d03ab969 |
1 | /* -*-c-*- |
2 | * |
dd517851 |
3 | * $Id: mpx.c,v 1.5 1999/11/20 22:23:27 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 $ |
dd517851 |
33 | * Revision 1.5 1999/11/20 22:23:27 mdw |
34 | * Add function versions of some low-level macros with wider use. |
35 | * |
f45a00c6 |
36 | * Revision 1.4 1999/11/17 18:04:09 mdw |
37 | * Add two's-complement functionality. Improve mpx_udiv a little by |
38 | * performing the multiplication of the divisor by q with the subtraction |
39 | * from r. |
40 | * |
501da53c |
41 | * Revision 1.3 1999/11/13 01:57:31 mdw |
42 | * Remove stray debugging code. |
43 | * |
c8a2f9ef |
44 | * Revision 1.2 1999/11/13 01:50:59 mdw |
45 | * Multiprecision routines finished and tested. |
46 | * |
d03ab969 |
47 | * Revision 1.1 1999/09/03 08:41:12 mdw |
48 | * Initial import. |
49 | * |
50 | */ |
51 | |
52 | /*----- Header files ------------------------------------------------------*/ |
53 | |
c8a2f9ef |
54 | #include <assert.h> |
d03ab969 |
55 | #include <stdio.h> |
56 | #include <stdlib.h> |
57 | #include <string.h> |
58 | |
59 | #include <mLib/bits.h> |
60 | |
61 | #include "mptypes.h" |
62 | #include "mpx.h" |
63 | |
64 | /*----- Loading and storing -----------------------------------------------*/ |
65 | |
66 | /* --- @mpx_storel@ --- * |
67 | * |
68 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
c8a2f9ef |
69 | * @void *pp@ = pointer to octet array |
d03ab969 |
70 | * @size_t sz@ = size of octet array |
71 | * |
72 | * Returns: --- |
73 | * |
74 | * Use: Stores an MP in an octet array, least significant octet |
75 | * first. High-end octets are silently discarded if there |
76 | * isn't enough space for them. |
77 | */ |
78 | |
c8a2f9ef |
79 | void mpx_storel(const mpw *v, const mpw *vl, void *pp, size_t sz) |
d03ab969 |
80 | { |
81 | mpw n, w = 0; |
c8a2f9ef |
82 | octet *p = pp, *q = p + sz; |
d03ab969 |
83 | unsigned bits = 0; |
84 | |
85 | while (p < q) { |
86 | if (bits < 8) { |
87 | if (v >= vl) { |
88 | *p++ = U8(w); |
89 | break; |
90 | } |
91 | n = *v++; |
92 | *p++ = U8(w | n << bits); |
93 | w = n >> (8 - bits); |
94 | bits += MPW_BITS - 8; |
95 | } else { |
96 | *p++ = U8(w); |
97 | w >>= 8; |
98 | bits -= 8; |
99 | } |
100 | } |
101 | memset(p, 0, q - p); |
102 | } |
103 | |
104 | /* --- @mpx_loadl@ --- * |
105 | * |
106 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
c8a2f9ef |
107 | * @const void *pp@ = pointer to octet array |
d03ab969 |
108 | * @size_t sz@ = size of octet array |
109 | * |
110 | * Returns: --- |
111 | * |
112 | * Use: Loads an MP in an octet array, least significant octet |
113 | * first. High-end octets are ignored if there isn't enough |
114 | * space for them. |
115 | */ |
116 | |
c8a2f9ef |
117 | void mpx_loadl(mpw *v, mpw *vl, const void *pp, size_t sz) |
d03ab969 |
118 | { |
119 | unsigned n; |
c8a2f9ef |
120 | mpw w = 0; |
121 | const octet *p = pp, *q = p + sz; |
d03ab969 |
122 | unsigned bits = 0; |
123 | |
124 | if (v >= vl) |
125 | return; |
126 | while (p < q) { |
127 | n = U8(*p++); |
128 | w |= n << bits; |
129 | bits += 8; |
130 | if (bits >= MPW_BITS) { |
131 | *v++ = MPW(w); |
132 | w = n >> (MPW_BITS - bits + 8); |
133 | bits -= MPW_BITS; |
134 | if (v >= vl) |
135 | return; |
136 | } |
137 | } |
138 | *v++ = w; |
139 | MPX_ZERO(v, vl); |
140 | } |
141 | |
142 | /* --- @mpx_storeb@ --- * |
143 | * |
144 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
c8a2f9ef |
145 | * @void *pp@ = pointer to octet array |
d03ab969 |
146 | * @size_t sz@ = size of octet array |
147 | * |
148 | * Returns: --- |
149 | * |
150 | * Use: Stores an MP in an octet array, most significant octet |
151 | * first. High-end octets are silently discarded if there |
152 | * isn't enough space for them. |
153 | */ |
154 | |
c8a2f9ef |
155 | void mpx_storeb(const mpw *v, const mpw *vl, void *pp, size_t sz) |
d03ab969 |
156 | { |
157 | mpw n, w = 0; |
c8a2f9ef |
158 | octet *p = pp, *q = p + sz; |
d03ab969 |
159 | unsigned bits = 0; |
160 | |
161 | while (q > p) { |
162 | if (bits < 8) { |
163 | if (v >= vl) { |
164 | *--q = U8(w); |
165 | break; |
166 | } |
167 | n = *v++; |
168 | *--q = U8(w | n << bits); |
169 | w = n >> (8 - bits); |
170 | bits += MPW_BITS - 8; |
171 | } else { |
172 | *--q = U8(w); |
173 | w >>= 8; |
174 | bits -= 8; |
175 | } |
176 | } |
177 | memset(p, 0, q - p); |
178 | } |
179 | |
180 | /* --- @mpx_loadb@ --- * |
181 | * |
182 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
c8a2f9ef |
183 | * @const void *pp@ = pointer to octet array |
d03ab969 |
184 | * @size_t sz@ = size of octet array |
185 | * |
186 | * Returns: --- |
187 | * |
188 | * Use: Loads an MP in an octet array, most significant octet |
189 | * first. High-end octets are ignored if there isn't enough |
190 | * space for them. |
191 | */ |
192 | |
c8a2f9ef |
193 | void mpx_loadb(mpw *v, mpw *vl, const void *pp, size_t sz) |
d03ab969 |
194 | { |
195 | unsigned n; |
c8a2f9ef |
196 | mpw w = 0; |
197 | const octet *p = pp, *q = p + sz; |
d03ab969 |
198 | unsigned bits = 0; |
199 | |
200 | if (v >= vl) |
201 | return; |
202 | while (q > p) { |
203 | n = U8(*--q); |
204 | w |= n << bits; |
205 | bits += 8; |
206 | if (bits >= MPW_BITS) { |
207 | *v++ = MPW(w); |
208 | w = n >> (MPW_BITS - bits + 8); |
209 | bits -= MPW_BITS; |
210 | if (v >= vl) |
211 | return; |
212 | } |
213 | } |
214 | *v++ = w; |
215 | MPX_ZERO(v, vl); |
216 | } |
217 | |
218 | /*----- Logical shifting --------------------------------------------------*/ |
219 | |
220 | /* --- @mpx_lsl@ --- * |
221 | * |
222 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
223 | * @const mpw *av, *avl@ = source vector base and limit |
224 | * @size_t n@ = number of bit positions to shift by |
225 | * |
226 | * Returns: --- |
227 | * |
228 | * Use: Performs a logical shift left operation on an integer. |
229 | */ |
230 | |
231 | void mpx_lsl(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
232 | { |
233 | size_t nw; |
234 | unsigned nb; |
235 | |
236 | /* --- Trivial special case --- */ |
237 | |
238 | if (n == 0) |
239 | MPX_COPY(dv, dvl, av, avl); |
240 | |
241 | /* --- Single bit shifting --- */ |
242 | |
243 | else if (n == 1) { |
244 | mpw w = 0; |
245 | while (av < avl) { |
246 | mpw t; |
247 | if (dv >= dvl) |
248 | goto done; |
249 | t = *av++; |
250 | *dv++ = MPW((t << 1) | w); |
251 | w = t >> (MPW_BITS - 1); |
252 | } |
253 | if (dv >= dvl) |
254 | goto done; |
255 | *dv++ = MPW(w); |
256 | MPX_ZERO(dv, dvl); |
c8a2f9ef |
257 | goto done; |
d03ab969 |
258 | } |
259 | |
260 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
261 | |
262 | nw = n / MPW_BITS; |
263 | nb = n % MPW_BITS; |
264 | |
265 | /* --- Handle a shift by a multiple of the word size --- */ |
266 | |
267 | if (nb == 0) { |
268 | MPX_COPY(dv + nw, dvl, av, avl); |
269 | memset(dv, 0, MPWS(nw)); |
270 | } |
271 | |
c8a2f9ef |
272 | /* --- And finally the difficult case --- * |
273 | * |
274 | * This is a little convoluted, because I have to start from the end and |
275 | * work backwards to avoid overwriting the source, if they're both the same |
276 | * block of memory. |
277 | */ |
d03ab969 |
278 | |
279 | else { |
280 | mpw w; |
281 | size_t nr = MPW_BITS - nb; |
c8a2f9ef |
282 | size_t dvn = dvl - dv; |
283 | size_t avn = avl - av; |
d03ab969 |
284 | |
c8a2f9ef |
285 | if (dvn <= nw) { |
d03ab969 |
286 | MPX_ZERO(dv, dvl); |
287 | goto done; |
288 | } |
d03ab969 |
289 | |
c8a2f9ef |
290 | if (dvn > avn + nw) { |
291 | size_t off = avn + nw + 1; |
292 | MPX_ZERO(dv + off, dvl); |
293 | dvl = dv + off; |
294 | w = 0; |
295 | } else { |
296 | avl = av + dvn - nw; |
297 | w = *--avl << nb; |
d03ab969 |
298 | } |
299 | |
c8a2f9ef |
300 | while (avl > av) { |
301 | mpw t = *--avl; |
302 | *--dvl = (t >> nr) | w; |
303 | w = t << nb; |
d03ab969 |
304 | } |
c8a2f9ef |
305 | |
306 | *--dvl = w; |
307 | MPX_ZERO(dv, dvl); |
d03ab969 |
308 | } |
309 | |
310 | done:; |
311 | } |
312 | |
313 | /* --- @mpx_lsr@ --- * |
314 | * |
315 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
316 | * @const mpw *av, *avl@ = source vector base and limit |
317 | * @size_t n@ = number of bit positions to shift by |
318 | * |
319 | * Returns: --- |
320 | * |
321 | * Use: Performs a logical shift right operation on an integer. |
322 | */ |
323 | |
324 | void mpx_lsr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
325 | { |
326 | size_t nw; |
327 | unsigned nb; |
328 | |
329 | /* --- Trivial special case --- */ |
330 | |
331 | if (n == 0) |
332 | MPX_COPY(dv, dvl, av, avl); |
333 | |
334 | /* --- Single bit shifting --- */ |
335 | |
336 | else if (n == 1) { |
337 | mpw w = *av++ >> 1; |
338 | while (av < avl) { |
339 | mpw t; |
340 | if (dv >= dvl) |
341 | goto done; |
342 | t = *av++; |
343 | *dv++ = MPW((t << (MPW_BITS - 1)) | w); |
344 | w = t >> 1; |
345 | } |
346 | if (dv >= dvl) |
347 | goto done; |
348 | *dv++ = MPW(w); |
349 | MPX_ZERO(dv, dvl); |
c8a2f9ef |
350 | goto done; |
d03ab969 |
351 | } |
352 | |
353 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
354 | |
355 | nw = n / MPW_BITS; |
356 | nb = n % MPW_BITS; |
357 | |
358 | /* --- Handle a shift by a multiple of the word size --- */ |
359 | |
360 | if (nb == 0) |
361 | MPX_COPY(dv, dvl, av + nw, avl); |
362 | |
363 | /* --- And finally the difficult case --- */ |
364 | |
365 | else { |
366 | mpw w; |
367 | size_t nr = MPW_BITS - nb; |
368 | |
369 | av += nw; |
370 | w = *av++; |
371 | while (av < avl) { |
372 | mpw t; |
373 | if (dv >= dvl) |
374 | goto done; |
375 | t = *av++; |
376 | *dv++ = MPW((w >> nb) | (t << nr)); |
377 | w = t; |
378 | } |
379 | if (dv < dvl) { |
380 | *dv++ = MPW(w >> nb); |
381 | MPX_ZERO(dv, dvl); |
382 | } |
383 | } |
384 | |
385 | done:; |
386 | } |
387 | |
388 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
389 | |
f45a00c6 |
390 | /* --- @mpx_2c@ --- * |
391 | * |
392 | * Arguments: @mpw *dv, *dvl@ = destination vector |
393 | * @const mpw *v, *vl@ = source vector |
394 | * |
395 | * Returns: --- |
396 | * |
397 | * Use: Calculates the two's complement of @v@. |
398 | */ |
399 | |
400 | void mpx_2c(mpw *dv, mpw *dvl, const mpw *v, const mpw *vl) |
401 | { |
402 | mpw c = 0; |
403 | while (dv < dvl && v < vl) |
404 | *dv++ = c = MPW(~*v++); |
405 | if (dv < dvl) { |
406 | if (c > MPW_MAX / 2) |
407 | c = MPW(~0); |
408 | while (dv < dvl) |
409 | *dv++ = c; |
410 | } |
411 | MPX_UADDN(dv, dvl, 1); |
412 | } |
413 | |
d03ab969 |
414 | /* --- @mpx_ucmp@ --- * |
415 | * |
416 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
417 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
418 | * |
419 | * Returns: Less than, equal to, or greater than zero depending on |
420 | * whether @a@ is less than, equal to or greater than @b@, |
421 | * respectively. |
422 | * |
423 | * Use: Performs an unsigned integer comparison. |
424 | */ |
425 | |
426 | int mpx_ucmp(const mpw *av, const mpw *avl, const mpw *bv, const mpw *bvl) |
427 | { |
428 | MPX_SHRINK(av, avl); |
429 | MPX_SHRINK(bv, bvl); |
430 | |
431 | if (avl - av > bvl - bv) |
432 | return (+1); |
433 | else if (avl - av < bvl - bv) |
434 | return (-1); |
435 | else while (avl > av) { |
436 | mpw a = *--avl, b = *--bvl; |
437 | if (a > b) |
438 | return (+1); |
439 | else if (a < b) |
440 | return (-1); |
441 | } |
442 | return (0); |
443 | } |
444 | |
445 | /* --- @mpx_uadd@ --- * |
446 | * |
447 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
448 | * @const mpw *av, *avl@ = first addend vector base and limit |
449 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
450 | * |
451 | * Returns: --- |
452 | * |
453 | * Use: Performs unsigned integer addition. If the result overflows |
454 | * the destination vector, high-order bits are discarded. This |
455 | * means that two's complement addition happens more or less for |
456 | * free, although that's more a side-effect than anything else. |
457 | * The result vector may be equal to either or both source |
458 | * vectors, but may not otherwise overlap them. |
459 | */ |
460 | |
461 | void mpx_uadd(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
462 | const mpw *bv, const mpw *bvl) |
463 | { |
464 | mpw c = 0; |
465 | |
466 | while (av < avl || bv < bvl) { |
467 | mpw a, b; |
468 | mpd x; |
469 | if (dv >= dvl) |
470 | return; |
471 | a = (av < avl) ? *av++ : 0; |
472 | b = (bv < bvl) ? *bv++ : 0; |
473 | x = (mpd)a + (mpd)b + c; |
474 | *dv++ = MPW(x); |
475 | c = x >> MPW_BITS; |
476 | } |
477 | if (dv < dvl) { |
478 | *dv++ = c; |
479 | MPX_ZERO(dv, dvl); |
480 | } |
481 | } |
482 | |
dd517851 |
483 | /* --- @mpx_uaddn@ --- * |
484 | * |
485 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
486 | * @mpw n@ = other addend |
487 | * |
488 | * Returns: --- |
489 | * |
490 | * Use: Adds a small integer to a multiprecision number. |
491 | */ |
492 | |
493 | void mpx_uaddn(mpw *dv, mpw *dvl, mpw n) { MPX_UADDN(dv, dvl, n); } |
494 | |
d03ab969 |
495 | /* --- @mpx_usub@ --- * |
496 | * |
497 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
498 | * @const mpw *av, *avl@ = first argument vector base and limit |
499 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
500 | * |
501 | * Returns: --- |
502 | * |
503 | * Use: Performs unsigned integer subtraction. If the result |
504 | * overflows the destination vector, high-order bits are |
505 | * discarded. This means that two's complement subtraction |
506 | * happens more or less for free, althuogh that's more a side- |
507 | * effect than anything else. The result vector may be equal to |
508 | * either or both source vectors, but may not otherwise overlap |
509 | * them. |
510 | */ |
511 | |
512 | void mpx_usub(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
513 | const mpw *bv, const mpw *bvl) |
514 | { |
515 | mpw c = 0; |
516 | |
517 | while (av < avl || bv < bvl) { |
518 | mpw a, b; |
519 | mpd x; |
520 | if (dv >= dvl) |
521 | return; |
522 | a = (av < avl) ? *av++ : 0; |
523 | b = (bv < bvl) ? *bv++ : 0; |
c8a2f9ef |
524 | x = (mpd)a - (mpd)b - c; |
d03ab969 |
525 | *dv++ = MPW(x); |
c8a2f9ef |
526 | if (x >> MPW_BITS) |
527 | c = 1; |
528 | else |
529 | c = 0; |
d03ab969 |
530 | } |
c8a2f9ef |
531 | if (c) |
532 | c = MPW_MAX; |
d03ab969 |
533 | while (dv < dvl) |
c8a2f9ef |
534 | *dv++ = c; |
d03ab969 |
535 | } |
536 | |
dd517851 |
537 | /* --- @mpx_usubn@ --- * |
538 | * |
539 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
540 | * @n@ = subtrahend |
541 | * |
542 | * Returns: --- |
543 | * |
544 | * Use: Subtracts a small integer from a multiprecision number. |
545 | */ |
546 | |
547 | void mpx_usubn(mpw *dv, mpw *dvl, mpw n) { MPX_USUBN(dv, dvl, n); } |
548 | |
d03ab969 |
549 | /* --- @mpx_umul@ --- * |
550 | * |
551 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
552 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
553 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
554 | * |
555 | * Returns: --- |
556 | * |
557 | * Use: Performs unsigned integer multiplication. If the result |
558 | * overflows the desination vector, high-order bits are |
559 | * discarded. The result vector may not overlap the argument |
560 | * vectors in any way. |
561 | */ |
562 | |
563 | void mpx_umul(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
564 | const mpw *bv, const mpw *bvl) |
565 | { |
566 | /* --- This is probably worthwhile on a multiply --- */ |
567 | |
568 | MPX_SHRINK(av, avl); |
569 | MPX_SHRINK(bv, bvl); |
570 | |
571 | /* --- Deal with a multiply by zero --- */ |
572 | |
573 | if (bv == bvl) { |
c8a2f9ef |
574 | MPX_ZERO(dv, dvl); |
d03ab969 |
575 | return; |
576 | } |
577 | |
578 | /* --- Do the initial multiply and initialize the accumulator --- */ |
579 | |
580 | MPX_UMULN(dv, dvl, av, avl, *bv++); |
581 | |
582 | /* --- Do the remaining multiply/accumulates --- */ |
583 | |
c8a2f9ef |
584 | while (dv < dvl && bv < bvl) { |
d03ab969 |
585 | mpw m = *bv++; |
c8a2f9ef |
586 | mpw c = 0; |
d03ab969 |
587 | const mpw *avv = av; |
588 | mpw *dvv = ++dv; |
589 | |
590 | while (avv < avl) { |
591 | mpd x; |
592 | if (dvv >= dvl) |
593 | goto next; |
c8a2f9ef |
594 | x = (mpd)*dvv + (mpd)m * (mpd)*avv++ + c; |
595 | *dvv++ = MPW(x); |
d03ab969 |
596 | c = x >> MPW_BITS; |
597 | } |
c8a2f9ef |
598 | MPX_UADDN(dvv, dvl, c); |
d03ab969 |
599 | next:; |
600 | } |
601 | } |
602 | |
dd517851 |
603 | /* --- @mpx_umuln@ --- * |
604 | * |
605 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
606 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
607 | * @mpw m@ = multiplier |
608 | * |
609 | * Returns: --- |
610 | * |
611 | * Use: Multiplies a multiprecision integer by a single-word value. |
612 | * The destination and source may be equal. The destination |
613 | * is completely cleared after use. |
614 | */ |
615 | |
616 | void mpx_umuln(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, mpw m) |
617 | { |
618 | MPX_UMULN(dv, dvl, av, avl, m); |
619 | } |
620 | |
621 | /* --- @mpx_umlan@ --- * |
622 | * |
623 | * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit |
624 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
625 | * @mpw m@ = multiplier |
626 | * |
627 | * Returns: --- |
628 | * |
629 | * Use: Multiplies a multiprecision integer by a single-word value |
630 | * and adds the result to an accumulator. |
631 | */ |
632 | |
633 | void mpx_umlan(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, mpw m) |
634 | { |
635 | MPX_UMLAN(dv, dvl, av, avl, m); |
636 | } |
637 | |
c8a2f9ef |
638 | /* --- @mpx_usqr@ --- * |
639 | * |
640 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
641 | * @const mpw *av, *av@ = source vector base and limit |
642 | * |
643 | * Returns: --- |
644 | * |
645 | * Use: Performs unsigned integer squaring. The result vector must |
646 | * not overlap the source vector in any way. |
647 | */ |
648 | |
649 | void mpx_usqr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl) |
650 | { |
651 | MPX_ZERO(dv, dvl); |
652 | |
653 | /* --- Main loop --- */ |
654 | |
655 | while (av < avl) { |
656 | const mpw *avv = av; |
657 | mpw *dvv = dv; |
658 | mpw a = *av; |
659 | mpd c; |
660 | |
661 | /* --- Stop if I've run out of destination --- */ |
662 | |
663 | if (dvv >= dvl) |
664 | break; |
665 | |
666 | /* --- Work out the square at this point in the proceedings --- */ |
667 | |
668 | { |
c8a2f9ef |
669 | mpd x = (mpd)a * (mpd)a + *dvv; |
670 | *dvv++ = MPW(x); |
671 | c = MPW(x >> MPW_BITS); |
672 | } |
673 | |
674 | /* --- Now fix up the rest of the vector upwards --- */ |
675 | |
676 | avv++; |
677 | while (dvv < dvl && avv < avl) { |
c8a2f9ef |
678 | mpd x = (mpd)a * (mpd)*avv++; |
679 | mpd y = ((x << 1) & MPW_MAX) + c + *dvv; |
680 | c = (x >> (MPW_BITS - 1)) + (y >> MPW_BITS); |
681 | *dvv++ = MPW(y); |
682 | } |
683 | while (dvv < dvl && c) { |
684 | mpd x = c + *dvv; |
685 | *dvv++ = MPW(x); |
686 | c = x >> MPW_BITS; |
687 | } |
688 | |
689 | /* --- Get ready for the next round --- */ |
690 | |
691 | av++; |
692 | dv += 2; |
693 | } |
694 | } |
695 | |
d03ab969 |
696 | /* --- @mpx_udiv@ --- * |
697 | * |
698 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
699 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
700 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
c8a2f9ef |
701 | * @mpw *sv, *svl@ = scratch workspace |
d03ab969 |
702 | * |
703 | * Returns: --- |
704 | * |
705 | * Use: Performs unsigned integer division. If the result overflows |
706 | * the quotient vector, high-order bits are discarded. (Clearly |
707 | * the remainder vector can't overflow.) The various vectors |
708 | * may not overlap in any way. Yes, I know it's a bit odd |
709 | * requiring the dividend to be in the result position but it |
710 | * does make some sense really. The remainder must have |
c8a2f9ef |
711 | * headroom for at least two extra words. The scratch space |
f45a00c6 |
712 | * must be at least one word larger than the divisor. |
d03ab969 |
713 | */ |
714 | |
715 | void mpx_udiv(mpw *qv, mpw *qvl, mpw *rv, mpw *rvl, |
c8a2f9ef |
716 | const mpw *dv, const mpw *dvl, |
717 | mpw *sv, mpw *svl) |
d03ab969 |
718 | { |
d03ab969 |
719 | unsigned norm = 0; |
720 | size_t scale; |
721 | mpw d, dd; |
722 | |
723 | /* --- Initialize the quotient --- */ |
724 | |
725 | MPX_ZERO(qv, qvl); |
726 | |
c8a2f9ef |
727 | /* --- Perform some sanity checks --- */ |
728 | |
729 | MPX_SHRINK(dv, dvl); |
730 | assert(((void)"division by zero in mpx_udiv", dv < dvl)); |
731 | |
d03ab969 |
732 | /* --- Normalize the divisor --- * |
733 | * |
734 | * The algorithm requires that the divisor be at least two digits long. |
735 | * This is easy to fix. |
736 | */ |
737 | |
c8a2f9ef |
738 | { |
739 | unsigned b; |
d03ab969 |
740 | |
c8a2f9ef |
741 | d = dvl[-1]; |
742 | for (b = MPW_BITS / 2; b; b >>= 1) { |
743 | if (d < (MPW_MAX >> b)) { |
744 | d <<= b; |
745 | norm += b; |
746 | } |
747 | } |
748 | if (dv + 1 == dvl) |
749 | norm += MPW_BITS; |
d03ab969 |
750 | } |
d03ab969 |
751 | |
752 | /* --- Normalize the dividend/remainder to match --- */ |
753 | |
c8a2f9ef |
754 | if (norm) { |
c8a2f9ef |
755 | mpx_lsl(rv, rvl, rv, rvl, norm); |
f45a00c6 |
756 | mpx_lsl(sv, svl, dv, dvl, norm); |
c8a2f9ef |
757 | dv = sv; |
f45a00c6 |
758 | dvl = svl; |
c8a2f9ef |
759 | MPX_SHRINK(dv, dvl); |
760 | } |
761 | |
d03ab969 |
762 | MPX_SHRINK(rv, rvl); |
c8a2f9ef |
763 | d = dvl[-1]; |
764 | dd = dvl[-2]; |
d03ab969 |
765 | |
766 | /* --- Work out the relative scales --- */ |
767 | |
768 | { |
769 | size_t rvn = rvl - rv; |
c8a2f9ef |
770 | size_t dvn = dvl - dv; |
d03ab969 |
771 | |
772 | /* --- If the divisor is clearly larger, notice this --- */ |
773 | |
774 | if (dvn > rvn) { |
775 | mpx_lsr(rv, rvl, rv, rvl, norm); |
776 | return; |
777 | } |
778 | |
779 | scale = rvn - dvn; |
780 | } |
781 | |
782 | /* --- Calculate the most significant quotient digit --- * |
783 | * |
784 | * Because the divisor has its top bit set, this can only happen once. The |
785 | * pointer arithmetic is a little contorted, to make sure that the |
786 | * behaviour is defined. |
787 | */ |
788 | |
789 | if (MPX_UCMP(rv + scale, rvl, >=, dv, dvl)) { |
790 | mpx_usub(rv + scale, rvl, rv + scale, rvl, dv, dvl); |
791 | if (qvl - qv > scale) |
792 | qv[scale] = 1; |
793 | } |
794 | |
795 | /* --- Now for the main loop --- */ |
796 | |
797 | { |
c8a2f9ef |
798 | mpw *rvv = rvl - 2; |
d03ab969 |
799 | |
800 | while (scale) { |
c8a2f9ef |
801 | mpw q; |
802 | mpd rh; |
d03ab969 |
803 | |
804 | /* --- Get an estimate for the next quotient digit --- */ |
805 | |
c8a2f9ef |
806 | mpw r = rvv[1]; |
807 | mpw rr = rvv[0]; |
808 | mpw rrr = *--rvv; |
809 | |
810 | scale--; |
811 | rh = ((mpd)r << MPW_BITS) | rr; |
d03ab969 |
812 | if (r == d) |
813 | q = MPW_MAX; |
c8a2f9ef |
814 | else |
815 | q = MPW(rh / d); |
d03ab969 |
816 | |
817 | /* --- Refine the estimate --- */ |
818 | |
819 | { |
820 | mpd yh = (mpd)d * q; |
821 | mpd yl = (mpd)dd * q; |
c8a2f9ef |
822 | |
823 | if (yl > MPW_MAX) { |
824 | yh += yl >> MPW_BITS; |
825 | yl &= MPW_MAX; |
826 | } |
827 | |
828 | while (yh > rh || (yh == rh && yl > rrr)) { |
829 | q--; |
830 | yh -= d; |
831 | if (yl < dd) { |
832 | yh++; |
833 | yl += MPW_MAX; |
834 | } |
835 | yl -= dd; |
836 | } |
837 | } |
838 | |
839 | /* --- Remove a chunk from the dividend --- */ |
840 | |
841 | { |
842 | mpw *svv; |
843 | const mpw *dvv; |
f45a00c6 |
844 | mpw mc = 0, sc = 0; |
c8a2f9ef |
845 | |
f45a00c6 |
846 | /* --- Calculate the size of the chunk --- * |
847 | * |
848 | * This does the whole job of calculating @r >> scale - qd@. |
849 | */ |
c8a2f9ef |
850 | |
f45a00c6 |
851 | for (svv = rv + scale, dvv = dv; |
852 | dvv < dvl && svv < rvl; |
853 | svv++, dvv++) { |
854 | mpd x = (mpd)*dvv * (mpd)q + mc; |
855 | mc = x >> MPW_BITS; |
856 | x = (mpd)*svv - MPW(x) - sc; |
c8a2f9ef |
857 | *svv = MPW(x); |
f45a00c6 |
858 | if (x >> MPW_BITS) |
859 | sc = 1; |
860 | else |
861 | sc = 0; |
862 | } |
863 | |
864 | if (svv < rvl) { |
865 | mpd x = (mpd)*svv - mc - sc; |
866 | *svv++ = MPW(x); |
867 | if (x >> MPW_BITS) |
868 | sc = MPW_MAX; |
869 | else |
870 | sc = 0; |
871 | while (svv < rvl) |
872 | *svv++ = sc; |
c8a2f9ef |
873 | } |
c8a2f9ef |
874 | |
f45a00c6 |
875 | /* --- Fix if the quotient was too large --- * |
c8a2f9ef |
876 | * |
f45a00c6 |
877 | * This doesn't seem to happen very often. |
c8a2f9ef |
878 | */ |
879 | |
c8a2f9ef |
880 | if (rvl[-1] > MPW_MAX / 2) { |
881 | mpx_uadd(rv + scale, rvl, rv + scale, rvl, dv, dvl); |
882 | q--; |
883 | } |
884 | } |
885 | |
886 | /* --- Done for another iteration --- */ |
887 | |
888 | if (qvl - qv > scale) |
889 | qv[scale] = q; |
890 | r = rr; |
891 | rr = rrr; |
892 | } |
893 | } |
894 | |
895 | /* --- Now fiddle with unnormalizing and things --- */ |
896 | |
897 | mpx_lsr(rv, rvl, rv, rvl, norm); |
d03ab969 |
898 | } |
899 | |
900 | /*----- That's all, folks -------------------------------------------------*/ |