2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 #include "isl_equalities.h"
12 #include "isl_map_private.h"
16 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
18 isl_int *t = bmap->eq[a];
19 bmap->eq[a] = bmap->eq[b];
23 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
26 isl_int *t = bmap->ineq[a];
27 bmap->ineq[a] = bmap->ineq[b];
32 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
34 swap_inequality((struct isl_basic_map *)bset, a, b);
37 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
39 isl_seq_cpy(c, c + n, rem);
40 isl_seq_clr(c + rem, n);
43 /* Drop n dimensions starting at first.
45 * In principle, this frees up some extra variables as the number
46 * of columns remains constant, but we would have to extend
47 * the div array too as the number of rows in this array is assumed
48 * to be equal to extra.
50 struct isl_basic_set *isl_basic_set_drop_dims(
51 struct isl_basic_set *bset, unsigned first, unsigned n)
58 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
63 bset = isl_basic_set_cow(bset);
67 for (i = 0; i < bset->n_eq; ++i)
68 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
69 (bset->dim->n_out-first-n)+bset->extra);
71 for (i = 0; i < bset->n_ineq; ++i)
72 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
73 (bset->dim->n_out-first-n)+bset->extra);
75 for (i = 0; i < bset->n_div; ++i)
76 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
77 (bset->dim->n_out-first-n)+bset->extra);
79 bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
83 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
84 bset = isl_basic_set_simplify(bset);
85 return isl_basic_set_finalize(bset);
87 isl_basic_set_free(bset);
91 struct isl_set *isl_set_drop_dims(
92 struct isl_set *set, unsigned first, unsigned n)
99 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
103 set = isl_set_cow(set);
106 set->dim = isl_dim_drop_outputs(set->dim, first, n);
110 for (i = 0; i < set->n; ++i) {
111 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
116 ISL_F_CLR(set, ISL_SET_NORMALIZED);
123 /* Move "n" divs starting at "first" to the end of the list of divs.
125 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
126 unsigned first, unsigned n)
131 if (first + n == bmap->n_div)
134 div = isl_alloc_array(bmap->ctx, isl_int *, n);
137 for (i = 0; i < n; ++i)
138 div[i] = bmap->div[first + i];
139 for (i = 0; i < bmap->n_div - first - n; ++i)
140 bmap->div[first + i] = bmap->div[first + n + i];
141 for (i = 0; i < n; ++i)
142 bmap->div[bmap->n_div - n + i] = div[i];
146 isl_basic_map_free(bmap);
150 /* Drop "n" dimensions of type "type" starting at "first".
152 * In principle, this frees up some extra variables as the number
153 * of columns remains constant, but we would have to extend
154 * the div array too as the number of rows in this array is assumed
155 * to be equal to extra.
157 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
158 enum isl_dim_type type, unsigned first, unsigned n)
168 dim = isl_basic_map_dim(bmap, type);
169 isl_assert(bmap->ctx, first + n <= dim, goto error);
174 bmap = isl_basic_map_cow(bmap);
178 offset = isl_basic_map_offset(bmap, type) + first;
179 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
180 for (i = 0; i < bmap->n_eq; ++i)
181 constraint_drop_vars(bmap->eq[i]+offset, n, left);
183 for (i = 0; i < bmap->n_ineq; ++i)
184 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
186 for (i = 0; i < bmap->n_div; ++i)
187 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
189 if (type == isl_dim_div) {
190 bmap = move_divs_last(bmap, first, n);
193 isl_basic_map_free_div(bmap, n);
195 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
199 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
200 bmap = isl_basic_map_simplify(bmap);
201 return isl_basic_map_finalize(bmap);
203 isl_basic_map_free(bmap);
207 struct isl_basic_map *isl_basic_map_drop_inputs(
208 struct isl_basic_map *bmap, unsigned first, unsigned n)
210 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
213 struct isl_map *isl_map_drop(struct isl_map *map,
214 enum isl_dim_type type, unsigned first, unsigned n)
221 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
225 map = isl_map_cow(map);
228 map->dim = isl_dim_drop(map->dim, type, first, n);
232 for (i = 0; i < map->n; ++i) {
233 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
237 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
245 struct isl_map *isl_map_drop_inputs(
246 struct isl_map *map, unsigned first, unsigned n)
248 return isl_map_drop(map, isl_dim_in, first, n);
252 * We don't cow, as the div is assumed to be redundant.
254 static struct isl_basic_map *isl_basic_map_drop_div(
255 struct isl_basic_map *bmap, unsigned div)
263 pos = 1 + isl_dim_total(bmap->dim) + div;
265 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
267 for (i = 0; i < bmap->n_eq; ++i)
268 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
270 for (i = 0; i < bmap->n_ineq; ++i) {
271 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
272 isl_basic_map_drop_inequality(bmap, i);
276 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
279 for (i = 0; i < bmap->n_div; ++i)
280 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
282 if (div != bmap->n_div - 1) {
284 isl_int *t = bmap->div[div];
286 for (j = div; j < bmap->n_div - 1; ++j)
287 bmap->div[j] = bmap->div[j+1];
289 bmap->div[bmap->n_div - 1] = t;
291 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
292 isl_basic_map_free_div(bmap, 1);
296 isl_basic_map_free(bmap);
300 struct isl_basic_map *isl_basic_map_normalize_constraints(
301 struct isl_basic_map *bmap)
305 unsigned total = isl_basic_map_total_dim(bmap);
308 for (i = bmap->n_eq - 1; i >= 0; --i) {
309 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
310 if (isl_int_is_zero(gcd)) {
311 if (!isl_int_is_zero(bmap->eq[i][0])) {
312 bmap = isl_basic_map_set_to_empty(bmap);
315 isl_basic_map_drop_equality(bmap, i);
318 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
319 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
320 if (isl_int_is_one(gcd))
322 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
323 bmap = isl_basic_map_set_to_empty(bmap);
326 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
329 for (i = bmap->n_ineq - 1; i >= 0; --i) {
330 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
331 if (isl_int_is_zero(gcd)) {
332 if (isl_int_is_neg(bmap->ineq[i][0])) {
333 bmap = isl_basic_map_set_to_empty(bmap);
336 isl_basic_map_drop_inequality(bmap, i);
339 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
340 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
341 if (isl_int_is_one(gcd))
343 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
344 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
351 struct isl_basic_set *isl_basic_set_normalize_constraints(
352 struct isl_basic_set *bset)
354 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
355 (struct isl_basic_map *)bset);
358 /* Assumes divs have been ordered if keep_divs is set.
360 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
361 unsigned pos, isl_int *eq, int keep_divs, int *progress)
367 total = isl_basic_map_total_dim(bmap);
368 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
370 for (k = 0; k < bmap->n_eq; ++k) {
371 if (bmap->eq[k] == eq)
373 if (isl_int_is_zero(bmap->eq[k][1+pos]))
377 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
380 for (k = 0; k < bmap->n_ineq; ++k) {
381 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
385 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
386 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
389 for (k = 0; k < bmap->n_div; ++k) {
390 if (isl_int_is_zero(bmap->div[k][0]))
392 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
396 /* We need to be careful about circular definitions,
397 * so for now we just remove the definition of div k
398 * if the equality contains any divs.
399 * If keep_divs is set, then the divs have been ordered
400 * and we can keep the definition as long as the result
403 if (last_div == -1 || (keep_divs && last_div < k))
404 isl_seq_elim(bmap->div[k]+1, eq,
405 1+pos, 1+total, &bmap->div[k][0]);
407 isl_seq_clr(bmap->div[k], 1 + total);
408 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
412 /* Assumes divs have been ordered if keep_divs is set.
414 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
415 unsigned div, int keep_divs)
417 unsigned pos = isl_dim_total(bmap->dim) + div;
419 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
421 isl_basic_map_drop_div(bmap, div);
424 /* Elimininate divs based on equalities
426 static struct isl_basic_map *eliminate_divs_eq(
427 struct isl_basic_map *bmap, int *progress)
434 bmap = isl_basic_map_order_divs(bmap);
439 off = 1 + isl_dim_total(bmap->dim);
441 for (d = bmap->n_div - 1; d >= 0 ; --d) {
442 for (i = 0; i < bmap->n_eq; ++i) {
443 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
444 !isl_int_is_negone(bmap->eq[i][off + d]))
448 eliminate_div(bmap, bmap->eq[i], d, 1);
449 isl_basic_map_drop_equality(bmap, i);
454 return eliminate_divs_eq(bmap, progress);
458 /* Elimininate divs based on inequalities
460 static struct isl_basic_map *eliminate_divs_ineq(
461 struct isl_basic_map *bmap, int *progress)
472 off = 1 + isl_dim_total(bmap->dim);
474 for (d = bmap->n_div - 1; d >= 0 ; --d) {
475 for (i = 0; i < bmap->n_eq; ++i)
476 if (!isl_int_is_zero(bmap->eq[i][off + d]))
480 for (i = 0; i < bmap->n_ineq; ++i)
481 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
483 if (i < bmap->n_ineq)
486 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
487 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
489 bmap = isl_basic_map_drop_div(bmap, d);
496 struct isl_basic_map *isl_basic_map_gauss(
497 struct isl_basic_map *bmap, int *progress)
505 bmap = isl_basic_map_order_divs(bmap);
510 total = isl_basic_map_total_dim(bmap);
511 total_var = total - bmap->n_div;
513 last_var = total - 1;
514 for (done = 0; done < bmap->n_eq; ++done) {
515 for (; last_var >= 0; --last_var) {
516 for (k = done; k < bmap->n_eq; ++k)
517 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
525 swap_equality(bmap, k, done);
526 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
527 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
529 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
532 if (last_var >= total_var &&
533 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
534 unsigned div = last_var - total_var;
535 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
536 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
537 isl_int_set(bmap->div[div][0],
538 bmap->eq[done][1+last_var]);
539 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
542 if (done == bmap->n_eq)
544 for (k = done; k < bmap->n_eq; ++k) {
545 if (isl_int_is_zero(bmap->eq[k][0]))
547 return isl_basic_map_set_to_empty(bmap);
549 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
553 struct isl_basic_set *isl_basic_set_gauss(
554 struct isl_basic_set *bset, int *progress)
556 return (struct isl_basic_set*)isl_basic_map_gauss(
557 (struct isl_basic_map *)bset, progress);
561 static unsigned int round_up(unsigned int v)
572 static int hash_index(isl_int ***index, unsigned int size, int bits,
573 struct isl_basic_map *bmap, int k)
576 unsigned total = isl_basic_map_total_dim(bmap);
577 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
578 for (h = hash; index[h]; h = (h+1) % size)
579 if (&bmap->ineq[k] != index[h] &&
580 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
585 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
586 struct isl_basic_set *bset, int k)
588 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
591 /* If we can eliminate more than one div, then we need to make
592 * sure we do it from last div to first div, in order not to
593 * change the position of the other divs that still need to
596 static struct isl_basic_map *remove_duplicate_divs(
597 struct isl_basic_map *bmap, int *progress)
605 unsigned total_var = isl_dim_total(bmap->dim);
606 unsigned total = total_var + bmap->n_div;
609 if (bmap->n_div <= 1)
613 for (k = bmap->n_div - 1; k >= 0; --k)
614 if (!isl_int_is_zero(bmap->div[k][0]))
619 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
620 size = round_up(4 * bmap->n_div / 3 - 1);
621 bits = ffs(size) - 1;
622 index = isl_calloc_array(ctx, int, size);
625 eq = isl_blk_alloc(ctx, 1+total);
626 if (isl_blk_is_error(eq))
629 isl_seq_clr(eq.data, 1+total);
630 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
631 for (--k; k >= 0; --k) {
634 if (isl_int_is_zero(bmap->div[k][0]))
637 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
638 for (h = hash; index[h]; h = (h+1) % size)
639 if (isl_seq_eq(bmap->div[k],
640 bmap->div[index[h]-1], 2+total))
649 for (l = bmap->n_div - 1; l >= 0; --l) {
653 isl_int_set_si(eq.data[1+total_var+k], -1);
654 isl_int_set_si(eq.data[1+total_var+l], 1);
655 eliminate_div(bmap, eq.data, l, 0);
656 isl_int_set_si(eq.data[1+total_var+k], 0);
657 isl_int_set_si(eq.data[1+total_var+l], 0);
660 isl_blk_free(ctx, eq);
667 static int n_pure_div_eq(struct isl_basic_map *bmap)
672 total = isl_dim_total(bmap->dim);
673 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
674 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
678 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
684 /* Normalize divs that appear in equalities.
686 * In particular, we assume that bmap contains some equalities
691 * and we want to replace the set of e_i by a minimal set and
692 * such that the new e_i have a canonical representation in terms
694 * If any of the equalities involves more than one divs, then
695 * we currently simply bail out.
697 * Let us first additionally assume that all equalities involve
698 * a div. The equalities then express modulo constraints on the
699 * remaining variables and we can use "parameter compression"
700 * to find a minimal set of constraints. The result is a transformation
702 * x = T(x') = x_0 + G x'
704 * with G a lower-triangular matrix with all elements below the diagonal
705 * non-negative and smaller than the diagonal element on the same row.
706 * We first normalize x_0 by making the same property hold in the affine
708 * The rows i of G with a 1 on the diagonal do not impose any modulo
709 * constraint and simply express x_i = x'_i.
710 * For each of the remaining rows i, we introduce a div and a corresponding
711 * equality. In particular
713 * g_ii e_j = x_i - g_i(x')
715 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
716 * corresponding div (if g_kk != 1).
718 * If there are any equalities not involving any div, then we
719 * first apply a variable compression on the variables x:
721 * x = C x'' x'' = C_2 x
723 * and perform the above parameter compression on A C instead of on A.
724 * The resulting compression is then of the form
726 * x'' = T(x') = x_0 + G x'
728 * and in constructing the new divs and the corresponding equalities,
729 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
730 * by the corresponding row from C_2.
732 static struct isl_basic_map *normalize_divs(
733 struct isl_basic_map *bmap, int *progress)
740 struct isl_mat *T = NULL;
741 struct isl_mat *C = NULL;
742 struct isl_mat *C2 = NULL;
750 if (bmap->n_div == 0)
756 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
759 total = isl_dim_total(bmap->dim);
760 div_eq = n_pure_div_eq(bmap);
764 if (div_eq < bmap->n_eq) {
765 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
766 bmap->n_eq - div_eq, 0, 1 + total);
767 C = isl_mat_variable_compression(B, &C2);
771 bmap = isl_basic_map_set_to_empty(bmap);
778 d = isl_vec_alloc(bmap->ctx, div_eq);
781 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
782 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
784 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
786 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
789 B = isl_mat_product(B, C);
793 T = isl_mat_parameter_compression(B, d);
797 bmap = isl_basic_map_set_to_empty(bmap);
803 for (i = 0; i < T->n_row - 1; ++i) {
804 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
805 if (isl_int_is_zero(v))
807 isl_mat_col_submul(T, 0, v, 1 + i);
810 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
811 /* We have to be careful because dropping equalities may reorder them */
813 for (j = bmap->n_div - 1; j >= 0; --j) {
814 for (i = 0; i < bmap->n_eq; ++i)
815 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
817 if (i < bmap->n_eq) {
818 bmap = isl_basic_map_drop_div(bmap, j);
819 isl_basic_map_drop_equality(bmap, i);
825 for (i = 1; i < T->n_row; ++i) {
826 if (isl_int_is_one(T->row[i][i]))
831 if (needed > dropped) {
832 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
837 for (i = 1; i < T->n_row; ++i) {
838 if (isl_int_is_one(T->row[i][i]))
840 k = isl_basic_map_alloc_div(bmap);
841 pos[i] = 1 + total + k;
842 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
843 isl_int_set(bmap->div[k][0], T->row[i][i]);
845 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
847 isl_int_set_si(bmap->div[k][1 + i], 1);
848 for (j = 0; j < i; ++j) {
849 if (isl_int_is_zero(T->row[i][j]))
851 if (pos[j] < T->n_row && C2)
852 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
853 C2->row[pos[j]], 1 + total);
855 isl_int_neg(bmap->div[k][1 + pos[j]],
858 j = isl_basic_map_alloc_equality(bmap);
859 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
860 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
869 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
879 static struct isl_basic_map *set_div_from_lower_bound(
880 struct isl_basic_map *bmap, int div, int ineq)
882 unsigned total = 1 + isl_dim_total(bmap->dim);
884 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
885 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
886 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
887 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
888 isl_int_set_si(bmap->div[div][1 + total + div], 0);
893 /* Check whether it is ok to define a div based on an inequality.
894 * To avoid the introduction of circular definitions of divs, we
895 * do not allow such a definition if the resulting expression would refer to
896 * any other undefined divs or if any known div is defined in
897 * terms of the unknown div.
899 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
903 unsigned total = 1 + isl_dim_total(bmap->dim);
905 /* Not defined in terms of unknown divs */
906 for (j = 0; j < bmap->n_div; ++j) {
909 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
911 if (isl_int_is_zero(bmap->div[j][0]))
915 /* No other div defined in terms of this one => avoid loops */
916 for (j = 0; j < bmap->n_div; ++j) {
919 if (isl_int_is_zero(bmap->div[j][0]))
921 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
928 /* Given two constraints "k" and "l" that are opposite to each other,
929 * except for the constant term, check if we can use them
930 * to obtain an expression for one of the hitherto unknown divs.
931 * "sum" is the sum of the constant terms of the constraints.
932 * If this sum is strictly smaller than the coefficient of one
933 * of the divs, then this pair can be used define the div.
934 * To avoid the introduction of circular definitions of divs, we
935 * do not use the pair if the resulting expression would refer to
936 * any other undefined divs or if any known div is defined in
937 * terms of the unknown div.
939 static struct isl_basic_map *check_for_div_constraints(
940 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
943 unsigned total = 1 + isl_dim_total(bmap->dim);
945 for (i = 0; i < bmap->n_div; ++i) {
946 if (!isl_int_is_zero(bmap->div[i][0]))
948 if (isl_int_is_zero(bmap->ineq[k][total + i]))
950 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
952 if (!ok_to_set_div_from_bound(bmap, i, k))
954 if (isl_int_is_pos(bmap->ineq[k][total + i]))
955 bmap = set_div_from_lower_bound(bmap, i, k);
957 bmap = set_div_from_lower_bound(bmap, i, l);
965 static struct isl_basic_map *remove_duplicate_constraints(
966 struct isl_basic_map *bmap, int *progress)
972 unsigned total = isl_basic_map_total_dim(bmap);
975 if (bmap->n_ineq <= 1)
978 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
979 bits = ffs(size) - 1;
980 index = isl_calloc_array(ctx, isl_int **, size);
984 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
985 for (k = 1; k < bmap->n_ineq; ++k) {
986 h = hash_index(index, size, bits, bmap, k);
988 index[h] = &bmap->ineq[k];
993 l = index[h] - &bmap->ineq[0];
994 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
995 swap_inequality(bmap, k, l);
996 isl_basic_map_drop_inequality(bmap, k);
1000 for (k = 0; k < bmap->n_ineq-1; ++k) {
1001 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1002 h = hash_index(index, size, bits, bmap, k);
1003 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1006 l = index[h] - &bmap->ineq[0];
1007 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1008 if (isl_int_is_pos(sum)) {
1009 bmap = check_for_div_constraints(bmap, k, l, sum,
1013 if (isl_int_is_zero(sum)) {
1014 /* We need to break out of the loop after these
1015 * changes since the contents of the hash
1016 * will no longer be valid.
1017 * Plus, we probably we want to regauss first.
1021 isl_basic_map_drop_inequality(bmap, l);
1022 isl_basic_map_inequality_to_equality(bmap, k);
1024 bmap = isl_basic_map_set_to_empty(bmap);
1034 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1041 bmap = isl_basic_map_normalize_constraints(bmap);
1042 bmap = remove_duplicate_divs(bmap, &progress);
1043 bmap = eliminate_divs_eq(bmap, &progress);
1044 bmap = eliminate_divs_ineq(bmap, &progress);
1045 bmap = isl_basic_map_gauss(bmap, &progress);
1046 /* requires equalities in normal form */
1047 bmap = normalize_divs(bmap, &progress);
1048 bmap = remove_duplicate_constraints(bmap, &progress);
1053 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1055 return (struct isl_basic_set *)
1056 isl_basic_map_simplify((struct isl_basic_map *)bset);
1060 /* If the only constraints a div d=floor(f/m)
1061 * appears in are its two defining constraints
1064 * -(f - (m - 1)) + m d >= 0
1066 * then it can safely be removed.
1068 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1071 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1073 for (i = 0; i < bmap->n_eq; ++i)
1074 if (!isl_int_is_zero(bmap->eq[i][pos]))
1077 for (i = 0; i < bmap->n_ineq; ++i) {
1078 if (isl_int_is_zero(bmap->ineq[i][pos]))
1080 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1082 isl_int_sub(bmap->div[div][1],
1083 bmap->div[div][1], bmap->div[div][0]);
1084 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1085 neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
1086 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1087 isl_int_add(bmap->div[div][1],
1088 bmap->div[div][1], bmap->div[div][0]);
1091 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1092 bmap->n_div-div-1) != -1)
1094 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1095 if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
1097 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1098 bmap->n_div-div-1) != -1)
1104 for (i = 0; i < bmap->n_div; ++i)
1105 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1112 * Remove divs that don't occur in any of the constraints or other divs.
1113 * These can arise when dropping some of the variables in a quast
1114 * returned by piplib.
1116 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1123 for (i = bmap->n_div-1; i >= 0; --i) {
1124 if (!div_is_redundant(bmap, i))
1126 bmap = isl_basic_map_drop_div(bmap, i);
1131 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1133 bmap = remove_redundant_divs(bmap);
1136 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1140 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1142 return (struct isl_basic_set *)
1143 isl_basic_map_finalize((struct isl_basic_map *)bset);
1146 struct isl_set *isl_set_finalize(struct isl_set *set)
1152 for (i = 0; i < set->n; ++i) {
1153 set->p[i] = isl_basic_set_finalize(set->p[i]);
1163 struct isl_map *isl_map_finalize(struct isl_map *map)
1169 for (i = 0; i < map->n; ++i) {
1170 map->p[i] = isl_basic_map_finalize(map->p[i]);
1174 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1182 /* Remove definition of any div that is defined in terms of the given variable.
1183 * The div itself is not removed. Functions such as
1184 * eliminate_divs_ineq depend on the other divs remaining in place.
1186 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1191 for (i = 0; i < bmap->n_div; ++i) {
1192 if (isl_int_is_zero(bmap->div[i][0]))
1194 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1196 isl_int_set_si(bmap->div[i][0], 0);
1201 /* Eliminate the specified variables from the constraints using
1202 * Fourier-Motzkin. The variables themselves are not removed.
1204 struct isl_basic_map *isl_basic_map_eliminate_vars(
1205 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1215 total = isl_basic_map_total_dim(bmap);
1217 bmap = isl_basic_map_cow(bmap);
1218 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1219 bmap = remove_dependent_vars(bmap, d);
1221 for (d = pos + n - 1;
1222 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1223 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1224 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1225 int n_lower, n_upper;
1228 for (i = 0; i < bmap->n_eq; ++i) {
1229 if (isl_int_is_zero(bmap->eq[i][1+d]))
1231 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1232 isl_basic_map_drop_equality(bmap, i);
1239 for (i = 0; i < bmap->n_ineq; ++i) {
1240 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1242 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1245 bmap = isl_basic_map_extend_constraints(bmap,
1246 0, n_lower * n_upper);
1247 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1249 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1252 for (j = 0; j < i; ++j) {
1253 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1256 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1257 isl_int_sgn(bmap->ineq[j][1+d]))
1259 k = isl_basic_map_alloc_inequality(bmap);
1262 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1264 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1265 1+d, 1+total, NULL);
1267 isl_basic_map_drop_inequality(bmap, i);
1270 if (n_lower > 0 && n_upper > 0) {
1271 bmap = isl_basic_map_normalize_constraints(bmap);
1272 bmap = remove_duplicate_constraints(bmap, NULL);
1273 bmap = isl_basic_map_gauss(bmap, NULL);
1274 bmap = isl_basic_map_convex_hull(bmap);
1277 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1281 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1284 isl_basic_map_free(bmap);
1288 struct isl_basic_set *isl_basic_set_eliminate_vars(
1289 struct isl_basic_set *bset, unsigned pos, unsigned n)
1291 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1292 (struct isl_basic_map *)bset, pos, n);
1295 /* Don't assume equalities are in order, because align_divs
1296 * may have changed the order of the divs.
1298 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1303 total = isl_dim_total(bmap->dim);
1304 for (d = 0; d < total; ++d)
1306 for (i = 0; i < bmap->n_eq; ++i) {
1307 for (d = total - 1; d >= 0; --d) {
1308 if (isl_int_is_zero(bmap->eq[i][1+d]))
1316 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1318 compute_elimination_index((struct isl_basic_map *)bset, elim);
1321 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1322 struct isl_basic_map *bmap, int *elim)
1328 total = isl_dim_total(bmap->dim);
1329 for (d = total - 1; d >= 0; --d) {
1330 if (isl_int_is_zero(src[1+d]))
1335 isl_seq_cpy(dst, src, 1 + total);
1338 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1343 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1344 struct isl_basic_set *bset, int *elim)
1346 return reduced_using_equalities(dst, src,
1347 (struct isl_basic_map *)bset, elim);
1350 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1351 struct isl_basic_set *bset, struct isl_basic_set *context)
1356 if (!bset || !context)
1359 bset = isl_basic_set_cow(bset);
1363 elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1366 set_compute_elimination_index(context, elim);
1367 for (i = 0; i < bset->n_eq; ++i)
1368 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1370 for (i = 0; i < bset->n_ineq; ++i)
1371 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1373 isl_basic_set_free(context);
1375 bset = isl_basic_set_simplify(bset);
1376 bset = isl_basic_set_finalize(bset);
1379 isl_basic_set_free(bset);
1380 isl_basic_set_free(context);
1384 static struct isl_basic_set *remove_shifted_constraints(
1385 struct isl_basic_set *bset, struct isl_basic_set *context)
1395 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1396 bits = ffs(size) - 1;
1397 index = isl_calloc_array(ctx, isl_int **, size);
1401 for (k = 0; k < context->n_ineq; ++k) {
1402 h = set_hash_index(index, size, bits, context, k);
1403 index[h] = &context->ineq[k];
1405 for (k = 0; k < bset->n_ineq; ++k) {
1406 h = set_hash_index(index, size, bits, bset, k);
1409 l = index[h] - &context->ineq[0];
1410 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1412 bset = isl_basic_set_cow(bset);
1415 isl_basic_set_drop_inequality(bset, k);
1425 /* Tighten (decrease) the constant terms of the inequalities based
1426 * on the equalities, without removing any integer points.
1427 * For example, if there is an equality
1435 * then we want to replace the inequality by
1439 * We do this by computing a variable compression and translating
1440 * the constraints to the compressed space.
1441 * If any constraint has coefficients (except the contant term)
1442 * with a common factor "f", then we can replace the constant term "c"
1449 * f * floor(c/f) - c = -fract(c/f)
1451 * and we can add the same value to the original constraint.
1453 * In the example, the compressed space only contains "j",
1454 * and the inequality translates to
1458 * We add -fract(-1/3) = -2 to the original constraint to obtain
1462 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1463 struct isl_basic_set *bset)
1467 struct isl_mat *B, *C;
1473 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1479 bset = isl_basic_set_cow(bset);
1483 total = isl_basic_set_total_dim(bset);
1484 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1485 C = isl_mat_variable_compression(B, NULL);
1488 if (C->n_col == 0) {
1490 return isl_basic_set_set_to_empty(bset);
1492 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1493 0, bset->n_ineq, 0, 1 + total);
1494 C = isl_mat_product(B, C);
1499 for (i = 0; i < bset->n_ineq; ++i) {
1500 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1501 if (isl_int_is_one(gcd))
1503 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1504 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1513 /* Remove all information from bset that is redundant in the context
1514 * of context. In particular, equalities that are linear combinations
1515 * of those in context are removed. Then the inequalities that are
1516 * redundant in the context of the equalities and inequalities of
1517 * context are removed.
1519 * We first simplify the constraints of "bset" in the context of the
1520 * equalities of "context".
1521 * Then we simplify the inequalities of the context in the context
1522 * of the equalities of bset and remove the inequalities from "bset"
1523 * that are obviously redundant with respect to some inequality in "context".
1525 * If there are any inequalities left, we construct a tableau for
1526 * the context and then add the inequalities of "bset".
1527 * Before adding these equalities, we freeze all constraints such that
1528 * they won't be considered redundant in terms of the constraints of "bset".
1529 * Then we detect all equalities and redundant constraints (among the
1530 * constraints that weren't frozen) and update bset according to the results.
1531 * We have to be careful here because we don't want any of the context
1532 * constraints to remain and because we haven't added the equalities of "bset"
1533 * to the tableau so we temporarily have to pretend that there were no
1536 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1537 struct isl_basic_set *context)
1540 struct isl_tab *tab;
1541 unsigned context_ineq;
1542 struct isl_basic_set *combined = NULL;
1544 if (!context || !bset)
1547 if (context->n_eq > 0)
1548 bset = isl_basic_set_reduce_using_equalities(bset,
1549 isl_basic_set_copy(context));
1552 if (isl_basic_set_fast_is_empty(bset))
1557 if (bset->n_eq > 0) {
1558 struct isl_basic_set *affine_hull;
1559 affine_hull = isl_basic_set_copy(bset);
1560 affine_hull = isl_basic_set_cow(affine_hull);
1563 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1564 context = isl_basic_set_intersect(context, affine_hull);
1565 context = isl_basic_set_gauss(context, NULL);
1566 context = normalize_constraints_in_compressed_space(context);
1570 if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
1571 isl_basic_set_free(bset);
1574 if (!context->n_ineq)
1576 bset = remove_shifted_constraints(bset, context);
1579 isl_basic_set_free_equality(context, context->n_eq);
1580 context_ineq = context->n_ineq;
1581 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1582 combined = isl_basic_set_extend_constraints(combined,
1583 bset->n_eq, bset->n_ineq);
1584 tab = isl_tab_from_basic_set(combined);
1587 for (i = 0; i < context_ineq; ++i)
1588 if (isl_tab_freeze_constraint(tab, i) < 0)
1590 tab = isl_tab_extend(tab, bset->n_ineq);
1593 for (i = 0; i < bset->n_ineq; ++i)
1594 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1596 bset = isl_basic_set_add_constraints(combined, bset, 0);
1597 tab = isl_tab_detect_implicit_equalities(tab);
1598 if (isl_tab_detect_redundant(tab) < 0) {
1602 for (i = 0; i < context_ineq; ++i) {
1603 tab->con[i].is_zero = 0;
1604 tab->con[i].is_redundant = 1;
1606 bset = isl_basic_set_update_from_tab(bset, tab);
1608 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1609 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1611 bset = isl_basic_set_simplify(bset);
1612 bset = isl_basic_set_finalize(bset);
1613 isl_basic_set_free(context);
1616 isl_basic_set_free(combined);
1618 isl_basic_set_free(bset);
1619 isl_basic_set_free(context);
1623 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1624 * We simply add the equalities in context to bmap and then do a regular
1625 * div normalizations. Better results can be obtained by normalizing
1626 * only the divs in bmap than do not also appear in context.
1627 * We need to be careful to reduce the divs using the equalities
1628 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1629 * spurious constraints.
1631 static struct isl_basic_map *normalize_divs_in_context(
1632 struct isl_basic_map *bmap, struct isl_basic_map *context)
1635 unsigned total_context;
1638 div_eq = n_pure_div_eq(bmap);
1642 if (context->n_div > 0)
1643 bmap = isl_basic_map_align_divs(bmap, context);
1645 total_context = isl_basic_map_total_dim(context);
1646 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1647 for (i = 0; i < context->n_eq; ++i) {
1649 k = isl_basic_map_alloc_equality(bmap);
1650 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1651 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1652 isl_basic_map_total_dim(bmap) - total_context);
1654 bmap = isl_basic_map_gauss(bmap, NULL);
1655 bmap = normalize_divs(bmap, NULL);
1656 bmap = isl_basic_map_gauss(bmap, NULL);
1660 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1661 struct isl_basic_map *context)
1663 struct isl_basic_set *bset;
1665 if (!bmap || !context)
1668 if (isl_basic_map_is_universe(context)) {
1669 isl_basic_map_free(context);
1672 if (isl_basic_map_is_universe(bmap)) {
1673 isl_basic_map_free(context);
1676 if (isl_basic_map_fast_is_empty(context)) {
1677 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1678 isl_basic_map_free(context);
1679 isl_basic_map_free(bmap);
1680 return isl_basic_map_universe(dim);
1682 if (isl_basic_map_fast_is_empty(bmap)) {
1683 isl_basic_map_free(context);
1687 bmap = isl_basic_map_convex_hull(bmap);
1688 context = isl_basic_map_convex_hull(context);
1691 bmap = normalize_divs_in_context(bmap, context);
1693 context = isl_basic_map_align_divs(context, bmap);
1694 bmap = isl_basic_map_align_divs(bmap, context);
1696 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1697 isl_basic_map_underlying_set(context));
1699 return isl_basic_map_overlying_set(bset, bmap);
1701 isl_basic_map_free(bmap);
1702 isl_basic_map_free(context);
1707 * Assumes context has no implicit divs.
1709 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1713 if (!map || !context)
1716 if (isl_basic_map_is_universe(context)) {
1717 isl_basic_map_free(context);
1720 if (isl_basic_map_fast_is_empty(context)) {
1721 struct isl_dim *dim = isl_dim_copy(map->dim);
1722 isl_basic_map_free(context);
1724 return isl_map_universe(dim);
1727 context = isl_basic_map_convex_hull(context);
1728 map = isl_map_cow(map);
1729 if (!map || !context)
1731 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1732 map = isl_map_compute_divs(map);
1733 for (i = 0; i < map->n; ++i)
1734 context = isl_basic_map_align_divs(context, map->p[i]);
1735 for (i = 0; i < map->n; ++i) {
1736 map->p[i] = isl_basic_map_gist(map->p[i],
1737 isl_basic_map_copy(context));
1741 isl_basic_map_free(context);
1742 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1746 isl_basic_map_free(context);
1750 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1751 struct isl_basic_set *context)
1753 return (struct isl_basic_set *)isl_basic_map_gist(
1754 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1757 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1759 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1760 (struct isl_basic_map *)context);
1763 /* Quick check to see if two basic maps are disjoint.
1764 * In particular, we reduce the equalities and inequalities of
1765 * one basic map in the context of the equalities of the other
1766 * basic map and check if we get a contradiction.
1768 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1769 struct isl_basic_map *bmap2)
1771 struct isl_vec *v = NULL;
1776 if (!bmap1 || !bmap2)
1778 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1780 if (bmap1->n_div || bmap2->n_div)
1782 if (!bmap1->n_eq && !bmap2->n_eq)
1785 total = isl_dim_total(bmap1->dim);
1788 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1791 elim = isl_alloc_array(bmap1->ctx, int, total);
1794 compute_elimination_index(bmap1, elim);
1795 for (i = 0; i < bmap2->n_eq; ++i) {
1797 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1799 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1800 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1803 for (i = 0; i < bmap2->n_ineq; ++i) {
1805 reduced = reduced_using_equalities(v->block.data,
1806 bmap2->ineq[i], bmap1, elim);
1807 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1808 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1811 compute_elimination_index(bmap2, elim);
1812 for (i = 0; i < bmap1->n_ineq; ++i) {
1814 reduced = reduced_using_equalities(v->block.data,
1815 bmap1->ineq[i], bmap2, elim);
1816 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1817 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1833 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1834 struct isl_basic_set *bset2)
1836 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1837 (struct isl_basic_map *)bset2);
1840 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1847 if (isl_map_fast_is_equal(map1, map2))
1850 for (i = 0; i < map1->n; ++i) {
1851 for (j = 0; j < map2->n; ++j) {
1852 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1861 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1863 return isl_map_fast_is_disjoint((struct isl_map *)set1,
1864 (struct isl_map *)set2);
1867 /* Check if we can combine a given div with lower bound l and upper
1868 * bound u with some other div and if so return that other div.
1869 * Otherwise return -1.
1871 * We first check that
1872 * - the bounds are opposites of each other (except for the constant
1874 * - the bounds do not reference any other div
1875 * - no div is defined in terms of this div
1877 * Let m be the size of the range allowed on the div by the bounds.
1878 * That is, the bounds are of the form
1880 * e <= a <= e + m - 1
1882 * with e some expression in the other variables.
1883 * We look for another div b such that no third div is defined in terms
1884 * of this second div b and such that in any constraint that contains
1885 * a (except for the given lower and upper bound), also contains b
1886 * with a coefficient that is m times that of b.
1887 * That is, all constraints (execpt for the lower and upper bound)
1890 * e + f (a + m b) >= 0
1892 * If so, we return b so that "a + m b" can be replaced by
1893 * a single div "c = a + m b".
1895 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
1896 unsigned div, unsigned l, unsigned u)
1902 if (bmap->n_div <= 1)
1904 dim = isl_dim_total(bmap->dim);
1905 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
1907 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
1908 bmap->n_div - div - 1) != -1)
1910 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
1914 for (i = 0; i < bmap->n_div; ++i) {
1915 if (isl_int_is_zero(bmap->div[i][0]))
1917 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
1921 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1922 if (isl_int_is_neg(bmap->ineq[l][0])) {
1923 isl_int_sub(bmap->ineq[l][0],
1924 bmap->ineq[l][0], bmap->ineq[u][0]);
1925 bmap = isl_basic_map_copy(bmap);
1926 bmap = isl_basic_map_set_to_empty(bmap);
1927 isl_basic_map_free(bmap);
1930 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1931 for (i = 0; i < bmap->n_div; ++i) {
1936 for (j = 0; j < bmap->n_div; ++j) {
1937 if (isl_int_is_zero(bmap->div[j][0]))
1939 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
1942 if (j < bmap->n_div)
1944 for (j = 0; j < bmap->n_ineq; ++j) {
1946 if (j == l || j == u)
1948 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
1950 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
1952 isl_int_mul(bmap->ineq[j][1 + dim + div],
1953 bmap->ineq[j][1 + dim + div],
1955 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
1956 bmap->ineq[j][1 + dim + i]);
1957 isl_int_divexact(bmap->ineq[j][1 + dim + div],
1958 bmap->ineq[j][1 + dim + div],
1963 if (j < bmap->n_ineq)
1968 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1969 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1973 /* Given a lower and an upper bound on div i, construct an inequality
1974 * that when nonnegative ensures that this pair of bounds always allows
1975 * for an integer value of the given div.
1976 * The lower bound is inequality l, while the upper bound is inequality u.
1977 * The constructed inequality is stored in ineq.
1978 * g, fl, fu are temporary scalars.
1980 * Let the upper bound be
1984 * and the lower bound
1988 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
1991 * - f_u e_l <= f_u f_l g a <= f_l e_u
1993 * Since all variables are integer valued, this is equivalent to
1995 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
1997 * If this interval is at least f_u f_l g, then it contains at least
1998 * one integer value for a.
1999 * That is, the test constraint is
2001 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2003 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2004 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2007 dim = isl_dim_total(bmap->dim);
2009 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2010 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2011 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2012 isl_int_neg(fu, fu);
2013 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2014 1 + dim + bmap->n_div);
2015 isl_int_add(ineq[0], ineq[0], fl);
2016 isl_int_add(ineq[0], ineq[0], fu);
2017 isl_int_sub_ui(ineq[0], ineq[0], 1);
2018 isl_int_mul(g, g, fl);
2019 isl_int_mul(g, g, fu);
2020 isl_int_sub(ineq[0], ineq[0], g);
2023 /* Remove more kinds of divs that are not strictly needed.
2024 * In particular, if all pairs of lower and upper bounds on a div
2025 * are such that they allow at least one integer value of the div,
2026 * the we can eliminate the div using Fourier-Motzkin without
2027 * introducing any spurious solutions.
2029 static struct isl_basic_map *drop_more_redundant_divs(
2030 struct isl_basic_map *bmap, int *pairs, int n)
2032 struct isl_tab *tab = NULL;
2033 struct isl_vec *vec = NULL;
2045 dim = isl_dim_total(bmap->dim);
2046 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2050 tab = isl_tab_from_basic_map(bmap);
2055 enum isl_lp_result res;
2057 for (i = 0; i < bmap->n_div; ++i) {
2060 if (best >= 0 && pairs[best] <= pairs[i])
2066 for (l = 0; l < bmap->n_ineq; ++l) {
2067 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2069 for (u = 0; u < bmap->n_ineq; ++u) {
2070 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2072 construct_test_ineq(bmap, i, l, u,
2073 vec->el, g, fl, fu);
2074 res = isl_tab_min(tab, vec->el,
2075 bmap->ctx->one, &g, NULL, 0);
2076 if (res == isl_lp_error)
2078 if (res == isl_lp_empty) {
2079 bmap = isl_basic_map_set_to_empty(bmap);
2082 if (res != isl_lp_ok || isl_int_is_neg(g))
2085 if (u < bmap->n_ineq)
2088 if (l == bmap->n_ineq) {
2108 bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2109 return isl_basic_map_drop_redundant_divs(bmap);
2112 isl_basic_map_free(bmap);
2121 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2122 * and the upper bound u, div1 always occurs together with div2 in the form
2123 * (div1 + m div2), where m is the constant range on the variable div1
2124 * allowed by l and u, replace the pair div1 and div2 by a single
2125 * div that is equal to div1 + m div2.
2127 * The new div will appear in the location that contains div2.
2128 * We need to modify all constraints that contain
2129 * div2 = (div - div1) / m
2130 * (If a constraint does not contain div2, it will also not contain div1.)
2131 * If the constraint also contains div1, then we know they appear
2132 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2133 * i.e., the coefficient of div is f.
2135 * Otherwise, we first need to introduce div1 into the constraint.
2144 * A lower bound on div2
2148 * can be replaced by
2150 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2152 * with g = gcd(m,n).
2157 * can be replaced by
2159 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2161 * These constraint are those that we would obtain from eliminating
2162 * div1 using Fourier-Motzkin.
2164 * After all constraints have been modified, we drop the lower and upper
2165 * bound and then drop div1.
2167 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2168 unsigned div1, unsigned div2, unsigned l, unsigned u)
2173 unsigned dim, total;
2176 dim = isl_dim_total(bmap->dim);
2177 total = 1 + dim + bmap->n_div;
2182 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2183 isl_int_add_ui(m, m, 1);
2185 for (i = 0; i < bmap->n_ineq; ++i) {
2186 if (i == l || i == u)
2188 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2190 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2191 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2192 isl_int_divexact(a, m, b);
2193 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2194 if (isl_int_is_pos(b)) {
2195 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2196 b, bmap->ineq[l], total);
2199 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2200 b, bmap->ineq[u], total);
2203 isl_int_set(bmap->ineq[i][1 + dim + div2],
2204 bmap->ineq[i][1 + dim + div1]);
2205 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2212 isl_basic_map_drop_inequality(bmap, l);
2213 isl_basic_map_drop_inequality(bmap, u);
2215 isl_basic_map_drop_inequality(bmap, u);
2216 isl_basic_map_drop_inequality(bmap, l);
2218 bmap = isl_basic_map_drop_div(bmap, div1);
2222 /* First check if we can coalesce any pair of divs and
2223 * then continue with dropping more redundant divs.
2225 * We loop over all pairs of lower and upper bounds on a div
2226 * with coefficient 1 and -1, respectively, check if there
2227 * is any other div "c" with which we can coalesce the div
2228 * and if so, perform the coalescing.
2230 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2231 struct isl_basic_map *bmap, int *pairs, int n)
2236 dim = isl_dim_total(bmap->dim);
2238 for (i = 0; i < bmap->n_div; ++i) {
2241 for (l = 0; l < bmap->n_ineq; ++l) {
2242 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2244 for (u = 0; u < bmap->n_ineq; ++u) {
2247 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2249 c = div_find_coalesce(bmap, pairs, i, l, u);
2253 bmap = coalesce_divs(bmap, i, c, l, u);
2254 return isl_basic_map_drop_redundant_divs(bmap);
2259 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2262 return drop_more_redundant_divs(bmap, pairs, n);
2265 /* Remove divs that are not strictly needed.
2266 * In particular, if a div only occurs positively (or negatively)
2267 * in constraints, then it can simply be dropped.
2268 * Also, if a div occurs only occurs in two constraints and if moreover
2269 * those two constraints are opposite to each other, except for the constant
2270 * term and if the sum of the constant terms is such that for any value
2271 * of the other values, there is always at least one integer value of the
2272 * div, i.e., if one plus this sum is greater than or equal to
2273 * the (absolute value) of the coefficent of the div in the constraints,
2274 * then we can also simply drop the div.
2276 * If any divs are left after these simple checks then we move on
2277 * to more complicated cases in drop_more_redundant_divs.
2279 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2280 struct isl_basic_map *bmap)
2290 off = isl_dim_total(bmap->dim);
2291 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2295 for (i = 0; i < bmap->n_div; ++i) {
2297 int last_pos, last_neg;
2301 defined = !isl_int_is_zero(bmap->div[i][0]);
2302 for (j = 0; j < bmap->n_eq; ++j)
2303 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2309 for (j = 0; j < bmap->n_ineq; ++j) {
2310 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2314 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2319 pairs[i] = pos * neg;
2320 if (pairs[i] == 0) {
2321 for (j = bmap->n_ineq - 1; j >= 0; --j)
2322 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2323 isl_basic_map_drop_inequality(bmap, j);
2324 bmap = isl_basic_map_drop_div(bmap, i);
2326 return isl_basic_map_drop_redundant_divs(bmap);
2330 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2331 bmap->ineq[last_neg] + 1,
2335 isl_int_add(bmap->ineq[last_pos][0],
2336 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2337 isl_int_add_ui(bmap->ineq[last_pos][0],
2338 bmap->ineq[last_pos][0], 1);
2339 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2340 bmap->ineq[last_pos][1+off+i]);
2341 isl_int_sub_ui(bmap->ineq[last_pos][0],
2342 bmap->ineq[last_pos][0], 1);
2343 isl_int_sub(bmap->ineq[last_pos][0],
2344 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2347 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2352 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2353 bmap = isl_basic_map_simplify(bmap);
2355 return isl_basic_map_drop_redundant_divs(bmap);
2357 if (last_pos > last_neg) {
2358 isl_basic_map_drop_inequality(bmap, last_pos);
2359 isl_basic_map_drop_inequality(bmap, last_neg);
2361 isl_basic_map_drop_inequality(bmap, last_neg);
2362 isl_basic_map_drop_inequality(bmap, last_pos);
2364 bmap = isl_basic_map_drop_div(bmap, i);
2366 return isl_basic_map_drop_redundant_divs(bmap);
2370 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2376 isl_basic_map_free(bmap);
2380 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2381 struct isl_basic_set *bset)
2383 return (struct isl_basic_set *)
2384 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2387 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2393 for (i = 0; i < map->n; ++i) {
2394 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2398 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2405 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2407 return (struct isl_set *)
2408 isl_map_drop_redundant_divs((struct isl_map *)set);