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465ae836 | 1 | // SPDX-License-Identifier: GPL-2.0-or-later |
cdec9cb5 DK |
2 | /* mpihelp-div.c - MPI helper functions |
3 | * Copyright (C) 1994, 1996 Free Software Foundation, Inc. | |
4 | * Copyright (C) 1998, 1999 Free Software Foundation, Inc. | |
5 | * | |
6 | * This file is part of GnuPG. | |
7 | * | |
cdec9cb5 DK |
8 | * Note: This code is heavily based on the GNU MP Library. |
9 | * Actually it's the same code with only minor changes in the | |
10 | * way the data is stored; this is to support the abstraction | |
11 | * of an optional secure memory allocation which may be used | |
12 | * to avoid revealing of sensitive data due to paging etc. | |
13 | * The GNU MP Library itself is published under the LGPL; | |
14 | * however I decided to publish this code under the plain GPL. | |
15 | */ | |
16 | ||
17 | #include "mpi-internal.h" | |
18 | #include "longlong.h" | |
19 | ||
20 | #ifndef UMUL_TIME | |
21 | #define UMUL_TIME 1 | |
22 | #endif | |
23 | #ifndef UDIV_TIME | |
24 | #define UDIV_TIME UMUL_TIME | |
25 | #endif | |
26 | ||
a8ea8bdd TZ |
27 | |
28 | mpi_limb_t | |
29 | mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size, | |
30 | mpi_limb_t divisor_limb) | |
31 | { | |
32 | mpi_size_t i; | |
33 | mpi_limb_t n1, n0, r; | |
ae6ee6ae | 34 | mpi_limb_t dummy __maybe_unused; |
a8ea8bdd TZ |
35 | |
36 | /* Botch: Should this be handled at all? Rely on callers? */ | |
37 | if (!dividend_size) | |
38 | return 0; | |
39 | ||
40 | /* If multiplication is much faster than division, and the | |
41 | * dividend is large, pre-invert the divisor, and use | |
42 | * only multiplications in the inner loop. | |
43 | * | |
44 | * This test should be read: | |
45 | * Does it ever help to use udiv_qrnnd_preinv? | |
46 | * && Does what we save compensate for the inversion overhead? | |
47 | */ | |
48 | if (UDIV_TIME > (2 * UMUL_TIME + 6) | |
49 | && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) { | |
50 | int normalization_steps; | |
51 | ||
52 | normalization_steps = count_leading_zeros(divisor_limb); | |
53 | if (normalization_steps) { | |
54 | mpi_limb_t divisor_limb_inverted; | |
55 | ||
56 | divisor_limb <<= normalization_steps; | |
57 | ||
58 | /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The | |
59 | * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the | |
60 | * most significant bit (with weight 2**N) implicit. | |
61 | * | |
62 | * Special case for DIVISOR_LIMB == 100...000. | |
63 | */ | |
64 | if (!(divisor_limb << 1)) | |
65 | divisor_limb_inverted = ~(mpi_limb_t)0; | |
66 | else | |
67 | udiv_qrnnd(divisor_limb_inverted, dummy, | |
68 | -divisor_limb, 0, divisor_limb); | |
69 | ||
70 | n1 = dividend_ptr[dividend_size - 1]; | |
71 | r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); | |
72 | ||
73 | /* Possible optimization: | |
74 | * if (r == 0 | |
75 | * && divisor_limb > ((n1 << normalization_steps) | |
76 | * | (dividend_ptr[dividend_size - 2] >> ...))) | |
77 | * ...one division less... | |
78 | */ | |
79 | for (i = dividend_size - 2; i >= 0; i--) { | |
80 | n0 = dividend_ptr[i]; | |
81 | UDIV_QRNND_PREINV(dummy, r, r, | |
82 | ((n1 << normalization_steps) | |
83 | | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))), | |
84 | divisor_limb, divisor_limb_inverted); | |
85 | n1 = n0; | |
86 | } | |
87 | UDIV_QRNND_PREINV(dummy, r, r, | |
88 | n1 << normalization_steps, | |
89 | divisor_limb, divisor_limb_inverted); | |
90 | return r >> normalization_steps; | |
91 | } else { | |
92 | mpi_limb_t divisor_limb_inverted; | |
93 | ||
94 | /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The | |
95 | * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the | |
96 | * most significant bit (with weight 2**N) implicit. | |
97 | * | |
98 | * Special case for DIVISOR_LIMB == 100...000. | |
99 | */ | |
100 | if (!(divisor_limb << 1)) | |
101 | divisor_limb_inverted = ~(mpi_limb_t)0; | |
102 | else | |
103 | udiv_qrnnd(divisor_limb_inverted, dummy, | |
104 | -divisor_limb, 0, divisor_limb); | |
105 | ||
106 | i = dividend_size - 1; | |
107 | r = dividend_ptr[i]; | |
108 | ||
109 | if (r >= divisor_limb) | |
110 | r = 0; | |
111 | else | |
112 | i--; | |
113 | ||
114 | for ( ; i >= 0; i--) { | |
115 | n0 = dividend_ptr[i]; | |
116 | UDIV_QRNND_PREINV(dummy, r, r, | |
117 | n0, divisor_limb, divisor_limb_inverted); | |
118 | } | |
119 | return r; | |
120 | } | |
121 | } else { | |
122 | if (UDIV_NEEDS_NORMALIZATION) { | |
123 | int normalization_steps; | |
124 | ||
125 | normalization_steps = count_leading_zeros(divisor_limb); | |
126 | if (normalization_steps) { | |
127 | divisor_limb <<= normalization_steps; | |
128 | ||
129 | n1 = dividend_ptr[dividend_size - 1]; | |
130 | r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); | |
131 | ||
132 | /* Possible optimization: | |
133 | * if (r == 0 | |
134 | * && divisor_limb > ((n1 << normalization_steps) | |
135 | * | (dividend_ptr[dividend_size - 2] >> ...))) | |
136 | * ...one division less... | |
137 | */ | |
138 | for (i = dividend_size - 2; i >= 0; i--) { | |
139 | n0 = dividend_ptr[i]; | |
140 | udiv_qrnnd(dummy, r, r, | |
141 | ((n1 << normalization_steps) | |
142 | | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))), | |
143 | divisor_limb); | |
144 | n1 = n0; | |
145 | } | |
146 | udiv_qrnnd(dummy, r, r, | |
147 | n1 << normalization_steps, | |
148 | divisor_limb); | |
149 | return r >> normalization_steps; | |
150 | } | |
151 | } | |
152 | /* No normalization needed, either because udiv_qrnnd doesn't require | |
153 | * it, or because DIVISOR_LIMB is already normalized. | |
154 | */ | |
155 | i = dividend_size - 1; | |
156 | r = dividend_ptr[i]; | |
157 | ||
158 | if (r >= divisor_limb) | |
159 | r = 0; | |
160 | else | |
161 | i--; | |
162 | ||
163 | for (; i >= 0; i--) { | |
164 | n0 = dividend_ptr[i]; | |
165 | udiv_qrnnd(dummy, r, r, n0, divisor_limb); | |
166 | } | |
167 | return r; | |
168 | } | |
169 | } | |
170 | ||
cdec9cb5 DK |
171 | /* Divide num (NP/NSIZE) by den (DP/DSIZE) and write |
172 | * the NSIZE-DSIZE least significant quotient limbs at QP | |
173 | * and the DSIZE long remainder at NP. If QEXTRA_LIMBS is | |
174 | * non-zero, generate that many fraction bits and append them after the | |
175 | * other quotient limbs. | |
176 | * Return the most significant limb of the quotient, this is always 0 or 1. | |
177 | * | |
178 | * Preconditions: | |
179 | * 0. NSIZE >= DSIZE. | |
180 | * 1. The most significant bit of the divisor must be set. | |
181 | * 2. QP must either not overlap with the input operands at all, or | |
182 | * QP + DSIZE >= NP must hold true. (This means that it's | |
183 | * possible to put the quotient in the high part of NUM, right after the | |
184 | * remainder in NUM. | |
185 | * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero. | |
186 | */ | |
187 | ||
188 | mpi_limb_t | |
189 | mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs, | |
190 | mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize) | |
191 | { | |
192 | mpi_limb_t most_significant_q_limb = 0; | |
193 | ||
194 | switch (dsize) { | |
195 | case 0: | |
196 | /* We are asked to divide by zero, so go ahead and do it! (To make | |
197 | the compiler not remove this statement, return the value.) */ | |
a6d68ecc DK |
198 | /* |
199 | * existing clients of this function have been modified | |
200 | * not to call it with dsize == 0, so this should not happen | |
201 | */ | |
cdec9cb5 DK |
202 | return 1 / dsize; |
203 | ||
204 | case 1: | |
205 | { | |
206 | mpi_size_t i; | |
207 | mpi_limb_t n1; | |
208 | mpi_limb_t d; | |
209 | ||
210 | d = dp[0]; | |
211 | n1 = np[nsize - 1]; | |
212 | ||
213 | if (n1 >= d) { | |
214 | n1 -= d; | |
215 | most_significant_q_limb = 1; | |
216 | } | |
217 | ||
218 | qp += qextra_limbs; | |
219 | for (i = nsize - 2; i >= 0; i--) | |
220 | udiv_qrnnd(qp[i], n1, n1, np[i], d); | |
221 | qp -= qextra_limbs; | |
222 | ||
223 | for (i = qextra_limbs - 1; i >= 0; i--) | |
224 | udiv_qrnnd(qp[i], n1, n1, 0, d); | |
225 | ||
226 | np[0] = n1; | |
227 | } | |
228 | break; | |
229 | ||
230 | case 2: | |
231 | { | |
232 | mpi_size_t i; | |
233 | mpi_limb_t n1, n0, n2; | |
234 | mpi_limb_t d1, d0; | |
235 | ||
236 | np += nsize - 2; | |
237 | d1 = dp[1]; | |
238 | d0 = dp[0]; | |
239 | n1 = np[1]; | |
240 | n0 = np[0]; | |
241 | ||
242 | if (n1 >= d1 && (n1 > d1 || n0 >= d0)) { | |
243 | sub_ddmmss(n1, n0, n1, n0, d1, d0); | |
244 | most_significant_q_limb = 1; | |
245 | } | |
246 | ||
247 | for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) { | |
248 | mpi_limb_t q; | |
249 | mpi_limb_t r; | |
250 | ||
251 | if (i >= qextra_limbs) | |
252 | np--; | |
253 | else | |
254 | np[0] = 0; | |
255 | ||
256 | if (n1 == d1) { | |
257 | /* Q should be either 111..111 or 111..110. Need special | |
258 | * treatment of this rare case as normal division would | |
259 | * give overflow. */ | |
260 | q = ~(mpi_limb_t) 0; | |
261 | ||
262 | r = n0 + d1; | |
263 | if (r < d1) { /* Carry in the addition? */ | |
264 | add_ssaaaa(n1, n0, r - d0, | |
265 | np[0], 0, d0); | |
266 | qp[i] = q; | |
267 | continue; | |
268 | } | |
269 | n1 = d0 - (d0 != 0 ? 1 : 0); | |
270 | n0 = -d0; | |
271 | } else { | |
272 | udiv_qrnnd(q, r, n1, n0, d1); | |
273 | umul_ppmm(n1, n0, d0, q); | |
274 | } | |
275 | ||
276 | n2 = np[0]; | |
277 | q_test: | |
278 | if (n1 > r || (n1 == r && n0 > n2)) { | |
279 | /* The estimated Q was too large. */ | |
280 | q--; | |
281 | sub_ddmmss(n1, n0, n1, n0, 0, d0); | |
282 | r += d1; | |
283 | if (r >= d1) /* If not carry, test Q again. */ | |
284 | goto q_test; | |
285 | } | |
286 | ||
287 | qp[i] = q; | |
288 | sub_ddmmss(n1, n0, r, n2, n1, n0); | |
289 | } | |
290 | np[1] = n1; | |
291 | np[0] = n0; | |
292 | } | |
293 | break; | |
294 | ||
295 | default: | |
296 | { | |
297 | mpi_size_t i; | |
298 | mpi_limb_t dX, d1, n0; | |
299 | ||
300 | np += nsize - dsize; | |
301 | dX = dp[dsize - 1]; | |
302 | d1 = dp[dsize - 2]; | |
303 | n0 = np[dsize - 1]; | |
304 | ||
305 | if (n0 >= dX) { | |
306 | if (n0 > dX | |
307 | || mpihelp_cmp(np, dp, dsize - 1) >= 0) { | |
308 | mpihelp_sub_n(np, np, dp, dsize); | |
309 | n0 = np[dsize - 1]; | |
310 | most_significant_q_limb = 1; | |
311 | } | |
312 | } | |
313 | ||
314 | for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) { | |
315 | mpi_limb_t q; | |
316 | mpi_limb_t n1, n2; | |
317 | mpi_limb_t cy_limb; | |
318 | ||
319 | if (i >= qextra_limbs) { | |
320 | np--; | |
321 | n2 = np[dsize]; | |
322 | } else { | |
323 | n2 = np[dsize - 1]; | |
324 | MPN_COPY_DECR(np + 1, np, dsize - 1); | |
325 | np[0] = 0; | |
326 | } | |
327 | ||
328 | if (n0 == dX) { | |
329 | /* This might over-estimate q, but it's probably not worth | |
330 | * the extra code here to find out. */ | |
331 | q = ~(mpi_limb_t) 0; | |
332 | } else { | |
333 | mpi_limb_t r; | |
334 | ||
335 | udiv_qrnnd(q, r, n0, np[dsize - 1], dX); | |
336 | umul_ppmm(n1, n0, d1, q); | |
337 | ||
338 | while (n1 > r | |
339 | || (n1 == r | |
340 | && n0 > np[dsize - 2])) { | |
341 | q--; | |
342 | r += dX; | |
343 | if (r < dX) /* I.e. "carry in previous addition?" */ | |
344 | break; | |
345 | n1 -= n0 < d1; | |
346 | n0 -= d1; | |
347 | } | |
348 | } | |
349 | ||
350 | /* Possible optimization: We already have (q * n0) and (1 * n1) | |
351 | * after the calculation of q. Taking advantage of that, we | |
352 | * could make this loop make two iterations less. */ | |
353 | cy_limb = mpihelp_submul_1(np, dp, dsize, q); | |
354 | ||
355 | if (n2 != cy_limb) { | |
356 | mpihelp_add_n(np, np, dp, dsize); | |
357 | q--; | |
358 | } | |
359 | ||
360 | qp[i] = q; | |
361 | n0 = np[dsize - 1]; | |
362 | } | |
363 | } | |
364 | } | |
365 | ||
366 | return most_significant_q_limb; | |
367 | } | |
a8ea8bdd TZ |
368 | |
369 | /**************** | |
370 | * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB. | |
371 | * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR. | |
372 | * Return the single-limb remainder. | |
373 | * There are no constraints on the value of the divisor. | |
374 | * | |
375 | * QUOT_PTR and DIVIDEND_PTR might point to the same limb. | |
376 | */ | |
377 | ||
378 | mpi_limb_t | |
379 | mpihelp_divmod_1(mpi_ptr_t quot_ptr, | |
380 | mpi_ptr_t dividend_ptr, mpi_size_t dividend_size, | |
381 | mpi_limb_t divisor_limb) | |
382 | { | |
383 | mpi_size_t i; | |
384 | mpi_limb_t n1, n0, r; | |
ae6ee6ae | 385 | mpi_limb_t dummy __maybe_unused; |
a8ea8bdd TZ |
386 | |
387 | if (!dividend_size) | |
388 | return 0; | |
389 | ||
390 | /* If multiplication is much faster than division, and the | |
391 | * dividend is large, pre-invert the divisor, and use | |
392 | * only multiplications in the inner loop. | |
393 | * | |
394 | * This test should be read: | |
395 | * Does it ever help to use udiv_qrnnd_preinv? | |
396 | * && Does what we save compensate for the inversion overhead? | |
397 | */ | |
398 | if (UDIV_TIME > (2 * UMUL_TIME + 6) | |
399 | && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) { | |
400 | int normalization_steps; | |
401 | ||
402 | normalization_steps = count_leading_zeros(divisor_limb); | |
403 | if (normalization_steps) { | |
404 | mpi_limb_t divisor_limb_inverted; | |
405 | ||
406 | divisor_limb <<= normalization_steps; | |
407 | ||
408 | /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The | |
409 | * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the | |
410 | * most significant bit (with weight 2**N) implicit. | |
411 | */ | |
412 | /* Special case for DIVISOR_LIMB == 100...000. */ | |
413 | if (!(divisor_limb << 1)) | |
414 | divisor_limb_inverted = ~(mpi_limb_t)0; | |
415 | else | |
416 | udiv_qrnnd(divisor_limb_inverted, dummy, | |
417 | -divisor_limb, 0, divisor_limb); | |
418 | ||
419 | n1 = dividend_ptr[dividend_size - 1]; | |
420 | r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); | |
421 | ||
422 | /* Possible optimization: | |
423 | * if (r == 0 | |
424 | * && divisor_limb > ((n1 << normalization_steps) | |
425 | * | (dividend_ptr[dividend_size - 2] >> ...))) | |
426 | * ...one division less... | |
427 | */ | |
428 | for (i = dividend_size - 2; i >= 0; i--) { | |
429 | n0 = dividend_ptr[i]; | |
430 | UDIV_QRNND_PREINV(quot_ptr[i + 1], r, r, | |
431 | ((n1 << normalization_steps) | |
432 | | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))), | |
433 | divisor_limb, divisor_limb_inverted); | |
434 | n1 = n0; | |
435 | } | |
436 | UDIV_QRNND_PREINV(quot_ptr[0], r, r, | |
437 | n1 << normalization_steps, | |
438 | divisor_limb, divisor_limb_inverted); | |
439 | return r >> normalization_steps; | |
440 | } else { | |
441 | mpi_limb_t divisor_limb_inverted; | |
442 | ||
443 | /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The | |
444 | * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the | |
445 | * most significant bit (with weight 2**N) implicit. | |
446 | */ | |
447 | /* Special case for DIVISOR_LIMB == 100...000. */ | |
448 | if (!(divisor_limb << 1)) | |
449 | divisor_limb_inverted = ~(mpi_limb_t) 0; | |
450 | else | |
451 | udiv_qrnnd(divisor_limb_inverted, dummy, | |
452 | -divisor_limb, 0, divisor_limb); | |
453 | ||
454 | i = dividend_size - 1; | |
455 | r = dividend_ptr[i]; | |
456 | ||
457 | if (r >= divisor_limb) | |
458 | r = 0; | |
459 | else | |
460 | quot_ptr[i--] = 0; | |
461 | ||
462 | for ( ; i >= 0; i--) { | |
463 | n0 = dividend_ptr[i]; | |
464 | UDIV_QRNND_PREINV(quot_ptr[i], r, r, | |
465 | n0, divisor_limb, divisor_limb_inverted); | |
466 | } | |
467 | return r; | |
468 | } | |
469 | } else { | |
470 | if (UDIV_NEEDS_NORMALIZATION) { | |
471 | int normalization_steps; | |
472 | ||
473 | normalization_steps = count_leading_zeros(divisor_limb); | |
474 | if (normalization_steps) { | |
475 | divisor_limb <<= normalization_steps; | |
476 | ||
477 | n1 = dividend_ptr[dividend_size - 1]; | |
478 | r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); | |
479 | ||
480 | /* Possible optimization: | |
481 | * if (r == 0 | |
482 | * && divisor_limb > ((n1 << normalization_steps) | |
483 | * | (dividend_ptr[dividend_size - 2] >> ...))) | |
484 | * ...one division less... | |
485 | */ | |
486 | for (i = dividend_size - 2; i >= 0; i--) { | |
487 | n0 = dividend_ptr[i]; | |
488 | udiv_qrnnd(quot_ptr[i + 1], r, r, | |
489 | ((n1 << normalization_steps) | |
490 | | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))), | |
491 | divisor_limb); | |
492 | n1 = n0; | |
493 | } | |
494 | udiv_qrnnd(quot_ptr[0], r, r, | |
495 | n1 << normalization_steps, | |
496 | divisor_limb); | |
497 | return r >> normalization_steps; | |
498 | } | |
499 | } | |
500 | /* No normalization needed, either because udiv_qrnnd doesn't require | |
501 | * it, or because DIVISOR_LIMB is already normalized. | |
502 | */ | |
503 | i = dividend_size - 1; | |
504 | r = dividend_ptr[i]; | |
505 | ||
506 | if (r >= divisor_limb) | |
507 | r = 0; | |
508 | else | |
509 | quot_ptr[i--] = 0; | |
510 | ||
511 | for (; i >= 0; i--) { | |
512 | n0 = dividend_ptr[i]; | |
513 | udiv_qrnnd(quot_ptr[i], r, r, n0, divisor_limb); | |
514 | } | |
515 | return r; | |
516 | } | |
517 | } |