isl_basic_map_drop: add memory management annotations
[isl.git] / isl_map_simplify.c
blob6b2cd7ce255849d61bd470b64a8c17f89b9ccb3e
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2012-2013 Ecole Normale Superieure
4 * Copyright 2014-2015 INRIA Rocquencourt
5 * Copyright 2016 Sven Verdoolaege
7 * Use of this software is governed by the MIT license
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
12 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
13 * B.P. 105 - 78153 Le Chesnay, France
16 #include <isl_ctx_private.h>
17 #include <isl_map_private.h>
18 #include "isl_equalities.h"
19 #include <isl/map.h>
20 #include <isl_seq.h>
21 #include "isl_tab.h"
22 #include <isl_space_private.h>
23 #include <isl_mat_private.h>
24 #include <isl_vec_private.h>
26 #include <bset_to_bmap.c>
27 #include <bset_from_bmap.c>
28 #include <set_to_map.c>
29 #include <set_from_map.c>
31 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
33 isl_int *t = bmap->eq[a];
34 bmap->eq[a] = bmap->eq[b];
35 bmap->eq[b] = t;
38 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
40 if (a != b) {
41 isl_int *t = bmap->ineq[a];
42 bmap->ineq[a] = bmap->ineq[b];
43 bmap->ineq[b] = t;
47 struct isl_basic_map *isl_basic_map_normalize_constraints(
48 struct isl_basic_map *bmap)
50 int i;
51 isl_int gcd;
52 unsigned total = isl_basic_map_total_dim(bmap);
54 if (!bmap)
55 return NULL;
57 isl_int_init(gcd);
58 for (i = bmap->n_eq - 1; i >= 0; --i) {
59 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
60 if (isl_int_is_zero(gcd)) {
61 if (!isl_int_is_zero(bmap->eq[i][0])) {
62 bmap = isl_basic_map_set_to_empty(bmap);
63 break;
65 isl_basic_map_drop_equality(bmap, i);
66 continue;
68 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
69 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
70 if (isl_int_is_one(gcd))
71 continue;
72 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
73 bmap = isl_basic_map_set_to_empty(bmap);
74 break;
76 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
79 for (i = bmap->n_ineq - 1; i >= 0; --i) {
80 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
81 if (isl_int_is_zero(gcd)) {
82 if (isl_int_is_neg(bmap->ineq[i][0])) {
83 bmap = isl_basic_map_set_to_empty(bmap);
84 break;
86 isl_basic_map_drop_inequality(bmap, i);
87 continue;
89 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
90 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
91 if (isl_int_is_one(gcd))
92 continue;
93 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
94 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
96 isl_int_clear(gcd);
98 return bmap;
101 struct isl_basic_set *isl_basic_set_normalize_constraints(
102 struct isl_basic_set *bset)
104 isl_basic_map *bmap = bset_to_bmap(bset);
105 return bset_from_bmap(isl_basic_map_normalize_constraints(bmap));
108 /* Reduce the coefficient of the variable at position "pos"
109 * in integer division "div", such that it lies in the half-open
110 * interval (1/2,1/2], extracting any excess value from this integer division.
111 * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
112 * corresponds to the constant term.
114 * That is, the integer division is of the form
116 * floor((... + (c * d + r) * x_pos + ...)/d)
118 * with -d < 2 * r <= d.
119 * Replace it by
121 * floor((... + r * x_pos + ...)/d) + c * x_pos
123 * If 2 * ((c * d + r) % d) <= d, then c = floor((c * d + r)/d).
124 * Otherwise, c = floor((c * d + r)/d) + 1.
126 * This is the same normalization that is performed by isl_aff_floor.
128 static __isl_give isl_basic_map *reduce_coefficient_in_div(
129 __isl_take isl_basic_map *bmap, int div, int pos)
131 isl_int shift;
132 int add_one;
134 isl_int_init(shift);
135 isl_int_fdiv_r(shift, bmap->div[div][1 + pos], bmap->div[div][0]);
136 isl_int_mul_ui(shift, shift, 2);
137 add_one = isl_int_gt(shift, bmap->div[div][0]);
138 isl_int_fdiv_q(shift, bmap->div[div][1 + pos], bmap->div[div][0]);
139 if (add_one)
140 isl_int_add_ui(shift, shift, 1);
141 isl_int_neg(shift, shift);
142 bmap = isl_basic_map_shift_div(bmap, div, pos, shift);
143 isl_int_clear(shift);
145 return bmap;
148 /* Does the coefficient of the variable at position "pos"
149 * in integer division "div" need to be reduced?
150 * That is, does it lie outside the half-open interval (1/2,1/2]?
151 * The coefficient c/d lies outside this interval if abs(2 * c) >= d and
152 * 2 * c != d.
154 static isl_bool needs_reduction(__isl_keep isl_basic_map *bmap, int div,
155 int pos)
157 isl_bool r;
159 if (isl_int_is_zero(bmap->div[div][1 + pos]))
160 return isl_bool_false;
162 isl_int_mul_ui(bmap->div[div][1 + pos], bmap->div[div][1 + pos], 2);
163 r = isl_int_abs_ge(bmap->div[div][1 + pos], bmap->div[div][0]) &&
164 !isl_int_eq(bmap->div[div][1 + pos], bmap->div[div][0]);
165 isl_int_divexact_ui(bmap->div[div][1 + pos],
166 bmap->div[div][1 + pos], 2);
168 return r;
171 /* Reduce the coefficients (including the constant term) of
172 * integer division "div", if needed.
173 * In particular, make sure all coefficients lie in
174 * the half-open interval (1/2,1/2].
176 static __isl_give isl_basic_map *reduce_div_coefficients_of_div(
177 __isl_take isl_basic_map *bmap, int div)
179 int i;
180 unsigned total = 1 + isl_basic_map_total_dim(bmap);
182 for (i = 0; i < total; ++i) {
183 isl_bool reduce;
185 reduce = needs_reduction(bmap, div, i);
186 if (reduce < 0)
187 return isl_basic_map_free(bmap);
188 if (!reduce)
189 continue;
190 bmap = reduce_coefficient_in_div(bmap, div, i);
191 if (!bmap)
192 break;
195 return bmap;
198 /* Reduce the coefficients (including the constant term) of
199 * the known integer divisions, if needed
200 * In particular, make sure all coefficients lie in
201 * the half-open interval (1/2,1/2].
203 static __isl_give isl_basic_map *reduce_div_coefficients(
204 __isl_take isl_basic_map *bmap)
206 int i;
208 if (!bmap)
209 return NULL;
210 if (bmap->n_div == 0)
211 return bmap;
213 for (i = 0; i < bmap->n_div; ++i) {
214 if (isl_int_is_zero(bmap->div[i][0]))
215 continue;
216 bmap = reduce_div_coefficients_of_div(bmap, i);
217 if (!bmap)
218 break;
221 return bmap;
224 /* Remove any common factor in numerator and denominator of the div expression,
225 * not taking into account the constant term.
226 * That is, if the div is of the form
228 * floor((a + m f(x))/(m d))
230 * then replace it by
232 * floor((floor(a/m) + f(x))/d)
234 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
235 * and can therefore not influence the result of the floor.
237 static void normalize_div_expression(__isl_keep isl_basic_map *bmap, int div)
239 unsigned total = isl_basic_map_total_dim(bmap);
240 isl_ctx *ctx = bmap->ctx;
242 if (isl_int_is_zero(bmap->div[div][0]))
243 return;
244 isl_seq_gcd(bmap->div[div] + 2, total, &ctx->normalize_gcd);
245 isl_int_gcd(ctx->normalize_gcd, ctx->normalize_gcd, bmap->div[div][0]);
246 if (isl_int_is_one(ctx->normalize_gcd))
247 return;
248 isl_int_fdiv_q(bmap->div[div][1], bmap->div[div][1],
249 ctx->normalize_gcd);
250 isl_int_divexact(bmap->div[div][0], bmap->div[div][0],
251 ctx->normalize_gcd);
252 isl_seq_scale_down(bmap->div[div] + 2, bmap->div[div] + 2,
253 ctx->normalize_gcd, total);
256 /* Remove any common factor in numerator and denominator of a div expression,
257 * not taking into account the constant term.
258 * That is, look for any div of the form
260 * floor((a + m f(x))/(m d))
262 * and replace it by
264 * floor((floor(a/m) + f(x))/d)
266 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
267 * and can therefore not influence the result of the floor.
269 static __isl_give isl_basic_map *normalize_div_expressions(
270 __isl_take isl_basic_map *bmap)
272 int i;
274 if (!bmap)
275 return NULL;
276 if (bmap->n_div == 0)
277 return bmap;
279 for (i = 0; i < bmap->n_div; ++i)
280 normalize_div_expression(bmap, i);
282 return bmap;
285 /* Assumes divs have been ordered if keep_divs is set.
287 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
288 unsigned pos, isl_int *eq, int keep_divs, int *progress)
290 unsigned total;
291 unsigned space_total;
292 int k;
293 int last_div;
295 total = isl_basic_map_total_dim(bmap);
296 space_total = isl_space_dim(bmap->dim, isl_dim_all);
297 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
298 for (k = 0; k < bmap->n_eq; ++k) {
299 if (bmap->eq[k] == eq)
300 continue;
301 if (isl_int_is_zero(bmap->eq[k][1+pos]))
302 continue;
303 if (progress)
304 *progress = 1;
305 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
306 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
309 for (k = 0; k < bmap->n_ineq; ++k) {
310 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
311 continue;
312 if (progress)
313 *progress = 1;
314 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
315 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
316 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
319 for (k = 0; k < bmap->n_div; ++k) {
320 if (isl_int_is_zero(bmap->div[k][0]))
321 continue;
322 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
323 continue;
324 if (progress)
325 *progress = 1;
326 /* We need to be careful about circular definitions,
327 * so for now we just remove the definition of div k
328 * if the equality contains any divs.
329 * If keep_divs is set, then the divs have been ordered
330 * and we can keep the definition as long as the result
331 * is still ordered.
333 if (last_div == -1 || (keep_divs && last_div < k)) {
334 isl_seq_elim(bmap->div[k]+1, eq,
335 1+pos, 1+total, &bmap->div[k][0]);
336 normalize_div_expression(bmap, k);
337 } else
338 isl_seq_clr(bmap->div[k], 1 + total);
339 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
343 /* Assumes divs have been ordered if keep_divs is set.
345 static __isl_give isl_basic_map *eliminate_div(__isl_take isl_basic_map *bmap,
346 isl_int *eq, unsigned div, int keep_divs)
348 unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div;
350 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
352 bmap = isl_basic_map_drop_div(bmap, div);
354 return bmap;
357 /* Check if elimination of div "div" using equality "eq" would not
358 * result in a div depending on a later div.
360 static isl_bool ok_to_eliminate_div(__isl_keep isl_basic_map *bmap, isl_int *eq,
361 unsigned div)
363 int k;
364 int last_div;
365 unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all);
366 unsigned pos = space_total + div;
368 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
369 if (last_div < 0 || last_div <= div)
370 return isl_bool_true;
372 for (k = 0; k <= last_div; ++k) {
373 if (isl_int_is_zero(bmap->div[k][0]))
374 continue;
375 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
376 return isl_bool_false;
379 return isl_bool_true;
382 /* Eliminate divs based on equalities
384 static __isl_give isl_basic_map *eliminate_divs_eq(
385 __isl_take isl_basic_map *bmap, int *progress)
387 int d;
388 int i;
389 int modified = 0;
390 unsigned off;
392 bmap = isl_basic_map_order_divs(bmap);
394 if (!bmap)
395 return NULL;
397 off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
399 for (d = bmap->n_div - 1; d >= 0 ; --d) {
400 for (i = 0; i < bmap->n_eq; ++i) {
401 isl_bool ok;
403 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
404 !isl_int_is_negone(bmap->eq[i][off + d]))
405 continue;
406 ok = ok_to_eliminate_div(bmap, bmap->eq[i], d);
407 if (ok < 0)
408 return isl_basic_map_free(bmap);
409 if (!ok)
410 continue;
411 modified = 1;
412 *progress = 1;
413 bmap = eliminate_div(bmap, bmap->eq[i], d, 1);
414 if (isl_basic_map_drop_equality(bmap, i) < 0)
415 return isl_basic_map_free(bmap);
416 break;
419 if (modified)
420 return eliminate_divs_eq(bmap, progress);
421 return bmap;
424 /* Eliminate divs based on inequalities
426 static __isl_give isl_basic_map *eliminate_divs_ineq(
427 __isl_take isl_basic_map *bmap, int *progress)
429 int d;
430 int i;
431 unsigned off;
432 struct isl_ctx *ctx;
434 if (!bmap)
435 return NULL;
437 ctx = bmap->ctx;
438 off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
440 for (d = bmap->n_div - 1; d >= 0 ; --d) {
441 for (i = 0; i < bmap->n_eq; ++i)
442 if (!isl_int_is_zero(bmap->eq[i][off + d]))
443 break;
444 if (i < bmap->n_eq)
445 continue;
446 for (i = 0; i < bmap->n_ineq; ++i)
447 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
448 break;
449 if (i < bmap->n_ineq)
450 continue;
451 *progress = 1;
452 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
453 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
454 break;
455 bmap = isl_basic_map_drop_div(bmap, d);
456 if (!bmap)
457 break;
459 return bmap;
462 /* Does the equality constraint at position "eq" in "bmap" involve
463 * any local variables in the range [first, first + n)
464 * that are not marked as having an explicit representation?
466 static isl_bool bmap_eq_involves_unknown_divs(__isl_keep isl_basic_map *bmap,
467 int eq, unsigned first, unsigned n)
469 unsigned o_div;
470 int i;
472 if (!bmap)
473 return isl_bool_error;
475 o_div = isl_basic_map_offset(bmap, isl_dim_div);
476 for (i = 0; i < n; ++i) {
477 isl_bool unknown;
479 if (isl_int_is_zero(bmap->eq[eq][o_div + first + i]))
480 continue;
481 unknown = isl_basic_map_div_is_marked_unknown(bmap, first + i);
482 if (unknown < 0)
483 return isl_bool_error;
484 if (unknown)
485 return isl_bool_true;
488 return isl_bool_false;
491 /* The last local variable involved in the equality constraint
492 * at position "eq" in "bmap" is the local variable at position "div".
493 * It can therefore be used to extract an explicit representation
494 * for that variable.
495 * Do so unless the local variable already has an explicit representation or
496 * the explicit representation would involve any other local variables
497 * that in turn do not have an explicit representation.
498 * An equality constraint involving local variables without an explicit
499 * representation can be used in isl_basic_map_drop_redundant_divs
500 * to separate out an independent local variable. Introducing
501 * an explicit representation here would block this transformation,
502 * while the partial explicit representation in itself is not very useful.
503 * Set *progress if anything is changed.
505 * The equality constraint is of the form
507 * f(x) + n e >= 0
509 * with n a positive number. The explicit representation derived from
510 * this constraint is
512 * floor((-f(x))/n)
514 static __isl_give isl_basic_map *set_div_from_eq(__isl_take isl_basic_map *bmap,
515 int div, int eq, int *progress)
517 unsigned total, o_div;
518 isl_bool involves;
520 if (!bmap)
521 return NULL;
523 if (!isl_int_is_zero(bmap->div[div][0]))
524 return bmap;
526 involves = bmap_eq_involves_unknown_divs(bmap, eq, 0, div);
527 if (involves < 0)
528 return isl_basic_map_free(bmap);
529 if (involves)
530 return bmap;
532 total = isl_basic_map_dim(bmap, isl_dim_all);
533 o_div = isl_basic_map_offset(bmap, isl_dim_div);
534 isl_seq_neg(bmap->div[div] + 1, bmap->eq[eq], 1 + total);
535 isl_int_set_si(bmap->div[div][1 + o_div + div], 0);
536 isl_int_set(bmap->div[div][0], bmap->eq[eq][o_div + div]);
537 if (progress)
538 *progress = 1;
539 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
541 return bmap;
544 struct isl_basic_map *isl_basic_map_gauss(
545 struct isl_basic_map *bmap, int *progress)
547 int k;
548 int done;
549 int last_var;
550 unsigned total_var;
551 unsigned total;
553 bmap = isl_basic_map_order_divs(bmap);
555 if (!bmap)
556 return NULL;
558 total = isl_basic_map_total_dim(bmap);
559 total_var = total - bmap->n_div;
561 last_var = total - 1;
562 for (done = 0; done < bmap->n_eq; ++done) {
563 for (; last_var >= 0; --last_var) {
564 for (k = done; k < bmap->n_eq; ++k)
565 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
566 break;
567 if (k < bmap->n_eq)
568 break;
570 if (last_var < 0)
571 break;
572 if (k != done)
573 swap_equality(bmap, k, done);
574 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
575 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
577 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
578 progress);
580 if (last_var >= total_var)
581 bmap = set_div_from_eq(bmap, last_var - total_var,
582 done, progress);
583 if (!bmap)
584 return NULL;
586 if (done == bmap->n_eq)
587 return bmap;
588 for (k = done; k < bmap->n_eq; ++k) {
589 if (isl_int_is_zero(bmap->eq[k][0]))
590 continue;
591 return isl_basic_map_set_to_empty(bmap);
593 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
594 return bmap;
597 struct isl_basic_set *isl_basic_set_gauss(
598 struct isl_basic_set *bset, int *progress)
600 return bset_from_bmap(isl_basic_map_gauss(bset_to_bmap(bset),
601 progress));
605 static unsigned int round_up(unsigned int v)
607 int old_v = v;
609 while (v) {
610 old_v = v;
611 v ^= v & -v;
613 return old_v << 1;
616 /* Hash table of inequalities in a basic map.
617 * "index" is an array of addresses of inequalities in the basic map, some
618 * of which are NULL. The inequalities are hashed on the coefficients
619 * except the constant term.
620 * "size" is the number of elements in the array and is always a power of two
621 * "bits" is the number of bits need to represent an index into the array.
622 * "total" is the total dimension of the basic map.
624 struct isl_constraint_index {
625 unsigned int size;
626 int bits;
627 isl_int ***index;
628 unsigned total;
631 /* Fill in the "ci" data structure for holding the inequalities of "bmap".
633 static isl_stat create_constraint_index(struct isl_constraint_index *ci,
634 __isl_keep isl_basic_map *bmap)
636 isl_ctx *ctx;
638 ci->index = NULL;
639 if (!bmap)
640 return isl_stat_error;
641 ci->total = isl_basic_set_total_dim(bmap);
642 if (bmap->n_ineq == 0)
643 return isl_stat_ok;
644 ci->size = round_up(4 * (bmap->n_ineq + 1) / 3 - 1);
645 ci->bits = ffs(ci->size) - 1;
646 ctx = isl_basic_map_get_ctx(bmap);
647 ci->index = isl_calloc_array(ctx, isl_int **, ci->size);
648 if (!ci->index)
649 return isl_stat_error;
651 return isl_stat_ok;
654 /* Free the memory allocated by create_constraint_index.
656 static void constraint_index_free(struct isl_constraint_index *ci)
658 free(ci->index);
661 /* Return the position in ci->index that contains the address of
662 * an inequality that is equal to *ineq up to the constant term,
663 * provided this address is not identical to "ineq".
664 * If there is no such inequality, then return the position where
665 * such an inequality should be inserted.
667 static int hash_index_ineq(struct isl_constraint_index *ci, isl_int **ineq)
669 int h;
670 uint32_t hash = isl_seq_get_hash_bits((*ineq) + 1, ci->total, ci->bits);
671 for (h = hash; ci->index[h]; h = (h+1) % ci->size)
672 if (ineq != ci->index[h] &&
673 isl_seq_eq((*ineq) + 1, ci->index[h][0]+1, ci->total))
674 break;
675 return h;
678 /* Return the position in ci->index that contains the address of
679 * an inequality that is equal to the k'th inequality of "bmap"
680 * up to the constant term, provided it does not point to the very
681 * same inequality.
682 * If there is no such inequality, then return the position where
683 * such an inequality should be inserted.
685 static int hash_index(struct isl_constraint_index *ci,
686 __isl_keep isl_basic_map *bmap, int k)
688 return hash_index_ineq(ci, &bmap->ineq[k]);
691 static int set_hash_index(struct isl_constraint_index *ci,
692 __isl_keep isl_basic_set *bset, int k)
694 return hash_index(ci, bset, k);
697 /* Fill in the "ci" data structure with the inequalities of "bset".
699 static isl_stat setup_constraint_index(struct isl_constraint_index *ci,
700 __isl_keep isl_basic_set *bset)
702 int k, h;
704 if (create_constraint_index(ci, bset) < 0)
705 return isl_stat_error;
707 for (k = 0; k < bset->n_ineq; ++k) {
708 h = set_hash_index(ci, bset, k);
709 ci->index[h] = &bset->ineq[k];
712 return isl_stat_ok;
715 /* Is the inequality ineq (obviously) redundant with respect
716 * to the constraints in "ci"?
718 * Look for an inequality in "ci" with the same coefficients and then
719 * check if the contant term of "ineq" is greater than or equal
720 * to the constant term of that inequality. If so, "ineq" is clearly
721 * redundant.
723 * Note that hash_index_ineq ignores a stored constraint if it has
724 * the same address as the passed inequality. It is ok to pass
725 * the address of a local variable here since it will never be
726 * the same as the address of a constraint in "ci".
728 static isl_bool constraint_index_is_redundant(struct isl_constraint_index *ci,
729 isl_int *ineq)
731 int h;
733 h = hash_index_ineq(ci, &ineq);
734 if (!ci->index[h])
735 return isl_bool_false;
736 return isl_int_ge(ineq[0], (*ci->index[h])[0]);
739 /* If we can eliminate more than one div, then we need to make
740 * sure we do it from last div to first div, in order not to
741 * change the position of the other divs that still need to
742 * be removed.
744 static __isl_give isl_basic_map *remove_duplicate_divs(
745 __isl_take isl_basic_map *bmap, int *progress)
747 unsigned int size;
748 int *index;
749 int *elim_for;
750 int k, l, h;
751 int bits;
752 struct isl_blk eq;
753 unsigned total_var;
754 unsigned total;
755 struct isl_ctx *ctx;
757 bmap = isl_basic_map_order_divs(bmap);
758 if (!bmap || bmap->n_div <= 1)
759 return bmap;
761 total_var = isl_space_dim(bmap->dim, isl_dim_all);
762 total = total_var + bmap->n_div;
764 ctx = bmap->ctx;
765 for (k = bmap->n_div - 1; k >= 0; --k)
766 if (!isl_int_is_zero(bmap->div[k][0]))
767 break;
768 if (k <= 0)
769 return bmap;
771 size = round_up(4 * bmap->n_div / 3 - 1);
772 if (size == 0)
773 return bmap;
774 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
775 bits = ffs(size) - 1;
776 index = isl_calloc_array(ctx, int, size);
777 if (!elim_for || !index)
778 goto out;
779 eq = isl_blk_alloc(ctx, 1+total);
780 if (isl_blk_is_error(eq))
781 goto out;
783 isl_seq_clr(eq.data, 1+total);
784 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
785 for (--k; k >= 0; --k) {
786 uint32_t hash;
788 if (isl_int_is_zero(bmap->div[k][0]))
789 continue;
791 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
792 for (h = hash; index[h]; h = (h+1) % size)
793 if (isl_seq_eq(bmap->div[k],
794 bmap->div[index[h]-1], 2+total))
795 break;
796 if (index[h]) {
797 *progress = 1;
798 l = index[h] - 1;
799 elim_for[l] = k + 1;
801 index[h] = k+1;
803 for (l = bmap->n_div - 1; l >= 0; --l) {
804 if (!elim_for[l])
805 continue;
806 k = elim_for[l] - 1;
807 isl_int_set_si(eq.data[1+total_var+k], -1);
808 isl_int_set_si(eq.data[1+total_var+l], 1);
809 bmap = eliminate_div(bmap, eq.data, l, 1);
810 if (!bmap)
811 break;
812 isl_int_set_si(eq.data[1+total_var+k], 0);
813 isl_int_set_si(eq.data[1+total_var+l], 0);
816 isl_blk_free(ctx, eq);
817 out:
818 free(index);
819 free(elim_for);
820 return bmap;
823 static int n_pure_div_eq(struct isl_basic_map *bmap)
825 int i, j;
826 unsigned total;
828 total = isl_space_dim(bmap->dim, isl_dim_all);
829 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
830 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
831 --j;
832 if (j < 0)
833 break;
834 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
835 return 0;
837 return i;
840 /* Normalize divs that appear in equalities.
842 * In particular, we assume that bmap contains some equalities
843 * of the form
845 * a x = m * e_i
847 * and we want to replace the set of e_i by a minimal set and
848 * such that the new e_i have a canonical representation in terms
849 * of the vector x.
850 * If any of the equalities involves more than one divs, then
851 * we currently simply bail out.
853 * Let us first additionally assume that all equalities involve
854 * a div. The equalities then express modulo constraints on the
855 * remaining variables and we can use "parameter compression"
856 * to find a minimal set of constraints. The result is a transformation
858 * x = T(x') = x_0 + G x'
860 * with G a lower-triangular matrix with all elements below the diagonal
861 * non-negative and smaller than the diagonal element on the same row.
862 * We first normalize x_0 by making the same property hold in the affine
863 * T matrix.
864 * The rows i of G with a 1 on the diagonal do not impose any modulo
865 * constraint and simply express x_i = x'_i.
866 * For each of the remaining rows i, we introduce a div and a corresponding
867 * equality. In particular
869 * g_ii e_j = x_i - g_i(x')
871 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
872 * corresponding div (if g_kk != 1).
874 * If there are any equalities not involving any div, then we
875 * first apply a variable compression on the variables x:
877 * x = C x'' x'' = C_2 x
879 * and perform the above parameter compression on A C instead of on A.
880 * The resulting compression is then of the form
882 * x'' = T(x') = x_0 + G x'
884 * and in constructing the new divs and the corresponding equalities,
885 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
886 * by the corresponding row from C_2.
888 static __isl_give isl_basic_map *normalize_divs(__isl_take isl_basic_map *bmap,
889 int *progress)
891 int i, j, k;
892 int total;
893 int div_eq;
894 struct isl_mat *B;
895 struct isl_vec *d;
896 struct isl_mat *T = NULL;
897 struct isl_mat *C = NULL;
898 struct isl_mat *C2 = NULL;
899 isl_int v;
900 int *pos = NULL;
901 int dropped, needed;
903 if (!bmap)
904 return NULL;
906 if (bmap->n_div == 0)
907 return bmap;
909 if (bmap->n_eq == 0)
910 return bmap;
912 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
913 return bmap;
915 total = isl_space_dim(bmap->dim, isl_dim_all);
916 div_eq = n_pure_div_eq(bmap);
917 if (div_eq == 0)
918 return bmap;
920 if (div_eq < bmap->n_eq) {
921 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
922 bmap->n_eq - div_eq, 0, 1 + total);
923 C = isl_mat_variable_compression(B, &C2);
924 if (!C || !C2)
925 goto error;
926 if (C->n_col == 0) {
927 bmap = isl_basic_map_set_to_empty(bmap);
928 isl_mat_free(C);
929 isl_mat_free(C2);
930 goto done;
934 d = isl_vec_alloc(bmap->ctx, div_eq);
935 if (!d)
936 goto error;
937 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
938 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
939 --j;
940 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
942 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
944 if (C) {
945 B = isl_mat_product(B, C);
946 C = NULL;
949 T = isl_mat_parameter_compression(B, d);
950 if (!T)
951 goto error;
952 if (T->n_col == 0) {
953 bmap = isl_basic_map_set_to_empty(bmap);
954 isl_mat_free(C2);
955 isl_mat_free(T);
956 goto done;
958 isl_int_init(v);
959 for (i = 0; i < T->n_row - 1; ++i) {
960 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
961 if (isl_int_is_zero(v))
962 continue;
963 isl_mat_col_submul(T, 0, v, 1 + i);
965 isl_int_clear(v);
966 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
967 if (!pos)
968 goto error;
969 /* We have to be careful because dropping equalities may reorder them */
970 dropped = 0;
971 for (j = bmap->n_div - 1; j >= 0; --j) {
972 for (i = 0; i < bmap->n_eq; ++i)
973 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
974 break;
975 if (i < bmap->n_eq) {
976 bmap = isl_basic_map_drop_div(bmap, j);
977 isl_basic_map_drop_equality(bmap, i);
978 ++dropped;
981 pos[0] = 0;
982 needed = 0;
983 for (i = 1; i < T->n_row; ++i) {
984 if (isl_int_is_one(T->row[i][i]))
985 pos[i] = i;
986 else
987 needed++;
989 if (needed > dropped) {
990 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
991 needed, needed, 0);
992 if (!bmap)
993 goto error;
995 for (i = 1; i < T->n_row; ++i) {
996 if (isl_int_is_one(T->row[i][i]))
997 continue;
998 k = isl_basic_map_alloc_div(bmap);
999 pos[i] = 1 + total + k;
1000 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
1001 isl_int_set(bmap->div[k][0], T->row[i][i]);
1002 if (C2)
1003 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
1004 else
1005 isl_int_set_si(bmap->div[k][1 + i], 1);
1006 for (j = 0; j < i; ++j) {
1007 if (isl_int_is_zero(T->row[i][j]))
1008 continue;
1009 if (pos[j] < T->n_row && C2)
1010 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
1011 C2->row[pos[j]], 1 + total);
1012 else
1013 isl_int_neg(bmap->div[k][1 + pos[j]],
1014 T->row[i][j]);
1016 j = isl_basic_map_alloc_equality(bmap);
1017 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
1018 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
1020 free(pos);
1021 isl_mat_free(C2);
1022 isl_mat_free(T);
1024 if (progress)
1025 *progress = 1;
1026 done:
1027 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1029 return bmap;
1030 error:
1031 free(pos);
1032 isl_mat_free(C);
1033 isl_mat_free(C2);
1034 isl_mat_free(T);
1035 return bmap;
1038 static __isl_give isl_basic_map *set_div_from_lower_bound(
1039 __isl_take isl_basic_map *bmap, int div, int ineq)
1041 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1043 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
1044 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
1045 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
1046 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1047 isl_int_set_si(bmap->div[div][1 + total + div], 0);
1049 return bmap;
1052 /* Check whether it is ok to define a div based on an inequality.
1053 * To avoid the introduction of circular definitions of divs, we
1054 * do not allow such a definition if the resulting expression would refer to
1055 * any other undefined divs or if any known div is defined in
1056 * terms of the unknown div.
1058 static isl_bool ok_to_set_div_from_bound(__isl_keep isl_basic_map *bmap,
1059 int div, int ineq)
1061 int j;
1062 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1064 /* Not defined in terms of unknown divs */
1065 for (j = 0; j < bmap->n_div; ++j) {
1066 if (div == j)
1067 continue;
1068 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
1069 continue;
1070 if (isl_int_is_zero(bmap->div[j][0]))
1071 return isl_bool_false;
1074 /* No other div defined in terms of this one => avoid loops */
1075 for (j = 0; j < bmap->n_div; ++j) {
1076 if (div == j)
1077 continue;
1078 if (isl_int_is_zero(bmap->div[j][0]))
1079 continue;
1080 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
1081 return isl_bool_false;
1084 return isl_bool_true;
1087 /* Would an expression for div "div" based on inequality "ineq" of "bmap"
1088 * be a better expression than the current one?
1090 * If we do not have any expression yet, then any expression would be better.
1091 * Otherwise we check if the last variable involved in the inequality
1092 * (disregarding the div that it would define) is in an earlier position
1093 * than the last variable involved in the current div expression.
1095 static isl_bool better_div_constraint(__isl_keep isl_basic_map *bmap,
1096 int div, int ineq)
1098 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1099 int last_div;
1100 int last_ineq;
1102 if (isl_int_is_zero(bmap->div[div][0]))
1103 return isl_bool_true;
1105 if (isl_seq_last_non_zero(bmap->ineq[ineq] + total + div + 1,
1106 bmap->n_div - (div + 1)) >= 0)
1107 return isl_bool_false;
1109 last_ineq = isl_seq_last_non_zero(bmap->ineq[ineq], total + div);
1110 last_div = isl_seq_last_non_zero(bmap->div[div] + 1,
1111 total + bmap->n_div);
1113 return last_ineq < last_div;
1116 /* Given two constraints "k" and "l" that are opposite to each other,
1117 * except for the constant term, check if we can use them
1118 * to obtain an expression for one of the hitherto unknown divs or
1119 * a "better" expression for a div for which we already have an expression.
1120 * "sum" is the sum of the constant terms of the constraints.
1121 * If this sum is strictly smaller than the coefficient of one
1122 * of the divs, then this pair can be used define the div.
1123 * To avoid the introduction of circular definitions of divs, we
1124 * do not use the pair if the resulting expression would refer to
1125 * any other undefined divs or if any known div is defined in
1126 * terms of the unknown div.
1128 static __isl_give isl_basic_map *check_for_div_constraints(
1129 __isl_take isl_basic_map *bmap, int k, int l, isl_int sum,
1130 int *progress)
1132 int i;
1133 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1135 for (i = 0; i < bmap->n_div; ++i) {
1136 isl_bool set_div;
1138 if (isl_int_is_zero(bmap->ineq[k][total + i]))
1139 continue;
1140 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1141 continue;
1142 set_div = better_div_constraint(bmap, i, k);
1143 if (set_div >= 0 && set_div)
1144 set_div = ok_to_set_div_from_bound(bmap, i, k);
1145 if (set_div < 0)
1146 return isl_basic_map_free(bmap);
1147 if (!set_div)
1148 break;
1149 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1150 bmap = set_div_from_lower_bound(bmap, i, k);
1151 else
1152 bmap = set_div_from_lower_bound(bmap, i, l);
1153 if (progress)
1154 *progress = 1;
1155 break;
1157 return bmap;
1160 __isl_give isl_basic_map *isl_basic_map_remove_duplicate_constraints(
1161 __isl_take isl_basic_map *bmap, int *progress, int detect_divs)
1163 struct isl_constraint_index ci;
1164 int k, l, h;
1165 unsigned total = isl_basic_map_total_dim(bmap);
1166 isl_int sum;
1168 if (!bmap || bmap->n_ineq <= 1)
1169 return bmap;
1171 if (create_constraint_index(&ci, bmap) < 0)
1172 return bmap;
1174 h = isl_seq_get_hash_bits(bmap->ineq[0] + 1, total, ci.bits);
1175 ci.index[h] = &bmap->ineq[0];
1176 for (k = 1; k < bmap->n_ineq; ++k) {
1177 h = hash_index(&ci, bmap, k);
1178 if (!ci.index[h]) {
1179 ci.index[h] = &bmap->ineq[k];
1180 continue;
1182 if (progress)
1183 *progress = 1;
1184 l = ci.index[h] - &bmap->ineq[0];
1185 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1186 swap_inequality(bmap, k, l);
1187 isl_basic_map_drop_inequality(bmap, k);
1188 --k;
1190 isl_int_init(sum);
1191 for (k = 0; k < bmap->n_ineq-1; ++k) {
1192 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1193 h = hash_index(&ci, bmap, k);
1194 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1195 if (!ci.index[h])
1196 continue;
1197 l = ci.index[h] - &bmap->ineq[0];
1198 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1199 if (isl_int_is_pos(sum)) {
1200 if (detect_divs)
1201 bmap = check_for_div_constraints(bmap, k, l,
1202 sum, progress);
1203 continue;
1205 if (isl_int_is_zero(sum)) {
1206 /* We need to break out of the loop after these
1207 * changes since the contents of the hash
1208 * will no longer be valid.
1209 * Plus, we probably we want to regauss first.
1211 if (progress)
1212 *progress = 1;
1213 isl_basic_map_drop_inequality(bmap, l);
1214 isl_basic_map_inequality_to_equality(bmap, k);
1215 } else
1216 bmap = isl_basic_map_set_to_empty(bmap);
1217 break;
1219 isl_int_clear(sum);
1221 constraint_index_free(&ci);
1222 return bmap;
1225 /* Detect all pairs of inequalities that form an equality.
1227 * isl_basic_map_remove_duplicate_constraints detects at most one such pair.
1228 * Call it repeatedly while it is making progress.
1230 __isl_give isl_basic_map *isl_basic_map_detect_inequality_pairs(
1231 __isl_take isl_basic_map *bmap, int *progress)
1233 int duplicate;
1235 do {
1236 duplicate = 0;
1237 bmap = isl_basic_map_remove_duplicate_constraints(bmap,
1238 &duplicate, 0);
1239 if (progress && duplicate)
1240 *progress = 1;
1241 } while (duplicate);
1243 return bmap;
1246 /* Eliminate knowns divs from constraints where they appear with
1247 * a (positive or negative) unit coefficient.
1249 * That is, replace
1251 * floor(e/m) + f >= 0
1253 * by
1255 * e + m f >= 0
1257 * and
1259 * -floor(e/m) + f >= 0
1261 * by
1263 * -e + m f + m - 1 >= 0
1265 * The first conversion is valid because floor(e/m) >= -f is equivalent
1266 * to e/m >= -f because -f is an integral expression.
1267 * The second conversion follows from the fact that
1269 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1272 * Note that one of the div constraints may have been eliminated
1273 * due to being redundant with respect to the constraint that is
1274 * being modified by this function. The modified constraint may
1275 * no longer imply this div constraint, so we add it back to make
1276 * sure we do not lose any information.
1278 * We skip integral divs, i.e., those with denominator 1, as we would
1279 * risk eliminating the div from the div constraints. We do not need
1280 * to handle those divs here anyway since the div constraints will turn
1281 * out to form an equality and this equality can then be used to eliminate
1282 * the div from all constraints.
1284 static __isl_give isl_basic_map *eliminate_unit_divs(
1285 __isl_take isl_basic_map *bmap, int *progress)
1287 int i, j;
1288 isl_ctx *ctx;
1289 unsigned total;
1291 if (!bmap)
1292 return NULL;
1294 ctx = isl_basic_map_get_ctx(bmap);
1295 total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1297 for (i = 0; i < bmap->n_div; ++i) {
1298 if (isl_int_is_zero(bmap->div[i][0]))
1299 continue;
1300 if (isl_int_is_one(bmap->div[i][0]))
1301 continue;
1302 for (j = 0; j < bmap->n_ineq; ++j) {
1303 int s;
1305 if (!isl_int_is_one(bmap->ineq[j][total + i]) &&
1306 !isl_int_is_negone(bmap->ineq[j][total + i]))
1307 continue;
1309 *progress = 1;
1311 s = isl_int_sgn(bmap->ineq[j][total + i]);
1312 isl_int_set_si(bmap->ineq[j][total + i], 0);
1313 if (s < 0)
1314 isl_seq_combine(bmap->ineq[j],
1315 ctx->negone, bmap->div[i] + 1,
1316 bmap->div[i][0], bmap->ineq[j],
1317 total + bmap->n_div);
1318 else
1319 isl_seq_combine(bmap->ineq[j],
1320 ctx->one, bmap->div[i] + 1,
1321 bmap->div[i][0], bmap->ineq[j],
1322 total + bmap->n_div);
1323 if (s < 0) {
1324 isl_int_add(bmap->ineq[j][0],
1325 bmap->ineq[j][0], bmap->div[i][0]);
1326 isl_int_sub_ui(bmap->ineq[j][0],
1327 bmap->ineq[j][0], 1);
1330 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
1331 if (isl_basic_map_add_div_constraint(bmap, i, s) < 0)
1332 return isl_basic_map_free(bmap);
1336 return bmap;
1339 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1341 int progress = 1;
1342 if (!bmap)
1343 return NULL;
1344 while (progress) {
1345 isl_bool empty;
1347 progress = 0;
1348 empty = isl_basic_map_plain_is_empty(bmap);
1349 if (empty < 0)
1350 return isl_basic_map_free(bmap);
1351 if (empty)
1352 break;
1353 bmap = isl_basic_map_normalize_constraints(bmap);
1354 bmap = reduce_div_coefficients(bmap);
1355 bmap = normalize_div_expressions(bmap);
1356 bmap = remove_duplicate_divs(bmap, &progress);
1357 bmap = eliminate_unit_divs(bmap, &progress);
1358 bmap = eliminate_divs_eq(bmap, &progress);
1359 bmap = eliminate_divs_ineq(bmap, &progress);
1360 bmap = isl_basic_map_gauss(bmap, &progress);
1361 /* requires equalities in normal form */
1362 bmap = normalize_divs(bmap, &progress);
1363 bmap = isl_basic_map_remove_duplicate_constraints(bmap,
1364 &progress, 1);
1365 if (bmap && progress)
1366 ISL_F_CLR(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS);
1368 return bmap;
1371 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1373 return bset_from_bmap(isl_basic_map_simplify(bset_to_bmap(bset)));
1377 isl_bool isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1378 isl_int *constraint, unsigned div)
1380 unsigned pos;
1382 if (!bmap)
1383 return isl_bool_error;
1385 pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1387 if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1388 int neg;
1389 isl_int_sub(bmap->div[div][1],
1390 bmap->div[div][1], bmap->div[div][0]);
1391 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1392 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1393 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1394 isl_int_add(bmap->div[div][1],
1395 bmap->div[div][1], bmap->div[div][0]);
1396 if (!neg)
1397 return isl_bool_false;
1398 if (isl_seq_first_non_zero(constraint+pos+1,
1399 bmap->n_div-div-1) != -1)
1400 return isl_bool_false;
1401 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1402 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1403 return isl_bool_false;
1404 if (isl_seq_first_non_zero(constraint+pos+1,
1405 bmap->n_div-div-1) != -1)
1406 return isl_bool_false;
1407 } else
1408 return isl_bool_false;
1410 return isl_bool_true;
1413 isl_bool isl_basic_set_is_div_constraint(__isl_keep isl_basic_set *bset,
1414 isl_int *constraint, unsigned div)
1416 return isl_basic_map_is_div_constraint(bset, constraint, div);
1420 /* If the only constraints a div d=floor(f/m)
1421 * appears in are its two defining constraints
1423 * f - m d >=0
1424 * -(f - (m - 1)) + m d >= 0
1426 * then it can safely be removed.
1428 static isl_bool div_is_redundant(__isl_keep isl_basic_map *bmap, int div)
1430 int i;
1431 unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1433 for (i = 0; i < bmap->n_eq; ++i)
1434 if (!isl_int_is_zero(bmap->eq[i][pos]))
1435 return isl_bool_false;
1437 for (i = 0; i < bmap->n_ineq; ++i) {
1438 isl_bool red;
1440 if (isl_int_is_zero(bmap->ineq[i][pos]))
1441 continue;
1442 red = isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div);
1443 if (red < 0 || !red)
1444 return red;
1447 for (i = 0; i < bmap->n_div; ++i) {
1448 if (isl_int_is_zero(bmap->div[i][0]))
1449 continue;
1450 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1451 return isl_bool_false;
1454 return isl_bool_true;
1458 * Remove divs that don't occur in any of the constraints or other divs.
1459 * These can arise when dropping constraints from a basic map or
1460 * when the divs of a basic map have been temporarily aligned
1461 * with the divs of another basic map.
1463 static __isl_give isl_basic_map *remove_redundant_divs(
1464 __isl_take isl_basic_map *bmap)
1466 int i;
1468 if (!bmap)
1469 return NULL;
1471 for (i = bmap->n_div-1; i >= 0; --i) {
1472 isl_bool redundant;
1474 redundant = div_is_redundant(bmap, i);
1475 if (redundant < 0)
1476 return isl_basic_map_free(bmap);
1477 if (!redundant)
1478 continue;
1479 bmap = isl_basic_map_drop_div(bmap, i);
1481 return bmap;
1484 /* Mark "bmap" as final, without checking for obviously redundant
1485 * integer divisions. This function should be used when "bmap"
1486 * is known not to involve any such integer divisions.
1488 __isl_give isl_basic_map *isl_basic_map_mark_final(
1489 __isl_take isl_basic_map *bmap)
1491 if (!bmap)
1492 return NULL;
1493 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1494 return bmap;
1497 /* Mark "bmap" as final, after removing obviously redundant integer divisions.
1499 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1501 bmap = remove_redundant_divs(bmap);
1502 bmap = isl_basic_map_mark_final(bmap);
1503 return bmap;
1506 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1508 return bset_from_bmap(isl_basic_map_finalize(bset_to_bmap(bset)));
1511 /* Remove definition of any div that is defined in terms of the given variable.
1512 * The div itself is not removed. Functions such as
1513 * eliminate_divs_ineq depend on the other divs remaining in place.
1515 static __isl_give isl_basic_map *remove_dependent_vars(
1516 __isl_take isl_basic_map *bmap, int pos)
1518 int i;
1520 if (!bmap)
1521 return NULL;
1523 for (i = 0; i < bmap->n_div; ++i) {
1524 if (isl_int_is_zero(bmap->div[i][0]))
1525 continue;
1526 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1527 continue;
1528 bmap = isl_basic_map_mark_div_unknown(bmap, i);
1529 if (!bmap)
1530 return NULL;
1532 return bmap;
1535 /* Eliminate the specified variables from the constraints using
1536 * Fourier-Motzkin. The variables themselves are not removed.
1538 struct isl_basic_map *isl_basic_map_eliminate_vars(
1539 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1541 int d;
1542 int i, j, k;
1543 unsigned total;
1544 int need_gauss = 0;
1546 if (n == 0)
1547 return bmap;
1548 if (!bmap)
1549 return NULL;
1550 total = isl_basic_map_total_dim(bmap);
1552 bmap = isl_basic_map_cow(bmap);
1553 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1554 bmap = remove_dependent_vars(bmap, d);
1555 if (!bmap)
1556 return NULL;
1558 for (d = pos + n - 1;
1559 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1560 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1561 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1562 int n_lower, n_upper;
1563 if (!bmap)
1564 return NULL;
1565 for (i = 0; i < bmap->n_eq; ++i) {
1566 if (isl_int_is_zero(bmap->eq[i][1+d]))
1567 continue;
1568 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1569 isl_basic_map_drop_equality(bmap, i);
1570 need_gauss = 1;
1571 break;
1573 if (i < bmap->n_eq)
1574 continue;
1575 n_lower = 0;
1576 n_upper = 0;
1577 for (i = 0; i < bmap->n_ineq; ++i) {
1578 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1579 n_lower++;
1580 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1581 n_upper++;
1583 bmap = isl_basic_map_extend_constraints(bmap,
1584 0, n_lower * n_upper);
1585 if (!bmap)
1586 goto error;
1587 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1588 int last;
1589 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1590 continue;
1591 last = -1;
1592 for (j = 0; j < i; ++j) {
1593 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1594 continue;
1595 last = j;
1596 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1597 isl_int_sgn(bmap->ineq[j][1+d]))
1598 continue;
1599 k = isl_basic_map_alloc_inequality(bmap);
1600 if (k < 0)
1601 goto error;
1602 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1603 1+total);
1604 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1605 1+d, 1+total, NULL);
1607 isl_basic_map_drop_inequality(bmap, i);
1608 i = last + 1;
1610 if (n_lower > 0 && n_upper > 0) {
1611 bmap = isl_basic_map_normalize_constraints(bmap);
1612 bmap = isl_basic_map_remove_duplicate_constraints(bmap,
1613 NULL, 0);
1614 bmap = isl_basic_map_gauss(bmap, NULL);
1615 bmap = isl_basic_map_remove_redundancies(bmap);
1616 need_gauss = 0;
1617 if (!bmap)
1618 goto error;
1619 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1620 break;
1623 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1624 if (need_gauss)
1625 bmap = isl_basic_map_gauss(bmap, NULL);
1626 return bmap;
1627 error:
1628 isl_basic_map_free(bmap);
1629 return NULL;
1632 struct isl_basic_set *isl_basic_set_eliminate_vars(
1633 struct isl_basic_set *bset, unsigned pos, unsigned n)
1635 return bset_from_bmap(isl_basic_map_eliminate_vars(bset_to_bmap(bset),
1636 pos, n));
1639 /* Eliminate the specified n dimensions starting at first from the
1640 * constraints, without removing the dimensions from the space.
1641 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1642 * Otherwise, they are projected out and the original space is restored.
1644 __isl_give isl_basic_map *isl_basic_map_eliminate(
1645 __isl_take isl_basic_map *bmap,
1646 enum isl_dim_type type, unsigned first, unsigned n)
1648 isl_space *space;
1650 if (!bmap)
1651 return NULL;
1652 if (n == 0)
1653 return bmap;
1655 if (first + n > isl_basic_map_dim(bmap, type) || first + n < first)
1656 isl_die(bmap->ctx, isl_error_invalid,
1657 "index out of bounds", goto error);
1659 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
1660 first += isl_basic_map_offset(bmap, type) - 1;
1661 bmap = isl_basic_map_eliminate_vars(bmap, first, n);
1662 return isl_basic_map_finalize(bmap);
1665 space = isl_basic_map_get_space(bmap);
1666 bmap = isl_basic_map_project_out(bmap, type, first, n);
1667 bmap = isl_basic_map_insert_dims(bmap, type, first, n);
1668 bmap = isl_basic_map_reset_space(bmap, space);
1669 return bmap;
1670 error:
1671 isl_basic_map_free(bmap);
1672 return NULL;
1675 __isl_give isl_basic_set *isl_basic_set_eliminate(
1676 __isl_take isl_basic_set *bset,
1677 enum isl_dim_type type, unsigned first, unsigned n)
1679 return isl_basic_map_eliminate(bset, type, first, n);
1682 /* Remove all constraints from "bmap" that reference any unknown local
1683 * variables (directly or indirectly).
1685 * Dropping all constraints on a local variable will make it redundant,
1686 * so it will get removed implicitly by
1687 * isl_basic_map_drop_constraints_involving_dims. Some other local
1688 * variables may also end up becoming redundant if they only appear
1689 * in constraints together with the unknown local variable.
1690 * Therefore, start over after calling
1691 * isl_basic_map_drop_constraints_involving_dims.
1693 __isl_give isl_basic_map *isl_basic_map_drop_constraint_involving_unknown_divs(
1694 __isl_take isl_basic_map *bmap)
1696 isl_bool known;
1697 int i, n_div, o_div;
1699 known = isl_basic_map_divs_known(bmap);
1700 if (known < 0)
1701 return isl_basic_map_free(bmap);
1702 if (known)
1703 return bmap;
1705 n_div = isl_basic_map_dim(bmap, isl_dim_div);
1706 o_div = isl_basic_map_offset(bmap, isl_dim_div) - 1;
1708 for (i = 0; i < n_div; ++i) {
1709 known = isl_basic_map_div_is_known(bmap, i);
1710 if (known < 0)
1711 return isl_basic_map_free(bmap);
1712 if (known)
1713 continue;
1714 bmap = remove_dependent_vars(bmap, o_div + i);
1715 bmap = isl_basic_map_drop_constraints_involving_dims(bmap,
1716 isl_dim_div, i, 1);
1717 if (!bmap)
1718 return NULL;
1719 n_div = isl_basic_map_dim(bmap, isl_dim_div);
1720 i = -1;
1723 return bmap;
1726 /* Remove all constraints from "map" that reference any unknown local
1727 * variables (directly or indirectly).
1729 * Since constraints may get dropped from the basic maps,
1730 * they may no longer be disjoint from each other.
1732 __isl_give isl_map *isl_map_drop_constraint_involving_unknown_divs(
1733 __isl_take isl_map *map)
1735 int i;
1736 isl_bool known;
1738 known = isl_map_divs_known(map);
1739 if (known < 0)
1740 return isl_map_free(map);
1741 if (known)
1742 return map;
1744 map = isl_map_cow(map);
1745 if (!map)
1746 return NULL;
1748 for (i = 0; i < map->n; ++i) {
1749 map->p[i] =
1750 isl_basic_map_drop_constraint_involving_unknown_divs(
1751 map->p[i]);
1752 if (!map->p[i])
1753 return isl_map_free(map);
1756 if (map->n > 1)
1757 ISL_F_CLR(map, ISL_MAP_DISJOINT);
1759 return map;
1762 /* Don't assume equalities are in order, because align_divs
1763 * may have changed the order of the divs.
1765 static void compute_elimination_index(__isl_keep isl_basic_map *bmap, int *elim)
1767 int d, i;
1768 unsigned total;
1770 total = isl_space_dim(bmap->dim, isl_dim_all);
1771 for (d = 0; d < total; ++d)
1772 elim[d] = -1;
1773 for (i = 0; i < bmap->n_eq; ++i) {
1774 for (d = total - 1; d >= 0; --d) {
1775 if (isl_int_is_zero(bmap->eq[i][1+d]))
1776 continue;
1777 elim[d] = i;
1778 break;
1783 static void set_compute_elimination_index(__isl_keep isl_basic_set *bset,
1784 int *elim)
1786 compute_elimination_index(bset_to_bmap(bset), elim);
1789 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1790 __isl_keep isl_basic_map *bmap, int *elim)
1792 int d;
1793 int copied = 0;
1794 unsigned total;
1796 total = isl_space_dim(bmap->dim, isl_dim_all);
1797 for (d = total - 1; d >= 0; --d) {
1798 if (isl_int_is_zero(src[1+d]))
1799 continue;
1800 if (elim[d] == -1)
1801 continue;
1802 if (!copied) {
1803 isl_seq_cpy(dst, src, 1 + total);
1804 copied = 1;
1806 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1808 return copied;
1811 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1812 __isl_keep isl_basic_set *bset, int *elim)
1814 return reduced_using_equalities(dst, src,
1815 bset_to_bmap(bset), elim);
1818 static __isl_give isl_basic_set *isl_basic_set_reduce_using_equalities(
1819 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *context)
1821 int i;
1822 int *elim;
1824 if (!bset || !context)
1825 goto error;
1827 if (context->n_eq == 0) {
1828 isl_basic_set_free(context);
1829 return bset;
1832 bset = isl_basic_set_cow(bset);
1833 if (!bset)
1834 goto error;
1836 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1837 if (!elim)
1838 goto error;
1839 set_compute_elimination_index(context, elim);
1840 for (i = 0; i < bset->n_eq; ++i)
1841 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1842 context, elim);
1843 for (i = 0; i < bset->n_ineq; ++i)
1844 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1845 context, elim);
1846 isl_basic_set_free(context);
1847 free(elim);
1848 bset = isl_basic_set_simplify(bset);
1849 bset = isl_basic_set_finalize(bset);
1850 return bset;
1851 error:
1852 isl_basic_set_free(bset);
1853 isl_basic_set_free(context);
1854 return NULL;
1857 /* For each inequality in "ineq" that is a shifted (more relaxed)
1858 * copy of an inequality in "context", mark the corresponding entry
1859 * in "row" with -1.
1860 * If an inequality only has a non-negative constant term, then
1861 * mark it as well.
1863 static isl_stat mark_shifted_constraints(__isl_keep isl_mat *ineq,
1864 __isl_keep isl_basic_set *context, int *row)
1866 struct isl_constraint_index ci;
1867 int n_ineq;
1868 unsigned total;
1869 int k;
1871 if (!ineq || !context)
1872 return isl_stat_error;
1873 if (context->n_ineq == 0)
1874 return isl_stat_ok;
1875 if (setup_constraint_index(&ci, context) < 0)
1876 return isl_stat_error;
1878 n_ineq = isl_mat_rows(ineq);
1879 total = isl_mat_cols(ineq) - 1;
1880 for (k = 0; k < n_ineq; ++k) {
1881 int l;
1882 isl_bool redundant;
1884 l = isl_seq_first_non_zero(ineq->row[k] + 1, total);
1885 if (l < 0 && isl_int_is_nonneg(ineq->row[k][0])) {
1886 row[k] = -1;
1887 continue;
1889 redundant = constraint_index_is_redundant(&ci, ineq->row[k]);
1890 if (redundant < 0)
1891 goto error;
1892 if (!redundant)
1893 continue;
1894 row[k] = -1;
1896 constraint_index_free(&ci);
1897 return isl_stat_ok;
1898 error:
1899 constraint_index_free(&ci);
1900 return isl_stat_error;
1903 static __isl_give isl_basic_set *remove_shifted_constraints(
1904 __isl_take isl_basic_set *bset, __isl_keep isl_basic_set *context)
1906 struct isl_constraint_index ci;
1907 int k;
1909 if (!bset || !context)
1910 return bset;
1912 if (context->n_ineq == 0)
1913 return bset;
1914 if (setup_constraint_index(&ci, context) < 0)
1915 return bset;
1917 for (k = 0; k < bset->n_ineq; ++k) {
1918 isl_bool redundant;
1920 redundant = constraint_index_is_redundant(&ci, bset->ineq[k]);
1921 if (redundant < 0)
1922 goto error;
1923 if (!redundant)
1924 continue;
1925 bset = isl_basic_set_cow(bset);
1926 if (!bset)
1927 goto error;
1928 isl_basic_set_drop_inequality(bset, k);
1929 --k;
1931 constraint_index_free(&ci);
1932 return bset;
1933 error:
1934 constraint_index_free(&ci);
1935 return bset;
1938 /* Remove constraints from "bmap" that are identical to constraints
1939 * in "context" or that are more relaxed (greater constant term).
1941 * We perform the test for shifted copies on the pure constraints
1942 * in remove_shifted_constraints.
1944 static __isl_give isl_basic_map *isl_basic_map_remove_shifted_constraints(
1945 __isl_take isl_basic_map *bmap, __isl_take isl_basic_map *context)
1947 isl_basic_set *bset, *bset_context;
1949 if (!bmap || !context)
1950 goto error;
1952 if (bmap->n_ineq == 0 || context->n_ineq == 0) {
1953 isl_basic_map_free(context);
1954 return bmap;
1957 context = isl_basic_map_align_divs(context, bmap);
1958 bmap = isl_basic_map_align_divs(bmap, context);
1960 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1961 bset_context = isl_basic_map_underlying_set(context);
1962 bset = remove_shifted_constraints(bset, bset_context);
1963 isl_basic_set_free(bset_context);
1965 bmap = isl_basic_map_overlying_set(bset, bmap);
1967 return bmap;
1968 error:
1969 isl_basic_map_free(bmap);
1970 isl_basic_map_free(context);
1971 return NULL;
1974 /* Does the (linear part of a) constraint "c" involve any of the "len"
1975 * "relevant" dimensions?
1977 static int is_related(isl_int *c, int len, int *relevant)
1979 int i;
1981 for (i = 0; i < len; ++i) {
1982 if (!relevant[i])
1983 continue;
1984 if (!isl_int_is_zero(c[i]))
1985 return 1;
1988 return 0;
1991 /* Drop constraints from "bmap" that do not involve any of
1992 * the dimensions marked "relevant".
1994 static __isl_give isl_basic_map *drop_unrelated_constraints(
1995 __isl_take isl_basic_map *bmap, int *relevant)
1997 int i, dim;
1999 dim = isl_basic_map_dim(bmap, isl_dim_all);
2000 for (i = 0; i < dim; ++i)
2001 if (!relevant[i])
2002 break;
2003 if (i >= dim)
2004 return bmap;
2006 for (i = bmap->n_eq - 1; i >= 0; --i)
2007 if (!is_related(bmap->eq[i] + 1, dim, relevant)) {
2008 bmap = isl_basic_map_cow(bmap);
2009 if (isl_basic_map_drop_equality(bmap, i) < 0)
2010 return isl_basic_map_free(bmap);
2013 for (i = bmap->n_ineq - 1; i >= 0; --i)
2014 if (!is_related(bmap->ineq[i] + 1, dim, relevant)) {
2015 bmap = isl_basic_map_cow(bmap);
2016 if (isl_basic_map_drop_inequality(bmap, i) < 0)
2017 return isl_basic_map_free(bmap);
2020 return bmap;
2023 /* Update the groups in "group" based on the (linear part of a) constraint "c".
2025 * In particular, for any variable involved in the constraint,
2026 * find the actual group id from before and replace the group
2027 * of the corresponding variable by the minimal group of all
2028 * the variables involved in the constraint considered so far
2029 * (if this minimum is smaller) or replace the minimum by this group
2030 * (if the minimum is larger).
2032 * At the end, all the variables in "c" will (indirectly) point
2033 * to the minimal of the groups that they referred to originally.
2035 static void update_groups(int dim, int *group, isl_int *c)
2037 int j;
2038 int min = dim;
2040 for (j = 0; j < dim; ++j) {
2041 if (isl_int_is_zero(c[j]))
2042 continue;
2043 while (group[j] >= 0 && group[group[j]] != group[j])
2044 group[j] = group[group[j]];
2045 if (group[j] == min)
2046 continue;
2047 if (group[j] < min) {
2048 if (min >= 0 && min < dim)
2049 group[min] = group[j];
2050 min = group[j];
2051 } else
2052 group[group[j]] = min;
2056 /* Allocate an array of groups of variables, one for each variable
2057 * in "context", initialized to zero.
2059 static int *alloc_groups(__isl_keep isl_basic_set *context)
2061 isl_ctx *ctx;
2062 int dim;
2064 dim = isl_basic_set_dim(context, isl_dim_set);
2065 ctx = isl_basic_set_get_ctx(context);
2066 return isl_calloc_array(ctx, int, dim);
2069 /* Drop constraints from "bmap" that only involve variables that are
2070 * not related to any of the variables marked with a "-1" in "group".
2072 * We construct groups of variables that collect variables that
2073 * (indirectly) appear in some common constraint of "bmap".
2074 * Each group is identified by the first variable in the group,
2075 * except for the special group of variables that was already identified
2076 * in the input as -1 (or are related to those variables).
2077 * If group[i] is equal to i (or -1), then the group of i is i (or -1),
2078 * otherwise the group of i is the group of group[i].
2080 * We first initialize groups for the remaining variables.
2081 * Then we iterate over the constraints of "bmap" and update the
2082 * group of the variables in the constraint by the smallest group.
2083 * Finally, we resolve indirect references to groups by running over
2084 * the variables.
2086 * After computing the groups, we drop constraints that do not involve
2087 * any variables in the -1 group.
2089 __isl_give isl_basic_map *isl_basic_map_drop_unrelated_constraints(
2090 __isl_take isl_basic_map *bmap, __isl_take int *group)
2092 int dim;
2093 int i;
2094 int last;
2096 if (!bmap)
2097 return NULL;
2099 dim = isl_basic_map_dim(bmap, isl_dim_all);
2101 last = -1;
2102 for (i = 0; i < dim; ++i)
2103 if (group[i] >= 0)
2104 last = group[i] = i;
2105 if (last < 0) {
2106 free(group);
2107 return bmap;
2110 for (i = 0; i < bmap->n_eq; ++i)
2111 update_groups(dim, group, bmap->eq[i] + 1);
2112 for (i = 0; i < bmap->n_ineq; ++i)
2113 update_groups(dim, group, bmap->ineq[i] + 1);
2115 for (i = 0; i < dim; ++i)
2116 if (group[i] >= 0)
2117 group[i] = group[group[i]];
2119 for (i = 0; i < dim; ++i)
2120 group[i] = group[i] == -1;
2122 bmap = drop_unrelated_constraints(bmap, group);
2124 free(group);
2125 return bmap;
2128 /* Drop constraints from "context" that are irrelevant for computing
2129 * the gist of "bset".
2131 * In particular, drop constraints in variables that are not related
2132 * to any of the variables involved in the constraints of "bset"
2133 * in the sense that there is no sequence of constraints that connects them.
2135 * We first mark all variables that appear in "bset" as belonging
2136 * to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
2138 static __isl_give isl_basic_set *drop_irrelevant_constraints(
2139 __isl_take isl_basic_set *context, __isl_keep isl_basic_set *bset)
2141 int *group;
2142 int dim;
2143 int i, j;
2145 if (!context || !bset)
2146 return isl_basic_set_free(context);
2148 group = alloc_groups(context);
2150 if (!group)
2151 return isl_basic_set_free(context);
2153 dim = isl_basic_set_dim(bset, isl_dim_set);
2154 for (i = 0; i < dim; ++i) {
2155 for (j = 0; j < bset->n_eq; ++j)
2156 if (!isl_int_is_zero(bset->eq[j][1 + i]))
2157 break;
2158 if (j < bset->n_eq) {
2159 group[i] = -1;
2160 continue;
2162 for (j = 0; j < bset->n_ineq; ++j)
2163 if (!isl_int_is_zero(bset->ineq[j][1 + i]))
2164 break;
2165 if (j < bset->n_ineq)
2166 group[i] = -1;
2169 return isl_basic_map_drop_unrelated_constraints(context, group);
2172 /* Drop constraints from "context" that are irrelevant for computing
2173 * the gist of the inequalities "ineq".
2174 * Inequalities in "ineq" for which the corresponding element of row
2175 * is set to -1 have already been marked for removal and should be ignored.
2177 * In particular, drop constraints in variables that are not related
2178 * to any of the variables involved in "ineq"
2179 * in the sense that there is no sequence of constraints that connects them.
2181 * We first mark all variables that appear in "bset" as belonging
2182 * to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
2184 static __isl_give isl_basic_set *drop_irrelevant_constraints_marked(
2185 __isl_take isl_basic_set *context, __isl_keep isl_mat *ineq, int *row)
2187 int *group;
2188 int dim;
2189 int i, j, n;
2191 if (!context || !ineq)
2192 return isl_basic_set_free(context);
2194 group = alloc_groups(context);
2196 if (!group)
2197 return isl_basic_set_free(context);
2199 dim = isl_basic_set_dim(context, isl_dim_set);
2200 n = isl_mat_rows(ineq);
2201 for (i = 0; i < dim; ++i) {
2202 for (j = 0; j < n; ++j) {
2203 if (row[j] < 0)
2204 continue;
2205 if (!isl_int_is_zero(ineq->row[j][1 + i]))
2206 break;
2208 if (j < n)
2209 group[i] = -1;
2212 return isl_basic_map_drop_unrelated_constraints(context, group);
2215 /* Do all "n" entries of "row" contain a negative value?
2217 static int all_neg(int *row, int n)
2219 int i;
2221 for (i = 0; i < n; ++i)
2222 if (row[i] >= 0)
2223 return 0;
2225 return 1;
2228 /* Update the inequalities in "bset" based on the information in "row"
2229 * and "tab".
2231 * In particular, the array "row" contains either -1, meaning that
2232 * the corresponding inequality of "bset" is redundant, or the index
2233 * of an inequality in "tab".
2235 * If the row entry is -1, then drop the inequality.
2236 * Otherwise, if the constraint is marked redundant in the tableau,
2237 * then drop the inequality. Similarly, if it is marked as an equality
2238 * in the tableau, then turn the inequality into an equality and
2239 * perform Gaussian elimination.
2241 static __isl_give isl_basic_set *update_ineq(__isl_take isl_basic_set *bset,
2242 __isl_keep int *row, struct isl_tab *tab)
2244 int i;
2245 unsigned n_ineq;
2246 unsigned n_eq;
2247 int found_equality = 0;
2249 if (!bset)
2250 return NULL;
2251 if (tab && tab->empty)
2252 return isl_basic_set_set_to_empty(bset);
2254 n_ineq = bset->n_ineq;
2255 for (i = n_ineq - 1; i >= 0; --i) {
2256 if (row[i] < 0) {
2257 if (isl_basic_set_drop_inequality(bset, i) < 0)
2258 return isl_basic_set_free(bset);
2259 continue;
2261 if (!tab)
2262 continue;
2263 n_eq = tab->n_eq;
2264 if (isl_tab_is_equality(tab, n_eq + row[i])) {
2265 isl_basic_map_inequality_to_equality(bset, i);
2266 found_equality = 1;
2267 } else if (isl_tab_is_redundant(tab, n_eq + row[i])) {
2268 if (isl_basic_set_drop_inequality(bset, i) < 0)
2269 return isl_basic_set_free(bset);
2273 if (found_equality)
2274 bset = isl_basic_set_gauss(bset, NULL);
2275 bset = isl_basic_set_finalize(bset);
2276 return bset;
2279 /* Update the inequalities in "bset" based on the information in "row"
2280 * and "tab" and free all arguments (other than "bset").
2282 static __isl_give isl_basic_set *update_ineq_free(
2283 __isl_take isl_basic_set *bset, __isl_take isl_mat *ineq,
2284 __isl_take isl_basic_set *context, __isl_take int *row,
2285 struct isl_tab *tab)
2287 isl_mat_free(ineq);
2288 isl_basic_set_free(context);
2290 bset = update_ineq(bset, row, tab);
2292 free(row);
2293 isl_tab_free(tab);
2294 return bset;
2297 /* Remove all information from bset that is redundant in the context
2298 * of context.
2299 * "ineq" contains the (possibly transformed) inequalities of "bset",
2300 * in the same order.
2301 * The (explicit) equalities of "bset" are assumed to have been taken
2302 * into account by the transformation such that only the inequalities
2303 * are relevant.
2304 * "context" is assumed not to be empty.
2306 * "row" keeps track of the constraint index of a "bset" inequality in "tab".
2307 * A value of -1 means that the inequality is obviously redundant and may
2308 * not even appear in "tab".
2310 * We first mark the inequalities of "bset"
2311 * that are obviously redundant with respect to some inequality in "context".
2312 * Then we remove those constraints from "context" that have become
2313 * irrelevant for computing the gist of "bset".
2314 * Note that this removal of constraints cannot be replaced by
2315 * a factorization because factors in "bset" may still be connected
2316 * to each other through constraints in "context".
2318 * If there are any inequalities left, we construct a tableau for
2319 * the context and then add the inequalities of "bset".
2320 * Before adding these inequalities, we freeze all constraints such that
2321 * they won't be considered redundant in terms of the constraints of "bset".
2322 * Then we detect all redundant constraints (among the
2323 * constraints that weren't frozen), first by checking for redundancy in the
2324 * the tableau and then by checking if replacing a constraint by its negation
2325 * would lead to an empty set. This last step is fairly expensive
2326 * and could be optimized by more reuse of the tableau.
2327 * Finally, we update bset according to the results.
2329 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
2330 __isl_take isl_mat *ineq, __isl_take isl_basic_set *context)
2332 int i, r;
2333 int *row = NULL;
2334 isl_ctx *ctx;
2335 isl_basic_set *combined = NULL;
2336 struct isl_tab *tab = NULL;
2337 unsigned n_eq, context_ineq;
2339 if (!bset || !ineq || !context)
2340 goto error;
2342 if (bset->n_ineq == 0 || isl_basic_set_plain_is_universe(context)) {
2343 isl_basic_set_free(context);
2344 isl_mat_free(ineq);
2345 return bset;
2348 ctx = isl_basic_set_get_ctx(context);
2349 row = isl_calloc_array(ctx, int, bset->n_ineq);
2350 if (!row)
2351 goto error;
2353 if (mark_shifted_constraints(ineq, context, row) < 0)
2354 goto error;
2355 if (all_neg(row, bset->n_ineq))
2356 return update_ineq_free(bset, ineq, context, row, NULL);
2358 context = drop_irrelevant_constraints_marked(context, ineq, row);
2359 if (!context)
2360 goto error;
2361 if (isl_basic_set_plain_is_universe(context))
2362 return update_ineq_free(bset, ineq, context, row, NULL);
2364 n_eq = context->n_eq;
2365 context_ineq = context->n_ineq;
2366 combined = isl_basic_set_cow(isl_basic_set_copy(context));
2367 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
2368 tab = isl_tab_from_basic_set(combined, 0);
2369 for (i = 0; i < context_ineq; ++i)
2370 if (isl_tab_freeze_constraint(tab, n_eq + i) < 0)
2371 goto error;
2372 if (isl_tab_extend_cons(tab, bset->n_ineq) < 0)
2373 goto error;
2374 r = context_ineq;
2375 for (i = 0; i < bset->n_ineq; ++i) {
2376 if (row[i] < 0)
2377 continue;
2378 combined = isl_basic_set_add_ineq(combined, ineq->row[i]);
2379 if (isl_tab_add_ineq(tab, ineq->row[i]) < 0)
2380 goto error;
2381 row[i] = r++;
2383 if (isl_tab_detect_implicit_equalities(tab) < 0)
2384 goto error;
2385 if (isl_tab_detect_redundant(tab) < 0)
2386 goto error;
2387 for (i = bset->n_ineq - 1; i >= 0; --i) {
2388 isl_basic_set *test;
2389 int is_empty;
2391 if (row[i] < 0)
2392 continue;
2393 r = row[i];
2394 if (tab->con[n_eq + r].is_redundant)
2395 continue;
2396 test = isl_basic_set_dup(combined);
2397 if (isl_inequality_negate(test, r) < 0)
2398 test = isl_basic_set_free(test);
2399 test = isl_basic_set_update_from_tab(test, tab);
2400 is_empty = isl_basic_set_is_empty(test);
2401 isl_basic_set_free(test);
2402 if (is_empty < 0)
2403 goto error;
2404 if (is_empty)
2405 tab->con[n_eq + r].is_redundant = 1;
2407 bset = update_ineq_free(bset, ineq, context, row, tab);
2408 if (bset) {
2409 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
2410 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
2413 isl_basic_set_free(combined);
2414 return bset;
2415 error:
2416 free(row);
2417 isl_mat_free(ineq);
2418 isl_tab_free(tab);
2419 isl_basic_set_free(combined);
2420 isl_basic_set_free(context);
2421 isl_basic_set_free(bset);
2422 return NULL;
2425 /* Extract the inequalities of "bset" as an isl_mat.
2427 static __isl_give isl_mat *extract_ineq(__isl_keep isl_basic_set *bset)
2429 unsigned total;
2430 isl_ctx *ctx;
2431 isl_mat *ineq;
2433 if (!bset)
2434 return NULL;
2436 ctx = isl_basic_set_get_ctx(bset);
2437 total = isl_basic_set_total_dim(bset);
2438 ineq = isl_mat_sub_alloc6(ctx, bset->ineq, 0, bset->n_ineq,
2439 0, 1 + total);
2441 return ineq;
2444 /* Remove all information from "bset" that is redundant in the context
2445 * of "context", for the case where both "bset" and "context" are
2446 * full-dimensional.
2448 static __isl_give isl_basic_set *uset_gist_uncompressed(
2449 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *context)
2451 isl_mat *ineq;
2453 ineq = extract_ineq(bset);
2454 return uset_gist_full(bset, ineq, context);
2457 /* Remove all information from "bset" that is redundant in the context
2458 * of "context", for the case where the combined equalities of
2459 * "bset" and "context" allow for a compression that can be obtained
2460 * by preapplication of "T".
2462 * "bset" itself is not transformed by "T". Instead, the inequalities
2463 * are extracted from "bset" and those are transformed by "T".
2464 * uset_gist_full then determines which of the transformed inequalities
2465 * are redundant with respect to the transformed "context" and removes
2466 * the corresponding inequalities from "bset".
2468 * After preapplying "T" to the inequalities, any common factor is
2469 * removed from the coefficients. If this results in a tightening
2470 * of the constant term, then the same tightening is applied to
2471 * the corresponding untransformed inequality in "bset".
2472 * That is, if after plugging in T, a constraint f(x) >= 0 is of the form
2474 * g f'(x) + r >= 0
2476 * with 0 <= r < g, then it is equivalent to
2478 * f'(x) >= 0
2480 * This means that f(x) >= 0 is equivalent to f(x) - r >= 0 in the affine
2481 * subspace compressed by T since the latter would be transformed to
2483 * g f'(x) >= 0
2485 static __isl_give isl_basic_set *uset_gist_compressed(
2486 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *context,
2487 __isl_take isl_mat *T)
2489 isl_ctx *ctx;
2490 isl_mat *ineq;
2491 int i, n_row, n_col;
2492 isl_int rem;
2494 ineq = extract_ineq(bset);
2495 ineq = isl_mat_product(ineq, isl_mat_copy(T));
2496 context = isl_basic_set_preimage(context, T);
2498 if (!ineq || !context)
2499 goto error;
2500 if (isl_basic_set_plain_is_empty(context)) {
2501 isl_mat_free(ineq);
2502 isl_basic_set_free(context);
2503 return isl_basic_set_set_to_empty(bset);
2506 ctx = isl_mat_get_ctx(ineq);
2507 n_row = isl_mat_rows(ineq);
2508 n_col = isl_mat_cols(ineq);
2509 isl_int_init(rem);
2510 for (i = 0; i < n_row; ++i) {
2511 isl_seq_gcd(ineq->row[i] + 1, n_col - 1, &ctx->normalize_gcd);
2512 if (isl_int_is_zero(ctx->normalize_gcd))
2513 continue;
2514 if (isl_int_is_one(ctx->normalize_gcd))
2515 continue;
2516 isl_seq_scale_down(ineq->row[i] + 1, ineq->row[i] + 1,
2517 ctx->normalize_gcd, n_col - 1);
2518 isl_int_fdiv_r(rem, ineq->row[i][0], ctx->normalize_gcd);
2519 isl_int_fdiv_q(ineq->row[i][0],
2520 ineq->row[i][0], ctx->normalize_gcd);
2521 if (isl_int_is_zero(rem))
2522 continue;
2523 bset = isl_basic_set_cow(bset);
2524 if (!bset)
2525 break;
2526 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], rem);
2528 isl_int_clear(rem);
2530 return uset_gist_full(bset, ineq, context);
2531 error:
2532 isl_mat_free(ineq);
2533 isl_basic_set_free(context);
2534 isl_basic_set_free(bset);
2535 return NULL;
2538 /* Project "bset" onto the variables that are involved in "template".
2540 static __isl_give isl_basic_set *project_onto_involved(
2541 __isl_take isl_basic_set *bset, __isl_keep isl_basic_set *template)
2543 int i, n;
2545 if (!bset || !template)
2546 return isl_basic_set_free(bset);
2548 n = isl_basic_set_dim(template, isl_dim_set);
2550 for (i = 0; i < n; ++i) {
2551 isl_bool involved;
2553 involved = isl_basic_set_involves_dims(template,
2554 isl_dim_set, i, 1);
2555 if (involved < 0)
2556 return isl_basic_set_free(bset);
2557 if (involved)
2558 continue;
2559 bset = isl_basic_set_eliminate_vars(bset, i, 1);
2562 return bset;
2565 /* Remove all information from bset that is redundant in the context
2566 * of context. In particular, equalities that are linear combinations
2567 * of those in context are removed. Then the inequalities that are
2568 * redundant in the context of the equalities and inequalities of
2569 * context are removed.
2571 * First of all, we drop those constraints from "context"
2572 * that are irrelevant for computing the gist of "bset".
2573 * Alternatively, we could factorize the intersection of "context" and "bset".
2575 * We first compute the intersection of the integer affine hulls
2576 * of "bset" and "context",
2577 * compute the gist inside this intersection and then reduce
2578 * the constraints with respect to the equalities of the context
2579 * that only involve variables already involved in the input.
2581 * If two constraints are mutually redundant, then uset_gist_full
2582 * will remove the second of those constraints. We therefore first
2583 * sort the constraints so that constraints not involving existentially
2584 * quantified variables are given precedence over those that do.
2585 * We have to perform this sorting before the variable compression,
2586 * because that may effect the order of the variables.
2588 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
2589 __isl_take isl_basic_set *context)
2591 isl_mat *eq;
2592 isl_mat *T;
2593 isl_basic_set *aff;
2594 isl_basic_set *aff_context;
2595 unsigned total;
2597 if (!bset || !context)
2598 goto error;
2600 context = drop_irrelevant_constraints(context, bset);
2602 bset = isl_basic_set_detect_equalities(bset);
2603 aff = isl_basic_set_copy(bset);
2604 aff = isl_basic_set_plain_affine_hull(aff);
2605 context = isl_basic_set_detect_equalities(context);
2606 aff_context = isl_basic_set_copy(context);
2607 aff_context = isl_basic_set_plain_affine_hull(aff_context);
2608 aff = isl_basic_set_intersect(aff, aff_context);
2609 if (!aff)
2610 goto error;
2611 if (isl_basic_set_plain_is_empty(aff)) {
2612 isl_basic_set_free(bset);
2613 isl_basic_set_free(context);
2614 return aff;
2616 bset = isl_basic_set_sort_constraints(bset);
2617 if (aff->n_eq == 0) {
2618 isl_basic_set_free(aff);
2619 return uset_gist_uncompressed(bset, context);
2621 total = isl_basic_set_total_dim(bset);
2622 eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
2623 eq = isl_mat_cow(eq);
2624 T = isl_mat_variable_compression(eq, NULL);
2625 isl_basic_set_free(aff);
2626 if (T && T->n_col == 0) {
2627 isl_mat_free(T);
2628 isl_basic_set_free(context);
2629 return isl_basic_set_set_to_empty(bset);
2632 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
2633 aff_context = project_onto_involved(aff_context, bset);
2635 bset = uset_gist_compressed(bset, context, T);
2636 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
2638 if (bset) {
2639 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
2640 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
2643 return bset;
2644 error:
2645 isl_basic_set_free(bset);
2646 isl_basic_set_free(context);
2647 return NULL;
2650 /* Return the number of equality constraints in "bmap" that involve
2651 * local variables. This function assumes that Gaussian elimination
2652 * has been applied to the equality constraints.
2654 static int n_div_eq(__isl_keep isl_basic_map *bmap)
2656 int i;
2657 int total, n_div;
2659 if (!bmap)
2660 return -1;
2662 if (bmap->n_eq == 0)
2663 return 0;
2665 total = isl_basic_map_dim(bmap, isl_dim_all);
2666 n_div = isl_basic_map_dim(bmap, isl_dim_div);
2667 total -= n_div;
2669 for (i = 0; i < bmap->n_eq; ++i)
2670 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total,
2671 n_div) == -1)
2672 return i;
2674 return bmap->n_eq;
2677 /* Construct a basic map in "space" defined by the equality constraints in "eq".
2678 * The constraints are assumed not to involve any local variables.
2680 static __isl_give isl_basic_map *basic_map_from_equalities(
2681 __isl_take isl_space *space, __isl_take isl_mat *eq)
2683 int i, k;
2684 isl_basic_map *bmap = NULL;
2686 if (!space || !eq)
2687 goto error;
2689 if (1 + isl_space_dim(space, isl_dim_all) != eq->n_col)
2690 isl_die(isl_space_get_ctx(space), isl_error_internal,
2691 "unexpected number of columns", goto error);
2693 bmap = isl_basic_map_alloc_space(isl_space_copy(space),
2694 0, eq->n_row, 0);
2695 for (i = 0; i < eq->n_row; ++i) {
2696 k = isl_basic_map_alloc_equality(bmap);
2697 if (k < 0)
2698 goto error;
2699 isl_seq_cpy(bmap->eq[k], eq->row[i], eq->n_col);
2702 isl_space_free(space);
2703 isl_mat_free(eq);
2704 return bmap;
2705 error:
2706 isl_space_free(space);
2707 isl_mat_free(eq);
2708 isl_basic_map_free(bmap);
2709 return NULL;
2712 /* Construct and return a variable compression based on the equality
2713 * constraints in "bmap1" and "bmap2" that do not involve the local variables.
2714 * "n1" is the number of (initial) equality constraints in "bmap1"
2715 * that do involve local variables.
2716 * "n2" is the number of (initial) equality constraints in "bmap2"
2717 * that do involve local variables.
2718 * "total" is the total number of other variables.
2719 * This function assumes that Gaussian elimination
2720 * has been applied to the equality constraints in both "bmap1" and "bmap2"
2721 * such that the equality constraints not involving local variables
2722 * are those that start at "n1" or "n2".
2724 * If either of "bmap1" and "bmap2" does not have such equality constraints,
2725 * then simply compute the compression based on the equality constraints
2726 * in the other basic map.
2727 * Otherwise, combine the equality constraints from both into a new
2728 * basic map such that Gaussian elimination can be applied to this combination
2729 * and then construct a variable compression from the resulting
2730 * equality constraints.
2732 static __isl_give isl_mat *combined_variable_compression(
2733 __isl_keep isl_basic_map *bmap1, int n1,
2734 __isl_keep isl_basic_map *bmap2, int n2, int total)
2736 isl_ctx *ctx;
2737 isl_mat *E1, *E2, *V;
2738 isl_basic_map *bmap;
2740 ctx = isl_basic_map_get_ctx(bmap1);
2741 if (bmap1->n_eq == n1) {
2742 E2 = isl_mat_sub_alloc6(ctx, bmap2->eq,
2743 n2, bmap2->n_eq - n2, 0, 1 + total);
2744 return isl_mat_variable_compression(E2, NULL);
2746 if (bmap2->n_eq == n2) {
2747 E1 = isl_mat_sub_alloc6(ctx, bmap1->eq,
2748 n1, bmap1->n_eq - n1, 0, 1 + total);
2749 return isl_mat_variable_compression(E1, NULL);
2751 E1 = isl_mat_sub_alloc6(ctx, bmap1->eq,
2752 n1, bmap1->n_eq - n1, 0, 1 + total);
2753 E2 = isl_mat_sub_alloc6(ctx, bmap2->eq,
2754 n2, bmap2->n_eq - n2, 0, 1 + total);
2755 E1 = isl_mat_concat(E1, E2);
2756 bmap = basic_map_from_equalities(isl_basic_map_get_space(bmap1), E1);
2757 bmap = isl_basic_map_gauss(bmap, NULL);
2758 if (!bmap)
2759 return NULL;
2760 E1 = isl_mat_sub_alloc6(ctx, bmap->eq, 0, bmap->n_eq, 0, 1 + total);
2761 V = isl_mat_variable_compression(E1, NULL);
2762 isl_basic_map_free(bmap);
2764 return V;
2767 /* Extract the stride constraints from "bmap", compressed
2768 * with respect to both the stride constraints in "context" and
2769 * the remaining equality constraints in both "bmap" and "context".
2770 * "bmap_n_eq" is the number of (initial) stride constraints in "bmap".
2771 * "context_n_eq" is the number of (initial) stride constraints in "context".
2773 * Let x be all variables in "bmap" (and "context") other than the local
2774 * variables. First compute a variable compression
2776 * x = V x'
2778 * based on the non-stride equality constraints in "bmap" and "context".
2779 * Consider the stride constraints of "context",
2781 * A(x) + B(y) = 0
2783 * with y the local variables and plug in the variable compression,
2784 * resulting in
2786 * A(V x') + B(y) = 0
2788 * Use these constraints to compute a parameter compression on x'
2790 * x' = T x''
2792 * Now consider the stride constraints of "bmap"
2794 * C(x) + D(y) = 0
2796 * and plug in x = V*T x''.
2797 * That is, return A = [C*V*T D].
2799 static __isl_give isl_mat *extract_compressed_stride_constraints(
2800 __isl_keep isl_basic_map *bmap, int bmap_n_eq,
2801 __isl_keep isl_basic_map *context, int context_n_eq)
2803 int total, n_div;
2804 isl_ctx *ctx;
2805 isl_mat *A, *B, *T, *V;
2807 total = isl_basic_map_dim(context, isl_dim_all);
2808 n_div = isl_basic_map_dim(context, isl_dim_div);
2809 total -= n_div;
2811 ctx = isl_basic_map_get_ctx(bmap);
2813 V = combined_variable_compression(bmap, bmap_n_eq,
2814 context, context_n_eq, total);
2816 A = isl_mat_sub_alloc6(ctx, context->eq, 0, context_n_eq, 0, 1 + total);
2817 B = isl_mat_sub_alloc6(ctx, context->eq,
2818 0, context_n_eq, 1 + total, n_div);
2819 A = isl_mat_product(A, isl_mat_copy(V));
2820 T = isl_mat_parameter_compression_ext(A, B);
2821 T = isl_mat_product(V, T);
2823 n_div = isl_basic_map_dim(bmap, isl_dim_div);
2824 T = isl_mat_diagonal(T, isl_mat_identity(ctx, n_div));
2826 A = isl_mat_sub_alloc6(ctx, bmap->eq,
2827 0, bmap_n_eq, 0, 1 + total + n_div);
2828 A = isl_mat_product(A, T);
2830 return A;
2833 /* Remove the prime factors from *g that have an exponent that
2834 * is strictly smaller than the exponent in "c".
2835 * All exponents in *g are known to be smaller than or equal
2836 * to those in "c".
2838 * That is, if *g is equal to
2840 * p_1^{e_1} p_2^{e_2} ... p_n^{e_n}
2842 * and "c" is equal to
2844 * p_1^{f_1} p_2^{f_2} ... p_n^{f_n}
2846 * then update *g to
2848 * p_1^{e_1 * (e_1 = f_1)} p_2^{e_2 * (e_2 = f_2)} ...
2849 * p_n^{e_n * (e_n = f_n)}
2851 * If e_i = f_i, then c / *g does not have any p_i factors and therefore
2852 * neither does the gcd of *g and c / *g.
2853 * If e_i < f_i, then the gcd of *g and c / *g has a positive
2854 * power min(e_i, s_i) of p_i with s_i = f_i - e_i among its factors.
2855 * Dividing *g by this gcd therefore strictly reduces the exponent
2856 * of the prime factors that need to be removed, while leaving the
2857 * other prime factors untouched.
2858 * Repeating this process until gcd(*g, c / *g) = 1 therefore
2859 * removes all undesired factors, without removing any others.
2861 static void remove_incomplete_powers(isl_int *g, isl_int c)
2863 isl_int t;
2865 isl_int_init(t);
2866 for (;;) {
2867 isl_int_divexact(t, c, *g);
2868 isl_int_gcd(t, t, *g);
2869 if (isl_int_is_one(t))
2870 break;
2871 isl_int_divexact(*g, *g, t);
2873 isl_int_clear(t);
2876 /* Reduce the "n" stride constraints in "bmap" based on a copy "A"
2877 * of the same stride constraints in a compressed space that exploits
2878 * all equalities in the context and the other equalities in "bmap".
2880 * If the stride constraints of "bmap" are of the form
2882 * C(x) + D(y) = 0
2884 * then A is of the form
2886 * B(x') + D(y) = 0
2888 * If any of these constraints involves only a single local variable y,
2889 * then the constraint appears as
2891 * f(x) + m y_i = 0
2893 * in "bmap" and as
2895 * h(x') + m y_i = 0
2897 * in "A".
2899 * Let g be the gcd of m and the coefficients of h.
2900 * Then, in particular, g is a divisor of the coefficients of h and
2902 * f(x) = h(x')
2904 * is known to be a multiple of g.
2905 * If some prime factor in m appears with the same exponent in g,
2906 * then it can be removed from m because f(x) is already known
2907 * to be a multiple of g and therefore in particular of this power
2908 * of the prime factors.
2909 * Prime factors that appear with a smaller exponent in g cannot
2910 * be removed from m.
2911 * Let g' be the divisor of g containing all prime factors that
2912 * appear with the same exponent in m and g, then
2914 * f(x) + m y_i = 0
2916 * can be replaced by
2918 * f(x) + m/g' y_i' = 0
2920 * Note that (if g' != 1) this changes the explicit representation
2921 * of y_i to that of y_i', so the integer division at position i
2922 * is marked unknown and later recomputed by a call to
2923 * isl_basic_map_gauss.
2925 static __isl_give isl_basic_map *reduce_stride_constraints(
2926 __isl_take isl_basic_map *bmap, int n, __isl_keep isl_mat *A)
2928 int i;
2929 int total, n_div;
2930 int any = 0;
2931 isl_int gcd;
2933 if (!bmap || !A)
2934 return isl_basic_map_free(bmap);
2936 total = isl_basic_map_dim(bmap, isl_dim_all);
2937 n_div = isl_basic_map_dim(bmap, isl_dim_div);
2938 total -= n_div;
2940 isl_int_init(gcd);
2941 for (i = 0; i < n; ++i) {
2942 int div;
2944 div = isl_seq_first_non_zero(bmap->eq[i] + 1 + total, n_div);
2945 if (div < 0)
2946 isl_die(isl_basic_map_get_ctx(bmap), isl_error_internal,
2947 "equality constraints modified unexpectedly",
2948 goto error);
2949 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total + div + 1,
2950 n_div - div - 1) != -1)
2951 continue;
2952 if (isl_mat_row_gcd(A, i, &gcd) < 0)
2953 goto error;
2954 if (isl_int_is_one(gcd))
2955 continue;
2956 remove_incomplete_powers(&gcd, bmap->eq[i][1 + total + div]);
2957 if (isl_int_is_one(gcd))
2958 continue;
2959 isl_int_divexact(bmap->eq[i][1 + total + div],
2960 bmap->eq[i][1 + total + div], gcd);
2961 bmap = isl_basic_map_mark_div_unknown(bmap, div);
2962 if (!bmap)
2963 goto error;
2964 any = 1;
2966 isl_int_clear(gcd);
2968 if (any)
2969 bmap = isl_basic_map_gauss(bmap, NULL);
2971 return bmap;
2972 error:
2973 isl_int_clear(gcd);
2974 isl_basic_map_free(bmap);
2975 return NULL;
2978 /* Simplify the stride constraints in "bmap" based on
2979 * the remaining equality constraints in "bmap" and all equality
2980 * constraints in "context".
2981 * Only do this if both "bmap" and "context" have stride constraints.
2983 * First extract a copy of the stride constraints in "bmap" in a compressed
2984 * space exploiting all the other equality constraints and then
2985 * use this compressed copy to simplify the original stride constraints.
2987 static __isl_give isl_basic_map *gist_strides(__isl_take isl_basic_map *bmap,
2988 __isl_keep isl_basic_map *context)
2990 int bmap_n_eq, context_n_eq;
2991 isl_mat *A;
2993 if (!bmap || !context)
2994 return isl_basic_map_free(bmap);
2996 bmap_n_eq = n_div_eq(bmap);
2997 context_n_eq = n_div_eq(context);
2999 if (bmap_n_eq < 0 || context_n_eq < 0)
3000 return isl_basic_map_free(bmap);
3001 if (bmap_n_eq == 0 || context_n_eq == 0)
3002 return bmap;
3004 A = extract_compressed_stride_constraints(bmap, bmap_n_eq,
3005 context, context_n_eq);
3006 bmap = reduce_stride_constraints(bmap, bmap_n_eq, A);
3008 isl_mat_free(A);
3010 return bmap;
3013 /* Return a basic map that has the same intersection with "context" as "bmap"
3014 * and that is as "simple" as possible.
3016 * The core computation is performed on the pure constraints.
3017 * When we add back the meaning of the integer divisions, we need
3018 * to (re)introduce the div constraints. If we happen to have
3019 * discovered that some of these integer divisions are equal to
3020 * some affine combination of other variables, then these div
3021 * constraints may end up getting simplified in terms of the equalities,
3022 * resulting in extra inequalities on the other variables that
3023 * may have been removed already or that may not even have been
3024 * part of the input. We try and remove those constraints of
3025 * this form that are most obviously redundant with respect to
3026 * the context. We also remove those div constraints that are
3027 * redundant with respect to the other constraints in the result.
3029 * The stride constraints among the equality constraints in "bmap" are
3030 * also simplified with respecting to the other equality constraints
3031 * in "bmap" and with respect to all equality constraints in "context".
3033 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
3034 struct isl_basic_map *context)
3036 isl_basic_set *bset, *eq;
3037 isl_basic_map *eq_bmap;
3038 unsigned total, n_div, extra, n_eq, n_ineq;
3040 if (!bmap || !context)
3041 goto error;
3043 if (isl_basic_map_plain_is_universe(bmap)) {
3044 isl_basic_map_free(context);
3045 return bmap;
3047 if (isl_basic_map_plain_is_empty(context)) {
3048 isl_space *space = isl_basic_map_get_space(bmap);
3049 isl_basic_map_free(bmap);
3050 isl_basic_map_free(context);
3051 return isl_basic_map_universe(space);
3053 if (isl_basic_map_plain_is_empty(bmap)) {
3054 isl_basic_map_free(context);
3055 return bmap;
3058 bmap = isl_basic_map_remove_redundancies(bmap);
3059 context = isl_basic_map_remove_redundancies(context);
3060 if (!context)
3061 goto error;
3063 context = isl_basic_map_align_divs(context, bmap);
3064 n_div = isl_basic_map_dim(context, isl_dim_div);
3065 total = isl_basic_map_dim(bmap, isl_dim_all);
3066 extra = n_div - isl_basic_map_dim(bmap, isl_dim_div);
3068 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
3069 bset = isl_basic_set_add_dims(bset, isl_dim_set, extra);
3070 bset = uset_gist(bset,
3071 isl_basic_map_underlying_set(isl_basic_map_copy(context)));
3072 bset = isl_basic_set_project_out(bset, isl_dim_set, total, extra);
3074 if (!bset || bset->n_eq == 0 || n_div == 0 ||
3075 isl_basic_set_plain_is_empty(bset)) {
3076 isl_basic_map_free(context);
3077 return isl_basic_map_overlying_set(bset, bmap);
3080 n_eq = bset->n_eq;
3081 n_ineq = bset->n_ineq;
3082 eq = isl_basic_set_copy(bset);
3083 eq = isl_basic_set_cow(eq);
3084 if (isl_basic_set_free_inequality(eq, n_ineq) < 0)
3085 eq = isl_basic_set_free(eq);
3086 if (isl_basic_set_free_equality(bset, n_eq) < 0)
3087 bset = isl_basic_set_free(bset);
3089 eq_bmap = isl_basic_map_overlying_set(eq, isl_basic_map_copy(bmap));
3090 eq_bmap = gist_strides(eq_bmap, context);
3091 eq_bmap = isl_basic_map_remove_shifted_constraints(eq_bmap, context);
3092 bmap = isl_basic_map_overlying_set(bset, bmap);
3093 bmap = isl_basic_map_intersect(bmap, eq_bmap);
3094 bmap = isl_basic_map_remove_redundancies(bmap);
3096 return bmap;
3097 error:
3098 isl_basic_map_free(bmap);
3099 isl_basic_map_free(context);
3100 return NULL;
3104 * Assumes context has no implicit divs.
3106 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
3107 __isl_take isl_basic_map *context)
3109 int i;
3111 if (!map || !context)
3112 goto error;
3114 if (isl_basic_map_plain_is_empty(context)) {
3115 isl_space *space = isl_map_get_space(map);
3116 isl_map_free(map);
3117 isl_basic_map_free(context);
3118 return isl_map_universe(space);
3121 context = isl_basic_map_remove_redundancies(context);
3122 map = isl_map_cow(map);
3123 if (!map || !context)
3124 goto error;
3125 isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
3126 map = isl_map_compute_divs(map);
3127 if (!map)
3128 goto error;
3129 for (i = map->n - 1; i >= 0; --i) {
3130 map->p[i] = isl_basic_map_gist(map->p[i],
3131 isl_basic_map_copy(context));
3132 if (!map->p[i])
3133 goto error;
3134 if (isl_basic_map_plain_is_empty(map->p[i])) {
3135 isl_basic_map_free(map->p[i]);
3136 if (i != map->n - 1)
3137 map->p[i] = map->p[map->n - 1];
3138 map->n--;
3141 isl_basic_map_free(context);
3142 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
3143 return map;
3144 error:
3145 isl_map_free(map);
3146 isl_basic_map_free(context);
3147 return NULL;
3150 /* Drop all inequalities from "bmap" that also appear in "context".
3151 * "context" is assumed to have only known local variables and
3152 * the initial local variables of "bmap" are assumed to be the same
3153 * as those of "context".
3154 * The constraints of both "bmap" and "context" are assumed
3155 * to have been sorted using isl_basic_map_sort_constraints.
3157 * Run through the inequality constraints of "bmap" and "context"
3158 * in sorted order.
3159 * If a constraint of "bmap" involves variables not in "context",
3160 * then it cannot appear in "context".
3161 * If a matching constraint is found, it is removed from "bmap".
3163 static __isl_give isl_basic_map *drop_inequalities(
3164 __isl_take isl_basic_map *bmap, __isl_keep isl_basic_map *context)
3166 int i1, i2;
3167 unsigned total, extra;
3169 if (!bmap || !context)
3170 return isl_basic_map_free(bmap);
3172 total = isl_basic_map_total_dim(context);
3173 extra = isl_basic_map_total_dim(bmap) - total;
3175 i1 = bmap->n_ineq - 1;
3176 i2 = context->n_ineq - 1;
3177 while (bmap && i1 >= 0 && i2 >= 0) {
3178 int cmp;
3180 if (isl_seq_first_non_zero(bmap->ineq[i1] + 1 + total,
3181 extra) != -1) {
3182 --i1;
3183 continue;
3185 cmp = isl_basic_map_constraint_cmp(context, bmap->ineq[i1],
3186 context->ineq[i2]);
3187 if (cmp < 0) {
3188 --i2;
3189 continue;
3191 if (cmp > 0) {
3192 --i1;
3193 continue;
3195 if (isl_int_eq(bmap->ineq[i1][0], context->ineq[i2][0])) {
3196 bmap = isl_basic_map_cow(bmap);
3197 if (isl_basic_map_drop_inequality(bmap, i1) < 0)
3198 bmap = isl_basic_map_free(bmap);
3200 --i1;
3201 --i2;
3204 return bmap;
3207 /* Drop all equalities from "bmap" that also appear in "context".
3208 * "context" is assumed to have only known local variables and
3209 * the initial local variables of "bmap" are assumed to be the same
3210 * as those of "context".
3212 * Run through the equality constraints of "bmap" and "context"
3213 * in sorted order.
3214 * If a constraint of "bmap" involves variables not in "context",
3215 * then it cannot appear in "context".
3216 * If a matching constraint is found, it is removed from "bmap".
3218 static __isl_give isl_basic_map *drop_equalities(
3219 __isl_take isl_basic_map *bmap, __isl_keep isl_basic_map *context)
3221 int i1, i2;
3222 unsigned total, extra;
3224 if (!bmap || !context)
3225 return isl_basic_map_free(bmap);
3227 total = isl_basic_map_total_dim(context);
3228 extra = isl_basic_map_total_dim(bmap) - total;
3230 i1 = bmap->n_eq - 1;
3231 i2 = context->n_eq - 1;
3233 while (bmap && i1 >= 0 && i2 >= 0) {
3234 int last1, last2;
3236 if (isl_seq_first_non_zero(bmap->eq[i1] + 1 + total,
3237 extra) != -1)
3238 break;
3239 last1 = isl_seq_last_non_zero(bmap->eq[i1] + 1, total);
3240 last2 = isl_seq_last_non_zero(context->eq[i2] + 1, total);
3241 if (last1 > last2) {
3242 --i2;
3243 continue;
3245 if (last1 < last2) {
3246 --i1;
3247 continue;
3249 if (isl_seq_eq(bmap->eq[i1], context->eq[i2], 1 + total)) {
3250 bmap = isl_basic_map_cow(bmap);
3251 if (isl_basic_map_drop_equality(bmap, i1) < 0)
3252 bmap = isl_basic_map_free(bmap);
3254 --i1;
3255 --i2;
3258 return bmap;
3261 /* Remove the constraints in "context" from "bmap".
3262 * "context" is assumed to have explicit representations
3263 * for all local variables.
3265 * First align the divs of "bmap" to those of "context" and
3266 * sort the constraints. Then drop all constraints from "bmap"
3267 * that appear in "context".
3269 __isl_give isl_basic_map *isl_basic_map_plain_gist(
3270 __isl_take isl_basic_map *bmap, __isl_take isl_basic_map *context)
3272 isl_bool done, known;
3274 done = isl_basic_map_plain_is_universe(context);
3275 if (done == isl_bool_false)
3276 done = isl_basic_map_plain_is_universe(bmap);
3277 if (done == isl_bool_false)
3278 done = isl_basic_map_plain_is_empty(context);
3279 if (done == isl_bool_false)
3280 done = isl_basic_map_plain_is_empty(bmap);
3281 if (done < 0)
3282 goto error;
3283 if (done) {
3284 isl_basic_map_free(context);
3285 return bmap;
3287 known = isl_basic_map_divs_known(context);
3288 if (known < 0)
3289 goto error;
3290 if (!known)
3291 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
3292 "context has unknown divs", goto error);
3294 bmap = isl_basic_map_align_divs(bmap, context);
3295 bmap = isl_basic_map_gauss(bmap, NULL);
3296 bmap = isl_basic_map_sort_constraints(bmap);
3297 context = isl_basic_map_sort_constraints(context);
3299 bmap = drop_inequalities(bmap, context);
3300 bmap = drop_equalities(bmap, context);
3302 isl_basic_map_free(context);
3303 bmap = isl_basic_map_finalize(bmap);
3304 return bmap;
3305 error:
3306 isl_basic_map_free(bmap);
3307 isl_basic_map_free(context);
3308 return NULL;
3311 /* Replace "map" by the disjunct at position "pos" and free "context".
3313 static __isl_give isl_map *replace_by_disjunct(__isl_take isl_map *map,
3314 int pos, __isl_take isl_basic_map *context)
3316 isl_basic_map *bmap;
3318 bmap = isl_basic_map_copy(map->p[pos]);
3319 isl_map_free(map);
3320 isl_basic_map_free(context);
3321 return isl_map_from_basic_map(bmap);
3324 /* Remove the constraints in "context" from "map".
3325 * If any of the disjuncts in the result turns out to be the universe,
3326 * then return this universe.
3327 * "context" is assumed to have explicit representations
3328 * for all local variables.
3330 __isl_give isl_map *isl_map_plain_gist_basic_map(__isl_take isl_map *map,
3331 __isl_take isl_basic_map *context)
3333 int i;
3334 isl_bool univ, known;
3336 univ = isl_basic_map_plain_is_universe(context);
3337 if (univ < 0)
3338 goto error;
3339 if (univ) {
3340 isl_basic_map_free(context);
3341 return map;
3343 known = isl_basic_map_divs_known(context);
3344 if (known < 0)
3345 goto error;
3346 if (!known)
3347 isl_die(isl_map_get_ctx(map), isl_error_invalid,
3348 "context has unknown divs", goto error);
3350 map = isl_map_cow(map);
3351 if (!map)
3352 goto error;
3353 for (i = 0; i < map->n; ++i) {
3354 map->p[i] = isl_basic_map_plain_gist(map->p[i],
3355 isl_basic_map_copy(context));
3356 univ = isl_basic_map_plain_is_universe(map->p[i]);
3357 if (univ < 0)
3358 goto error;
3359 if (univ && map->n > 1)
3360 return replace_by_disjunct(map, i, context);
3363 isl_basic_map_free(context);
3364 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
3365 if (map->n > 1)
3366 ISL_F_CLR(map, ISL_MAP_DISJOINT);
3367 return map;
3368 error:
3369 isl_map_free(map);
3370 isl_basic_map_free(context);
3371 return NULL;
3374 /* Replace "map" by a universe map in the same space and free "drop".
3376 static __isl_give isl_map *replace_by_universe(__isl_take isl_map *map,
3377 __isl_take isl_map *drop)
3379 isl_map *res;
3381 res = isl_map_universe(isl_map_get_space(map));
3382 isl_map_free(map);
3383 isl_map_free(drop);
3384 return res;
3387 /* Return a map that has the same intersection with "context" as "map"
3388 * and that is as "simple" as possible.
3390 * If "map" is already the universe, then we cannot make it any simpler.
3391 * Similarly, if "context" is the universe, then we cannot exploit it
3392 * to simplify "map"
3393 * If "map" and "context" are identical to each other, then we can
3394 * return the corresponding universe.
3396 * If either "map" or "context" consists of multiple disjuncts,
3397 * then check if "context" happens to be a subset of "map",
3398 * in which case all constraints can be removed.
3399 * In case of multiple disjuncts, the standard procedure
3400 * may not be able to detect that all constraints can be removed.
3402 * If none of these cases apply, we have to work a bit harder.
3403 * During this computation, we make use of a single disjunct context,
3404 * so if the original context consists of more than one disjunct
3405 * then we need to approximate the context by a single disjunct set.
3406 * Simply taking the simple hull may drop constraints that are
3407 * only implicitly available in each disjunct. We therefore also
3408 * look for constraints among those defining "map" that are valid
3409 * for the context. These can then be used to simplify away
3410 * the corresponding constraints in "map".
3412 static __isl_give isl_map *map_gist(__isl_take isl_map *map,
3413 __isl_take isl_map *context)
3415 int equal;
3416 int is_universe;
3417 int single_disjunct_map, single_disjunct_context;
3418 isl_bool subset;
3419 isl_basic_map *hull;
3421 is_universe = isl_map_plain_is_universe(map);
3422 if (is_universe >= 0 && !is_universe)
3423 is_universe = isl_map_plain_is_universe(context);
3424 if (is_universe < 0)
3425 goto error;
3426 if (is_universe) {
3427 isl_map_free(context);
3428 return map;
3431 equal = isl_map_plain_is_equal(map, context);
3432 if (equal < 0)
3433 goto error;
3434 if (equal)
3435 return replace_by_universe(map, context);
3437 single_disjunct_map = isl_map_n_basic_map(map) == 1;
3438 single_disjunct_context = isl_map_n_basic_map(context) == 1;
3439 if (!single_disjunct_map || !single_disjunct_context) {
3440 subset = isl_map_is_subset(context, map);
3441 if (subset < 0)
3442 goto error;
3443 if (subset)
3444 return replace_by_universe(map, context);
3447 context = isl_map_compute_divs(context);
3448 if (!context)
3449 goto error;
3450 if (single_disjunct_context) {
3451 hull = isl_map_simple_hull(context);
3452 } else {
3453 isl_ctx *ctx;
3454 isl_map_list *list;
3456 ctx = isl_map_get_ctx(map);
3457 list = isl_map_list_alloc(ctx, 2);
3458 list = isl_map_list_add(list, isl_map_copy(context));
3459 list = isl_map_list_add(list, isl_map_copy(map));
3460 hull = isl_map_unshifted_simple_hull_from_map_list(context,
3461 list);
3463 return isl_map_gist_basic_map(map, hull);
3464 error:
3465 isl_map_free(map);
3466 isl_map_free(context);
3467 return NULL;
3470 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3471 __isl_take isl_map *context)
3473 return isl_map_align_params_map_map_and(map, context, &map_gist);
3476 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
3477 struct isl_basic_set *context)
3479 return bset_from_bmap(isl_basic_map_gist(bset_to_bmap(bset),
3480 bset_to_bmap(context)));
3483 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
3484 __isl_take isl_basic_set *context)
3486 return set_from_map(isl_map_gist_basic_map(set_to_map(set),
3487 bset_to_bmap(context)));
3490 __isl_give isl_set *isl_set_gist_params_basic_set(__isl_take isl_set *set,
3491 __isl_take isl_basic_set *context)
3493 isl_space *space = isl_set_get_space(set);
3494 isl_basic_set *dom_context = isl_basic_set_universe(space);
3495 dom_context = isl_basic_set_intersect_params(dom_context, context);
3496 return isl_set_gist_basic_set(set, dom_context);
3499 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3500 __isl_take isl_set *context)
3502 return set_from_map(isl_map_gist(set_to_map(set), set_to_map(context)));
3505 /* Compute the gist of "bmap" with respect to the constraints "context"
3506 * on the domain.
3508 __isl_give isl_basic_map *isl_basic_map_gist_domain(
3509 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *context)
3511 isl_space *space = isl_basic_map_get_space(bmap);
3512 isl_basic_map *bmap_context = isl_basic_map_universe(space);
3514 bmap_context = isl_basic_map_intersect_domain(bmap_context, context);
3515 return isl_basic_map_gist(bmap, bmap_context);
3518 __isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map,
3519 __isl_take isl_set *context)
3521 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
3522 map_context = isl_map_intersect_domain(map_context, context);
3523 return isl_map_gist(map, map_context);
3526 __isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map,
3527 __isl_take isl_set *context)
3529 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
3530 map_context = isl_map_intersect_range(map_context, context);
3531 return isl_map_gist(map, map_context);
3534 __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
3535 __isl_take isl_set *context)
3537 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
3538 map_context = isl_map_intersect_params(map_context, context);
3539 return isl_map_gist(map, map_context);
3542 __isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
3543 __isl_take isl_set *context)
3545 return isl_map_gist_params(set, context);
3548 /* Quick check to see if two basic maps are disjoint.
3549 * In particular, we reduce the equalities and inequalities of
3550 * one basic map in the context of the equalities of the other
3551 * basic map and check if we get a contradiction.
3553 isl_bool isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
3554 __isl_keep isl_basic_map *bmap2)
3556 struct isl_vec *v = NULL;
3557 int *elim = NULL;
3558 unsigned total;
3559 int i;
3561 if (!bmap1 || !bmap2)
3562 return isl_bool_error;
3563 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
3564 return isl_bool_error);
3565 if (bmap1->n_div || bmap2->n_div)
3566 return isl_bool_false;
3567 if (!bmap1->n_eq && !bmap2->n_eq)
3568 return isl_bool_false;
3570 total = isl_space_dim(bmap1->dim, isl_dim_all);
3571 if (total == 0)
3572 return isl_bool_false;
3573 v = isl_vec_alloc(bmap1->ctx, 1 + total);
3574 if (!v)
3575 goto error;
3576 elim = isl_alloc_array(bmap1->ctx, int, total);
3577 if (!elim)
3578 goto error;
3579 compute_elimination_index(bmap1, elim);
3580 for (i = 0; i < bmap2->n_eq; ++i) {
3581 int reduced;
3582 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
3583 bmap1, elim);
3584 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
3585 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
3586 goto disjoint;
3588 for (i = 0; i < bmap2->n_ineq; ++i) {
3589 int reduced;
3590 reduced = reduced_using_equalities(v->block.data,
3591 bmap2->ineq[i], bmap1, elim);
3592 if (reduced && isl_int_is_neg(v->block.data[0]) &&
3593 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
3594 goto disjoint;
3596 compute_elimination_index(bmap2, elim);
3597 for (i = 0; i < bmap1->n_ineq; ++i) {
3598 int reduced;
3599 reduced = reduced_using_equalities(v->block.data,
3600 bmap1->ineq[i], bmap2, elim);
3601 if (reduced && isl_int_is_neg(v->block.data[0]) &&
3602 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
3603 goto disjoint;
3605 isl_vec_free(v);
3606 free(elim);
3607 return isl_bool_false;
3608 disjoint:
3609 isl_vec_free(v);
3610 free(elim);
3611 return isl_bool_true;
3612 error:
3613 isl_vec_free(v);
3614 free(elim);
3615 return isl_bool_error;
3618 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
3619 __isl_keep isl_basic_set *bset2)
3621 return isl_basic_map_plain_is_disjoint(bset_to_bmap(bset1),
3622 bset_to_bmap(bset2));
3625 /* Does "test" hold for all pairs of basic maps in "map1" and "map2"?
3627 static isl_bool all_pairs(__isl_keep isl_map *map1, __isl_keep isl_map *map2,
3628 isl_bool (*test)(__isl_keep isl_basic_map *bmap1,
3629 __isl_keep isl_basic_map *bmap2))
3631 int i, j;
3633 if (!map1 || !map2)
3634 return isl_bool_error;
3636 for (i = 0; i < map1->n; ++i) {
3637 for (j = 0; j < map2->n; ++j) {
3638 isl_bool d = test(map1->p[i], map2->p[j]);
3639 if (d != isl_bool_true)
3640 return d;
3644 return isl_bool_true;
3647 /* Are "map1" and "map2" obviously disjoint, based on information
3648 * that can be derived without looking at the individual basic maps?
3650 * In particular, if one of them is empty or if they live in different spaces
3651 * (ignoring parameters), then they are clearly disjoint.
3653 static isl_bool isl_map_plain_is_disjoint_global(__isl_keep isl_map *map1,
3654 __isl_keep isl_map *map2)
3656 isl_bool disjoint;
3657 isl_bool match;
3659 if (!map1 || !map2)
3660 return isl_bool_error;
3662 disjoint = isl_map_plain_is_empty(map1);
3663 if (disjoint < 0 || disjoint)
3664 return disjoint;
3666 disjoint = isl_map_plain_is_empty(map2);
3667 if (disjoint < 0 || disjoint)
3668 return disjoint;
3670 match = isl_space_tuple_is_equal(map1->dim, isl_dim_in,
3671 map2->dim, isl_dim_in);
3672 if (match < 0 || !match)
3673 return match < 0 ? isl_bool_error : isl_bool_true;
3675 match = isl_space_tuple_is_equal(map1->dim, isl_dim_out,
3676 map2->dim, isl_dim_out);
3677 if (match < 0 || !match)
3678 return match < 0 ? isl_bool_error : isl_bool_true;
3680 return isl_bool_false;
3683 /* Are "map1" and "map2" obviously disjoint?
3685 * If one of them is empty or if they live in different spaces (ignoring
3686 * parameters), then they are clearly disjoint.
3687 * This is checked by isl_map_plain_is_disjoint_global.
3689 * If they have different parameters, then we skip any further tests.
3691 * If they are obviously equal, but not obviously empty, then we will
3692 * not be able to detect if they are disjoint.
3694 * Otherwise we check if each basic map in "map1" is obviously disjoint
3695 * from each basic map in "map2".
3697 isl_bool isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
3698 __isl_keep isl_map *map2)
3700 isl_bool disjoint;
3701 isl_bool intersect;
3702 isl_bool match;
3704 disjoint = isl_map_plain_is_disjoint_global(map1, map2);
3705 if (disjoint < 0 || disjoint)
3706 return disjoint;
3708 match = isl_map_has_equal_params(map1, map2);
3709 if (match < 0 || !match)
3710 return match < 0 ? isl_bool_error : isl_bool_false;
3712 intersect = isl_map_plain_is_equal(map1, map2);
3713 if (intersect < 0 || intersect)
3714 return intersect < 0 ? isl_bool_error : isl_bool_false;
3716 return all_pairs(map1, map2, &isl_basic_map_plain_is_disjoint);
3719 /* Are "map1" and "map2" disjoint?
3721 * They are disjoint if they are "obviously disjoint" or if one of them
3722 * is empty. Otherwise, they are not disjoint if one of them is universal.
3723 * If the two inputs are (obviously) equal and not empty, then they are
3724 * not disjoint.
3725 * If none of these cases apply, then check if all pairs of basic maps
3726 * are disjoint.
3728 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
3730 isl_bool disjoint;
3731 isl_bool intersect;
3733 disjoint = isl_map_plain_is_disjoint_global(map1, map2);
3734 if (disjoint < 0 || disjoint)
3735 return disjoint;
3737 disjoint = isl_map_is_empty(map1);
3738 if (disjoint < 0 || disjoint)
3739 return disjoint;
3741 disjoint = isl_map_is_empty(map2);
3742 if (disjoint < 0 || disjoint)
3743 return disjoint;
3745 intersect = isl_map_plain_is_universe(map1);
3746 if (intersect < 0 || intersect)
3747 return intersect < 0 ? isl_bool_error : isl_bool_false;
3749 intersect = isl_map_plain_is_universe(map2);
3750 if (intersect < 0 || intersect)
3751 return intersect < 0 ? isl_bool_error : isl_bool_false;
3753 intersect = isl_map_plain_is_equal(map1, map2);
3754 if (intersect < 0 || intersect)
3755 return isl_bool_not(intersect);
3757 return all_pairs(map1, map2, &isl_basic_map_is_disjoint);
3760 /* Are "bmap1" and "bmap2" disjoint?
3762 * They are disjoint if they are "obviously disjoint" or if one of them
3763 * is empty. Otherwise, they are not disjoint if one of them is universal.
3764 * If none of these cases apply, we compute the intersection and see if
3765 * the result is empty.
3767 isl_bool isl_basic_map_is_disjoint(__isl_keep isl_basic_map *bmap1,
3768 __isl_keep isl_basic_map *bmap2)
3770 isl_bool disjoint;
3771 isl_bool intersect;
3772 isl_basic_map *test;
3774 disjoint = isl_basic_map_plain_is_disjoint(bmap1, bmap2);
3775 if (disjoint < 0 || disjoint)
3776 return disjoint;
3778 disjoint = isl_basic_map_is_empty(bmap1);
3779 if (disjoint < 0 || disjoint)
3780 return disjoint;
3782 disjoint = isl_basic_map_is_empty(bmap2);
3783 if (disjoint < 0 || disjoint)
3784 return disjoint;
3786 intersect = isl_basic_map_plain_is_universe(bmap1);
3787 if (intersect < 0 || intersect)
3788 return intersect < 0 ? isl_bool_error : isl_bool_false;
3790 intersect = isl_basic_map_plain_is_universe(bmap2);
3791 if (intersect < 0 || intersect)
3792 return intersect < 0 ? isl_bool_error : isl_bool_false;
3794 test = isl_basic_map_intersect(isl_basic_map_copy(bmap1),
3795 isl_basic_map_copy(bmap2));
3796 disjoint = isl_basic_map_is_empty(test);
3797 isl_basic_map_free(test);
3799 return disjoint;
3802 /* Are "bset1" and "bset2" disjoint?
3804 isl_bool isl_basic_set_is_disjoint(__isl_keep isl_basic_set *bset1,
3805 __isl_keep isl_basic_set *bset2)
3807 return isl_basic_map_is_disjoint(bset1, bset2);
3810 isl_bool isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3811 __isl_keep isl_set *set2)
3813 return isl_map_plain_is_disjoint(set_to_map(set1), set_to_map(set2));
3816 /* Are "set1" and "set2" disjoint?
3818 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
3820 return isl_map_is_disjoint(set1, set2);
3823 /* Is "v" equal to 0, 1 or -1?
3825 static int is_zero_or_one(isl_int v)
3827 return isl_int_is_zero(v) || isl_int_is_one(v) || isl_int_is_negone(v);
3830 /* Check if we can combine a given div with lower bound l and upper
3831 * bound u with some other div and if so return that other div.
3832 * Otherwise return -1.
3834 * We first check that
3835 * - the bounds are opposites of each other (except for the constant
3836 * term)
3837 * - the bounds do not reference any other div
3838 * - no div is defined in terms of this div
3840 * Let m be the size of the range allowed on the div by the bounds.
3841 * That is, the bounds are of the form
3843 * e <= a <= e + m - 1
3845 * with e some expression in the other variables.
3846 * We look for another div b such that no third div is defined in terms
3847 * of this second div b and such that in any constraint that contains
3848 * a (except for the given lower and upper bound), also contains b
3849 * with a coefficient that is m times that of b.
3850 * That is, all constraints (execpt for the lower and upper bound)
3851 * are of the form
3853 * e + f (a + m b) >= 0
3855 * Furthermore, in the constraints that only contain b, the coefficient
3856 * of b should be equal to 1 or -1.
3857 * If so, we return b so that "a + m b" can be replaced by
3858 * a single div "c = a + m b".
3860 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
3861 unsigned div, unsigned l, unsigned u)
3863 int i, j;
3864 unsigned dim;
3865 int coalesce = -1;
3867 if (bmap->n_div <= 1)
3868 return -1;
3869 dim = isl_space_dim(bmap->dim, isl_dim_all);
3870 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
3871 return -1;
3872 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
3873 bmap->n_div - div - 1) != -1)
3874 return -1;
3875 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
3876 dim + bmap->n_div))
3877 return -1;
3879 for (i = 0; i < bmap->n_div; ++i) {
3880 if (isl_int_is_zero(bmap->div[i][0]))
3881 continue;
3882 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
3883 return -1;
3886 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
3887 if (isl_int_is_neg(bmap->ineq[l][0])) {
3888 isl_int_sub(bmap->ineq[l][0],
3889 bmap->ineq[l][0], bmap->ineq[u][0]);
3890 bmap = isl_basic_map_copy(bmap);
3891 bmap = isl_basic_map_set_to_empty(bmap);
3892 isl_basic_map_free(bmap);
3893 return -1;
3895 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
3896 for (i = 0; i < bmap->n_div; ++i) {
3897 if (i == div)
3898 continue;
3899 if (!pairs[i])
3900 continue;
3901 for (j = 0; j < bmap->n_div; ++j) {
3902 if (isl_int_is_zero(bmap->div[j][0]))
3903 continue;
3904 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
3905 break;
3907 if (j < bmap->n_div)
3908 continue;
3909 for (j = 0; j < bmap->n_ineq; ++j) {
3910 int valid;
3911 if (j == l || j == u)
3912 continue;
3913 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div])) {
3914 if (is_zero_or_one(bmap->ineq[j][1 + dim + i]))
3915 continue;
3916 break;
3918 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
3919 break;
3920 isl_int_mul(bmap->ineq[j][1 + dim + div],
3921 bmap->ineq[j][1 + dim + div],
3922 bmap->ineq[l][0]);
3923 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
3924 bmap->ineq[j][1 + dim + i]);
3925 isl_int_divexact(bmap->ineq[j][1 + dim + div],
3926 bmap->ineq[j][1 + dim + div],
3927 bmap->ineq[l][0]);
3928 if (!valid)
3929 break;
3931 if (j < bmap->n_ineq)
3932 continue;
3933 coalesce = i;
3934 break;
3936 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
3937 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
3938 return coalesce;
3941 /* Internal data structure used during the construction and/or evaluation of
3942 * an inequality that ensures that a pair of bounds always allows
3943 * for an integer value.
3945 * "tab" is the tableau in which the inequality is evaluated. It may
3946 * be NULL until it is actually needed.
3947 * "v" contains the inequality coefficients.
3948 * "g", "fl" and "fu" are temporary scalars used during the construction and
3949 * evaluation.
3951 struct test_ineq_data {
3952 struct isl_tab *tab;
3953 isl_vec *v;
3954 isl_int g;
3955 isl_int fl;
3956 isl_int fu;
3959 /* Free all the memory allocated by the fields of "data".
3961 static void test_ineq_data_clear(struct test_ineq_data *data)
3963 isl_tab_free(data->tab);
3964 isl_vec_free(data->v);
3965 isl_int_clear(data->g);
3966 isl_int_clear(data->fl);
3967 isl_int_clear(data->fu);
3970 /* Is the inequality stored in data->v satisfied by "bmap"?
3971 * That is, does it only attain non-negative values?
3972 * data->tab is a tableau corresponding to "bmap".
3974 static isl_bool test_ineq_is_satisfied(__isl_keep isl_basic_map *bmap,
3975 struct test_ineq_data *data)
3977 isl_ctx *ctx;
3978 enum isl_lp_result res;
3980 ctx = isl_basic_map_get_ctx(bmap);
3981 if (!data->tab)
3982 data->tab = isl_tab_from_basic_map(bmap, 0);
3983 res = isl_tab_min(data->tab, data->v->el, ctx->one, &data->g, NULL, 0);
3984 if (res == isl_lp_error)
3985 return isl_bool_error;
3986 return res == isl_lp_ok && isl_int_is_nonneg(data->g);
3989 /* Given a lower and an upper bound on div i, do they always allow
3990 * for an integer value of the given div?
3991 * Determine this property by constructing an inequality
3992 * such that the property is guaranteed when the inequality is nonnegative.
3993 * The lower bound is inequality l, while the upper bound is inequality u.
3994 * The constructed inequality is stored in data->v.
3996 * Let the upper bound be
3998 * -n_u a + e_u >= 0
4000 * and the lower bound
4002 * n_l a + e_l >= 0
4004 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
4005 * We have
4007 * - f_u e_l <= f_u f_l g a <= f_l e_u
4009 * Since all variables are integer valued, this is equivalent to
4011 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
4013 * If this interval is at least f_u f_l g, then it contains at least
4014 * one integer value for a.
4015 * That is, the test constraint is
4017 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
4019 * or
4021 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 - f_u f_l g >= 0
4023 * If the coefficients of f_l e_u + f_u e_l have a common divisor g',
4024 * then the constraint can be scaled down by a factor g',
4025 * with the constant term replaced by
4026 * floor((f_l e_{u,0} + f_u e_{l,0} + f_l - 1 + f_u - 1 + 1 - f_u f_l g)/g').
4027 * Note that the result of applying Fourier-Motzkin to this pair
4028 * of constraints is
4030 * f_l e_u + f_u e_l >= 0
4032 * If the constant term of the scaled down version of this constraint,
4033 * i.e., floor((f_l e_{u,0} + f_u e_{l,0})/g') is equal to the constant
4034 * term of the scaled down test constraint, then the test constraint
4035 * is known to hold and no explicit evaluation is required.
4036 * This is essentially the Omega test.
4038 * If the test constraint consists of only a constant term, then
4039 * it is sufficient to look at the sign of this constant term.
4041 static isl_bool int_between_bounds(__isl_keep isl_basic_map *bmap, int i,
4042 int l, int u, struct test_ineq_data *data)
4044 unsigned offset, n_div;
4045 offset = isl_basic_map_offset(bmap, isl_dim_div);
4046 n_div = isl_basic_map_dim(bmap, isl_dim_div);
4048 isl_int_gcd(data->g,
4049 bmap->ineq[l][offset + i], bmap->ineq[u][offset + i]);
4050 isl_int_divexact(data->fl, bmap->ineq[l][offset + i], data->g);
4051 isl_int_divexact(data->fu, bmap->ineq[u][offset + i], data->g);
4052 isl_int_neg(data->fu, data->fu);
4053 isl_seq_combine(data->v->el, data->fl, bmap->ineq[u],
4054 data->fu, bmap->ineq[l], offset + n_div);
4055 isl_int_mul(data->g, data->g, data->fl);
4056 isl_int_mul(data->g, data->g, data->fu);
4057 isl_int_sub(data->g, data->g, data->fl);
4058 isl_int_sub(data->g, data->g, data->fu);
4059 isl_int_add_ui(data->g, data->g, 1);
4060 isl_int_sub(data->fl, data->v->el[0], data->g);
4062 isl_seq_gcd(data->v->el + 1, offset - 1 + n_div, &data->g);
4063 if (isl_int_is_zero(data->g))
4064 return isl_int_is_nonneg(data->fl);
4065 if (isl_int_is_one(data->g)) {
4066 isl_int_set(data->v->el[0], data->fl);
4067 return test_ineq_is_satisfied(bmap, data);
4069 isl_int_fdiv_q(data->fl, data->fl, data->g);
4070 isl_int_fdiv_q(data->v->el[0], data->v->el[0], data->g);
4071 if (isl_int_eq(data->fl, data->v->el[0]))
4072 return isl_bool_true;
4073 isl_int_set(data->v->el[0], data->fl);
4074 isl_seq_scale_down(data->v->el + 1, data->v->el + 1, data->g,
4075 offset - 1 + n_div);
4077 return test_ineq_is_satisfied(bmap, data);
4080 /* Remove more kinds of divs that are not strictly needed.
4081 * In particular, if all pairs of lower and upper bounds on a div
4082 * are such that they allow at least one integer value of the div,
4083 * then we can eliminate the div using Fourier-Motzkin without
4084 * introducing any spurious solutions.
4086 * If at least one of the two constraints has a unit coefficient for the div,
4087 * then the presence of such a value is guaranteed so there is no need to check.
4088 * In particular, the value attained by the bound with unit coefficient
4089 * can serve as this intermediate value.
4091 static __isl_give isl_basic_map *drop_more_redundant_divs(
4092 __isl_take isl_basic_map *bmap, __isl_take int *pairs, int n)
4094 isl_ctx *ctx;
4095 struct test_ineq_data data = { NULL, NULL };
4096 unsigned off, n_div;
4097 int remove = -1;
4099 isl_int_init(data.g);
4100 isl_int_init(data.fl);
4101 isl_int_init(data.fu);
4103 if (!bmap)
4104 goto error;
4106 ctx = isl_basic_map_get_ctx(bmap);
4107 off = isl_basic_map_offset(bmap, isl_dim_div);
4108 n_div = isl_basic_map_dim(bmap, isl_dim_div);
4109 data.v = isl_vec_alloc(ctx, off + n_div);
4110 if (!data.v)
4111 goto error;
4113 while (n > 0) {
4114 int i, l, u;
4115 int best = -1;
4116 isl_bool has_int;
4118 for (i = 0; i < n_div; ++i) {
4119 if (!pairs[i])
4120 continue;
4121 if (best >= 0 && pairs[best] <= pairs[i])
4122 continue;
4123 best = i;
4126 i = best;
4127 for (l = 0; l < bmap->n_ineq; ++l) {
4128 if (!isl_int_is_pos(bmap->ineq[l][off + i]))
4129 continue;
4130 if (isl_int_is_one(bmap->ineq[l][off + i]))
4131 continue;
4132 for (u = 0; u < bmap->n_ineq; ++u) {
4133 if (!isl_int_is_neg(bmap->ineq[u][off + i]))
4134 continue;
4135 if (isl_int_is_negone(bmap->ineq[u][off + i]))
4136 continue;
4137 has_int = int_between_bounds(bmap, i, l, u,
4138 &data);
4139 if (has_int < 0)
4140 goto error;
4141 if (data.tab && data.tab->empty)
4142 break;
4143 if (!has_int)
4144 break;
4146 if (u < bmap->n_ineq)
4147 break;
4149 if (data.tab && data.tab->empty) {
4150 bmap = isl_basic_map_set_to_empty(bmap);
4151 break;
4153 if (l == bmap->n_ineq) {
4154 remove = i;
4155 break;
4157 pairs[i] = 0;
4158 --n;
4161 test_ineq_data_clear(&data);
4163 free(pairs);
4165 if (remove < 0)
4166 return bmap;
4168 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
4169 return isl_basic_map_drop_redundant_divs(bmap);
4170 error:
4171 free(pairs);
4172 isl_basic_map_free(bmap);
4173 test_ineq_data_clear(&data);
4174 return NULL;
4177 /* Given a pair of divs div1 and div2 such that, except for the lower bound l
4178 * and the upper bound u, div1 always occurs together with div2 in the form
4179 * (div1 + m div2), where m is the constant range on the variable div1
4180 * allowed by l and u, replace the pair div1 and div2 by a single
4181 * div that is equal to div1 + m div2.
4183 * The new div will appear in the location that contains div2.
4184 * We need to modify all constraints that contain
4185 * div2 = (div - div1) / m
4186 * The coefficient of div2 is known to be equal to 1 or -1.
4187 * (If a constraint does not contain div2, it will also not contain div1.)
4188 * If the constraint also contains div1, then we know they appear
4189 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
4190 * i.e., the coefficient of div is f.
4192 * Otherwise, we first need to introduce div1 into the constraint.
4193 * Let the l be
4195 * div1 + f >=0
4197 * and u
4199 * -div1 + f' >= 0
4201 * A lower bound on div2
4203 * div2 + t >= 0
4205 * can be replaced by
4207 * m div2 + div1 + m t + f >= 0
4209 * An upper bound
4211 * -div2 + t >= 0
4213 * can be replaced by
4215 * -(m div2 + div1) + m t + f' >= 0
4217 * These constraint are those that we would obtain from eliminating
4218 * div1 using Fourier-Motzkin.
4220 * After all constraints have been modified, we drop the lower and upper
4221 * bound and then drop div1.
4222 * Since the new div is only placed in the same location that used
4223 * to store div2, but otherwise has a different meaning, any possible
4224 * explicit representation of the original div2 is removed.
4226 static __isl_give isl_basic_map *coalesce_divs(__isl_take isl_basic_map *bmap,
4227 unsigned div1, unsigned div2, unsigned l, unsigned u)
4229 isl_ctx *ctx;
4230 isl_int m;
4231 unsigned dim, total;
4232 int i;
4234 ctx = isl_basic_map_get_ctx(bmap);
4236 dim = isl_space_dim(bmap->dim, isl_dim_all);
4237 total = 1 + dim + bmap->n_div;
4239 isl_int_init(m);
4240 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
4241 isl_int_add_ui(m, m, 1);
4243 for (i = 0; i < bmap->n_ineq; ++i) {
4244 if (i == l || i == u)
4245 continue;
4246 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
4247 continue;
4248 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
4249 if (isl_int_is_pos(bmap->ineq[i][1 + dim + div2]))
4250 isl_seq_combine(bmap->ineq[i], m, bmap->ineq[i],
4251 ctx->one, bmap->ineq[l], total);
4252 else
4253 isl_seq_combine(bmap->ineq[i], m, bmap->ineq[i],
4254 ctx->one, bmap->ineq[u], total);
4256 isl_int_set(bmap->ineq[i][1 + dim + div2],
4257 bmap->ineq[i][1 + dim + div1]);
4258 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
4261 isl_int_clear(m);
4262 if (l > u) {
4263 isl_basic_map_drop_inequality(bmap, l);
4264 isl_basic_map_drop_inequality(bmap, u);
4265 } else {
4266 isl_basic_map_drop_inequality(bmap, u);
4267 isl_basic_map_drop_inequality(bmap, l);
4269 bmap = isl_basic_map_mark_div_unknown(bmap, div2);
4270 bmap = isl_basic_map_drop_div(bmap, div1);
4271 return bmap;
4274 /* First check if we can coalesce any pair of divs and
4275 * then continue with dropping more redundant divs.
4277 * We loop over all pairs of lower and upper bounds on a div
4278 * with coefficient 1 and -1, respectively, check if there
4279 * is any other div "c" with which we can coalesce the div
4280 * and if so, perform the coalescing.
4282 static __isl_give isl_basic_map *coalesce_or_drop_more_redundant_divs(
4283 __isl_take isl_basic_map *bmap, int *pairs, int n)
4285 int i, l, u;
4286 unsigned dim;
4288 dim = isl_space_dim(bmap->dim, isl_dim_all);
4290 for (i = 0; i < bmap->n_div; ++i) {
4291 if (!pairs[i])
4292 continue;
4293 for (l = 0; l < bmap->n_ineq; ++l) {
4294 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
4295 continue;
4296 for (u = 0; u < bmap->n_ineq; ++u) {
4297 int c;
4299 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
4300 continue;
4301 c = div_find_coalesce(bmap, pairs, i, l, u);
4302 if (c < 0)
4303 continue;
4304 free(pairs);
4305 bmap = coalesce_divs(bmap, i, c, l, u);
4306 return isl_basic_map_drop_redundant_divs(bmap);
4311 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
4312 free(pairs);
4313 return bmap;
4316 return drop_more_redundant_divs(bmap, pairs, n);
4319 /* Are the "n" coefficients starting at "first" of inequality constraints
4320 * "i" and "j" of "bmap" equal to each other?
4322 static int is_parallel_part(__isl_keep isl_basic_map *bmap, int i, int j,
4323 int first, int n)
4325 return isl_seq_eq(bmap->ineq[i] + first, bmap->ineq[j] + first, n);
4328 /* Are the "n" coefficients starting at "first" of inequality constraints
4329 * "i" and "j" of "bmap" opposite to each other?
4331 static int is_opposite_part(__isl_keep isl_basic_map *bmap, int i, int j,
4332 int first, int n)
4334 return isl_seq_is_neg(bmap->ineq[i] + first, bmap->ineq[j] + first, n);
4337 /* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
4338 * apart from the constant term?
4340 static isl_bool is_opposite(__isl_keep isl_basic_map *bmap, int i, int j)
4342 unsigned total;
4344 total = isl_basic_map_dim(bmap, isl_dim_all);
4345 return is_opposite_part(bmap, i, j, 1, total);
4348 /* Are inequality constraints "i" and "j" of "bmap" equal to each other,
4349 * apart from the constant term and the coefficient at position "pos"?
4351 static int is_parallel_except(__isl_keep isl_basic_map *bmap, int i, int j,
4352 int pos)
4354 unsigned total;
4356 total = isl_basic_map_dim(bmap, isl_dim_all);
4357 return is_parallel_part(bmap, i, j, 1, pos - 1) &&
4358 is_parallel_part(bmap, i, j, pos + 1, total - pos);
4361 /* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
4362 * apart from the constant term and the coefficient at position "pos"?
4364 static int is_opposite_except(__isl_keep isl_basic_map *bmap, int i, int j,
4365 int pos)
4367 unsigned total;
4369 total = isl_basic_map_dim(bmap, isl_dim_all);
4370 return is_opposite_part(bmap, i, j, 1, pos - 1) &&
4371 is_opposite_part(bmap, i, j, pos + 1, total - pos);
4374 /* Restart isl_basic_map_drop_redundant_divs after "bmap" has
4375 * been modified, simplying it if "simplify" is set.
4376 * Free the temporary data structure "pairs" that was associated
4377 * to the old version of "bmap".
4379 static __isl_give isl_basic_map *drop_redundant_divs_again(
4380 __isl_take isl_basic_map *bmap, __isl_take int *pairs, int simplify)
4382 if (simplify)
4383 bmap = isl_basic_map_simplify(bmap);
4384 free(pairs);
4385 return isl_basic_map_drop_redundant_divs(bmap);
4388 /* Is "div" the single unknown existentially quantified variable
4389 * in inequality constraint "ineq" of "bmap"?
4390 * "div" is known to have a non-zero coefficient in "ineq".
4392 static isl_bool single_unknown(__isl_keep isl_basic_map *bmap, int ineq,
4393 int div)
4395 int i;
4396 unsigned n_div, o_div;
4397 isl_bool known;
4399 known = isl_basic_map_div_is_known(bmap, div);
4400 if (known < 0 || known)
4401 return isl_bool_not(known);
4402 n_div = isl_basic_map_dim(bmap, isl_dim_div);
4403 if (n_div == 1)
4404 return isl_bool_true;
4405 o_div = isl_basic_map_offset(bmap, isl_dim_div);
4406 for (i = 0; i < n_div; ++i) {
4407 isl_bool known;
4409 if (i == div)
4410 continue;
4411 if (isl_int_is_zero(bmap->ineq[ineq][o_div + i]))
4412 continue;
4413 known = isl_basic_map_div_is_known(bmap, i);
4414 if (known < 0 || !known)
4415 return known;
4418 return isl_bool_true;
4421 /* Does integer division "div" have coefficient 1 in inequality constraint
4422 * "ineq" of "map"?
4424 static isl_bool has_coef_one(__isl_keep isl_basic_map *bmap, int div, int ineq)
4426 unsigned o_div;
4428 o_div = isl_basic_map_offset(bmap, isl_dim_div);
4429 if (isl_int_is_one(bmap->ineq[ineq][o_div + div]))
4430 return isl_bool_true;
4432 return isl_bool_false;
4435 /* Turn inequality constraint "ineq" of "bmap" into an equality and
4436 * then try and drop redundant divs again,
4437 * freeing the temporary data structure "pairs" that was associated
4438 * to the old version of "bmap".
4440 static __isl_give isl_basic_map *set_eq_and_try_again(
4441 __isl_take isl_basic_map *bmap, int ineq, __isl_take int *pairs)
4443 bmap = isl_basic_map_cow(bmap);
4444 isl_basic_map_inequality_to_equality(bmap, ineq);
4445 return drop_redundant_divs_again(bmap, pairs, 1);
4448 /* Drop the integer division at position "div", along with the two
4449 * inequality constraints "ineq1" and "ineq2" in which it appears
4450 * from "bmap" and then try and drop redundant divs again,
4451 * freeing the temporary data structure "pairs" that was associated
4452 * to the old version of "bmap".
4454 static __isl_give isl_basic_map *drop_div_and_try_again(
4455 __isl_take isl_basic_map *bmap, int div, int ineq1, int ineq2,
4456 __isl_take int *pairs)
4458 if (ineq1 > ineq2) {
4459 isl_basic_map_drop_inequality(bmap, ineq1);
4460 isl_basic_map_drop_inequality(bmap, ineq2);
4461 } else {
4462 isl_basic_map_drop_inequality(bmap, ineq2);
4463 isl_basic_map_drop_inequality(bmap, ineq1);
4465 bmap = isl_basic_map_drop_div(bmap, div);
4466 return drop_redundant_divs_again(bmap, pairs, 0);
4469 /* Given two inequality constraints
4471 * f(x) + n d + c >= 0, (ineq)
4473 * with d the variable at position "pos", and
4475 * f(x) + c0 >= 0, (lower)
4477 * compute the maximal value of the lower bound ceil((-f(x) - c)/n)
4478 * determined by the first constraint.
4479 * That is, store
4481 * ceil((c0 - c)/n)
4483 * in *l.
4485 static void lower_bound_from_parallel(__isl_keep isl_basic_map *bmap,
4486 int ineq, int lower, int pos, isl_int *l)
4488 isl_int_neg(*l, bmap->ineq[ineq][0]);
4489 isl_int_add(*l, *l, bmap->ineq[lower][0]);
4490 isl_int_cdiv_q(*l, *l, bmap->ineq[ineq][pos]);
4493 /* Given two inequality constraints
4495 * f(x) + n d + c >= 0, (ineq)
4497 * with d the variable at position "pos", and
4499 * -f(x) - c0 >= 0, (upper)
4501 * compute the minimal value of the lower bound ceil((-f(x) - c)/n)
4502 * determined by the first constraint.
4503 * That is, store
4505 * ceil((-c1 - c)/n)
4507 * in *u.
4509 static void lower_bound_from_opposite(__isl_keep isl_basic_map *bmap,
4510 int ineq, int upper, int pos, isl_int *u)
4512 isl_int_neg(*u, bmap->ineq[ineq][0]);
4513 isl_int_sub(*u, *u, bmap->ineq[upper][0]);
4514 isl_int_cdiv_q(*u, *u, bmap->ineq[ineq][pos]);
4517 /* Given a lower bound constraint "ineq" on "div" in "bmap",
4518 * does the corresponding lower bound have a fixed value in "bmap"?
4520 * In particular, "ineq" is of the form
4522 * f(x) + n d + c >= 0
4524 * with n > 0, c the constant term and
4525 * d the existentially quantified variable "div".
4526 * That is, the lower bound is
4528 * ceil((-f(x) - c)/n)
4530 * Look for a pair of constraints
4532 * f(x) + c0 >= 0
4533 * -f(x) + c1 >= 0
4535 * i.e., -c1 <= -f(x) <= c0, that fix ceil((-f(x) - c)/n) to a constant value.
4536 * That is, check that
4538 * ceil((-c1 - c)/n) = ceil((c0 - c)/n)
4540 * If so, return the index of inequality f(x) + c0 >= 0.
4541 * Otherwise, return -1.
4543 static int lower_bound_is_cst(__isl_keep isl_basic_map *bmap, int div, int ineq)
4545 int i;
4546 int lower = -1, upper = -1;
4547 unsigned o_div;
4548 isl_int l, u;
4549 int equal;
4551 o_div = isl_basic_map_offset(bmap, isl_dim_div);
4552 for (i = 0; i < bmap->n_ineq && (lower < 0 || upper < 0); ++i) {
4553 if (i == ineq)
4554 continue;
4555 if (!isl_int_is_zero(bmap->ineq[i][o_div + div]))
4556 continue;
4557 if (lower < 0 &&
4558 is_parallel_except(bmap, ineq, i, o_div + div)) {
4559 lower = i;
4560 continue;
4562 if (upper < 0 &&
4563 is_opposite_except(bmap, ineq, i, o_div + div)) {
4564 upper = i;
4568 if (lower < 0 || upper < 0)
4569 return -1;
4571 isl_int_init(l);
4572 isl_int_init(u);
4574 lower_bound_from_parallel(bmap, ineq, lower, o_div + div, &l);
4575 lower_bound_from_opposite(bmap, ineq, upper, o_div + div, &u);
4577 equal = isl_int_eq(l, u);
4579 isl_int_clear(l);
4580 isl_int_clear(u);
4582 return equal ? lower : -1;
4585 /* Given a lower bound constraint "ineq" on the existentially quantified
4586 * variable "div", such that the corresponding lower bound has
4587 * a fixed value in "bmap", assign this fixed value to the variable and
4588 * then try and drop redundant divs again,
4589 * freeing the temporary data structure "pairs" that was associated
4590 * to the old version of "bmap".
4591 * "lower" determines the constant value for the lower bound.
4593 * In particular, "ineq" is of the form
4595 * f(x) + n d + c >= 0,
4597 * while "lower" is of the form
4599 * f(x) + c0 >= 0
4601 * The lower bound is ceil((-f(x) - c)/n) and its constant value
4602 * is ceil((c0 - c)/n).
4604 static __isl_give isl_basic_map *fix_cst_lower(__isl_take isl_basic_map *bmap,
4605 int div, int ineq, int lower, int *pairs)
4607 isl_int c;
4608 unsigned o_div;
4610 isl_int_init(c);
4612 o_div = isl_basic_map_offset(bmap, isl_dim_div);
4613 lower_bound_from_parallel(bmap, ineq, lower, o_div + div, &c);
4614 bmap = isl_basic_map_fix(bmap, isl_dim_div, div, c);
4615 free(pairs);
4617 isl_int_clear(c);
4619 return isl_basic_map_drop_redundant_divs(bmap);
4622 /* Remove divs that are not strictly needed based on the inequality
4623 * constraints.
4624 * In particular, if a div only occurs positively (or negatively)
4625 * in constraints, then it can simply be dropped.
4626 * Also, if a div occurs in only two constraints and if moreover
4627 * those two constraints are opposite to each other, except for the constant
4628 * term and if the sum of the constant terms is such that for any value
4629 * of the other values, there is always at least one integer value of the
4630 * div, i.e., if one plus this sum is greater than or equal to
4631 * the (absolute value) of the coefficient of the div in the constraints,
4632 * then we can also simply drop the div.
4634 * If an existentially quantified variable does not have an explicit
4635 * representation, appears in only a single lower bound that does not
4636 * involve any other such existentially quantified variables and appears
4637 * in this lower bound with coefficient 1,
4638 * then fix the variable to the value of the lower bound. That is,
4639 * turn the inequality into an equality.
4640 * If for any value of the other variables, there is any value
4641 * for the existentially quantified variable satisfying the constraints,
4642 * then this lower bound also satisfies the constraints.
4643 * It is therefore safe to pick this lower bound.
4645 * The same reasoning holds even if the coefficient is not one.
4646 * However, fixing the variable to the value of the lower bound may
4647 * in general introduce an extra integer division, in which case
4648 * it may be better to pick another value.
4649 * If this integer division has a known constant value, then plugging
4650 * in this constant value removes the existentially quantified variable
4651 * completely. In particular, if the lower bound is of the form
4652 * ceil((-f(x) - c)/n) and there are two constraints, f(x) + c0 >= 0 and
4653 * -f(x) + c1 >= 0 such that ceil((-c1 - c)/n) = ceil((c0 - c)/n),
4654 * then the existentially quantified variable can be assigned this
4655 * shared value.
4657 * We skip divs that appear in equalities or in the definition of other divs.
4658 * Divs that appear in the definition of other divs usually occur in at least
4659 * 4 constraints, but the constraints may have been simplified.
4661 * If any divs are left after these simple checks then we move on
4662 * to more complicated cases in drop_more_redundant_divs.
4664 static __isl_give isl_basic_map *isl_basic_map_drop_redundant_divs_ineq(
4665 __isl_take isl_basic_map *bmap)
4667 int i, j;
4668 unsigned off;
4669 int *pairs = NULL;
4670 int n = 0;
4672 if (!bmap)
4673 goto error;
4674 if (bmap->n_div == 0)
4675 return bmap;
4677 off = isl_space_dim(bmap->dim, isl_dim_all);
4678 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
4679 if (!pairs)
4680 goto error;
4682 for (i = 0; i < bmap->n_div; ++i) {
4683 int pos, neg;
4684 int last_pos, last_neg;
4685 int redundant;
4686 int defined;
4687 isl_bool opp, set_div;
4689 defined = !isl_int_is_zero(bmap->div[i][0]);
4690 for (j = i; j < bmap->n_div; ++j)
4691 if (!isl_int_is_zero(bmap->div[j][1 + 1 + off + i]))
4692 break;
4693 if (j < bmap->n_div)
4694 continue;
4695 for (j = 0; j < bmap->n_eq; ++j)
4696 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
4697 break;
4698 if (j < bmap->n_eq)
4699 continue;
4700 ++n;
4701 pos = neg = 0;
4702 for (j = 0; j < bmap->n_ineq; ++j) {
4703 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
4704 last_pos = j;
4705 ++pos;
4707 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
4708 last_neg = j;
4709 ++neg;
4712 pairs[i] = pos * neg;
4713 if (pairs[i] == 0) {
4714 for (j = bmap->n_ineq - 1; j >= 0; --j)
4715 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
4716 isl_basic_map_drop_inequality(bmap, j);
4717 bmap = isl_basic_map_drop_div(bmap, i);
4718 return drop_redundant_divs_again(bmap, pairs, 0);
4720 if (pairs[i] != 1)
4721 opp = isl_bool_false;
4722 else
4723 opp = is_opposite(bmap, last_pos, last_neg);
4724 if (opp < 0)
4725 goto error;
4726 if (!opp) {
4727 int lower;
4728 isl_bool single, one;
4730 if (pos != 1)
4731 continue;
4732 single = single_unknown(bmap, last_pos, i);
4733 if (single < 0)
4734 goto error;
4735 if (!single)
4736 continue;
4737 one = has_coef_one(bmap, i, last_pos);
4738 if (one < 0)
4739 goto error;
4740 if (one)
4741 return set_eq_and_try_again(bmap, last_pos,
4742 pairs);
4743 lower = lower_bound_is_cst(bmap, i, last_pos);
4744 if (lower >= 0)
4745 return fix_cst_lower(bmap, i, last_pos, lower,
4746 pairs);
4747 continue;
4750 isl_int_add(bmap->ineq[last_pos][0],
4751 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
4752 isl_int_add_ui(bmap->ineq[last_pos][0],
4753 bmap->ineq[last_pos][0], 1);
4754 redundant = isl_int_ge(bmap->ineq[last_pos][0],
4755 bmap->ineq[last_pos][1+off+i]);
4756 isl_int_sub_ui(bmap->ineq[last_pos][0],
4757 bmap->ineq[last_pos][0], 1);
4758 isl_int_sub(bmap->ineq[last_pos][0],
4759 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
4760 if (redundant)
4761 return drop_div_and_try_again(bmap, i,
4762 last_pos, last_neg, pairs);
4763 if (defined)
4764 set_div = isl_bool_false;
4765 else
4766 set_div = ok_to_set_div_from_bound(bmap, i, last_pos);
4767 if (set_div < 0)
4768 return isl_basic_map_free(bmap);
4769 if (set_div) {
4770 bmap = set_div_from_lower_bound(bmap, i, last_pos);
4771 return drop_redundant_divs_again(bmap, pairs, 1);
4773 pairs[i] = 0;
4774 --n;
4777 if (n > 0)
4778 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
4780 free(pairs);
4781 return bmap;
4782 error:
4783 free(pairs);
4784 isl_basic_map_free(bmap);
4785 return NULL;
4788 /* Consider the coefficients at "c" as a row vector and replace
4789 * them with their product with "T". "T" is assumed to be a square matrix.
4791 static isl_stat preimage(isl_int *c, __isl_keep isl_mat *T)
4793 int n;
4794 isl_ctx *ctx;
4795 isl_vec *v;
4797 if (!T)
4798 return isl_stat_error;
4799 n = isl_mat_rows(T);
4800 if (isl_seq_first_non_zero(c, n) == -1)
4801 return isl_stat_ok;
4802 ctx = isl_mat_get_ctx(T);
4803 v = isl_vec_alloc(ctx, n);
4804 if (!v)
4805 return isl_stat_error;
4806 isl_seq_swp_or_cpy(v->el, c, n);
4807 v = isl_vec_mat_product(v, isl_mat_copy(T));
4808 if (!v)
4809 return isl_stat_error;
4810 isl_seq_swp_or_cpy(c, v->el, n);
4811 isl_vec_free(v);
4813 return isl_stat_ok;
4816 /* Plug in T for the variables in "bmap" starting at "pos".
4817 * T is a linear unimodular matrix, i.e., without constant term.
4819 static __isl_give isl_basic_map *isl_basic_map_preimage_vars(
4820 __isl_take isl_basic_map *bmap, unsigned pos, __isl_take isl_mat *T)
4822 int i;
4823 unsigned n, total;
4825 bmap = isl_basic_map_cow(bmap);
4826 if (!bmap || !T)
4827 goto error;
4829 n = isl_mat_cols(T);
4830 if (n != isl_mat_rows(T))
4831 isl_die(isl_mat_get_ctx(T), isl_error_invalid,
4832 "expecting square matrix", goto error);
4834 total = isl_basic_map_dim(bmap, isl_dim_all);
4835 if (pos + n > total || pos + n < pos)
4836 isl_die(isl_mat_get_ctx(T), isl_error_invalid,
4837 "invalid range", goto error);
4839 for (i = 0; i < bmap->n_eq; ++i)
4840 if (preimage(bmap->eq[i] + 1 + pos, T) < 0)
4841 goto error;
4842 for (i = 0; i < bmap->n_ineq; ++i)
4843 if (preimage(bmap->ineq[i] + 1 + pos, T) < 0)
4844 goto error;
4845 for (i = 0; i < bmap->n_div; ++i) {
4846 if (isl_basic_map_div_is_marked_unknown(bmap, i))
4847 continue;
4848 if (preimage(bmap->div[i] + 1 + 1 + pos, T) < 0)
4849 goto error;
4852 isl_mat_free(T);
4853 return bmap;
4854 error:
4855 isl_basic_map_free(bmap);
4856 isl_mat_free(T);
4857 return NULL;
4860 /* Remove divs that are not strictly needed.
4862 * First look for an equality constraint involving two or more
4863 * existentially quantified variables without an explicit
4864 * representation. Replace the combination that appears
4865 * in the equality constraint by a single existentially quantified
4866 * variable such that the equality can be used to derive
4867 * an explicit representation for the variable.
4868 * If there are no more such equality constraints, then continue
4869 * with isl_basic_map_drop_redundant_divs_ineq.
4871 * In particular, if the equality constraint is of the form
4873 * f(x) + \sum_i c_i a_i = 0
4875 * with a_i existentially quantified variable without explicit
4876 * representation, then apply a transformation on the existentially
4877 * quantified variables to turn the constraint into
4879 * f(x) + g a_1' = 0
4881 * with g the gcd of the c_i.
4882 * In order to easily identify which existentially quantified variables
4883 * have a complete explicit representation, i.e., without being defined
4884 * in terms of other existentially quantified variables without
4885 * an explicit representation, the existentially quantified variables
4886 * are first sorted.
4888 * The variable transformation is computed by extending the row
4889 * [c_1/g ... c_n/g] to a unimodular matrix, obtaining the transformation
4891 * [a_1'] [c_1/g ... c_n/g] [ a_1 ]
4892 * [a_2'] [ a_2 ]
4893 * ... = U ....
4894 * [a_n'] [ a_n ]
4896 * with [c_1/g ... c_n/g] representing the first row of U.
4897 * The inverse of U is then plugged into the original constraints.
4898 * The call to isl_basic_map_simplify makes sure the explicit
4899 * representation for a_1' is extracted from the equality constraint.
4901 __isl_give isl_basic_map *isl_basic_map_drop_redundant_divs(
4902 __isl_take isl_basic_map *bmap)
4904 int first;
4905 int i;
4906 unsigned o_div, n_div;
4907 int l;
4908 isl_ctx *ctx;
4909 isl_mat *T;
4911 if (!bmap)
4912 return NULL;
4913 if (isl_basic_map_divs_known(bmap))
4914 return isl_basic_map_drop_redundant_divs_ineq(bmap);
4915 if (bmap->n_eq == 0)
4916 return isl_basic_map_drop_redundant_divs_ineq(bmap);
4917 bmap = isl_basic_map_sort_divs(bmap);
4918 if (!bmap)
4919 return NULL;
4921 first = isl_basic_map_first_unknown_div(bmap);
4922 if (first < 0)
4923 return isl_basic_map_free(bmap);
4925 o_div = isl_basic_map_offset(bmap, isl_dim_div);
4926 n_div = isl_basic_map_dim(bmap, isl_dim_div);
4928 for (i = 0; i < bmap->n_eq; ++i) {
4929 l = isl_seq_first_non_zero(bmap->eq[i] + o_div + first,
4930 n_div - (first));
4931 if (l < 0)
4932 continue;
4933 l += first;
4934 if (isl_seq_first_non_zero(bmap->eq[i] + o_div + l + 1,
4935 n_div - (l + 1)) == -1)
4936 continue;
4937 break;
4939 if (i >= bmap->n_eq)
4940 return isl_basic_map_drop_redundant_divs_ineq(bmap);
4942 ctx = isl_basic_map_get_ctx(bmap);
4943 T = isl_mat_alloc(ctx, n_div - l, n_div - l);
4944 if (!T)
4945 return isl_basic_map_free(bmap);
4946 isl_seq_cpy(T->row[0], bmap->eq[i] + o_div + l, n_div - l);
4947 T = isl_mat_normalize_row(T, 0);
4948 T = isl_mat_unimodular_complete(T, 1);
4949 T = isl_mat_right_inverse(T);
4951 for (i = l; i < n_div; ++i)
4952 bmap = isl_basic_map_mark_div_unknown(bmap, i);
4953 bmap = isl_basic_map_preimage_vars(bmap, o_div - 1 + l, T);
4954 bmap = isl_basic_map_simplify(bmap);
4956 return isl_basic_map_drop_redundant_divs(bmap);
4959 /* Does "bmap" satisfy any equality that involves more than 2 variables
4960 * and/or has coefficients different from -1 and 1?
4962 static int has_multiple_var_equality(__isl_keep isl_basic_map *bmap)
4964 int i;
4965 unsigned total;
4967 total = isl_basic_map_dim(bmap, isl_dim_all);
4969 for (i = 0; i < bmap->n_eq; ++i) {
4970 int j, k;
4972 j = isl_seq_first_non_zero(bmap->eq[i] + 1, total);
4973 if (j < 0)
4974 continue;
4975 if (!isl_int_is_one(bmap->eq[i][1 + j]) &&
4976 !isl_int_is_negone(bmap->eq[i][1 + j]))
4977 return 1;
4979 j += 1;
4980 k = isl_seq_first_non_zero(bmap->eq[i] + 1 + j, total - j);
4981 if (k < 0)
4982 continue;
4983 j += k;
4984 if (!isl_int_is_one(bmap->eq[i][1 + j]) &&
4985 !isl_int_is_negone(bmap->eq[i][1 + j]))
4986 return 1;
4988 j += 1;
4989 k = isl_seq_first_non_zero(bmap->eq[i] + 1 + j, total - j);
4990 if (k >= 0)
4991 return 1;
4994 return 0;
4997 /* Remove any common factor g from the constraint coefficients in "v".
4998 * The constant term is stored in the first position and is replaced
4999 * by floor(c/g). If any common factor is removed and if this results
5000 * in a tightening of the constraint, then set *tightened.
5002 static __isl_give isl_vec *normalize_constraint(__isl_take isl_vec *v,
5003 int *tightened)
5005 isl_ctx *ctx;
5007 if (!v)
5008 return NULL;
5009 ctx = isl_vec_get_ctx(v);
5010 isl_seq_gcd(v->el + 1, v->size - 1, &ctx->normalize_gcd);
5011 if (isl_int_is_zero(ctx->normalize_gcd))
5012 return v;
5013 if (isl_int_is_one(ctx->normalize_gcd))
5014 return v;
5015 v = isl_vec_cow(v);
5016 if (!v)
5017 return NULL;
5018 if (tightened && !isl_int_is_divisible_by(v->el[0], ctx->normalize_gcd))
5019 *tightened = 1;
5020 isl_int_fdiv_q(v->el[0], v->el[0], ctx->normalize_gcd);
5021 isl_seq_scale_down(v->el + 1, v->el + 1, ctx->normalize_gcd,
5022 v->size - 1);
5023 return v;
5026 /* If "bmap" is an integer set that satisfies any equality involving
5027 * more than 2 variables and/or has coefficients different from -1 and 1,
5028 * then use variable compression to reduce the coefficients by removing
5029 * any (hidden) common factor.
5030 * In particular, apply the variable compression to each constraint,
5031 * factor out any common factor in the non-constant coefficients and
5032 * then apply the inverse of the compression.
5033 * At the end, we mark the basic map as having reduced constants.
5034 * If this flag is still set on the next invocation of this function,
5035 * then we skip the computation.
5037 * Removing a common factor may result in a tightening of some of
5038 * the constraints. If this happens, then we may end up with two
5039 * opposite inequalities that can be replaced by an equality.
5040 * We therefore call isl_basic_map_detect_inequality_pairs,
5041 * which checks for such pairs of inequalities as well as eliminate_divs_eq
5042 * and isl_basic_map_gauss if such a pair was found.
5044 * Note that this function may leave the result in an inconsistent state.
5045 * In particular, the constraints may not be gaussed.
5046 * Unfortunately, isl_map_coalesce actually depends on this inconsistent state
5047 * for some of the test cases to pass successfully.
5048 * Any potential modification of the representation is therefore only
5049 * performed on a single copy of the basic map.
5051 __isl_give isl_basic_map *isl_basic_map_reduce_coefficients(
5052 __isl_take isl_basic_map *bmap)
5054 unsigned total;
5055 isl_ctx *ctx;
5056 isl_vec *v;
5057 isl_mat *eq, *T, *T2;
5058 int i;
5059 int tightened;
5061 if (!bmap)
5062 return NULL;
5063 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS))
5064 return bmap;
5065 if (isl_basic_map_is_rational(bmap))
5066 return bmap;
5067 if (bmap->n_eq == 0)
5068 return bmap;
5069 if (!has_multiple_var_equality(bmap))
5070 return bmap;
5072 total = isl_basic_map_dim(bmap, isl_dim_all);
5073 ctx = isl_basic_map_get_ctx(bmap);
5074 v = isl_vec_alloc(ctx, 1 + total);
5075 if (!v)
5076 return isl_basic_map_free(bmap);
5078 eq = isl_mat_sub_alloc6(ctx, bmap->eq, 0, bmap->n_eq, 0, 1 + total);
5079 T = isl_mat_variable_compression(eq, &T2);
5080 if (!T || !T2)
5081 goto error;
5082 if (T->n_col == 0) {
5083 isl_mat_free(T);
5084 isl_mat_free(T2);
5085 isl_vec_free(v);
5086 return isl_basic_map_set_to_empty(bmap);
5089 bmap = isl_basic_map_cow(bmap);
5090 if (!bmap)
5091 goto error;
5093 tightened = 0;
5094 for (i = 0; i < bmap->n_ineq; ++i) {
5095 isl_seq_cpy(v->el, bmap->ineq[i], 1 + total);
5096 v = isl_vec_mat_product(v, isl_mat_copy(T));
5097 v = normalize_constraint(v, &tightened);
5098 v = isl_vec_mat_product(v, isl_mat_copy(T2));
5099 if (!v)
5100 goto error;
5101 isl_seq_cpy(bmap->ineq[i], v->el, 1 + total);
5104 isl_mat_free(T);
5105 isl_mat_free(T2);
5106 isl_vec_free(v);
5108 ISL_F_SET(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS);
5110 if (tightened) {
5111 int progress = 0;
5113 bmap = isl_basic_map_detect_inequality_pairs(bmap, &progress);
5114 if (progress) {
5115 bmap = eliminate_divs_eq(bmap, &progress);
5116 bmap = isl_basic_map_gauss(bmap, NULL);
5120 return bmap;
5121 error:
5122 isl_mat_free(T);
5123 isl_mat_free(T2);
5124 isl_vec_free(v);
5125 return isl_basic_map_free(bmap);
5128 /* Shift the integer division at position "div" of "bmap"
5129 * by "shift" times the variable at position "pos".
5130 * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
5131 * corresponds to the constant term.
5133 * That is, if the integer division has the form
5135 * floor(f(x)/d)
5137 * then replace it by
5139 * floor((f(x) + shift * d * x_pos)/d) - shift * x_pos
5141 __isl_give isl_basic_map *isl_basic_map_shift_div(
5142 __isl_take isl_basic_map *bmap, int div, int pos, isl_int shift)
5144 int i;
5145 unsigned total;
5147 if (isl_int_is_zero(shift))
5148 return bmap;
5149 if (!bmap)
5150 return NULL;
5152 total = isl_basic_map_dim(bmap, isl_dim_all);
5153 total -= isl_basic_map_dim(bmap, isl_dim_div);
5155 isl_int_addmul(bmap->div[div][1 + pos], shift, bmap->div[div][0]);
5157 for (i = 0; i < bmap->n_eq; ++i) {
5158 if (isl_int_is_zero(bmap->eq[i][1 + total + div]))
5159 continue;
5160 isl_int_submul(bmap->eq[i][pos],
5161 shift, bmap->eq[i][1 + total + div]);
5163 for (i = 0; i < bmap->n_ineq; ++i) {
5164 if (isl_int_is_zero(bmap->ineq[i][1 + total + div]))
5165 continue;
5166 isl_int_submul(bmap->ineq[i][pos],
5167 shift, bmap->ineq[i][1 + total + div]);
5169 for (i = 0; i < bmap->n_div; ++i) {
5170 if (isl_int_is_zero(bmap->div[i][0]))
5171 continue;
5172 if (isl_int_is_zero(bmap->div[i][1 + 1 + total + div]))
5173 continue;
5174 isl_int_submul(bmap->div[i][1 + pos],
5175 shift, bmap->div[i][1 + 1 + total + div]);
5178 return bmap;