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