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 /* Move "n" divs starting at "first" to the end of the list of divs.
115 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
116 unsigned first, unsigned n)
121 if (first + n == bmap->n_div)
124 div = isl_alloc_array(bmap->ctx, isl_int *, n);
127 for (i = 0; i < n; ++i)
128 div[i] = bmap->div[first + i];
129 for (i = 0; i < bmap->n_div - first - n; ++i)
130 bmap->div[first + i] = bmap->div[first + n + i];
131 for (i = 0; i < n; ++i)
132 bmap->div[bmap->n_div - n + i] = div[i];
136 isl_basic_map_free(bmap);
140 /* Drop "n" dimensions of type "type" starting at "first".
142 * In principle, this frees up some extra variables as the number
143 * of columns remains constant, but we would have to extend
144 * the div array too as the number of rows in this array is assumed
145 * to be equal to extra.
147 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
148 enum isl_dim_type type, unsigned first, unsigned n)
158 dim = isl_basic_map_dim(bmap, type);
159 isl_assert(bmap->ctx, first + n <= dim, goto error);
164 bmap = isl_basic_map_cow(bmap);
168 offset = isl_basic_map_offset(bmap, type) + first;
169 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
170 for (i = 0; i < bmap->n_eq; ++i)
171 constraint_drop_vars(bmap->eq[i]+offset, n, left);
173 for (i = 0; i < bmap->n_ineq; ++i)
174 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
176 for (i = 0; i < bmap->n_div; ++i)
177 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
179 if (type == isl_dim_div) {
180 bmap = move_divs_last(bmap, first, n);
183 isl_basic_map_free_div(bmap, n);
185 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
189 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
190 bmap = isl_basic_map_simplify(bmap);
191 return isl_basic_map_finalize(bmap);
193 isl_basic_map_free(bmap);
197 struct isl_basic_map *isl_basic_map_drop_inputs(
198 struct isl_basic_map *bmap, unsigned first, unsigned n)
200 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
203 struct isl_map *isl_map_drop(struct isl_map *map,
204 enum isl_dim_type type, unsigned first, unsigned n)
211 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
215 map = isl_map_cow(map);
218 map->dim = isl_dim_drop(map->dim, type, first, n);
222 for (i = 0; i < map->n; ++i) {
223 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
227 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
235 struct isl_map *isl_map_drop_inputs(
236 struct isl_map *map, unsigned first, unsigned n)
238 return isl_map_drop(map, isl_dim_in, first, n);
242 * We don't cow, as the div is assumed to be redundant.
244 static struct isl_basic_map *isl_basic_map_drop_div(
245 struct isl_basic_map *bmap, unsigned div)
253 pos = 1 + isl_dim_total(bmap->dim) + div;
255 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
257 for (i = 0; i < bmap->n_eq; ++i)
258 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
260 for (i = 0; i < bmap->n_ineq; ++i) {
261 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
262 isl_basic_map_drop_inequality(bmap, i);
266 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
269 for (i = 0; i < bmap->n_div; ++i)
270 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
272 if (div != bmap->n_div - 1) {
274 isl_int *t = bmap->div[div];
276 for (j = div; j < bmap->n_div - 1; ++j)
277 bmap->div[j] = bmap->div[j+1];
279 bmap->div[bmap->n_div - 1] = t;
281 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
282 isl_basic_map_free_div(bmap, 1);
286 isl_basic_map_free(bmap);
290 struct isl_basic_map *isl_basic_map_normalize_constraints(
291 struct isl_basic_map *bmap)
295 unsigned total = isl_basic_map_total_dim(bmap);
298 for (i = bmap->n_eq - 1; i >= 0; --i) {
299 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
300 if (isl_int_is_zero(gcd)) {
301 if (!isl_int_is_zero(bmap->eq[i][0])) {
302 bmap = isl_basic_map_set_to_empty(bmap);
305 isl_basic_map_drop_equality(bmap, i);
308 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
309 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
310 if (isl_int_is_one(gcd))
312 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
313 bmap = isl_basic_map_set_to_empty(bmap);
316 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
319 for (i = bmap->n_ineq - 1; i >= 0; --i) {
320 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
321 if (isl_int_is_zero(gcd)) {
322 if (isl_int_is_neg(bmap->ineq[i][0])) {
323 bmap = isl_basic_map_set_to_empty(bmap);
326 isl_basic_map_drop_inequality(bmap, i);
329 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
330 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
331 if (isl_int_is_one(gcd))
333 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
334 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
341 struct isl_basic_set *isl_basic_set_normalize_constraints(
342 struct isl_basic_set *bset)
344 (struct isl_basic_set *)isl_basic_map_normalize_constraints(
345 (struct isl_basic_map *)bset);
348 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
351 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
353 len = 1 + isl_basic_map_total_dim(bmap);
355 for (i = 0; i < bmap->n_eq; ++i)
356 if (bmap->eq[i] != eq)
357 isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
359 for (i = 0; i < bmap->n_ineq; ++i)
360 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
362 /* We need to be careful about circular definitions,
363 * so for now we just remove the definitions of other divs that
364 * depend on this div and (possibly) recompute them later.
366 for (i = 0; i < bmap->n_div; ++i)
367 if (!isl_int_is_zero(bmap->div[i][0]) &&
368 !isl_int_is_zero(bmap->div[i][1 + pos]))
369 isl_seq_clr(bmap->div[i], 1 + len);
371 isl_basic_map_drop_div(bmap, div);
374 /* Elimininate divs based on equalities
376 static struct isl_basic_map *eliminate_divs_eq(
377 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_one(bmap->eq[i][off + d]) &&
392 !isl_int_is_negone(bmap->eq[i][off + d]))
396 eliminate_div(bmap, bmap->eq[i], d);
397 isl_basic_map_drop_equality(bmap, i);
402 return eliminate_divs_eq(bmap, progress);
406 /* Elimininate divs based on inequalities
408 static struct isl_basic_map *eliminate_divs_ineq(
409 struct isl_basic_map *bmap, int *progress)
420 off = 1 + isl_dim_total(bmap->dim);
422 for (d = bmap->n_div - 1; d >= 0 ; --d) {
423 for (i = 0; i < bmap->n_eq; ++i)
424 if (!isl_int_is_zero(bmap->eq[i][off + d]))
428 for (i = 0; i < bmap->n_ineq; ++i)
429 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
431 if (i < bmap->n_ineq)
434 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
435 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
437 bmap = isl_basic_map_drop_div(bmap, d);
444 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
445 unsigned pos, isl_int *eq, int *progress)
451 total = isl_basic_map_total_dim(bmap);
453 isl_seq_first_non_zero(eq + 1 + isl_dim_total(bmap->dim),
455 for (k = 0; k < bmap->n_eq; ++k) {
456 if (bmap->eq[k] == eq)
458 if (isl_int_is_zero(bmap->eq[k][1+pos]))
462 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
465 for (k = 0; k < bmap->n_ineq; ++k) {
466 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
470 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
471 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
474 for (k = 0; k < bmap->n_div; ++k) {
475 if (isl_int_is_zero(bmap->div[k][0]))
477 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
481 /* We need to be careful about circular definitions,
482 * so for now we just remove the definition of div k
483 * if the equality contains any divs.
486 isl_seq_clr(bmap->div[k], 1 + total);
488 isl_seq_elim(bmap->div[k]+1, eq,
489 1+pos, 1+total, &bmap->div[k][0]);
490 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
494 struct isl_basic_map *isl_basic_map_gauss(
495 struct isl_basic_map *bmap, int *progress)
506 total = isl_basic_map_total_dim(bmap);
507 total_var = total - bmap->n_div;
509 last_var = total - 1;
510 for (done = 0; done < bmap->n_eq; ++done) {
511 for (; last_var >= 0; --last_var) {
512 for (k = done; k < bmap->n_eq; ++k)
513 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
521 swap_equality(bmap, k, done);
522 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
523 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
525 eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
528 if (last_var >= total_var &&
529 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
530 unsigned div = last_var - total_var;
531 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
532 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
533 isl_int_set(bmap->div[div][0],
534 bmap->eq[done][1+last_var]);
535 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
538 if (done == bmap->n_eq)
540 for (k = done; k < bmap->n_eq; ++k) {
541 if (isl_int_is_zero(bmap->eq[k][0]))
543 return isl_basic_map_set_to_empty(bmap);
545 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
549 struct isl_basic_set *isl_basic_set_gauss(
550 struct isl_basic_set *bset, int *progress)
552 return (struct isl_basic_set*)isl_basic_map_gauss(
553 (struct isl_basic_map *)bset, progress);
557 static unsigned int round_up(unsigned int v)
568 static int hash_index(isl_int ***index, unsigned int size, int bits,
569 struct isl_basic_map *bmap, int k)
572 unsigned total = isl_basic_map_total_dim(bmap);
573 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
574 for (h = hash; index[h]; h = (h+1) % size)
575 if (&bmap->ineq[k] != index[h] &&
576 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
581 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
582 struct isl_basic_set *bset, int k)
584 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
587 /* If we can eliminate more than one div, then we need to make
588 * sure we do it from last div to first div, in order not to
589 * change the position of the other divs that still need to
592 static struct isl_basic_map *remove_duplicate_divs(
593 struct isl_basic_map *bmap, int *progress)
601 unsigned total_var = isl_dim_total(bmap->dim);
602 unsigned total = total_var + bmap->n_div;
605 if (bmap->n_div <= 1)
609 for (k = bmap->n_div - 1; k >= 0; --k)
610 if (!isl_int_is_zero(bmap->div[k][0]))
615 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
616 size = round_up(4 * bmap->n_div / 3 - 1);
617 bits = ffs(size) - 1;
618 index = isl_calloc_array(ctx, int, size);
621 eq = isl_blk_alloc(ctx, 1+total);
622 if (isl_blk_is_error(eq))
625 isl_seq_clr(eq.data, 1+total);
626 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
627 for (--k; k >= 0; --k) {
630 if (isl_int_is_zero(bmap->div[k][0]))
633 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
634 for (h = hash; index[h]; h = (h+1) % size)
635 if (isl_seq_eq(bmap->div[k],
636 bmap->div[index[h]-1], 2+total))
645 for (l = bmap->n_div - 1; l >= 0; --l) {
649 isl_int_set_si(eq.data[1+total_var+k], -1);
650 isl_int_set_si(eq.data[1+total_var+l], 1);
651 eliminate_div(bmap, eq.data, l);
652 isl_int_set_si(eq.data[1+total_var+k], 0);
653 isl_int_set_si(eq.data[1+total_var+l], 0);
656 isl_blk_free(ctx, eq);
663 static int n_pure_div_eq(struct isl_basic_map *bmap)
668 total = isl_dim_total(bmap->dim);
669 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
670 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
674 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
680 /* Normalize divs that appear in equalities.
682 * In particular, we assume that bmap contains some equalities
687 * and we want to replace the set of e_i by a minimal set and
688 * such that the new e_i have a canonical representation in terms
690 * If any of the equalities involves more than one divs, then
691 * we currently simply bail out.
693 * Let us first additionally assume that all equalities involve
694 * a div. The equalities then express modulo constraints on the
695 * remaining variables and we can use "parameter compression"
696 * to find a minimal set of constraints. The result is a transformation
698 * x = T(x') = x_0 + G x'
700 * with G a lower-triangular matrix with all elements below the diagonal
701 * non-negative and smaller than the diagonal element on the same row.
702 * We first normalize x_0 by making the same property hold in the affine
704 * The rows i of G with a 1 on the diagonal do not impose any modulo
705 * constraint and simply express x_i = x'_i.
706 * For each of the remaining rows i, we introduce a div and a corresponding
707 * equality. In particular
709 * g_ii e_j = x_i - g_i(x')
711 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
712 * corresponding div (if g_kk != 1).
714 * If there are any equalities not involving any div, then we
715 * first apply a variable compression on the variables x:
717 * x = C x'' x'' = C_2 x
719 * and perform the above parameter compression on A C instead of on A.
720 * The resulting compression is then of the form
722 * x'' = T(x') = x_0 + G x'
724 * and in constructing the new divs and the corresponding equalities,
725 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
726 * by the corresponding row from C_2.
728 static struct isl_basic_map *normalize_divs(
729 struct isl_basic_map *bmap, int *progress)
736 struct isl_mat *T = NULL;
737 struct isl_mat *C = NULL;
738 struct isl_mat *C2 = NULL;
746 if (bmap->n_div == 0)
752 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
755 total = isl_dim_total(bmap->dim);
756 div_eq = n_pure_div_eq(bmap);
760 if (div_eq < bmap->n_eq) {
761 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
762 bmap->n_eq - div_eq, 0, 1 + total);
763 C = isl_mat_variable_compression(bmap->ctx, B, &C2);
767 bmap = isl_basic_map_set_to_empty(bmap);
768 isl_mat_free(bmap->ctx, C);
769 isl_mat_free(bmap->ctx, C2);
774 d = isl_vec_alloc(bmap->ctx, div_eq);
777 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
778 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
780 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
782 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
785 B = isl_mat_product(bmap->ctx, B, C);
789 T = isl_mat_parameter_compression(bmap->ctx, B, d);
793 bmap = isl_basic_map_set_to_empty(bmap);
794 isl_mat_free(bmap->ctx, C2);
795 isl_mat_free(bmap->ctx, T);
799 for (i = 0; i < T->n_row - 1; ++i) {
800 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
801 if (isl_int_is_zero(v))
803 isl_mat_col_submul(T, 0, v, 1 + i);
806 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
807 /* We have to be careful because dropping equalities may reorder them */
809 for (j = bmap->n_div - 1; j >= 0; --j) {
810 for (i = 0; i < bmap->n_eq; ++i)
811 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
813 if (i < bmap->n_eq) {
814 bmap = isl_basic_map_drop_div(bmap, j);
815 isl_basic_map_drop_equality(bmap, i);
821 for (i = 1; i < T->n_row; ++i) {
822 if (isl_int_is_one(T->row[i][i]))
827 if (needed > dropped) {
828 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
833 for (i = 1; i < T->n_row; ++i) {
834 if (isl_int_is_one(T->row[i][i]))
836 k = isl_basic_map_alloc_div(bmap);
837 pos[i] = 1 + total + k;
838 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
839 isl_int_set(bmap->div[k][0], T->row[i][i]);
841 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
843 isl_int_set_si(bmap->div[k][1 + i], 1);
844 for (j = 0; j < i; ++j) {
845 if (isl_int_is_zero(T->row[i][j]))
847 if (pos[j] < T->n_row && C2)
848 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
849 C2->row[pos[j]], 1 + total);
851 isl_int_neg(bmap->div[k][1 + pos[j]],
854 j = isl_basic_map_alloc_equality(bmap);
855 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
856 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
859 isl_mat_free(bmap->ctx, C2);
860 isl_mat_free(bmap->ctx, T);
865 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
869 isl_mat_free(bmap->ctx, C);
870 isl_mat_free(bmap->ctx, C2);
871 isl_mat_free(bmap->ctx, T);
875 static struct isl_basic_map *remove_duplicate_constraints(
876 struct isl_basic_map *bmap, int *progress)
882 unsigned total = isl_basic_map_total_dim(bmap);
885 if (bmap->n_ineq <= 1)
888 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
889 bits = ffs(size) - 1;
890 index = isl_calloc_array(ctx, isl_int **, size);
894 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
895 for (k = 1; k < bmap->n_ineq; ++k) {
896 h = hash_index(index, size, bits, bmap, k);
898 index[h] = &bmap->ineq[k];
903 l = index[h] - &bmap->ineq[0];
904 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
905 swap_inequality(bmap, k, l);
906 isl_basic_map_drop_inequality(bmap, k);
910 for (k = 0; k < bmap->n_ineq-1; ++k) {
911 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
912 h = hash_index(index, size, bits, bmap, k);
913 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
916 l = index[h] - &bmap->ineq[0];
917 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
918 if (isl_int_is_pos(sum))
920 if (isl_int_is_zero(sum)) {
921 /* We need to break out of the loop after these
922 * changes since the contents of the hash
923 * will no longer be valid.
924 * Plus, we probably we want to regauss first.
926 isl_basic_map_drop_inequality(bmap, l);
927 isl_basic_map_inequality_to_equality(bmap, k);
929 bmap = isl_basic_map_set_to_empty(bmap);
939 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
946 bmap = isl_basic_map_normalize_constraints(bmap);
947 bmap = remove_duplicate_divs(bmap, &progress);
948 bmap = eliminate_divs_eq(bmap, &progress);
949 bmap = eliminate_divs_ineq(bmap, &progress);
950 bmap = isl_basic_map_gauss(bmap, &progress);
951 /* requires equalities in normal form */
952 bmap = normalize_divs(bmap, &progress);
953 bmap = remove_duplicate_constraints(bmap, &progress);
958 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
960 return (struct isl_basic_set *)
961 isl_basic_map_simplify((struct isl_basic_map *)bset);
965 /* If the only constraints a div d=floor(f/m)
966 * appears in are its two defining constraints
969 * -(f - (m - 1)) + m d >= 0
971 * then it can safely be removed.
973 static int div_is_redundant(struct isl_basic_map *bmap, int div)
976 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
978 for (i = 0; i < bmap->n_eq; ++i)
979 if (!isl_int_is_zero(bmap->eq[i][pos]))
982 for (i = 0; i < bmap->n_ineq; ++i) {
983 if (isl_int_is_zero(bmap->ineq[i][pos]))
985 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
987 isl_int_sub(bmap->div[div][1],
988 bmap->div[div][1], bmap->div[div][0]);
989 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
990 neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
991 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
992 isl_int_add(bmap->div[div][1],
993 bmap->div[div][1], bmap->div[div][0]);
996 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
997 bmap->n_div-div-1) != -1)
999 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1000 if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
1002 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1003 bmap->n_div-div-1) != -1)
1009 for (i = 0; i < bmap->n_div; ++i)
1010 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1017 * Remove divs that don't occur in any of the constraints or other divs.
1018 * These can arise when dropping some of the variables in a quast
1019 * returned by piplib.
1021 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1028 for (i = bmap->n_div-1; i >= 0; --i) {
1029 if (!div_is_redundant(bmap, i))
1031 bmap = isl_basic_map_drop_div(bmap, i);
1036 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1038 bmap = remove_redundant_divs(bmap);
1041 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1045 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1047 return (struct isl_basic_set *)
1048 isl_basic_map_finalize((struct isl_basic_map *)bset);
1051 struct isl_set *isl_set_finalize(struct isl_set *set)
1057 for (i = 0; i < set->n; ++i) {
1058 set->p[i] = isl_basic_set_finalize(set->p[i]);
1068 struct isl_map *isl_map_finalize(struct isl_map *map)
1074 for (i = 0; i < map->n; ++i) {
1075 map->p[i] = isl_basic_map_finalize(map->p[i]);
1079 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1087 /* Remove any div that is defined in terms of the given variable.
1089 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1093 unsigned dim = isl_dim_total(bmap->dim);
1095 for (i = 0; i < bmap->n_div; ++i) {
1096 if (isl_int_is_zero(bmap->div[i][0]))
1098 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1100 bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
1107 /* Eliminate the specified variables from the constraints using
1108 * Fourier-Motzkin. The variables themselves are not removed.
1110 struct isl_basic_map *isl_basic_map_eliminate_vars(
1111 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1121 total = isl_basic_map_total_dim(bmap);
1123 bmap = isl_basic_map_cow(bmap);
1124 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1125 bmap = remove_dependent_vars(bmap, d);
1127 for (d = pos + n - 1;
1128 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1129 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1130 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1131 int n_lower, n_upper;
1134 for (i = 0; i < bmap->n_eq; ++i) {
1135 if (isl_int_is_zero(bmap->eq[i][1+d]))
1137 eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1138 isl_basic_map_drop_equality(bmap, i);
1145 for (i = 0; i < bmap->n_ineq; ++i) {
1146 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1148 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1151 bmap = isl_basic_map_extend_constraints(bmap,
1152 0, n_lower * n_upper);
1153 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1155 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1158 for (j = 0; j < i; ++j) {
1159 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1162 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1163 isl_int_sgn(bmap->ineq[j][1+d]))
1165 k = isl_basic_map_alloc_inequality(bmap);
1168 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1170 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1171 1+d, 1+total, NULL);
1173 isl_basic_map_drop_inequality(bmap, i);
1176 if (n_lower > 0 && n_upper > 0) {
1177 bmap = isl_basic_map_normalize_constraints(bmap);
1178 bmap = remove_duplicate_constraints(bmap, NULL);
1179 bmap = isl_basic_map_gauss(bmap, NULL);
1180 bmap = isl_basic_map_convex_hull(bmap);
1183 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1187 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1190 isl_basic_map_free(bmap);
1194 struct isl_basic_set *isl_basic_set_eliminate_vars(
1195 struct isl_basic_set *bset, unsigned pos, unsigned n)
1197 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1198 (struct isl_basic_map *)bset, pos, n);
1201 /* Don't assume equalities are in order, because align_divs
1202 * may have changed the order of the divs.
1204 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1209 total = isl_dim_total(bmap->dim);
1210 for (d = 0; d < total; ++d)
1212 for (i = 0; i < bmap->n_eq; ++i) {
1213 for (d = total - 1; d >= 0; --d) {
1214 if (isl_int_is_zero(bmap->eq[i][1+d]))
1222 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1224 return compute_elimination_index((struct isl_basic_map *)bset, elim);
1227 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1228 struct isl_basic_map *bmap, int *elim)
1234 total = isl_dim_total(bmap->dim);
1235 for (d = total - 1; d >= 0; --d) {
1236 if (isl_int_is_zero(src[1+d]))
1241 isl_seq_cpy(dst, src, 1 + total);
1244 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1249 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1250 struct isl_basic_set *bset, int *elim)
1252 return reduced_using_equalities(dst, src,
1253 (struct isl_basic_map *)bset, elim);
1256 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1257 struct isl_basic_set *bset, struct isl_basic_set *context)
1262 if (!bset || !context)
1265 bset = isl_basic_set_cow(bset);
1269 elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1272 set_compute_elimination_index(context, elim);
1273 for (i = 0; i < bset->n_eq; ++i)
1274 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1276 for (i = 0; i < bset->n_ineq; ++i)
1277 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1279 isl_basic_set_free(context);
1281 bset = isl_basic_set_simplify(bset);
1282 bset = isl_basic_set_finalize(bset);
1285 isl_basic_set_free(bset);
1286 isl_basic_set_free(context);
1290 static struct isl_basic_set *remove_shifted_constraints(
1291 struct isl_basic_set *bset, struct isl_basic_set *context)
1301 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1302 bits = ffs(size) - 1;
1303 index = isl_calloc_array(ctx, isl_int **, size);
1307 for (k = 0; k < context->n_ineq; ++k) {
1308 h = set_hash_index(index, size, bits, context, k);
1309 index[h] = &context->ineq[k];
1311 for (k = 0; k < bset->n_ineq; ++k) {
1312 h = set_hash_index(index, size, bits, bset, k);
1315 l = index[h] - &context->ineq[0];
1316 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1318 bset = isl_basic_set_cow(bset);
1321 isl_basic_set_drop_inequality(bset, k);
1331 /* Tighten (decrease) the constant terms of the inequalities based
1332 * on the equalities, without removing any integer points.
1333 * For example, if there is an equality
1341 * then we want to replace the inequality by
1345 * We do this by computing a variable compression and translating
1346 * the constraints to the compressed space.
1347 * If any constraint has coefficients (except the contant term)
1348 * with a common factor "f", then we can replace the constant term "c"
1355 * f * floor(c/f) - c = -fract(c/f)
1357 * and we can add the same value to the original constraint.
1359 * In the example, the compressed space only contains "j",
1360 * and the inequality translates to
1364 * We add -fract(-1/3) = -2 to the original constraint to obtain
1368 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1369 struct isl_basic_set *bset)
1373 struct isl_mat *B, *C;
1379 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1385 bset = isl_basic_set_cow(bset);
1389 total = isl_basic_set_total_dim(bset);
1390 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1391 C = isl_mat_variable_compression(bset->ctx, B, NULL);
1394 if (C->n_col == 0) {
1395 isl_mat_free(bset->ctx, C);
1396 return isl_basic_set_set_to_empty(bset);
1398 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1399 0, bset->n_ineq, 0, 1 + total);
1400 C = isl_mat_product(bset->ctx, B, C);
1405 for (i = 0; i < bset->n_ineq; ++i) {
1406 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1407 if (isl_int_is_one(gcd))
1409 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1410 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1414 isl_mat_free(bset->ctx, C);
1419 /* Remove all information from bset that is redundant in the context
1420 * of context. In particular, equalities that are linear combinations
1421 * of those in context are removed. Then the inequalities that are
1422 * redundant in the context of the equalities and inequalities of
1423 * context are removed.
1425 * We first simplify the constraints of "bset" in the context of the
1426 * equalities of "context".
1427 * Then we simplify the inequalities of the context in the context
1428 * of the equalities of bset and remove the inequalities from "bset"
1429 * that are obviously redundant with respect to some inequality in "context".
1431 * If there are any inequalities left, we construct a tableau for
1432 * the context and then add the inequalities of "bset".
1433 * Before adding these equalities, we freeze all constraints such that
1434 * they won't be considered redundant in terms of the constraints of "bset".
1435 * Then we detect all equalities and redundant constraints (among the
1436 * constraints that weren't frozen) and update bset according to the results.
1437 * We have to be careful here because we don't want any of the context
1438 * constraints to remain and because we haven't added the equalities of "bset"
1439 * to the tableau so we temporarily have to pretend that there were no
1442 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1443 struct isl_basic_set *context)
1446 struct isl_tab *tab;
1447 unsigned context_ineq;
1448 struct isl_basic_set *combined = NULL;
1450 if (!context || !bset)
1453 if (context->n_eq > 0)
1454 bset = isl_basic_set_reduce_using_equalities(bset,
1455 isl_basic_set_copy(context));
1458 if (isl_basic_set_fast_is_empty(bset))
1463 if (bset->n_eq > 0) {
1464 struct isl_basic_set *affine_hull;
1465 affine_hull = isl_basic_set_copy(bset);
1466 affine_hull = isl_basic_set_cow(affine_hull);
1469 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1470 context = isl_basic_set_intersect(context, affine_hull);
1471 context = isl_basic_set_gauss(context, NULL);
1472 context = normalize_constraints_in_compressed_space(context);
1476 if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
1477 isl_basic_set_free(bset);
1480 if (!context->n_ineq)
1482 bset = remove_shifted_constraints(bset, context);
1485 isl_basic_set_free_equality(context, context->n_eq);
1486 context_ineq = context->n_ineq;
1487 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1488 combined = isl_basic_set_extend_constraints(combined,
1489 bset->n_eq, bset->n_ineq);
1490 tab = isl_tab_from_basic_set(combined);
1493 for (i = 0; i < context_ineq; ++i)
1494 tab->con[i].frozen = 1;
1495 tab = isl_tab_extend(bset->ctx, tab, bset->n_ineq);
1498 for (i = 0; i < bset->n_ineq; ++i)
1499 tab = isl_tab_add_ineq(bset->ctx, tab, bset->ineq[i]);
1500 bset = isl_basic_set_add_constraints(combined, bset, 0);
1501 tab = isl_tab_detect_equalities(bset->ctx, tab);
1502 tab = isl_tab_detect_redundant(bset->ctx, tab);
1505 for (i = 0; i < context_ineq; ++i) {
1506 tab->con[i].is_zero = 0;
1507 tab->con[i].is_redundant = 1;
1509 bset = isl_basic_set_update_from_tab(bset, tab);
1510 isl_tab_free(bset->ctx, tab);
1511 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1512 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1514 bset = isl_basic_set_simplify(bset);
1515 bset = isl_basic_set_finalize(bset);
1516 isl_basic_set_free(context);
1519 isl_basic_set_free(combined);
1521 isl_basic_set_free(bset);
1522 isl_basic_set_free(context);
1526 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1527 * We simply add the equalities in context to bmap and then do a regular
1528 * div normalizations. Better results can be obtained by normalizing
1529 * only the divs in bmap than do not also appear in context.
1530 * We need to be careful to reduce the divs using the equalities
1531 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1532 * spurious constraints.
1534 static struct isl_basic_map *normalize_divs_in_context(
1535 struct isl_basic_map *bmap, struct isl_basic_map *context)
1538 unsigned total_context;
1541 div_eq = n_pure_div_eq(bmap);
1545 if (context->n_div > 0)
1546 bmap = isl_basic_map_align_divs(bmap, context);
1548 total_context = isl_basic_map_total_dim(context);
1549 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1550 for (i = 0; i < context->n_eq; ++i) {
1552 k = isl_basic_map_alloc_equality(bmap);
1553 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1554 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1555 isl_basic_map_total_dim(bmap) - total_context);
1557 bmap = isl_basic_map_gauss(bmap, NULL);
1558 bmap = normalize_divs(bmap, NULL);
1559 bmap = isl_basic_map_gauss(bmap, NULL);
1563 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1564 struct isl_basic_map *context)
1566 struct isl_basic_set *bset;
1568 if (!bmap || !context)
1571 if (isl_basic_map_is_universe(context)) {
1572 isl_basic_map_free(context);
1575 if (isl_basic_map_is_universe(bmap)) {
1576 isl_basic_map_free(context);
1579 if (isl_basic_map_fast_is_empty(context)) {
1580 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1581 isl_basic_map_free(context);
1582 isl_basic_map_free(bmap);
1583 return isl_basic_map_universe(dim);
1585 if (isl_basic_map_fast_is_empty(bmap)) {
1586 isl_basic_map_free(context);
1590 bmap = isl_basic_map_convex_hull(bmap);
1591 context = isl_basic_map_convex_hull(context);
1594 bmap = normalize_divs_in_context(bmap, context);
1596 context = isl_basic_map_align_divs(context, bmap);
1597 bmap = isl_basic_map_align_divs(bmap, context);
1599 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1600 isl_basic_map_underlying_set(context));
1602 return isl_basic_map_overlying_set(bset, bmap);
1604 isl_basic_map_free(bmap);
1605 isl_basic_map_free(context);
1610 * Assumes context has no implicit divs.
1612 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1616 if (!map || !context)
1619 if (isl_basic_map_is_universe(context)) {
1620 isl_basic_map_free(context);
1623 if (isl_basic_map_fast_is_empty(context)) {
1624 struct isl_dim *dim = isl_dim_copy(map->dim);
1625 isl_basic_map_free(context);
1627 return isl_map_universe(dim);
1630 context = isl_basic_map_convex_hull(context);
1631 map = isl_map_cow(map);
1632 if (!map || !context)
1634 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1635 map = isl_map_compute_divs(map);
1636 for (i = 0; i < map->n; ++i)
1637 context = isl_basic_map_align_divs(context, map->p[i]);
1638 for (i = 0; i < map->n; ++i) {
1639 map->p[i] = isl_basic_map_gist(map->p[i],
1640 isl_basic_map_copy(context));
1644 isl_basic_map_free(context);
1645 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1649 isl_basic_map_free(context);
1653 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1654 struct isl_basic_set *context)
1656 return (struct isl_basic_set *)isl_basic_map_gist(
1657 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1660 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1662 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1663 (struct isl_basic_map *)context);
1666 /* Quick check to see if two basic maps are disjoint.
1667 * In particular, we reduce the equalities and inequalities of
1668 * one basic map in the context of the equalities of the other
1669 * basic map and check if we get a contradiction.
1671 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1672 struct isl_basic_map *bmap2)
1674 struct isl_vec *v = NULL;
1679 if (!bmap1 || !bmap2)
1681 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1683 if (bmap1->n_div || bmap2->n_div)
1685 if (!bmap1->n_eq && !bmap2->n_eq)
1688 total = isl_dim_total(bmap1->dim);
1691 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1694 elim = isl_alloc_array(bmap1->ctx, int, total);
1697 compute_elimination_index(bmap1, elim);
1698 for (i = 0; i < bmap2->n_eq; ++i) {
1700 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1702 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1703 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1706 for (i = 0; i < bmap2->n_ineq; ++i) {
1708 reduced = reduced_using_equalities(v->block.data,
1709 bmap2->ineq[i], bmap1, elim);
1710 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1711 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1714 compute_elimination_index(bmap2, elim);
1715 for (i = 0; i < bmap1->n_ineq; ++i) {
1717 reduced = reduced_using_equalities(v->block.data,
1718 bmap1->ineq[i], bmap2, elim);
1719 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1720 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1723 isl_vec_free(bmap1->ctx, v);
1727 isl_vec_free(bmap1->ctx, v);
1731 isl_vec_free(bmap1->ctx, v);
1736 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1737 struct isl_basic_set *bset2)
1739 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1740 (struct isl_basic_map *)bset2);
1743 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1750 if (isl_map_fast_is_equal(map1, map2))
1753 for (i = 0; i < map1->n; ++i) {
1754 for (j = 0; j < map2->n; ++j) {
1755 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1764 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1766 return isl_map_fast_is_disjoint((struct isl_map *)set1,
1767 (struct isl_map *)set2);