1 #include "isl_equalities.h"
3 #include "isl_map_private.h"
5 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
7 isl_int *t = bmap->eq[a];
8 bmap->eq[a] = bmap->eq[b];
12 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
15 isl_int *t = bmap->ineq[a];
16 bmap->ineq[a] = bmap->ineq[b];
21 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
23 swap_inequality((struct isl_basic_map *)bset, a, b);
26 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
28 isl_seq_cpy(c, c + n, rem);
29 isl_seq_clr(c + rem, n);
32 /* Drop n dimensions starting at first.
34 * In principle, this frees up some extra variables as the number
35 * of columns remains constant, but we would have to extend
36 * the div array too as the number of rows in this array is assumed
37 * to be equal to extra.
39 struct isl_basic_set *isl_basic_set_drop_dims(
40 struct isl_basic_set *bset, unsigned first, unsigned n)
47 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
52 bset = isl_basic_set_cow(bset);
56 for (i = 0; i < bset->n_eq; ++i)
57 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
58 (bset->dim->n_out-first-n)+bset->extra);
60 for (i = 0; i < bset->n_ineq; ++i)
61 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
62 (bset->dim->n_out-first-n)+bset->extra);
64 for (i = 0; i < bset->n_div; ++i)
65 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
66 (bset->dim->n_out-first-n)+bset->extra);
68 bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
72 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
73 bset = isl_basic_set_simplify(bset);
74 return isl_basic_set_finalize(bset);
76 isl_basic_set_free(bset);
80 struct isl_set *isl_set_drop_dims(
81 struct isl_set *set, unsigned first, unsigned n)
88 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
92 set = isl_set_cow(set);
95 set->dim = isl_dim_drop_outputs(set->dim, first, n);
99 for (i = 0; i < set->n; ++i) {
100 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
105 ISL_F_CLR(set, ISL_SET_NORMALIZED);
112 /* Drop n input dimensions starting at first.
114 * In principle, this frees up some extra variables as the number
115 * of columns remains constant, but we would have to extend
116 * the div array too as the number of rows in this array is assumed
117 * to be equal to extra.
119 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
120 enum isl_dim_type type, unsigned first, unsigned n)
130 dim = isl_basic_map_dim(bmap, type);
131 isl_assert(bmap->ctx, first + n <= dim, goto error);
136 bmap = isl_basic_map_cow(bmap);
140 offset = isl_basic_map_offset(bmap, type) + first;
141 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
142 for (i = 0; i < bmap->n_eq; ++i)
143 constraint_drop_vars(bmap->eq[i]+offset, n, left);
145 for (i = 0; i < bmap->n_ineq; ++i)
146 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
148 for (i = 0; i < bmap->n_div; ++i)
149 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
151 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
155 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
156 bmap = isl_basic_map_simplify(bmap);
157 return isl_basic_map_finalize(bmap);
159 isl_basic_map_free(bmap);
163 struct isl_basic_map *isl_basic_map_drop_inputs(
164 struct isl_basic_map *bmap, unsigned first, unsigned n)
166 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
169 struct isl_map *isl_map_drop(struct isl_map *map,
170 enum isl_dim_type type, unsigned first, unsigned n)
177 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
181 map = isl_map_cow(map);
184 map->dim = isl_dim_drop(map->dim, type, first, n);
188 for (i = 0; i < map->n; ++i) {
189 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
193 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
201 struct isl_map *isl_map_drop_inputs(
202 struct isl_map *map, unsigned first, unsigned n)
204 return isl_map_drop(map, isl_dim_in, first, n);
208 * We don't cow, as the div is assumed to be redundant.
210 static struct isl_basic_map *isl_basic_map_drop_div(
211 struct isl_basic_map *bmap, unsigned div)
219 pos = 1 + isl_dim_total(bmap->dim) + div;
221 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
223 for (i = 0; i < bmap->n_eq; ++i)
224 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
226 for (i = 0; i < bmap->n_ineq; ++i) {
227 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
228 isl_basic_map_drop_inequality(bmap, i);
232 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
235 for (i = 0; i < bmap->n_div; ++i)
236 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
238 if (div != bmap->n_div - 1) {
240 isl_int *t = bmap->div[div];
242 for (j = div; j < bmap->n_div - 1; ++j)
243 bmap->div[j] = bmap->div[j+1];
245 bmap->div[bmap->n_div - 1] = t;
247 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
248 isl_basic_map_free_div(bmap, 1);
252 isl_basic_map_free(bmap);
256 static struct isl_basic_map *normalize_constraints(struct isl_basic_map *bmap)
260 unsigned total = isl_basic_map_total_dim(bmap);
263 for (i = bmap->n_eq - 1; i >= 0; --i) {
264 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
265 if (isl_int_is_zero(gcd)) {
266 if (!isl_int_is_zero(bmap->eq[i][0])) {
267 bmap = isl_basic_map_set_to_empty(bmap);
270 isl_basic_map_drop_equality(bmap, i);
273 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
274 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
275 if (isl_int_is_one(gcd))
277 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
278 bmap = isl_basic_map_set_to_empty(bmap);
281 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
284 for (i = bmap->n_ineq - 1; i >= 0; --i) {
285 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
286 if (isl_int_is_zero(gcd)) {
287 if (isl_int_is_neg(bmap->ineq[i][0])) {
288 bmap = isl_basic_map_set_to_empty(bmap);
291 isl_basic_map_drop_inequality(bmap, i);
294 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
295 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
296 if (isl_int_is_one(gcd))
298 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
299 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
306 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
309 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
311 len = 1 + isl_basic_map_total_dim(bmap);
313 for (i = 0; i < bmap->n_eq; ++i)
314 if (bmap->eq[i] != eq)
315 isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
317 for (i = 0; i < bmap->n_ineq; ++i)
318 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
320 /* We need to be careful about circular definitions,
321 * so for now we just remove the definitions of other divs that
322 * depend on this div and (possibly) recompute them later.
324 for (i = 0; i < bmap->n_div; ++i)
325 if (!isl_int_is_zero(bmap->div[i][0]) &&
326 !isl_int_is_zero(bmap->div[i][1 + pos]))
327 isl_seq_clr(bmap->div[i], 1 + len);
329 isl_basic_map_drop_div(bmap, div);
332 /* Elimininate divs based on equalities
334 static struct isl_basic_map *eliminate_divs_eq(
335 struct isl_basic_map *bmap, int *progress)
345 off = 1 + isl_dim_total(bmap->dim);
347 for (d = bmap->n_div - 1; d >= 0 ; --d) {
348 for (i = 0; i < bmap->n_eq; ++i) {
349 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
350 !isl_int_is_negone(bmap->eq[i][off + d]))
354 eliminate_div(bmap, bmap->eq[i], d);
355 isl_basic_map_drop_equality(bmap, i);
360 return eliminate_divs_eq(bmap, progress);
364 /* Elimininate divs based on inequalities
366 static struct isl_basic_map *eliminate_divs_ineq(
367 struct isl_basic_map *bmap, int *progress)
378 off = 1 + isl_dim_total(bmap->dim);
380 for (d = bmap->n_div - 1; d >= 0 ; --d) {
381 for (i = 0; i < bmap->n_eq; ++i)
382 if (!isl_int_is_zero(bmap->eq[i][off + d]))
386 for (i = 0; i < bmap->n_ineq; ++i)
387 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
389 if (i < bmap->n_ineq)
392 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
393 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
395 bmap = isl_basic_map_drop_div(bmap, d);
402 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
403 unsigned pos, isl_int *eq, int *progress)
409 total = isl_basic_map_total_dim(bmap);
411 isl_seq_first_non_zero(eq + 1 + isl_dim_total(bmap->dim),
413 for (k = 0; k < bmap->n_eq; ++k) {
414 if (bmap->eq[k] == eq)
416 if (isl_int_is_zero(bmap->eq[k][1+pos]))
420 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
423 for (k = 0; k < bmap->n_ineq; ++k) {
424 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
428 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
429 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
432 for (k = 0; k < bmap->n_div; ++k) {
433 if (isl_int_is_zero(bmap->div[k][0]))
435 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
439 /* We need to be careful about circular definitions,
440 * so for now we just remove the definition of div k
441 * if the equality contains any divs.
444 isl_seq_clr(bmap->div[k], 1 + total);
446 isl_seq_elim(bmap->div[k]+1, eq,
447 1+pos, 1+total, &bmap->div[k][0]);
448 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
452 struct isl_basic_map *isl_basic_map_gauss(
453 struct isl_basic_map *bmap, int *progress)
464 total = isl_basic_map_total_dim(bmap);
465 total_var = total - bmap->n_div;
467 last_var = total - 1;
468 for (done = 0; done < bmap->n_eq; ++done) {
469 for (; last_var >= 0; --last_var) {
470 for (k = done; k < bmap->n_eq; ++k)
471 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
479 swap_equality(bmap, k, done);
480 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
481 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
483 eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
486 if (last_var >= total_var &&
487 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
488 unsigned div = last_var - total_var;
489 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
490 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
491 isl_int_set(bmap->div[div][0],
492 bmap->eq[done][1+last_var]);
493 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
496 if (done == bmap->n_eq)
498 for (k = done; k < bmap->n_eq; ++k) {
499 if (isl_int_is_zero(bmap->eq[k][0]))
501 return isl_basic_map_set_to_empty(bmap);
503 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
507 struct isl_basic_set *isl_basic_set_gauss(
508 struct isl_basic_set *bset, int *progress)
510 return (struct isl_basic_set*)isl_basic_map_gauss(
511 (struct isl_basic_map *)bset, progress);
515 static unsigned int round_up(unsigned int v)
526 static int hash_index(isl_int ***index, unsigned int size, int bits,
527 struct isl_basic_map *bmap, int k)
530 unsigned total = isl_basic_map_total_dim(bmap);
531 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
532 for (h = hash; index[h]; h = (h+1) % size)
533 if (&bmap->ineq[k] != index[h] &&
534 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
539 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
540 struct isl_basic_set *bset, int k)
542 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
545 /* If we can eliminate more than one div, then we need to make
546 * sure we do it from last div to first div, in order not to
547 * change the position of the other divs that still need to
550 static struct isl_basic_map *remove_duplicate_divs(
551 struct isl_basic_map *bmap, int *progress)
559 unsigned total_var = isl_dim_total(bmap->dim);
560 unsigned total = total_var + bmap->n_div;
563 if (bmap->n_div <= 1)
567 for (k = bmap->n_div - 1; k >= 0; --k)
568 if (!isl_int_is_zero(bmap->div[k][0]))
573 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
574 size = round_up(4 * bmap->n_div / 3 - 1);
575 bits = ffs(size) - 1;
576 index = isl_calloc_array(ctx, int, size);
579 eq = isl_blk_alloc(ctx, 1+total);
580 if (isl_blk_is_error(eq))
583 isl_seq_clr(eq.data, 1+total);
584 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
585 for (--k; k >= 0; --k) {
588 if (isl_int_is_zero(bmap->div[k][0]))
591 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
592 for (h = hash; index[h]; h = (h+1) % size)
593 if (isl_seq_eq(bmap->div[k],
594 bmap->div[index[h]-1], 2+total))
603 for (l = bmap->n_div - 1; l >= 0; --l) {
607 isl_int_set_si(eq.data[1+total_var+k], -1);
608 isl_int_set_si(eq.data[1+total_var+l], 1);
609 eliminate_div(bmap, eq.data, l);
610 isl_int_set_si(eq.data[1+total_var+k], 0);
611 isl_int_set_si(eq.data[1+total_var+l], 0);
614 isl_blk_free(ctx, eq);
621 /* Normalize divs that appear in equalities.
623 * In particular, we assume that bmap contains some equalities
628 * and we want to replace the set of e_i by a minimal set and
629 * such that the new e_i have a canonical representation in terms
631 * If any of the equalities involves more than one divs, then
632 * we currently simply bail out.
634 * Let us first additionally assume that all equalities involve
635 * a div. The equalities then express modulo constraints on the
636 * remaining variables and we can use "parameter compression"
637 * to find a minimal set of constraints. The result is a transformation
639 * x = T(x') = x_0 + G x'
641 * with G a lower-triangular matrix with all elements below the diagonal
642 * non-negative and smaller than the diagonal element on the same row.
643 * We first normalize x_0 by making the same property hold in the affine
645 * The rows i of G with a 1 on the diagonal do not impose any modulo
646 * constraint and simply express x_i = x'_i.
647 * For each of the remaining rows i, we introduce a div and a corresponding
648 * equality. In particular
650 * g_ii e_j = x_i - g_i(x')
652 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
653 * corresponding div (if g_kk != 1).
655 * If there are any equalities not involving any div, then we
656 * first apply a variable compression on the variables x:
658 * x = C x'' x'' = C_2 x
660 * and perform the above parameter compression on A C instead of on A.
661 * The resulting compression is then of the form
663 * x'' = T(x') = x_0 + G x'
665 * and in constructing the new divs and the corresponding equalities,
666 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
667 * by the corresponding row from C_2.
669 static struct isl_basic_map *normalize_divs(
670 struct isl_basic_map *bmap, int *progress)
677 struct isl_mat *T = NULL;
678 struct isl_mat *C = NULL;
679 struct isl_mat *C2 = NULL;
687 if (bmap->n_div == 0)
693 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
696 total = isl_dim_total(bmap->dim);
697 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
698 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
702 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
709 if (div_eq < bmap->n_eq) {
710 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
711 bmap->n_eq - div_eq, 0, 1 + total);
712 C = isl_mat_variable_compression(bmap->ctx, B, &C2);
716 bmap = isl_basic_map_set_to_empty(bmap);
717 isl_mat_free(bmap->ctx, C);
718 isl_mat_free(bmap->ctx, C2);
723 d = isl_vec_alloc(bmap->ctx, div_eq);
726 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
727 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
729 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
731 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
734 B = isl_mat_product(bmap->ctx, B, C);
738 T = isl_mat_parameter_compression(bmap->ctx, B, d);
742 bmap = isl_basic_map_set_to_empty(bmap);
743 isl_mat_free(bmap->ctx, C2);
744 isl_mat_free(bmap->ctx, T);
748 for (i = 0; i < T->n_row - 1; ++i) {
749 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
750 if (isl_int_is_zero(v))
752 isl_mat_col_submul(T, 0, v, 1 + i);
755 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
756 /* We have to be careful because dropping equalities may reorder them */
758 for (j = bmap->n_div - 1; j >= 0; --j) {
759 for (i = 0; i < bmap->n_eq; ++i)
760 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
762 if (i < bmap->n_eq) {
763 bmap = isl_basic_map_drop_div(bmap, j);
764 isl_basic_map_drop_equality(bmap, i);
770 for (i = 1; i < T->n_row; ++i) {
771 if (isl_int_is_one(T->row[i][i]))
776 if (needed > dropped) {
777 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
782 for (i = 1; i < T->n_row; ++i) {
783 if (isl_int_is_one(T->row[i][i]))
785 k = isl_basic_map_alloc_div(bmap);
786 pos[i] = 1 + total + k;
787 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
788 isl_int_set(bmap->div[k][0], T->row[i][i]);
790 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
792 isl_int_set_si(bmap->div[k][1 + i], 1);
793 for (j = 0; j < i; ++j) {
794 if (isl_int_is_zero(T->row[i][j]))
796 if (pos[j] < T->n_row && C2)
797 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
798 C2->row[pos[j]], 1 + total);
800 isl_int_neg(bmap->div[k][1 + pos[j]],
803 j = isl_basic_map_alloc_equality(bmap);
804 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
805 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
808 isl_mat_free(bmap->ctx, C2);
809 isl_mat_free(bmap->ctx, T);
813 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
817 isl_mat_free(bmap->ctx, C);
818 isl_mat_free(bmap->ctx, C2);
819 isl_mat_free(bmap->ctx, T);
823 static struct isl_basic_map *remove_duplicate_constraints(
824 struct isl_basic_map *bmap, int *progress)
830 unsigned total = isl_basic_map_total_dim(bmap);
833 if (bmap->n_ineq <= 1)
836 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
837 bits = ffs(size) - 1;
838 index = isl_calloc_array(ctx, isl_int **, size);
842 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
843 for (k = 1; k < bmap->n_ineq; ++k) {
844 h = hash_index(index, size, bits, bmap, k);
846 index[h] = &bmap->ineq[k];
851 l = index[h] - &bmap->ineq[0];
852 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
853 swap_inequality(bmap, k, l);
854 isl_basic_map_drop_inequality(bmap, k);
858 for (k = 0; k < bmap->n_ineq-1; ++k) {
859 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
860 h = hash_index(index, size, bits, bmap, k);
861 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
864 l = index[h] - &bmap->ineq[0];
865 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
866 if (isl_int_is_pos(sum))
868 if (isl_int_is_zero(sum)) {
869 /* We need to break out of the loop after these
870 * changes since the contents of the hash
871 * will no longer be valid.
872 * Plus, we probably we want to regauss first.
874 isl_basic_map_drop_inequality(bmap, l);
875 isl_basic_map_inequality_to_equality(bmap, k);
877 bmap = isl_basic_map_set_to_empty(bmap);
887 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
894 bmap = normalize_constraints(bmap);
895 bmap = eliminate_divs_eq(bmap, &progress);
896 bmap = eliminate_divs_ineq(bmap, &progress);
897 bmap = isl_basic_map_gauss(bmap, &progress);
898 /* requires equalities in normal form */
899 bmap = normalize_divs(bmap, &progress);
900 bmap = remove_duplicate_divs(bmap, &progress);
901 bmap = remove_duplicate_constraints(bmap, &progress);
906 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
908 return (struct isl_basic_set *)
909 isl_basic_map_simplify((struct isl_basic_map *)bset);
913 /* If the only constraints a div d=floor(f/m)
914 * appears in are its two defining constraints
917 * -(f - (m - 1)) + m d >= 0
919 * then it can safely be removed.
921 static int div_is_redundant(struct isl_basic_map *bmap, int div)
924 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
926 for (i = 0; i < bmap->n_eq; ++i)
927 if (!isl_int_is_zero(bmap->eq[i][pos]))
930 for (i = 0; i < bmap->n_ineq; ++i) {
931 if (isl_int_is_zero(bmap->ineq[i][pos]))
933 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
935 isl_int_sub(bmap->div[div][1],
936 bmap->div[div][1], bmap->div[div][0]);
937 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
938 neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
939 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
940 isl_int_add(bmap->div[div][1],
941 bmap->div[div][1], bmap->div[div][0]);
944 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
945 bmap->n_div-div-1) != -1)
947 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
948 if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
950 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
951 bmap->n_div-div-1) != -1)
957 for (i = 0; i < bmap->n_div; ++i)
958 if (!isl_int_is_zero(bmap->div[i][1+pos]))
965 * Remove divs that don't occur in any of the constraints or other divs.
966 * These can arise when dropping some of the variables in a quast
967 * returned by piplib.
969 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
976 for (i = bmap->n_div-1; i >= 0; --i) {
977 if (!div_is_redundant(bmap, i))
979 bmap = isl_basic_map_drop_div(bmap, i);
984 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
986 bmap = remove_redundant_divs(bmap);
989 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
993 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
995 return (struct isl_basic_set *)
996 isl_basic_map_finalize((struct isl_basic_map *)bset);
999 struct isl_set *isl_set_finalize(struct isl_set *set)
1005 for (i = 0; i < set->n; ++i) {
1006 set->p[i] = isl_basic_set_finalize(set->p[i]);
1016 struct isl_map *isl_map_finalize(struct isl_map *map)
1022 for (i = 0; i < map->n; ++i) {
1023 map->p[i] = isl_basic_map_finalize(map->p[i]);
1027 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1035 /* Remove any div that is defined in terms of the given variable.
1037 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1041 unsigned dim = isl_dim_total(bmap->dim);
1043 for (i = 0; i < bmap->n_div; ++i) {
1044 if (isl_int_is_zero(bmap->div[i][0]))
1046 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1048 bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
1055 /* Eliminate the specified variables from the constraints using
1056 * Fourier-Motzkin. The variables themselves are not removed.
1058 struct isl_basic_map *isl_basic_map_eliminate_vars(
1059 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1069 total = isl_basic_map_total_dim(bmap);
1071 bmap = isl_basic_map_cow(bmap);
1072 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1073 int n_lower, n_upper;
1074 bmap = remove_dependent_vars(bmap, d);
1077 if (d >= total - bmap->n_div)
1078 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1079 for (i = 0; i < bmap->n_eq; ++i) {
1080 if (isl_int_is_zero(bmap->eq[i][1+d]))
1082 eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1083 isl_basic_map_drop_equality(bmap, i);
1090 for (i = 0; i < bmap->n_ineq; ++i) {
1091 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1093 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1096 bmap = isl_basic_map_extend_constraints(bmap,
1097 0, n_lower * n_upper);
1098 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1100 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1103 for (j = 0; j < i; ++j) {
1104 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1107 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1108 isl_int_sgn(bmap->ineq[j][1+d]))
1110 k = isl_basic_map_alloc_inequality(bmap);
1113 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1115 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1116 1+d, 1+total, NULL);
1118 isl_basic_map_drop_inequality(bmap, i);
1121 if (n_lower > 0 && n_upper > 0) {
1122 bmap = normalize_constraints(bmap);
1123 bmap = remove_duplicate_constraints(bmap, NULL);
1124 bmap = isl_basic_map_gauss(bmap, NULL);
1125 bmap = isl_basic_map_convex_hull(bmap);
1128 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1132 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1135 isl_basic_map_free(bmap);
1139 struct isl_basic_set *isl_basic_set_eliminate_vars(
1140 struct isl_basic_set *bset, unsigned pos, unsigned n)
1142 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1143 (struct isl_basic_map *)bset, pos, n);
1146 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1151 total = isl_dim_total(bmap->dim);
1152 for (d = 0; d < total; ++d)
1154 for (d = total - 1, i = 0; d >= 0 && i < bmap->n_eq; ++i) {
1155 for (; d >= 0; --d) {
1156 if (isl_int_is_zero(bmap->eq[i][1+d]))
1164 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1166 return compute_elimination_index((struct isl_basic_map *)bset, elim);
1169 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1170 struct isl_basic_map *bmap, int *elim)
1176 total = isl_dim_total(bmap->dim);
1177 for (d = total - 1; d >= 0; --d) {
1178 if (isl_int_is_zero(src[1+d]))
1183 isl_seq_cpy(dst, src, 1 + total);
1186 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1191 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1192 struct isl_basic_set *bset, int *elim)
1194 return reduced_using_equalities(dst, src,
1195 (struct isl_basic_map *)bset, elim);
1198 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1199 struct isl_basic_set *bset, struct isl_basic_set *context)
1204 if (!bset || !context)
1207 bset = isl_basic_set_cow(bset);
1211 elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1214 set_compute_elimination_index(context, elim);
1215 for (i = 0; i < bset->n_eq; ++i)
1216 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1218 for (i = 0; i < bset->n_ineq; ++i)
1219 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1221 isl_basic_set_free(context);
1223 bset = isl_basic_set_simplify(bset);
1224 bset = isl_basic_set_finalize(bset);
1227 isl_basic_set_free(bset);
1228 isl_basic_set_free(context);
1232 static struct isl_basic_set *remove_shifted_constraints(
1233 struct isl_basic_set *bset, struct isl_basic_set *context)
1243 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1244 bits = ffs(size) - 1;
1245 index = isl_calloc_array(ctx, isl_int **, size);
1249 for (k = 0; k < context->n_ineq; ++k) {
1250 h = set_hash_index(index, size, bits, context, k);
1251 index[h] = &context->ineq[k];
1253 for (k = 0; k < bset->n_ineq; ++k) {
1254 h = set_hash_index(index, size, bits, bset, k);
1257 l = index[h] - &context->ineq[0];
1258 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1260 bset = isl_basic_set_cow(bset);
1263 isl_basic_set_drop_inequality(bset, k);
1273 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1274 struct isl_basic_set *context);
1276 static struct isl_basic_set *uset_gist_context_eq(struct isl_basic_set *bset,
1277 struct isl_basic_set *context)
1281 struct isl_ctx *ctx = context->ctx;
1282 struct isl_basic_set *reduced_context;
1283 reduced_context = isl_basic_set_remove_equalities(
1284 isl_basic_set_copy(context), &T, &T2);
1285 if (!reduced_context)
1287 bset = isl_basic_set_preimage(bset, T);
1288 bset = uset_gist(bset, reduced_context);
1289 bset = isl_basic_set_preimage(bset, T2);
1290 bset = isl_basic_set_reduce_using_equalities(bset, context);
1293 isl_basic_set_free(context);
1294 isl_basic_set_free(bset);
1298 static struct isl_basic_set *uset_gist_set_eq(struct isl_basic_set *bset,
1299 struct isl_basic_set *context)
1303 struct isl_ctx *ctx = context->ctx;
1304 struct isl_basic_set *affine_hull = NULL;
1306 affine_hull = isl_basic_set_copy(bset);
1307 affine_hull = isl_basic_set_cow(affine_hull);
1310 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1312 bset = isl_basic_set_remove_equalities(bset, &T, &T2);
1315 context = isl_basic_set_preimage(context, T);
1316 bset = uset_gist(bset, context);
1317 bset = isl_basic_set_preimage(bset, T2);
1318 bset = isl_basic_set_intersect(bset, affine_hull);
1321 isl_basic_set_free(affine_hull);
1322 isl_basic_set_free(context);
1323 isl_basic_set_free(bset);
1327 /* Remove all information from bset that is redundant in the context
1328 * of context. In particular, equalities that are linear combinations
1329 * of those in context are removed. Then the inequalities that are
1330 * redundant in the context of the equalities and inequalities of
1331 * context are removed.
1333 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1334 struct isl_basic_set *context)
1338 struct isl_basic_set *combined;
1339 struct isl_ctx *ctx;
1341 if (!bset || !context)
1344 if (context->n_eq > 0)
1345 return uset_gist_context_eq(bset, context);
1346 if (!context->n_ineq)
1349 return uset_gist_set_eq(bset, context);
1350 bset = remove_shifted_constraints(bset, context);
1351 combined = isl_basic_set_extend_constraints(isl_basic_set_copy(bset),
1352 context->n_eq, context->n_ineq);
1353 context = isl_basic_set_add_constraints(combined, context, 0);
1358 for (i = bset->n_ineq-1; i >= 0; --i) {
1360 set_swap_inequality(context, i, context->n_ineq-1);
1362 redundant = isl_basic_set_constraint_is_redundant(&context,
1363 context->ineq[context->n_ineq], &opt, NULL);
1364 if (redundant == -1) {
1368 if (ISL_F_ISSET(context, ISL_BASIC_MAP_EMPTY)) {
1369 bset = isl_basic_set_set_to_empty(bset);
1373 set_swap_inequality(context, i, context->n_ineq-1);
1375 isl_basic_set_drop_inequality(context, i);
1376 isl_basic_set_drop_inequality(bset, i);
1381 isl_basic_set_free(context);
1384 isl_basic_set_free(context);
1385 isl_basic_set_free(bset);
1389 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1390 struct isl_basic_map *context)
1392 struct isl_basic_set *bset;
1394 if (!bmap || !context)
1397 context = isl_basic_map_align_divs(context, bmap);
1398 bmap = isl_basic_map_align_divs(bmap, context);
1400 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1401 isl_basic_map_underlying_set(context));
1403 return isl_basic_map_overlying_set(bset, bmap);
1405 isl_basic_map_free(bmap);
1406 isl_basic_map_free(context);
1411 * Assumes context has no implicit divs.
1413 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1417 map = isl_map_cow(map);
1418 if (!map || !context)
1420 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1421 map = isl_map_compute_divs(map);
1422 for (i = 0; i < map->n; ++i)
1423 context = isl_basic_map_align_divs(context, map->p[i]);
1424 for (i = 0; i < map->n; ++i) {
1425 map->p[i] = isl_basic_map_gist(map->p[i],
1426 isl_basic_map_copy(context));
1430 isl_basic_map_free(context);
1431 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1435 isl_basic_map_free(context);
1439 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1440 struct isl_basic_set *context)
1442 return (struct isl_basic_set *)isl_basic_map_gist(
1443 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1446 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1448 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1449 (struct isl_basic_map *)context);
1452 /* Quick check to see if two basic maps are disjoint.
1453 * In particular, we reduce the equalities and inequalities of
1454 * one basic map in the context of the equalities of the other
1455 * basic map and check if we get a contradiction.
1457 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1458 struct isl_basic_map *bmap2)
1460 struct isl_vec *v = NULL;
1465 if (!bmap1 || !bmap2)
1467 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1469 if (bmap1->n_div || bmap2->n_div)
1471 if (!bmap1->n_eq && !bmap2->n_eq)
1474 total = isl_dim_total(bmap1->dim);
1477 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1480 elim = isl_alloc_array(bmap1->ctx, int, total);
1483 compute_elimination_index(bmap1, elim);
1484 for (i = 0; i < bmap2->n_eq; ++i) {
1486 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1488 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1489 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1492 for (i = 0; i < bmap2->n_ineq; ++i) {
1494 reduced = reduced_using_equalities(v->block.data,
1495 bmap2->ineq[i], bmap1, elim);
1496 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1497 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1500 compute_elimination_index(bmap2, elim);
1501 for (i = 0; i < bmap1->n_ineq; ++i) {
1503 reduced = reduced_using_equalities(v->block.data,
1504 bmap1->ineq[i], bmap2, elim);
1505 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1506 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1509 isl_vec_free(bmap1->ctx, v);
1513 isl_vec_free(bmap1->ctx, v);
1517 isl_vec_free(bmap1->ctx, v);
1522 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1523 struct isl_basic_set *bset2)
1525 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1526 (struct isl_basic_map *)bset2);
1529 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1536 if (isl_map_fast_is_equal(map1, map2))
1539 for (i = 0; i < map1->n; ++i) {
1540 for (j = 0; j < map2->n; ++j) {
1541 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1550 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1552 return isl_map_fast_is_disjoint((struct isl_map *)set1,
1553 (struct isl_map *)set2);