include <stdlib.h> | |
33 | #include <string.h> | |
34 | ||
35 | #include <mLib/bits.h> | |
36 | ||
37 | #include "mptypes.h" | |
38 | #include "mpx.h" | |
75263f25 | 39 | #include "bitops.h" |
d03ab969 | 40 | |
41 | /*----- Loading and storing -----------------------------------------------*/ | |
42 | ||
43 | /* --- @mpx_storel@ --- * | |
44 | * | |
45 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector | |
c8a2f9ef | 46 | * @void *pp@ = pointer to octet array |
d03ab969 | 47 | * @size_t sz@ = size of octet array |
48 | * | |
49 | * Returns: --- | |
50 | * | |
51 | * Use: Stores an MP in an octet array, least significant octet | |
52 | * first. High-end octets are silently discarded if there | |
53 | * isn't enough space for them. | |
54 | */ | |
55 | ||
c8a2f9ef | 56 | void mpx_storel(const mpw *v, const mpw *vl, void *pp, size_t sz) |
d03ab969 | 57 | { |
58 | mpw n, w = 0; | |
c8a2f9ef | 59 | octet *p = pp, *q = p + sz; |
d03ab969 | 60 | unsigned bits = 0; |
61 | ||
62 | while (p < q) { | |
63 | if (bits < 8) { | |
64 | if (v >= vl) { | |
65 | *p++ = U8(w); | |
66 | break; | |
67 | } | |
68 | n = *v++; | |
69 | *p++ = U8(w | n << bits); | |
70 | w = n >> (8 - bits); | |
71 | bits += MPW_BITS - 8; | |
72 | } else { | |
73 | *p++ = U8(w); | |
74 | w >>= 8; | |
75 | bits -= 8; | |
76 | } | |
77 | } | |
78 | memset(p, 0, q - p); | |
79 | } | |
80 | ||
81 | /* --- @mpx_loadl@ --- * | |
82 | * | |
83 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector | |
c8a2f9ef | 84 | * @const void *pp@ = pointer to octet array |
d03ab969 | 85 | * @size_t sz@ = size of octet array |
86 | * | |
87 | * Returns: --- | |
88 | * | |
89 | * Use: Loads an MP in an octet array, least significant octet | |
90 | * first. High-end octets are ignored if there isn't enough | |
91 | * space for them. | |
92 | */ | |
93 | ||
c8a2f9ef | 94 | void mpx_loadl(mpw *v, mpw *vl, const void *pp, size_t sz) |
d03ab969 | 95 | { |
96 | unsigned n; | |
c8a2f9ef | 97 | mpw w = 0; |
98 | const octet *p = pp, *q = p + sz; | |
d03ab969 | 99 | unsigned bits = 0; |
100 | ||
101 | if (v >= vl) | |
102 | return; | |
103 | while (p < q) { | |
104 | n = U8(*p++); | |
105 | w |= n << bits; | |
106 | bits += 8; | |
107 | if (bits >= MPW_BITS) { | |
108 | *v++ = MPW(w); | |
109 | w = n >> (MPW_BITS - bits + 8); | |
110 | bits -= MPW_BITS; | |
111 | if (v >= vl) | |
112 | return; | |
113 | } | |
114 | } | |
115 | *v++ = w; | |
116 | MPX_ZERO(v, vl); | |
117 | } | |
118 | ||
119 | /* --- @mpx_storeb@ --- * | |
120 | * | |
121 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector | |
c8a2f9ef | 122 | * @void *pp@ = pointer to octet array |
d03ab969 | 123 | * @size_t sz@ = size of octet array |
124 | * | |
125 | * Returns: --- | |
126 | * | |
127 | * Use: Stores an MP in an octet array, most significant octet | |
128 | * first. High-end octets are silently discarded if there | |
129 | * isn't enough space for them. | |
130 | */ | |
131 | ||
c8a2f9ef | 132 | void mpx_storeb(const mpw *v, const mpw *vl, void *pp, size_t sz) |
d03ab969 | 133 | { |
134 | mpw n, w = 0; | |
c8a2f9ef | 135 | octet *p = pp, *q = p + sz; |
d03ab969 | 136 | unsigned bits = 0; |
137 | ||
138 | while (q > p) { | |
139 | if (bits < 8) { | |
140 | if (v >= vl) { | |
141 | *--q = U8(w); | |
142 | break; | |
143 | } | |
144 | n = *v++; | |
145 | *--q = U8(w | n << bits); | |
146 | w = n >> (8 - bits); | |
147 | bits += MPW_BITS - 8; | |
148 | } else { | |
149 | *--q = U8(w); | |
150 | w >>= 8; | |
151 | bits -= 8; | |
152 | } | |
153 | } | |
154 | memset(p, 0, q - p); | |
155 | } | |
156 | ||
157 | /* --- @mpx_loadb@ --- * | |
158 | * | |
159 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector | |
c8a2f9ef | 160 | * @const void *pp@ = pointer to octet array |
d03ab969 | 161 | * @size_t sz@ = size of octet array |
162 | * | |
163 | * Returns: --- | |
164 | * | |
165 | * Use: Loads an MP in an octet array, most significant octet | |
166 | * first. High-end octets are ignored if there isn't enough | |
167 | * space for them. | |
168 | */ | |
169 | ||
c8a2f9ef | 170 | void mpx_loadb(mpw *v, mpw *vl, const void *pp, size_t sz) |
d03ab969 | 171 | { |
172 | unsigned n; | |
c8a2f9ef | 173 | mpw w = 0; |
174 | const octet *p = pp, *q = p + sz; | |
d03ab969 | 175 | unsigned bits = 0; |
176 | ||
177 | if (v >= vl) | |
178 | return; | |
179 | while (q > p) { | |
180 | n = U8(*--q); | |
181 | w |= n << bits; | |
182 | bits += 8; | |
183 | if (bits >= MPW_BITS) { | |
184 | *v++ = MPW(w); | |
185 | w = n >> (MPW_BITS - bits + 8); | |
186 | bits -= MPW_BITS; | |
187 | if (v >= vl) | |
188 | return; | |
189 | } | |
190 | } | |
191 | *v++ = w; | |
192 | MPX_ZERO(v, vl); | |
193 | } | |
194 | ||
f09e814a | 195 | /* --- @mpx_storel2cn@ --- * |
196 | * | |
197 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector | |
198 | * @void *pp@ = pointer to octet array | |
199 | * @size_t sz@ = size of octet array | |
200 | * | |
201 | * Returns: --- | |
202 | * | |
203 | * Use: Stores a negative MP in an octet array, least significant | |
204 | * octet first, as two's complement. High-end octets are | |
205 | * silently discarded if there isn't enough space for them. | |
206 | * This obviously makes the output bad. | |
207 | */ | |
208 | ||
209 | void mpx_storel2cn(const mpw *v, const mpw *vl, void *pp, size_t sz) | |
210 | { | |
211 | unsigned c = 1; | |
212 | unsigned b = 0; | |
213 | mpw n, w = 0; | |
214 | octet *p = pp, *q = p + sz; | |
215 | unsigned bits = 0; | |
216 | ||
217 | while (p < q) { | |
218 | if (bits < 8) { | |
219 | if (v >= vl) { | |
220 | b = w; | |
221 | break; | |
222 | } | |
223 | n = *v++; | |
224 | b = w | n << bits; | |
225 | w = n >> (8 - bits); | |
226 | bits += MPW_BITS - 8; | |
227 | } else { | |
228 | b = w; | |
229 | w >>= 8; | |
230 | bits -= 8; | |
231 | } | |
232 | b = U8(~b + c); | |
2bd53494 | 233 | c = c && !b; |
f09e814a | 234 | *p++ = b; |
235 | } | |
236 | while (p < q) { | |
237 | b = U8(~b + c); | |
2bd53494 | 238 | c = c && !b; |
f09e814a | 239 | *p++ = b; |
240 | b = 0; | |
241 | } | |
242 | } | |
243 | ||
244 | /* --- @mpx_loadl2cn@ --- * | |
245 | * | |
246 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector | |
247 | * @const void *pp@ = pointer to octet array | |
248 | * @size_t sz@ = size of octet array | |
249 | * | |
250 | * Returns: --- | |
251 | * | |
252 | * Use: Loads a negative MP in an octet array, least significant | |
253 | * octet first, as two's complement. High-end octets are | |
254 | * ignored if there isn't enough space for them. This probably | |
255 | * means you made the wrong choice coming here. | |
256 | */ | |
257 | ||
258 | void mpx_loadl2cn(mpw *v, mpw *vl, const void *pp, size_t sz) | |
259 | { | |
260 | unsigned n; | |
261 | unsigned c = 1; | |
262 | mpw w = 0; | |
263 | const octet *p = pp, *q = p + sz; | |
264 | unsigned bits = 0; | |
265 | ||
266 | if (v >= vl) | |
267 | return; | |
268 | while (p < q) { | |
269 | n = U8(~(*p++) + c); | |
2bd53494 | 270 | c = c && !n; |
f09e814a | 271 | w |= n << bits; |
272 | bits += 8; | |
273 | if (bits >= MPW_BITS) { | |
274 | *v++ = MPW(w); | |
275 | w = n >> (MPW_BITS - bits + 8); | |
276 | bits -= MPW_BITS; | |
277 | if (v >= vl) | |
278 | return; | |
279 | } | |
280 | } | |
281 | *v++ = w; | |
282 | MPX_ZERO(v, vl); | |
283 | } | |
284 | ||
285 | /* --- @mpx_storeb2cn@ --- * | |
286 | * | |
287 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector | |
288 | * @void *pp@ = pointer to octet array | |
289 | * @size_t sz@ = size of octet array | |
290 | * | |
291 | * Returns: --- | |
292 | * | |
293 | * Use: Stores a negative MP in an octet array, most significant | |
294 | * octet first, as two's complement. High-end octets are | |
295 | * silently discarded if there isn't enough space for them, | |
296 | * which probably isn't what you meant. | |
297 | */ | |
298 | ||
299 | void mpx_storeb2cn(const mpw *v, const mpw *vl, void *pp, size_t sz) | |
300 | { | |
301 | mpw n, w = 0; | |
302 | unsigned b = 0; | |
303 | unsigned c = 1; | |
304 | octet *p = pp, *q = p + sz; | |
305 | unsigned bits = 0; | |
306 | ||
307 | while (q > p) { | |
308 | if (bits < 8) { | |
309 | if (v >= vl) { | |
310 | b = w; | |
311 | break; | |
312 | } | |
313 | n = *v++; | |
314 | b = w | n << bits; | |
315 | w = n >> (8 - bits); | |
316 | bits += MPW_BITS - 8; | |
317 | } else { | |
318 | b = w; | |
319 | w >>= 8; | |
320 | bits -= 8; | |
321 | } | |
322 | b = U8(~b + c); | |
2bd53494 | 323 | c = c && !b; |
f09e814a | 324 | *--q = b; |
325 | } | |
326 | while (q > p) { | |
327 | b = ~b + c; | |
2bd53494 | 328 | c = c && !(b & 0xff); |
f09e814a | 329 | *--q = b; |
330 | b = 0; | |
331 | } | |
332 | } | |
333 | ||
334 | /* --- @mpx_loadb2cn@ --- * | |
335 | * | |
336 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector | |
337 | * @const void *pp@ = pointer to octet array | |
338 | * @size_t sz@ = size of octet array | |
339 | * | |
340 | * Returns: --- | |
341 | * | |
342 | * Use: Loads a negative MP in an octet array, most significant octet | |
343 | * first as two's complement. High-end octets are ignored if | |
344 | * there isn't enough space for them. This probably means you | |
345 | * chose this function wrongly. | |
346 | */ | |
347 | ||
348 | void mpx_loadb2cn(mpw *v, mpw *vl, const void *pp, size_t sz) | |
349 | { | |
350 | unsigned n; | |
351 | unsigned c = 1; | |
352 | mpw w = 0; | |
353 | const octet *p = pp, *q = p + sz; | |
354 | unsigned bits = 0; | |
355 | ||
356 | if (v >= vl) | |
357 | return; | |
358 | while (q > p) { | |
359 | n = U8(~(*--q) + c); | |
2bd53494 | 360 | c = c && !n; |
f09e814a | 361 | w |= n << bits; |
362 | bits += 8; | |
363 | if (bits >= MPW_BITS) { | |
364 | *v++ = MPW(w); | |
365 | w = n >> (MPW_BITS - bits + 8); | |
366 | bits -= MPW_BITS; | |
367 | if (v >= vl) | |
368 | return; | |
369 | } | |
370 | } | |
371 | *v++ = w; | |
372 | MPX_ZERO(v, vl); | |
373 | } | |
374 | ||
d03ab969 | 375 | /*----- Logical shifting --------------------------------------------------*/ |
376 | ||
377 | /* --- @mpx_lsl@ --- * | |
378 | * | |
379 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
380 | * @const mpw *av, *avl@ = source vector base and limit | |
381 | * @size_t n@ = number of bit positions to shift by | |
382 | * | |
383 | * Returns: --- | |
384 | * | |
385 | * Use: Performs a logical shift left operation on an integer. | |
386 | */ | |
387 | ||
388 | void mpx_lsl(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) | |
389 | { | |
390 | size_t nw; | |
391 | unsigned nb; | |
392 | ||
393 | /* --- Trivial special case --- */ | |
394 | ||
395 | if (n == 0) | |
396 | MPX_COPY(dv, dvl, av, avl); | |
397 | ||
398 | /* --- Single bit shifting --- */ | |
399 | ||
400 | else if (n == 1) { | |
401 | mpw w = 0; | |
402 | while (av < avl) { | |
403 | mpw t; | |
404 | if (dv >= dvl) | |
405 | goto done; | |
406 | t = *av++; | |
407 | *dv++ = MPW((t << 1) | w); | |
408 | w = t >> (MPW_BITS - 1); | |
409 | } | |
410 | if (dv >= dvl) | |
411 | goto done; | |
412 | *dv++ = MPW(w); | |
413 | MPX_ZERO(dv, dvl); | |
c8a2f9ef | 414 | goto done; |
d03ab969 | 415 | } |
416 | ||
417 | /* --- Break out word and bit shifts for more sophisticated work --- */ | |
45c0fd36 | 418 | |
d03ab969 | 419 | nw = n / MPW_BITS; |
420 | nb = n % MPW_BITS; | |
421 | ||
422 | /* --- Handle a shift by a multiple of the word size --- */ | |
423 | ||
424 | if (nb == 0) { | |
4f29a732 | 425 | if (nw >= dvl - dv) |
426 | MPX_ZERO(dv, dvl); | |
427 | else { | |
428 | MPX_COPY(dv + nw, dvl, av, avl); | |
429 | memset(dv, 0, MPWS(nw)); | |
430 | } | |
d03ab969 | 431 | } |
432 | ||
c8a2f9ef | 433 | /* --- And finally the difficult case --- * |
434 | * | |
435 | * This is a little convoluted, because I have to start from the end and | |
436 | * work backwards to avoid overwriting the source, if they're both the same | |
437 | * block of memory. | |
438 | */ | |
d03ab969 | 439 | |
440 | else { | |
441 | mpw w; | |
442 | size_t nr = MPW_BITS - nb; | |
c8a2f9ef | 443 | size_t dvn = dvl - dv; |
444 | size_t avn = avl - av; | |
d03ab969 | 445 | |
c8a2f9ef | 446 | if (dvn <= nw) { |
d03ab969 | 447 | MPX_ZERO(dv, dvl); |
448 | goto done; | |
449 | } | |
d03ab969 | 450 | |
c8a2f9ef | 451 | if (dvn > avn + nw) { |
452 | size_t off = avn + nw + 1; | |
453 | MPX_ZERO(dv + off, dvl); | |
454 | dvl = dv + off; | |
455 | w = 0; | |
456 | } else { | |
457 | avl = av + dvn - nw; | |
458 | w = *--avl << nb; | |
d03ab969 | 459 | } |
460 | ||
c8a2f9ef | 461 | while (avl > av) { |
462 | mpw t = *--avl; | |
c29970a7 | 463 | *--dvl = MPW((t >> nr) | w); |
c8a2f9ef | 464 | w = t << nb; |
d03ab969 | 465 | } |
c8a2f9ef | 466 | |
c29970a7 | 467 | *--dvl = MPW(w); |
c8a2f9ef | 468 | MPX_ZERO(dv, dvl); |
d03ab969 | 469 | } |
470 | ||
471 | done:; | |
472 | } | |
473 | ||
81578196 | 474 | /* --- @mpx_lslc@ --- * |
475 | * | |
476 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
477 | * @const mpw *av, *avl@ = source vector base and limit | |
478 | * @size_t n@ = number of bit positions to shift by | |
479 | * | |
480 | * Returns: --- | |
481 | * | |
482 | * Use: Performs a logical shift left operation on an integer, only | |
483 | * it fills in the bits with ones instead of zeroes. | |
484 | */ | |
485 | ||
486 | void mpx_lslc(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) | |
487 | { | |
488 | size_t nw; | |
489 | unsigned nb; | |
490 | ||
491 | /* --- Trivial special case --- */ | |
492 | ||
493 | if (n == 0) | |
494 | MPX_COPY(dv, dvl, av, avl); | |
495 | ||
496 | /* --- Single bit shifting --- */ | |
497 | ||
498 | else if (n == 1) { | |
499 | mpw w = 1; | |
500 | while (av < avl) { | |
501 | mpw t; | |
502 | if (dv >= dvl) | |
503 | goto done; | |
504 | t = *av++; | |
505 | *dv++ = MPW((t << 1) | w); | |
506 | w = t >> (MPW_BITS - 1); | |
507 | } | |
508 | if (dv >= dvl) | |
509 | goto done; | |
510 | *dv++ = MPW(w); | |
511 | MPX_ZERO(dv, dvl); | |
512 | goto done; | |
513 | } | |
514 | ||
515 | /* --- Break out word and bit shifts for more sophisticated work --- */ | |
45c0fd36 | 516 | |
81578196 | 517 | nw = n / MPW_BITS; |
518 | nb = n % MPW_BITS; | |
519 | ||
520 | /* --- Handle a shift by a multiple of the word size --- */ | |
521 | ||
522 | if (nb == 0) { | |
523 | if (nw >= dvl - dv) | |
524 | MPX_ONE(dv, dvl); | |
525 | else { | |
526 | MPX_COPY(dv + nw, dvl, av, avl); | |
527 | MPX_ONE(dv, dv + nw); | |
528 | } | |
529 | } | |
530 | ||
531 | /* --- And finally the difficult case --- * | |
532 | * | |
533 | * This is a little convoluted, because I have to start from the end and | |
534 | * work backwards to avoid overwriting the source, if they're both the same | |
535 | * block of memory. | |
536 | */ | |
537 | ||
538 | else { | |
539 | mpw w; | |
540 | size_t nr = MPW_BITS - nb; | |
541 | size_t dvn = dvl - dv; | |
542 | size_t avn = avl - av; | |
543 | ||
544 | if (dvn <= nw) { | |
545 | MPX_ONE(dv, dvl); | |
546 | goto done; | |
547 | } | |
548 | ||
549 | if (dvn > avn + nw) { | |
550 | size_t off = avn + nw + 1; | |
551 | MPX_ZERO(dv + off, dvl); | |
552 | dvl = dv + off; | |
553 | w = 0; | |
554 | } else { | |
555 | avl = av + dvn - nw; | |
556 | w = *--avl << nb; | |
557 | } | |
558 | ||
559 | while (avl > av) { | |
560 | mpw t = *--avl; | |
c29970a7 | 561 | *--dvl = MPW((t >> nr) | w); |
81578196 | 562 | w = t << nb; |
563 | } | |
564 | ||
c29970a7 | 565 | *--dvl = MPW((MPW_MAX >> nr) | w); |
81578196 | 566 | MPX_ONE(dv, dvl); |
567 | } | |
568 | ||
569 | done:; | |
570 | } | |
571 | ||
d03ab969 | 572 | /* --- @mpx_lsr@ --- * |
573 | * | |
574 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
575 | * @const mpw *av, *avl@ = source vector base and limit | |
576 | * @size_t n@ = number of bit positions to shift by | |
577 | * | |
578 | * Returns: --- | |
579 | * | |
580 | * Use: Performs a logical shift right operation on an integer. | |
581 | */ | |
582 | ||
583 | void mpx_lsr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) | |
584 | { | |
585 | size_t nw; | |
586 | unsigned nb; | |
587 | ||
588 | /* --- Trivial special case --- */ | |
589 | ||
590 | if (n == 0) | |
591 | MPX_COPY(dv, dvl, av, avl); | |
592 | ||
593 | /* --- Single bit shifting --- */ | |
594 | ||
595 | else if (n == 1) { | |
f40868de | 596 | mpw w = av < avl ? *av++ >> 1 : 0; |
d03ab969 | 597 | while (av < avl) { |
598 | mpw t; | |
599 | if (dv >= dvl) | |
600 | goto done; | |
601 | t = *av++; | |
602 | *dv++ = MPW((t << (MPW_BITS - 1)) | w); | |
603 | w = t >> 1; | |
604 | } | |
605 | if (dv >= dvl) | |
606 | goto done; | |
607 | *dv++ = MPW(w); | |
608 | MPX_ZERO(dv, dvl); | |
c8a2f9ef | 609 | goto done; |
d03ab969 | 610 | } |
611 | ||
612 | /* --- Break out word and bit shifts for more sophisticated work --- */ | |
613 | ||
614 | nw = n / MPW_BITS; | |
615 | nb = n % MPW_BITS; | |
616 | ||
617 | /* --- Handle a shift by a multiple of the word size --- */ | |
618 | ||
4f29a732 | 619 | if (nb == 0) { |
620 | if (nw >= avl - av) | |
621 | MPX_ZERO(dv, dvl); | |
622 | else | |
623 | MPX_COPY(dv, dvl, av + nw, avl); | |
624 | } | |
d03ab969 | 625 | |
626 | /* --- And finally the difficult case --- */ | |
627 | ||
628 | else { | |
629 | mpw w; | |
630 | size_t nr = MPW_BITS - nb; | |
631 | ||
632 | av += nw; | |
4f29a732 | 633 | w = av < avl ? *av++ : 0; |
d03ab969 | 634 | while (av < avl) { |
635 | mpw t; | |
636 | if (dv >= dvl) | |
637 | goto done; | |
638 | t = *av++; | |
639 | *dv++ = MPW((w >> nb) | (t << nr)); | |
640 | w = t; | |
641 | } | |
642 | if (dv < dvl) { | |
643 | *dv++ = MPW(w >> nb); | |
644 | MPX_ZERO(dv, dvl); | |
645 | } | |
646 | } | |
647 | ||
648 | done:; | |
649 | } | |
650 | ||
0f32e0f8 | 651 | /*----- Bitwise operations ------------------------------------------------*/ |
652 | ||
f09e814a | 653 | /* --- @mpx_bitop@ --- * |
0f32e0f8 | 654 | * |
655 | * Arguments: @mpw *dv, *dvl@ = destination vector | |
656 | * @const mpw *av, *avl@ = first source vector | |
657 | * @const mpw *bv, *bvl@ = second source vector | |
658 | * | |
659 | * Returns: --- | |
660 | * | |
f09e814a | 661 | * Use; Provides the dyadic boolean functions. |
0f32e0f8 | 662 | */ |
663 | ||
f09e814a | 664 | #define MPX_BITBINOP(string) \ |
0f32e0f8 | 665 | \ |
f09e814a | 666 | void mpx_bit##string(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, \ |
667 | const mpw *bv, const mpw *bvl) \ | |
0f32e0f8 | 668 | { \ |
669 | MPX_SHRINK(av, avl); \ | |
670 | MPX_SHRINK(bv, bvl); \ | |
671 | \ | |
672 | while (dv < dvl) { \ | |
673 | mpw a, b; \ | |
674 | a = (av < avl) ? *av++ : 0; \ | |
675 | b = (bv < bvl) ? *bv++ : 0; \ | |
75263f25 | 676 | *dv++ = B##string(a, b); \ |
0f32e0f8 | 677 | } \ |
678 | } | |
679 | ||
f09e814a | 680 | MPX_DOBIN(MPX_BITBINOP) |
0f32e0f8 | 681 | |
682 | void mpx_not(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl) | |
683 | { | |
684 | MPX_SHRINK(av, avl); | |
685 | ||
686 | while (dv < dvl) { | |
687 | mpw a; | |
688 | a = (av < avl) ? *av++ : 0; | |
689 | *dv++ = ~a; | |
690 | } | |
691 | } | |
692 | ||
d03ab969 | 693 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
694 | ||
f45a00c6 | 695 | /* --- @mpx_2c@ --- * |
696 | * | |
697 | * Arguments: @mpw *dv, *dvl@ = destination vector | |
698 | * @const mpw *v, *vl@ = source vector | |
699 | * | |
700 | * Returns: --- | |
701 | * | |
702 | * Use: Calculates the two's complement of @v@. | |
703 | */ | |
704 | ||
705 | void mpx_2c(mpw *dv, mpw *dvl, const mpw *v, const mpw *vl) | |
706 | { | |
707 | mpw c = 0; | |
708 | while (dv < dvl && v < vl) | |
709 | *dv++ = c = MPW(~*v++); | |
710 | if (dv < dvl) { | |
711 | if (c > MPW_MAX / 2) | |
712 | c = MPW(~0); | |
713 | while (dv < dvl) | |
714 | *dv++ = c; | |
715 | } | |
716 | MPX_UADDN(dv, dvl, 1); | |
717 | } | |
718 | ||
1a05a8ef | 719 | /* --- @mpx_ueq@ --- * |
720 | * | |
721 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit | |
722 | * @const mpw *bv, *bvl@ = second argument vector base and limit | |
723 | * | |
724 | * Returns: Nonzero if the two vectors are equal. | |
725 | * | |
726 | * Use: Performs an unsigned integer test for equality. | |
727 | */ | |
728 | ||
729 | int mpx_ueq(const mpw *av, const mpw *avl, const mpw *bv, const mpw *bvl) | |
730 | { | |
731 | MPX_SHRINK(av, avl); | |
732 | MPX_SHRINK(bv, bvl); | |
733 | if (avl - av != bvl - bv) | |
734 | return (0); | |
735 | while (av < avl) { | |
736 | if (*av++ != *bv++) | |
737 | return (0); | |
738 | } | |
739 | return (1); | |
740 | } | |
741 | ||
d03ab969 | 742 | /* --- @mpx_ucmp@ --- * |
743 | * | |
744 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit | |
745 | * @const mpw *bv, *bvl@ = second argument vector base and limit | |
746 | * | |
747 | * Returns: Less than, equal to, or greater than zero depending on | |
748 | * whether @a@ is less than, equal to or greater than @b@, | |
749 | * respectively. | |
750 | * | |
751 | * Use: Performs an unsigned integer comparison. | |
752 | */ | |
753 | ||
754 | int mpx_ucmp(const mpw *av, const mpw *avl, const mpw *bv, const mpw *bvl) | |
755 | { | |
756 | MPX_SHRINK(av, avl); | |
757 | MPX_SHRINK(bv, bvl); | |
758 | ||
759 | if (avl - av > bvl - bv) | |
760 | return (+1); | |
761 | else if (avl - av < bvl - bv) | |
762 | return (-1); | |
763 | else while (avl > av) { | |
764 | mpw a = *--avl, b = *--bvl; | |
765 | if (a > b) | |
766 | return (+1); | |
767 | else if (a < b) | |
768 | return (-1); | |
769 | } | |
770 | return (0); | |
771 | } | |
1a05a8ef | 772 | |
d03ab969 | 773 | /* --- @mpx_uadd@ --- * |
774 | * | |
775 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
776 | * @const mpw *av, *avl@ = first addend vector base and limit | |
777 | * @const mpw *bv, *bvl@ = second addend vector base and limit | |
778 | * | |
779 | * Returns: --- | |
780 | * | |
781 | * Use: Performs unsigned integer addition. If the result overflows | |
782 | * the destination vector, high-order bits are discarded. This | |
783 | * means that two's complement addition happens more or less for | |
784 | * free, although that's more a side-effect than anything else. | |
785 | * The result vector may be equal to either or both source | |
786 | * vectors, but may not otherwise overlap them. | |
787 | */ | |
788 | ||
789 | void mpx_uadd(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, | |
790 | const mpw *bv, const mpw *bvl) | |
791 | { | |
792 | mpw c = 0; | |
793 | ||
794 | while (av < avl || bv < bvl) { | |
795 | mpw a, b; | |
796 | mpd x; | |
797 | if (dv >= dvl) | |
798 | return; | |
799 | a = (av < avl) ? *av++ : 0; | |
800 | b = (bv < bvl) ? *bv++ : 0; | |
801 | x = (mpd)a + (mpd)b + c; | |
802 | *dv++ = MPW(x); | |
803 | c = x >> MPW_BITS; | |
804 | } | |
805 | if (dv < dvl) { | |
806 | *dv++ = c; | |
807 | MPX_ZERO(dv, dvl); | |
808 | } | |
809 | } | |
810 | ||
dd517851 | 811 | /* --- @mpx_uaddn@ --- * |
812 | * | |
813 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit | |
814 | * @mpw n@ = other addend | |
815 | * | |
816 | * Returns: --- | |
817 | * | |
818 | * Use: Adds a small integer to a multiprecision number. | |
819 | */ | |
820 | ||
821 | void mpx_uaddn(mpw *dv, mpw *dvl, mpw n) { MPX_UADDN(dv, dvl, n); } | |
822 | ||
f46efa79 | 823 | /* --- @mpx_uaddnlsl@ --- * |
824 | * | |
825 | * Arguments: @mpw *dv, *dvl@ = destination and first argument vector | |
826 | * @mpw a@ = second argument | |
827 | * @unsigned o@ = offset in bits | |
828 | * | |
829 | * Returns: --- | |
830 | * | |
831 | * Use: Computes %$d + 2^o a$%. If the result overflows then | |
832 | * high-order bits are discarded, as usual. We must have | |
833 | * @0 < o < MPW_BITS@. | |
834 | */ | |
835 | ||
836 | void mpx_uaddnlsl(mpw *dv, mpw *dvl, mpw a, unsigned o) | |
837 | { | |
838 | mpd x = (mpd)a << o; | |
839 | ||
840 | while (x && dv < dvl) { | |
841 | x += *dv; | |
842 | *dv++ = MPW(x); | |
843 | x >>= MPW_BITS; | |
844 | } | |
845 | } | |
846 | ||
d03ab969 | 847 | /* --- @mpx_usub@ --- * |
848 | * | |
849 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
850 | * @const mpw *av, *avl@ = first argument vector base and limit | |
851 | * @const mpw *bv, *bvl@ = second argument vector base and limit | |
852 | * | |
853 | * Returns: --- | |
854 | * | |
855 | * Use: Performs unsigned integer subtraction. If the result | |
856 | * overflows the destination vector, high-order bits are | |
857 | * discarded. This means that two's complement subtraction | |
858 | * happens more or less for free, althuogh that's more a side- | |
859 | * effect than anything else. The result vector may be equal to | |
860 | * either or both source vectors, but may not otherwise overlap | |
861 | * them. | |
862 | */ | |
863 | ||
864 | void mpx_usub(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, | |
865 | const mpw *bv, const mpw *bvl) | |
866 | { | |
867 | mpw c = 0; | |
868 | ||
869 | while (av < avl || bv < bvl) { | |
870 | mpw a, b; | |
871 | mpd x; | |
872 | if (dv >= dvl) | |
873 | return; | |
874 | a = (av < avl) ? *av++ : 0; | |
875 | b = (bv < bvl) ? *bv++ : 0; | |
c8a2f9ef | 876 | x = (mpd)a - (mpd)b - c; |
d03ab969 | 877 | *dv++ = MPW(x); |
c8a2f9ef | 878 | if (x >> MPW_BITS) |
879 | c = 1; | |
880 | else | |
881 | c = 0; | |
d03ab969 | 882 | } |
c8a2f9ef | 883 | if (c) |
884 | c = MPW_MAX; | |
d03ab969 | 885 | while (dv < dvl) |
c8a2f9ef | 886 | *dv++ = c; |
d03ab969 | 887 | } |
888 | ||
dd517851 | 889 | /* --- @mpx_usubn@ --- * |
890 | * | |
891 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit | |
892 | * @n@ = subtrahend | |
893 | * | |
894 | * Returns: --- | |
895 | * | |
896 | * Use: Subtracts a small integer from a multiprecision number. | |
897 | */ | |
898 | ||
899 | void mpx_usubn(mpw *dv, mpw *dvl, mpw n) { MPX_USUBN(dv, dvl, n); } | |
900 | ||
f46efa79 | 901 | /* --- @mpx_uaddnlsl@ --- * |
902 | * | |
903 | * Arguments: @mpw *dv, *dvl@ = destination and first argument vector | |
904 | * @mpw a@ = second argument | |
905 | * @unsigned o@ = offset in bits | |
906 | * | |
907 | * Returns: --- | |
908 | * | |
909 | * Use: Computes %$d + 2^o a$%. If the result overflows then | |
910 | * high-order bits are discarded, as usual. We must have | |
911 | * @0 < o < MPW_BITS@. | |
912 | */ | |
913 | ||
914 | void mpx_usubnlsl(mpw *dv, mpw *dvl, mpw a, unsigned o) | |
915 | { | |
916 | mpw b = a >> (MPW_BITS - o); | |
917 | a <<= o; | |
918 | ||
919 | if (dv < dvl) { | |
c29970a7 | 920 | mpd x = (mpd)*dv - MPW(a); |
f46efa79 | 921 | *dv++ = MPW(x); |
922 | if (x >> MPW_BITS) | |
923 | b++; | |
924 | MPX_USUBN(dv, dvl, b); | |
925 | } | |
926 | } | |
927 | ||
d03ab969 | 928 | /* --- @mpx_umul@ --- * |
929 | * | |
930 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
931 | * @const mpw *av, *avl@ = multiplicand vector base and limit | |
932 | * @const mpw *bv, *bvl@ = multiplier vector base and limit | |
933 | * | |
934 | * Returns: --- | |
935 | * | |
936 | * Use: Performs unsigned integer multiplication. If the result | |
937 | * overflows the desination vector, high-order bits are | |
938 | * discarded. The result vector may not overlap the argument | |
939 | * vectors in any way. | |
940 | */ | |
941 | ||
942 | void mpx_umul(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, | |
943 | const mpw *bv, const mpw *bvl) | |
944 | { | |
945 | /* --- This is probably worthwhile on a multiply --- */ | |
946 | ||
947 | MPX_SHRINK(av, avl); | |
948 | MPX_SHRINK(bv, bvl); | |
949 | ||
950 | /* --- Deal with a multiply by zero --- */ | |
45c0fd36 | 951 | |
d03ab969 | 952 | if (bv == bvl) { |
c8a2f9ef | 953 | MPX_ZERO(dv, dvl); |
d03ab969 | 954 | return; |
955 | } | |
956 | ||
957 | /* --- Do the initial multiply and initialize the accumulator --- */ | |
958 | ||
959 | MPX_UMULN(dv, dvl, av, avl, *bv++); | |
960 | ||
961 | /* --- Do the remaining multiply/accumulates --- */ | |
962 | ||
c8a2f9ef | 963 | while (dv < dvl && bv < bvl) { |
d03ab969 | 964 | mpw m = *bv++; |
c8a2f9ef | 965 | mpw c = 0; |
d03ab969 | 966 | const mpw *avv = av; |
967 | mpw *dvv = ++dv; | |
968 | ||
969 | while (avv < avl) { | |
970 | mpd x; | |
971 | if (dvv >= dvl) | |
972 | goto next; | |
c8a2f9ef | 973 | x = (mpd)*dvv + (mpd)m * (mpd)*avv++ + c; |
974 | *dvv++ = MPW(x); | |
d03ab969 | 975 | c = x >> MPW_BITS; |
976 | } | |
c8a2f9ef | 977 | MPX_UADDN(dvv, dvl, c); |
d03ab969 | 978 | next:; |
979 | } | |
980 | } | |
981 | ||
dd517851 | 982 | /* --- @mpx_umuln@ --- * |
983 | * | |
984 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
985 | * @const mpw *av, *avl@ = multiplicand vector base and limit | |
986 | * @mpw m@ = multiplier | |
987 | * | |
988 | * Returns: --- | |
989 | * | |
990 | * Use: Multiplies a multiprecision integer by a single-word value. | |
991 | * The destination and source may be equal. The destination | |
992 | * is completely cleared after use. | |
993 | */ | |
994 | ||
995 | void mpx_umuln(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, mpw m) | |
106b481c | 996 | { MPX_UMULN(dv, dvl, av, avl, m); } |
dd517851 | 997 | |
998 | /* --- @mpx_umlan@ --- * | |
999 | * | |
1000 | * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit | |
1001 | * @const mpw *av, *avl@ = multiplicand vector base and limit | |
1002 | * @mpw m@ = multiplier | |
1003 | * | |
1004 | * Returns: --- | |
1005 | * | |
1006 | * Use: Multiplies a multiprecision integer by a single-word value | |
1007 | * and adds the result to an accumulator. | |
1008 | */ | |
1009 | ||
1010 | void mpx_umlan(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, mpw m) | |
106b481c | 1011 | { MPX_UMLAN(dv, dvl, av, avl, m); } |
dd517851 | 1012 | |
c8a2f9ef | 1013 | /* --- @mpx_usqr@ --- * |
1014 | * | |
1015 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit | |
1016 | * @const mpw *av, *av@ = source vector base and limit | |
1017 | * | |
1018 | * Returns: --- | |
1019 | * | |
1020 | * Use: Performs unsigned integer squaring. The result vector must | |
1021 | * not overlap the source vector in any way. | |
1022 | */ | |
1023 | ||
1024 | void mpx_usqr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl) | |
1025 | { | |
1026 | MPX_ZERO(dv, dvl); | |
1027 | ||
1028 | /* --- Main loop --- */ | |
1029 | ||
1030 | while (av < avl) { | |
1031 | const mpw *avv = av; | |
1032 | mpw *dvv = dv; | |
1033 | mpw a = *av; | |
1034 | mpd c; | |
1035 | ||
1036 | /* --- Stop if I've run out of destination --- */ | |
1037 | ||
1038 | if (dvv >= dvl) | |
1039 | break; | |
1040 | ||
1041 | /* --- Work out the square at this point in the proceedings --- */ | |
1042 | ||
1043 | { | |
c8a2f9ef | 1044 | mpd x = (mpd)a * (mpd)a + *dvv; |
1045 | *dvv++ = MPW(x); | |
1046 | c = MPW(x >> MPW_BITS); | |
1047 | } | |
1048 | ||
1049 | /* --- Now fix up the rest of the vector upwards --- */ | |
1050 | ||
1051 | avv++; | |
1052 | while (dvv < dvl && avv < avl) { | |
c8a2f9ef | 1053 | mpd x = (mpd)a * (mpd)*avv++; |
1054 | mpd y = ((x << 1) & MPW_MAX) + c + *dvv; | |
1055 | c = (x >> (MPW_BITS - 1)) + (y >> MPW_BITS); | |
1056 | *dvv++ = MPW(y); | |
1057 | } | |
1058 | while (dvv < dvl && c) { | |
1059 | mpd x = c + *dvv; | |
1060 | *dvv++ = MPW(x); | |
1061 | c = x >> MPW_BITS; | |
1062 | } | |
1063 | ||
1064 | /* --- Get ready for the next round --- */ | |
1065 | ||
1066 | av++; | |
1067 | dv += 2; | |
1068 | } | |
1069 | } | |
1070 | ||
d03ab969 | 1071 | /* --- @mpx_udiv@ --- * |
1072 | * | |
1073 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit | |
1074 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit | |
1075 | * @const mpw *dv, *dvl@ = divisor vector base and limit | |
c8a2f9ef | 1076 | * @mpw *sv, *svl@ = scratch workspace |
d03ab969 | 1077 | * |
1078 | * Returns: --- | |
1079 | * | |
1080 | * Use: Performs unsigned integer division. If the result overflows | |
1081 | * the quotient vector, high-order bits are discarded. (Clearly | |
1082 | * the remainder vector can't overflow.) The various vectors | |
1083 | * may not overlap in any way. Yes, I know it's a bit odd | |
1084 | * requiring the dividend to be in the result position but it | |
1085 | * does make some sense really. The remainder must have | |
c8a2f9ef | 1086 | * headroom for at least two extra words. The scratch space |
f45a00c6 | 1087 | * must be at least one word larger than the divisor. |
d03ab969 | 1088 | */ |
1089 | ||
1090 | void mpx_udiv(mpw *qv, mpw *qvl, mpw *rv, mpw *rvl, | |
c8a2f9ef | 1091 | const mpw *dv, const mpw *dvl, |
1092 | mpw *sv, mpw *svl) | |
d03ab969 | 1093 | { |
d03ab969 | 1094 | unsigned norm = 0; |
1095 | size_t scale; | |
1096 | mpw d, dd; | |
1097 | ||
1098 | /* --- Initialize the quotient --- */ | |
1099 | ||
1100 | MPX_ZERO(qv, qvl); | |
1101 | ||
c8a2f9ef | 1102 | /* --- Perform some sanity checks --- */ |
1103 | ||
1104 | MPX_SHRINK(dv, dvl); | |
1105 | assert(((void)"division by zero in mpx_udiv", dv < dvl)); | |
1106 | ||
d03ab969 | 1107 | /* --- Normalize the divisor --- * |
1108 | * | |
1109 | * The algorithm requires that the divisor be at least two digits long. | |
1110 | * This is easy to fix. | |
1111 | */ | |
1112 | ||
c8a2f9ef | 1113 | { |
1114 | unsigned b; | |
d03ab969 | 1115 | |
c8a2f9ef | 1116 | d = dvl[-1]; |
c29970a7 | 1117 | for (b = MPW_P2; b; b >>= 1) { |
34e4f738 | 1118 | if (d <= (MPW_MAX >> b)) { |
c8a2f9ef | 1119 | d <<= b; |
1120 | norm += b; | |
1121 | } | |
1122 | } | |
1123 | if (dv + 1 == dvl) | |
1124 | norm += MPW_BITS; | |
d03ab969 | 1125 | } |
d03ab969 | 1126 | |
1127 | /* --- Normalize the dividend/remainder to match --- */ | |
1128 | ||
c8a2f9ef | 1129 | if (norm) { |
c8a2f9ef | 1130 | mpx_lsl(rv, rvl, rv, rvl, norm); |
f45a00c6 | 1131 | mpx_lsl(sv, svl, dv, dvl, norm); |
c8a2f9ef | 1132 | dv = sv; |
f45a00c6 | 1133 | dvl = svl; |
c8a2f9ef | 1134 | MPX_SHRINK(dv, dvl); |
1135 | } | |
1136 | ||
d03ab969 | 1137 | MPX_SHRINK(rv, rvl); |
c8a2f9ef | 1138 | d = dvl[-1]; |
1139 | dd = dvl[-2]; | |
d03ab969 | 1140 | |
1141 | /* --- Work out the relative scales --- */ | |
1142 | ||
1143 | { | |
1144 | size_t rvn = rvl - rv; | |
c8a2f9ef | 1145 | size_t dvn = dvl - dv; |
d03ab969 | 1146 | |
1147 | /* --- If the divisor is clearly larger, notice this --- */ | |
1148 | ||
1149 | if (dvn > rvn) { | |
1150 | mpx_lsr(rv, rvl, rv, rvl, norm); | |
1151 | return; | |
1152 | } | |
1153 | ||
1154 | scale = rvn - dvn; | |
1155 | } | |
1156 | ||
1157 | /* --- Calculate the most significant quotient digit --- * | |
1158 | * | |
1159 | * Because the divisor has its top bit set, this can only happen once. The | |
1160 | * pointer arithmetic is a little contorted, to make sure that the | |
1161 | * behaviour is defined. | |
1162 | */ | |
1163 | ||
1164 | if (MPX_UCMP(rv + scale, rvl, >=, dv, dvl)) { | |
1165 | mpx_usub(rv + scale, rvl, rv + scale, rvl, dv, dvl); | |
1166 | if (qvl - qv > scale) | |
1167 | qv[scale] = 1; | |
1168 | } | |
1169 | ||
1170 | /* --- Now for the main loop --- */ | |
1171 | ||
1172 | { | |
c8a2f9ef | 1173 | mpw *rvv = rvl - 2; |
d03ab969 | 1174 | |
1175 | while (scale) { | |
c8a2f9ef | 1176 | mpw q; |
1177 | mpd rh; | |
d03ab969 | 1178 | |
1179 | /* --- Get an estimate for the next quotient digit --- */ | |
1180 | ||
c8a2f9ef | 1181 | mpw r = rvv[1]; |
1182 | mpw rr = rvv[0]; | |
1183 | mpw rrr = *--rvv; | |
1184 | ||
1185 | scale--; | |
1186 | rh = ((mpd)r << MPW_BITS) | rr; | |
d03ab969 | 1187 | if (r == d) |
1188 | q = MPW_MAX; | |
c8a2f9ef | 1189 | else |
1190 | q = MPW(rh / d); | |
d03ab969 | 1191 | |
1192 | /* --- Refine the estimate --- */ | |
1193 | ||
1194 | { | |
1195 | mpd yh = (mpd)d * q; | |
ce76ff16 | 1196 | mpd yy = (mpd)dd * q; |
1197 | mpw yl; | |
c8a2f9ef | 1198 | |
ce76ff16 | 1199 | if (yy > MPW_MAX) |
1200 | yh += yy >> MPW_BITS; | |
1201 | yl = MPW(yy); | |
c8a2f9ef | 1202 | |
1203 | while (yh > rh || (yh == rh && yl > rrr)) { | |
1204 | q--; | |
1205 | yh -= d; | |
ce76ff16 | 1206 | if (yl < dd) |
1207 | yh--; | |
99b30c23 | 1208 | yl = MPW(yl - dd); |
c8a2f9ef | 1209 | } |
1210 | } | |
1211 | ||
1212 | /* --- Remove a chunk from the dividend --- */ | |
1213 | ||
1214 | { | |
1215 | mpw *svv; | |
1216 | const mpw *dvv; | |
f45a00c6 | 1217 | mpw mc = 0, sc = 0; |
c8a2f9ef | 1218 | |
f45a00c6 | 1219 | /* --- Calculate the size of the chunk --- * |
1220 | * | |
1221 | * This does the whole job of calculating @r >> scale - qd@. | |
1222 | */ | |
c8a2f9ef | 1223 | |
f45a00c6 | 1224 | for (svv = rv + scale, dvv = dv; |
1225 | dvv < dvl && svv < rvl; | |
1226 | svv++, dvv++) { | |
1227 | mpd x = (mpd)*dvv * (mpd)q + mc; | |
1228 | mc = x >> MPW_BITS; | |
1229 | x = (mpd)*svv - MPW(x) - sc; | |
c8a2f9ef | 1230 | *svv = MPW(x); |
f45a00c6 | 1231 | if (x >> MPW_BITS) |
1232 | sc = 1; | |
1233 | else | |
1234 | sc = 0; | |
1235 | } | |
1236 | ||
1237 | if (svv < rvl) { | |
1238 | mpd x = (mpd)*svv - mc - sc; | |
1239 | *svv++ = MPW(x); | |
1240 | if (x >> MPW_BITS) | |
1241 | sc = MPW_MAX; | |
1242 | else | |
1243 | sc = 0; | |
1244 | while (svv < rvl) | |
1245 | *svv++ = sc; | |
c8a2f9ef | 1246 | } |
c8a2f9ef | 1247 | |
f45a00c6 | 1248 | /* --- Fix if the quotient was too large --- * |
c8a2f9ef | 1249 | * |
f45a00c6 | 1250 | * This doesn't seem to happen very often. |
c8a2f9ef | 1251 | */ |
1252 | ||
c8a2f9ef | 1253 | if (rvl[-1] > MPW_MAX / 2) { |
1254 | mpx_uadd(rv + scale, rvl, rv + scale, rvl, dv, dvl); | |
1255 | q--; | |
1256 | } | |
1257 | } | |
1258 | ||
1259 | /* --- Done for another iteration --- */ | |
1260 | ||
1261 | if (qvl - qv > scale) | |
1262 | qv[scale] = q; | |
1263 | r = rr; | |
1264 | rr = rrr; | |
1265 | } | |
1266 | } | |
1267 | ||
1268 | /* --- Now fiddle with unnormalizing and things --- */ | |
1269 | ||
1270 | mpx_lsr(rv, rvl, rv, rvl, norm); | |
d03ab969 | 1271 | } |
1272 | ||
698bd937 | 1273 | /* --- @mpx_udivn@ --- * |
1274 | * | |
1275 | * Arguments: @mpw *qv, *qvl@ = storage for the quotient (may overlap | |
1276 | * dividend) | |
1277 | * @const mpw *rv, *rvl@ = dividend | |
1278 | * @mpw d@ = single-precision divisor | |
1279 | * | |
1280 | * Returns: Remainder after divison. | |
1281 | * | |
1282 | * Use: Performs a single-precision division operation. | |
1283 | */ | |
1284 | ||
1285 | mpw mpx_udivn(mpw *qv, mpw *qvl, const mpw *rv, const mpw *rvl, mpw d) | |
1286 | { | |
1287 | size_t i; | |
1288 | size_t ql = qvl - qv; | |
1289 | mpd r = 0; | |
1290 | ||
1291 | i = rvl - rv; | |
1292 | while (i > 0) { | |
1293 | i--; | |
1294 | r = (r << MPW_BITS) | rv[i]; | |
1295 | if (i < ql) | |
1296 | qv[i] = r / d; | |
1297 | r %= d; | |
1298 | } | |
1299 | return (MPW(r)); | |
1300 | } | |
1301 | ||
42684bdb | 1302 | /*----- Test rig ----------------------------------------------------------*/ |
1303 | ||
1304 | #ifdef TEST_RIG | |
1305 | ||
1306 | #include <mLib/alloc.h> | |
1307 | #include <mLib/dstr.h> | |
1308 | #include <mLib/quis.h> | |
1309 | #include <mLib/testrig.h> | |
1310 | ||
1311 | #include "mpscan.h" | |
1312 | ||
1313 | #define ALLOC(v, vl, sz) do { \ | |
1314 | size_t _sz = (sz); \ | |
1315 | mpw *_vv = xmalloc(MPWS(_sz)); \ | |
1316 | mpw *_vvl = _vv + _sz; \ | |
1317 | (v) = _vv; \ | |
1318 | (vl) = _vvl; \ | |
1319 | } while (0) | |
1320 | ||
1321 | #define LOAD(v, vl, d) do { \ | |
1322 | const dstr *_d = (d); \ | |
1323 | mpw *_v, *_vl; \ | |
1324 | ALLOC(_v, _vl, MPW_RQ(_d->len)); \ | |
1325 | mpx_loadb(_v, _vl, _d->buf, _d->len); \ | |
1326 | (v) = _v; \ | |
1327 | (vl) = _vl; \ | |
1328 | } while (0) | |
1329 | ||
1330 | #define MAX(x, y) ((x) > (y) ? (x) : (y)) | |
45c0fd36 | 1331 | |
42684bdb | 1332 | static void dumpbits(const char *msg, const void *pp, size_t sz) |
1333 | { | |
1334 | const octet *p = pp; | |
1335 | fputs(msg, stderr); | |
1336 | for (; sz; sz--) | |
1337 | fprintf(stderr, " %02x", *p++); | |
1338 | fputc('\n', stderr); | |
1339 | } | |
1340 | ||
1341 | static void dumpmp(const char *msg, const mpw *v, const mpw *vl) | |
1342 | { | |
1343 | fputs(msg, stderr); | |
1344 | MPX_SHRINK(v, vl); | |
1345 | while (v < vl) | |
1346 | fprintf(stderr, " %08lx", (unsigned long)*--vl); | |
1347 | fputc('\n', stderr); | |
1348 | } | |
1349 | ||
1350 | static int chkscan(const mpw *v, const mpw *vl, | |
1351 | const void *pp, size_t sz, int step) | |
1352 | { | |
1353 | mpscan mps; | |
1354 | const octet *p = pp; | |
1355 | unsigned bit = 0; | |
1356 | int ok = 1; | |
1357 | ||
1358 | mpscan_initx(&mps, v, vl); | |
1359 | while (sz) { | |
1360 | unsigned x = *p; | |
1361 | int i; | |
1362 | p += step; | |
1363 | for (i = 0; i < 8 && MPSCAN_STEP(&mps); i++) { | |
1364 | if (MPSCAN_BIT(&mps) != (x & 1)) { | |
1365 | fprintf(stderr, | |
1366 | "\n*** error, step %i, bit %u, expected %u, found %u\n", | |
1367 | step, bit, x & 1, MPSCAN_BIT(&mps)); | |
1368 | ok = 0; | |
1369 | } | |
1370 | x >>= 1; | |
1371 | bit++; | |
1372 | } | |
1373 | sz--; | |
1374 | } | |
1375 | ||
1376 | return (ok); | |
1377 | } | |
1378 | ||
1379 | static int loadstore(dstr *v) | |
1380 | { | |
1381 | dstr d = DSTR_INIT; | |
1382 | size_t sz = MPW_RQ(v->len) * 2, diff; | |
1383 | mpw *m, *ml; | |
1384 | int ok = 1; | |
1385 | ||
1386 | dstr_ensure(&d, v->len); | |
1387 | m = xmalloc(MPWS(sz)); | |
1388 | ||
1389 | for (diff = 0; diff < sz; diff += 5) { | |
1390 | size_t oct; | |
1391 | ||
1392 | ml = m + sz - diff; | |
1393 | ||
1394 | mpx_loadl(m, ml, v->buf, v->len); | |
1395 | if (!chkscan(m, ml, v->buf, v->len, +1)) | |
1396 | ok = 0; | |
1397 | MPX_OCTETS(oct, m, ml); | |
1398 | mpx_storel(m, ml, d.buf, d.sz); | |
1399 | if (memcmp(d.buf, v->buf, oct) != 0) { | |
1400 | dumpbits("\n*** storel failed", d.buf, d.sz); | |
1401 | ok = 0; | |
1402 | } | |
1403 | ||
1404 | mpx_loadb(m, ml, v->buf, v->len); | |
1405 | if (!chkscan(m, ml, v->buf + v->len - 1, v->len, -1)) | |
1406 | ok = 0; | |
1407 | MPX_OCTETS(oct, m, ml); | |
1408 | mpx_storeb(m, ml, d.buf, d.sz); | |
1409 | if (memcmp(d.buf + d.sz - oct, v->buf + v->len - oct, oct) != 0) { | |
1410 | dumpbits("\n*** storeb failed", d.buf, d.sz); | |
1411 | ok = 0; | |
1412 | } | |
1413 | } | |
1414 | ||
1415 | if (!ok) | |
1416 | dumpbits("input data", v->buf, v->len); | |
1417 | ||
12ed8a1f | 1418 | xfree(m); |
42684bdb | 1419 | dstr_destroy(&d); |
1420 | return (ok); | |
1421 | } | |
1422 | ||
f09e814a | 1423 | static int twocl(dstr *v) |
1424 | { | |
1425 | dstr d = DSTR_INIT; | |
1426 | mpw *m, *ml; | |
1427 | size_t sz; | |
1428 | int ok = 1; | |
1429 | ||
1430 | sz = v[0].len; if (v[1].len > sz) sz = v[1].len; | |
1431 | dstr_ensure(&d, sz); | |
1432 | ||
1433 | sz = MPW_RQ(sz); | |
1434 | m = xmalloc(MPWS(sz)); | |
1435 | ml = m + sz; | |
1436 | ||
1437 | mpx_loadl(m, ml, v[0].buf, v[0].len); | |
1438 | mpx_storel2cn(m, ml, d.buf, v[1].len); | |
1439 | if (memcmp(d.buf, v[1].buf, v[1].len)) { | |
1440 | dumpbits("\n*** storel2cn failed", d.buf, v[1].len); | |
1441 | ok = 0; | |
1442 | } | |
1443 | ||
1444 | mpx_loadl2cn(m, ml, v[1].buf, v[1].len); | |
1445 | mpx_storel(m, ml, d.buf, v[0].len); | |
1446 | if (memcmp(d.buf, v[0].buf, v[0].len)) { | |
1447 | dumpbits("\n*** loadl2cn failed", d.buf, v[0].len); | |
1448 | ok = 0; | |
1449 | } | |
1450 | ||
1451 | if (!ok) { | |
1452 | dumpbits("pos", v[0].buf, v[0].len); | |
1453 | dumpbits("neg", v[1].buf, v[1].len); | |
1454 | } | |
1455 | ||
12ed8a1f | 1456 | xfree(m); |
f09e814a | 1457 | dstr_destroy(&d); |
1458 | ||
1459 | return (ok); | |
1460 | } | |
1461 | ||
1462 | static int twocb(dstr *v) | |
1463 | { | |
1464 | dstr d = DSTR_INIT; | |
1465 | mpw *m, *ml; | |
1466 | size_t sz; | |
1467 | int ok = 1; | |
1468 | ||
1469 | sz = v[0].len; if (v[1].len > sz) sz = v[1].len; | |
1470 | dstr_ensure(&d, sz); | |
1471 | ||
1472 | sz = MPW_RQ(sz); | |
1473 | m = xmalloc(MPWS(sz)); | |
1474 | ml = m + sz; | |
1475 | ||
1476 | mpx_loadb(m, ml, v[0].buf, v[0].len); | |
1477 | mpx_storeb2cn(m, ml, d.buf, v[1].len); | |
1478 | if (memcmp(d.buf, v[1].buf, v[1].len)) { | |
1479 | dumpbits("\n*** storeb2cn failed", d.buf, v[1].len); | |
1480 | ok = 0; | |
1481 | } | |
1482 | ||
1483 | mpx_loadb2cn(m, ml, v[1].buf, v[1].len); | |
1484 | mpx_storeb(m, ml, d.buf, v[0].len); | |
1485 | if (memcmp(d.buf, v[0].buf, v[0].len)) { | |
1486 | dumpbits("\n*** loadb2cn failed", d.buf, v[0].len); | |
1487 | ok = 0; | |
1488 | } | |
1489 | ||
1490 | if (!ok) { | |
1491 | dumpbits("pos", v[0].buf, v[0].len); | |
1492 | dumpbits("neg", v[1].buf, v[1].len); | |
1493 | } | |
1494 | ||
12ed8a1f | 1495 | xfree(m); |
f09e814a | 1496 | dstr_destroy(&d); |
1497 | ||
1498 | return (ok); | |
1499 | } | |
1500 | ||
42684bdb | 1501 | static int lsl(dstr *v) |
1502 | { | |
1503 | mpw *a, *al; | |
1504 | int n = *(int *)v[1].buf; | |
1505 | mpw *c, *cl; | |
1506 | mpw *d, *dl; | |
1507 | int ok = 1; | |
1508 | ||
1509 | LOAD(a, al, &v[0]); | |
1510 | LOAD(c, cl, &v[2]); | |
1511 | ALLOC(d, dl, al - a + (n + MPW_BITS - 1) / MPW_BITS); | |
1512 | ||
1513 | mpx_lsl(d, dl, a, al, n); | |
1a05a8ef | 1514 | if (!mpx_ueq(d, dl, c, cl)) { |
42684bdb | 1515 | fprintf(stderr, "\n*** lsl(%i) failed\n", n); |
45c0fd36 | 1516 | dumpmp(" a", a, al); |
42684bdb | 1517 | dumpmp("expected", c, cl); |
1518 | dumpmp(" result", d, dl); | |
1519 | ok = 0; | |
1520 | } | |
1521 | ||
12ed8a1f | 1522 | xfree(a); xfree(c); xfree(d); |
42684bdb | 1523 | return (ok); |
1524 | } | |
1525 | ||
81578196 | 1526 | static int lslc(dstr *v) |
1527 | { | |
1528 | mpw *a, *al; | |
1529 | int n = *(int *)v[1].buf; | |
1530 | mpw *c, *cl; | |
1531 | mpw *d, *dl; | |
1532 | int ok = 1; | |
1533 | ||
1534 | LOAD(a, al, &v[0]); | |
1535 | LOAD(c, cl, &v[2]); | |
1536 | ALLOC(d, dl, al - a + (n + MPW_BITS - 1) / MPW_BITS); | |
1537 | ||
1538 | mpx_lslc(d, dl, a, al, n); | |
1539 | if (!mpx_ueq(d, dl, c, cl)) { | |
1540 | fprintf(stderr, "\n*** lslc(%i) failed\n", n); | |
45c0fd36 | 1541 | dumpmp(" a", a, al); |
81578196 | 1542 | dumpmp("expected", c, cl); |
1543 | dumpmp(" result", d, dl); | |
1544 | ok = 0; | |
1545 | } | |
1546 | ||
12ed8a1f | 1547 | xfree(a); xfree(c); xfree(d); |
81578196 | 1548 | return (ok); |
1549 | } | |
1550 | ||
42684bdb | 1551 | static int lsr(dstr *v) |
1552 | { | |
1553 | mpw *a, *al; | |
1554 | int n = *(int *)v[1].buf; | |
1555 | mpw *c, *cl; | |
1556 | mpw *d, *dl; | |
1557 | int ok = 1; | |
1558 | ||
1559 | LOAD(a, al, &v[0]); | |
1560 | LOAD(c, cl, &v[2]); | |
1561 | ALLOC(d, dl, al - a + (n + MPW_BITS - 1) / MPW_BITS + 1); | |
1562 | ||
1563 | mpx_lsr(d, dl, a, al, n); | |
1a05a8ef | 1564 | if (!mpx_ueq(d, dl, c, cl)) { |
42684bdb | 1565 | fprintf(stderr, "\n*** lsr(%i) failed\n", n); |
45c0fd36 | 1566 | dumpmp(" a", a, al); |
42684bdb | 1567 | dumpmp("expected", c, cl); |
1568 | dumpmp(" result", d, dl); | |
1569 | ok = 0; | |
1570 | } | |
1571 | ||
12ed8a1f | 1572 | xfree(a); xfree(c); xfree(d); |
42684bdb | 1573 | return (ok); |
1574 | } | |
1575 | ||
1576 | static int uadd(dstr *v) | |
1577 | { | |
1578 | mpw *a, *al; | |
1579 | mpw *b, *bl; | |
1580 | mpw *c, *cl; | |
1581 | mpw *d, *dl; | |
1582 | int ok = 1; | |
1583 | ||
1584 | LOAD(a, al, &v[0]); | |
1585 | LOAD(b, bl, &v[1]); | |
1586 | LOAD(c, cl, &v[2]); | |
1587 | ALLOC(d, dl, MAX(al - a, bl - b) + 1); | |
1588 | ||
1589 | mpx_uadd(d, dl, a, al, b, bl); | |
1a05a8ef | 1590 | if (!mpx_ueq(d, dl, c, cl)) { |
42684bdb | 1591 | fprintf(stderr, "\n*** uadd failed\n"); |
45c0fd36 MW |
1592 | dumpmp(" a", a, al); |
1593 | dumpmp(" b", b, bl); | |
42684bdb | 1594 | dumpmp("expected", c, cl); |
1595 | dumpmp(" result", d, dl); | |
1596 | ok = 0; | |
1597 | } | |
1598 | ||
12ed8a1f | 1599 | xfree(a); xfree(b); xfree(c); xfree(d); |
42684bdb | 1600 | return (ok); |
1601 | } | |
1602 | ||
1603 | static int usub(dstr *v) | |
1604 | { | |
1605 | mpw *a, *al; | |
1606 | mpw *b, *bl; | |
1607 | mpw *c, *cl; | |
1608 | mpw *d, *dl; | |
1609 | int ok = 1; | |
1610 | ||
1611 | LOAD(a, al, &v[0]); | |
1612 | LOAD(b, bl, &v[1]); | |
1613 | LOAD(c, cl, &v[2]); | |
1614 | ALLOC(d, dl, al - a); | |
1615 | ||
1616 | mpx_usub(d, dl, a, al, b, bl); | |
1a05a8ef | 1617 | if (!mpx_ueq(d, dl, c, cl)) { |
42684bdb | 1618 | fprintf(stderr, "\n*** usub failed\n"); |
45c0fd36 MW |
1619 | dumpmp(" a", a, al); |
1620 | dumpmp(" b", b, bl); | |
42684bdb | 1621 | dumpmp("expected", c, cl); |
1622 | dumpmp(" result", d, dl); | |
1623 | ok = 0; | |
1624 | } | |
1625 | ||
12ed8a1f | 1626 | xfree(a); xfree(b); xfree(c); xfree(d); |
42684bdb | 1627 | return (ok); |
1628 | } | |
1629 | ||
1630 | static int umul(dstr *v) | |
1631 | { | |
1632 | mpw *a, *al; | |
1633 | mpw *b, *bl; | |
1634 | mpw *c, *cl; | |
1635 | mpw *d, *dl; | |
1636 | int ok = 1; | |
1637 | ||
1638 | LOAD(a, al, &v[0]); | |
1639 | LOAD(b, bl, &v[1]); | |
1640 | LOAD(c, cl, &v[2]); | |
1641 | ALLOC(d, dl, (al - a) + (bl - b)); | |
1642 | ||
1643 | mpx_umul(d, dl, a, al, b, bl); | |
1a05a8ef | 1644 | if (!mpx_ueq(d, dl, c, cl)) { |
42684bdb | 1645 | fprintf(stderr, "\n*** umul failed\n"); |
45c0fd36 MW |
1646 | dumpmp(" a", a, al); |
1647 | dumpmp(" b", b, bl); | |
42684bdb | 1648 | dumpmp("expected", c, cl); |
1649 | dumpmp(" result", d, dl); | |
1650 | ok = 0; | |
1651 | } | |
1652 | ||
12ed8a1f | 1653 | xfree(a); xfree(b); xfree(c); xfree(d); |
42684bdb | 1654 | return (ok); |
1655 | } | |
1656 | ||
1657 | static int usqr(dstr *v) | |
1658 | { | |
1659 | mpw *a, *al; | |
1660 | mpw *c, *cl; | |
1661 | mpw *d, *dl; | |
1662 | int ok = 1; | |
1663 | ||
1664 | LOAD(a, al, &v[0]); | |
1665 | LOAD(c, cl, &v[1]); | |
1666 | ALLOC(d, dl, 2 * (al - a)); | |
1667 | ||
1668 | mpx_usqr(d, dl, a, al); | |
1a05a8ef | 1669 | if (!mpx_ueq(d, dl, c, cl)) { |
42684bdb | 1670 | fprintf(stderr, "\n*** usqr failed\n"); |
45c0fd36 | 1671 | dumpmp(" a", a, al); |
42684bdb | 1672 | dumpmp("expected", c, cl); |
1673 | dumpmp(" result", d, dl); | |
1674 | ok = 0; | |
1675 | } | |
1676 | ||
12ed8a1f | 1677 | xfree(a); xfree(c); xfree(d); |
42684bdb | 1678 | return (ok); |
1679 | } | |
1680 | ||
1681 | static int udiv(dstr *v) | |
1682 | { | |
1683 | mpw *a, *al; | |
1684 | mpw *b, *bl; | |
1685 | mpw *q, *ql; | |
1686 | mpw *r, *rl; | |
1687 | mpw *qq, *qql; | |
1688 | mpw *s, *sl; | |
1689 | int ok = 1; | |
1690 | ||
1691 | ALLOC(a, al, MPW_RQ(v[0].len) + 2); mpx_loadb(a, al, v[0].buf, v[0].len); | |
1692 | LOAD(b, bl, &v[1]); | |
1693 | LOAD(q, ql, &v[2]); | |
1694 | LOAD(r, rl, &v[3]); | |
1695 | ALLOC(qq, qql, al - a); | |
1696 | ALLOC(s, sl, (bl - b) + 1); | |
1697 | ||
1698 | mpx_udiv(qq, qql, a, al, b, bl, s, sl); | |
1a05a8ef | 1699 | if (!mpx_ueq(qq, qql, q, ql) || |
1700 | !mpx_ueq(a, al, r, rl)) { | |
42684bdb | 1701 | fprintf(stderr, "\n*** udiv failed\n"); |
1702 | dumpmp(" divisor", b, bl); | |
1703 | dumpmp("expect r", r, rl); | |
1704 | dumpmp("result r", a, al); | |
1705 | dumpmp("expect q", q, ql); | |
1706 | dumpmp("result q", qq, qql); | |
1707 | ok = 0; | |
1708 | } | |
1709 | ||
12ed8a1f | 1710 | xfree(a); xfree(b); xfree(r); xfree(q); xfree(s); xfree(qq); |
42684bdb | 1711 | return (ok); |
1712 | } | |
1713 | ||
1714 | static test_chunk defs[] = { | |
1715 | { "load-store", loadstore, { &type_hex, 0 } }, | |
f09e814a | 1716 | { "2cl", twocl, { &type_hex, &type_hex, } }, |
1717 | { "2cb", twocb, { &type_hex, &type_hex, } }, | |
42684bdb | 1718 | { "lsl", lsl, { &type_hex, &type_int, &type_hex, 0 } }, |
81578196 | 1719 | { "lslc", lslc, { &type_hex, &type_int, &type_hex, 0 } }, |
42684bdb | 1720 | { "lsr", lsr, { &type_hex, &type_int, &type_hex, 0 } }, |
1721 | { "uadd", uadd, { &type_hex, &type_hex, &type_hex, 0 } }, | |
1722 | { "usub", usub, { &type_hex, &type_hex, &type_hex, 0 } }, | |
1723 | { "umul", umul, { &type_hex, &type_hex, &type_hex, 0 } }, | |
1724 | { "usqr", usqr, { &type_hex, &type_hex, 0 } }, | |
1725 | { "udiv", udiv, { &type_hex, &type_hex, &type_hex, &type_hex, 0 } }, | |
1726 | { 0, 0, { 0 } } | |
1727 | }; | |
1728 | ||
1729 | int main(int argc, char *argv[]) | |
1730 | { | |
0f00dc4c | 1731 | test_run(argc, argv, defs, SRCDIR"/t/mpx"); |
42684bdb | 1732 | return (0); |
1733 | } | |
1734 | ||
42684bdb | 1735 | #endif |
1736 | ||
d03ab969 | 1737 | /*----- That's all, folks -------------------------------------------------*/ |