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cdec9cb5 DK |
1 | /* mpihelp-div.c - MPI helper functions |
2 | * Copyright (C) 1994, 1996 Free Software Foundation, Inc. | |
3 | * Copyright (C) 1998, 1999 Free Software Foundation, Inc. | |
4 | * | |
5 | * This file is part of GnuPG. | |
6 | * | |
7 | * GnuPG is free software; you can redistribute it and/or modify | |
8 | * it under the terms of the GNU General Public License as published by | |
9 | * the Free Software Foundation; either version 2 of the License, or | |
10 | * (at your option) any later version. | |
11 | * | |
12 | * GnuPG is distributed in the hope that it will be useful, | |
13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
15 | * GNU General Public License for more details. | |
16 | * | |
17 | * You should have received a copy of the GNU General Public License | |
18 | * along with this program; if not, write to the Free Software | |
19 | * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA | |
20 | * | |
21 | * Note: This code is heavily based on the GNU MP Library. | |
22 | * Actually it's the same code with only minor changes in the | |
23 | * way the data is stored; this is to support the abstraction | |
24 | * of an optional secure memory allocation which may be used | |
25 | * to avoid revealing of sensitive data due to paging etc. | |
26 | * The GNU MP Library itself is published under the LGPL; | |
27 | * however I decided to publish this code under the plain GPL. | |
28 | */ | |
29 | ||
30 | #include "mpi-internal.h" | |
31 | #include "longlong.h" | |
32 | ||
33 | #ifndef UMUL_TIME | |
34 | #define UMUL_TIME 1 | |
35 | #endif | |
36 | #ifndef UDIV_TIME | |
37 | #define UDIV_TIME UMUL_TIME | |
38 | #endif | |
39 | ||
40 | /* FIXME: We should be using invert_limb (or invert_normalized_limb) | |
41 | * here (not udiv_qrnnd). | |
42 | */ | |
43 | ||
44 | mpi_limb_t | |
45 | mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size, | |
46 | mpi_limb_t divisor_limb) | |
47 | { | |
48 | mpi_size_t i; | |
49 | mpi_limb_t n1, n0, r; | |
50 | int dummy; | |
51 | ||
52 | /* Botch: Should this be handled at all? Rely on callers? */ | |
53 | if (!dividend_size) | |
54 | return 0; | |
55 | ||
56 | /* If multiplication is much faster than division, and the | |
57 | * dividend is large, pre-invert the divisor, and use | |
58 | * only multiplications in the inner loop. | |
59 | * | |
60 | * This test should be read: | |
61 | * Does it ever help to use udiv_qrnnd_preinv? | |
62 | * && Does what we save compensate for the inversion overhead? | |
63 | */ | |
64 | if (UDIV_TIME > (2 * UMUL_TIME + 6) | |
65 | && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) { | |
66 | int normalization_steps; | |
67 | ||
68 | count_leading_zeros(normalization_steps, divisor_limb); | |
69 | if (normalization_steps) { | |
70 | mpi_limb_t divisor_limb_inverted; | |
71 | ||
72 | divisor_limb <<= normalization_steps; | |
73 | ||
74 | /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The | |
75 | * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the | |
76 | * most significant bit (with weight 2**N) implicit. | |
77 | * | |
78 | * Special case for DIVISOR_LIMB == 100...000. | |
79 | */ | |
80 | if (!(divisor_limb << 1)) | |
81 | divisor_limb_inverted = ~(mpi_limb_t) 0; | |
82 | else | |
83 | udiv_qrnnd(divisor_limb_inverted, dummy, | |
84 | -divisor_limb, 0, divisor_limb); | |
85 | ||
86 | n1 = dividend_ptr[dividend_size - 1]; | |
87 | r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); | |
88 | ||
89 | /* Possible optimization: | |
90 | * if (r == 0 | |
91 | * && divisor_limb > ((n1 << normalization_steps) | |
92 | * | (dividend_ptr[dividend_size - 2] >> ...))) | |
93 | * ...one division less... | |
94 | */ | |
95 | for (i = dividend_size - 2; i >= 0; i--) { | |
96 | n0 = dividend_ptr[i]; | |
97 | UDIV_QRNND_PREINV(dummy, r, r, | |
98 | ((n1 << normalization_steps) | |
99 | | (n0 >> | |
100 | (BITS_PER_MPI_LIMB - | |
101 | normalization_steps))), | |
102 | divisor_limb, | |
103 | divisor_limb_inverted); | |
104 | n1 = n0; | |
105 | } | |
106 | UDIV_QRNND_PREINV(dummy, r, r, | |
107 | n1 << normalization_steps, | |
108 | divisor_limb, divisor_limb_inverted); | |
109 | return r >> normalization_steps; | |
110 | } else { | |
111 | mpi_limb_t divisor_limb_inverted; | |
112 | ||
113 | /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The | |
114 | * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the | |
115 | * most significant bit (with weight 2**N) implicit. | |
116 | * | |
117 | * Special case for DIVISOR_LIMB == 100...000. | |
118 | */ | |
119 | if (!(divisor_limb << 1)) | |
120 | divisor_limb_inverted = ~(mpi_limb_t) 0; | |
121 | else | |
122 | udiv_qrnnd(divisor_limb_inverted, dummy, | |
123 | -divisor_limb, 0, divisor_limb); | |
124 | ||
125 | i = dividend_size - 1; | |
126 | r = dividend_ptr[i]; | |
127 | ||
128 | if (r >= divisor_limb) | |
129 | r = 0; | |
130 | else | |
131 | i--; | |
132 | ||
133 | for (; i >= 0; i--) { | |
134 | n0 = dividend_ptr[i]; | |
135 | UDIV_QRNND_PREINV(dummy, r, r, | |
136 | n0, divisor_limb, | |
137 | divisor_limb_inverted); | |
138 | } | |
139 | return r; | |
140 | } | |
141 | } else { | |
142 | if (UDIV_NEEDS_NORMALIZATION) { | |
143 | int normalization_steps; | |
144 | ||
145 | count_leading_zeros(normalization_steps, divisor_limb); | |
146 | if (normalization_steps) { | |
147 | divisor_limb <<= normalization_steps; | |
148 | ||
149 | n1 = dividend_ptr[dividend_size - 1]; | |
150 | r = n1 >> (BITS_PER_MPI_LIMB - | |
151 | normalization_steps); | |
152 | ||
153 | /* Possible optimization: | |
154 | * if (r == 0 | |
155 | * && divisor_limb > ((n1 << normalization_steps) | |
156 | * | (dividend_ptr[dividend_size - 2] >> ...))) | |
157 | * ...one division less... | |
158 | */ | |
159 | for (i = dividend_size - 2; i >= 0; i--) { | |
160 | n0 = dividend_ptr[i]; | |
161 | udiv_qrnnd(dummy, r, r, | |
162 | ((n1 << normalization_steps) | |
163 | | (n0 >> | |
164 | (BITS_PER_MPI_LIMB - | |
165 | normalization_steps))), | |
166 | divisor_limb); | |
167 | n1 = n0; | |
168 | } | |
169 | udiv_qrnnd(dummy, r, r, | |
170 | n1 << normalization_steps, | |
171 | divisor_limb); | |
172 | return r >> normalization_steps; | |
173 | } | |
174 | } | |
175 | /* No normalization needed, either because udiv_qrnnd doesn't require | |
176 | * it, or because DIVISOR_LIMB is already normalized. */ | |
177 | i = dividend_size - 1; | |
178 | r = dividend_ptr[i]; | |
179 | ||
180 | if (r >= divisor_limb) | |
181 | r = 0; | |
182 | else | |
183 | i--; | |
184 | ||
185 | for (; i >= 0; i--) { | |
186 | n0 = dividend_ptr[i]; | |
187 | udiv_qrnnd(dummy, r, r, n0, divisor_limb); | |
188 | } | |
189 | return r; | |
190 | } | |
191 | } | |
192 | ||
193 | /* Divide num (NP/NSIZE) by den (DP/DSIZE) and write | |
194 | * the NSIZE-DSIZE least significant quotient limbs at QP | |
195 | * and the DSIZE long remainder at NP. If QEXTRA_LIMBS is | |
196 | * non-zero, generate that many fraction bits and append them after the | |
197 | * other quotient limbs. | |
198 | * Return the most significant limb of the quotient, this is always 0 or 1. | |
199 | * | |
200 | * Preconditions: | |
201 | * 0. NSIZE >= DSIZE. | |
202 | * 1. The most significant bit of the divisor must be set. | |
203 | * 2. QP must either not overlap with the input operands at all, or | |
204 | * QP + DSIZE >= NP must hold true. (This means that it's | |
205 | * possible to put the quotient in the high part of NUM, right after the | |
206 | * remainder in NUM. | |
207 | * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero. | |
208 | */ | |
209 | ||
210 | mpi_limb_t | |
211 | mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs, | |
212 | mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize) | |
213 | { | |
214 | mpi_limb_t most_significant_q_limb = 0; | |
215 | ||
216 | switch (dsize) { | |
217 | case 0: | |
218 | /* We are asked to divide by zero, so go ahead and do it! (To make | |
219 | the compiler not remove this statement, return the value.) */ | |
220 | return 1 / dsize; | |
221 | ||
222 | case 1: | |
223 | { | |
224 | mpi_size_t i; | |
225 | mpi_limb_t n1; | |
226 | mpi_limb_t d; | |
227 | ||
228 | d = dp[0]; | |
229 | n1 = np[nsize - 1]; | |
230 | ||
231 | if (n1 >= d) { | |
232 | n1 -= d; | |
233 | most_significant_q_limb = 1; | |
234 | } | |
235 | ||
236 | qp += qextra_limbs; | |
237 | for (i = nsize - 2; i >= 0; i--) | |
238 | udiv_qrnnd(qp[i], n1, n1, np[i], d); | |
239 | qp -= qextra_limbs; | |
240 | ||
241 | for (i = qextra_limbs - 1; i >= 0; i--) | |
242 | udiv_qrnnd(qp[i], n1, n1, 0, d); | |
243 | ||
244 | np[0] = n1; | |
245 | } | |
246 | break; | |
247 | ||
248 | case 2: | |
249 | { | |
250 | mpi_size_t i; | |
251 | mpi_limb_t n1, n0, n2; | |
252 | mpi_limb_t d1, d0; | |
253 | ||
254 | np += nsize - 2; | |
255 | d1 = dp[1]; | |
256 | d0 = dp[0]; | |
257 | n1 = np[1]; | |
258 | n0 = np[0]; | |
259 | ||
260 | if (n1 >= d1 && (n1 > d1 || n0 >= d0)) { | |
261 | sub_ddmmss(n1, n0, n1, n0, d1, d0); | |
262 | most_significant_q_limb = 1; | |
263 | } | |
264 | ||
265 | for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) { | |
266 | mpi_limb_t q; | |
267 | mpi_limb_t r; | |
268 | ||
269 | if (i >= qextra_limbs) | |
270 | np--; | |
271 | else | |
272 | np[0] = 0; | |
273 | ||
274 | if (n1 == d1) { | |
275 | /* Q should be either 111..111 or 111..110. Need special | |
276 | * treatment of this rare case as normal division would | |
277 | * give overflow. */ | |
278 | q = ~(mpi_limb_t) 0; | |
279 | ||
280 | r = n0 + d1; | |
281 | if (r < d1) { /* Carry in the addition? */ | |
282 | add_ssaaaa(n1, n0, r - d0, | |
283 | np[0], 0, d0); | |
284 | qp[i] = q; | |
285 | continue; | |
286 | } | |
287 | n1 = d0 - (d0 != 0 ? 1 : 0); | |
288 | n0 = -d0; | |
289 | } else { | |
290 | udiv_qrnnd(q, r, n1, n0, d1); | |
291 | umul_ppmm(n1, n0, d0, q); | |
292 | } | |
293 | ||
294 | n2 = np[0]; | |
295 | q_test: | |
296 | if (n1 > r || (n1 == r && n0 > n2)) { | |
297 | /* The estimated Q was too large. */ | |
298 | q--; | |
299 | sub_ddmmss(n1, n0, n1, n0, 0, d0); | |
300 | r += d1; | |
301 | if (r >= d1) /* If not carry, test Q again. */ | |
302 | goto q_test; | |
303 | } | |
304 | ||
305 | qp[i] = q; | |
306 | sub_ddmmss(n1, n0, r, n2, n1, n0); | |
307 | } | |
308 | np[1] = n1; | |
309 | np[0] = n0; | |
310 | } | |
311 | break; | |
312 | ||
313 | default: | |
314 | { | |
315 | mpi_size_t i; | |
316 | mpi_limb_t dX, d1, n0; | |
317 | ||
318 | np += nsize - dsize; | |
319 | dX = dp[dsize - 1]; | |
320 | d1 = dp[dsize - 2]; | |
321 | n0 = np[dsize - 1]; | |
322 | ||
323 | if (n0 >= dX) { | |
324 | if (n0 > dX | |
325 | || mpihelp_cmp(np, dp, dsize - 1) >= 0) { | |
326 | mpihelp_sub_n(np, np, dp, dsize); | |
327 | n0 = np[dsize - 1]; | |
328 | most_significant_q_limb = 1; | |
329 | } | |
330 | } | |
331 | ||
332 | for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) { | |
333 | mpi_limb_t q; | |
334 | mpi_limb_t n1, n2; | |
335 | mpi_limb_t cy_limb; | |
336 | ||
337 | if (i >= qextra_limbs) { | |
338 | np--; | |
339 | n2 = np[dsize]; | |
340 | } else { | |
341 | n2 = np[dsize - 1]; | |
342 | MPN_COPY_DECR(np + 1, np, dsize - 1); | |
343 | np[0] = 0; | |
344 | } | |
345 | ||
346 | if (n0 == dX) { | |
347 | /* This might over-estimate q, but it's probably not worth | |
348 | * the extra code here to find out. */ | |
349 | q = ~(mpi_limb_t) 0; | |
350 | } else { | |
351 | mpi_limb_t r; | |
352 | ||
353 | udiv_qrnnd(q, r, n0, np[dsize - 1], dX); | |
354 | umul_ppmm(n1, n0, d1, q); | |
355 | ||
356 | while (n1 > r | |
357 | || (n1 == r | |
358 | && n0 > np[dsize - 2])) { | |
359 | q--; | |
360 | r += dX; | |
361 | if (r < dX) /* I.e. "carry in previous addition?" */ | |
362 | break; | |
363 | n1 -= n0 < d1; | |
364 | n0 -= d1; | |
365 | } | |
366 | } | |
367 | ||
368 | /* Possible optimization: We already have (q * n0) and (1 * n1) | |
369 | * after the calculation of q. Taking advantage of that, we | |
370 | * could make this loop make two iterations less. */ | |
371 | cy_limb = mpihelp_submul_1(np, dp, dsize, q); | |
372 | ||
373 | if (n2 != cy_limb) { | |
374 | mpihelp_add_n(np, np, dp, dsize); | |
375 | q--; | |
376 | } | |
377 | ||
378 | qp[i] = q; | |
379 | n0 = np[dsize - 1]; | |
380 | } | |
381 | } | |
382 | } | |
383 | ||
384 | return most_significant_q_limb; | |
385 | } | |
386 | ||
387 | /**************** | |
388 | * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB. | |
389 | * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR. | |
390 | * Return the single-limb remainder. | |
391 | * There are no constraints on the value of the divisor. | |
392 | * | |
393 | * QUOT_PTR and DIVIDEND_PTR might point to the same limb. | |
394 | */ | |
395 | ||
396 | mpi_limb_t | |
397 | mpihelp_divmod_1(mpi_ptr_t quot_ptr, | |
398 | mpi_ptr_t dividend_ptr, mpi_size_t dividend_size, | |
399 | mpi_limb_t divisor_limb) | |
400 | { | |
401 | mpi_size_t i; | |
402 | mpi_limb_t n1, n0, r; | |
403 | int dummy; | |
404 | ||
405 | if (!dividend_size) | |
406 | return 0; | |
407 | ||
408 | /* If multiplication is much faster than division, and the | |
409 | * dividend is large, pre-invert the divisor, and use | |
410 | * only multiplications in the inner loop. | |
411 | * | |
412 | * This test should be read: | |
413 | * Does it ever help to use udiv_qrnnd_preinv? | |
414 | * && Does what we save compensate for the inversion overhead? | |
415 | */ | |
416 | if (UDIV_TIME > (2 * UMUL_TIME + 6) | |
417 | && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) { | |
418 | int normalization_steps; | |
419 | ||
420 | count_leading_zeros(normalization_steps, divisor_limb); | |
421 | if (normalization_steps) { | |
422 | mpi_limb_t divisor_limb_inverted; | |
423 | ||
424 | divisor_limb <<= normalization_steps; | |
425 | ||
426 | /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The | |
427 | * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the | |
428 | * most significant bit (with weight 2**N) implicit. | |
429 | */ | |
430 | /* Special case for DIVISOR_LIMB == 100...000. */ | |
431 | if (!(divisor_limb << 1)) | |
432 | divisor_limb_inverted = ~(mpi_limb_t) 0; | |
433 | else | |
434 | udiv_qrnnd(divisor_limb_inverted, dummy, | |
435 | -divisor_limb, 0, divisor_limb); | |
436 | ||
437 | n1 = dividend_ptr[dividend_size - 1]; | |
438 | r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); | |
439 | ||
440 | /* Possible optimization: | |
441 | * if (r == 0 | |
442 | * && divisor_limb > ((n1 << normalization_steps) | |
443 | * | (dividend_ptr[dividend_size - 2] >> ...))) | |
444 | * ...one division less... | |
445 | */ | |
446 | for (i = dividend_size - 2; i >= 0; i--) { | |
447 | n0 = dividend_ptr[i]; | |
448 | UDIV_QRNND_PREINV(quot_ptr[i + 1], r, r, | |
449 | ((n1 << normalization_steps) | |
450 | | (n0 >> | |
451 | (BITS_PER_MPI_LIMB - | |
452 | normalization_steps))), | |
453 | divisor_limb, | |
454 | divisor_limb_inverted); | |
455 | n1 = n0; | |
456 | } | |
457 | UDIV_QRNND_PREINV(quot_ptr[0], r, r, | |
458 | n1 << normalization_steps, | |
459 | divisor_limb, divisor_limb_inverted); | |
460 | return r >> normalization_steps; | |
461 | } else { | |
462 | mpi_limb_t divisor_limb_inverted; | |
463 | ||
464 | /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The | |
465 | * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the | |
466 | * most significant bit (with weight 2**N) implicit. | |
467 | */ | |
468 | /* Special case for DIVISOR_LIMB == 100...000. */ | |
469 | if (!(divisor_limb << 1)) | |
470 | divisor_limb_inverted = ~(mpi_limb_t) 0; | |
471 | else | |
472 | udiv_qrnnd(divisor_limb_inverted, dummy, | |
473 | -divisor_limb, 0, divisor_limb); | |
474 | ||
475 | i = dividend_size - 1; | |
476 | r = dividend_ptr[i]; | |
477 | ||
478 | if (r >= divisor_limb) | |
479 | r = 0; | |
480 | else | |
481 | quot_ptr[i--] = 0; | |
482 | ||
483 | for (; i >= 0; i--) { | |
484 | n0 = dividend_ptr[i]; | |
485 | UDIV_QRNND_PREINV(quot_ptr[i], r, r, | |
486 | n0, divisor_limb, | |
487 | divisor_limb_inverted); | |
488 | } | |
489 | return r; | |
490 | } | |
491 | } else { | |
492 | if (UDIV_NEEDS_NORMALIZATION) { | |
493 | int normalization_steps; | |
494 | ||
495 | count_leading_zeros(normalization_steps, divisor_limb); | |
496 | if (normalization_steps) { | |
497 | divisor_limb <<= normalization_steps; | |
498 | ||
499 | n1 = dividend_ptr[dividend_size - 1]; | |
500 | r = n1 >> (BITS_PER_MPI_LIMB - | |
501 | normalization_steps); | |
502 | ||
503 | /* Possible optimization: | |
504 | * if (r == 0 | |
505 | * && divisor_limb > ((n1 << normalization_steps) | |
506 | * | (dividend_ptr[dividend_size - 2] >> ...))) | |
507 | * ...one division less... | |
508 | */ | |
509 | for (i = dividend_size - 2; i >= 0; i--) { | |
510 | n0 = dividend_ptr[i]; | |
511 | udiv_qrnnd(quot_ptr[i + 1], r, r, | |
512 | ((n1 << normalization_steps) | |
513 | | (n0 >> | |
514 | (BITS_PER_MPI_LIMB - | |
515 | normalization_steps))), | |
516 | divisor_limb); | |
517 | n1 = n0; | |
518 | } | |
519 | udiv_qrnnd(quot_ptr[0], r, r, | |
520 | n1 << normalization_steps, | |
521 | divisor_limb); | |
522 | return r >> normalization_steps; | |
523 | } | |
524 | } | |
525 | /* No normalization needed, either because udiv_qrnnd doesn't require | |
526 | * it, or because DIVISOR_LIMB is already normalized. */ | |
527 | i = dividend_size - 1; | |
528 | r = dividend_ptr[i]; | |
529 | ||
530 | if (r >= divisor_limb) | |
531 | r = 0; | |
532 | else | |
533 | quot_ptr[i--] = 0; | |
534 | ||
535 | for (; i >= 0; i--) { | |
536 | n0 = dividend_ptr[i]; | |
537 | udiv_qrnnd(quot_ptr[i], r, r, n0, divisor_limb); | |
538 | } | |
539 | return r; | |
540 | } | |
541 | } |