2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2012 Ecole Normale Superieure
5 * Use of this software is governed by the GNU LGPLv2.1 license
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include "isl_equalities.h"
19 #include <isl_space_private.h>
20 #include <isl_mat_private.h>
22 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
24 isl_int *t = bmap->eq[a];
25 bmap->eq[a] = bmap->eq[b];
29 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
32 isl_int *t = bmap->ineq[a];
33 bmap->ineq[a] = bmap->ineq[b];
38 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
40 isl_seq_cpy(c, c + n, rem);
41 isl_seq_clr(c + rem, n);
44 /* Drop n dimensions starting at first.
46 * In principle, this frees up some extra variables as the number
47 * of columns remains constant, but we would have to extend
48 * the div array too as the number of rows in this array is assumed
49 * to be equal to extra.
51 struct isl_basic_set *isl_basic_set_drop_dims(
52 struct isl_basic_set *bset, unsigned first, unsigned n)
59 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
61 if (n == 0 && !isl_space_get_tuple_name(bset->dim, isl_dim_set))
64 bset = isl_basic_set_cow(bset);
68 for (i = 0; i < bset->n_eq; ++i)
69 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
70 (bset->dim->n_out-first-n)+bset->extra);
72 for (i = 0; i < bset->n_ineq; ++i)
73 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
74 (bset->dim->n_out-first-n)+bset->extra);
76 for (i = 0; i < bset->n_div; ++i)
77 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
78 (bset->dim->n_out-first-n)+bset->extra);
80 bset->dim = isl_space_drop_outputs(bset->dim, first, n);
84 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
85 bset = isl_basic_set_simplify(bset);
86 return isl_basic_set_finalize(bset);
88 isl_basic_set_free(bset);
92 struct isl_set *isl_set_drop_dims(
93 struct isl_set *set, unsigned first, unsigned n)
100 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
102 if (n == 0 && !isl_space_get_tuple_name(set->dim, isl_dim_set))
104 set = isl_set_cow(set);
107 set->dim = isl_space_drop_outputs(set->dim, first, n);
111 for (i = 0; i < set->n; ++i) {
112 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
117 ISL_F_CLR(set, ISL_SET_NORMALIZED);
124 /* Move "n" divs starting at "first" to the end of the list of divs.
126 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
127 unsigned first, unsigned n)
132 if (first + n == bmap->n_div)
135 div = isl_alloc_array(bmap->ctx, isl_int *, n);
138 for (i = 0; i < n; ++i)
139 div[i] = bmap->div[first + i];
140 for (i = 0; i < bmap->n_div - first - n; ++i)
141 bmap->div[first + i] = bmap->div[first + n + i];
142 for (i = 0; i < n; ++i)
143 bmap->div[bmap->n_div - n + i] = div[i];
147 isl_basic_map_free(bmap);
151 /* Drop "n" dimensions of type "type" starting at "first".
153 * In principle, this frees up some extra variables as the number
154 * of columns remains constant, but we would have to extend
155 * the div array too as the number of rows in this array is assumed
156 * to be equal to extra.
158 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
159 enum isl_dim_type type, unsigned first, unsigned n)
169 dim = isl_basic_map_dim(bmap, type);
170 isl_assert(bmap->ctx, first + n <= dim, goto error);
172 if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
175 bmap = isl_basic_map_cow(bmap);
179 offset = isl_basic_map_offset(bmap, type) + first;
180 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
181 for (i = 0; i < bmap->n_eq; ++i)
182 constraint_drop_vars(bmap->eq[i]+offset, n, left);
184 for (i = 0; i < bmap->n_ineq; ++i)
185 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
187 for (i = 0; i < bmap->n_div; ++i)
188 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
190 if (type == isl_dim_div) {
191 bmap = move_divs_last(bmap, first, n);
194 isl_basic_map_free_div(bmap, n);
196 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
200 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
201 bmap = isl_basic_map_simplify(bmap);
202 return isl_basic_map_finalize(bmap);
204 isl_basic_map_free(bmap);
208 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
209 enum isl_dim_type type, unsigned first, unsigned n)
211 return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
215 struct isl_basic_map *isl_basic_map_drop_inputs(
216 struct isl_basic_map *bmap, unsigned first, unsigned n)
218 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
221 struct isl_map *isl_map_drop(struct isl_map *map,
222 enum isl_dim_type type, unsigned first, unsigned n)
229 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
231 if (n == 0 && !isl_space_get_tuple_name(map->dim, type))
233 map = isl_map_cow(map);
236 map->dim = isl_space_drop_dims(map->dim, type, first, n);
240 for (i = 0; i < map->n; ++i) {
241 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
245 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
253 struct isl_set *isl_set_drop(struct isl_set *set,
254 enum isl_dim_type type, unsigned first, unsigned n)
256 return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
259 struct isl_map *isl_map_drop_inputs(
260 struct isl_map *map, unsigned first, unsigned n)
262 return isl_map_drop(map, isl_dim_in, first, n);
266 * We don't cow, as the div is assumed to be redundant.
268 static struct isl_basic_map *isl_basic_map_drop_div(
269 struct isl_basic_map *bmap, unsigned div)
277 pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
279 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
281 for (i = 0; i < bmap->n_eq; ++i)
282 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
284 for (i = 0; i < bmap->n_ineq; ++i) {
285 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
286 isl_basic_map_drop_inequality(bmap, i);
290 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
293 for (i = 0; i < bmap->n_div; ++i)
294 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
296 if (div != bmap->n_div - 1) {
298 isl_int *t = bmap->div[div];
300 for (j = div; j < bmap->n_div - 1; ++j)
301 bmap->div[j] = bmap->div[j+1];
303 bmap->div[bmap->n_div - 1] = t;
305 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
306 isl_basic_map_free_div(bmap, 1);
310 isl_basic_map_free(bmap);
314 struct isl_basic_map *isl_basic_map_normalize_constraints(
315 struct isl_basic_map *bmap)
319 unsigned total = isl_basic_map_total_dim(bmap);
325 for (i = bmap->n_eq - 1; i >= 0; --i) {
326 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
327 if (isl_int_is_zero(gcd)) {
328 if (!isl_int_is_zero(bmap->eq[i][0])) {
329 bmap = isl_basic_map_set_to_empty(bmap);
332 isl_basic_map_drop_equality(bmap, i);
335 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
336 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
337 if (isl_int_is_one(gcd))
339 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
340 bmap = isl_basic_map_set_to_empty(bmap);
343 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
346 for (i = bmap->n_ineq - 1; i >= 0; --i) {
347 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
348 if (isl_int_is_zero(gcd)) {
349 if (isl_int_is_neg(bmap->ineq[i][0])) {
350 bmap = isl_basic_map_set_to_empty(bmap);
353 isl_basic_map_drop_inequality(bmap, i);
356 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
357 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
358 if (isl_int_is_one(gcd))
360 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
361 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
368 struct isl_basic_set *isl_basic_set_normalize_constraints(
369 struct isl_basic_set *bset)
371 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
372 (struct isl_basic_map *)bset);
375 /* Remove any common factor in numerator and denominator of a div expression,
376 * not taking into account the constant term.
377 * That is, look for any div of the form
379 * floor((a + m f(x))/(m d))
383 * floor((floor(a/m) + f(x))/d)
385 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
386 * and can therefore not influence the result of the floor.
388 static __isl_give isl_basic_map *normalize_div_expressions(
389 __isl_take isl_basic_map *bmap)
393 unsigned total = isl_basic_map_total_dim(bmap);
397 if (bmap->n_div == 0)
401 for (i = 0; i < bmap->n_div; ++i) {
402 if (isl_int_is_zero(bmap->div[i][0]))
404 isl_seq_gcd(bmap->div[i] + 2, total, &gcd);
405 isl_int_gcd(gcd, gcd, bmap->div[i][0]);
406 if (isl_int_is_one(gcd))
408 isl_int_fdiv_q(bmap->div[i][1], bmap->div[i][1], gcd);
409 isl_int_divexact(bmap->div[i][0], bmap->div[i][0], gcd);
410 isl_seq_scale_down(bmap->div[i] + 2, bmap->div[i] + 2, gcd,
418 /* Assumes divs have been ordered if keep_divs is set.
420 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
421 unsigned pos, isl_int *eq, int keep_divs, int *progress)
424 unsigned space_total;
428 total = isl_basic_map_total_dim(bmap);
429 space_total = isl_space_dim(bmap->dim, isl_dim_all);
430 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
431 for (k = 0; k < bmap->n_eq; ++k) {
432 if (bmap->eq[k] == eq)
434 if (isl_int_is_zero(bmap->eq[k][1+pos]))
438 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
439 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
442 for (k = 0; k < bmap->n_ineq; ++k) {
443 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
447 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
448 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
449 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
452 for (k = 0; k < bmap->n_div; ++k) {
453 if (isl_int_is_zero(bmap->div[k][0]))
455 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
459 /* We need to be careful about circular definitions,
460 * so for now we just remove the definition of div k
461 * if the equality contains any divs.
462 * If keep_divs is set, then the divs have been ordered
463 * and we can keep the definition as long as the result
466 if (last_div == -1 || (keep_divs && last_div < k))
467 isl_seq_elim(bmap->div[k]+1, eq,
468 1+pos, 1+total, &bmap->div[k][0]);
470 isl_seq_clr(bmap->div[k], 1 + total);
471 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
475 /* Assumes divs have been ordered if keep_divs is set.
477 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
478 unsigned div, int keep_divs)
480 unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div;
482 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
484 isl_basic_map_drop_div(bmap, div);
487 /* Check if elimination of div "div" using equality "eq" would not
488 * result in a div depending on a later div.
490 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
495 unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all);
496 unsigned pos = space_total + div;
498 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
499 if (last_div < 0 || last_div <= div)
502 for (k = 0; k <= last_div; ++k) {
503 if (isl_int_is_zero(bmap->div[k][0]))
505 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
512 /* Elimininate divs based on equalities
514 static struct isl_basic_map *eliminate_divs_eq(
515 struct isl_basic_map *bmap, int *progress)
522 bmap = isl_basic_map_order_divs(bmap);
527 off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
529 for (d = bmap->n_div - 1; d >= 0 ; --d) {
530 for (i = 0; i < bmap->n_eq; ++i) {
531 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
532 !isl_int_is_negone(bmap->eq[i][off + d]))
534 if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
538 eliminate_div(bmap, bmap->eq[i], d, 1);
539 isl_basic_map_drop_equality(bmap, i);
544 return eliminate_divs_eq(bmap, progress);
548 /* Elimininate divs based on inequalities
550 static struct isl_basic_map *eliminate_divs_ineq(
551 struct isl_basic_map *bmap, int *progress)
562 off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
564 for (d = bmap->n_div - 1; d >= 0 ; --d) {
565 for (i = 0; i < bmap->n_eq; ++i)
566 if (!isl_int_is_zero(bmap->eq[i][off + d]))
570 for (i = 0; i < bmap->n_ineq; ++i)
571 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
573 if (i < bmap->n_ineq)
576 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
577 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
579 bmap = isl_basic_map_drop_div(bmap, d);
586 struct isl_basic_map *isl_basic_map_gauss(
587 struct isl_basic_map *bmap, int *progress)
595 bmap = isl_basic_map_order_divs(bmap);
600 total = isl_basic_map_total_dim(bmap);
601 total_var = total - bmap->n_div;
603 last_var = total - 1;
604 for (done = 0; done < bmap->n_eq; ++done) {
605 for (; last_var >= 0; --last_var) {
606 for (k = done; k < bmap->n_eq; ++k)
607 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
615 swap_equality(bmap, k, done);
616 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
617 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
619 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
622 if (last_var >= total_var &&
623 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
624 unsigned div = last_var - total_var;
625 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
626 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
627 isl_int_set(bmap->div[div][0],
628 bmap->eq[done][1+last_var]);
629 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
632 if (done == bmap->n_eq)
634 for (k = done; k < bmap->n_eq; ++k) {
635 if (isl_int_is_zero(bmap->eq[k][0]))
637 return isl_basic_map_set_to_empty(bmap);
639 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
643 struct isl_basic_set *isl_basic_set_gauss(
644 struct isl_basic_set *bset, int *progress)
646 return (struct isl_basic_set*)isl_basic_map_gauss(
647 (struct isl_basic_map *)bset, progress);
651 static unsigned int round_up(unsigned int v)
662 static int hash_index(isl_int ***index, unsigned int size, int bits,
663 struct isl_basic_map *bmap, int k)
666 unsigned total = isl_basic_map_total_dim(bmap);
667 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
668 for (h = hash; index[h]; h = (h+1) % size)
669 if (&bmap->ineq[k] != index[h] &&
670 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
675 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
676 struct isl_basic_set *bset, int k)
678 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
681 /* If we can eliminate more than one div, then we need to make
682 * sure we do it from last div to first div, in order not to
683 * change the position of the other divs that still need to
686 static struct isl_basic_map *remove_duplicate_divs(
687 struct isl_basic_map *bmap, int *progress)
699 if (!bmap || bmap->n_div <= 1)
702 total_var = isl_space_dim(bmap->dim, isl_dim_all);
703 total = total_var + bmap->n_div;
706 for (k = bmap->n_div - 1; k >= 0; --k)
707 if (!isl_int_is_zero(bmap->div[k][0]))
712 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
713 size = round_up(4 * bmap->n_div / 3 - 1);
714 bits = ffs(size) - 1;
715 index = isl_calloc_array(ctx, int, size);
718 eq = isl_blk_alloc(ctx, 1+total);
719 if (isl_blk_is_error(eq))
722 isl_seq_clr(eq.data, 1+total);
723 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
724 for (--k; k >= 0; --k) {
727 if (isl_int_is_zero(bmap->div[k][0]))
730 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
731 for (h = hash; index[h]; h = (h+1) % size)
732 if (isl_seq_eq(bmap->div[k],
733 bmap->div[index[h]-1], 2+total))
742 for (l = bmap->n_div - 1; l >= 0; --l) {
746 isl_int_set_si(eq.data[1+total_var+k], -1);
747 isl_int_set_si(eq.data[1+total_var+l], 1);
748 eliminate_div(bmap, eq.data, l, 0);
749 isl_int_set_si(eq.data[1+total_var+k], 0);
750 isl_int_set_si(eq.data[1+total_var+l], 0);
753 isl_blk_free(ctx, eq);
760 static int n_pure_div_eq(struct isl_basic_map *bmap)
765 total = isl_space_dim(bmap->dim, isl_dim_all);
766 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
767 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
771 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
777 /* Normalize divs that appear in equalities.
779 * In particular, we assume that bmap contains some equalities
784 * and we want to replace the set of e_i by a minimal set and
785 * such that the new e_i have a canonical representation in terms
787 * If any of the equalities involves more than one divs, then
788 * we currently simply bail out.
790 * Let us first additionally assume that all equalities involve
791 * a div. The equalities then express modulo constraints on the
792 * remaining variables and we can use "parameter compression"
793 * to find a minimal set of constraints. The result is a transformation
795 * x = T(x') = x_0 + G x'
797 * with G a lower-triangular matrix with all elements below the diagonal
798 * non-negative and smaller than the diagonal element on the same row.
799 * We first normalize x_0 by making the same property hold in the affine
801 * The rows i of G with a 1 on the diagonal do not impose any modulo
802 * constraint and simply express x_i = x'_i.
803 * For each of the remaining rows i, we introduce a div and a corresponding
804 * equality. In particular
806 * g_ii e_j = x_i - g_i(x')
808 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
809 * corresponding div (if g_kk != 1).
811 * If there are any equalities not involving any div, then we
812 * first apply a variable compression on the variables x:
814 * x = C x'' x'' = C_2 x
816 * and perform the above parameter compression on A C instead of on A.
817 * The resulting compression is then of the form
819 * x'' = T(x') = x_0 + G x'
821 * and in constructing the new divs and the corresponding equalities,
822 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
823 * by the corresponding row from C_2.
825 static struct isl_basic_map *normalize_divs(
826 struct isl_basic_map *bmap, int *progress)
833 struct isl_mat *T = NULL;
834 struct isl_mat *C = NULL;
835 struct isl_mat *C2 = NULL;
843 if (bmap->n_div == 0)
849 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
852 total = isl_space_dim(bmap->dim, isl_dim_all);
853 div_eq = n_pure_div_eq(bmap);
857 if (div_eq < bmap->n_eq) {
858 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
859 bmap->n_eq - div_eq, 0, 1 + total);
860 C = isl_mat_variable_compression(B, &C2);
864 bmap = isl_basic_map_set_to_empty(bmap);
871 d = isl_vec_alloc(bmap->ctx, div_eq);
874 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
875 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
877 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
879 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
882 B = isl_mat_product(B, C);
886 T = isl_mat_parameter_compression(B, d);
890 bmap = isl_basic_map_set_to_empty(bmap);
896 for (i = 0; i < T->n_row - 1; ++i) {
897 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
898 if (isl_int_is_zero(v))
900 isl_mat_col_submul(T, 0, v, 1 + i);
903 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
906 /* We have to be careful because dropping equalities may reorder them */
908 for (j = bmap->n_div - 1; j >= 0; --j) {
909 for (i = 0; i < bmap->n_eq; ++i)
910 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
912 if (i < bmap->n_eq) {
913 bmap = isl_basic_map_drop_div(bmap, j);
914 isl_basic_map_drop_equality(bmap, i);
920 for (i = 1; i < T->n_row; ++i) {
921 if (isl_int_is_one(T->row[i][i]))
926 if (needed > dropped) {
927 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
932 for (i = 1; i < T->n_row; ++i) {
933 if (isl_int_is_one(T->row[i][i]))
935 k = isl_basic_map_alloc_div(bmap);
936 pos[i] = 1 + total + k;
937 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
938 isl_int_set(bmap->div[k][0], T->row[i][i]);
940 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
942 isl_int_set_si(bmap->div[k][1 + i], 1);
943 for (j = 0; j < i; ++j) {
944 if (isl_int_is_zero(T->row[i][j]))
946 if (pos[j] < T->n_row && C2)
947 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
948 C2->row[pos[j]], 1 + total);
950 isl_int_neg(bmap->div[k][1 + pos[j]],
953 j = isl_basic_map_alloc_equality(bmap);
954 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
955 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
964 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
974 static struct isl_basic_map *set_div_from_lower_bound(
975 struct isl_basic_map *bmap, int div, int ineq)
977 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
979 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
980 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
981 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
982 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
983 isl_int_set_si(bmap->div[div][1 + total + div], 0);
988 /* Check whether it is ok to define a div based on an inequality.
989 * To avoid the introduction of circular definitions of divs, we
990 * do not allow such a definition if the resulting expression would refer to
991 * any other undefined divs or if any known div is defined in
992 * terms of the unknown div.
994 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
998 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1000 /* Not defined in terms of unknown divs */
1001 for (j = 0; j < bmap->n_div; ++j) {
1004 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
1006 if (isl_int_is_zero(bmap->div[j][0]))
1010 /* No other div defined in terms of this one => avoid loops */
1011 for (j = 0; j < bmap->n_div; ++j) {
1014 if (isl_int_is_zero(bmap->div[j][0]))
1016 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
1023 /* Given two constraints "k" and "l" that are opposite to each other,
1024 * except for the constant term, check if we can use them
1025 * to obtain an expression for one of the hitherto unknown divs.
1026 * "sum" is the sum of the constant terms of the constraints.
1027 * If this sum is strictly smaller than the coefficient of one
1028 * of the divs, then this pair can be used define the div.
1029 * To avoid the introduction of circular definitions of divs, we
1030 * do not use the pair if the resulting expression would refer to
1031 * any other undefined divs or if any known div is defined in
1032 * terms of the unknown div.
1034 static struct isl_basic_map *check_for_div_constraints(
1035 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
1038 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1040 for (i = 0; i < bmap->n_div; ++i) {
1041 if (!isl_int_is_zero(bmap->div[i][0]))
1043 if (isl_int_is_zero(bmap->ineq[k][total + i]))
1045 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1047 if (!ok_to_set_div_from_bound(bmap, i, k))
1049 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1050 bmap = set_div_from_lower_bound(bmap, i, k);
1052 bmap = set_div_from_lower_bound(bmap, i, l);
1060 static struct isl_basic_map *remove_duplicate_constraints(
1061 struct isl_basic_map *bmap, int *progress, int detect_divs)
1067 unsigned total = isl_basic_map_total_dim(bmap);
1071 if (!bmap || bmap->n_ineq <= 1)
1074 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1075 bits = ffs(size) - 1;
1076 ctx = isl_basic_map_get_ctx(bmap);
1077 index = isl_calloc_array(ctx, isl_int **, size);
1081 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1082 for (k = 1; k < bmap->n_ineq; ++k) {
1083 h = hash_index(index, size, bits, bmap, k);
1085 index[h] = &bmap->ineq[k];
1090 l = index[h] - &bmap->ineq[0];
1091 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1092 swap_inequality(bmap, k, l);
1093 isl_basic_map_drop_inequality(bmap, k);
1097 for (k = 0; k < bmap->n_ineq-1; ++k) {
1098 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1099 h = hash_index(index, size, bits, bmap, k);
1100 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1103 l = index[h] - &bmap->ineq[0];
1104 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1105 if (isl_int_is_pos(sum)) {
1107 bmap = check_for_div_constraints(bmap, k, l,
1111 if (isl_int_is_zero(sum)) {
1112 /* We need to break out of the loop after these
1113 * changes since the contents of the hash
1114 * will no longer be valid.
1115 * Plus, we probably we want to regauss first.
1119 isl_basic_map_drop_inequality(bmap, l);
1120 isl_basic_map_inequality_to_equality(bmap, k);
1122 bmap = isl_basic_map_set_to_empty(bmap);
1132 /* Eliminate knowns divs from constraints where they appear with
1133 * a (positive or negative) unit coefficient.
1137 * floor(e/m) + f >= 0
1145 * -floor(e/m) + f >= 0
1149 * -e + m f + m - 1 >= 0
1151 * The first conversion is valid because floor(e/m) >= -f is equivalent
1152 * to e/m >= -f because -f is an integral expression.
1153 * The second conversion follows from the fact that
1155 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1158 * We skip integral divs, i.e., those with denominator 1, as we would
1159 * risk eliminating the div from the div constraints. We do not need
1160 * to handle those divs here anyway since the div constraints will turn
1161 * out to form an equality and this equality can then be use to eliminate
1162 * the div from all constraints.
1164 static __isl_give isl_basic_map *eliminate_unit_divs(
1165 __isl_take isl_basic_map *bmap, int *progress)
1174 ctx = isl_basic_map_get_ctx(bmap);
1175 total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1177 for (i = 0; i < bmap->n_div; ++i) {
1178 if (isl_int_is_zero(bmap->div[i][0]))
1180 if (isl_int_is_one(bmap->div[i][0]))
1182 for (j = 0; j < bmap->n_ineq; ++j) {
1185 if (!isl_int_is_one(bmap->ineq[j][total + i]) &&
1186 !isl_int_is_negone(bmap->ineq[j][total + i]))
1191 s = isl_int_sgn(bmap->ineq[j][total + i]);
1192 isl_int_set_si(bmap->ineq[j][total + i], 0);
1194 isl_seq_combine(bmap->ineq[j],
1195 ctx->negone, bmap->div[i] + 1,
1196 bmap->div[i][0], bmap->ineq[j],
1197 total + bmap->n_div);
1199 isl_seq_combine(bmap->ineq[j],
1200 ctx->one, bmap->div[i] + 1,
1201 bmap->div[i][0], bmap->ineq[j],
1202 total + bmap->n_div);
1204 isl_int_add(bmap->ineq[j][0],
1205 bmap->ineq[j][0], bmap->div[i][0]);
1206 isl_int_sub_ui(bmap->ineq[j][0],
1207 bmap->ineq[j][0], 1);
1215 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1222 bmap = isl_basic_map_normalize_constraints(bmap);
1223 bmap = normalize_div_expressions(bmap);
1224 bmap = remove_duplicate_divs(bmap, &progress);
1225 bmap = eliminate_unit_divs(bmap, &progress);
1226 bmap = eliminate_divs_eq(bmap, &progress);
1227 bmap = eliminate_divs_ineq(bmap, &progress);
1228 bmap = isl_basic_map_gauss(bmap, &progress);
1229 /* requires equalities in normal form */
1230 bmap = normalize_divs(bmap, &progress);
1231 bmap = remove_duplicate_constraints(bmap, &progress, 1);
1236 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1238 return (struct isl_basic_set *)
1239 isl_basic_map_simplify((struct isl_basic_map *)bset);
1243 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1244 isl_int *constraint, unsigned div)
1251 pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1253 if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1255 isl_int_sub(bmap->div[div][1],
1256 bmap->div[div][1], bmap->div[div][0]);
1257 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1258 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1259 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1260 isl_int_add(bmap->div[div][1],
1261 bmap->div[div][1], bmap->div[div][0]);
1264 if (isl_seq_first_non_zero(constraint+pos+1,
1265 bmap->n_div-div-1) != -1)
1267 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1268 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1270 if (isl_seq_first_non_zero(constraint+pos+1,
1271 bmap->n_div-div-1) != -1)
1279 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set *bset,
1280 isl_int *constraint, unsigned div)
1282 return isl_basic_map_is_div_constraint(bset, constraint, div);
1286 /* If the only constraints a div d=floor(f/m)
1287 * appears in are its two defining constraints
1290 * -(f - (m - 1)) + m d >= 0
1292 * then it can safely be removed.
1294 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1297 unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1299 for (i = 0; i < bmap->n_eq; ++i)
1300 if (!isl_int_is_zero(bmap->eq[i][pos]))
1303 for (i = 0; i < bmap->n_ineq; ++i) {
1304 if (isl_int_is_zero(bmap->ineq[i][pos]))
1306 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1310 for (i = 0; i < bmap->n_div; ++i)
1311 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1318 * Remove divs that don't occur in any of the constraints or other divs.
1319 * These can arise when dropping some of the variables in a quast
1320 * returned by piplib.
1322 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1329 for (i = bmap->n_div-1; i >= 0; --i) {
1330 if (!div_is_redundant(bmap, i))
1332 bmap = isl_basic_map_drop_div(bmap, i);
1337 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1339 bmap = remove_redundant_divs(bmap);
1342 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1346 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1348 return (struct isl_basic_set *)
1349 isl_basic_map_finalize((struct isl_basic_map *)bset);
1352 struct isl_set *isl_set_finalize(struct isl_set *set)
1358 for (i = 0; i < set->n; ++i) {
1359 set->p[i] = isl_basic_set_finalize(set->p[i]);
1369 struct isl_map *isl_map_finalize(struct isl_map *map)
1375 for (i = 0; i < map->n; ++i) {
1376 map->p[i] = isl_basic_map_finalize(map->p[i]);
1380 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1388 /* Remove definition of any div that is defined in terms of the given variable.
1389 * The div itself is not removed. Functions such as
1390 * eliminate_divs_ineq depend on the other divs remaining in place.
1392 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1397 for (i = 0; i < bmap->n_div; ++i) {
1398 if (isl_int_is_zero(bmap->div[i][0]))
1400 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1402 isl_int_set_si(bmap->div[i][0], 0);
1407 /* Eliminate the specified variables from the constraints using
1408 * Fourier-Motzkin. The variables themselves are not removed.
1410 struct isl_basic_map *isl_basic_map_eliminate_vars(
1411 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1422 total = isl_basic_map_total_dim(bmap);
1424 bmap = isl_basic_map_cow(bmap);
1425 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1426 bmap = remove_dependent_vars(bmap, d);
1428 for (d = pos + n - 1;
1429 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1430 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1431 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1432 int n_lower, n_upper;
1435 for (i = 0; i < bmap->n_eq; ++i) {
1436 if (isl_int_is_zero(bmap->eq[i][1+d]))
1438 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1439 isl_basic_map_drop_equality(bmap, i);
1447 for (i = 0; i < bmap->n_ineq; ++i) {
1448 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1450 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1453 bmap = isl_basic_map_extend_constraints(bmap,
1454 0, n_lower * n_upper);
1457 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1459 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1462 for (j = 0; j < i; ++j) {
1463 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1466 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1467 isl_int_sgn(bmap->ineq[j][1+d]))
1469 k = isl_basic_map_alloc_inequality(bmap);
1472 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1474 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1475 1+d, 1+total, NULL);
1477 isl_basic_map_drop_inequality(bmap, i);
1480 if (n_lower > 0 && n_upper > 0) {
1481 bmap = isl_basic_map_normalize_constraints(bmap);
1482 bmap = remove_duplicate_constraints(bmap, NULL, 0);
1483 bmap = isl_basic_map_gauss(bmap, NULL);
1484 bmap = isl_basic_map_remove_redundancies(bmap);
1488 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1492 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1494 bmap = isl_basic_map_gauss(bmap, NULL);
1497 isl_basic_map_free(bmap);
1501 struct isl_basic_set *isl_basic_set_eliminate_vars(
1502 struct isl_basic_set *bset, unsigned pos, unsigned n)
1504 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1505 (struct isl_basic_map *)bset, pos, n);
1508 /* Eliminate the specified n dimensions starting at first from the
1509 * constraints, without removing the dimensions from the space.
1510 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1511 * Otherwise, they are projected out and the original space is restored.
1513 __isl_give isl_basic_map *isl_basic_map_eliminate(
1514 __isl_take isl_basic_map *bmap,
1515 enum isl_dim_type type, unsigned first, unsigned n)
1524 if (first + n > isl_basic_map_dim(bmap, type) || first + n < first)
1525 isl_die(bmap->ctx, isl_error_invalid,
1526 "index out of bounds", goto error);
1528 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
1529 first += isl_basic_map_offset(bmap, type) - 1;
1530 bmap = isl_basic_map_eliminate_vars(bmap, first, n);
1531 return isl_basic_map_finalize(bmap);
1534 space = isl_basic_map_get_space(bmap);
1535 bmap = isl_basic_map_project_out(bmap, type, first, n);
1536 bmap = isl_basic_map_insert(bmap, type, first, n);
1537 bmap = isl_basic_map_reset_space(bmap, space);
1540 isl_basic_map_free(bmap);
1544 /* Don't assume equalities are in order, because align_divs
1545 * may have changed the order of the divs.
1547 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1552 total = isl_space_dim(bmap->dim, isl_dim_all);
1553 for (d = 0; d < total; ++d)
1555 for (i = 0; i < bmap->n_eq; ++i) {
1556 for (d = total - 1; d >= 0; --d) {
1557 if (isl_int_is_zero(bmap->eq[i][1+d]))
1565 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1567 compute_elimination_index((struct isl_basic_map *)bset, elim);
1570 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1571 struct isl_basic_map *bmap, int *elim)
1577 total = isl_space_dim(bmap->dim, isl_dim_all);
1578 for (d = total - 1; d >= 0; --d) {
1579 if (isl_int_is_zero(src[1+d]))
1584 isl_seq_cpy(dst, src, 1 + total);
1587 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1592 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1593 struct isl_basic_set *bset, int *elim)
1595 return reduced_using_equalities(dst, src,
1596 (struct isl_basic_map *)bset, elim);
1599 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1600 struct isl_basic_set *bset, struct isl_basic_set *context)
1605 if (!bset || !context)
1608 if (context->n_eq == 0) {
1609 isl_basic_set_free(context);
1613 bset = isl_basic_set_cow(bset);
1617 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1620 set_compute_elimination_index(context, elim);
1621 for (i = 0; i < bset->n_eq; ++i)
1622 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1624 for (i = 0; i < bset->n_ineq; ++i)
1625 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1627 isl_basic_set_free(context);
1629 bset = isl_basic_set_simplify(bset);
1630 bset = isl_basic_set_finalize(bset);
1633 isl_basic_set_free(bset);
1634 isl_basic_set_free(context);
1638 static struct isl_basic_set *remove_shifted_constraints(
1639 struct isl_basic_set *bset, struct isl_basic_set *context)
1650 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1651 bits = ffs(size) - 1;
1652 ctx = isl_basic_set_get_ctx(bset);
1653 index = isl_calloc_array(ctx, isl_int **, size);
1657 for (k = 0; k < context->n_ineq; ++k) {
1658 h = set_hash_index(index, size, bits, context, k);
1659 index[h] = &context->ineq[k];
1661 for (k = 0; k < bset->n_ineq; ++k) {
1662 h = set_hash_index(index, size, bits, bset, k);
1665 l = index[h] - &context->ineq[0];
1666 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1668 bset = isl_basic_set_cow(bset);
1671 isl_basic_set_drop_inequality(bset, k);
1681 /* Remove all information from bset that is redundant in the context
1682 * of context. Both bset and context are assumed to be full-dimensional.
1684 * We first * remove the inequalities from "bset"
1685 * that are obviously redundant with respect to some inequality in "context".
1687 * If there are any inequalities left, we construct a tableau for
1688 * the context and then add the inequalities of "bset".
1689 * Before adding these inequalities, we freeze all constraints such that
1690 * they won't be considered redundant in terms of the constraints of "bset".
1691 * Then we detect all redundant constraints (among the
1692 * constraints that weren't frozen), first by checking for redundancy in the
1693 * the tableau and then by checking if replacing a constraint by its negation
1694 * would lead to an empty set. This last step is fairly expensive
1695 * and could be optimized by more reuse of the tableau.
1696 * Finally, we update bset according to the results.
1698 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1699 __isl_take isl_basic_set *context)
1702 isl_basic_set *combined = NULL;
1703 struct isl_tab *tab = NULL;
1704 unsigned context_ineq;
1707 if (!bset || !context)
1710 if (isl_basic_set_is_universe(bset)) {
1711 isl_basic_set_free(context);
1715 if (isl_basic_set_is_universe(context)) {
1716 isl_basic_set_free(context);
1720 bset = remove_shifted_constraints(bset, context);
1723 if (bset->n_ineq == 0)
1726 context_ineq = context->n_ineq;
1727 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1728 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1729 tab = isl_tab_from_basic_set(combined, 0);
1730 for (i = 0; i < context_ineq; ++i)
1731 if (isl_tab_freeze_constraint(tab, i) < 0)
1733 tab = isl_tab_extend(tab, bset->n_ineq);
1734 for (i = 0; i < bset->n_ineq; ++i)
1735 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1737 bset = isl_basic_set_add_constraints(combined, bset, 0);
1741 if (isl_tab_detect_redundant(tab) < 0)
1743 total = isl_basic_set_total_dim(bset);
1744 for (i = context_ineq; i < bset->n_ineq; ++i) {
1746 if (tab->con[i].is_redundant)
1748 tab->con[i].is_redundant = 1;
1749 combined = isl_basic_set_dup(bset);
1750 combined = isl_basic_set_update_from_tab(combined, tab);
1751 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1752 k = isl_basic_set_alloc_inequality(combined);
1755 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1756 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1757 is_empty = isl_basic_set_is_empty(combined);
1760 isl_basic_set_free(combined);
1763 tab->con[i].is_redundant = 0;
1765 for (i = 0; i < context_ineq; ++i)
1766 tab->con[i].is_redundant = 1;
1767 bset = isl_basic_set_update_from_tab(bset, tab);
1769 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1770 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1775 bset = isl_basic_set_simplify(bset);
1776 bset = isl_basic_set_finalize(bset);
1777 isl_basic_set_free(context);
1781 isl_basic_set_free(combined);
1782 isl_basic_set_free(context);
1783 isl_basic_set_free(bset);
1787 /* Remove all information from bset that is redundant in the context
1788 * of context. In particular, equalities that are linear combinations
1789 * of those in context are removed. Then the inequalities that are
1790 * redundant in the context of the equalities and inequalities of
1791 * context are removed.
1793 * We first compute the integer affine hull of the intersection,
1794 * compute the gist inside this affine hull and then add back
1795 * those equalities that are not implied by the context.
1797 * If two constraints are mutually redundant, then uset_gist_full
1798 * will remove the second of those constraints. We therefore first
1799 * sort the constraints so that constraints not involving existentially
1800 * quantified variables are given precedence over those that do.
1801 * We have to perform this sorting before the variable compression,
1802 * because that may effect the order of the variables.
1804 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1805 __isl_take isl_basic_set *context)
1810 isl_basic_set *aff_context;
1813 if (!bset || !context)
1816 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1817 if (isl_basic_set_plain_is_empty(bset)) {
1818 isl_basic_set_free(context);
1821 bset = isl_basic_set_sort_constraints(bset);
1822 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1825 if (isl_basic_set_plain_is_empty(aff)) {
1826 isl_basic_set_free(aff);
1827 isl_basic_set_free(context);
1830 if (aff->n_eq == 0) {
1831 isl_basic_set_free(aff);
1832 return uset_gist_full(bset, context);
1834 total = isl_basic_set_total_dim(bset);
1835 eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1836 eq = isl_mat_cow(eq);
1837 T = isl_mat_variable_compression(eq, &T2);
1838 if (T && T->n_col == 0) {
1841 isl_basic_set_free(context);
1842 isl_basic_set_free(aff);
1843 return isl_basic_set_set_to_empty(bset);
1846 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1848 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1849 context = isl_basic_set_preimage(context, T);
1851 bset = uset_gist_full(bset, context);
1852 bset = isl_basic_set_preimage(bset, T2);
1853 bset = isl_basic_set_intersect(bset, aff);
1854 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1857 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1858 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1863 isl_basic_set_free(bset);
1864 isl_basic_set_free(context);
1868 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1869 * We simply add the equalities in context to bmap and then do a regular
1870 * div normalizations. Better results can be obtained by normalizing
1871 * only the divs in bmap than do not also appear in context.
1872 * We need to be careful to reduce the divs using the equalities
1873 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1874 * spurious constraints.
1876 static struct isl_basic_map *normalize_divs_in_context(
1877 struct isl_basic_map *bmap, struct isl_basic_map *context)
1880 unsigned total_context;
1883 div_eq = n_pure_div_eq(bmap);
1887 if (context->n_div > 0)
1888 bmap = isl_basic_map_align_divs(bmap, context);
1890 total_context = isl_basic_map_total_dim(context);
1891 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1892 for (i = 0; i < context->n_eq; ++i) {
1894 k = isl_basic_map_alloc_equality(bmap);
1895 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1896 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1897 isl_basic_map_total_dim(bmap) - total_context);
1899 bmap = isl_basic_map_gauss(bmap, NULL);
1900 bmap = normalize_divs(bmap, NULL);
1901 bmap = isl_basic_map_gauss(bmap, NULL);
1905 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1906 struct isl_basic_map *context)
1908 struct isl_basic_set *bset;
1910 if (!bmap || !context)
1913 if (isl_basic_map_is_universe(bmap)) {
1914 isl_basic_map_free(context);
1917 if (isl_basic_map_plain_is_empty(context)) {
1918 isl_basic_map_free(bmap);
1921 if (isl_basic_map_plain_is_empty(bmap)) {
1922 isl_basic_map_free(context);
1926 bmap = isl_basic_map_remove_redundancies(bmap);
1927 context = isl_basic_map_remove_redundancies(context);
1930 bmap = normalize_divs_in_context(bmap, context);
1932 context = isl_basic_map_align_divs(context, bmap);
1933 bmap = isl_basic_map_align_divs(bmap, context);
1935 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1936 isl_basic_map_underlying_set(context));
1938 return isl_basic_map_overlying_set(bset, bmap);
1940 isl_basic_map_free(bmap);
1941 isl_basic_map_free(context);
1946 * Assumes context has no implicit divs.
1948 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1949 __isl_take isl_basic_map *context)
1953 if (!map || !context)
1956 if (isl_basic_map_plain_is_empty(context)) {
1958 return isl_map_from_basic_map(context);
1961 context = isl_basic_map_remove_redundancies(context);
1962 map = isl_map_cow(map);
1963 if (!map || !context)
1965 isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
1966 map = isl_map_compute_divs(map);
1967 for (i = 0; i < map->n; ++i)
1968 context = isl_basic_map_align_divs(context, map->p[i]);
1969 for (i = map->n - 1; i >= 0; --i) {
1970 map->p[i] = isl_basic_map_gist(map->p[i],
1971 isl_basic_map_copy(context));
1974 if (isl_basic_map_plain_is_empty(map->p[i])) {
1975 isl_basic_map_free(map->p[i]);
1976 if (i != map->n - 1)
1977 map->p[i] = map->p[map->n - 1];
1981 isl_basic_map_free(context);
1982 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1986 isl_basic_map_free(context);
1990 static __isl_give isl_map *map_gist(__isl_take isl_map *map,
1991 __isl_take isl_map *context)
1993 context = isl_map_compute_divs(context);
1994 return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1997 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1998 __isl_take isl_map *context)
2000 return isl_map_align_params_map_map_and(map, context, &map_gist);
2003 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
2004 struct isl_basic_set *context)
2006 return (struct isl_basic_set *)isl_basic_map_gist(
2007 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
2010 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
2011 __isl_take isl_basic_set *context)
2013 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
2014 (struct isl_basic_map *)context);
2017 __isl_give isl_set *isl_set_gist_params_basic_set(__isl_take isl_set *set,
2018 __isl_take isl_basic_set *context)
2020 isl_space *space = isl_set_get_space(set);
2021 isl_basic_set *dom_context = isl_basic_set_universe(space);
2022 dom_context = isl_basic_set_intersect_params(dom_context, context);
2023 return isl_set_gist_basic_set(set, dom_context);
2026 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2027 __isl_take isl_set *context)
2029 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
2030 (struct isl_map *)context);
2033 __isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map,
2034 __isl_take isl_set *context)
2036 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2037 map_context = isl_map_intersect_domain(map_context, context);
2038 return isl_map_gist(map, map_context);
2041 __isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map,
2042 __isl_take isl_set *context)
2044 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2045 map_context = isl_map_intersect_range(map_context, context);
2046 return isl_map_gist(map, map_context);
2049 __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
2050 __isl_take isl_set *context)
2052 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2053 map_context = isl_map_intersect_params(map_context, context);
2054 return isl_map_gist(map, map_context);
2057 __isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
2058 __isl_take isl_set *context)
2060 return isl_map_gist_params(set, context);
2063 /* Quick check to see if two basic maps are disjoint.
2064 * In particular, we reduce the equalities and inequalities of
2065 * one basic map in the context of the equalities of the other
2066 * basic map and check if we get a contradiction.
2068 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
2069 __isl_keep isl_basic_map *bmap2)
2071 struct isl_vec *v = NULL;
2076 if (!bmap1 || !bmap2)
2078 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
2080 if (bmap1->n_div || bmap2->n_div)
2082 if (!bmap1->n_eq && !bmap2->n_eq)
2085 total = isl_space_dim(bmap1->dim, isl_dim_all);
2088 v = isl_vec_alloc(bmap1->ctx, 1 + total);
2091 elim = isl_alloc_array(bmap1->ctx, int, total);
2094 compute_elimination_index(bmap1, elim);
2095 for (i = 0; i < bmap2->n_eq; ++i) {
2097 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
2099 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
2100 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2103 for (i = 0; i < bmap2->n_ineq; ++i) {
2105 reduced = reduced_using_equalities(v->block.data,
2106 bmap2->ineq[i], bmap1, elim);
2107 if (reduced && isl_int_is_neg(v->block.data[0]) &&
2108 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2111 compute_elimination_index(bmap2, elim);
2112 for (i = 0; i < bmap1->n_ineq; ++i) {
2114 reduced = reduced_using_equalities(v->block.data,
2115 bmap1->ineq[i], bmap2, elim);
2116 if (reduced && isl_int_is_neg(v->block.data[0]) &&
2117 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2133 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
2134 __isl_keep isl_basic_set *bset2)
2136 return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
2137 (struct isl_basic_map *)bset2);
2140 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
2141 __isl_keep isl_map *map2)
2148 if (isl_map_plain_is_equal(map1, map2))
2151 for (i = 0; i < map1->n; ++i) {
2152 for (j = 0; j < map2->n; ++j) {
2153 int d = isl_basic_map_plain_is_disjoint(map1->p[i],
2162 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2163 __isl_keep isl_set *set2)
2165 return isl_map_plain_is_disjoint((struct isl_map *)set1,
2166 (struct isl_map *)set2);
2169 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
2171 return isl_set_plain_is_disjoint(set1, set2);
2174 /* Check if we can combine a given div with lower bound l and upper
2175 * bound u with some other div and if so return that other div.
2176 * Otherwise return -1.
2178 * We first check that
2179 * - the bounds are opposites of each other (except for the constant
2181 * - the bounds do not reference any other div
2182 * - no div is defined in terms of this div
2184 * Let m be the size of the range allowed on the div by the bounds.
2185 * That is, the bounds are of the form
2187 * e <= a <= e + m - 1
2189 * with e some expression in the other variables.
2190 * We look for another div b such that no third div is defined in terms
2191 * of this second div b and such that in any constraint that contains
2192 * a (except for the given lower and upper bound), also contains b
2193 * with a coefficient that is m times that of b.
2194 * That is, all constraints (execpt for the lower and upper bound)
2197 * e + f (a + m b) >= 0
2199 * If so, we return b so that "a + m b" can be replaced by
2200 * a single div "c = a + m b".
2202 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2203 unsigned div, unsigned l, unsigned u)
2209 if (bmap->n_div <= 1)
2211 dim = isl_space_dim(bmap->dim, isl_dim_all);
2212 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2214 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2215 bmap->n_div - div - 1) != -1)
2217 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2221 for (i = 0; i < bmap->n_div; ++i) {
2222 if (isl_int_is_zero(bmap->div[i][0]))
2224 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2228 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2229 if (isl_int_is_neg(bmap->ineq[l][0])) {
2230 isl_int_sub(bmap->ineq[l][0],
2231 bmap->ineq[l][0], bmap->ineq[u][0]);
2232 bmap = isl_basic_map_copy(bmap);
2233 bmap = isl_basic_map_set_to_empty(bmap);
2234 isl_basic_map_free(bmap);
2237 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2238 for (i = 0; i < bmap->n_div; ++i) {
2243 for (j = 0; j < bmap->n_div; ++j) {
2244 if (isl_int_is_zero(bmap->div[j][0]))
2246 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2249 if (j < bmap->n_div)
2251 for (j = 0; j < bmap->n_ineq; ++j) {
2253 if (j == l || j == u)
2255 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2257 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2259 isl_int_mul(bmap->ineq[j][1 + dim + div],
2260 bmap->ineq[j][1 + dim + div],
2262 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2263 bmap->ineq[j][1 + dim + i]);
2264 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2265 bmap->ineq[j][1 + dim + div],
2270 if (j < bmap->n_ineq)
2275 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2276 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2280 /* Given a lower and an upper bound on div i, construct an inequality
2281 * that when nonnegative ensures that this pair of bounds always allows
2282 * for an integer value of the given div.
2283 * The lower bound is inequality l, while the upper bound is inequality u.
2284 * The constructed inequality is stored in ineq.
2285 * g, fl, fu are temporary scalars.
2287 * Let the upper bound be
2291 * and the lower bound
2295 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2298 * - f_u e_l <= f_u f_l g a <= f_l e_u
2300 * Since all variables are integer valued, this is equivalent to
2302 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2304 * If this interval is at least f_u f_l g, then it contains at least
2305 * one integer value for a.
2306 * That is, the test constraint is
2308 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2310 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2311 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2314 dim = isl_space_dim(bmap->dim, isl_dim_all);
2316 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2317 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2318 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2319 isl_int_neg(fu, fu);
2320 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2321 1 + dim + bmap->n_div);
2322 isl_int_add(ineq[0], ineq[0], fl);
2323 isl_int_add(ineq[0], ineq[0], fu);
2324 isl_int_sub_ui(ineq[0], ineq[0], 1);
2325 isl_int_mul(g, g, fl);
2326 isl_int_mul(g, g, fu);
2327 isl_int_sub(ineq[0], ineq[0], g);
2330 /* Remove more kinds of divs that are not strictly needed.
2331 * In particular, if all pairs of lower and upper bounds on a div
2332 * are such that they allow at least one integer value of the div,
2333 * the we can eliminate the div using Fourier-Motzkin without
2334 * introducing any spurious solutions.
2336 static struct isl_basic_map *drop_more_redundant_divs(
2337 struct isl_basic_map *bmap, int *pairs, int n)
2339 struct isl_tab *tab = NULL;
2340 struct isl_vec *vec = NULL;
2352 dim = isl_space_dim(bmap->dim, isl_dim_all);
2353 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2357 tab = isl_tab_from_basic_map(bmap, 0);
2362 enum isl_lp_result res;
2364 for (i = 0; i < bmap->n_div; ++i) {
2367 if (best >= 0 && pairs[best] <= pairs[i])
2373 for (l = 0; l < bmap->n_ineq; ++l) {
2374 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2376 for (u = 0; u < bmap->n_ineq; ++u) {
2377 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2379 construct_test_ineq(bmap, i, l, u,
2380 vec->el, g, fl, fu);
2381 res = isl_tab_min(tab, vec->el,
2382 bmap->ctx->one, &g, NULL, 0);
2383 if (res == isl_lp_error)
2385 if (res == isl_lp_empty) {
2386 bmap = isl_basic_map_set_to_empty(bmap);
2389 if (res != isl_lp_ok || isl_int_is_neg(g))
2392 if (u < bmap->n_ineq)
2395 if (l == bmap->n_ineq) {
2415 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2416 return isl_basic_map_drop_redundant_divs(bmap);
2419 isl_basic_map_free(bmap);
2428 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2429 * and the upper bound u, div1 always occurs together with div2 in the form
2430 * (div1 + m div2), where m is the constant range on the variable div1
2431 * allowed by l and u, replace the pair div1 and div2 by a single
2432 * div that is equal to div1 + m div2.
2434 * The new div will appear in the location that contains div2.
2435 * We need to modify all constraints that contain
2436 * div2 = (div - div1) / m
2437 * (If a constraint does not contain div2, it will also not contain div1.)
2438 * If the constraint also contains div1, then we know they appear
2439 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2440 * i.e., the coefficient of div is f.
2442 * Otherwise, we first need to introduce div1 into the constraint.
2451 * A lower bound on div2
2455 * can be replaced by
2457 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2459 * with g = gcd(m,n).
2464 * can be replaced by
2466 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2468 * These constraint are those that we would obtain from eliminating
2469 * div1 using Fourier-Motzkin.
2471 * After all constraints have been modified, we drop the lower and upper
2472 * bound and then drop div1.
2474 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2475 unsigned div1, unsigned div2, unsigned l, unsigned u)
2480 unsigned dim, total;
2483 dim = isl_space_dim(bmap->dim, isl_dim_all);
2484 total = 1 + dim + bmap->n_div;
2489 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2490 isl_int_add_ui(m, m, 1);
2492 for (i = 0; i < bmap->n_ineq; ++i) {
2493 if (i == l || i == u)
2495 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2497 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2498 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2499 isl_int_divexact(a, m, b);
2500 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2501 if (isl_int_is_pos(b)) {
2502 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2503 b, bmap->ineq[l], total);
2506 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2507 b, bmap->ineq[u], total);
2510 isl_int_set(bmap->ineq[i][1 + dim + div2],
2511 bmap->ineq[i][1 + dim + div1]);
2512 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2519 isl_basic_map_drop_inequality(bmap, l);
2520 isl_basic_map_drop_inequality(bmap, u);
2522 isl_basic_map_drop_inequality(bmap, u);
2523 isl_basic_map_drop_inequality(bmap, l);
2525 bmap = isl_basic_map_drop_div(bmap, div1);
2529 /* First check if we can coalesce any pair of divs and
2530 * then continue with dropping more redundant divs.
2532 * We loop over all pairs of lower and upper bounds on a div
2533 * with coefficient 1 and -1, respectively, check if there
2534 * is any other div "c" with which we can coalesce the div
2535 * and if so, perform the coalescing.
2537 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2538 struct isl_basic_map *bmap, int *pairs, int n)
2543 dim = isl_space_dim(bmap->dim, isl_dim_all);
2545 for (i = 0; i < bmap->n_div; ++i) {
2548 for (l = 0; l < bmap->n_ineq; ++l) {
2549 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2551 for (u = 0; u < bmap->n_ineq; ++u) {
2554 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2556 c = div_find_coalesce(bmap, pairs, i, l, u);
2560 bmap = coalesce_divs(bmap, i, c, l, u);
2561 return isl_basic_map_drop_redundant_divs(bmap);
2566 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2569 return drop_more_redundant_divs(bmap, pairs, n);
2572 /* Remove divs that are not strictly needed.
2573 * In particular, if a div only occurs positively (or negatively)
2574 * in constraints, then it can simply be dropped.
2575 * Also, if a div occurs only occurs in two constraints and if moreover
2576 * those two constraints are opposite to each other, except for the constant
2577 * term and if the sum of the constant terms is such that for any value
2578 * of the other values, there is always at least one integer value of the
2579 * div, i.e., if one plus this sum is greater than or equal to
2580 * the (absolute value) of the coefficent of the div in the constraints,
2581 * then we can also simply drop the div.
2583 * If any divs are left after these simple checks then we move on
2584 * to more complicated cases in drop_more_redundant_divs.
2586 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2587 struct isl_basic_map *bmap)
2597 off = isl_space_dim(bmap->dim, isl_dim_all);
2598 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2602 for (i = 0; i < bmap->n_div; ++i) {
2604 int last_pos, last_neg;
2608 defined = !isl_int_is_zero(bmap->div[i][0]);
2609 for (j = 0; j < bmap->n_eq; ++j)
2610 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2616 for (j = 0; j < bmap->n_ineq; ++j) {
2617 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2621 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2626 pairs[i] = pos * neg;
2627 if (pairs[i] == 0) {
2628 for (j = bmap->n_ineq - 1; j >= 0; --j)
2629 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2630 isl_basic_map_drop_inequality(bmap, j);
2631 bmap = isl_basic_map_drop_div(bmap, i);
2633 return isl_basic_map_drop_redundant_divs(bmap);
2637 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2638 bmap->ineq[last_neg] + 1,
2642 isl_int_add(bmap->ineq[last_pos][0],
2643 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2644 isl_int_add_ui(bmap->ineq[last_pos][0],
2645 bmap->ineq[last_pos][0], 1);
2646 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2647 bmap->ineq[last_pos][1+off+i]);
2648 isl_int_sub_ui(bmap->ineq[last_pos][0],
2649 bmap->ineq[last_pos][0], 1);
2650 isl_int_sub(bmap->ineq[last_pos][0],
2651 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2654 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2659 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2660 bmap = isl_basic_map_simplify(bmap);
2662 return isl_basic_map_drop_redundant_divs(bmap);
2664 if (last_pos > last_neg) {
2665 isl_basic_map_drop_inequality(bmap, last_pos);
2666 isl_basic_map_drop_inequality(bmap, last_neg);
2668 isl_basic_map_drop_inequality(bmap, last_neg);
2669 isl_basic_map_drop_inequality(bmap, last_pos);
2671 bmap = isl_basic_map_drop_div(bmap, i);
2673 return isl_basic_map_drop_redundant_divs(bmap);
2677 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2683 isl_basic_map_free(bmap);
2687 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2688 struct isl_basic_set *bset)
2690 return (struct isl_basic_set *)
2691 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2694 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2700 for (i = 0; i < map->n; ++i) {
2701 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2705 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2712 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2714 return (struct isl_set *)
2715 isl_map_drop_redundant_divs((struct isl_map *)set);