1 | |
---|
2 | #include <NTL/LLL.h> |
---|
3 | #include <NTL/fileio.h> |
---|
4 | #include <NTL/vec_double.h> |
---|
5 | |
---|
6 | |
---|
7 | #include <NTL/new.h> |
---|
8 | |
---|
9 | NTL_START_IMPL |
---|
10 | |
---|
11 | static inline |
---|
12 | void CheckFinite(double *p) |
---|
13 | { |
---|
14 | if (!IsFinite(p)) Error("G_LLL_FP: numbers too big...use G_LLL_XD"); |
---|
15 | } |
---|
16 | |
---|
17 | |
---|
18 | |
---|
19 | static void RowTransform(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1) |
---|
20 | // x = x - y*MU |
---|
21 | { |
---|
22 | static ZZ T, MU; |
---|
23 | long k; |
---|
24 | |
---|
25 | long n = A.length(); |
---|
26 | long i; |
---|
27 | |
---|
28 | MU = MU1; |
---|
29 | |
---|
30 | if (MU == 1) { |
---|
31 | for (i = 1; i <= n; i++) |
---|
32 | sub(A(i), A(i), B(i)); |
---|
33 | |
---|
34 | return; |
---|
35 | } |
---|
36 | |
---|
37 | if (MU == -1) { |
---|
38 | for (i = 1; i <= n; i++) |
---|
39 | add(A(i), A(i), B(i)); |
---|
40 | |
---|
41 | return; |
---|
42 | } |
---|
43 | |
---|
44 | if (MU == 0) return; |
---|
45 | |
---|
46 | if (NumTwos(MU) >= NTL_ZZ_NBITS) |
---|
47 | k = MakeOdd(MU); |
---|
48 | else |
---|
49 | k = 0; |
---|
50 | |
---|
51 | |
---|
52 | if (MU.WideSinglePrecision()) { |
---|
53 | long mu1; |
---|
54 | conv(mu1, MU); |
---|
55 | |
---|
56 | for (i = 1; i <= n; i++) { |
---|
57 | mul(T, B(i), mu1); |
---|
58 | if (k > 0) LeftShift(T, T, k); |
---|
59 | sub(A(i), A(i), T); |
---|
60 | } |
---|
61 | } |
---|
62 | else { |
---|
63 | for (i = 1; i <= n; i++) { |
---|
64 | mul(T, B(i), MU); |
---|
65 | if (k > 0) LeftShift(T, T, k); |
---|
66 | sub(A(i), A(i), T); |
---|
67 | } |
---|
68 | } |
---|
69 | } |
---|
70 | |
---|
71 | |
---|
72 | #define TR_BND (NTL_FDOUBLE_PRECISION/2.0) |
---|
73 | // Just to be safe!! |
---|
74 | |
---|
75 | static double max_abs(double *v, long n) |
---|
76 | { |
---|
77 | long i; |
---|
78 | double res, t; |
---|
79 | |
---|
80 | res = 0; |
---|
81 | |
---|
82 | for (i = 1; i <= n; i++) { |
---|
83 | t = fabs(v[i]); |
---|
84 | if (t > res) res = t; |
---|
85 | } |
---|
86 | |
---|
87 | return res; |
---|
88 | } |
---|
89 | |
---|
90 | |
---|
91 | static void RowTransformStart(double *a, long *in_a, long& in_float, long n) |
---|
92 | { |
---|
93 | long i; |
---|
94 | long inf = 1; |
---|
95 | |
---|
96 | for (i = 1; i <= n; i++) { |
---|
97 | in_a[i] = (a[i] < TR_BND && a[i] > -TR_BND); |
---|
98 | inf = inf & in_a[i]; |
---|
99 | } |
---|
100 | |
---|
101 | in_float = inf; |
---|
102 | } |
---|
103 | |
---|
104 | |
---|
105 | static void RowTransformFinish(vec_ZZ& A, double *a, long *in_a) |
---|
106 | { |
---|
107 | long n = A.length(); |
---|
108 | long i; |
---|
109 | |
---|
110 | for (i = 1; i <= n; i++) { |
---|
111 | if (in_a[i]) { |
---|
112 | conv(A(i), a[i]); |
---|
113 | } |
---|
114 | else { |
---|
115 | conv(a[i], A(i)); |
---|
116 | CheckFinite(&a[i]); |
---|
117 | } |
---|
118 | } |
---|
119 | } |
---|
120 | |
---|
121 | |
---|
122 | static void RowTransform(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1, |
---|
123 | double *a, double *b, long *in_a, |
---|
124 | double& max_a, double max_b, long& in_float) |
---|
125 | // x = x - y*MU |
---|
126 | { |
---|
127 | static ZZ T, MU; |
---|
128 | long k; |
---|
129 | double mu; |
---|
130 | |
---|
131 | conv(mu, MU1); |
---|
132 | CheckFinite(&mu); |
---|
133 | |
---|
134 | long n = A.length(); |
---|
135 | long i; |
---|
136 | |
---|
137 | if (in_float) { |
---|
138 | double mu_abs = fabs(mu); |
---|
139 | if (mu_abs > 0 && max_b > 0 && (mu_abs >= TR_BND || max_b >= TR_BND)) { |
---|
140 | in_float = 0; |
---|
141 | } |
---|
142 | else { |
---|
143 | max_a += mu_abs*max_b; |
---|
144 | if (max_a >= TR_BND) |
---|
145 | in_float = 0; |
---|
146 | } |
---|
147 | } |
---|
148 | |
---|
149 | if (in_float) { |
---|
150 | if (mu == 1) { |
---|
151 | for (i = 1; i <= n; i++) |
---|
152 | a[i] -= b[i]; |
---|
153 | |
---|
154 | return; |
---|
155 | } |
---|
156 | |
---|
157 | if (mu == -1) { |
---|
158 | for (i = 1; i <= n; i++) |
---|
159 | a[i] += b[i]; |
---|
160 | |
---|
161 | return; |
---|
162 | } |
---|
163 | |
---|
164 | if (mu == 0) return; |
---|
165 | |
---|
166 | for (i = 1; i <= n; i++) |
---|
167 | a[i] -= mu*b[i]; |
---|
168 | |
---|
169 | |
---|
170 | return; |
---|
171 | } |
---|
172 | |
---|
173 | |
---|
174 | MU = MU1; |
---|
175 | |
---|
176 | if (MU == 1) { |
---|
177 | for (i = 1; i <= n; i++) { |
---|
178 | if (in_a[i] && a[i] < TR_BND && a[i] > -TR_BND && |
---|
179 | b[i] < TR_BND && b[i] > -TR_BND) { |
---|
180 | |
---|
181 | a[i] -= b[i]; |
---|
182 | } |
---|
183 | else { |
---|
184 | if (in_a[i]) { |
---|
185 | conv(A(i), a[i]); |
---|
186 | in_a[i] = 0; |
---|
187 | } |
---|
188 | |
---|
189 | sub(A(i), A(i), B(i)); |
---|
190 | } |
---|
191 | } |
---|
192 | return; |
---|
193 | } |
---|
194 | |
---|
195 | if (MU == -1) { |
---|
196 | for (i = 1; i <= n; i++) { |
---|
197 | if (in_a[i] && a[i] < TR_BND && a[i] > -TR_BND && |
---|
198 | b[i] < TR_BND && b[i] > -TR_BND) { |
---|
199 | |
---|
200 | a[i] += b[i]; |
---|
201 | } |
---|
202 | else { |
---|
203 | if (in_a[i]) { |
---|
204 | conv(A(i), a[i]); |
---|
205 | in_a[i] = 0; |
---|
206 | } |
---|
207 | |
---|
208 | add(A(i), A(i), B(i)); |
---|
209 | } |
---|
210 | } |
---|
211 | return; |
---|
212 | } |
---|
213 | |
---|
214 | if (MU == 0) return; |
---|
215 | |
---|
216 | double b_bnd = fabs(TR_BND/mu) - 1; |
---|
217 | if (b_bnd < 0) b_bnd = 0; |
---|
218 | |
---|
219 | if (NumTwos(MU) >= NTL_ZZ_NBITS) |
---|
220 | k = MakeOdd(MU); |
---|
221 | else |
---|
222 | k = 0; |
---|
223 | |
---|
224 | |
---|
225 | if (MU.WideSinglePrecision()) { |
---|
226 | long mu1; |
---|
227 | conv(mu1, MU); |
---|
228 | |
---|
229 | if (k > 0) { |
---|
230 | for (i = 1; i <= n; i++) { |
---|
231 | if (in_a[i]) { |
---|
232 | conv(A(i), a[i]); |
---|
233 | in_a[i] = 0; |
---|
234 | } |
---|
235 | |
---|
236 | mul(T, B(i), mu1); |
---|
237 | LeftShift(T, T, k); |
---|
238 | sub(A(i), A(i), T); |
---|
239 | } |
---|
240 | } |
---|
241 | else { |
---|
242 | for (i = 1; i <= n; i++) { |
---|
243 | if (in_a[i] && a[i] < TR_BND && a[i] > -TR_BND && |
---|
244 | b[i] < b_bnd && b[i] > -b_bnd) { |
---|
245 | |
---|
246 | a[i] -= b[i]*mu; |
---|
247 | } |
---|
248 | else { |
---|
249 | if (in_a[i]) { |
---|
250 | conv(A(i), a[i]); |
---|
251 | in_a[i] = 0; |
---|
252 | } |
---|
253 | mul(T, B(i), mu1); |
---|
254 | sub(A(i), A(i), T); |
---|
255 | } |
---|
256 | } |
---|
257 | } |
---|
258 | } |
---|
259 | else { |
---|
260 | for (i = 1; i <= n; i++) { |
---|
261 | if (in_a[i]) { |
---|
262 | conv(A(i), a[i]); |
---|
263 | in_a[i] = 0; |
---|
264 | } |
---|
265 | mul(T, B(i), MU); |
---|
266 | if (k > 0) LeftShift(T, T, k); |
---|
267 | sub(A(i), A(i), T); |
---|
268 | } |
---|
269 | } |
---|
270 | } |
---|
271 | |
---|
272 | static void RowTransform2(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1) |
---|
273 | // x = x + y*MU |
---|
274 | |
---|
275 | { |
---|
276 | static ZZ T, MU; |
---|
277 | long k; |
---|
278 | |
---|
279 | long n = A.length(); |
---|
280 | long i; |
---|
281 | |
---|
282 | MU = MU1; |
---|
283 | |
---|
284 | if (MU == 1) { |
---|
285 | for (i = 1; i <= n; i++) |
---|
286 | add(A(i), A(i), B(i)); |
---|
287 | |
---|
288 | return; |
---|
289 | } |
---|
290 | |
---|
291 | if (MU == -1) { |
---|
292 | for (i = 1; i <= n; i++) |
---|
293 | sub(A(i), A(i), B(i)); |
---|
294 | |
---|
295 | return; |
---|
296 | } |
---|
297 | |
---|
298 | if (MU == 0) return; |
---|
299 | |
---|
300 | if (NumTwos(MU) >= NTL_ZZ_NBITS) |
---|
301 | k = MakeOdd(MU); |
---|
302 | else |
---|
303 | k = 0; |
---|
304 | |
---|
305 | if (MU.WideSinglePrecision()) { |
---|
306 | long mu1; |
---|
307 | conv(mu1, MU); |
---|
308 | |
---|
309 | for (i = 1; i <= n; i++) { |
---|
310 | mul(T, B(i), mu1); |
---|
311 | if (k > 0) LeftShift(T, T, k); |
---|
312 | add(A(i), A(i), T); |
---|
313 | } |
---|
314 | } |
---|
315 | else { |
---|
316 | for (i = 1; i <= n; i++) { |
---|
317 | mul(T, B(i), MU); |
---|
318 | if (k > 0) LeftShift(T, T, k); |
---|
319 | add(A(i), A(i), T); |
---|
320 | } |
---|
321 | } |
---|
322 | } |
---|
323 | |
---|
324 | |
---|
325 | |
---|
326 | class GivensCache_FP { |
---|
327 | public: |
---|
328 | GivensCache_FP(long m, long n); |
---|
329 | ~GivensCache_FP(); |
---|
330 | |
---|
331 | void flush(); |
---|
332 | void selective_flush(long l); |
---|
333 | void swap(long l); |
---|
334 | void swap(); |
---|
335 | void touch(); |
---|
336 | void incr(); |
---|
337 | |
---|
338 | long sz; |
---|
339 | |
---|
340 | double **buf; |
---|
341 | long *bl; |
---|
342 | long *bv; |
---|
343 | long bp; |
---|
344 | }; |
---|
345 | |
---|
346 | |
---|
347 | GivensCache_FP::GivensCache_FP(long m, long n) |
---|
348 | { |
---|
349 | sz = min(m, n)/10; |
---|
350 | if (sz < 2) |
---|
351 | sz = 2; |
---|
352 | else if (sz > 20) |
---|
353 | sz = 20; |
---|
354 | |
---|
355 | typedef double *doubleptr; |
---|
356 | |
---|
357 | long i; |
---|
358 | buf = NTL_NEW_OP doubleptr[sz]; |
---|
359 | if (!buf) Error("out of memory"); |
---|
360 | for (i = 0; i < sz; i++) |
---|
361 | if (!(buf[i] = NTL_NEW_OP double[n+1])) Error("out of memory"); |
---|
362 | |
---|
363 | bl = NTL_NEW_OP long[sz]; |
---|
364 | if (!bl) Error("out of memory"); |
---|
365 | for (i = 0; i < sz; i++) bl[0] = 0; |
---|
366 | |
---|
367 | bv = NTL_NEW_OP long[sz]; |
---|
368 | if (!bv) Error("out of memory"); |
---|
369 | for (i = 0; i < sz; i++) bv[0] = 0; |
---|
370 | |
---|
371 | bp = 0; |
---|
372 | } |
---|
373 | |
---|
374 | GivensCache_FP::~GivensCache_FP() |
---|
375 | { |
---|
376 | long i; |
---|
377 | |
---|
378 | for (i = 0; i < sz; i++) delete [] buf[i]; |
---|
379 | delete [] buf; |
---|
380 | delete [] bl; |
---|
381 | delete [] bv; |
---|
382 | } |
---|
383 | |
---|
384 | void GivensCache_FP::flush() |
---|
385 | { |
---|
386 | long i; |
---|
387 | for (i = 0; i < sz; i++) bl[i] = 0; |
---|
388 | } |
---|
389 | |
---|
390 | void GivensCache_FP::selective_flush(long l) |
---|
391 | { |
---|
392 | long i; |
---|
393 | |
---|
394 | for (i = 0; i < sz; i++) |
---|
395 | if (bl[i] && bv[i] >= l) |
---|
396 | bl[i] = 0; |
---|
397 | } |
---|
398 | |
---|
399 | void GivensCache_FP::swap(long l) |
---|
400 | { |
---|
401 | long k = bl[bp]; |
---|
402 | long i; |
---|
403 | |
---|
404 | i = 0; |
---|
405 | while (i < sz && bl[i] != l) |
---|
406 | i++; |
---|
407 | |
---|
408 | if (i < sz) { |
---|
409 | bl[bp] = l; |
---|
410 | bl[i] = k; |
---|
411 | } |
---|
412 | else |
---|
413 | bl[bp] = l; |
---|
414 | |
---|
415 | selective_flush(l); |
---|
416 | } |
---|
417 | |
---|
418 | void GivensCache_FP::swap() |
---|
419 | { |
---|
420 | swap(bl[bp] - 1); |
---|
421 | } |
---|
422 | |
---|
423 | void GivensCache_FP::touch() |
---|
424 | { |
---|
425 | long k = bl[bp]; |
---|
426 | bl[bp] = 0; |
---|
427 | selective_flush(k); |
---|
428 | } |
---|
429 | |
---|
430 | void GivensCache_FP::incr() |
---|
431 | { |
---|
432 | long k = bl[bp]; |
---|
433 | long k1 = k+1; |
---|
434 | long i; |
---|
435 | |
---|
436 | i = 0; |
---|
437 | while (i < sz && bl[i] != k1) |
---|
438 | i++; |
---|
439 | |
---|
440 | if (i < sz) { |
---|
441 | bp = i; |
---|
442 | return; |
---|
443 | } |
---|
444 | |
---|
445 | i = 0; |
---|
446 | while (i < sz && bl[i] != 0) |
---|
447 | i++; |
---|
448 | |
---|
449 | if (i < sz) { |
---|
450 | bp = i; |
---|
451 | return; |
---|
452 | } |
---|
453 | |
---|
454 | long max_val = 0; |
---|
455 | long max_index = 0; |
---|
456 | for (i = 0; i < sz; i++) { |
---|
457 | long t = labs(bl[i]-k1); |
---|
458 | if (t > max_val) { |
---|
459 | max_val = t; |
---|
460 | max_index = i; |
---|
461 | } |
---|
462 | } |
---|
463 | |
---|
464 | bp = max_index; |
---|
465 | bl[max_index] = 0; |
---|
466 | } |
---|
467 | |
---|
468 | |
---|
469 | static |
---|
470 | void GivensComputeGS(double **B1, double **mu, double **aux, long k, long n, |
---|
471 | GivensCache_FP& cache) |
---|
472 | { |
---|
473 | long i, j; |
---|
474 | |
---|
475 | double c, s, a, b, t; |
---|
476 | |
---|
477 | double *p = mu[k]; |
---|
478 | |
---|
479 | double *pp = cache.buf[cache.bp]; |
---|
480 | |
---|
481 | if (!cache.bl[cache.bp]) { |
---|
482 | for (j = 1; j <= n; j++) |
---|
483 | pp[j] = B1[k][j]; |
---|
484 | |
---|
485 | long backoff; |
---|
486 | backoff = k/4; |
---|
487 | if (backoff < 2) |
---|
488 | backoff = 2; |
---|
489 | else if (backoff > cache.sz + 2) |
---|
490 | backoff = cache.sz + 2; |
---|
491 | |
---|
492 | long ub = k-(backoff-1); |
---|
493 | |
---|
494 | for (i = 1; i < ub; i++) { |
---|
495 | double *cptr = mu[i]; |
---|
496 | double *sptr = aux[i]; |
---|
497 | |
---|
498 | for (j = n; j > i; j--) { |
---|
499 | c = cptr[j]; |
---|
500 | s = sptr[j]; |
---|
501 | |
---|
502 | a = c*pp[j-1] - s*pp[j]; |
---|
503 | b = s*pp[j-1] + c*pp[j]; |
---|
504 | |
---|
505 | pp[j-1] = a; |
---|
506 | pp[j] = b; |
---|
507 | } |
---|
508 | |
---|
509 | pp[i] = pp[i]/mu[i][i]; |
---|
510 | } |
---|
511 | |
---|
512 | cache.bl[cache.bp] = k; |
---|
513 | cache.bv[cache.bp] = k-backoff; |
---|
514 | } |
---|
515 | |
---|
516 | for (j = 1; j <= n; j++) |
---|
517 | p[j] = pp[j]; |
---|
518 | |
---|
519 | for (i = max(cache.bv[cache.bp]+1, 1); i < k; i++) { |
---|
520 | double *cptr = mu[i]; |
---|
521 | double *sptr = aux[i]; |
---|
522 | |
---|
523 | for (j = n; j > i; j--) { |
---|
524 | c = cptr[j]; |
---|
525 | s = sptr[j]; |
---|
526 | |
---|
527 | a = c*p[j-1] - s*p[j]; |
---|
528 | b = s*p[j-1] + c*p[j]; |
---|
529 | |
---|
530 | p[j-1] = a; |
---|
531 | p[j] = b; |
---|
532 | } |
---|
533 | |
---|
534 | p[i] = p[i]/mu[i][i]; |
---|
535 | } |
---|
536 | |
---|
537 | for (j = n; j > k; j--) { |
---|
538 | a = p[j-1]; |
---|
539 | b = p[j]; |
---|
540 | |
---|
541 | if (b == 0) { |
---|
542 | c = 1; |
---|
543 | s = 0; |
---|
544 | } |
---|
545 | else if (fabs(b) > fabs(a)) { |
---|
546 | t = -a/b; |
---|
547 | s = 1/sqrt(1 + t*t); |
---|
548 | c = s*t; |
---|
549 | } |
---|
550 | else { |
---|
551 | t = -b/a; |
---|
552 | c = 1/sqrt(1 + t*t); |
---|
553 | s = c*t; |
---|
554 | } |
---|
555 | |
---|
556 | p[j-1] = c*a - s*b; |
---|
557 | p[j] = c; |
---|
558 | aux[k][j] = s; |
---|
559 | } |
---|
560 | |
---|
561 | if (k > n+1) Error("G_LLL_FP: internal error"); |
---|
562 | if (k > n) p[k] = 0; |
---|
563 | |
---|
564 | for (i = 1; i <= k; i++) |
---|
565 | CheckFinite(&p[i]); |
---|
566 | } |
---|
567 | |
---|
568 | static double red_fudge = 0; |
---|
569 | static long log_red = 0; |
---|
570 | |
---|
571 | static long verbose = 0; |
---|
572 | |
---|
573 | static unsigned long NumSwaps = 0; |
---|
574 | static double StartTime = 0; |
---|
575 | static double LastTime = 0; |
---|
576 | |
---|
577 | |
---|
578 | |
---|
579 | static void G_LLLStatus(long max_k, double t, long m, const mat_ZZ& B) |
---|
580 | { |
---|
581 | ZZ t1; |
---|
582 | long i; |
---|
583 | double prodlen = 0; |
---|
584 | |
---|
585 | for (i = 1; i <= m; i++) { |
---|
586 | InnerProduct(t1, B(i), B(i)); |
---|
587 | if (!IsZero(t1)) |
---|
588 | prodlen += log(t1); |
---|
589 | } |
---|
590 | |
---|
591 | LastTime = t; |
---|
592 | |
---|
593 | } |
---|
594 | |
---|
595 | static void init_red_fudge() |
---|
596 | { |
---|
597 | long i; |
---|
598 | |
---|
599 | log_red = long(0.50*NTL_DOUBLE_PRECISION); |
---|
600 | red_fudge = 1; |
---|
601 | |
---|
602 | for (i = log_red; i > 0; i--) |
---|
603 | red_fudge = red_fudge*0.5; |
---|
604 | } |
---|
605 | |
---|
606 | static void inc_red_fudge() |
---|
607 | { |
---|
608 | |
---|
609 | red_fudge = red_fudge * 2; |
---|
610 | log_red--; |
---|
611 | |
---|
612 | |
---|
613 | if (log_red < 4) |
---|
614 | Error("G_LLL_FP: too much loss of precision...stop!"); |
---|
615 | } |
---|
616 | |
---|
617 | |
---|
618 | #if 0 |
---|
619 | |
---|
620 | static void print_mus(double **mu, long k) |
---|
621 | { |
---|
622 | long i; |
---|
623 | |
---|
624 | for (i = k-1; i >= 1; i--) |
---|
625 | cerr << mu[k][i] << " "; |
---|
626 | cerr << "\n"; |
---|
627 | } |
---|
628 | |
---|
629 | #endif |
---|
630 | |
---|
631 | |
---|
632 | |
---|
633 | static |
---|
634 | long ll_G_LLL_FP(mat_ZZ& B, mat_ZZ* U, double delta, long deep, |
---|
635 | LLLCheckFct check, double **B1, double **mu, |
---|
636 | double **aux, |
---|
637 | long m, long init_k, long &quit, GivensCache_FP& cache) |
---|
638 | { |
---|
639 | long n = B.NumCols(); |
---|
640 | |
---|
641 | long i, j, k, Fc1; |
---|
642 | ZZ MU; |
---|
643 | double mu1; |
---|
644 | |
---|
645 | double t1; |
---|
646 | ZZ T1; |
---|
647 | double *tp; |
---|
648 | |
---|
649 | double half_plus_fudge = 0.5 + red_fudge; |
---|
650 | |
---|
651 | quit = 0; |
---|
652 | k = init_k; |
---|
653 | |
---|
654 | vec_long in_vec_mem; |
---|
655 | in_vec_mem.SetLength(n+1); |
---|
656 | long *in_vec = in_vec_mem.elts(); |
---|
657 | |
---|
658 | double *max_b; |
---|
659 | max_b = NTL_NEW_OP double [m+1]; |
---|
660 | if (!max_b) Error("out of memory in lll_G_LLL_FP"); |
---|
661 | |
---|
662 | for (i = 1; i <= m; i++) |
---|
663 | max_b[i] = max_abs(B1[i], n); |
---|
664 | |
---|
665 | long in_float; |
---|
666 | |
---|
667 | long counter; |
---|
668 | |
---|
669 | long trigger_index; |
---|
670 | long small_trigger; |
---|
671 | long cnt; |
---|
672 | |
---|
673 | |
---|
674 | long max_k = 0; |
---|
675 | |
---|
676 | double tt; |
---|
677 | |
---|
678 | long swap_cnt = 0; |
---|
679 | |
---|
680 | cache.flush(); |
---|
681 | |
---|
682 | while (k <= m) { |
---|
683 | |
---|
684 | if (k > max_k) { |
---|
685 | max_k = k; |
---|
686 | swap_cnt = 0; |
---|
687 | } |
---|
688 | |
---|
689 | if (verbose) { |
---|
690 | tt = GetTime(); |
---|
691 | |
---|
692 | if (tt > LastTime + LLLStatusInterval) |
---|
693 | G_LLLStatus(max_k, tt, m, B); |
---|
694 | } |
---|
695 | |
---|
696 | GivensComputeGS(B1, mu, aux, k, n, cache); |
---|
697 | |
---|
698 | if (swap_cnt > 200000) { |
---|
699 | //cerr << "G_LLL_FP: swap loop?\n"; |
---|
700 | swap_cnt = 0; |
---|
701 | } |
---|
702 | |
---|
703 | counter = 0; |
---|
704 | trigger_index = k; |
---|
705 | small_trigger = 0; |
---|
706 | cnt = 0; |
---|
707 | |
---|
708 | long sz=0, new_sz; |
---|
709 | |
---|
710 | do { |
---|
711 | // size reduction |
---|
712 | |
---|
713 | counter++; |
---|
714 | if ((counter & 127) == 0) { |
---|
715 | |
---|
716 | new_sz = 0; |
---|
717 | for (j = 1; j <= n; j++) |
---|
718 | new_sz += NumBits(B(k,j)); |
---|
719 | |
---|
720 | if ((counter >> 7) == 1 || new_sz < sz) { |
---|
721 | sz = new_sz; |
---|
722 | } |
---|
723 | //else { |
---|
724 | // cerr << "G_LLL_FP: warning--infinite loop? (" << k << ")\n"; |
---|
725 | //} |
---|
726 | } |
---|
727 | |
---|
728 | Fc1 = 0; |
---|
729 | |
---|
730 | for (j = k-1; j >= 1; j--) { |
---|
731 | t1 = fabs(mu[k][j]); |
---|
732 | if (t1 > half_plus_fudge) { |
---|
733 | |
---|
734 | |
---|
735 | if (!Fc1) { |
---|
736 | if (j > trigger_index || |
---|
737 | (j == trigger_index && small_trigger)) { |
---|
738 | |
---|
739 | cnt++; |
---|
740 | |
---|
741 | if (cnt > 10) { |
---|
742 | inc_red_fudge(); |
---|
743 | half_plus_fudge = 0.5 + red_fudge; |
---|
744 | cnt = 0; |
---|
745 | } |
---|
746 | } |
---|
747 | |
---|
748 | trigger_index = j; |
---|
749 | small_trigger = (t1 < 4); |
---|
750 | |
---|
751 | Fc1 = 1; |
---|
752 | RowTransformStart(B1[k], in_vec, in_float, n); |
---|
753 | } |
---|
754 | |
---|
755 | |
---|
756 | mu1 = mu[k][j]; |
---|
757 | if (mu1 >= 0) |
---|
758 | mu1 = ceil(mu1-0.5); |
---|
759 | else |
---|
760 | mu1 = floor(mu1+0.5); |
---|
761 | |
---|
762 | double *mu_k = mu[k]; |
---|
763 | double *mu_j = mu[j]; |
---|
764 | |
---|
765 | if (mu1 == 1) { |
---|
766 | for (i = 1; i <= j-1; i++) |
---|
767 | mu_k[i] -= mu_j[i]; |
---|
768 | } |
---|
769 | else if (mu1 == -1) { |
---|
770 | for (i = 1; i <= j-1; i++) |
---|
771 | mu_k[i] += mu_j[i]; |
---|
772 | } |
---|
773 | else { |
---|
774 | for (i = 1; i <= j-1; i++) |
---|
775 | mu_k[i] -= mu1*mu_j[i]; |
---|
776 | } |
---|
777 | |
---|
778 | mu_k[j] -= mu1; |
---|
779 | |
---|
780 | conv(MU, mu1); |
---|
781 | |
---|
782 | RowTransform(B(k), B(j), MU, B1[k], B1[j], in_vec, |
---|
783 | max_b[k], max_b[j], in_float); |
---|
784 | if (U) RowTransform((*U)(k), (*U)(j), MU); |
---|
785 | } |
---|
786 | } |
---|
787 | |
---|
788 | |
---|
789 | if (Fc1) { |
---|
790 | RowTransformFinish(B(k), B1[k], in_vec); |
---|
791 | max_b[k] = max_abs(B1[k], n); |
---|
792 | cache.touch(); |
---|
793 | GivensComputeGS(B1, mu, aux, k, n, cache); |
---|
794 | } |
---|
795 | } while (Fc1); |
---|
796 | |
---|
797 | if (check && (*check)(B(k))) |
---|
798 | quit = 1; |
---|
799 | |
---|
800 | if (IsZero(B(k))) { |
---|
801 | for (i = k; i < m; i++) { |
---|
802 | // swap i, i+1 |
---|
803 | swap(B(i), B(i+1)); |
---|
804 | tp = B1[i]; B1[i] = B1[i+1]; B1[i+1] = tp; |
---|
805 | t1 = max_b[i]; max_b[i] = max_b[i+1]; max_b[i+1] = t1; |
---|
806 | if (U) swap((*U)(i), (*U)(i+1)); |
---|
807 | } |
---|
808 | |
---|
809 | cache.flush(); |
---|
810 | |
---|
811 | m--; |
---|
812 | if (quit) break; |
---|
813 | continue; |
---|
814 | } |
---|
815 | |
---|
816 | if (quit) break; |
---|
817 | |
---|
818 | if (deep > 0) { |
---|
819 | // deep insertions |
---|
820 | |
---|
821 | Error("sorry...deep insertions not implemented"); |
---|
822 | } // end deep insertions |
---|
823 | |
---|
824 | // test G_LLL reduction condition |
---|
825 | |
---|
826 | if (k > 1 && |
---|
827 | sqrt(delta - mu[k][k-1]*mu[k][k-1])*fabs(mu[k-1][k-1]) > |
---|
828 | fabs(mu[k][k])) { |
---|
829 | // swap rows k, k-1 |
---|
830 | |
---|
831 | swap(B(k), B(k-1)); |
---|
832 | tp = B1[k]; B1[k] = B1[k-1]; B1[k-1] = tp; |
---|
833 | t1 = max_b[k]; max_b[k] = max_b[k-1]; max_b[k-1] = t1; |
---|
834 | if (U) swap((*U)(k), (*U)(k-1)); |
---|
835 | |
---|
836 | cache.swap(); |
---|
837 | |
---|
838 | k--; |
---|
839 | NumSwaps++; |
---|
840 | swap_cnt++; |
---|
841 | // cout << "-\n"; |
---|
842 | } |
---|
843 | else { |
---|
844 | |
---|
845 | cache.incr(); |
---|
846 | |
---|
847 | k++; |
---|
848 | // cout << "+\n"; |
---|
849 | } |
---|
850 | |
---|
851 | } |
---|
852 | |
---|
853 | if (verbose) { |
---|
854 | G_LLLStatus(m+1, GetTime(), m, B); |
---|
855 | } |
---|
856 | |
---|
857 | |
---|
858 | delete [] max_b; |
---|
859 | |
---|
860 | return m; |
---|
861 | } |
---|
862 | |
---|
863 | |
---|
864 | |
---|
865 | |
---|
866 | |
---|
867 | static |
---|
868 | long G_LLL_FP(mat_ZZ& B, mat_ZZ* U, double delta, long deep, |
---|
869 | LLLCheckFct check) |
---|
870 | { |
---|
871 | long m = B.NumRows(); |
---|
872 | long n = B.NumCols(); |
---|
873 | |
---|
874 | long i, j; |
---|
875 | long new_m, dep, quit; |
---|
876 | ZZ MU; |
---|
877 | |
---|
878 | ZZ T1; |
---|
879 | |
---|
880 | init_red_fudge(); |
---|
881 | |
---|
882 | if (U) ident(*U, m); |
---|
883 | |
---|
884 | double **B1; // approximates B |
---|
885 | |
---|
886 | typedef double *doubleptr; |
---|
887 | |
---|
888 | B1 = NTL_NEW_OP doubleptr[m+1]; |
---|
889 | if (!B1) Error("G_LLL_FP: out of memory"); |
---|
890 | |
---|
891 | for (i = 1; i <= m; i++) { |
---|
892 | B1[i] = NTL_NEW_OP double[n+1]; |
---|
893 | if (!B1[i]) Error("G_LLL_FP: out of memory"); |
---|
894 | } |
---|
895 | |
---|
896 | double **mu; |
---|
897 | mu = NTL_NEW_OP doubleptr[m+1]; |
---|
898 | if (!mu) Error("G_LLL_FP: out of memory"); |
---|
899 | |
---|
900 | for (i = 1; i <= m; i++) { |
---|
901 | mu[i] = NTL_NEW_OP double[n+2]; |
---|
902 | if (!mu[i]) Error("G_LLL_FP: out of memory"); |
---|
903 | } |
---|
904 | |
---|
905 | double **aux; |
---|
906 | aux = NTL_NEW_OP doubleptr[m+1]; |
---|
907 | if (!aux) Error("G_LLL_FP: out of memory"); |
---|
908 | |
---|
909 | for (i = 1; i <= m; i++) { |
---|
910 | aux[i] = NTL_NEW_OP double[n+1]; |
---|
911 | if (!aux[i]) Error("G_LLL_FP: out of memory"); |
---|
912 | } |
---|
913 | |
---|
914 | for (i = 1; i <=m; i++) |
---|
915 | for (j = 1; j <= n; j++) { |
---|
916 | conv(B1[i][j], B(i, j)); |
---|
917 | CheckFinite(&B1[i][j]); |
---|
918 | } |
---|
919 | |
---|
920 | |
---|
921 | GivensCache_FP cache(m, n); |
---|
922 | |
---|
923 | new_m = ll_G_LLL_FP(B, U, delta, deep, check, B1, mu, aux, m, 1, quit, cache); |
---|
924 | dep = m - new_m; |
---|
925 | m = new_m; |
---|
926 | |
---|
927 | if (dep > 0) { |
---|
928 | // for consistency, we move all of the zero rows to the front |
---|
929 | |
---|
930 | for (i = 0; i < m; i++) { |
---|
931 | swap(B(m+dep-i), B(m-i)); |
---|
932 | if (U) swap((*U)(m+dep-i), (*U)(m-i)); |
---|
933 | } |
---|
934 | } |
---|
935 | |
---|
936 | |
---|
937 | // clean-up |
---|
938 | |
---|
939 | for (i = 1; i <= m; i++) { |
---|
940 | delete [] B1[i]; |
---|
941 | } |
---|
942 | |
---|
943 | delete [] B1; |
---|
944 | |
---|
945 | for (i = 1; i <= m; i++) { |
---|
946 | delete [] mu[i]; |
---|
947 | } |
---|
948 | |
---|
949 | delete [] mu; |
---|
950 | |
---|
951 | for (i = 1; i <= m; i++) { |
---|
952 | delete [] aux[i]; |
---|
953 | } |
---|
954 | |
---|
955 | delete [] aux; |
---|
956 | |
---|
957 | return m; |
---|
958 | } |
---|
959 | |
---|
960 | |
---|
961 | |
---|
962 | long G_LLL_FP(mat_ZZ& B, double delta, long deep, LLLCheckFct check, |
---|
963 | long verb) |
---|
964 | { |
---|
965 | verbose = verb; |
---|
966 | NumSwaps = 0; |
---|
967 | if (verbose) { |
---|
968 | StartTime = GetTime(); |
---|
969 | LastTime = StartTime; |
---|
970 | } |
---|
971 | |
---|
972 | if (delta < 0.50 || delta >= 1) Error("G_LLL_FP: bad delta"); |
---|
973 | if (deep < 0) Error("G_LLL_FP: bad deep"); |
---|
974 | return G_LLL_FP(B, 0, delta, deep, check); |
---|
975 | } |
---|
976 | |
---|
977 | long G_LLL_FP(mat_ZZ& B, mat_ZZ& U, double delta, long deep, |
---|
978 | LLLCheckFct check, long verb) |
---|
979 | { |
---|
980 | verbose = verb; |
---|
981 | NumSwaps = 0; |
---|
982 | if (verbose) { |
---|
983 | StartTime = GetTime(); |
---|
984 | LastTime = StartTime; |
---|
985 | } |
---|
986 | |
---|
987 | if (delta < 0.50 || delta >= 1) Error("G_LLL_FP: bad delta"); |
---|
988 | if (deep < 0) Error("G_LLL_FP: bad deep"); |
---|
989 | return G_LLL_FP(B, &U, delta, deep, check); |
---|
990 | } |
---|
991 | |
---|
992 | |
---|
993 | |
---|
994 | static vec_double G_BKZConstant; |
---|
995 | |
---|
996 | static |
---|
997 | void ComputeG_BKZConstant(long beta, long p) |
---|
998 | { |
---|
999 | const double c_PI = 3.14159265358979323846264338328; |
---|
1000 | const double LogPI = 1.14472988584940017414342735135; |
---|
1001 | |
---|
1002 | G_BKZConstant.SetLength(beta-1); |
---|
1003 | |
---|
1004 | vec_double Log; |
---|
1005 | Log.SetLength(beta); |
---|
1006 | |
---|
1007 | |
---|
1008 | long i, j, k; |
---|
1009 | double x, y; |
---|
1010 | |
---|
1011 | for (j = 1; j <= beta; j++) |
---|
1012 | Log(j) = log(double(j)); |
---|
1013 | |
---|
1014 | for (i = 1; i <= beta-1; i++) { |
---|
1015 | // First, we compute x = gamma(i/2)^{2/i} |
---|
1016 | |
---|
1017 | k = i/2; |
---|
1018 | |
---|
1019 | if ((i & 1) == 0) { // i even |
---|
1020 | x = 0; |
---|
1021 | for (j = 1; j <= k; j++) |
---|
1022 | x = x + Log(j); |
---|
1023 | |
---|
1024 | x = x * (1/double(k)); |
---|
1025 | |
---|
1026 | x = exp(x); |
---|
1027 | } |
---|
1028 | else { // i odd |
---|
1029 | x = 0; |
---|
1030 | for (j = k + 2; j <= 2*k + 2; j++) |
---|
1031 | x = x + Log(j); |
---|
1032 | |
---|
1033 | x = 0.5*LogPI + x - 2*(k+1)*Log(2); |
---|
1034 | |
---|
1035 | x = x * (2.0/double(i)); |
---|
1036 | |
---|
1037 | x = exp(x); |
---|
1038 | } |
---|
1039 | |
---|
1040 | // Second, we compute y = 2^{2*p/i} |
---|
1041 | |
---|
1042 | y = -(2*p/double(i))*Log(2); |
---|
1043 | y = exp(y); |
---|
1044 | |
---|
1045 | G_BKZConstant(i) = x*y/c_PI; |
---|
1046 | } |
---|
1047 | } |
---|
1048 | |
---|
1049 | static vec_double G_BKZThresh; |
---|
1050 | |
---|
1051 | static |
---|
1052 | void ComputeG_BKZThresh(double *c, long beta) |
---|
1053 | { |
---|
1054 | G_BKZThresh.SetLength(beta-1); |
---|
1055 | |
---|
1056 | long i; |
---|
1057 | double x; |
---|
1058 | |
---|
1059 | x = 0; |
---|
1060 | |
---|
1061 | for (i = 1; i <= beta-1; i++) { |
---|
1062 | x += log(c[i-1]); |
---|
1063 | G_BKZThresh(i) = exp(x/double(i))*G_BKZConstant(i); |
---|
1064 | if (!IsFinite(&G_BKZThresh(i))) G_BKZThresh(i) = 0; |
---|
1065 | } |
---|
1066 | } |
---|
1067 | |
---|
1068 | static |
---|
1069 | void G_BKZStatus(double tt, double enum_time, unsigned long NumIterations, |
---|
1070 | unsigned long NumTrivial, unsigned long NumNonTrivial, |
---|
1071 | unsigned long NumNoOps, long m, |
---|
1072 | const mat_ZZ& B) |
---|
1073 | { |
---|
1074 | |
---|
1075 | ZZ t1; |
---|
1076 | long i; |
---|
1077 | double prodlen = 0; |
---|
1078 | |
---|
1079 | for (i = 1; i <= m; i++) { |
---|
1080 | InnerProduct(t1, B(i), B(i)); |
---|
1081 | if (!IsZero(t1)) |
---|
1082 | prodlen += log(t1); |
---|
1083 | } |
---|
1084 | |
---|
1085 | LastTime = tt; |
---|
1086 | |
---|
1087 | } |
---|
1088 | |
---|
1089 | |
---|
1090 | |
---|
1091 | static |
---|
1092 | long G_BKZ_FP(mat_ZZ& BB, mat_ZZ* UU, double delta, |
---|
1093 | long beta, long prune, LLLCheckFct check) |
---|
1094 | { |
---|
1095 | |
---|
1096 | |
---|
1097 | |
---|
1098 | long m = BB.NumRows(); |
---|
1099 | long n = BB.NumCols(); |
---|
1100 | long m_orig = m; |
---|
1101 | |
---|
1102 | long i, j; |
---|
1103 | ZZ MU; |
---|
1104 | |
---|
1105 | double t1; |
---|
1106 | ZZ T1; |
---|
1107 | double *tp; |
---|
1108 | |
---|
1109 | init_red_fudge(); |
---|
1110 | |
---|
1111 | mat_ZZ B; |
---|
1112 | B = BB; |
---|
1113 | |
---|
1114 | B.SetDims(m+1, n); |
---|
1115 | |
---|
1116 | |
---|
1117 | double **B1; // approximates B |
---|
1118 | |
---|
1119 | typedef double *doubleptr; |
---|
1120 | |
---|
1121 | B1 = NTL_NEW_OP doubleptr[m+2]; |
---|
1122 | if (!B1) Error("G_BKZ_FP: out of memory"); |
---|
1123 | |
---|
1124 | for (i = 1; i <= m+1; i++) { |
---|
1125 | B1[i] = NTL_NEW_OP double[n+1]; |
---|
1126 | if (!B1[i]) Error("G_BKZ_FP: out of memory"); |
---|
1127 | } |
---|
1128 | |
---|
1129 | double **mu; |
---|
1130 | mu = NTL_NEW_OP doubleptr[m+2]; |
---|
1131 | if (!mu) Error("G_LLL_FP: out of memory"); |
---|
1132 | |
---|
1133 | for (i = 1; i <= m+1; i++) { |
---|
1134 | mu[i] = NTL_NEW_OP double[n+2]; |
---|
1135 | if (!mu[i]) Error("G_BKZ_FP: out of memory"); |
---|
1136 | } |
---|
1137 | |
---|
1138 | double **aux; |
---|
1139 | aux = NTL_NEW_OP doubleptr[m+2]; |
---|
1140 | if (!aux) Error("G_LLL_FP: out of memory"); |
---|
1141 | |
---|
1142 | for (i = 1; i <= m+1; i++) { |
---|
1143 | aux[i] = NTL_NEW_OP double[n+1]; |
---|
1144 | if (!aux[i]) Error("G_BKZ_FP: out of memory"); |
---|
1145 | } |
---|
1146 | |
---|
1147 | |
---|
1148 | double *c; // squared lengths of Gramm-Schmidt basis vectors |
---|
1149 | |
---|
1150 | c = NTL_NEW_OP double[m+2]; |
---|
1151 | if (!c) Error("G_BKZ_FP: out of memory"); |
---|
1152 | |
---|
1153 | double cbar; |
---|
1154 | |
---|
1155 | double *ctilda; |
---|
1156 | ctilda = NTL_NEW_OP double[m+2]; |
---|
1157 | if (!ctilda) Error("G_BKZ_FP: out of memory"); |
---|
1158 | |
---|
1159 | double *vvec; |
---|
1160 | vvec = NTL_NEW_OP double[m+2]; |
---|
1161 | if (!vvec) Error("G_BKZ_FP: out of memory"); |
---|
1162 | |
---|
1163 | double *yvec; |
---|
1164 | yvec = NTL_NEW_OP double[m+2]; |
---|
1165 | if (!yvec) Error("G_BKZ_FP: out of memory"); |
---|
1166 | |
---|
1167 | double *uvec; |
---|
1168 | uvec = NTL_NEW_OP double[m+2]; |
---|
1169 | if (!uvec) Error("G_BKZ_FP: out of memory"); |
---|
1170 | |
---|
1171 | double *utildavec; |
---|
1172 | utildavec = NTL_NEW_OP double[m+2]; |
---|
1173 | if (!utildavec) Error("G_BKZ_FP: out of memory"); |
---|
1174 | |
---|
1175 | |
---|
1176 | long *Deltavec; |
---|
1177 | Deltavec = NTL_NEW_OP long[m+2]; |
---|
1178 | if (!Deltavec) Error("G_BKZ_FP: out of memory"); |
---|
1179 | |
---|
1180 | long *deltavec; |
---|
1181 | deltavec = NTL_NEW_OP long[m+2]; |
---|
1182 | if (!deltavec) Error("G_BKZ_FP: out of memory"); |
---|
1183 | |
---|
1184 | mat_ZZ Ulocal; |
---|
1185 | mat_ZZ *U; |
---|
1186 | |
---|
1187 | if (UU) { |
---|
1188 | Ulocal.SetDims(m+1, m); |
---|
1189 | for (i = 1; i <= m; i++) |
---|
1190 | conv(Ulocal(i, i), 1); |
---|
1191 | U = &Ulocal; |
---|
1192 | } |
---|
1193 | else |
---|
1194 | U = 0; |
---|
1195 | |
---|
1196 | long quit; |
---|
1197 | long new_m; |
---|
1198 | long z, jj, kk; |
---|
1199 | long s, t; |
---|
1200 | long h; |
---|
1201 | double eta; |
---|
1202 | |
---|
1203 | |
---|
1204 | for (i = 1; i <=m; i++) |
---|
1205 | for (j = 1; j <= n; j++) { |
---|
1206 | conv(B1[i][j], B(i, j)); |
---|
1207 | CheckFinite(&B1[i][j]); |
---|
1208 | } |
---|
1209 | |
---|
1210 | |
---|
1211 | GivensCache_FP cache(m, n); |
---|
1212 | |
---|
1213 | m = ll_G_LLL_FP(B, U, delta, 0, check, B1, mu, aux, m, 1, quit, cache); |
---|
1214 | |
---|
1215 | double tt; |
---|
1216 | |
---|
1217 | double enum_time = 0; |
---|
1218 | unsigned long NumIterations = 0; |
---|
1219 | unsigned long NumTrivial = 0; |
---|
1220 | unsigned long NumNonTrivial = 0; |
---|
1221 | unsigned long NumNoOps = 0; |
---|
1222 | |
---|
1223 | long verb = verbose; |
---|
1224 | |
---|
1225 | verbose = 0; |
---|
1226 | |
---|
1227 | long clean = 1; |
---|
1228 | |
---|
1229 | if (m < m_orig) { |
---|
1230 | for (i = m_orig+1; i >= m+2; i--) { |
---|
1231 | // swap i, i-1 |
---|
1232 | |
---|
1233 | swap(B(i), B(i-1)); |
---|
1234 | if (U) swap((*U)(i), (*U)(i-1)); |
---|
1235 | } |
---|
1236 | } |
---|
1237 | |
---|
1238 | if (!quit && m > 1) { |
---|
1239 | if (beta > m) beta = m; |
---|
1240 | |
---|
1241 | if (prune > 0) |
---|
1242 | ComputeG_BKZConstant(beta, prune); |
---|
1243 | |
---|
1244 | z = 0; |
---|
1245 | jj = 0; |
---|
1246 | |
---|
1247 | while (z < m-1) { |
---|
1248 | jj++; |
---|
1249 | kk = min(jj+beta-1, m); |
---|
1250 | |
---|
1251 | if (jj == m) { |
---|
1252 | jj = 1; |
---|
1253 | kk = beta; |
---|
1254 | clean = 1; |
---|
1255 | } |
---|
1256 | |
---|
1257 | if (verb) { |
---|
1258 | tt = GetTime(); |
---|
1259 | if (tt > LastTime + LLLStatusInterval) |
---|
1260 | G_BKZStatus(tt, enum_time, NumIterations, NumTrivial, |
---|
1261 | NumNonTrivial, NumNoOps, m, B); |
---|
1262 | } |
---|
1263 | |
---|
1264 | |
---|
1265 | // ENUM |
---|
1266 | |
---|
1267 | double tt1; |
---|
1268 | |
---|
1269 | if (verb) { |
---|
1270 | tt1 = GetTime(); |
---|
1271 | } |
---|
1272 | |
---|
1273 | for (i = jj; i <= kk; i++) { |
---|
1274 | c[i] = mu[i][i]*mu[i][i]; |
---|
1275 | CheckFinite(&c[i]); |
---|
1276 | } |
---|
1277 | |
---|
1278 | if (prune > 0) |
---|
1279 | ComputeG_BKZThresh(&c[jj], kk-jj+1); |
---|
1280 | |
---|
1281 | cbar = c[jj]; |
---|
1282 | utildavec[jj] = uvec[jj] = 1; |
---|
1283 | |
---|
1284 | yvec[jj] = vvec[jj] = 0; |
---|
1285 | Deltavec[jj] = 0; |
---|
1286 | |
---|
1287 | |
---|
1288 | s = t = jj; |
---|
1289 | deltavec[jj] = 1; |
---|
1290 | |
---|
1291 | for (i = jj+1; i <= kk+1; i++) { |
---|
1292 | ctilda[i] = uvec[i] = utildavec[i] = yvec[i] = 0; |
---|
1293 | Deltavec[i] = 0; |
---|
1294 | vvec[i] = 0; |
---|
1295 | deltavec[i] = 1; |
---|
1296 | } |
---|
1297 | |
---|
1298 | long enum_cnt = 0; |
---|
1299 | |
---|
1300 | while (t <= kk) { |
---|
1301 | if (verb) { |
---|
1302 | enum_cnt++; |
---|
1303 | if (enum_cnt > 100000) { |
---|
1304 | enum_cnt = 0; |
---|
1305 | tt = GetTime(); |
---|
1306 | if (tt > LastTime + LLLStatusInterval) { |
---|
1307 | enum_time += tt - tt1; |
---|
1308 | tt1 = tt; |
---|
1309 | G_BKZStatus(tt, enum_time, NumIterations, NumTrivial, |
---|
1310 | NumNonTrivial, NumNoOps, m, B); |
---|
1311 | } |
---|
1312 | } |
---|
1313 | } |
---|
1314 | |
---|
1315 | ctilda[t] = ctilda[t+1] + |
---|
1316 | (yvec[t]+utildavec[t])*(yvec[t]+utildavec[t])*c[t]; |
---|
1317 | |
---|
1318 | if (prune > 0 && t > jj) { |
---|
1319 | eta = G_BKZThresh(t-jj); |
---|
1320 | } |
---|
1321 | else |
---|
1322 | eta = 0; |
---|
1323 | |
---|
1324 | if (ctilda[t] < cbar - eta) { |
---|
1325 | if (t > jj) { |
---|
1326 | t--; |
---|
1327 | t1 = 0; |
---|
1328 | for (i = t+1; i <= s; i++) |
---|
1329 | t1 += utildavec[i]*mu[i][t]; |
---|
1330 | yvec[t] = t1; |
---|
1331 | t1 = -t1; |
---|
1332 | if (t1 >= 0) |
---|
1333 | t1 = ceil(t1-0.5); |
---|
1334 | else |
---|
1335 | t1 = floor(t1+0.5); |
---|
1336 | utildavec[t] = vvec[t] = t1; |
---|
1337 | Deltavec[t] = 0; |
---|
1338 | if (utildavec[t] > -yvec[t]) |
---|
1339 | deltavec[t] = -1; |
---|
1340 | else |
---|
1341 | deltavec[t] = 1; |
---|
1342 | } |
---|
1343 | else { |
---|
1344 | cbar = ctilda[jj]; |
---|
1345 | for (i = jj; i <= kk; i++) { |
---|
1346 | uvec[i] = utildavec[i]; |
---|
1347 | } |
---|
1348 | } |
---|
1349 | } |
---|
1350 | else { |
---|
1351 | t++; |
---|
1352 | s = max(s, t); |
---|
1353 | if (t < s) Deltavec[t] = -Deltavec[t]; |
---|
1354 | if (Deltavec[t]*deltavec[t] >= 0) Deltavec[t] += deltavec[t]; |
---|
1355 | utildavec[t] = vvec[t] + Deltavec[t]; |
---|
1356 | } |
---|
1357 | } |
---|
1358 | |
---|
1359 | if (verb) { |
---|
1360 | tt1 = GetTime() - tt1; |
---|
1361 | enum_time += tt1; |
---|
1362 | } |
---|
1363 | |
---|
1364 | NumIterations++; |
---|
1365 | |
---|
1366 | h = min(kk+1, m); |
---|
1367 | |
---|
1368 | if ((delta - 8*red_fudge)*c[jj] > cbar) { |
---|
1369 | |
---|
1370 | clean = 0; |
---|
1371 | |
---|
1372 | // we treat the case that the new vector is b_s (jj < s <= kk) |
---|
1373 | // as a special case that appears to occur most of the time. |
---|
1374 | |
---|
1375 | s = 0; |
---|
1376 | for (i = jj+1; i <= kk; i++) { |
---|
1377 | if (uvec[i] != 0) { |
---|
1378 | if (s == 0) |
---|
1379 | s = i; |
---|
1380 | else |
---|
1381 | s = -1; |
---|
1382 | } |
---|
1383 | } |
---|
1384 | |
---|
1385 | if (s == 0) Error("G_BKZ_FP: internal error"); |
---|
1386 | |
---|
1387 | if (s > 0) { |
---|
1388 | // special case |
---|
1389 | |
---|
1390 | NumTrivial++; |
---|
1391 | |
---|
1392 | for (i = s; i > jj; i--) { |
---|
1393 | // swap i, i-1 |
---|
1394 | swap(B(i-1), B(i)); |
---|
1395 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
1396 | tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp; |
---|
1397 | } |
---|
1398 | |
---|
1399 | // cerr << "special case\n"; |
---|
1400 | new_m = ll_G_LLL_FP(B, U, delta, 0, check, |
---|
1401 | B1, mu, aux, h, jj, quit, cache); |
---|
1402 | if (new_m != h) Error("G_BKZ_FP: internal error"); |
---|
1403 | if (quit) break; |
---|
1404 | } |
---|
1405 | else { |
---|
1406 | // the general case |
---|
1407 | |
---|
1408 | NumNonTrivial++; |
---|
1409 | |
---|
1410 | for (i = 1; i <= n; i++) conv(B(m+1, i), 0); |
---|
1411 | |
---|
1412 | if (U) { |
---|
1413 | for (i = 1; i <= m_orig; i++) |
---|
1414 | conv((*U)(m+1, i), 0); |
---|
1415 | } |
---|
1416 | |
---|
1417 | for (i = jj; i <= kk; i++) { |
---|
1418 | if (uvec[i] == 0) continue; |
---|
1419 | conv(MU, uvec[i]); |
---|
1420 | RowTransform2(B(m+1), B(i), MU); |
---|
1421 | if (U) RowTransform2((*U)(m+1), (*U)(i), MU); |
---|
1422 | } |
---|
1423 | |
---|
1424 | for (i = m+1; i >= jj+1; i--) { |
---|
1425 | // swap i, i-1 |
---|
1426 | swap(B(i-1), B(i)); |
---|
1427 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
1428 | tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp; |
---|
1429 | } |
---|
1430 | |
---|
1431 | for (i = 1; i <= n; i++) { |
---|
1432 | conv(B1[jj][i], B(jj, i)); |
---|
1433 | CheckFinite(&B1[jj][i]); |
---|
1434 | } |
---|
1435 | |
---|
1436 | if (IsZero(B(jj))) Error("G_BKZ_FP: internal error"); |
---|
1437 | |
---|
1438 | // remove linear dependencies |
---|
1439 | |
---|
1440 | // cerr << "general case\n"; |
---|
1441 | new_m = ll_G_LLL_FP(B, U, delta, 0, 0, B1, mu, aux, |
---|
1442 | kk+1, jj, quit, cache); |
---|
1443 | |
---|
1444 | if (new_m != kk) Error("G_BKZ_FP: internal error"); |
---|
1445 | |
---|
1446 | // remove zero vector |
---|
1447 | |
---|
1448 | for (i = kk+2; i <= m+1; i++) { |
---|
1449 | // swap i, i-1 |
---|
1450 | swap(B(i-1), B(i)); |
---|
1451 | if (U) swap((*U)(i-1), (*U)(i)); |
---|
1452 | tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp; |
---|
1453 | } |
---|
1454 | |
---|
1455 | quit = 0; |
---|
1456 | if (check) { |
---|
1457 | for (i = 1; i <= kk; i++) |
---|
1458 | if ((*check)(B(i))) { |
---|
1459 | quit = 1; |
---|
1460 | break; |
---|
1461 | } |
---|
1462 | } |
---|
1463 | |
---|
1464 | if (quit) break; |
---|
1465 | |
---|
1466 | if (h > kk) { |
---|
1467 | // extend reduced basis |
---|
1468 | |
---|
1469 | new_m = ll_G_LLL_FP(B, U, delta, 0, check, |
---|
1470 | B1, mu, aux, h, h, quit, cache); |
---|
1471 | |
---|
1472 | if (new_m != h) Error("G_BKZ_FP: internal error"); |
---|
1473 | if (quit) break; |
---|
1474 | } |
---|
1475 | } |
---|
1476 | |
---|
1477 | z = 0; |
---|
1478 | } |
---|
1479 | else { |
---|
1480 | // G_LLL_FP |
---|
1481 | // cerr << "progress\n"; |
---|
1482 | |
---|
1483 | NumNoOps++; |
---|
1484 | |
---|
1485 | if (!clean) { |
---|
1486 | new_m = ll_G_LLL_FP(B, U, delta, 0, check, B1, mu, aux, |
---|
1487 | h, h, quit, cache); |
---|
1488 | if (new_m != h) Error("G_BKZ_FP: internal error"); |
---|
1489 | if (quit) break; |
---|
1490 | } |
---|
1491 | |
---|
1492 | z++; |
---|
1493 | } |
---|
1494 | } |
---|
1495 | } |
---|
1496 | |
---|
1497 | |
---|
1498 | if (verb) { |
---|
1499 | G_BKZStatus(GetTime(), enum_time, NumIterations, NumTrivial, NumNonTrivial, |
---|
1500 | NumNoOps, m, B); |
---|
1501 | } |
---|
1502 | |
---|
1503 | // clean up |
---|
1504 | |
---|
1505 | |
---|
1506 | if (m_orig > m) { |
---|
1507 | // for consistency, we move zero vectors to the front |
---|
1508 | |
---|
1509 | for (i = m+1; i <= m_orig; i++) { |
---|
1510 | swap(B(i), B(i+1)); |
---|
1511 | if (U) swap((*U)(i), (*U)(i+1)); |
---|
1512 | } |
---|
1513 | |
---|
1514 | for (i = 0; i < m; i++) { |
---|
1515 | swap(B(m_orig-i), B(m-i)); |
---|
1516 | if (U) swap((*U)(m_orig-i), (*U)(m-i)); |
---|
1517 | } |
---|
1518 | } |
---|
1519 | |
---|
1520 | B.SetDims(m_orig, n); |
---|
1521 | BB = B; |
---|
1522 | |
---|
1523 | if (U) { |
---|
1524 | U->SetDims(m_orig, m_orig); |
---|
1525 | *UU = *U; |
---|
1526 | } |
---|
1527 | |
---|
1528 | for (i = 1; i <= m+1; i++) { |
---|
1529 | delete [] B1[i]; |
---|
1530 | } |
---|
1531 | |
---|
1532 | delete [] B1; |
---|
1533 | |
---|
1534 | for (i = 1; i <= m+1; i++) { |
---|
1535 | delete [] mu[i]; |
---|
1536 | } |
---|
1537 | |
---|
1538 | delete [] mu; |
---|
1539 | |
---|
1540 | for (i = 1; i <= m+1; i++) { |
---|
1541 | delete [] aux[i]; |
---|
1542 | } |
---|
1543 | |
---|
1544 | delete [] aux; |
---|
1545 | |
---|
1546 | delete [] c; |
---|
1547 | delete [] ctilda; |
---|
1548 | delete [] vvec; |
---|
1549 | delete [] yvec; |
---|
1550 | delete [] uvec; |
---|
1551 | delete [] utildavec; |
---|
1552 | delete [] Deltavec; |
---|
1553 | delete [] deltavec; |
---|
1554 | |
---|
1555 | return m; |
---|
1556 | } |
---|
1557 | |
---|
1558 | long G_BKZ_FP(mat_ZZ& BB, mat_ZZ& UU, double delta, |
---|
1559 | long beta, long prune, LLLCheckFct check, long verb) |
---|
1560 | { |
---|
1561 | verbose = verb; |
---|
1562 | NumSwaps = 0; |
---|
1563 | if (verbose) { |
---|
1564 | StartTime = GetTime(); |
---|
1565 | LastTime = StartTime; |
---|
1566 | } |
---|
1567 | |
---|
1568 | if (delta < 0.50 || delta >= 1) Error("G_BKZ_FP: bad delta"); |
---|
1569 | if (beta < 2) Error("G_BKZ_FP: bad block size"); |
---|
1570 | |
---|
1571 | return G_BKZ_FP(BB, &UU, delta, beta, prune, check); |
---|
1572 | } |
---|
1573 | |
---|
1574 | long G_BKZ_FP(mat_ZZ& BB, double delta, |
---|
1575 | long beta, long prune, LLLCheckFct check, long verb) |
---|
1576 | { |
---|
1577 | verbose = verb; |
---|
1578 | NumSwaps = 0; |
---|
1579 | if (verbose) { |
---|
1580 | StartTime = GetTime(); |
---|
1581 | LastTime = StartTime; |
---|
1582 | } |
---|
1583 | |
---|
1584 | if (delta < 0.50 || delta >= 1) Error("G_BKZ_FP: bad delta"); |
---|
1585 | if (beta < 2) Error("G_BKZ_FP: bad block size"); |
---|
1586 | |
---|
1587 | return G_BKZ_FP(BB, 0, delta, beta, prune, check); |
---|
1588 | } |
---|
1589 | |
---|
1590 | NTL_END_IMPL |
---|