d3409d5e |
1 | /* -*-c-*- |
2 | * |
a69a3efd |
3 | * $Id$ |
d3409d5e |
4 | * |
5 | * Basic arithmetic on multiprecision integers |
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 | |
d3409d5e |
30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include "mp.h" |
33 | |
ef5f4810 |
34 | /*----- Macros ------------------------------------------------------------*/ |
35 | |
36 | #define MAX(x, y) ((x) >= (y) ? (x) : (y)) |
37 | |
d3409d5e |
38 | /*----- Main code ---------------------------------------------------------*/ |
39 | |
81578196 |
40 | /* --- @mp_lsl@, @mp_lslc@, @mp_lsr@ --- * |
d3409d5e |
41 | * |
f09e814a |
42 | * Arguments: @mp *d@ = destination |
43 | * @mp *a@ = source |
44 | * @size_t n@ = number of bits to move |
d3409d5e |
45 | * |
f09e814a |
46 | * Returns: Result, @a@ shifted left or right by @n@. |
81578196 |
47 | * |
48 | * Use: Bitwise shift operators. @mp_lslc@ fills the bits introduced |
49 | * on the right with ones instead of zeroes: it's used |
50 | * internally by @mp_lsl2c@, though it may be useful on its |
51 | * own. |
d3409d5e |
52 | */ |
53 | |
f09e814a |
54 | mp *mp_lsl(mp *d, mp *a, size_t n) |
d3409d5e |
55 | { |
f09e814a |
56 | MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f); |
57 | mpx_lsl(d->v, d->vl, a->v, a->vl, n); |
58 | d->f = a->f & (MP_NEG | MP_BURN); |
59 | MP_SHRINK(d); |
60 | return (d); |
61 | } |
d3409d5e |
62 | |
81578196 |
63 | mp *mp_lslc(mp *d, mp *a, size_t n) |
64 | { |
65 | MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f); |
66 | mpx_lslc(d->v, d->vl, a->v, a->vl, n); |
67 | d->f = a->f & (MP_NEG | MP_BURN); |
68 | MP_SHRINK(d); |
69 | return (d); |
70 | } |
71 | |
f09e814a |
72 | mp *mp_lsr(mp *d, mp *a, size_t n) |
73 | { |
d34decd2 |
74 | MP_DEST(d, MP_LEN(a), a->f); |
f09e814a |
75 | mpx_lsr(d->v, d->vl, a->v, a->vl, n); |
76 | d->f = a->f & (MP_NEG | MP_BURN); |
d3409d5e |
77 | MP_SHRINK(d); |
78 | return (d); |
79 | } |
80 | |
f09e814a |
81 | /* --- @mp_lsl2c@, @mp_lsr2c@ --- * |
d3409d5e |
82 | * |
83 | * Arguments: @mp *d@ = destination |
84 | * @mp *a@ = source |
f09e814a |
85 | * @size_t n@ = number of bits to move |
d3409d5e |
86 | * |
f09e814a |
87 | * Returns: Result, @a@ shifted left or right by @n@. Handles the |
88 | * pretence of sign-extension for negative numbers. |
d3409d5e |
89 | */ |
90 | |
f09e814a |
91 | mp *mp_lsl2c(mp *d, mp *a, size_t n) |
d3409d5e |
92 | { |
a69a3efd |
93 | if (!MP_NEGP(a)) |
f09e814a |
94 | return (mp_lsl(d, a, n)); |
95 | d = mp_not2c(d, a); |
81578196 |
96 | d = mp_lslc(d, d, n); |
f09e814a |
97 | d = mp_not2c(d, d); |
98 | return (d); |
99 | } |
d3409d5e |
100 | |
f09e814a |
101 | mp *mp_lsr2c(mp *d, mp *a, size_t n) |
102 | { |
a69a3efd |
103 | if (!MP_NEGP(a)) |
f09e814a |
104 | return (mp_lsr(d, a, n)); |
105 | d = mp_not2c(d, a); |
106 | d = mp_lsr(d, d, n); |
107 | d = mp_not2c(d, d); |
108 | return (d); |
d3409d5e |
109 | } |
110 | |
f09e814a |
111 | /* --- @mp_testbit@ --- * |
d3409d5e |
112 | * |
f09e814a |
113 | * Arguments: @mp *x@ = a large integer |
09d00c6b |
114 | * @unsigned long n@ = which bit to test |
d3409d5e |
115 | * |
f09e814a |
116 | * Returns: Nonzero if the bit is set, zero if not. |
d3409d5e |
117 | */ |
118 | |
09d00c6b |
119 | int mp_testbit(mp *x, unsigned long n) |
d3409d5e |
120 | { |
f09e814a |
121 | if (n > MPW_BITS * MP_LEN(x)) |
122 | return (0); |
09d00c6b |
123 | return ((x->v[n/MPW_BITS] >> n%MPW_BITS) & 1u); |
d3409d5e |
124 | } |
125 | |
f09e814a |
126 | /* --- @mp_testbit2c@ --- * |
d3409d5e |
127 | * |
f09e814a |
128 | * Arguments: @mp *x@ = a large integer |
09d00c6b |
129 | * @unsigned long n@ = which bit to test |
d3409d5e |
130 | * |
f09e814a |
131 | * Returns: Nonzero if the bit is set, zero if not. Fakes up two's |
132 | * complement representation. |
d3409d5e |
133 | */ |
134 | |
09d00c6b |
135 | int mp_testbit2c(mp *x, unsigned long n) |
d3409d5e |
136 | { |
f09e814a |
137 | int r; |
a69a3efd |
138 | if (!MP_NEGP(x)) |
f09e814a |
139 | return (mp_testbit(x, n)); |
140 | x = mp_not2c(MP_NEW, x); |
141 | r = !mp_testbit(x, n); |
142 | MP_DROP(x); |
143 | return (r); |
d3409d5e |
144 | } |
145 | |
09d00c6b |
146 | /* --- @mp_setbit@, @mp_clearbit@ --- * |
147 | * |
148 | * Arguments: @mp *d@ = a destination |
149 | * @mp *x@ = a large integer |
150 | * @unsigned long n@ = which bit to modify |
151 | * |
152 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
153 | */ |
154 | |
155 | mp *mp_setbit(mp *d, mp *x, unsigned long n) |
156 | { |
157 | size_t rq; |
158 | |
159 | rq = n + MPW_BITS; rq -= rq % MPW_BITS; |
160 | if (d != x) { |
161 | if (d) MP_DROP(d); |
162 | d = MP_COPY(x); |
163 | } |
164 | MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN)); |
165 | d->v[n/MPW_BITS] |= 1 << n%MPW_BITS; |
166 | return (d); |
167 | } |
168 | |
169 | mp *mp_clearbit(mp *d, mp *x, unsigned long n) |
170 | { |
171 | size_t rq; |
172 | |
173 | rq = n + MPW_BITS; rq -= rq % MPW_BITS; |
174 | if (d != x) { |
175 | if (d) MP_DROP(d); |
176 | d = MP_COPY(x); |
177 | } |
178 | MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN)); |
179 | d->v[n/MPW_BITS] &= ~(1 << n%MPW_BITS); |
180 | return (d); |
181 | } |
182 | |
183 | /* --- @mp_setbit2c@, @mp_clearbit2c@ --- * |
184 | * |
185 | * Arguments: @mp *d@ = a destination |
186 | * @mp *x@ = a large integer |
187 | * @unsigned long n@ = which bit to modify |
188 | * |
189 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
190 | * Fakes up two's complement representation. |
191 | */ |
192 | |
193 | mp *mp_setbit2c(mp *d, mp *x, unsigned long n) |
194 | { |
a69a3efd |
195 | if (!MP_NEGP(x)) |
09d00c6b |
196 | return mp_setbit(d, x, n); |
197 | d = mp_not2c(d, x); |
198 | d = mp_clearbit(d, d, n); |
199 | d = mp_not2c(d, d); |
200 | return (d); |
201 | } |
202 | |
203 | mp *mp_clearbit2c(mp *d, mp *x, unsigned long n) |
204 | { |
a69a3efd |
205 | if (!MP_NEGP(x)) |
09d00c6b |
206 | return mp_clearbit(d, x, n); |
207 | d = mp_not2c(d, x); |
208 | d = mp_setbit(d, d, n); |
209 | d = mp_not2c(d, d); |
210 | return (d); |
211 | } |
212 | |
4b536f42 |
213 | /* --- @mp_eq@ --- * |
214 | * |
215 | * Arguments: @const mp *a, *b@ = two numbers |
216 | * |
217 | * Returns: Nonzero if the numbers are equal. |
218 | */ |
219 | |
220 | int mp_eq(const mp *a, const mp *b) { return (MP_EQ(a, b)); } |
221 | |
d3409d5e |
222 | /* --- @mp_cmp@ --- * |
223 | * |
224 | * Arguments: @const mp *a, *b@ = two numbers |
225 | * |
226 | * Returns: Less than, equal to or greater than zero, according to |
227 | * whether @a@ is less than, equal to or greater than @b@. |
228 | */ |
229 | |
230 | int mp_cmp(const mp *a, const mp *b) |
231 | { |
4108c8d2 |
232 | if (!((a->f ^ b->f) & MP_NEG)) { |
233 | if (a->f & MP_NEG) |
234 | return (-mpx_ucmp(a->v, a->vl, b->v, b->vl)); |
235 | else |
236 | return (mpx_ucmp(a->v, a->vl, b->v, b->vl)); |
237 | } else if (a->f & MP_NEG) |
d3409d5e |
238 | return (-1); |
239 | else |
240 | return (+1); |
241 | } |
242 | |
397041a9 |
243 | /* --- @mp_neg@ --- * |
244 | * |
245 | * Arguments: @mp *d@ = destination |
246 | * @mp *a@ = argument |
247 | * |
248 | * Returns: The negation of the argument. |
249 | * |
250 | * Use: Negates its argument. |
251 | */ |
252 | |
253 | mp *mp_neg(mp *d, mp *a) |
254 | { |
255 | /* --- Surprising amounts of messing about required --- */ |
256 | |
257 | MP_SHRINK(a); |
258 | MP_COPY(a); |
81578196 |
259 | if (d) |
260 | MP_DROP(d); |
261 | if (a->v == a->vl) |
397041a9 |
262 | return (a); |
397041a9 |
263 | MP_DEST(a, MP_LEN(a), a->f); |
264 | a->f ^= MP_NEG; |
265 | return (a); |
266 | } |
267 | |
f09e814a |
268 | /* --- @mp_bitop@ --- * |
0f32e0f8 |
269 | * |
270 | * Arguments: @mp *d@ = destination |
271 | * @mp *a, *b@ = sources |
272 | * |
f09e814a |
273 | * Returns: The result of the given bitwise operation. These functions |
274 | * don't handle negative numbers at all sensibly. For that, use |
275 | * the @...2c@ variants. The functions are named after the |
276 | * truth tables they generate: |
277 | * |
278 | * a: 0011 |
279 | * b: 0101 |
280 | * @mpx_bitXXXX@ |
0f32e0f8 |
281 | */ |
282 | |
f09e814a |
283 | #define MP_BITBINOP(string) \ |
0f32e0f8 |
284 | \ |
f09e814a |
285 | mp *mp_bit##string(mp *d, mp *a, mp *b) \ |
0f32e0f8 |
286 | { \ |
75263f25 |
287 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & ~MP_NEG); \ |
f09e814a |
288 | mpx_bit##string(d->v, d->vl, a->v, a->vl, b->v, b->vl); \ |
0f32e0f8 |
289 | d->f = (a->f | b->f) & MP_BURN; \ |
290 | MP_SHRINK(d); \ |
291 | return (d); \ |
292 | } |
293 | |
f09e814a |
294 | MPX_DOBIN(MP_BITBINOP) |
295 | |
296 | /* --- @mp_not@ --- * |
297 | * |
298 | * Arguments: @mp *d@ = destination |
299 | * @mp *a@ = source |
300 | * |
301 | * Returns: The bitwise complement of the source. |
302 | */ |
0f32e0f8 |
303 | |
304 | mp *mp_not(mp *d, mp *a) |
305 | { |
306 | MP_DEST(d, MP_LEN(a), a->f); |
307 | mpx_not(d->v, d->vl, a->v, a->vl); |
308 | d->f = a->f & MP_BURN; |
309 | MP_SHRINK(d); |
310 | return (d); |
311 | } |
312 | |
f09e814a |
313 | /* --- @mp_bitop2c@ --- * |
314 | * |
315 | * Arguments: @mp *d@ = destination |
316 | * @mp *a, *b@ = sources |
317 | * |
318 | * Returns: The result of the given bitwise operation. Negative numbers |
319 | * are treated as two's complement, sign-extended infinitely to |
320 | * the left. The functions are named after the truth tables |
321 | * they generate: |
322 | * |
323 | * a: 0011 |
324 | * b: 0101 |
325 | * @mpx_bitXXXX@ |
326 | */ |
327 | |
328 | /* --- How this actually works --- * |
329 | * |
330 | * The two arguments are inverted (with a sign-swap) if they're currently |
331 | * negative. This means that we end up using a different function (one which |
332 | * reinverts as we go) for the main operation. Also, if the sign would be |
333 | * negative at the end, we preinvert the output and then invert again with a |
334 | * sign-swap. |
335 | * |
336 | * Start with: wxyz WXYZ |
337 | * If @a@ negative: yzwx or YZWX |
338 | * If @b@ negative: xwzy XWZY |
339 | * If both negative: zyxw ZYXW |
340 | */ |
341 | |
342 | #define MP_BIT2CBINOP(n, base, an, bn, abn, p_base, p_an, p_bn, p_abn) \ |
343 | \ |
344 | mp *mp_bit##n##2c(mp *d, mp *a, mp *b) \ |
345 | { \ |
346 | if (!((a->f | b->f) & MP_NEG)) { /* Both positive */ \ |
347 | d = mp_bit##base(d, a, b); \ |
348 | p_base \ |
349 | } else if (!(b->f & MP_NEG)) { /* Only @b@ positive */ \ |
350 | MP_COPY(b); \ |
351 | d = mp_not2c(d, a); \ |
352 | d = mp_bit##an(d, d, b); \ |
353 | MP_DROP(b); \ |
354 | p_an \ |
355 | } else if (!(a->f & MP_NEG)) { /* Only @a@ positive */ \ |
356 | MP_COPY(a); \ |
357 | d = mp_not2c(d, b); \ |
358 | d = mp_bit##bn(d, a, d); \ |
359 | MP_DROP(a); \ |
360 | p_bn \ |
361 | } else { /* Both negative */ \ |
362 | mp *t = mp_not2c(MP_NEW, a); \ |
363 | mp *d = mp_not2c(d, b); \ |
364 | d = mp_bit##abn(d, t, d); \ |
365 | MP_DROP(t); \ |
366 | p_abn \ |
367 | } \ |
368 | return (d); \ |
369 | } \ |
370 | |
371 | #define NEG d = mp_not2c(d, d); |
372 | #define POS |
373 | MP_BIT2CBINOP(0000, 0000, 0000, 0000, 0000, POS, POS, POS, POS) |
374 | MP_BIT2CBINOP(0001, 0001, 0100, 0010, 0111, POS, POS, POS, NEG) |
375 | MP_BIT2CBINOP(0010, 0010, 0111, 0001, 0100, POS, NEG, POS, POS) |
376 | MP_BIT2CBINOP(0011, 0011, 0011, 0011, 0011, POS, NEG, POS, NEG) |
377 | MP_BIT2CBINOP(0100, 0100, 0001, 0111, 0010, POS, POS, NEG, POS) |
378 | MP_BIT2CBINOP(0101, 0101, 0101, 0101, 0101, POS, POS, NEG, NEG) |
379 | MP_BIT2CBINOP(0110, 0110, 0110, 0110, 0110, POS, NEG, NEG, POS) |
380 | MP_BIT2CBINOP(0111, 0111, 0010, 0100, 0001, POS, NEG, NEG, NEG) |
381 | MP_BIT2CBINOP(1000, 0111, 0010, 0100, 0001, NEG, POS, POS, POS) |
382 | MP_BIT2CBINOP(1001, 0110, 0110, 0110, 0110, NEG, POS, POS, NEG) |
383 | MP_BIT2CBINOP(1010, 0101, 0101, 0101, 0101, NEG, NEG, POS, POS) |
384 | MP_BIT2CBINOP(1011, 0100, 0001, 0111, 0010, NEG, NEG, POS, NEG) |
385 | MP_BIT2CBINOP(1100, 0011, 0011, 0011, 0011, NEG, POS, NEG, POS) |
386 | MP_BIT2CBINOP(1101, 0010, 0111, 0001, 0100, NEG, POS, NEG, NEG) |
387 | MP_BIT2CBINOP(1110, 0001, 0100, 0010, 0111, NEG, NEG, NEG, POS) |
388 | MP_BIT2CBINOP(1111, 0000, 0000, 0000, 0000, NEG, NEG, NEG, NEG) |
389 | #undef NEG |
390 | #undef POS |
391 | |
392 | /* --- @mp_not2c@ --- * |
393 | * |
394 | * Arguments: @mp *d@ = destination |
395 | * @mp *a@ = source |
396 | * |
397 | * Returns: The sign-extended complement of the argument. |
398 | */ |
399 | |
400 | mp *mp_not2c(mp *d, mp *a) |
401 | { |
402 | mpw one = 1; |
403 | |
404 | MP_DEST(d, MP_LEN(a) + 1, a->f); |
405 | if (d == a) { |
a69a3efd |
406 | if (MP_NEGP(a)) |
f09e814a |
407 | MPX_USUBN(d->v, d->vl, 1); |
408 | else |
409 | MPX_UADDN(d->v, d->vl, 1); |
410 | } else { |
a69a3efd |
411 | if (MP_NEGP(a)) |
f09e814a |
412 | mpx_usub(d->v, d->vl, a->v, a->vl, &one, &one + 1); |
413 | else |
414 | mpx_uadd(d->v, d->vl, a->v, a->vl, &one, &one + 1); |
415 | } |
416 | d->f = (a->f & (MP_NEG | MP_BURN)) ^ MP_NEG; |
417 | MP_SHRINK(d); |
418 | return (d); |
419 | } |
420 | |
d3409d5e |
421 | /* --- @mp_add@ --- * |
422 | * |
423 | * Arguments: @mp *d@ = destination |
ef5f4810 |
424 | * @mp *a, *b@ = sources |
d3409d5e |
425 | * |
426 | * Returns: Result, @a@ added to @b@. |
427 | */ |
428 | |
ef5f4810 |
429 | mp *mp_add(mp *d, mp *a, mp *b) |
d3409d5e |
430 | { |
d34decd2 |
431 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f); |
d3409d5e |
432 | if (!((a->f ^ b->f) & MP_NEG)) |
433 | mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
434 | else { |
435 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
ef5f4810 |
436 | mp *t = a; a = b; b = t; |
d3409d5e |
437 | } |
438 | mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
439 | } |
440 | d->f = ((a->f | b->f) & MP_BURN) | (a->f & MP_NEG); |
441 | MP_SHRINK(d); |
442 | return (d); |
443 | } |
444 | |
445 | /* --- @mp_sub@ --- * |
446 | * |
447 | * Arguments: @mp *d@ = destination |
ef5f4810 |
448 | * @mp *a, *b@ = sources |
d3409d5e |
449 | * |
450 | * Returns: Result, @b@ subtracted from @a@. |
451 | */ |
452 | |
ef5f4810 |
453 | mp *mp_sub(mp *d, mp *a, mp *b) |
d3409d5e |
454 | { |
455 | unsigned sgn = 0; |
d34decd2 |
456 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f); |
d3409d5e |
457 | if ((a->f ^ b->f) & MP_NEG) |
458 | mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
459 | else { |
460 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
ef5f4810 |
461 | mp *t = a; a = b; b = t; |
d3409d5e |
462 | sgn = MP_NEG; |
463 | } |
464 | mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
465 | } |
466 | d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG); |
467 | MP_SHRINK(d); |
468 | return (d); |
469 | } |
470 | |
471 | /* --- @mp_mul@ --- * |
472 | * |
473 | * Arguments: @mp *d@ = destination |
ef5f4810 |
474 | * @mp *a, *b@ = sources |
d3409d5e |
475 | * |
476 | * Returns: Result, @a@ multiplied by @b@. |
477 | */ |
478 | |
ef5f4810 |
479 | mp *mp_mul(mp *d, mp *a, mp *b) |
d3409d5e |
480 | { |
ef5f4810 |
481 | a = MP_COPY(a); |
482 | b = MP_COPY(b); |
483 | |
52cdaca9 |
484 | if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= MPK_THRESH) { |
d34decd2 |
485 | MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF); |
ef5f4810 |
486 | mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
8017495b |
487 | } else { |
dd22938e |
488 | size_t m = MAX(MP_LEN(a), MP_LEN(b)); |
ef5f4810 |
489 | mpw *s; |
dd22938e |
490 | MP_DEST(d, 3 * m, a->f | b->f | MP_UNDEF); |
491 | s = mpalloc(d->a, 5 * m); |
492 | mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 5 * m); |
d34decd2 |
493 | mpfree(d->a, s); |
ef5f4810 |
494 | } |
495 | |
d3409d5e |
496 | d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG); |
497 | MP_SHRINK(d); |
ef5f4810 |
498 | MP_DROP(a); |
499 | MP_DROP(b); |
d3409d5e |
500 | return (d); |
501 | } |
502 | |
503 | /* --- @mp_sqr@ --- * |
504 | * |
505 | * Arguments: @mp *d@ = destination |
ef5f4810 |
506 | * @mp *a@ = source |
d3409d5e |
507 | * |
508 | * Returns: Result, @a@ squared. |
509 | */ |
510 | |
ef5f4810 |
511 | mp *mp_sqr(mp *d, mp *a) |
d3409d5e |
512 | { |
ef5f4810 |
513 | size_t m = MP_LEN(a); |
514 | |
515 | a = MP_COPY(a); |
52cdaca9 |
516 | if (m > MPK_THRESH) { |
ef5f4810 |
517 | mpw *s; |
dd22938e |
518 | MP_DEST(d, 3 * m, a->f | MP_UNDEF); |
519 | s = mpalloc(d->a, 5 * m); |
520 | mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + 5 * m); |
d34decd2 |
521 | mpfree(d->a, s); |
dd22938e |
522 | } else { |
523 | MP_DEST(d, 2 * m + 2, a->f | MP_UNDEF); |
ef5f4810 |
524 | mpx_usqr(d->v, d->vl, a->v, a->vl); |
dd22938e |
525 | } |
d3409d5e |
526 | d->f = a->f & MP_BURN; |
527 | MP_SHRINK(d); |
ef5f4810 |
528 | MP_DROP(a); |
d3409d5e |
529 | return (d); |
530 | } |
531 | |
532 | /* --- @mp_div@ --- * |
533 | * |
534 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
ef5f4810 |
535 | * @mp *a, *b@ = sources |
d3409d5e |
536 | * |
537 | * Use: Calculates the quotient and remainder when @a@ is divided by |
538 | * @b@. The destinations @*qq@ and @*rr@ must be distinct. |
539 | * Either of @qq@ or @rr@ may be null to indicate that the |
540 | * result is irrelevant. (Discarding both results is silly.) |
541 | * There is a performance advantage if @a == *rr@. |
542 | * |
543 | * The behaviour when @a@ and @b@ have the same sign is |
544 | * straightforward. When the signs differ, this implementation |
545 | * chooses @r@ to have the same sign as @b@, rather than the |
546 | * more normal choice that the remainder has the same sign as |
547 | * the dividend. This makes modular arithmetic a little more |
548 | * straightforward. |
549 | */ |
550 | |
ef5f4810 |
551 | void mp_div(mp **qq, mp **rr, mp *a, mp *b) |
d3409d5e |
552 | { |
553 | mp *r = rr ? *rr : MP_NEW; |
554 | mp *q = qq ? *qq : MP_NEW; |
555 | mpw *sv, *svl; |
556 | |
d3409d5e |
557 | /* --- Set the remainder up right --- * |
558 | * |
559 | * Just in case the divisor is larger, be able to cope with this. It's not |
560 | * important in @mpx_udiv@, but it is here because of the sign correction. |
561 | */ |
562 | |
d34decd2 |
563 | b = MP_COPY(b); |
564 | a = MP_COPY(a); |
565 | if (r) |
566 | MP_DROP(r); |
567 | r = a; |
a9c8f3d6 |
568 | MP_DEST(r, MAX(MP_LEN(a), MP_LEN(b)) + 2, a->f | b->f); |
d3409d5e |
569 | |
570 | /* --- Fix up the quotient too --- */ |
571 | |
d34decd2 |
572 | r = MP_COPY(r); |
573 | MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF); |
574 | MP_DROP(r); |
575 | |
576 | /* --- Set up some temporary workspace --- */ |
577 | |
578 | { |
579 | size_t rq = MP_LEN(b) + 1; |
580 | sv = mpalloc(r->a, rq); |
581 | svl = sv + rq; |
582 | } |
d3409d5e |
583 | |
584 | /* --- Perform the calculation --- */ |
585 | |
586 | mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl); |
587 | |
588 | /* --- Sort out the sign of the results --- * |
589 | * |
590 | * If the signs of the arguments differ, and the remainder is nonzero, I |
591 | * must add one to the absolute value of the quotient and subtract the |
592 | * remainder from @b@. |
593 | */ |
594 | |
d34decd2 |
595 | q->f = ((r->f | b->f) & MP_BURN) | ((r->f ^ b->f) & MP_NEG); |
a69a3efd |
596 | if (MP_NEGP(q)) { |
ef5f4810 |
597 | mpw *v; |
598 | for (v = r->v; v < r->vl; v++) { |
d3409d5e |
599 | if (*v) { |
600 | MPX_UADDN(q->v, q->vl, 1); |
601 | mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl); |
602 | break; |
603 | } |
604 | } |
605 | } |
606 | |
d34decd2 |
607 | r->f = ((r->f | b->f) & MP_BURN) | (b->f & MP_NEG); |
d3409d5e |
608 | |
609 | /* --- Store the return values --- */ |
610 | |
d34decd2 |
611 | mpfree(r->a, sv); |
612 | MP_DROP(b); |
613 | |
d3409d5e |
614 | if (!qq) |
615 | MP_DROP(q); |
616 | else { |
617 | MP_SHRINK(q); |
618 | *qq = q; |
619 | } |
620 | |
621 | if (!rr) |
622 | MP_DROP(r); |
623 | else { |
624 | MP_SHRINK(r); |
625 | *rr = r; |
626 | } |
d3409d5e |
627 | } |
628 | |
f1713c63 |
629 | /* --- @mp_odd@ --- * |
630 | * |
631 | * Arguments: @mp *d@ = pointer to destination integer |
632 | * @mp *m@ = pointer to source integer |
633 | * @size_t *s@ = where to store the power of 2 |
634 | * |
635 | * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%. |
636 | * |
637 | * Use: Computes a power of two and an odd integer which, when |
638 | * multiplied, give a specified result. This sort of thing is |
639 | * useful in number theory quite often. |
640 | */ |
641 | |
642 | mp *mp_odd(mp *d, mp *m, size_t *s) |
643 | { |
644 | size_t ss = 0; |
645 | const mpw *v, *vl; |
646 | |
647 | v = m->v; |
648 | vl = m->vl; |
649 | for (; !*v && v < vl; v++) |
650 | ss += MPW_BITS; |
651 | if (v >= vl) |
652 | ss = 0; |
653 | else { |
654 | mpw x = *v; |
655 | mpw mask = MPW_MAX; |
656 | unsigned z = MPW_BITS / 2; |
657 | |
658 | while (z) { |
659 | mask >>= z; |
660 | if (!(x & mask)) { |
661 | x >>= z; |
662 | ss += z; |
663 | } |
664 | z >>= 1; |
665 | } |
666 | } |
667 | |
668 | *s = ss; |
669 | return (mp_lsr(d, m, ss)); |
670 | } |
671 | |
d3409d5e |
672 | /*----- Test rig ----------------------------------------------------------*/ |
673 | |
674 | #ifdef TEST_RIG |
675 | |
676 | static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b) |
677 | { |
4b536f42 |
678 | if (!MP_EQ(expect, result)) { |
d3409d5e |
679 | fprintf(stderr, "\n*** %s failed", op); |
680 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
681 | fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10); |
682 | fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10); |
683 | fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10); |
684 | fputc('\n', stderr); |
685 | return (0); |
686 | } |
687 | return (1); |
688 | } |
689 | |
690 | #define RIG(name, op) \ |
ef5f4810 |
691 | static int t##name(dstr *v) \ |
d3409d5e |
692 | { \ |
693 | mp *a = *(mp **)v[0].buf; \ |
694 | mpw n = *(int *)v[1].buf; \ |
695 | mp b; \ |
696 | mp *r = *(mp **)v[2].buf; \ |
697 | mp *c = op(MP_NEW, a, n); \ |
698 | int ok; \ |
699 | mp_build(&b, &n, &n + 1); \ |
700 | ok = verify(#name, r, c, a, &b); \ |
701 | mp_drop(a); mp_drop(c); mp_drop(r); \ |
ef5f4810 |
702 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ |
d3409d5e |
703 | return (ok); \ |
704 | } |
705 | |
706 | RIG(lsl, mp_lsl) |
707 | RIG(lsr, mp_lsr) |
f09e814a |
708 | RIG(lsl2c, mp_lsl2c) |
709 | RIG(lsr2c, mp_lsr2c) |
d3409d5e |
710 | |
711 | #undef RIG |
712 | |
713 | #define RIG(name, op) \ |
ef5f4810 |
714 | static int t##name(dstr *v) \ |
d3409d5e |
715 | { \ |
716 | mp *a = *(mp **)v[0].buf; \ |
717 | mp *b = *(mp **)v[1].buf; \ |
718 | mp *r = *(mp **)v[2].buf; \ |
719 | mp *c = op(MP_NEW, a, b); \ |
720 | int ok = verify(#name, r, c, a, b); \ |
721 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \ |
ef5f4810 |
722 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ |
d3409d5e |
723 | return (ok); \ |
724 | } |
725 | |
726 | RIG(add, mp_add) |
727 | RIG(sub, mp_sub) |
728 | RIG(mul, mp_mul) |
f4535c64 |
729 | RIG(exp, mp_exp) |
d3409d5e |
730 | |
731 | #undef RIG |
732 | |
733 | static int tdiv(dstr *v) |
734 | { |
735 | mp *a = *(mp **)v[0].buf; |
736 | mp *b = *(mp **)v[1].buf; |
737 | mp *q = *(mp **)v[2].buf; |
738 | mp *r = *(mp **)v[3].buf; |
739 | mp *c = MP_NEW, *d = MP_NEW; |
740 | int ok = 1; |
741 | mp_div(&c, &d, a, b); |
742 | ok &= verify("div(quotient)", q, c, a, b); |
743 | ok &= verify("div(remainder)", r, d, a, b); |
744 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q); |
ef5f4810 |
745 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
746 | return (ok); |
747 | } |
748 | |
f09e814a |
749 | static int tbin(dstr *v) |
750 | { |
751 | static mp *(*fn[])(mp *, mp *, mp *) = { |
752 | #define DO(string) mp_bit##string##2c, |
753 | MPX_DOBIN(DO) |
754 | #undef DO |
755 | }; |
756 | int ok = 1; |
757 | unsigned op = 0; |
758 | mp *a = *(mp **)v[1].buf; |
759 | mp *b = *(mp **)v[2].buf; |
760 | mp *r = *(mp **)v[3].buf; |
761 | mp *c; |
762 | |
763 | if (strcmp(v[0].buf, "and") == 0) op = 1; |
764 | else if (strcmp(v[0].buf, "or") == 0) op = 7; |
765 | else if (strcmp(v[0].buf, "nand") == 0) op = 14; |
766 | else if (strcmp(v[0].buf, "nor") == 0) op = 8; |
767 | else if (strcmp(v[0].buf, "xor") == 0) op = 6; |
768 | else { |
769 | char *p = v[0].buf; |
770 | while (*p) { |
771 | op <<= 1; |
772 | if (*p++ == '1') |
773 | op |= 1; |
774 | } |
775 | } |
776 | |
777 | c = fn[op](MP_NEW, a, b); |
778 | ok = verify(v[0].buf, r, c, a, b); |
779 | mp_drop(a); mp_drop(b); mp_drop(r); mp_drop(c); |
780 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
781 | return (ok); |
782 | } |
783 | |
09d00c6b |
784 | static int tset(dstr *v) |
785 | { |
786 | mp *a = *(mp **)v[0].buf; |
787 | unsigned long n = *(unsigned long *)v[1].buf; |
788 | mp *r = *(mp **)v[2].buf; |
789 | mp *c; |
790 | int ok = 1; |
791 | |
792 | c = mp_setbit2c(MP_NEW, a, n); |
793 | if (!MP_EQ(c, r)) { |
794 | ok = 0; |
795 | fprintf(stderr, "\n***setbit (set) failed"); |
796 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
797 | fprintf(stderr, "\n*** n = %lu", n); |
798 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
799 | fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16); |
800 | fputc('\n', stderr); |
801 | } |
802 | if (!mp_testbit2c(r, n)) { |
803 | ok = 0; |
804 | fprintf(stderr, "\n***setbit (test) failed"); |
805 | fprintf(stderr, "\n*** n = %lu", n); |
806 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
807 | fputc('\n', stderr); |
808 | } |
809 | mp_drop(a); |
810 | mp_drop(r); |
811 | mp_drop(c); |
812 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
813 | return (ok); |
814 | } |
815 | |
816 | static int tclr(dstr *v) |
817 | { |
818 | mp *a = *(mp **)v[0].buf; |
819 | unsigned long n = *(unsigned long *)v[1].buf; |
820 | mp *r = *(mp **)v[2].buf; |
821 | mp *c; |
822 | int ok = 1; |
823 | |
824 | c = mp_clearbit2c(MP_NEW, a, n); |
825 | if (!MP_EQ(c, r)) { |
826 | ok = 0; |
827 | fprintf(stderr, "\n***clrbit (set) failed"); |
828 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
829 | fprintf(stderr, "\n*** n = %lu", n); |
830 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
831 | fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16); |
832 | fputc('\n', stderr); |
833 | } |
834 | if (mp_testbit2c(r, n)) { |
835 | ok = 0; |
836 | fprintf(stderr, "\n***clrbit (test) failed"); |
837 | fprintf(stderr, "\n*** n = %lu", n); |
838 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
839 | fputc('\n', stderr); |
840 | } |
841 | mp_drop(a); |
842 | mp_drop(c); |
843 | mp_drop(r); |
844 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
845 | return (ok); |
846 | } |
847 | |
397041a9 |
848 | static int tneg(dstr *v) |
849 | { |
850 | mp *a = *(mp **)v[0].buf; |
851 | mp *r = *(mp **)v[1].buf; |
852 | int ok = 1; |
853 | mp *n = mp_neg(MP_NEW, a); |
854 | if (!MP_EQ(r, n)) { |
855 | ok = 0; |
856 | fprintf(stderr, "\n*** neg failed\n"); |
857 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
858 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10); |
859 | fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10); |
860 | fputc('\n', stderr); |
861 | } |
862 | mp_drop(n); |
863 | n = mp_neg(a, a); |
864 | if (!MP_EQ(r, n)) { |
865 | ok = 0; |
866 | fprintf(stderr, "\n*** neg failed\n"); |
867 | fputs("\n*** a* = ", stderr); mp_writefile(a, stderr, 10); |
868 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10); |
869 | fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10); |
870 | fputc('\n', stderr); |
871 | } |
872 | mp_drop(a); |
873 | mp_drop(r); |
874 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
875 | return (ok); |
876 | } |
877 | |
f1713c63 |
878 | static int todd(dstr *v) |
879 | { |
880 | mp *a = *(mp **)v[0].buf; |
881 | size_t rs = *(uint32 *)v[1].buf; |
882 | mp *rt = *(mp **)v[2].buf; |
883 | int ok = 1; |
884 | mp *t; |
885 | size_t s; |
886 | t = mp_odd(MP_NEW, a, &s); |
4b536f42 |
887 | if (s != rs || !MP_EQ(t, rt)) { |
f1713c63 |
888 | ok = 0; |
889 | fprintf(stderr, "\n*** odd failed"); |
890 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
891 | fprintf(stderr, "\n*** s = %lu", (unsigned long)s); |
892 | fputs("\n*** t = ", stderr); mp_writefile(t, stderr, 10); |
893 | fprintf(stderr, "\n*** rs = %lu", (unsigned long)rs); |
894 | fputs("\n*** rt = ", stderr); mp_writefile(rt, stderr, 10); |
895 | fputc('\n', stderr); |
896 | } |
897 | mp_drop(a); |
898 | mp_drop(rt); |
899 | mp_drop(t); |
09d00c6b |
900 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
f1713c63 |
901 | return (ok); |
902 | } |
903 | |
d3409d5e |
904 | static test_chunk tests[] = { |
f09e814a |
905 | { "lsl", tlsl, { &type_mp, &type_int, &type_mp, 0 } }, |
906 | { "lsr", tlsr, { &type_mp, &type_int, &type_mp, 0 } }, |
907 | { "lsl2c", tlsl2c, { &type_mp, &type_int, &type_mp, 0 } }, |
908 | { "lsr2c", tlsr2c, { &type_mp, &type_int, &type_mp, 0 } }, |
09d00c6b |
909 | { "setbit", tset, { &type_mp, &type_ulong, &type_mp, 0 } }, |
910 | { "clrbit", tclr, { &type_mp, &type_ulong, &type_mp, 0 } }, |
d3409d5e |
911 | { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } }, |
912 | { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } }, |
913 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } }, |
914 | { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
f4535c64 |
915 | { "exp", texp, { &type_mp, &type_mp, &type_mp, 0 } }, |
f09e814a |
916 | { "bin2c", tbin, { &type_string, &type_mp, &type_mp, &type_mp, 0 } }, |
f1713c63 |
917 | { "odd", todd, { &type_mp, &type_uint32, &type_mp, 0 } }, |
397041a9 |
918 | { "neg", tneg, { &type_mp, &type_mp, 0 } }, |
d3409d5e |
919 | { 0, 0, { 0 } }, |
920 | }; |
921 | |
922 | int main(int argc, char *argv[]) |
923 | { |
924 | sub_init(); |
925 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
926 | return (0); |
927 | } |
928 | |
929 | #endif |
930 | |
931 | /*----- That's all, folks -------------------------------------------------*/ |