2 * Copyright 2011 INRIA Saclay
3 * Copyright 2012 Ecole Normale Superieure
5 * Use of this software is governed by the GNU LGPLv2.1 license
7 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
8 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
10 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_local_space_private.h>
16 #include <isl_space_private.h>
17 #include <isl_mat_private.h>
18 #include <isl_aff_private.h>
21 isl_ctx *isl_local_space_get_ctx(__isl_keep isl_local_space *ls)
23 return ls ? ls->dim->ctx : NULL;
26 __isl_give isl_local_space *isl_local_space_alloc_div(__isl_take isl_space *dim,
27 __isl_take isl_mat *div)
30 isl_local_space *ls = NULL;
35 ctx = isl_space_get_ctx(dim);
36 ls = isl_calloc_type(ctx, struct isl_local_space);
48 isl_local_space_free(ls);
52 __isl_give isl_local_space *isl_local_space_alloc(__isl_take isl_space *dim,
62 total = isl_space_dim(dim, isl_dim_all);
64 ctx = isl_space_get_ctx(dim);
65 div = isl_mat_alloc(ctx, n_div, 1 + 1 + total + n_div);
66 return isl_local_space_alloc_div(dim, div);
69 __isl_give isl_local_space *isl_local_space_from_space(__isl_take isl_space *dim)
71 return isl_local_space_alloc(dim, 0);
74 __isl_give isl_local_space *isl_local_space_copy(__isl_keep isl_local_space *ls)
83 __isl_give isl_local_space *isl_local_space_dup(__isl_keep isl_local_space *ls)
88 return isl_local_space_alloc_div(isl_space_copy(ls->dim),
89 isl_mat_copy(ls->div));
93 __isl_give isl_local_space *isl_local_space_cow(__isl_take isl_local_space *ls)
101 return isl_local_space_dup(ls);
104 void *isl_local_space_free(__isl_take isl_local_space *ls)
112 isl_space_free(ls->dim);
113 isl_mat_free(ls->div);
120 /* Is the local space that of a set?
122 int isl_local_space_is_set(__isl_keep isl_local_space *ls)
124 return ls ? isl_space_is_set(ls->dim) : -1;
127 /* Return true if the two local spaces are identical, with identical
128 * expressions for the integer divisions.
130 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
131 __isl_keep isl_local_space *ls2)
138 equal = isl_space_is_equal(ls1->dim, ls2->dim);
139 if (equal < 0 || !equal)
142 if (!isl_local_space_divs_known(ls1))
144 if (!isl_local_space_divs_known(ls2))
147 return isl_mat_is_equal(ls1->div, ls2->div);
150 int isl_local_space_dim(__isl_keep isl_local_space *ls,
151 enum isl_dim_type type)
155 if (type == isl_dim_div)
156 return ls->div->n_row;
157 if (type == isl_dim_all)
158 return isl_space_dim(ls->dim, isl_dim_all) + ls->div->n_row;
159 return isl_space_dim(ls->dim, type);
162 unsigned isl_local_space_offset(__isl_keep isl_local_space *ls,
163 enum isl_dim_type type)
172 case isl_dim_cst: return 0;
173 case isl_dim_param: return 1;
174 case isl_dim_in: return 1 + dim->nparam;
175 case isl_dim_out: return 1 + dim->nparam + dim->n_in;
176 case isl_dim_div: return 1 + dim->nparam + dim->n_in + dim->n_out;
181 const char *isl_local_space_get_dim_name(__isl_keep isl_local_space *ls,
182 enum isl_dim_type type, unsigned pos)
184 return ls ? isl_space_get_dim_name(ls->dim, type, pos) : NULL;
187 __isl_give isl_aff *isl_local_space_get_div(__isl_keep isl_local_space *ls,
195 if (pos < 0 || pos >= ls->div->n_row)
196 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
197 "index out of bounds", return NULL);
199 if (isl_int_is_zero(ls->div->row[pos][0]))
200 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
201 "expression of div unknown", return NULL);
203 aff = isl_aff_alloc(isl_local_space_copy(ls));
206 isl_seq_cpy(aff->v->el, ls->div->row[pos], aff->v->size);
210 __isl_give isl_space *isl_local_space_get_space(__isl_keep isl_local_space *ls)
215 return isl_space_copy(ls->dim);
218 __isl_give isl_local_space *isl_local_space_set_dim_name(
219 __isl_take isl_local_space *ls,
220 enum isl_dim_type type, unsigned pos, const char *s)
222 ls = isl_local_space_cow(ls);
225 ls->dim = isl_space_set_dim_name(ls->dim, type, pos, s);
227 return isl_local_space_free(ls);
232 __isl_give isl_local_space *isl_local_space_set_dim_id(
233 __isl_take isl_local_space *ls,
234 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
236 ls = isl_local_space_cow(ls);
238 return isl_id_free(id);
239 ls->dim = isl_space_set_dim_id(ls->dim, type, pos, id);
241 return isl_local_space_free(ls);
246 __isl_give isl_local_space *isl_local_space_reset_space(
247 __isl_take isl_local_space *ls, __isl_take isl_space *dim)
249 ls = isl_local_space_cow(ls);
253 isl_space_free(ls->dim);
258 isl_local_space_free(ls);
263 /* Reorder the columns of the given div definitions according to the
265 * The order of the divs themselves is assumed not to change.
267 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
268 __isl_take isl_reordering *r)
277 extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
278 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
282 for (i = 0; i < div->n_row; ++i) {
283 isl_seq_cpy(mat->row[i], div->row[i], 2);
284 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
285 for (j = 0; j < r->len; ++j)
286 isl_int_set(mat->row[i][2 + r->pos[j]],
290 isl_reordering_free(r);
294 isl_reordering_free(r);
299 /* Reorder the dimensions of "ls" according to the given reordering.
300 * The reordering r is assumed to have been extended with the local
301 * variables, leaving them in the same order.
303 __isl_give isl_local_space *isl_local_space_realign(
304 __isl_take isl_local_space *ls, __isl_take isl_reordering *r)
306 ls = isl_local_space_cow(ls);
310 ls->div = reorder_divs(ls->div, isl_reordering_copy(r));
314 ls = isl_local_space_reset_space(ls, isl_space_copy(r->dim));
316 isl_reordering_free(r);
319 isl_local_space_free(ls);
320 isl_reordering_free(r);
324 __isl_give isl_local_space *isl_local_space_add_div(
325 __isl_take isl_local_space *ls, __isl_take isl_vec *div)
327 ls = isl_local_space_cow(ls);
331 if (ls->div->n_col != div->size)
332 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
333 "incompatible dimensions", goto error);
335 ls->div = isl_mat_add_zero_cols(ls->div, 1);
336 ls->div = isl_mat_add_rows(ls->div, 1);
340 isl_seq_cpy(ls->div->row[ls->div->n_row - 1], div->el, div->size);
341 isl_int_set_si(ls->div->row[ls->div->n_row - 1][div->size], 0);
346 isl_local_space_free(ls);
351 __isl_give isl_local_space *isl_local_space_replace_divs(
352 __isl_take isl_local_space *ls, __isl_take isl_mat *div)
354 ls = isl_local_space_cow(ls);
359 isl_mat_free(ls->div);
364 isl_local_space_free(ls);
368 /* Copy row "s" of "src" to row "d" of "dst", applying the expansion
371 static void expand_row(__isl_keep isl_mat *dst, int d,
372 __isl_keep isl_mat *src, int s, int *exp)
375 unsigned c = src->n_col - src->n_row;
377 isl_seq_cpy(dst->row[d], src->row[s], c);
378 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
380 for (i = 0; i < s; ++i)
381 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
384 /* Compare (known) divs.
385 * Return non-zero if at least one of the two divs is unknown.
386 * In particular, if both divs are unknown, we respect their
387 * current order. Otherwise, we sort the known div after the unknown
388 * div only if the known div depends on the unknown div.
390 static int cmp_row(isl_int *row_i, isl_int *row_j, int i, int j,
391 unsigned n_row, unsigned n_col)
394 int unknown_i, unknown_j;
396 unknown_i = isl_int_is_zero(row_i[0]);
397 unknown_j = isl_int_is_zero(row_j[0]);
399 if (unknown_i && unknown_j)
403 li = n_col - n_row + i;
405 li = isl_seq_last_non_zero(row_i, n_col);
407 lj = n_col - n_row + j;
409 lj = isl_seq_last_non_zero(row_j, n_col);
414 return isl_seq_cmp(row_i, row_j, n_col);
417 /* Call cmp_row for divs in a matrix.
419 static int mat_cmp_row(__isl_keep isl_mat *div, int i, int j)
421 return cmp_row(div->row[i], div->row[j], i, j, div->n_row, div->n_col);
424 /* Call cmp_row for divs in a basic map.
426 static int bmap_cmp_row(__isl_keep isl_basic_map *bmap, int i, int j,
429 return cmp_row(bmap->div[i], bmap->div[j], i, j, bmap->n_div, total);
432 /* Sort the divs in "bmap".
434 * We first make sure divs are placed after divs on which they depend.
435 * Then we perform a simple insertion sort based on the same ordering
436 * that is used in isl_merge_divs.
438 __isl_give isl_basic_map *isl_basic_map_sort_divs(
439 __isl_take isl_basic_map *bmap)
444 bmap = isl_basic_map_order_divs(bmap);
447 if (bmap->n_div <= 1)
450 total = 2 + isl_basic_map_total_dim(bmap);
451 for (i = 1; i < bmap->n_div; ++i) {
452 for (j = i - 1; j >= 0; --j) {
453 if (bmap_cmp_row(bmap, j, j + 1, total) <= 0)
455 isl_basic_map_swap_div(bmap, j, j + 1);
462 /* Sort the divs in the basic maps of "map".
464 __isl_give isl_map *isl_map_sort_divs(__isl_take isl_map *map)
466 return isl_map_inline_foreach_basic_map(map, &isl_basic_map_sort_divs);
469 /* Combine the two lists of divs into a single list.
470 * For each row i in div1, exp1[i] is set to the position of the corresponding
471 * row in the result. Similarly for div2 and exp2.
472 * This function guarantees
474 * exp1[i+1] > exp1[i]
475 * For optimal merging, the two input list should have been sorted.
477 __isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
478 __isl_keep isl_mat *div2, int *exp1, int *exp2)
487 d = div1->n_col - div1->n_row;
488 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
489 d + div1->n_row + div2->n_row);
493 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
496 expand_row(div, k, div1, i, exp1);
497 expand_row(div, k + 1, div2, j, exp2);
499 cmp = mat_cmp_row(div, k, k + 1);
503 } else if (cmp < 0) {
507 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
510 for (; i < div1->n_row; ++i, ++k) {
511 expand_row(div, k, div1, i, exp1);
514 for (; j < div2->n_row; ++j, ++k) {
515 expand_row(div, k, div2, j, exp2);
525 /* Construct a local space that contains all the divs in either
528 __isl_give isl_local_space *isl_local_space_intersect(
529 __isl_take isl_local_space *ls1, __isl_take isl_local_space *ls2)
539 ctx = isl_local_space_get_ctx(ls1);
540 if (!isl_space_is_equal(ls1->dim, ls2->dim))
541 isl_die(ctx, isl_error_invalid,
542 "spaces should be identical", goto error);
544 if (ls2->div->n_row == 0) {
545 isl_local_space_free(ls2);
549 if (ls1->div->n_row == 0) {
550 isl_local_space_free(ls1);
554 exp1 = isl_alloc_array(ctx, int, ls1->div->n_row);
555 exp2 = isl_alloc_array(ctx, int, ls2->div->n_row);
559 div = isl_merge_divs(ls1->div, ls2->div, exp1, exp2);
565 isl_local_space_free(ls2);
566 isl_mat_free(ls1->div);
573 isl_local_space_free(ls1);
574 isl_local_space_free(ls2);
578 int isl_local_space_divs_known(__isl_keep isl_local_space *ls)
585 for (i = 0; i < ls->div->n_row; ++i)
586 if (isl_int_is_zero(ls->div->row[i][0]))
592 __isl_give isl_local_space *isl_local_space_domain(
593 __isl_take isl_local_space *ls)
595 ls = isl_local_space_drop_dims(ls, isl_dim_out,
596 0, isl_local_space_dim(ls, isl_dim_out));
597 ls = isl_local_space_cow(ls);
600 ls->dim = isl_space_domain(ls->dim);
602 return isl_local_space_free(ls);
606 __isl_give isl_local_space *isl_local_space_range(
607 __isl_take isl_local_space *ls)
609 ls = isl_local_space_drop_dims(ls, isl_dim_in,
610 0, isl_local_space_dim(ls, isl_dim_in));
611 ls = isl_local_space_cow(ls);
615 ls->dim = isl_space_range(ls->dim);
617 return isl_local_space_free(ls);
621 /* Construct a local space for a map that has the given local
622 * space as domain and that has a zero-dimensional range.
624 __isl_give isl_local_space *isl_local_space_from_domain(
625 __isl_take isl_local_space *ls)
627 ls = isl_local_space_cow(ls);
630 ls->dim = isl_space_from_domain(ls->dim);
632 return isl_local_space_free(ls);
636 __isl_give isl_local_space *isl_local_space_add_dims(
637 __isl_take isl_local_space *ls, enum isl_dim_type type, unsigned n)
643 pos = isl_local_space_dim(ls, type);
644 return isl_local_space_insert_dims(ls, type, pos, n);
647 /* Remove common factor of non-constant terms and denominator.
649 static void normalize_div(__isl_keep isl_local_space *ls, int div)
651 isl_ctx *ctx = ls->div->ctx;
652 unsigned total = ls->div->n_col - 2;
654 isl_seq_gcd(ls->div->row[div] + 2, total, &ctx->normalize_gcd);
655 isl_int_gcd(ctx->normalize_gcd,
656 ctx->normalize_gcd, ls->div->row[div][0]);
657 if (isl_int_is_one(ctx->normalize_gcd))
660 isl_seq_scale_down(ls->div->row[div] + 2, ls->div->row[div] + 2,
661 ctx->normalize_gcd, total);
662 isl_int_divexact(ls->div->row[div][0], ls->div->row[div][0],
664 isl_int_fdiv_q(ls->div->row[div][1], ls->div->row[div][1],
668 /* Exploit the equalities in "eq" to simplify the expressions of
669 * the integer divisions in "ls".
670 * The integer divisions in "ls" are assumed to appear as regular
671 * dimensions in "eq".
673 __isl_give isl_local_space *isl_local_space_substitute_equalities(
674 __isl_take isl_local_space *ls, __isl_take isl_basic_set *eq)
680 ls = isl_local_space_cow(ls);
684 total = isl_space_dim(eq->dim, isl_dim_all);
685 if (isl_local_space_dim(ls, isl_dim_all) != total)
686 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
687 "dimensions don't match", goto error);
690 for (i = 0; i < eq->n_eq; ++i) {
691 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
692 if (j < 0 || j == 0 || j >= total)
695 for (k = 0; k < ls->div->n_row; ++k) {
696 if (isl_int_is_zero(ls->div->row[k][1 + j]))
698 isl_seq_elim(ls->div->row[k] + 1, eq->eq[i], j, total,
699 &ls->div->row[k][0]);
700 normalize_div(ls, k);
704 isl_basic_set_free(eq);
707 isl_basic_set_free(eq);
708 isl_local_space_free(ls);
712 /* Plug in "subs" for dimension "type", "pos" in the integer divisions
715 * Let i be the dimension to replace and let "subs" be of the form
719 * Any integer division with a non-zero coefficient for i,
725 * floor((a f + d g)/(m d))
727 __isl_give isl_local_space *isl_local_space_substitute(
728 __isl_take isl_local_space *ls,
729 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
734 ls = isl_local_space_cow(ls);
736 return isl_local_space_free(ls);
738 if (!isl_space_is_equal(ls->dim, subs->ls->dim))
739 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
740 "spaces don't match", return isl_local_space_free(ls));
741 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
742 isl_die(isl_local_space_get_ctx(ls), isl_error_unsupported,
743 "cannot handle divs yet",
744 return isl_local_space_free(ls));
746 pos += isl_local_space_offset(ls, type);
749 for (i = 0; i < ls->div->n_row; ++i) {
750 if (isl_int_is_zero(ls->div->row[i][1 + pos]))
752 isl_int_set(v, ls->div->row[i][1 + pos]);
753 isl_int_set_si(ls->div->row[i][1 + pos], 0);
754 isl_seq_combine(ls->div->row[i] + 1,
755 subs->v->el[0], ls->div->row[i] + 1,
756 v, subs->v->el + 1, subs->v->size - 1);
757 isl_int_mul(ls->div->row[i][0],
758 ls->div->row[i][0], subs->v->el[0]);
759 normalize_div(ls, i);
766 int isl_local_space_is_named_or_nested(__isl_keep isl_local_space *ls,
767 enum isl_dim_type type)
771 return isl_space_is_named_or_nested(ls->dim, type);
774 __isl_give isl_local_space *isl_local_space_drop_dims(
775 __isl_take isl_local_space *ls,
776 enum isl_dim_type type, unsigned first, unsigned n)
782 if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
785 ctx = isl_local_space_get_ctx(ls);
786 if (first + n > isl_local_space_dim(ls, type))
787 isl_die(ctx, isl_error_invalid, "range out of bounds",
788 return isl_local_space_free(ls));
790 ls = isl_local_space_cow(ls);
794 if (type == isl_dim_div) {
795 ls->div = isl_mat_drop_rows(ls->div, first, n);
797 ls->dim = isl_space_drop_dims(ls->dim, type, first, n);
799 return isl_local_space_free(ls);
802 first += 1 + isl_local_space_offset(ls, type);
803 ls->div = isl_mat_drop_cols(ls->div, first, n);
805 return isl_local_space_free(ls);
810 __isl_give isl_local_space *isl_local_space_insert_dims(
811 __isl_take isl_local_space *ls,
812 enum isl_dim_type type, unsigned first, unsigned n)
818 if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
821 ctx = isl_local_space_get_ctx(ls);
822 if (first > isl_local_space_dim(ls, type))
823 isl_die(ctx, isl_error_invalid, "position out of bounds",
824 return isl_local_space_free(ls));
826 ls = isl_local_space_cow(ls);
830 if (type == isl_dim_div) {
831 ls->div = isl_mat_insert_zero_rows(ls->div, first, n);
833 ls->dim = isl_space_insert_dims(ls->dim, type, first, n);
835 return isl_local_space_free(ls);
838 first += 1 + isl_local_space_offset(ls, type);
839 ls->div = isl_mat_insert_zero_cols(ls->div, first, n);
841 return isl_local_space_free(ls);
846 /* Check if the constraints pointed to by "constraint" is a div
847 * constraint corresponding to div "div" in "ls".
849 * That is, if div = floor(f/m), then check if the constraint is
853 * -(f-(m-1)) + m d >= 0
855 int isl_local_space_is_div_constraint(__isl_keep isl_local_space *ls,
856 isl_int *constraint, unsigned div)
863 if (isl_int_is_zero(ls->div->row[div][0]))
866 pos = isl_local_space_offset(ls, isl_dim_div) + div;
868 if (isl_int_eq(constraint[pos], ls->div->row[div][0])) {
870 isl_int_sub(ls->div->row[div][1],
871 ls->div->row[div][1], ls->div->row[div][0]);
872 isl_int_add_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
873 neg = isl_seq_is_neg(constraint, ls->div->row[div]+1, pos);
874 isl_int_sub_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
875 isl_int_add(ls->div->row[div][1],
876 ls->div->row[div][1], ls->div->row[div][0]);
879 if (isl_seq_first_non_zero(constraint+pos+1,
880 ls->div->n_row-div-1) != -1)
882 } else if (isl_int_abs_eq(constraint[pos], ls->div->row[div][0])) {
883 if (!isl_seq_eq(constraint, ls->div->row[div]+1, pos))
885 if (isl_seq_first_non_zero(constraint+pos+1,
886 ls->div->n_row-div-1) != -1)
895 * Set active[i] to 1 if the dimension at position i is involved
896 * in the linear expression l.
898 int *isl_local_space_get_active(__isl_keep isl_local_space *ls, isl_int *l)
906 ctx = isl_local_space_get_ctx(ls);
907 total = isl_local_space_dim(ls, isl_dim_all);
908 active = isl_calloc_array(ctx, int, total);
912 for (i = 0; i < total; ++i)
913 active[i] = !isl_int_is_zero(l[i]);
915 offset = isl_local_space_offset(ls, isl_dim_div) - 1;
916 for (i = ls->div->n_row - 1; i >= 0; --i) {
917 if (!active[offset + i])
919 for (j = 0; j < total; ++j)
920 active[j] |= !isl_int_is_zero(ls->div->row[i][2 + j]);
926 /* Given a local space "ls" of a set, create a local space
927 * for the lift of the set. In particular, the result
928 * is of the form [dim -> local[..]], with ls->div->n_row variables in the
929 * range of the wrapped map.
931 __isl_give isl_local_space *isl_local_space_lift(
932 __isl_take isl_local_space *ls)
934 ls = isl_local_space_cow(ls);
938 ls->dim = isl_space_lift(ls->dim, ls->div->n_row);
939 ls->div = isl_mat_drop_rows(ls->div, 0, ls->div->n_row);
940 if (!ls->dim || !ls->div)
941 return isl_local_space_free(ls);
946 /* Construct a basic map that maps a set living in local space "ls"
947 * to the corresponding lifted local space.
949 __isl_give isl_basic_map *isl_local_space_lifting(
950 __isl_take isl_local_space *ls)
952 isl_basic_map *lifting;
957 if (!isl_local_space_is_set(ls))
958 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
959 "lifting only defined on set spaces",
960 return isl_local_space_free(ls));
962 bset = isl_basic_set_from_local_space(ls);
963 lifting = isl_basic_set_unwrap(isl_basic_set_lift(bset));
964 lifting = isl_basic_map_domain_map(lifting);
965 lifting = isl_basic_map_reverse(lifting);