1 #include "isl_equalities.h"
3 #include "isl_map_private.h"
6 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
8 isl_int *t = bmap->eq[a];
9 bmap->eq[a] = bmap->eq[b];
13 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
16 isl_int *t = bmap->ineq[a];
17 bmap->ineq[a] = bmap->ineq[b];
22 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
24 swap_inequality((struct isl_basic_map *)bset, a, b);
27 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
29 isl_seq_cpy(c, c + n, rem);
30 isl_seq_clr(c + rem, n);
33 /* Drop n dimensions starting at first.
35 * In principle, this frees up some extra variables as the number
36 * of columns remains constant, but we would have to extend
37 * the div array too as the number of rows in this array is assumed
38 * to be equal to extra.
40 struct isl_basic_set *isl_basic_set_drop_dims(
41 struct isl_basic_set *bset, unsigned first, unsigned n)
48 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
53 bset = isl_basic_set_cow(bset);
57 for (i = 0; i < bset->n_eq; ++i)
58 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
59 (bset->dim->n_out-first-n)+bset->extra);
61 for (i = 0; i < bset->n_ineq; ++i)
62 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
63 (bset->dim->n_out-first-n)+bset->extra);
65 for (i = 0; i < bset->n_div; ++i)
66 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
67 (bset->dim->n_out-first-n)+bset->extra);
69 bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
73 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
74 bset = isl_basic_set_simplify(bset);
75 return isl_basic_set_finalize(bset);
77 isl_basic_set_free(bset);
81 struct isl_set *isl_set_drop_dims(
82 struct isl_set *set, unsigned first, unsigned n)
89 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
93 set = isl_set_cow(set);
96 set->dim = isl_dim_drop_outputs(set->dim, first, n);
100 for (i = 0; i < set->n; ++i) {
101 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
106 ISL_F_CLR(set, ISL_SET_NORMALIZED);
113 /* Drop n input dimensions starting at first.
115 * In principle, this frees up some extra variables as the number
116 * of columns remains constant, but we would have to extend
117 * the div array too as the number of rows in this array is assumed
118 * to be equal to extra.
120 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
121 enum isl_dim_type type, unsigned first, unsigned n)
131 dim = isl_basic_map_dim(bmap, type);
132 isl_assert(bmap->ctx, first + n <= dim, goto error);
137 bmap = isl_basic_map_cow(bmap);
141 offset = isl_basic_map_offset(bmap, type) + first;
142 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
143 for (i = 0; i < bmap->n_eq; ++i)
144 constraint_drop_vars(bmap->eq[i]+offset, n, left);
146 for (i = 0; i < bmap->n_ineq; ++i)
147 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
149 for (i = 0; i < bmap->n_div; ++i)
150 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
152 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
156 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
157 bmap = isl_basic_map_simplify(bmap);
158 return isl_basic_map_finalize(bmap);
160 isl_basic_map_free(bmap);
164 struct isl_basic_map *isl_basic_map_drop_inputs(
165 struct isl_basic_map *bmap, unsigned first, unsigned n)
167 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
170 struct isl_map *isl_map_drop(struct isl_map *map,
171 enum isl_dim_type type, unsigned first, unsigned n)
178 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
182 map = isl_map_cow(map);
185 map->dim = isl_dim_drop(map->dim, type, first, n);
189 for (i = 0; i < map->n; ++i) {
190 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
194 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
202 struct isl_map *isl_map_drop_inputs(
203 struct isl_map *map, unsigned first, unsigned n)
205 return isl_map_drop(map, isl_dim_in, first, n);
209 * We don't cow, as the div is assumed to be redundant.
211 static struct isl_basic_map *isl_basic_map_drop_div(
212 struct isl_basic_map *bmap, unsigned div)
220 pos = 1 + isl_dim_total(bmap->dim) + div;
222 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
224 for (i = 0; i < bmap->n_eq; ++i)
225 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
227 for (i = 0; i < bmap->n_ineq; ++i) {
228 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
229 isl_basic_map_drop_inequality(bmap, i);
233 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
236 for (i = 0; i < bmap->n_div; ++i)
237 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
239 if (div != bmap->n_div - 1) {
241 isl_int *t = bmap->div[div];
243 for (j = div; j < bmap->n_div - 1; ++j)
244 bmap->div[j] = bmap->div[j+1];
246 bmap->div[bmap->n_div - 1] = t;
248 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
249 isl_basic_map_free_div(bmap, 1);
253 isl_basic_map_free(bmap);
257 struct isl_basic_map *isl_basic_map_normalize_constraints(
258 struct isl_basic_map *bmap)
262 unsigned total = isl_basic_map_total_dim(bmap);
265 for (i = bmap->n_eq - 1; i >= 0; --i) {
266 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
267 if (isl_int_is_zero(gcd)) {
268 if (!isl_int_is_zero(bmap->eq[i][0])) {
269 bmap = isl_basic_map_set_to_empty(bmap);
272 isl_basic_map_drop_equality(bmap, i);
275 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
276 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
277 if (isl_int_is_one(gcd))
279 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
280 bmap = isl_basic_map_set_to_empty(bmap);
283 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
286 for (i = bmap->n_ineq - 1; i >= 0; --i) {
287 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
288 if (isl_int_is_zero(gcd)) {
289 if (isl_int_is_neg(bmap->ineq[i][0])) {
290 bmap = isl_basic_map_set_to_empty(bmap);
293 isl_basic_map_drop_inequality(bmap, i);
296 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
297 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
298 if (isl_int_is_one(gcd))
300 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
301 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
308 struct isl_basic_set *isl_basic_set_normalize_constraints(
309 struct isl_basic_set *bset)
311 (struct isl_basic_set *)isl_basic_map_normalize_constraints(
312 (struct isl_basic_map *)bset);
315 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
318 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
320 len = 1 + isl_basic_map_total_dim(bmap);
322 for (i = 0; i < bmap->n_eq; ++i)
323 if (bmap->eq[i] != eq)
324 isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
326 for (i = 0; i < bmap->n_ineq; ++i)
327 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
329 /* We need to be careful about circular definitions,
330 * so for now we just remove the definitions of other divs that
331 * depend on this div and (possibly) recompute them later.
333 for (i = 0; i < bmap->n_div; ++i)
334 if (!isl_int_is_zero(bmap->div[i][0]) &&
335 !isl_int_is_zero(bmap->div[i][1 + pos]))
336 isl_seq_clr(bmap->div[i], 1 + len);
338 isl_basic_map_drop_div(bmap, div);
341 /* Elimininate divs based on equalities
343 static struct isl_basic_map *eliminate_divs_eq(
344 struct isl_basic_map *bmap, int *progress)
354 off = 1 + isl_dim_total(bmap->dim);
356 for (d = bmap->n_div - 1; d >= 0 ; --d) {
357 for (i = 0; i < bmap->n_eq; ++i) {
358 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
359 !isl_int_is_negone(bmap->eq[i][off + d]))
363 eliminate_div(bmap, bmap->eq[i], d);
364 isl_basic_map_drop_equality(bmap, i);
369 return eliminate_divs_eq(bmap, progress);
373 /* Elimininate divs based on inequalities
375 static struct isl_basic_map *eliminate_divs_ineq(
376 struct isl_basic_map *bmap, int *progress)
387 off = 1 + isl_dim_total(bmap->dim);
389 for (d = bmap->n_div - 1; d >= 0 ; --d) {
390 for (i = 0; i < bmap->n_eq; ++i)
391 if (!isl_int_is_zero(bmap->eq[i][off + d]))
395 for (i = 0; i < bmap->n_ineq; ++i)
396 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
398 if (i < bmap->n_ineq)
401 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
402 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
404 bmap = isl_basic_map_drop_div(bmap, d);
411 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
412 unsigned pos, isl_int *eq, int *progress)
418 total = isl_basic_map_total_dim(bmap);
420 isl_seq_first_non_zero(eq + 1 + isl_dim_total(bmap->dim),
422 for (k = 0; k < bmap->n_eq; ++k) {
423 if (bmap->eq[k] == eq)
425 if (isl_int_is_zero(bmap->eq[k][1+pos]))
429 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
432 for (k = 0; k < bmap->n_ineq; ++k) {
433 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
437 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
438 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
441 for (k = 0; k < bmap->n_div; ++k) {
442 if (isl_int_is_zero(bmap->div[k][0]))
444 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
448 /* We need to be careful about circular definitions,
449 * so for now we just remove the definition of div k
450 * if the equality contains any divs.
453 isl_seq_clr(bmap->div[k], 1 + total);
455 isl_seq_elim(bmap->div[k]+1, eq,
456 1+pos, 1+total, &bmap->div[k][0]);
457 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
461 struct isl_basic_map *isl_basic_map_gauss(
462 struct isl_basic_map *bmap, int *progress)
473 total = isl_basic_map_total_dim(bmap);
474 total_var = total - bmap->n_div;
476 last_var = total - 1;
477 for (done = 0; done < bmap->n_eq; ++done) {
478 for (; last_var >= 0; --last_var) {
479 for (k = done; k < bmap->n_eq; ++k)
480 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
488 swap_equality(bmap, k, done);
489 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
490 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
492 eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
495 if (last_var >= total_var &&
496 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
497 unsigned div = last_var - total_var;
498 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
499 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
500 isl_int_set(bmap->div[div][0],
501 bmap->eq[done][1+last_var]);
502 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
505 if (done == bmap->n_eq)
507 for (k = done; k < bmap->n_eq; ++k) {
508 if (isl_int_is_zero(bmap->eq[k][0]))
510 return isl_basic_map_set_to_empty(bmap);
512 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
516 struct isl_basic_set *isl_basic_set_gauss(
517 struct isl_basic_set *bset, int *progress)
519 return (struct isl_basic_set*)isl_basic_map_gauss(
520 (struct isl_basic_map *)bset, progress);
524 static unsigned int round_up(unsigned int v)
535 static int hash_index(isl_int ***index, unsigned int size, int bits,
536 struct isl_basic_map *bmap, int k)
539 unsigned total = isl_basic_map_total_dim(bmap);
540 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
541 for (h = hash; index[h]; h = (h+1) % size)
542 if (&bmap->ineq[k] != index[h] &&
543 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
548 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
549 struct isl_basic_set *bset, int k)
551 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
554 /* If we can eliminate more than one div, then we need to make
555 * sure we do it from last div to first div, in order not to
556 * change the position of the other divs that still need to
559 static struct isl_basic_map *remove_duplicate_divs(
560 struct isl_basic_map *bmap, int *progress)
568 unsigned total_var = isl_dim_total(bmap->dim);
569 unsigned total = total_var + bmap->n_div;
572 if (bmap->n_div <= 1)
576 for (k = bmap->n_div - 1; k >= 0; --k)
577 if (!isl_int_is_zero(bmap->div[k][0]))
582 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
583 size = round_up(4 * bmap->n_div / 3 - 1);
584 bits = ffs(size) - 1;
585 index = isl_calloc_array(ctx, int, size);
588 eq = isl_blk_alloc(ctx, 1+total);
589 if (isl_blk_is_error(eq))
592 isl_seq_clr(eq.data, 1+total);
593 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
594 for (--k; k >= 0; --k) {
597 if (isl_int_is_zero(bmap->div[k][0]))
600 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
601 for (h = hash; index[h]; h = (h+1) % size)
602 if (isl_seq_eq(bmap->div[k],
603 bmap->div[index[h]-1], 2+total))
612 for (l = bmap->n_div - 1; l >= 0; --l) {
616 isl_int_set_si(eq.data[1+total_var+k], -1);
617 isl_int_set_si(eq.data[1+total_var+l], 1);
618 eliminate_div(bmap, eq.data, l);
619 isl_int_set_si(eq.data[1+total_var+k], 0);
620 isl_int_set_si(eq.data[1+total_var+l], 0);
623 isl_blk_free(ctx, eq);
630 /* Normalize divs that appear in equalities.
632 * In particular, we assume that bmap contains some equalities
637 * and we want to replace the set of e_i by a minimal set and
638 * such that the new e_i have a canonical representation in terms
640 * If any of the equalities involves more than one divs, then
641 * we currently simply bail out.
643 * Let us first additionally assume that all equalities involve
644 * a div. The equalities then express modulo constraints on the
645 * remaining variables and we can use "parameter compression"
646 * to find a minimal set of constraints. The result is a transformation
648 * x = T(x') = x_0 + G x'
650 * with G a lower-triangular matrix with all elements below the diagonal
651 * non-negative and smaller than the diagonal element on the same row.
652 * We first normalize x_0 by making the same property hold in the affine
654 * The rows i of G with a 1 on the diagonal do not impose any modulo
655 * constraint and simply express x_i = x'_i.
656 * For each of the remaining rows i, we introduce a div and a corresponding
657 * equality. In particular
659 * g_ii e_j = x_i - g_i(x')
661 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
662 * corresponding div (if g_kk != 1).
664 * If there are any equalities not involving any div, then we
665 * first apply a variable compression on the variables x:
667 * x = C x'' x'' = C_2 x
669 * and perform the above parameter compression on A C instead of on A.
670 * The resulting compression is then of the form
672 * x'' = T(x') = x_0 + G x'
674 * and in constructing the new divs and the corresponding equalities,
675 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
676 * by the corresponding row from C_2.
678 static struct isl_basic_map *normalize_divs(
679 struct isl_basic_map *bmap, int *progress)
686 struct isl_mat *T = NULL;
687 struct isl_mat *C = NULL;
688 struct isl_mat *C2 = NULL;
696 if (bmap->n_div == 0)
702 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
705 total = isl_dim_total(bmap->dim);
706 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
707 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
711 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
718 if (div_eq < bmap->n_eq) {
719 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
720 bmap->n_eq - div_eq, 0, 1 + total);
721 C = isl_mat_variable_compression(bmap->ctx, B, &C2);
725 bmap = isl_basic_map_set_to_empty(bmap);
726 isl_mat_free(bmap->ctx, C);
727 isl_mat_free(bmap->ctx, C2);
732 d = isl_vec_alloc(bmap->ctx, div_eq);
735 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
736 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
738 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
740 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
743 B = isl_mat_product(bmap->ctx, B, C);
747 T = isl_mat_parameter_compression(bmap->ctx, B, d);
751 bmap = isl_basic_map_set_to_empty(bmap);
752 isl_mat_free(bmap->ctx, C2);
753 isl_mat_free(bmap->ctx, T);
757 for (i = 0; i < T->n_row - 1; ++i) {
758 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
759 if (isl_int_is_zero(v))
761 isl_mat_col_submul(T, 0, v, 1 + i);
764 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
765 /* We have to be careful because dropping equalities may reorder them */
767 for (j = bmap->n_div - 1; j >= 0; --j) {
768 for (i = 0; i < bmap->n_eq; ++i)
769 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
771 if (i < bmap->n_eq) {
772 bmap = isl_basic_map_drop_div(bmap, j);
773 isl_basic_map_drop_equality(bmap, i);
779 for (i = 1; i < T->n_row; ++i) {
780 if (isl_int_is_one(T->row[i][i]))
785 if (needed > dropped) {
786 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
791 for (i = 1; i < T->n_row; ++i) {
792 if (isl_int_is_one(T->row[i][i]))
794 k = isl_basic_map_alloc_div(bmap);
795 pos[i] = 1 + total + k;
796 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
797 isl_int_set(bmap->div[k][0], T->row[i][i]);
799 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
801 isl_int_set_si(bmap->div[k][1 + i], 1);
802 for (j = 0; j < i; ++j) {
803 if (isl_int_is_zero(T->row[i][j]))
805 if (pos[j] < T->n_row && C2)
806 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
807 C2->row[pos[j]], 1 + total);
809 isl_int_neg(bmap->div[k][1 + pos[j]],
812 j = isl_basic_map_alloc_equality(bmap);
813 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
814 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
817 isl_mat_free(bmap->ctx, C2);
818 isl_mat_free(bmap->ctx, T);
822 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
826 isl_mat_free(bmap->ctx, C);
827 isl_mat_free(bmap->ctx, C2);
828 isl_mat_free(bmap->ctx, T);
832 static struct isl_basic_map *remove_duplicate_constraints(
833 struct isl_basic_map *bmap, int *progress)
839 unsigned total = isl_basic_map_total_dim(bmap);
842 if (bmap->n_ineq <= 1)
845 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
846 bits = ffs(size) - 1;
847 index = isl_calloc_array(ctx, isl_int **, size);
851 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
852 for (k = 1; k < bmap->n_ineq; ++k) {
853 h = hash_index(index, size, bits, bmap, k);
855 index[h] = &bmap->ineq[k];
860 l = index[h] - &bmap->ineq[0];
861 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
862 swap_inequality(bmap, k, l);
863 isl_basic_map_drop_inequality(bmap, k);
867 for (k = 0; k < bmap->n_ineq-1; ++k) {
868 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
869 h = hash_index(index, size, bits, bmap, k);
870 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
873 l = index[h] - &bmap->ineq[0];
874 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
875 if (isl_int_is_pos(sum))
877 if (isl_int_is_zero(sum)) {
878 /* We need to break out of the loop after these
879 * changes since the contents of the hash
880 * will no longer be valid.
881 * Plus, we probably we want to regauss first.
883 isl_basic_map_drop_inequality(bmap, l);
884 isl_basic_map_inequality_to_equality(bmap, k);
886 bmap = isl_basic_map_set_to_empty(bmap);
896 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
903 bmap = isl_basic_map_normalize_constraints(bmap);
904 bmap = eliminate_divs_eq(bmap, &progress);
905 bmap = eliminate_divs_ineq(bmap, &progress);
906 bmap = isl_basic_map_gauss(bmap, &progress);
907 /* requires equalities in normal form */
908 bmap = normalize_divs(bmap, &progress);
909 bmap = remove_duplicate_divs(bmap, &progress);
910 bmap = remove_duplicate_constraints(bmap, &progress);
915 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
917 return (struct isl_basic_set *)
918 isl_basic_map_simplify((struct isl_basic_map *)bset);
922 /* If the only constraints a div d=floor(f/m)
923 * appears in are its two defining constraints
926 * -(f - (m - 1)) + m d >= 0
928 * then it can safely be removed.
930 static int div_is_redundant(struct isl_basic_map *bmap, int div)
933 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
935 for (i = 0; i < bmap->n_eq; ++i)
936 if (!isl_int_is_zero(bmap->eq[i][pos]))
939 for (i = 0; i < bmap->n_ineq; ++i) {
940 if (isl_int_is_zero(bmap->ineq[i][pos]))
942 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
944 isl_int_sub(bmap->div[div][1],
945 bmap->div[div][1], bmap->div[div][0]);
946 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
947 neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
948 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
949 isl_int_add(bmap->div[div][1],
950 bmap->div[div][1], bmap->div[div][0]);
953 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
954 bmap->n_div-div-1) != -1)
956 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
957 if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
959 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
960 bmap->n_div-div-1) != -1)
966 for (i = 0; i < bmap->n_div; ++i)
967 if (!isl_int_is_zero(bmap->div[i][1+pos]))
974 * Remove divs that don't occur in any of the constraints or other divs.
975 * These can arise when dropping some of the variables in a quast
976 * returned by piplib.
978 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
985 for (i = bmap->n_div-1; i >= 0; --i) {
986 if (!div_is_redundant(bmap, i))
988 bmap = isl_basic_map_drop_div(bmap, i);
993 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
995 bmap = remove_redundant_divs(bmap);
998 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1002 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1004 return (struct isl_basic_set *)
1005 isl_basic_map_finalize((struct isl_basic_map *)bset);
1008 struct isl_set *isl_set_finalize(struct isl_set *set)
1014 for (i = 0; i < set->n; ++i) {
1015 set->p[i] = isl_basic_set_finalize(set->p[i]);
1025 struct isl_map *isl_map_finalize(struct isl_map *map)
1031 for (i = 0; i < map->n; ++i) {
1032 map->p[i] = isl_basic_map_finalize(map->p[i]);
1036 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1044 /* Remove any div that is defined in terms of the given variable.
1046 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1050 unsigned dim = isl_dim_total(bmap->dim);
1052 for (i = 0; i < bmap->n_div; ++i) {
1053 if (isl_int_is_zero(bmap->div[i][0]))
1055 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1057 bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
1064 /* Eliminate the specified variables from the constraints using
1065 * Fourier-Motzkin. The variables themselves are not removed.
1067 struct isl_basic_map *isl_basic_map_eliminate_vars(
1068 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1078 total = isl_basic_map_total_dim(bmap);
1080 bmap = isl_basic_map_cow(bmap);
1081 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1082 bmap = remove_dependent_vars(bmap, d);
1084 for (d = pos + n - 1;
1085 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1086 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1087 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1088 int n_lower, n_upper;
1091 for (i = 0; i < bmap->n_eq; ++i) {
1092 if (isl_int_is_zero(bmap->eq[i][1+d]))
1094 eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1095 isl_basic_map_drop_equality(bmap, i);
1102 for (i = 0; i < bmap->n_ineq; ++i) {
1103 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1105 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1108 bmap = isl_basic_map_extend_constraints(bmap,
1109 0, n_lower * n_upper);
1110 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1112 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1115 for (j = 0; j < i; ++j) {
1116 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1119 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1120 isl_int_sgn(bmap->ineq[j][1+d]))
1122 k = isl_basic_map_alloc_inequality(bmap);
1125 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1127 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1128 1+d, 1+total, NULL);
1130 isl_basic_map_drop_inequality(bmap, i);
1133 if (n_lower > 0 && n_upper > 0) {
1134 bmap = isl_basic_map_normalize_constraints(bmap);
1135 bmap = remove_duplicate_constraints(bmap, NULL);
1136 bmap = isl_basic_map_gauss(bmap, NULL);
1137 bmap = isl_basic_map_convex_hull(bmap);
1140 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1144 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1147 isl_basic_map_free(bmap);
1151 struct isl_basic_set *isl_basic_set_eliminate_vars(
1152 struct isl_basic_set *bset, unsigned pos, unsigned n)
1154 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1155 (struct isl_basic_map *)bset, pos, n);
1158 /* Don't assume equalities are in order, because align_divs
1159 * may have changed the order of the divs.
1161 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1166 total = isl_dim_total(bmap->dim);
1167 for (d = 0; d < total; ++d)
1169 for (i = 0; i < bmap->n_eq; ++i) {
1170 for (d = total - 1; d >= 0; --d) {
1171 if (isl_int_is_zero(bmap->eq[i][1+d]))
1179 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1181 return compute_elimination_index((struct isl_basic_map *)bset, elim);
1184 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1185 struct isl_basic_map *bmap, int *elim)
1191 total = isl_dim_total(bmap->dim);
1192 for (d = total - 1; d >= 0; --d) {
1193 if (isl_int_is_zero(src[1+d]))
1198 isl_seq_cpy(dst, src, 1 + total);
1201 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1206 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1207 struct isl_basic_set *bset, int *elim)
1209 return reduced_using_equalities(dst, src,
1210 (struct isl_basic_map *)bset, elim);
1213 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1214 struct isl_basic_set *bset, struct isl_basic_set *context)
1219 if (!bset || !context)
1222 bset = isl_basic_set_cow(bset);
1226 elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1229 set_compute_elimination_index(context, elim);
1230 for (i = 0; i < bset->n_eq; ++i)
1231 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1233 for (i = 0; i < bset->n_ineq; ++i)
1234 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1236 isl_basic_set_free(context);
1238 bset = isl_basic_set_simplify(bset);
1239 bset = isl_basic_set_finalize(bset);
1242 isl_basic_set_free(bset);
1243 isl_basic_set_free(context);
1247 static struct isl_basic_set *remove_shifted_constraints(
1248 struct isl_basic_set *bset, struct isl_basic_set *context)
1258 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1259 bits = ffs(size) - 1;
1260 index = isl_calloc_array(ctx, isl_int **, size);
1264 for (k = 0; k < context->n_ineq; ++k) {
1265 h = set_hash_index(index, size, bits, context, k);
1266 index[h] = &context->ineq[k];
1268 for (k = 0; k < bset->n_ineq; ++k) {
1269 h = set_hash_index(index, size, bits, bset, k);
1272 l = index[h] - &context->ineq[0];
1273 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1275 bset = isl_basic_set_cow(bset);
1278 isl_basic_set_drop_inequality(bset, k);
1288 /* Tighten (decrease) the constant terms of the inequalities based
1289 * on the equalities, without removing any integer points.
1290 * For example, if there is an equality
1298 * then we want to replace the inequality by
1302 * We do this by computing a variable compression and translating
1303 * the constraints to the compressed space.
1304 * If any constraint has coefficients (except the contant term)
1305 * with a common factor "f", then we can replace the constant term "c"
1312 * f * floor(c/f) - c = -fract(c/f)
1314 * and we can add the same value to the original constraint.
1316 * In the example, the compressed space only contains "j",
1317 * and the inequality translates to
1321 * We add -fract(-1/3) = -2 to the original constraint to obtain
1325 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1326 struct isl_basic_set *bset)
1330 struct isl_mat *B, *C;
1336 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1342 bset = isl_basic_set_cow(bset);
1346 total = isl_basic_set_total_dim(bset);
1347 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1348 C = isl_mat_variable_compression(bset->ctx, B, NULL);
1351 if (C->n_col == 0) {
1352 isl_mat_free(bset->ctx, C);
1353 return isl_basic_set_set_to_empty(bset);
1355 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1356 0, bset->n_ineq, 0, 1 + total);
1357 C = isl_mat_product(bset->ctx, B, C);
1362 for (i = 0; i < bset->n_ineq; ++i) {
1363 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1364 if (isl_int_is_one(gcd))
1366 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1367 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1371 isl_mat_free(bset->ctx, C);
1376 /* Remove all information from bset that is redundant in the context
1377 * of context. In particular, equalities that are linear combinations
1378 * of those in context are removed. Then the inequalities that are
1379 * redundant in the context of the equalities and inequalities of
1380 * context are removed.
1382 * We first simplify the constraints of "bset" in the context of the
1383 * equalities of "context".
1384 * Then we simplify the inequalities of the context in the context
1385 * of the equalities of bset and remove the inequalities from "bset"
1386 * that are obviously redundant with respect to some inequality in "context".
1388 * If there are any inequalities left, we construct a tableau for
1389 * the context and then add the inequalities of "bset".
1390 * Before adding these equalities, we freeze all constraints such that
1391 * they won't be considered redundant in terms of the constraints of "bset".
1392 * Then we detect all equalities and redundant constraints (among the
1393 * constraints that weren't frozen) and update bset according to the results.
1394 * We have to be careful here because we don't want any of the context
1395 * constraints to remain and because we haven't added the equalities of "bset"
1396 * to the tableau so we temporarily have to pretend that there were no
1399 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1400 struct isl_basic_set *context)
1403 struct isl_tab *tab;
1404 unsigned context_ineq;
1405 struct isl_basic_set *combined = NULL;
1407 if (!context || !bset)
1410 if (context->n_eq > 0)
1411 bset = isl_basic_set_reduce_using_equalities(bset,
1412 isl_basic_set_copy(context));
1415 if (isl_basic_set_fast_is_empty(bset))
1420 if (bset->n_eq > 0) {
1421 struct isl_basic_set *affine_hull;
1422 affine_hull = isl_basic_set_copy(bset);
1423 affine_hull = isl_basic_set_cow(affine_hull);
1426 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1427 context = isl_basic_set_intersect(context, affine_hull);
1428 context = isl_basic_set_gauss(context, NULL);
1429 context = normalize_constraints_in_compressed_space(context);
1433 if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
1434 isl_basic_set_free(bset);
1437 if (!context->n_ineq)
1439 bset = remove_shifted_constraints(bset, context);
1442 isl_basic_set_free_equality(context, context->n_eq);
1443 context_ineq = context->n_ineq;
1444 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1445 combined = isl_basic_set_extend_constraints(combined,
1446 bset->n_eq, bset->n_ineq);
1447 tab = isl_tab_from_basic_set(combined);
1450 for (i = 0; i < context_ineq; ++i)
1451 tab->con[i].frozen = 1;
1452 tab = isl_tab_extend(bset->ctx, tab, bset->n_ineq);
1455 for (i = 0; i < bset->n_ineq; ++i)
1456 tab = isl_tab_add_ineq(bset->ctx, tab, bset->ineq[i]);
1457 bset = isl_basic_set_add_constraints(combined, bset, 0);
1458 tab = isl_tab_detect_equalities(bset->ctx, tab);
1459 tab = isl_tab_detect_redundant(bset->ctx, tab);
1462 for (i = 0; i < context_ineq; ++i) {
1463 tab->con[i].is_zero = 0;
1464 tab->con[i].is_redundant = 1;
1466 bset = isl_basic_set_update_from_tab(bset, tab);
1467 isl_tab_free(bset->ctx, tab);
1468 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1469 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1471 bset = isl_basic_set_simplify(bset);
1472 bset = isl_basic_set_finalize(bset);
1473 isl_basic_set_free(context);
1476 isl_basic_set_free(combined);
1478 isl_basic_set_free(bset);
1479 isl_basic_set_free(context);
1483 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1484 struct isl_basic_map *context)
1486 struct isl_basic_set *bset;
1488 if (!bmap || !context)
1491 if (isl_basic_map_is_universe(context)) {
1492 isl_basic_map_free(context);
1495 if (isl_basic_map_is_universe(bmap)) {
1496 isl_basic_map_free(context);
1499 if (isl_basic_map_fast_is_empty(context)) {
1500 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1501 isl_basic_map_free(context);
1502 isl_basic_map_free(bmap);
1503 return isl_basic_map_universe(dim);
1505 if (isl_basic_map_fast_is_empty(bmap)) {
1506 isl_basic_map_free(context);
1510 bmap = isl_basic_map_convex_hull(bmap);
1511 context = isl_basic_map_convex_hull(context);
1513 context = isl_basic_map_align_divs(context, bmap);
1514 bmap = isl_basic_map_align_divs(bmap, context);
1516 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1517 isl_basic_map_underlying_set(context));
1519 return isl_basic_map_overlying_set(bset, bmap);
1521 isl_basic_map_free(bmap);
1522 isl_basic_map_free(context);
1527 * Assumes context has no implicit divs.
1529 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1533 if (!map || !context)
1536 if (isl_basic_map_is_universe(context)) {
1537 isl_basic_map_free(context);
1540 if (isl_basic_map_fast_is_empty(context)) {
1541 struct isl_dim *dim = isl_dim_copy(map->dim);
1542 isl_basic_map_free(context);
1544 return isl_map_universe(dim);
1547 context = isl_basic_map_convex_hull(context);
1548 map = isl_map_cow(map);
1549 if (!map || !context)
1551 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1552 map = isl_map_compute_divs(map);
1553 for (i = 0; i < map->n; ++i)
1554 context = isl_basic_map_align_divs(context, map->p[i]);
1555 for (i = 0; i < map->n; ++i) {
1556 map->p[i] = isl_basic_map_gist(map->p[i],
1557 isl_basic_map_copy(context));
1561 isl_basic_map_free(context);
1562 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1566 isl_basic_map_free(context);
1570 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1571 struct isl_basic_set *context)
1573 return (struct isl_basic_set *)isl_basic_map_gist(
1574 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1577 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1579 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1580 (struct isl_basic_map *)context);
1583 /* Quick check to see if two basic maps are disjoint.
1584 * In particular, we reduce the equalities and inequalities of
1585 * one basic map in the context of the equalities of the other
1586 * basic map and check if we get a contradiction.
1588 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1589 struct isl_basic_map *bmap2)
1591 struct isl_vec *v = NULL;
1596 if (!bmap1 || !bmap2)
1598 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1600 if (bmap1->n_div || bmap2->n_div)
1602 if (!bmap1->n_eq && !bmap2->n_eq)
1605 total = isl_dim_total(bmap1->dim);
1608 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1611 elim = isl_alloc_array(bmap1->ctx, int, total);
1614 compute_elimination_index(bmap1, elim);
1615 for (i = 0; i < bmap2->n_eq; ++i) {
1617 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1619 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1620 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1623 for (i = 0; i < bmap2->n_ineq; ++i) {
1625 reduced = reduced_using_equalities(v->block.data,
1626 bmap2->ineq[i], bmap1, elim);
1627 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1628 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1631 compute_elimination_index(bmap2, elim);
1632 for (i = 0; i < bmap1->n_ineq; ++i) {
1634 reduced = reduced_using_equalities(v->block.data,
1635 bmap1->ineq[i], bmap2, elim);
1636 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1637 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1640 isl_vec_free(bmap1->ctx, v);
1644 isl_vec_free(bmap1->ctx, v);
1648 isl_vec_free(bmap1->ctx, v);
1653 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1654 struct isl_basic_set *bset2)
1656 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1657 (struct isl_basic_map *)bset2);
1660 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1667 if (isl_map_fast_is_equal(map1, map2))
1670 for (i = 0; i < map1->n; ++i) {
1671 for (j = 0; j < map2->n; ++j) {
1672 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1681 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1683 return isl_map_fast_is_disjoint((struct isl_map *)set1,
1684 (struct isl_map *)set2);