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