d03ab969 |
1 | /* -*-c-*- |
2 | * |
f45a00c6 |
3 | * $Id: mpx.c,v 1.4 1999/11/17 18:04:09 mdw Exp $ |
d03ab969 |
4 | * |
5 | * Low-level multiprecision arithmetic |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: mpx.c,v $ |
f45a00c6 |
33 | * Revision 1.4 1999/11/17 18:04:09 mdw |
34 | * Add two's-complement functionality. Improve mpx_udiv a little by |
35 | * performing the multiplication of the divisor by q with the subtraction |
36 | * from r. |
37 | * |
501da53c |
38 | * Revision 1.3 1999/11/13 01:57:31 mdw |
39 | * Remove stray debugging code. |
40 | * |
c8a2f9ef |
41 | * Revision 1.2 1999/11/13 01:50:59 mdw |
42 | * Multiprecision routines finished and tested. |
43 | * |
d03ab969 |
44 | * Revision 1.1 1999/09/03 08:41:12 mdw |
45 | * Initial import. |
46 | * |
47 | */ |
48 | |
49 | /*----- Header files ------------------------------------------------------*/ |
50 | |
c8a2f9ef |
51 | #include <assert.h> |
d03ab969 |
52 | #include <stdio.h> |
53 | #include <stdlib.h> |
54 | #include <string.h> |
55 | |
56 | #include <mLib/bits.h> |
57 | |
58 | #include "mptypes.h" |
59 | #include "mpx.h" |
60 | |
61 | /*----- Loading and storing -----------------------------------------------*/ |
62 | |
63 | /* --- @mpx_storel@ --- * |
64 | * |
65 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
c8a2f9ef |
66 | * @void *pp@ = pointer to octet array |
d03ab969 |
67 | * @size_t sz@ = size of octet array |
68 | * |
69 | * Returns: --- |
70 | * |
71 | * Use: Stores an MP in an octet array, least significant octet |
72 | * first. High-end octets are silently discarded if there |
73 | * isn't enough space for them. |
74 | */ |
75 | |
c8a2f9ef |
76 | void mpx_storel(const mpw *v, const mpw *vl, void *pp, size_t sz) |
d03ab969 |
77 | { |
78 | mpw n, w = 0; |
c8a2f9ef |
79 | octet *p = pp, *q = p + sz; |
d03ab969 |
80 | unsigned bits = 0; |
81 | |
82 | while (p < q) { |
83 | if (bits < 8) { |
84 | if (v >= vl) { |
85 | *p++ = U8(w); |
86 | break; |
87 | } |
88 | n = *v++; |
89 | *p++ = U8(w | n << bits); |
90 | w = n >> (8 - bits); |
91 | bits += MPW_BITS - 8; |
92 | } else { |
93 | *p++ = U8(w); |
94 | w >>= 8; |
95 | bits -= 8; |
96 | } |
97 | } |
98 | memset(p, 0, q - p); |
99 | } |
100 | |
101 | /* --- @mpx_loadl@ --- * |
102 | * |
103 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
c8a2f9ef |
104 | * @const void *pp@ = pointer to octet array |
d03ab969 |
105 | * @size_t sz@ = size of octet array |
106 | * |
107 | * Returns: --- |
108 | * |
109 | * Use: Loads an MP in an octet array, least significant octet |
110 | * first. High-end octets are ignored if there isn't enough |
111 | * space for them. |
112 | */ |
113 | |
c8a2f9ef |
114 | void mpx_loadl(mpw *v, mpw *vl, const void *pp, size_t sz) |
d03ab969 |
115 | { |
116 | unsigned n; |
c8a2f9ef |
117 | mpw w = 0; |
118 | const octet *p = pp, *q = p + sz; |
d03ab969 |
119 | unsigned bits = 0; |
120 | |
121 | if (v >= vl) |
122 | return; |
123 | while (p < q) { |
124 | n = U8(*p++); |
125 | w |= n << bits; |
126 | bits += 8; |
127 | if (bits >= MPW_BITS) { |
128 | *v++ = MPW(w); |
129 | w = n >> (MPW_BITS - bits + 8); |
130 | bits -= MPW_BITS; |
131 | if (v >= vl) |
132 | return; |
133 | } |
134 | } |
135 | *v++ = w; |
136 | MPX_ZERO(v, vl); |
137 | } |
138 | |
139 | /* --- @mpx_storeb@ --- * |
140 | * |
141 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
c8a2f9ef |
142 | * @void *pp@ = pointer to octet array |
d03ab969 |
143 | * @size_t sz@ = size of octet array |
144 | * |
145 | * Returns: --- |
146 | * |
147 | * Use: Stores an MP in an octet array, most significant octet |
148 | * first. High-end octets are silently discarded if there |
149 | * isn't enough space for them. |
150 | */ |
151 | |
c8a2f9ef |
152 | void mpx_storeb(const mpw *v, const mpw *vl, void *pp, size_t sz) |
d03ab969 |
153 | { |
154 | mpw n, w = 0; |
c8a2f9ef |
155 | octet *p = pp, *q = p + sz; |
d03ab969 |
156 | unsigned bits = 0; |
157 | |
158 | while (q > p) { |
159 | if (bits < 8) { |
160 | if (v >= vl) { |
161 | *--q = U8(w); |
162 | break; |
163 | } |
164 | n = *v++; |
165 | *--q = U8(w | n << bits); |
166 | w = n >> (8 - bits); |
167 | bits += MPW_BITS - 8; |
168 | } else { |
169 | *--q = U8(w); |
170 | w >>= 8; |
171 | bits -= 8; |
172 | } |
173 | } |
174 | memset(p, 0, q - p); |
175 | } |
176 | |
177 | /* --- @mpx_loadb@ --- * |
178 | * |
179 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
c8a2f9ef |
180 | * @const void *pp@ = pointer to octet array |
d03ab969 |
181 | * @size_t sz@ = size of octet array |
182 | * |
183 | * Returns: --- |
184 | * |
185 | * Use: Loads an MP in an octet array, most significant octet |
186 | * first. High-end octets are ignored if there isn't enough |
187 | * space for them. |
188 | */ |
189 | |
c8a2f9ef |
190 | void mpx_loadb(mpw *v, mpw *vl, const void *pp, size_t sz) |
d03ab969 |
191 | { |
192 | unsigned n; |
c8a2f9ef |
193 | mpw w = 0; |
194 | const octet *p = pp, *q = p + sz; |
d03ab969 |
195 | unsigned bits = 0; |
196 | |
197 | if (v >= vl) |
198 | return; |
199 | while (q > p) { |
200 | n = U8(*--q); |
201 | w |= n << bits; |
202 | bits += 8; |
203 | if (bits >= MPW_BITS) { |
204 | *v++ = MPW(w); |
205 | w = n >> (MPW_BITS - bits + 8); |
206 | bits -= MPW_BITS; |
207 | if (v >= vl) |
208 | return; |
209 | } |
210 | } |
211 | *v++ = w; |
212 | MPX_ZERO(v, vl); |
213 | } |
214 | |
215 | /*----- Logical shifting --------------------------------------------------*/ |
216 | |
217 | /* --- @mpx_lsl@ --- * |
218 | * |
219 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
220 | * @const mpw *av, *avl@ = source vector base and limit |
221 | * @size_t n@ = number of bit positions to shift by |
222 | * |
223 | * Returns: --- |
224 | * |
225 | * Use: Performs a logical shift left operation on an integer. |
226 | */ |
227 | |
228 | void mpx_lsl(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
229 | { |
230 | size_t nw; |
231 | unsigned nb; |
232 | |
233 | /* --- Trivial special case --- */ |
234 | |
235 | if (n == 0) |
236 | MPX_COPY(dv, dvl, av, avl); |
237 | |
238 | /* --- Single bit shifting --- */ |
239 | |
240 | else if (n == 1) { |
241 | mpw w = 0; |
242 | while (av < avl) { |
243 | mpw t; |
244 | if (dv >= dvl) |
245 | goto done; |
246 | t = *av++; |
247 | *dv++ = MPW((t << 1) | w); |
248 | w = t >> (MPW_BITS - 1); |
249 | } |
250 | if (dv >= dvl) |
251 | goto done; |
252 | *dv++ = MPW(w); |
253 | MPX_ZERO(dv, dvl); |
c8a2f9ef |
254 | goto done; |
d03ab969 |
255 | } |
256 | |
257 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
258 | |
259 | nw = n / MPW_BITS; |
260 | nb = n % MPW_BITS; |
261 | |
262 | /* --- Handle a shift by a multiple of the word size --- */ |
263 | |
264 | if (nb == 0) { |
265 | MPX_COPY(dv + nw, dvl, av, avl); |
266 | memset(dv, 0, MPWS(nw)); |
267 | } |
268 | |
c8a2f9ef |
269 | /* --- And finally the difficult case --- * |
270 | * |
271 | * This is a little convoluted, because I have to start from the end and |
272 | * work backwards to avoid overwriting the source, if they're both the same |
273 | * block of memory. |
274 | */ |
d03ab969 |
275 | |
276 | else { |
277 | mpw w; |
278 | size_t nr = MPW_BITS - nb; |
c8a2f9ef |
279 | size_t dvn = dvl - dv; |
280 | size_t avn = avl - av; |
d03ab969 |
281 | |
c8a2f9ef |
282 | if (dvn <= nw) { |
d03ab969 |
283 | MPX_ZERO(dv, dvl); |
284 | goto done; |
285 | } |
d03ab969 |
286 | |
c8a2f9ef |
287 | if (dvn > avn + nw) { |
288 | size_t off = avn + nw + 1; |
289 | MPX_ZERO(dv + off, dvl); |
290 | dvl = dv + off; |
291 | w = 0; |
292 | } else { |
293 | avl = av + dvn - nw; |
294 | w = *--avl << nb; |
d03ab969 |
295 | } |
296 | |
c8a2f9ef |
297 | while (avl > av) { |
298 | mpw t = *--avl; |
299 | *--dvl = (t >> nr) | w; |
300 | w = t << nb; |
d03ab969 |
301 | } |
c8a2f9ef |
302 | |
303 | *--dvl = w; |
304 | MPX_ZERO(dv, dvl); |
d03ab969 |
305 | } |
306 | |
307 | done:; |
308 | } |
309 | |
310 | /* --- @mpx_lsr@ --- * |
311 | * |
312 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
313 | * @const mpw *av, *avl@ = source vector base and limit |
314 | * @size_t n@ = number of bit positions to shift by |
315 | * |
316 | * Returns: --- |
317 | * |
318 | * Use: Performs a logical shift right operation on an integer. |
319 | */ |
320 | |
321 | void mpx_lsr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
322 | { |
323 | size_t nw; |
324 | unsigned nb; |
325 | |
326 | /* --- Trivial special case --- */ |
327 | |
328 | if (n == 0) |
329 | MPX_COPY(dv, dvl, av, avl); |
330 | |
331 | /* --- Single bit shifting --- */ |
332 | |
333 | else if (n == 1) { |
334 | mpw w = *av++ >> 1; |
335 | while (av < avl) { |
336 | mpw t; |
337 | if (dv >= dvl) |
338 | goto done; |
339 | t = *av++; |
340 | *dv++ = MPW((t << (MPW_BITS - 1)) | w); |
341 | w = t >> 1; |
342 | } |
343 | if (dv >= dvl) |
344 | goto done; |
345 | *dv++ = MPW(w); |
346 | MPX_ZERO(dv, dvl); |
c8a2f9ef |
347 | goto done; |
d03ab969 |
348 | } |
349 | |
350 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
351 | |
352 | nw = n / MPW_BITS; |
353 | nb = n % MPW_BITS; |
354 | |
355 | /* --- Handle a shift by a multiple of the word size --- */ |
356 | |
357 | if (nb == 0) |
358 | MPX_COPY(dv, dvl, av + nw, avl); |
359 | |
360 | /* --- And finally the difficult case --- */ |
361 | |
362 | else { |
363 | mpw w; |
364 | size_t nr = MPW_BITS - nb; |
365 | |
366 | av += nw; |
367 | w = *av++; |
368 | while (av < avl) { |
369 | mpw t; |
370 | if (dv >= dvl) |
371 | goto done; |
372 | t = *av++; |
373 | *dv++ = MPW((w >> nb) | (t << nr)); |
374 | w = t; |
375 | } |
376 | if (dv < dvl) { |
377 | *dv++ = MPW(w >> nb); |
378 | MPX_ZERO(dv, dvl); |
379 | } |
380 | } |
381 | |
382 | done:; |
383 | } |
384 | |
385 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
386 | |
f45a00c6 |
387 | /* --- @mpx_2c@ --- * |
388 | * |
389 | * Arguments: @mpw *dv, *dvl@ = destination vector |
390 | * @const mpw *v, *vl@ = source vector |
391 | * |
392 | * Returns: --- |
393 | * |
394 | * Use: Calculates the two's complement of @v@. |
395 | */ |
396 | |
397 | void mpx_2c(mpw *dv, mpw *dvl, const mpw *v, const mpw *vl) |
398 | { |
399 | mpw c = 0; |
400 | while (dv < dvl && v < vl) |
401 | *dv++ = c = MPW(~*v++); |
402 | if (dv < dvl) { |
403 | if (c > MPW_MAX / 2) |
404 | c = MPW(~0); |
405 | while (dv < dvl) |
406 | *dv++ = c; |
407 | } |
408 | MPX_UADDN(dv, dvl, 1); |
409 | } |
410 | |
d03ab969 |
411 | /* --- @mpx_ucmp@ --- * |
412 | * |
413 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
414 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
415 | * |
416 | * Returns: Less than, equal to, or greater than zero depending on |
417 | * whether @a@ is less than, equal to or greater than @b@, |
418 | * respectively. |
419 | * |
420 | * Use: Performs an unsigned integer comparison. |
421 | */ |
422 | |
423 | int mpx_ucmp(const mpw *av, const mpw *avl, const mpw *bv, const mpw *bvl) |
424 | { |
425 | MPX_SHRINK(av, avl); |
426 | MPX_SHRINK(bv, bvl); |
427 | |
428 | if (avl - av > bvl - bv) |
429 | return (+1); |
430 | else if (avl - av < bvl - bv) |
431 | return (-1); |
432 | else while (avl > av) { |
433 | mpw a = *--avl, b = *--bvl; |
434 | if (a > b) |
435 | return (+1); |
436 | else if (a < b) |
437 | return (-1); |
438 | } |
439 | return (0); |
440 | } |
441 | |
442 | /* --- @mpx_uadd@ --- * |
443 | * |
444 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
445 | * @const mpw *av, *avl@ = first addend vector base and limit |
446 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
447 | * |
448 | * Returns: --- |
449 | * |
450 | * Use: Performs unsigned integer addition. If the result overflows |
451 | * the destination vector, high-order bits are discarded. This |
452 | * means that two's complement addition happens more or less for |
453 | * free, although that's more a side-effect than anything else. |
454 | * The result vector may be equal to either or both source |
455 | * vectors, but may not otherwise overlap them. |
456 | */ |
457 | |
458 | void mpx_uadd(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
459 | const mpw *bv, const mpw *bvl) |
460 | { |
461 | mpw c = 0; |
462 | |
463 | while (av < avl || bv < bvl) { |
464 | mpw a, b; |
465 | mpd x; |
466 | if (dv >= dvl) |
467 | return; |
468 | a = (av < avl) ? *av++ : 0; |
469 | b = (bv < bvl) ? *bv++ : 0; |
470 | x = (mpd)a + (mpd)b + c; |
471 | *dv++ = MPW(x); |
472 | c = x >> MPW_BITS; |
473 | } |
474 | if (dv < dvl) { |
475 | *dv++ = c; |
476 | MPX_ZERO(dv, dvl); |
477 | } |
478 | } |
479 | |
480 | /* --- @mpx_usub@ --- * |
481 | * |
482 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
483 | * @const mpw *av, *avl@ = first argument vector base and limit |
484 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
485 | * |
486 | * Returns: --- |
487 | * |
488 | * Use: Performs unsigned integer subtraction. If the result |
489 | * overflows the destination vector, high-order bits are |
490 | * discarded. This means that two's complement subtraction |
491 | * happens more or less for free, althuogh that's more a side- |
492 | * effect than anything else. The result vector may be equal to |
493 | * either or both source vectors, but may not otherwise overlap |
494 | * them. |
495 | */ |
496 | |
497 | void mpx_usub(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
498 | const mpw *bv, const mpw *bvl) |
499 | { |
500 | mpw c = 0; |
501 | |
502 | while (av < avl || bv < bvl) { |
503 | mpw a, b; |
504 | mpd x; |
505 | if (dv >= dvl) |
506 | return; |
507 | a = (av < avl) ? *av++ : 0; |
508 | b = (bv < bvl) ? *bv++ : 0; |
c8a2f9ef |
509 | x = (mpd)a - (mpd)b - c; |
d03ab969 |
510 | *dv++ = MPW(x); |
c8a2f9ef |
511 | if (x >> MPW_BITS) |
512 | c = 1; |
513 | else |
514 | c = 0; |
d03ab969 |
515 | } |
c8a2f9ef |
516 | if (c) |
517 | c = MPW_MAX; |
d03ab969 |
518 | while (dv < dvl) |
c8a2f9ef |
519 | *dv++ = c; |
d03ab969 |
520 | } |
521 | |
522 | /* --- @mpx_umul@ --- * |
523 | * |
524 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
525 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
526 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
527 | * |
528 | * Returns: --- |
529 | * |
530 | * Use: Performs unsigned integer multiplication. If the result |
531 | * overflows the desination vector, high-order bits are |
532 | * discarded. The result vector may not overlap the argument |
533 | * vectors in any way. |
534 | */ |
535 | |
536 | void mpx_umul(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
537 | const mpw *bv, const mpw *bvl) |
538 | { |
539 | /* --- This is probably worthwhile on a multiply --- */ |
540 | |
541 | MPX_SHRINK(av, avl); |
542 | MPX_SHRINK(bv, bvl); |
543 | |
544 | /* --- Deal with a multiply by zero --- */ |
545 | |
546 | if (bv == bvl) { |
c8a2f9ef |
547 | MPX_ZERO(dv, dvl); |
d03ab969 |
548 | return; |
549 | } |
550 | |
551 | /* --- Do the initial multiply and initialize the accumulator --- */ |
552 | |
553 | MPX_UMULN(dv, dvl, av, avl, *bv++); |
554 | |
555 | /* --- Do the remaining multiply/accumulates --- */ |
556 | |
c8a2f9ef |
557 | while (dv < dvl && bv < bvl) { |
d03ab969 |
558 | mpw m = *bv++; |
c8a2f9ef |
559 | mpw c = 0; |
d03ab969 |
560 | const mpw *avv = av; |
561 | mpw *dvv = ++dv; |
562 | |
563 | while (avv < avl) { |
564 | mpd x; |
565 | if (dvv >= dvl) |
566 | goto next; |
c8a2f9ef |
567 | x = (mpd)*dvv + (mpd)m * (mpd)*avv++ + c; |
568 | *dvv++ = MPW(x); |
d03ab969 |
569 | c = x >> MPW_BITS; |
570 | } |
c8a2f9ef |
571 | MPX_UADDN(dvv, dvl, c); |
d03ab969 |
572 | next:; |
573 | } |
574 | } |
575 | |
c8a2f9ef |
576 | /* --- @mpx_usqr@ --- * |
577 | * |
578 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
579 | * @const mpw *av, *av@ = source vector base and limit |
580 | * |
581 | * Returns: --- |
582 | * |
583 | * Use: Performs unsigned integer squaring. The result vector must |
584 | * not overlap the source vector in any way. |
585 | */ |
586 | |
587 | void mpx_usqr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl) |
588 | { |
589 | MPX_ZERO(dv, dvl); |
590 | |
591 | /* --- Main loop --- */ |
592 | |
593 | while (av < avl) { |
594 | const mpw *avv = av; |
595 | mpw *dvv = dv; |
596 | mpw a = *av; |
597 | mpd c; |
598 | |
599 | /* --- Stop if I've run out of destination --- */ |
600 | |
601 | if (dvv >= dvl) |
602 | break; |
603 | |
604 | /* --- Work out the square at this point in the proceedings --- */ |
605 | |
606 | { |
c8a2f9ef |
607 | mpd x = (mpd)a * (mpd)a + *dvv; |
608 | *dvv++ = MPW(x); |
609 | c = MPW(x >> MPW_BITS); |
610 | } |
611 | |
612 | /* --- Now fix up the rest of the vector upwards --- */ |
613 | |
614 | avv++; |
615 | while (dvv < dvl && avv < avl) { |
c8a2f9ef |
616 | mpd x = (mpd)a * (mpd)*avv++; |
617 | mpd y = ((x << 1) & MPW_MAX) + c + *dvv; |
618 | c = (x >> (MPW_BITS - 1)) + (y >> MPW_BITS); |
619 | *dvv++ = MPW(y); |
620 | } |
621 | while (dvv < dvl && c) { |
622 | mpd x = c + *dvv; |
623 | *dvv++ = MPW(x); |
624 | c = x >> MPW_BITS; |
625 | } |
626 | |
627 | /* --- Get ready for the next round --- */ |
628 | |
629 | av++; |
630 | dv += 2; |
631 | } |
632 | } |
633 | |
d03ab969 |
634 | /* --- @mpx_udiv@ --- * |
635 | * |
636 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
637 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
638 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
c8a2f9ef |
639 | * @mpw *sv, *svl@ = scratch workspace |
d03ab969 |
640 | * |
641 | * Returns: --- |
642 | * |
643 | * Use: Performs unsigned integer division. If the result overflows |
644 | * the quotient vector, high-order bits are discarded. (Clearly |
645 | * the remainder vector can't overflow.) The various vectors |
646 | * may not overlap in any way. Yes, I know it's a bit odd |
647 | * requiring the dividend to be in the result position but it |
648 | * does make some sense really. The remainder must have |
c8a2f9ef |
649 | * headroom for at least two extra words. The scratch space |
f45a00c6 |
650 | * must be at least one word larger than the divisor. |
d03ab969 |
651 | */ |
652 | |
653 | void mpx_udiv(mpw *qv, mpw *qvl, mpw *rv, mpw *rvl, |
c8a2f9ef |
654 | const mpw *dv, const mpw *dvl, |
655 | mpw *sv, mpw *svl) |
d03ab969 |
656 | { |
d03ab969 |
657 | unsigned norm = 0; |
658 | size_t scale; |
659 | mpw d, dd; |
660 | |
661 | /* --- Initialize the quotient --- */ |
662 | |
663 | MPX_ZERO(qv, qvl); |
664 | |
c8a2f9ef |
665 | /* --- Perform some sanity checks --- */ |
666 | |
667 | MPX_SHRINK(dv, dvl); |
668 | assert(((void)"division by zero in mpx_udiv", dv < dvl)); |
669 | |
d03ab969 |
670 | /* --- Normalize the divisor --- * |
671 | * |
672 | * The algorithm requires that the divisor be at least two digits long. |
673 | * This is easy to fix. |
674 | */ |
675 | |
c8a2f9ef |
676 | { |
677 | unsigned b; |
d03ab969 |
678 | |
c8a2f9ef |
679 | d = dvl[-1]; |
680 | for (b = MPW_BITS / 2; b; b >>= 1) { |
681 | if (d < (MPW_MAX >> b)) { |
682 | d <<= b; |
683 | norm += b; |
684 | } |
685 | } |
686 | if (dv + 1 == dvl) |
687 | norm += MPW_BITS; |
d03ab969 |
688 | } |
d03ab969 |
689 | |
690 | /* --- Normalize the dividend/remainder to match --- */ |
691 | |
c8a2f9ef |
692 | if (norm) { |
c8a2f9ef |
693 | mpx_lsl(rv, rvl, rv, rvl, norm); |
f45a00c6 |
694 | mpx_lsl(sv, svl, dv, dvl, norm); |
c8a2f9ef |
695 | dv = sv; |
f45a00c6 |
696 | dvl = svl; |
c8a2f9ef |
697 | MPX_SHRINK(dv, dvl); |
698 | } |
699 | |
d03ab969 |
700 | MPX_SHRINK(rv, rvl); |
c8a2f9ef |
701 | d = dvl[-1]; |
702 | dd = dvl[-2]; |
d03ab969 |
703 | |
704 | /* --- Work out the relative scales --- */ |
705 | |
706 | { |
707 | size_t rvn = rvl - rv; |
c8a2f9ef |
708 | size_t dvn = dvl - dv; |
d03ab969 |
709 | |
710 | /* --- If the divisor is clearly larger, notice this --- */ |
711 | |
712 | if (dvn > rvn) { |
713 | mpx_lsr(rv, rvl, rv, rvl, norm); |
714 | return; |
715 | } |
716 | |
717 | scale = rvn - dvn; |
718 | } |
719 | |
720 | /* --- Calculate the most significant quotient digit --- * |
721 | * |
722 | * Because the divisor has its top bit set, this can only happen once. The |
723 | * pointer arithmetic is a little contorted, to make sure that the |
724 | * behaviour is defined. |
725 | */ |
726 | |
727 | if (MPX_UCMP(rv + scale, rvl, >=, dv, dvl)) { |
728 | mpx_usub(rv + scale, rvl, rv + scale, rvl, dv, dvl); |
729 | if (qvl - qv > scale) |
730 | qv[scale] = 1; |
731 | } |
732 | |
733 | /* --- Now for the main loop --- */ |
734 | |
735 | { |
c8a2f9ef |
736 | mpw *rvv = rvl - 2; |
d03ab969 |
737 | |
738 | while (scale) { |
c8a2f9ef |
739 | mpw q; |
740 | mpd rh; |
d03ab969 |
741 | |
742 | /* --- Get an estimate for the next quotient digit --- */ |
743 | |
c8a2f9ef |
744 | mpw r = rvv[1]; |
745 | mpw rr = rvv[0]; |
746 | mpw rrr = *--rvv; |
747 | |
748 | scale--; |
749 | rh = ((mpd)r << MPW_BITS) | rr; |
d03ab969 |
750 | if (r == d) |
751 | q = MPW_MAX; |
c8a2f9ef |
752 | else |
753 | q = MPW(rh / d); |
d03ab969 |
754 | |
755 | /* --- Refine the estimate --- */ |
756 | |
757 | { |
758 | mpd yh = (mpd)d * q; |
759 | mpd yl = (mpd)dd * q; |
c8a2f9ef |
760 | |
761 | if (yl > MPW_MAX) { |
762 | yh += yl >> MPW_BITS; |
763 | yl &= MPW_MAX; |
764 | } |
765 | |
766 | while (yh > rh || (yh == rh && yl > rrr)) { |
767 | q--; |
768 | yh -= d; |
769 | if (yl < dd) { |
770 | yh++; |
771 | yl += MPW_MAX; |
772 | } |
773 | yl -= dd; |
774 | } |
775 | } |
776 | |
777 | /* --- Remove a chunk from the dividend --- */ |
778 | |
779 | { |
780 | mpw *svv; |
781 | const mpw *dvv; |
f45a00c6 |
782 | mpw mc = 0, sc = 0; |
c8a2f9ef |
783 | |
f45a00c6 |
784 | /* --- Calculate the size of the chunk --- * |
785 | * |
786 | * This does the whole job of calculating @r >> scale - qd@. |
787 | */ |
c8a2f9ef |
788 | |
f45a00c6 |
789 | for (svv = rv + scale, dvv = dv; |
790 | dvv < dvl && svv < rvl; |
791 | svv++, dvv++) { |
792 | mpd x = (mpd)*dvv * (mpd)q + mc; |
793 | mc = x >> MPW_BITS; |
794 | x = (mpd)*svv - MPW(x) - sc; |
c8a2f9ef |
795 | *svv = MPW(x); |
f45a00c6 |
796 | if (x >> MPW_BITS) |
797 | sc = 1; |
798 | else |
799 | sc = 0; |
800 | } |
801 | |
802 | if (svv < rvl) { |
803 | mpd x = (mpd)*svv - mc - sc; |
804 | *svv++ = MPW(x); |
805 | if (x >> MPW_BITS) |
806 | sc = MPW_MAX; |
807 | else |
808 | sc = 0; |
809 | while (svv < rvl) |
810 | *svv++ = sc; |
c8a2f9ef |
811 | } |
c8a2f9ef |
812 | |
f45a00c6 |
813 | /* --- Fix if the quotient was too large --- * |
c8a2f9ef |
814 | * |
f45a00c6 |
815 | * This doesn't seem to happen very often. |
c8a2f9ef |
816 | */ |
817 | |
c8a2f9ef |
818 | if (rvl[-1] > MPW_MAX / 2) { |
819 | mpx_uadd(rv + scale, rvl, rv + scale, rvl, dv, dvl); |
820 | q--; |
821 | } |
822 | } |
823 | |
824 | /* --- Done for another iteration --- */ |
825 | |
826 | if (qvl - qv > scale) |
827 | qv[scale] = q; |
828 | r = rr; |
829 | rr = rrr; |
830 | } |
831 | } |
832 | |
833 | /* --- Now fiddle with unnormalizing and things --- */ |
834 | |
835 | mpx_lsr(rv, rvl, rv, rvl, norm); |
d03ab969 |
836 | } |
837 | |
838 | /*----- That's all, folks -------------------------------------------------*/ |