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"
15 #include <isl_dim_private.h>
16 #include <isl_mat_private.h>
18 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
20 isl_int *t = bmap->eq[a];
21 bmap->eq[a] = bmap->eq[b];
25 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
28 isl_int *t = bmap->ineq[a];
29 bmap->ineq[a] = bmap->ineq[b];
34 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
36 swap_inequality((struct isl_basic_map *)bset, a, b);
39 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
41 isl_seq_cpy(c, c + n, rem);
42 isl_seq_clr(c + rem, n);
45 /* Drop n dimensions starting at first.
47 * In principle, this frees up some extra variables as the number
48 * of columns remains constant, but we would have to extend
49 * the div array too as the number of rows in this array is assumed
50 * to be equal to extra.
52 struct isl_basic_set *isl_basic_set_drop_dims(
53 struct isl_basic_set *bset, unsigned first, unsigned n)
60 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
62 if (n == 0 && !isl_dim_get_tuple_name(bset->dim, isl_dim_set))
65 bset = isl_basic_set_cow(bset);
69 for (i = 0; i < bset->n_eq; ++i)
70 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
71 (bset->dim->n_out-first-n)+bset->extra);
73 for (i = 0; i < bset->n_ineq; ++i)
74 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
75 (bset->dim->n_out-first-n)+bset->extra);
77 for (i = 0; i < bset->n_div; ++i)
78 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
79 (bset->dim->n_out-first-n)+bset->extra);
81 bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
85 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
86 bset = isl_basic_set_simplify(bset);
87 return isl_basic_set_finalize(bset);
89 isl_basic_set_free(bset);
93 struct isl_set *isl_set_drop_dims(
94 struct isl_set *set, unsigned first, unsigned n)
101 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
103 if (n == 0 && !isl_dim_get_tuple_name(set->dim, isl_dim_set))
105 set = isl_set_cow(set);
108 set->dim = isl_dim_drop_outputs(set->dim, first, n);
112 for (i = 0; i < set->n; ++i) {
113 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
118 ISL_F_CLR(set, ISL_SET_NORMALIZED);
125 /* Move "n" divs starting at "first" to the end of the list of divs.
127 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
128 unsigned first, unsigned n)
133 if (first + n == bmap->n_div)
136 div = isl_alloc_array(bmap->ctx, isl_int *, n);
139 for (i = 0; i < n; ++i)
140 div[i] = bmap->div[first + i];
141 for (i = 0; i < bmap->n_div - first - n; ++i)
142 bmap->div[first + i] = bmap->div[first + n + i];
143 for (i = 0; i < n; ++i)
144 bmap->div[bmap->n_div - n + i] = div[i];
148 isl_basic_map_free(bmap);
152 /* Drop "n" dimensions of type "type" starting at "first".
154 * In principle, this frees up some extra variables as the number
155 * of columns remains constant, but we would have to extend
156 * the div array too as the number of rows in this array is assumed
157 * to be equal to extra.
159 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
160 enum isl_dim_type type, unsigned first, unsigned n)
170 dim = isl_basic_map_dim(bmap, type);
171 isl_assert(bmap->ctx, first + n <= dim, goto error);
173 if (n == 0 && !isl_dim_get_tuple_name(bmap->dim, type))
176 bmap = isl_basic_map_cow(bmap);
180 offset = isl_basic_map_offset(bmap, type) + first;
181 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
182 for (i = 0; i < bmap->n_eq; ++i)
183 constraint_drop_vars(bmap->eq[i]+offset, n, left);
185 for (i = 0; i < bmap->n_ineq; ++i)
186 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
188 for (i = 0; i < bmap->n_div; ++i)
189 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
191 if (type == isl_dim_div) {
192 bmap = move_divs_last(bmap, first, n);
195 isl_basic_map_free_div(bmap, n);
197 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
201 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
202 bmap = isl_basic_map_simplify(bmap);
203 return isl_basic_map_finalize(bmap);
205 isl_basic_map_free(bmap);
209 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
210 enum isl_dim_type type, unsigned first, unsigned n)
212 return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
216 struct isl_basic_map *isl_basic_map_drop_inputs(
217 struct isl_basic_map *bmap, unsigned first, unsigned n)
219 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
222 struct isl_map *isl_map_drop(struct isl_map *map,
223 enum isl_dim_type type, unsigned first, unsigned n)
230 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
232 if (n == 0 && !isl_dim_get_tuple_name(map->dim, type))
234 map = isl_map_cow(map);
237 map->dim = isl_dim_drop(map->dim, type, first, n);
241 for (i = 0; i < map->n; ++i) {
242 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
246 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
254 struct isl_set *isl_set_drop(struct isl_set *set,
255 enum isl_dim_type type, unsigned first, unsigned n)
257 return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
260 struct isl_map *isl_map_drop_inputs(
261 struct isl_map *map, unsigned first, unsigned n)
263 return isl_map_drop(map, isl_dim_in, first, n);
267 * We don't cow, as the div is assumed to be redundant.
269 static struct isl_basic_map *isl_basic_map_drop_div(
270 struct isl_basic_map *bmap, unsigned div)
278 pos = 1 + isl_dim_total(bmap->dim) + div;
280 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
282 for (i = 0; i < bmap->n_eq; ++i)
283 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
285 for (i = 0; i < bmap->n_ineq; ++i) {
286 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
287 isl_basic_map_drop_inequality(bmap, i);
291 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
294 for (i = 0; i < bmap->n_div; ++i)
295 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
297 if (div != bmap->n_div - 1) {
299 isl_int *t = bmap->div[div];
301 for (j = div; j < bmap->n_div - 1; ++j)
302 bmap->div[j] = bmap->div[j+1];
304 bmap->div[bmap->n_div - 1] = t;
306 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
307 isl_basic_map_free_div(bmap, 1);
311 isl_basic_map_free(bmap);
315 struct isl_basic_map *isl_basic_map_normalize_constraints(
316 struct isl_basic_map *bmap)
320 unsigned total = isl_basic_map_total_dim(bmap);
326 for (i = bmap->n_eq - 1; i >= 0; --i) {
327 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
328 if (isl_int_is_zero(gcd)) {
329 if (!isl_int_is_zero(bmap->eq[i][0])) {
330 bmap = isl_basic_map_set_to_empty(bmap);
333 isl_basic_map_drop_equality(bmap, i);
336 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
337 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
338 if (isl_int_is_one(gcd))
340 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
341 bmap = isl_basic_map_set_to_empty(bmap);
344 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
347 for (i = bmap->n_ineq - 1; i >= 0; --i) {
348 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
349 if (isl_int_is_zero(gcd)) {
350 if (isl_int_is_neg(bmap->ineq[i][0])) {
351 bmap = isl_basic_map_set_to_empty(bmap);
354 isl_basic_map_drop_inequality(bmap, i);
357 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
358 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
359 if (isl_int_is_one(gcd))
361 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
362 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
369 struct isl_basic_set *isl_basic_set_normalize_constraints(
370 struct isl_basic_set *bset)
372 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
373 (struct isl_basic_map *)bset);
376 /* Assumes divs have been ordered if keep_divs is set.
378 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
379 unsigned pos, isl_int *eq, int keep_divs, int *progress)
385 total = isl_basic_map_total_dim(bmap);
386 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
388 for (k = 0; k < bmap->n_eq; ++k) {
389 if (bmap->eq[k] == eq)
391 if (isl_int_is_zero(bmap->eq[k][1+pos]))
395 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
398 for (k = 0; k < bmap->n_ineq; ++k) {
399 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
403 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
404 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
407 for (k = 0; k < bmap->n_div; ++k) {
408 if (isl_int_is_zero(bmap->div[k][0]))
410 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
414 /* We need to be careful about circular definitions,
415 * so for now we just remove the definition of div k
416 * if the equality contains any divs.
417 * If keep_divs is set, then the divs have been ordered
418 * and we can keep the definition as long as the result
421 if (last_div == -1 || (keep_divs && last_div < k))
422 isl_seq_elim(bmap->div[k]+1, eq,
423 1+pos, 1+total, &bmap->div[k][0]);
425 isl_seq_clr(bmap->div[k], 1 + total);
426 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
430 /* Assumes divs have been ordered if keep_divs is set.
432 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
433 unsigned div, int keep_divs)
435 unsigned pos = isl_dim_total(bmap->dim) + div;
437 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
439 isl_basic_map_drop_div(bmap, div);
442 /* Check if elimination of div "div" using equality "eq" would not
443 * result in a div depending on a later div.
445 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
450 unsigned pos = isl_dim_total(bmap->dim) + div;
452 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
454 if (last_div < 0 || last_div <= div)
457 for (k = 0; k <= last_div; ++k) {
458 if (isl_int_is_zero(bmap->div[k][0]))
460 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
467 /* Elimininate divs based on equalities
469 static struct isl_basic_map *eliminate_divs_eq(
470 struct isl_basic_map *bmap, int *progress)
477 bmap = isl_basic_map_order_divs(bmap);
482 off = 1 + isl_dim_total(bmap->dim);
484 for (d = bmap->n_div - 1; d >= 0 ; --d) {
485 for (i = 0; i < bmap->n_eq; ++i) {
486 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
487 !isl_int_is_negone(bmap->eq[i][off + d]))
489 if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
493 eliminate_div(bmap, bmap->eq[i], d, 1);
494 isl_basic_map_drop_equality(bmap, i);
499 return eliminate_divs_eq(bmap, progress);
503 /* Elimininate divs based on inequalities
505 static struct isl_basic_map *eliminate_divs_ineq(
506 struct isl_basic_map *bmap, int *progress)
517 off = 1 + isl_dim_total(bmap->dim);
519 for (d = bmap->n_div - 1; d >= 0 ; --d) {
520 for (i = 0; i < bmap->n_eq; ++i)
521 if (!isl_int_is_zero(bmap->eq[i][off + d]))
525 for (i = 0; i < bmap->n_ineq; ++i)
526 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
528 if (i < bmap->n_ineq)
531 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
532 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
534 bmap = isl_basic_map_drop_div(bmap, d);
541 struct isl_basic_map *isl_basic_map_gauss(
542 struct isl_basic_map *bmap, int *progress)
550 bmap = isl_basic_map_order_divs(bmap);
555 total = isl_basic_map_total_dim(bmap);
556 total_var = total - bmap->n_div;
558 last_var = total - 1;
559 for (done = 0; done < bmap->n_eq; ++done) {
560 for (; last_var >= 0; --last_var) {
561 for (k = done; k < bmap->n_eq; ++k)
562 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
570 swap_equality(bmap, k, done);
571 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
572 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
574 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
577 if (last_var >= total_var &&
578 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
579 unsigned div = last_var - total_var;
580 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
581 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
582 isl_int_set(bmap->div[div][0],
583 bmap->eq[done][1+last_var]);
584 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
587 if (done == bmap->n_eq)
589 for (k = done; k < bmap->n_eq; ++k) {
590 if (isl_int_is_zero(bmap->eq[k][0]))
592 return isl_basic_map_set_to_empty(bmap);
594 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
598 struct isl_basic_set *isl_basic_set_gauss(
599 struct isl_basic_set *bset, int *progress)
601 return (struct isl_basic_set*)isl_basic_map_gauss(
602 (struct isl_basic_map *)bset, progress);
606 static unsigned int round_up(unsigned int v)
617 static int hash_index(isl_int ***index, unsigned int size, int bits,
618 struct isl_basic_map *bmap, int k)
621 unsigned total = isl_basic_map_total_dim(bmap);
622 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
623 for (h = hash; index[h]; h = (h+1) % size)
624 if (&bmap->ineq[k] != index[h] &&
625 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
630 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
631 struct isl_basic_set *bset, int k)
633 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
636 /* If we can eliminate more than one div, then we need to make
637 * sure we do it from last div to first div, in order not to
638 * change the position of the other divs that still need to
641 static struct isl_basic_map *remove_duplicate_divs(
642 struct isl_basic_map *bmap, int *progress)
654 if (!bmap || bmap->n_div <= 1)
657 total_var = isl_dim_total(bmap->dim);
658 total = total_var + bmap->n_div;
661 for (k = bmap->n_div - 1; k >= 0; --k)
662 if (!isl_int_is_zero(bmap->div[k][0]))
667 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
668 size = round_up(4 * bmap->n_div / 3 - 1);
669 bits = ffs(size) - 1;
670 index = isl_calloc_array(ctx, int, size);
673 eq = isl_blk_alloc(ctx, 1+total);
674 if (isl_blk_is_error(eq))
677 isl_seq_clr(eq.data, 1+total);
678 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
679 for (--k; k >= 0; --k) {
682 if (isl_int_is_zero(bmap->div[k][0]))
685 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
686 for (h = hash; index[h]; h = (h+1) % size)
687 if (isl_seq_eq(bmap->div[k],
688 bmap->div[index[h]-1], 2+total))
697 for (l = bmap->n_div - 1; l >= 0; --l) {
701 isl_int_set_si(eq.data[1+total_var+k], -1);
702 isl_int_set_si(eq.data[1+total_var+l], 1);
703 eliminate_div(bmap, eq.data, l, 0);
704 isl_int_set_si(eq.data[1+total_var+k], 0);
705 isl_int_set_si(eq.data[1+total_var+l], 0);
708 isl_blk_free(ctx, eq);
715 static int n_pure_div_eq(struct isl_basic_map *bmap)
720 total = isl_dim_total(bmap->dim);
721 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
722 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
726 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
732 /* Normalize divs that appear in equalities.
734 * In particular, we assume that bmap contains some equalities
739 * and we want to replace the set of e_i by a minimal set and
740 * such that the new e_i have a canonical representation in terms
742 * If any of the equalities involves more than one divs, then
743 * we currently simply bail out.
745 * Let us first additionally assume that all equalities involve
746 * a div. The equalities then express modulo constraints on the
747 * remaining variables and we can use "parameter compression"
748 * to find a minimal set of constraints. The result is a transformation
750 * x = T(x') = x_0 + G x'
752 * with G a lower-triangular matrix with all elements below the diagonal
753 * non-negative and smaller than the diagonal element on the same row.
754 * We first normalize x_0 by making the same property hold in the affine
756 * The rows i of G with a 1 on the diagonal do not impose any modulo
757 * constraint and simply express x_i = x'_i.
758 * For each of the remaining rows i, we introduce a div and a corresponding
759 * equality. In particular
761 * g_ii e_j = x_i - g_i(x')
763 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
764 * corresponding div (if g_kk != 1).
766 * If there are any equalities not involving any div, then we
767 * first apply a variable compression on the variables x:
769 * x = C x'' x'' = C_2 x
771 * and perform the above parameter compression on A C instead of on A.
772 * The resulting compression is then of the form
774 * x'' = T(x') = x_0 + G x'
776 * and in constructing the new divs and the corresponding equalities,
777 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
778 * by the corresponding row from C_2.
780 static struct isl_basic_map *normalize_divs(
781 struct isl_basic_map *bmap, int *progress)
788 struct isl_mat *T = NULL;
789 struct isl_mat *C = NULL;
790 struct isl_mat *C2 = NULL;
798 if (bmap->n_div == 0)
804 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
807 total = isl_dim_total(bmap->dim);
808 div_eq = n_pure_div_eq(bmap);
812 if (div_eq < bmap->n_eq) {
813 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
814 bmap->n_eq - div_eq, 0, 1 + total);
815 C = isl_mat_variable_compression(B, &C2);
819 bmap = isl_basic_map_set_to_empty(bmap);
826 d = isl_vec_alloc(bmap->ctx, div_eq);
829 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
830 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
832 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
834 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
837 B = isl_mat_product(B, C);
841 T = isl_mat_parameter_compression(B, d);
845 bmap = isl_basic_map_set_to_empty(bmap);
851 for (i = 0; i < T->n_row - 1; ++i) {
852 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
853 if (isl_int_is_zero(v))
855 isl_mat_col_submul(T, 0, v, 1 + i);
858 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
861 /* We have to be careful because dropping equalities may reorder them */
863 for (j = bmap->n_div - 1; j >= 0; --j) {
864 for (i = 0; i < bmap->n_eq; ++i)
865 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
867 if (i < bmap->n_eq) {
868 bmap = isl_basic_map_drop_div(bmap, j);
869 isl_basic_map_drop_equality(bmap, i);
875 for (i = 1; i < T->n_row; ++i) {
876 if (isl_int_is_one(T->row[i][i]))
881 if (needed > dropped) {
882 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
887 for (i = 1; i < T->n_row; ++i) {
888 if (isl_int_is_one(T->row[i][i]))
890 k = isl_basic_map_alloc_div(bmap);
891 pos[i] = 1 + total + k;
892 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
893 isl_int_set(bmap->div[k][0], T->row[i][i]);
895 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
897 isl_int_set_si(bmap->div[k][1 + i], 1);
898 for (j = 0; j < i; ++j) {
899 if (isl_int_is_zero(T->row[i][j]))
901 if (pos[j] < T->n_row && C2)
902 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
903 C2->row[pos[j]], 1 + total);
905 isl_int_neg(bmap->div[k][1 + pos[j]],
908 j = isl_basic_map_alloc_equality(bmap);
909 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
910 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
919 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
929 static struct isl_basic_map *set_div_from_lower_bound(
930 struct isl_basic_map *bmap, int div, int ineq)
932 unsigned total = 1 + isl_dim_total(bmap->dim);
934 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
935 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
936 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
937 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
938 isl_int_set_si(bmap->div[div][1 + total + div], 0);
943 /* Check whether it is ok to define a div based on an inequality.
944 * To avoid the introduction of circular definitions of divs, we
945 * do not allow such a definition if the resulting expression would refer to
946 * any other undefined divs or if any known div is defined in
947 * terms of the unknown div.
949 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
953 unsigned total = 1 + isl_dim_total(bmap->dim);
955 /* Not defined in terms of unknown divs */
956 for (j = 0; j < bmap->n_div; ++j) {
959 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
961 if (isl_int_is_zero(bmap->div[j][0]))
965 /* No other div defined in terms of this one => avoid loops */
966 for (j = 0; j < bmap->n_div; ++j) {
969 if (isl_int_is_zero(bmap->div[j][0]))
971 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
978 /* Given two constraints "k" and "l" that are opposite to each other,
979 * except for the constant term, check if we can use them
980 * to obtain an expression for one of the hitherto unknown divs.
981 * "sum" is the sum of the constant terms of the constraints.
982 * If this sum is strictly smaller than the coefficient of one
983 * of the divs, then this pair can be used define the div.
984 * To avoid the introduction of circular definitions of divs, we
985 * do not use the pair if the resulting expression would refer to
986 * any other undefined divs or if any known div is defined in
987 * terms of the unknown div.
989 static struct isl_basic_map *check_for_div_constraints(
990 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
993 unsigned total = 1 + isl_dim_total(bmap->dim);
995 for (i = 0; i < bmap->n_div; ++i) {
996 if (!isl_int_is_zero(bmap->div[i][0]))
998 if (isl_int_is_zero(bmap->ineq[k][total + i]))
1000 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1002 if (!ok_to_set_div_from_bound(bmap, i, k))
1004 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1005 bmap = set_div_from_lower_bound(bmap, i, k);
1007 bmap = set_div_from_lower_bound(bmap, i, l);
1015 static struct isl_basic_map *remove_duplicate_constraints(
1016 struct isl_basic_map *bmap, int *progress)
1022 unsigned total = isl_basic_map_total_dim(bmap);
1025 if (!bmap || bmap->n_ineq <= 1)
1028 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1029 bits = ffs(size) - 1;
1030 index = isl_calloc_array(ctx, isl_int **, size);
1034 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1035 for (k = 1; k < bmap->n_ineq; ++k) {
1036 h = hash_index(index, size, bits, bmap, k);
1038 index[h] = &bmap->ineq[k];
1043 l = index[h] - &bmap->ineq[0];
1044 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1045 swap_inequality(bmap, k, l);
1046 isl_basic_map_drop_inequality(bmap, k);
1050 for (k = 0; k < bmap->n_ineq-1; ++k) {
1051 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1052 h = hash_index(index, size, bits, bmap, k);
1053 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1056 l = index[h] - &bmap->ineq[0];
1057 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1058 if (isl_int_is_pos(sum)) {
1059 bmap = check_for_div_constraints(bmap, k, l, sum,
1063 if (isl_int_is_zero(sum)) {
1064 /* We need to break out of the loop after these
1065 * changes since the contents of the hash
1066 * will no longer be valid.
1067 * Plus, we probably we want to regauss first.
1071 isl_basic_map_drop_inequality(bmap, l);
1072 isl_basic_map_inequality_to_equality(bmap, k);
1074 bmap = isl_basic_map_set_to_empty(bmap);
1084 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1091 bmap = isl_basic_map_normalize_constraints(bmap);
1092 bmap = remove_duplicate_divs(bmap, &progress);
1093 bmap = eliminate_divs_eq(bmap, &progress);
1094 bmap = eliminate_divs_ineq(bmap, &progress);
1095 bmap = isl_basic_map_gauss(bmap, &progress);
1096 /* requires equalities in normal form */
1097 bmap = normalize_divs(bmap, &progress);
1098 bmap = remove_duplicate_constraints(bmap, &progress);
1103 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1105 return (struct isl_basic_set *)
1106 isl_basic_map_simplify((struct isl_basic_map *)bset);
1110 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1111 isl_int *constraint, unsigned div)
1118 pos = 1 + isl_dim_total(bmap->dim) + div;
1120 if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1122 isl_int_sub(bmap->div[div][1],
1123 bmap->div[div][1], bmap->div[div][0]);
1124 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1125 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1126 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1127 isl_int_add(bmap->div[div][1],
1128 bmap->div[div][1], bmap->div[div][0]);
1131 if (isl_seq_first_non_zero(constraint+pos+1,
1132 bmap->n_div-div-1) != -1)
1134 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1135 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1137 if (isl_seq_first_non_zero(constraint+pos+1,
1138 bmap->n_div-div-1) != -1)
1147 /* If the only constraints a div d=floor(f/m)
1148 * appears in are its two defining constraints
1151 * -(f - (m - 1)) + m d >= 0
1153 * then it can safely be removed.
1155 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1158 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1160 for (i = 0; i < bmap->n_eq; ++i)
1161 if (!isl_int_is_zero(bmap->eq[i][pos]))
1164 for (i = 0; i < bmap->n_ineq; ++i) {
1165 if (isl_int_is_zero(bmap->ineq[i][pos]))
1167 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1171 for (i = 0; i < bmap->n_div; ++i)
1172 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1179 * Remove divs that don't occur in any of the constraints or other divs.
1180 * These can arise when dropping some of the variables in a quast
1181 * returned by piplib.
1183 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1190 for (i = bmap->n_div-1; i >= 0; --i) {
1191 if (!div_is_redundant(bmap, i))
1193 bmap = isl_basic_map_drop_div(bmap, i);
1198 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1200 bmap = remove_redundant_divs(bmap);
1203 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1207 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1209 return (struct isl_basic_set *)
1210 isl_basic_map_finalize((struct isl_basic_map *)bset);
1213 struct isl_set *isl_set_finalize(struct isl_set *set)
1219 for (i = 0; i < set->n; ++i) {
1220 set->p[i] = isl_basic_set_finalize(set->p[i]);
1230 struct isl_map *isl_map_finalize(struct isl_map *map)
1236 for (i = 0; i < map->n; ++i) {
1237 map->p[i] = isl_basic_map_finalize(map->p[i]);
1241 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1249 /* Remove definition of any div that is defined in terms of the given variable.
1250 * The div itself is not removed. Functions such as
1251 * eliminate_divs_ineq depend on the other divs remaining in place.
1253 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1258 for (i = 0; i < bmap->n_div; ++i) {
1259 if (isl_int_is_zero(bmap->div[i][0]))
1261 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1263 isl_int_set_si(bmap->div[i][0], 0);
1268 /* Eliminate the specified variables from the constraints using
1269 * Fourier-Motzkin. The variables themselves are not removed.
1271 struct isl_basic_map *isl_basic_map_eliminate_vars(
1272 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1282 total = isl_basic_map_total_dim(bmap);
1284 bmap = isl_basic_map_cow(bmap);
1285 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1286 bmap = remove_dependent_vars(bmap, d);
1288 for (d = pos + n - 1;
1289 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1290 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1291 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1292 int n_lower, n_upper;
1295 for (i = 0; i < bmap->n_eq; ++i) {
1296 if (isl_int_is_zero(bmap->eq[i][1+d]))
1298 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1299 isl_basic_map_drop_equality(bmap, i);
1306 for (i = 0; i < bmap->n_ineq; ++i) {
1307 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1309 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1312 bmap = isl_basic_map_extend_constraints(bmap,
1313 0, n_lower * n_upper);
1316 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1318 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1321 for (j = 0; j < i; ++j) {
1322 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1325 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1326 isl_int_sgn(bmap->ineq[j][1+d]))
1328 k = isl_basic_map_alloc_inequality(bmap);
1331 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1333 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1334 1+d, 1+total, NULL);
1336 isl_basic_map_drop_inequality(bmap, i);
1339 if (n_lower > 0 && n_upper > 0) {
1340 bmap = isl_basic_map_normalize_constraints(bmap);
1341 bmap = remove_duplicate_constraints(bmap, NULL);
1342 bmap = isl_basic_map_gauss(bmap, NULL);
1343 bmap = isl_basic_map_remove_redundancies(bmap);
1346 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1350 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1353 isl_basic_map_free(bmap);
1357 struct isl_basic_set *isl_basic_set_eliminate_vars(
1358 struct isl_basic_set *bset, unsigned pos, unsigned n)
1360 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1361 (struct isl_basic_map *)bset, pos, n);
1364 /* Don't assume equalities are in order, because align_divs
1365 * may have changed the order of the divs.
1367 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1372 total = isl_dim_total(bmap->dim);
1373 for (d = 0; d < total; ++d)
1375 for (i = 0; i < bmap->n_eq; ++i) {
1376 for (d = total - 1; d >= 0; --d) {
1377 if (isl_int_is_zero(bmap->eq[i][1+d]))
1385 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1387 compute_elimination_index((struct isl_basic_map *)bset, elim);
1390 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1391 struct isl_basic_map *bmap, int *elim)
1397 total = isl_dim_total(bmap->dim);
1398 for (d = total - 1; d >= 0; --d) {
1399 if (isl_int_is_zero(src[1+d]))
1404 isl_seq_cpy(dst, src, 1 + total);
1407 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1412 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1413 struct isl_basic_set *bset, int *elim)
1415 return reduced_using_equalities(dst, src,
1416 (struct isl_basic_map *)bset, elim);
1419 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1420 struct isl_basic_set *bset, struct isl_basic_set *context)
1425 if (!bset || !context)
1428 if (context->n_eq == 0) {
1429 isl_basic_set_free(context);
1433 bset = isl_basic_set_cow(bset);
1437 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1440 set_compute_elimination_index(context, elim);
1441 for (i = 0; i < bset->n_eq; ++i)
1442 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1444 for (i = 0; i < bset->n_ineq; ++i)
1445 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1447 isl_basic_set_free(context);
1449 bset = isl_basic_set_simplify(bset);
1450 bset = isl_basic_set_finalize(bset);
1453 isl_basic_set_free(bset);
1454 isl_basic_set_free(context);
1458 static struct isl_basic_set *remove_shifted_constraints(
1459 struct isl_basic_set *bset, struct isl_basic_set *context)
1469 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1470 bits = ffs(size) - 1;
1471 index = isl_calloc_array(ctx, isl_int **, size);
1475 for (k = 0; k < context->n_ineq; ++k) {
1476 h = set_hash_index(index, size, bits, context, k);
1477 index[h] = &context->ineq[k];
1479 for (k = 0; k < bset->n_ineq; ++k) {
1480 h = set_hash_index(index, size, bits, bset, k);
1483 l = index[h] - &context->ineq[0];
1484 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1486 bset = isl_basic_set_cow(bset);
1489 isl_basic_set_drop_inequality(bset, k);
1499 /* Tighten (decrease) the constant terms of the inequalities based
1500 * on the equalities, without removing any integer points.
1501 * For example, if there is an equality
1509 * then we want to replace the inequality by
1513 * We do this by computing a variable compression and translating
1514 * the constraints to the compressed space.
1515 * If any constraint has coefficients (except the contant term)
1516 * with a common factor "f", then we can replace the constant term "c"
1523 * f * floor(c/f) - c = -fract(c/f)
1525 * and we can add the same value to the original constraint.
1527 * In the example, the compressed space only contains "j",
1528 * and the inequality translates to
1532 * We add -fract(-1/3) = -2 to the original constraint to obtain
1536 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1537 struct isl_basic_set *bset)
1541 struct isl_mat *B, *C;
1547 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1553 bset = isl_basic_set_cow(bset);
1557 total = isl_basic_set_total_dim(bset);
1558 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1559 C = isl_mat_variable_compression(B, NULL);
1562 if (C->n_col == 0) {
1564 return isl_basic_set_set_to_empty(bset);
1566 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1567 0, bset->n_ineq, 0, 1 + total);
1568 C = isl_mat_product(B, C);
1573 for (i = 0; i < bset->n_ineq; ++i) {
1574 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1575 if (isl_int_is_one(gcd))
1577 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1578 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1587 /* Remove all information from bset that is redundant in the context
1588 * of context. Both bset and context are assumed to be full-dimensional.
1590 * We first * remove the inequalities from "bset"
1591 * that are obviously redundant with respect to some inequality in "context".
1593 * If there are any inequalities left, we construct a tableau for
1594 * the context and then add the inequalities of "bset".
1595 * Before adding these inequalities, we freeze all constraints such that
1596 * they won't be considered redundant in terms of the constraints of "bset".
1597 * Then we detect all redundant constraints (among the
1598 * constraints that weren't frozen), first by checking for redundancy in the
1599 * the tableau and then by checking if replacing a constraint by its negation
1600 * would lead to an empty set. This last step is fairly expensive
1601 * and could be optimized by more reuse of the tableau.
1602 * Finally, we update bset according to the results.
1604 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1605 __isl_take isl_basic_set *context)
1608 isl_basic_set *combined = NULL;
1609 struct isl_tab *tab = NULL;
1610 unsigned context_ineq;
1613 if (!bset || !context)
1616 if (isl_basic_set_is_universe(bset)) {
1617 isl_basic_set_free(context);
1621 if (isl_basic_set_is_universe(context)) {
1622 isl_basic_set_free(context);
1626 bset = remove_shifted_constraints(bset, context);
1629 if (bset->n_ineq == 0)
1632 context_ineq = context->n_ineq;
1633 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1634 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1635 tab = isl_tab_from_basic_set(combined);
1636 for (i = 0; i < context_ineq; ++i)
1637 if (isl_tab_freeze_constraint(tab, i) < 0)
1639 tab = isl_tab_extend(tab, bset->n_ineq);
1640 for (i = 0; i < bset->n_ineq; ++i)
1641 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1643 bset = isl_basic_set_add_constraints(combined, bset, 0);
1647 if (isl_tab_detect_redundant(tab) < 0)
1649 total = isl_basic_set_total_dim(bset);
1650 for (i = context_ineq; i < bset->n_ineq; ++i) {
1652 if (tab->con[i].is_redundant)
1654 tab->con[i].is_redundant = 1;
1655 combined = isl_basic_set_dup(bset);
1656 combined = isl_basic_set_update_from_tab(combined, tab);
1657 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1658 k = isl_basic_set_alloc_inequality(combined);
1661 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1662 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1663 is_empty = isl_basic_set_is_empty(combined);
1666 isl_basic_set_free(combined);
1669 tab->con[i].is_redundant = 0;
1671 for (i = 0; i < context_ineq; ++i)
1672 tab->con[i].is_redundant = 1;
1673 bset = isl_basic_set_update_from_tab(bset, tab);
1675 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1676 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1681 bset = isl_basic_set_simplify(bset);
1682 bset = isl_basic_set_finalize(bset);
1683 isl_basic_set_free(context);
1687 isl_basic_set_free(combined);
1688 isl_basic_set_free(context);
1689 isl_basic_set_free(bset);
1693 /* Remove all information from bset that is redundant in the context
1694 * of context. In particular, equalities that are linear combinations
1695 * of those in context are removed. Then the inequalities that are
1696 * redundant in the context of the equalities and inequalities of
1697 * context are removed.
1699 * We first compute the integer affine hull of the intersection,
1700 * compute the gist inside this affine hull and then add back
1701 * those equalities that are not implied by the context.
1703 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1704 __isl_take isl_basic_set *context)
1709 isl_basic_set *aff_context;
1712 if (!bset || !context)
1715 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1716 if (isl_basic_set_fast_is_empty(bset)) {
1717 isl_basic_set_free(context);
1720 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1723 if (isl_basic_set_fast_is_empty(aff)) {
1724 isl_basic_set_free(aff);
1725 isl_basic_set_free(context);
1728 if (aff->n_eq == 0) {
1729 isl_basic_set_free(aff);
1730 return uset_gist_full(bset, context);
1732 total = isl_basic_set_total_dim(bset);
1733 eq = isl_mat_sub_alloc(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1734 eq = isl_mat_cow(eq);
1735 T = isl_mat_variable_compression(eq, &T2);
1736 if (T && T->n_col == 0) {
1739 isl_basic_set_free(context);
1740 isl_basic_set_free(aff);
1741 return isl_basic_set_set_to_empty(bset);
1744 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1746 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1747 context = isl_basic_set_preimage(context, T);
1749 bset = uset_gist_full(bset, context);
1750 bset = isl_basic_set_preimage(bset, T2);
1751 bset = isl_basic_set_intersect(bset, aff);
1752 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1755 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1756 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1761 isl_basic_set_free(bset);
1762 isl_basic_set_free(context);
1766 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1767 * We simply add the equalities in context to bmap and then do a regular
1768 * div normalizations. Better results can be obtained by normalizing
1769 * only the divs in bmap than do not also appear in context.
1770 * We need to be careful to reduce the divs using the equalities
1771 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1772 * spurious constraints.
1774 static struct isl_basic_map *normalize_divs_in_context(
1775 struct isl_basic_map *bmap, struct isl_basic_map *context)
1778 unsigned total_context;
1781 div_eq = n_pure_div_eq(bmap);
1785 if (context->n_div > 0)
1786 bmap = isl_basic_map_align_divs(bmap, context);
1788 total_context = isl_basic_map_total_dim(context);
1789 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1790 for (i = 0; i < context->n_eq; ++i) {
1792 k = isl_basic_map_alloc_equality(bmap);
1793 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1794 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1795 isl_basic_map_total_dim(bmap) - total_context);
1797 bmap = isl_basic_map_gauss(bmap, NULL);
1798 bmap = normalize_divs(bmap, NULL);
1799 bmap = isl_basic_map_gauss(bmap, NULL);
1803 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1804 struct isl_basic_map *context)
1806 struct isl_basic_set *bset;
1808 if (!bmap || !context)
1811 if (isl_basic_map_is_universe(bmap)) {
1812 isl_basic_map_free(context);
1815 if (isl_basic_map_fast_is_empty(context)) {
1816 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1817 isl_basic_map_free(context);
1818 isl_basic_map_free(bmap);
1819 return isl_basic_map_universe(dim);
1821 if (isl_basic_map_fast_is_empty(bmap)) {
1822 isl_basic_map_free(context);
1826 bmap = isl_basic_map_remove_redundancies(bmap);
1827 context = isl_basic_map_remove_redundancies(context);
1830 bmap = normalize_divs_in_context(bmap, context);
1832 context = isl_basic_map_align_divs(context, bmap);
1833 bmap = isl_basic_map_align_divs(bmap, context);
1835 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1836 isl_basic_map_underlying_set(context));
1838 return isl_basic_map_overlying_set(bset, bmap);
1840 isl_basic_map_free(bmap);
1841 isl_basic_map_free(context);
1846 * Assumes context has no implicit divs.
1848 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1849 __isl_take isl_basic_map *context)
1853 if (!map || !context)
1856 if (isl_basic_map_fast_is_empty(context)) {
1857 struct isl_dim *dim = isl_dim_copy(map->dim);
1858 isl_basic_map_free(context);
1860 return isl_map_universe(dim);
1863 context = isl_basic_map_remove_redundancies(context);
1864 map = isl_map_cow(map);
1865 if (!map || !context)
1867 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1868 map = isl_map_compute_divs(map);
1869 for (i = 0; i < map->n; ++i)
1870 context = isl_basic_map_align_divs(context, map->p[i]);
1871 for (i = 0; i < map->n; ++i) {
1872 map->p[i] = isl_basic_map_gist(map->p[i],
1873 isl_basic_map_copy(context));
1877 isl_basic_map_free(context);
1878 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1882 isl_basic_map_free(context);
1886 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1887 __isl_take isl_map *context)
1889 return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1892 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1893 struct isl_basic_set *context)
1895 return (struct isl_basic_set *)isl_basic_map_gist(
1896 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1899 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1900 __isl_take isl_basic_set *context)
1902 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1903 (struct isl_basic_map *)context);
1906 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1907 __isl_take isl_set *context)
1909 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1910 (struct isl_map *)context);
1913 /* Quick check to see if two basic maps are disjoint.
1914 * In particular, we reduce the equalities and inequalities of
1915 * one basic map in the context of the equalities of the other
1916 * basic map and check if we get a contradiction.
1918 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1919 struct isl_basic_map *bmap2)
1921 struct isl_vec *v = NULL;
1926 if (!bmap1 || !bmap2)
1928 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1930 if (bmap1->n_div || bmap2->n_div)
1932 if (!bmap1->n_eq && !bmap2->n_eq)
1935 total = isl_dim_total(bmap1->dim);
1938 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1941 elim = isl_alloc_array(bmap1->ctx, int, total);
1944 compute_elimination_index(bmap1, elim);
1945 for (i = 0; i < bmap2->n_eq; ++i) {
1947 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1949 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1950 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1953 for (i = 0; i < bmap2->n_ineq; ++i) {
1955 reduced = reduced_using_equalities(v->block.data,
1956 bmap2->ineq[i], bmap1, elim);
1957 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1958 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1961 compute_elimination_index(bmap2, elim);
1962 for (i = 0; i < bmap1->n_ineq; ++i) {
1964 reduced = reduced_using_equalities(v->block.data,
1965 bmap1->ineq[i], bmap2, elim);
1966 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1967 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1983 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1984 struct isl_basic_set *bset2)
1986 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1987 (struct isl_basic_map *)bset2);
1990 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1997 if (isl_map_fast_is_equal(map1, map2))
2000 for (i = 0; i < map1->n; ++i) {
2001 for (j = 0; j < map2->n; ++j) {
2002 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
2011 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
2013 return isl_map_fast_is_disjoint((struct isl_map *)set1,
2014 (struct isl_map *)set2);
2017 /* Check if we can combine a given div with lower bound l and upper
2018 * bound u with some other div and if so return that other div.
2019 * Otherwise return -1.
2021 * We first check that
2022 * - the bounds are opposites of each other (except for the constant
2024 * - the bounds do not reference any other div
2025 * - no div is defined in terms of this div
2027 * Let m be the size of the range allowed on the div by the bounds.
2028 * That is, the bounds are of the form
2030 * e <= a <= e + m - 1
2032 * with e some expression in the other variables.
2033 * We look for another div b such that no third div is defined in terms
2034 * of this second div b and such that in any constraint that contains
2035 * a (except for the given lower and upper bound), also contains b
2036 * with a coefficient that is m times that of b.
2037 * That is, all constraints (execpt for the lower and upper bound)
2040 * e + f (a + m b) >= 0
2042 * If so, we return b so that "a + m b" can be replaced by
2043 * a single div "c = a + m b".
2045 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2046 unsigned div, unsigned l, unsigned u)
2052 if (bmap->n_div <= 1)
2054 dim = isl_dim_total(bmap->dim);
2055 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2057 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2058 bmap->n_div - div - 1) != -1)
2060 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2064 for (i = 0; i < bmap->n_div; ++i) {
2065 if (isl_int_is_zero(bmap->div[i][0]))
2067 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2071 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2072 if (isl_int_is_neg(bmap->ineq[l][0])) {
2073 isl_int_sub(bmap->ineq[l][0],
2074 bmap->ineq[l][0], bmap->ineq[u][0]);
2075 bmap = isl_basic_map_copy(bmap);
2076 bmap = isl_basic_map_set_to_empty(bmap);
2077 isl_basic_map_free(bmap);
2080 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2081 for (i = 0; i < bmap->n_div; ++i) {
2086 for (j = 0; j < bmap->n_div; ++j) {
2087 if (isl_int_is_zero(bmap->div[j][0]))
2089 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2092 if (j < bmap->n_div)
2094 for (j = 0; j < bmap->n_ineq; ++j) {
2096 if (j == l || j == u)
2098 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2100 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2102 isl_int_mul(bmap->ineq[j][1 + dim + div],
2103 bmap->ineq[j][1 + dim + div],
2105 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2106 bmap->ineq[j][1 + dim + i]);
2107 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2108 bmap->ineq[j][1 + dim + div],
2113 if (j < bmap->n_ineq)
2118 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2119 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2123 /* Given a lower and an upper bound on div i, construct an inequality
2124 * that when nonnegative ensures that this pair of bounds always allows
2125 * for an integer value of the given div.
2126 * The lower bound is inequality l, while the upper bound is inequality u.
2127 * The constructed inequality is stored in ineq.
2128 * g, fl, fu are temporary scalars.
2130 * Let the upper bound be
2134 * and the lower bound
2138 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2141 * - f_u e_l <= f_u f_l g a <= f_l e_u
2143 * Since all variables are integer valued, this is equivalent to
2145 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2147 * If this interval is at least f_u f_l g, then it contains at least
2148 * one integer value for a.
2149 * That is, the test constraint is
2151 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2153 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2154 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2157 dim = isl_dim_total(bmap->dim);
2159 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2160 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2161 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2162 isl_int_neg(fu, fu);
2163 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2164 1 + dim + bmap->n_div);
2165 isl_int_add(ineq[0], ineq[0], fl);
2166 isl_int_add(ineq[0], ineq[0], fu);
2167 isl_int_sub_ui(ineq[0], ineq[0], 1);
2168 isl_int_mul(g, g, fl);
2169 isl_int_mul(g, g, fu);
2170 isl_int_sub(ineq[0], ineq[0], g);
2173 /* Remove more kinds of divs that are not strictly needed.
2174 * In particular, if all pairs of lower and upper bounds on a div
2175 * are such that they allow at least one integer value of the div,
2176 * the we can eliminate the div using Fourier-Motzkin without
2177 * introducing any spurious solutions.
2179 static struct isl_basic_map *drop_more_redundant_divs(
2180 struct isl_basic_map *bmap, int *pairs, int n)
2182 struct isl_tab *tab = NULL;
2183 struct isl_vec *vec = NULL;
2195 dim = isl_dim_total(bmap->dim);
2196 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2200 tab = isl_tab_from_basic_map(bmap);
2205 enum isl_lp_result res;
2207 for (i = 0; i < bmap->n_div; ++i) {
2210 if (best >= 0 && pairs[best] <= pairs[i])
2216 for (l = 0; l < bmap->n_ineq; ++l) {
2217 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2219 for (u = 0; u < bmap->n_ineq; ++u) {
2220 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2222 construct_test_ineq(bmap, i, l, u,
2223 vec->el, g, fl, fu);
2224 res = isl_tab_min(tab, vec->el,
2225 bmap->ctx->one, &g, NULL, 0);
2226 if (res == isl_lp_error)
2228 if (res == isl_lp_empty) {
2229 bmap = isl_basic_map_set_to_empty(bmap);
2232 if (res != isl_lp_ok || isl_int_is_neg(g))
2235 if (u < bmap->n_ineq)
2238 if (l == bmap->n_ineq) {
2258 bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2259 return isl_basic_map_drop_redundant_divs(bmap);
2262 isl_basic_map_free(bmap);
2271 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2272 * and the upper bound u, div1 always occurs together with div2 in the form
2273 * (div1 + m div2), where m is the constant range on the variable div1
2274 * allowed by l and u, replace the pair div1 and div2 by a single
2275 * div that is equal to div1 + m div2.
2277 * The new div will appear in the location that contains div2.
2278 * We need to modify all constraints that contain
2279 * div2 = (div - div1) / m
2280 * (If a constraint does not contain div2, it will also not contain div1.)
2281 * If the constraint also contains div1, then we know they appear
2282 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2283 * i.e., the coefficient of div is f.
2285 * Otherwise, we first need to introduce div1 into the constraint.
2294 * A lower bound on div2
2298 * can be replaced by
2300 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2302 * with g = gcd(m,n).
2307 * can be replaced by
2309 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2311 * These constraint are those that we would obtain from eliminating
2312 * div1 using Fourier-Motzkin.
2314 * After all constraints have been modified, we drop the lower and upper
2315 * bound and then drop div1.
2317 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2318 unsigned div1, unsigned div2, unsigned l, unsigned u)
2323 unsigned dim, total;
2326 dim = isl_dim_total(bmap->dim);
2327 total = 1 + dim + bmap->n_div;
2332 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2333 isl_int_add_ui(m, m, 1);
2335 for (i = 0; i < bmap->n_ineq; ++i) {
2336 if (i == l || i == u)
2338 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2340 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2341 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2342 isl_int_divexact(a, m, b);
2343 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2344 if (isl_int_is_pos(b)) {
2345 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2346 b, bmap->ineq[l], total);
2349 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2350 b, bmap->ineq[u], total);
2353 isl_int_set(bmap->ineq[i][1 + dim + div2],
2354 bmap->ineq[i][1 + dim + div1]);
2355 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2362 isl_basic_map_drop_inequality(bmap, l);
2363 isl_basic_map_drop_inequality(bmap, u);
2365 isl_basic_map_drop_inequality(bmap, u);
2366 isl_basic_map_drop_inequality(bmap, l);
2368 bmap = isl_basic_map_drop_div(bmap, div1);
2372 /* First check if we can coalesce any pair of divs and
2373 * then continue with dropping more redundant divs.
2375 * We loop over all pairs of lower and upper bounds on a div
2376 * with coefficient 1 and -1, respectively, check if there
2377 * is any other div "c" with which we can coalesce the div
2378 * and if so, perform the coalescing.
2380 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2381 struct isl_basic_map *bmap, int *pairs, int n)
2386 dim = isl_dim_total(bmap->dim);
2388 for (i = 0; i < bmap->n_div; ++i) {
2391 for (l = 0; l < bmap->n_ineq; ++l) {
2392 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2394 for (u = 0; u < bmap->n_ineq; ++u) {
2397 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2399 c = div_find_coalesce(bmap, pairs, i, l, u);
2403 bmap = coalesce_divs(bmap, i, c, l, u);
2404 return isl_basic_map_drop_redundant_divs(bmap);
2409 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2412 return drop_more_redundant_divs(bmap, pairs, n);
2415 /* Remove divs that are not strictly needed.
2416 * In particular, if a div only occurs positively (or negatively)
2417 * in constraints, then it can simply be dropped.
2418 * Also, if a div occurs only occurs in two constraints and if moreover
2419 * those two constraints are opposite to each other, except for the constant
2420 * term and if the sum of the constant terms is such that for any value
2421 * of the other values, there is always at least one integer value of the
2422 * div, i.e., if one plus this sum is greater than or equal to
2423 * the (absolute value) of the coefficent of the div in the constraints,
2424 * then we can also simply drop the div.
2426 * If any divs are left after these simple checks then we move on
2427 * to more complicated cases in drop_more_redundant_divs.
2429 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2430 struct isl_basic_map *bmap)
2440 off = isl_dim_total(bmap->dim);
2441 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2445 for (i = 0; i < bmap->n_div; ++i) {
2447 int last_pos, last_neg;
2451 defined = !isl_int_is_zero(bmap->div[i][0]);
2452 for (j = 0; j < bmap->n_eq; ++j)
2453 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2459 for (j = 0; j < bmap->n_ineq; ++j) {
2460 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2464 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2469 pairs[i] = pos * neg;
2470 if (pairs[i] == 0) {
2471 for (j = bmap->n_ineq - 1; j >= 0; --j)
2472 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2473 isl_basic_map_drop_inequality(bmap, j);
2474 bmap = isl_basic_map_drop_div(bmap, i);
2476 return isl_basic_map_drop_redundant_divs(bmap);
2480 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2481 bmap->ineq[last_neg] + 1,
2485 isl_int_add(bmap->ineq[last_pos][0],
2486 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2487 isl_int_add_ui(bmap->ineq[last_pos][0],
2488 bmap->ineq[last_pos][0], 1);
2489 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2490 bmap->ineq[last_pos][1+off+i]);
2491 isl_int_sub_ui(bmap->ineq[last_pos][0],
2492 bmap->ineq[last_pos][0], 1);
2493 isl_int_sub(bmap->ineq[last_pos][0],
2494 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2497 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2502 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2503 bmap = isl_basic_map_simplify(bmap);
2505 return isl_basic_map_drop_redundant_divs(bmap);
2507 if (last_pos > last_neg) {
2508 isl_basic_map_drop_inequality(bmap, last_pos);
2509 isl_basic_map_drop_inequality(bmap, last_neg);
2511 isl_basic_map_drop_inequality(bmap, last_neg);
2512 isl_basic_map_drop_inequality(bmap, last_pos);
2514 bmap = isl_basic_map_drop_div(bmap, i);
2516 return isl_basic_map_drop_redundant_divs(bmap);
2520 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2526 isl_basic_map_free(bmap);
2530 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2531 struct isl_basic_set *bset)
2533 return (struct isl_basic_set *)
2534 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2537 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2543 for (i = 0; i < map->n; ++i) {
2544 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2548 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2555 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2557 return (struct isl_set *)
2558 isl_map_drop_redundant_divs((struct isl_map *)set);