2 * Copyright 2011 INRIA Saclay
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
11 #include <isl_ctx_private.h>
12 #include <isl_map_private.h>
13 #include <isl_local_space_private.h>
14 #include <isl_space_private.h>
15 #include <isl_mat_private.h>
16 #include <isl_aff_private.h>
19 isl_ctx *isl_local_space_get_ctx(__isl_keep isl_local_space *ls)
21 return ls ? ls->dim->ctx : NULL;
24 __isl_give isl_local_space *isl_local_space_alloc_div(__isl_take isl_space *dim,
25 __isl_take isl_mat *div)
28 isl_local_space *ls = NULL;
33 ctx = isl_space_get_ctx(dim);
34 ls = isl_calloc_type(ctx, struct isl_local_space);
45 isl_local_space_free(ls);
49 __isl_give isl_local_space *isl_local_space_alloc(__isl_take isl_space *dim,
59 total = isl_space_dim(dim, isl_dim_all);
61 ctx = isl_space_get_ctx(dim);
62 div = isl_mat_alloc(ctx, n_div, 1 + 1 + total + n_div);
63 return isl_local_space_alloc_div(dim, div);
66 __isl_give isl_local_space *isl_local_space_from_space(__isl_take isl_space *dim)
68 return isl_local_space_alloc(dim, 0);
71 __isl_give isl_local_space *isl_local_space_copy(__isl_keep isl_local_space *ls)
80 __isl_give isl_local_space *isl_local_space_dup(__isl_keep isl_local_space *ls)
85 return isl_local_space_alloc_div(isl_space_copy(ls->dim),
86 isl_mat_copy(ls->div));
90 __isl_give isl_local_space *isl_local_space_cow(__isl_take isl_local_space *ls)
98 return isl_local_space_dup(ls);
101 void *isl_local_space_free(__isl_take isl_local_space *ls)
109 isl_space_free(ls->dim);
110 isl_mat_free(ls->div);
117 /* Is the local space that of a set?
119 int isl_local_space_is_set(__isl_keep isl_local_space *ls)
121 return ls ? isl_space_is_set(ls->dim) : -1;
124 /* Return true if the two local spaces are identical, with identical
125 * expressions for the integer divisions.
127 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
128 __isl_keep isl_local_space *ls2)
135 equal = isl_space_is_equal(ls1->dim, ls2->dim);
136 if (equal < 0 || !equal)
139 if (!isl_local_space_divs_known(ls1))
141 if (!isl_local_space_divs_known(ls2))
144 return isl_mat_is_equal(ls1->div, ls2->div);
147 int isl_local_space_dim(__isl_keep isl_local_space *ls,
148 enum isl_dim_type type)
152 if (type == isl_dim_div)
153 return ls->div->n_row;
154 if (type == isl_dim_all)
155 return isl_space_dim(ls->dim, isl_dim_all) + ls->div->n_row;
156 return isl_space_dim(ls->dim, type);
159 unsigned isl_local_space_offset(__isl_keep isl_local_space *ls,
160 enum isl_dim_type type)
169 case isl_dim_cst: return 0;
170 case isl_dim_param: return 1;
171 case isl_dim_in: return 1 + dim->nparam;
172 case isl_dim_out: return 1 + dim->nparam + dim->n_in;
173 case isl_dim_div: return 1 + dim->nparam + dim->n_in + dim->n_out;
178 const char *isl_local_space_get_dim_name(__isl_keep isl_local_space *ls,
179 enum isl_dim_type type, unsigned pos)
181 return ls ? isl_space_get_dim_name(ls->dim, type, pos) : NULL;
184 __isl_give isl_aff *isl_local_space_get_div(__isl_keep isl_local_space *ls,
192 if (pos < 0 || pos >= ls->div->n_row)
193 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
194 "index out of bounds", return NULL);
196 if (isl_int_is_zero(ls->div->row[pos][0]))
197 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
198 "expression of div unknown", return NULL);
200 aff = isl_aff_alloc(isl_local_space_copy(ls));
203 isl_seq_cpy(aff->v->el, ls->div->row[pos], aff->v->size);
207 __isl_give isl_space *isl_local_space_get_space(__isl_keep isl_local_space *ls)
212 return isl_space_copy(ls->dim);
215 __isl_give isl_local_space *isl_local_space_set_dim_name(
216 __isl_take isl_local_space *ls,
217 enum isl_dim_type type, unsigned pos, const char *s)
219 ls = isl_local_space_cow(ls);
222 ls->dim = isl_space_set_dim_name(ls->dim, type, pos, s);
224 return isl_local_space_free(ls);
229 __isl_give isl_local_space *isl_local_space_set_dim_id(
230 __isl_take isl_local_space *ls,
231 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
233 ls = isl_local_space_cow(ls);
235 return isl_id_free(id);
236 ls->dim = isl_space_set_dim_id(ls->dim, type, pos, id);
238 return isl_local_space_free(ls);
243 __isl_give isl_local_space *isl_local_space_reset_space(
244 __isl_take isl_local_space *ls, __isl_take isl_space *dim)
246 ls = isl_local_space_cow(ls);
250 isl_space_free(ls->dim);
255 isl_local_space_free(ls);
260 /* Reorder the columns of the given div definitions according to the
262 * The order of the divs themselves is assumed not to change.
264 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
265 __isl_take isl_reordering *r)
274 extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
275 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
279 for (i = 0; i < div->n_row; ++i) {
280 isl_seq_cpy(mat->row[i], div->row[i], 2);
281 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
282 for (j = 0; j < r->len; ++j)
283 isl_int_set(mat->row[i][2 + r->pos[j]],
287 isl_reordering_free(r);
291 isl_reordering_free(r);
296 /* Reorder the dimensions of "ls" according to the given reordering.
297 * The reordering r is assumed to have been extended with the local
298 * variables, leaving them in the same order.
300 __isl_give isl_local_space *isl_local_space_realign(
301 __isl_take isl_local_space *ls, __isl_take isl_reordering *r)
303 ls = isl_local_space_cow(ls);
307 ls->div = reorder_divs(ls->div, isl_reordering_copy(r));
311 ls = isl_local_space_reset_space(ls, isl_space_copy(r->dim));
313 isl_reordering_free(r);
316 isl_local_space_free(ls);
317 isl_reordering_free(r);
321 __isl_give isl_local_space *isl_local_space_add_div(
322 __isl_take isl_local_space *ls, __isl_take isl_vec *div)
324 ls = isl_local_space_cow(ls);
328 if (ls->div->n_col != div->size)
329 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
330 "incompatible dimensions", goto error);
332 ls->div = isl_mat_add_zero_cols(ls->div, 1);
333 ls->div = isl_mat_add_rows(ls->div, 1);
337 isl_seq_cpy(ls->div->row[ls->div->n_row - 1], div->el, div->size);
338 isl_int_set_si(ls->div->row[ls->div->n_row - 1][div->size], 0);
343 isl_local_space_free(ls);
348 __isl_give isl_local_space *isl_local_space_replace_divs(
349 __isl_take isl_local_space *ls, __isl_take isl_mat *div)
351 ls = isl_local_space_cow(ls);
356 isl_mat_free(ls->div);
361 isl_local_space_free(ls);
365 /* Copy row "s" of "src" to row "d" of "dst", applying the expansion
368 static void expand_row(__isl_keep isl_mat *dst, int d,
369 __isl_keep isl_mat *src, int s, int *exp)
372 unsigned c = src->n_col - src->n_row;
374 isl_seq_cpy(dst->row[d], src->row[s], c);
375 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
377 for (i = 0; i < s; ++i)
378 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
381 /* Compare (known) divs.
382 * Return non-zero if at least one of the two divs is unknown.
384 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
388 if (isl_int_is_zero(div->row[j][0]))
390 if (isl_int_is_zero(div->row[i][0]))
393 li = isl_seq_last_non_zero(div->row[i], div->n_col);
394 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
399 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
402 /* Combine the two lists of divs into a single list.
403 * For each row i in div1, exp1[i] is set to the position of the corresponding
404 * row in the result. Similarly for div2 and exp2.
405 * This function guarantees
407 * exp1[i+1] > exp1[i]
408 * For optimal merging, the two input list should have been sorted.
410 __isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
411 __isl_keep isl_mat *div2, int *exp1, int *exp2)
415 unsigned d = div1->n_col - div1->n_row;
417 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
418 d + div1->n_row + div2->n_row);
422 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
425 expand_row(div, k, div1, i, exp1);
426 expand_row(div, k + 1, div2, j, exp2);
428 cmp = cmp_row(div, k, k + 1);
432 } else if (cmp < 0) {
436 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
439 for (; i < div1->n_row; ++i, ++k) {
440 expand_row(div, k, div1, i, exp1);
443 for (; j < div2->n_row; ++j, ++k) {
444 expand_row(div, k, div2, j, exp2);
454 /* Construct a local space that contains all the divs in either
457 __isl_give isl_local_space *isl_local_space_intersect(
458 __isl_take isl_local_space *ls1, __isl_take isl_local_space *ls2)
468 ctx = isl_local_space_get_ctx(ls1);
469 if (!isl_space_is_equal(ls1->dim, ls2->dim))
470 isl_die(ctx, isl_error_invalid,
471 "spaces should be identical", goto error);
473 if (ls2->div->n_row == 0) {
474 isl_local_space_free(ls2);
478 if (ls1->div->n_row == 0) {
479 isl_local_space_free(ls1);
483 exp1 = isl_alloc_array(ctx, int, ls1->div->n_row);
484 exp2 = isl_alloc_array(ctx, int, ls2->div->n_row);
488 div = isl_merge_divs(ls1->div, ls2->div, exp1, exp2);
494 isl_local_space_free(ls2);
495 isl_mat_free(ls1->div);
502 isl_local_space_free(ls1);
503 isl_local_space_free(ls2);
507 int isl_local_space_divs_known(__isl_keep isl_local_space *ls)
514 for (i = 0; i < ls->div->n_row; ++i)
515 if (isl_int_is_zero(ls->div->row[i][0]))
521 __isl_give isl_local_space *isl_local_space_domain(
522 __isl_take isl_local_space *ls)
524 ls = isl_local_space_drop_dims(ls, isl_dim_out,
525 0, isl_local_space_dim(ls, isl_dim_out));
526 ls = isl_local_space_cow(ls);
529 ls->dim = isl_space_domain(ls->dim);
531 return isl_local_space_free(ls);
535 __isl_give isl_local_space *isl_local_space_range(
536 __isl_take isl_local_space *ls)
538 ls = isl_local_space_drop_dims(ls, isl_dim_in,
539 0, isl_local_space_dim(ls, isl_dim_in));
540 ls = isl_local_space_cow(ls);
544 ls->dim = isl_space_range(ls->dim);
546 return isl_local_space_free(ls);
550 /* Construct a local space for a map that has the given local
551 * space as domain and that has a zero-dimensional range.
553 __isl_give isl_local_space *isl_local_space_from_domain(
554 __isl_take isl_local_space *ls)
556 ls = isl_local_space_cow(ls);
559 ls->dim = isl_space_from_domain(ls->dim);
561 return isl_local_space_free(ls);
565 __isl_give isl_local_space *isl_local_space_add_dims(
566 __isl_take isl_local_space *ls, enum isl_dim_type type, unsigned n)
572 pos = isl_local_space_dim(ls, type);
573 return isl_local_space_insert_dims(ls, type, pos, n);
576 /* Remove common factor of non-constant terms and denominator.
578 static void normalize_div(__isl_keep isl_local_space *ls, int div)
580 isl_ctx *ctx = ls->div->ctx;
581 unsigned total = ls->div->n_col - 2;
583 isl_seq_gcd(ls->div->row[div] + 2, total, &ctx->normalize_gcd);
584 isl_int_gcd(ctx->normalize_gcd,
585 ctx->normalize_gcd, ls->div->row[div][0]);
586 if (isl_int_is_one(ctx->normalize_gcd))
589 isl_seq_scale_down(ls->div->row[div] + 2, ls->div->row[div] + 2,
590 ctx->normalize_gcd, total);
591 isl_int_divexact(ls->div->row[div][0], ls->div->row[div][0],
593 isl_int_fdiv_q(ls->div->row[div][1], ls->div->row[div][1],
597 /* Exploit the equalities in "eq" to simplify the expressions of
598 * the integer divisions in "ls".
599 * The integer divisions in "ls" are assumed to appear as regular
600 * dimensions in "eq".
602 __isl_give isl_local_space *isl_local_space_substitute_equalities(
603 __isl_take isl_local_space *ls, __isl_take isl_basic_set *eq)
609 ls = isl_local_space_cow(ls);
613 total = isl_space_dim(eq->dim, isl_dim_all);
614 if (isl_local_space_dim(ls, isl_dim_all) != total)
615 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
616 "dimensions don't match", goto error);
619 for (i = 0; i < eq->n_eq; ++i) {
620 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
621 if (j < 0 || j == 0 || j >= total)
624 for (k = 0; k < ls->div->n_row; ++k) {
625 if (isl_int_is_zero(ls->div->row[k][1 + j]))
627 isl_seq_elim(ls->div->row[k] + 1, eq->eq[i], j, total,
628 &ls->div->row[k][0]);
629 normalize_div(ls, k);
633 isl_basic_set_free(eq);
636 isl_basic_set_free(eq);
637 isl_local_space_free(ls);
641 /* Plug in "subs" for dimension "type", "pos" in the integer divisions
644 * Let i be the dimension to replace and let "subs" be of the form
648 * Any integer division with a non-zero coefficient for i,
654 * floor((a f + d g)/(m d))
656 __isl_give isl_local_space *isl_local_space_substitute(
657 __isl_take isl_local_space *ls,
658 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
663 ls = isl_local_space_cow(ls);
665 return isl_local_space_free(ls);
667 if (!isl_space_is_equal(ls->dim, subs->ls->dim))
668 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
669 "spaces don't match", return isl_local_space_free(ls));
670 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
671 isl_die(isl_local_space_get_ctx(ls), isl_error_unsupported,
672 "cannot handle divs yet",
673 return isl_local_space_free(ls));
675 pos += isl_local_space_offset(ls, type);
678 for (i = 0; i < ls->div->n_row; ++i) {
679 if (isl_int_is_zero(ls->div->row[i][1 + pos]))
681 isl_int_set(v, ls->div->row[i][1 + pos]);
682 isl_int_set_si(ls->div->row[i][1 + pos], 0);
683 isl_seq_combine(ls->div->row[i] + 1,
684 subs->v->el[0], ls->div->row[i] + 1,
685 v, subs->v->el + 1, subs->v->size - 1);
686 isl_int_mul(ls->div->row[i][0],
687 ls->div->row[i][0], subs->v->el[0]);
688 normalize_div(ls, i);
695 int isl_local_space_is_named_or_nested(__isl_keep isl_local_space *ls,
696 enum isl_dim_type type)
700 return isl_space_is_named_or_nested(ls->dim, type);
703 __isl_give isl_local_space *isl_local_space_drop_dims(
704 __isl_take isl_local_space *ls,
705 enum isl_dim_type type, unsigned first, unsigned n)
711 if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
714 ctx = isl_local_space_get_ctx(ls);
715 if (first + n > isl_local_space_dim(ls, type))
716 isl_die(ctx, isl_error_invalid, "range out of bounds",
717 return isl_local_space_free(ls));
719 ls = isl_local_space_cow(ls);
723 if (type == isl_dim_div) {
724 ls->div = isl_mat_drop_rows(ls->div, first, n);
726 ls->dim = isl_space_drop_dims(ls->dim, type, first, n);
728 return isl_local_space_free(ls);
731 first += 1 + isl_local_space_offset(ls, type);
732 ls->div = isl_mat_drop_cols(ls->div, first, n);
734 return isl_local_space_free(ls);
739 __isl_give isl_local_space *isl_local_space_insert_dims(
740 __isl_take isl_local_space *ls,
741 enum isl_dim_type type, unsigned first, unsigned n)
747 if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
750 ctx = isl_local_space_get_ctx(ls);
751 if (first > isl_local_space_dim(ls, type))
752 isl_die(ctx, isl_error_invalid, "position out of bounds",
753 return isl_local_space_free(ls));
755 ls = isl_local_space_cow(ls);
759 if (type == isl_dim_div) {
760 ls->div = isl_mat_insert_zero_rows(ls->div, first, n);
762 ls->dim = isl_space_insert_dims(ls->dim, type, first, n);
764 return isl_local_space_free(ls);
767 first += 1 + isl_local_space_offset(ls, type);
768 ls->div = isl_mat_insert_zero_cols(ls->div, first, n);
770 return isl_local_space_free(ls);
775 /* Check if the constraints pointed to by "constraint" is a div
776 * constraint corresponding to div "div" in "ls".
778 * That is, if div = floor(f/m), then check if the constraint is
782 * -(f-(m-1)) + m d >= 0
784 int isl_local_space_is_div_constraint(__isl_keep isl_local_space *ls,
785 isl_int *constraint, unsigned div)
792 if (isl_int_is_zero(ls->div->row[div][0]))
795 pos = isl_local_space_offset(ls, isl_dim_div) + div;
797 if (isl_int_eq(constraint[pos], ls->div->row[div][0])) {
799 isl_int_sub(ls->div->row[div][1],
800 ls->div->row[div][1], ls->div->row[div][0]);
801 isl_int_add_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
802 neg = isl_seq_is_neg(constraint, ls->div->row[div]+1, pos);
803 isl_int_sub_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
804 isl_int_add(ls->div->row[div][1],
805 ls->div->row[div][1], ls->div->row[div][0]);
808 if (isl_seq_first_non_zero(constraint+pos+1,
809 ls->div->n_row-div-1) != -1)
811 } else if (isl_int_abs_eq(constraint[pos], ls->div->row[div][0])) {
812 if (!isl_seq_eq(constraint, ls->div->row[div]+1, pos))
814 if (isl_seq_first_non_zero(constraint+pos+1,
815 ls->div->n_row-div-1) != -1)
824 * Set active[i] to 1 if the dimension at position i is involved
825 * in the linear expression l.
827 int *isl_local_space_get_active(__isl_keep isl_local_space *ls, isl_int *l)
835 ctx = isl_local_space_get_ctx(ls);
836 total = isl_local_space_dim(ls, isl_dim_all);
837 active = isl_calloc_array(ctx, int, total);
841 for (i = 0; i < total; ++i)
842 active[i] = !isl_int_is_zero(l[i]);
844 offset = isl_local_space_offset(ls, isl_dim_div) - 1;
845 for (i = ls->div->n_row - 1; i >= 0; --i) {
846 if (!active[offset + i])
848 for (j = 0; j < total; ++j)
849 active[j] |= !isl_int_is_zero(ls->div->row[i][2 + j]);
855 /* Given a local space "ls" of a set, create a local space
856 * for the lift of the set. In particular, the result
857 * is of the form [dim -> local[..]], with ls->div->n_row variables in the
858 * range of the wrapped map.
860 __isl_give isl_local_space *isl_local_space_lift(
861 __isl_take isl_local_space *ls)
863 ls = isl_local_space_cow(ls);
867 ls->dim = isl_space_lift(ls->dim, ls->div->n_row);
868 ls->div = isl_mat_drop_rows(ls->div, 0, ls->div->n_row);
869 if (!ls->dim || !ls->div)
870 return isl_local_space_free(ls);
875 /* Construct a basic map that maps a set living in local space "ls"
876 * to the corresponding lifted local space.
878 __isl_give isl_basic_map *isl_local_space_lifting(
879 __isl_take isl_local_space *ls)
881 isl_basic_map *lifting;
886 if (!isl_local_space_is_set(ls))
887 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
888 "lifting only defined on set spaces",
889 return isl_local_space_free(ls));
891 bset = isl_basic_set_from_local_space(ls);
892 lifting = isl_basic_set_unwrap(isl_basic_set_lift(bset));
893 lifting = isl_basic_map_domain_map(lifting);
894 lifting = isl_basic_map_reverse(lifting);