5 #include "isl_equalities.h"
10 #include "isl_map_private.h"
11 #include "isl_map_piplib.h"
12 #include "isl_sample.h"
15 static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
16 struct isl_basic_map *bmap,
17 unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
18 unsigned n_eq, unsigned n_ineq)
21 size_t row_size = 1 + nparam + n_in + n_out + extra;
23 bmap->block = isl_blk_alloc(ctx, (n_eq + n_ineq) * row_size);
24 if (isl_blk_is_error(bmap->block)) {
29 bmap->eq = isl_alloc_array(ctx, isl_int *, n_eq + n_ineq);
31 isl_blk_free(ctx, bmap->block);
37 bmap->block2 = isl_blk_empty();
40 bmap->block2 = isl_blk_alloc(ctx, extra * (1 + row_size));
41 if (isl_blk_is_error(bmap->block2)) {
43 isl_blk_free(ctx, bmap->block);
48 bmap->div = isl_alloc_array(ctx, isl_int *, extra);
50 isl_blk_free(ctx, bmap->block2);
52 isl_blk_free(ctx, bmap->block);
58 for (i = 0; i < n_eq + n_ineq; ++i)
59 bmap->eq[i] = bmap->block.data + i * row_size;
61 for (i = 0; i < extra; ++i)
62 bmap->div[i] = bmap->block2.data + i * (1 + row_size);
68 bmap->c_size = n_eq + n_ineq;
69 bmap->ineq = bmap->eq + n_eq;
70 bmap->nparam = nparam;
82 struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
83 unsigned nparam, unsigned dim, unsigned extra,
84 unsigned n_eq, unsigned n_ineq)
86 struct isl_basic_map *bmap;
87 bmap = isl_basic_map_alloc(ctx, nparam, 0, dim, extra, n_eq, n_ineq);
88 return (struct isl_basic_set *)bmap;
91 struct isl_basic_map *isl_basic_map_alloc(struct isl_ctx *ctx,
92 unsigned nparam, unsigned in, unsigned out, unsigned extra,
93 unsigned n_eq, unsigned n_ineq)
95 struct isl_basic_map *bmap;
97 bmap = isl_alloc_type(ctx, struct isl_basic_map);
101 return basic_map_init(ctx, bmap,
102 nparam, in, out, extra, n_eq, n_ineq);
105 static void dup_constraints(
106 struct isl_basic_map *dst, struct isl_basic_map *src)
109 unsigned total = src->nparam + src->n_in + src->n_out + src->n_div;
111 for (i = 0; i < src->n_eq; ++i) {
112 int j = isl_basic_map_alloc_equality(dst);
113 isl_seq_cpy(dst->eq[j], src->eq[i], 1+total);
116 for (i = 0; i < src->n_ineq; ++i) {
117 int j = isl_basic_map_alloc_inequality(dst);
118 isl_seq_cpy(dst->ineq[j], src->ineq[i], 1+total);
121 for (i = 0; i < src->n_div; ++i) {
122 int j = isl_basic_map_alloc_div(dst);
123 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
125 F_SET(dst, ISL_BASIC_SET_FINAL);
128 struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
130 struct isl_basic_map *dup;
134 dup = isl_basic_map_alloc(bmap->ctx, bmap->nparam,
135 bmap->n_in, bmap->n_out,
136 bmap->n_div, bmap->n_eq, bmap->n_ineq);
139 dup->flags = bmap->flags;
140 dup_constraints(dup, bmap);
141 dup->sample = isl_vec_copy(bmap->ctx, bmap->sample);
145 struct isl_basic_set *isl_basic_set_dup(struct isl_basic_set *bset)
147 struct isl_basic_map *dup;
149 dup = isl_basic_map_dup((struct isl_basic_map *)bset);
150 return (struct isl_basic_set *)dup;
153 struct isl_basic_set *isl_basic_set_copy(struct isl_basic_set *bset)
158 if (F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
162 return isl_basic_set_dup(bset);
165 struct isl_set *isl_set_copy(struct isl_set *set)
174 struct isl_basic_map *isl_basic_map_copy(struct isl_basic_map *bmap)
179 if (F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
183 return isl_basic_map_dup(bmap);
186 struct isl_map *isl_map_copy(struct isl_map *map)
195 void isl_basic_map_free(struct isl_basic_map *bmap)
203 isl_ctx_deref(bmap->ctx);
205 isl_blk_free(bmap->ctx, bmap->block2);
207 isl_blk_free(bmap->ctx, bmap->block);
208 isl_vec_free(bmap->ctx, bmap->sample);
212 void isl_basic_set_free(struct isl_basic_set *bset)
214 isl_basic_map_free((struct isl_basic_map *)bset);
217 int isl_basic_map_alloc_equality(struct isl_basic_map *bmap)
223 isl_assert(ctx, bmap->n_eq + bmap->n_ineq < bmap->c_size, return -1);
224 isl_assert(ctx, bmap->eq + bmap->n_eq <= bmap->ineq, return -1);
225 if (bmap->eq + bmap->n_eq == bmap->ineq) {
227 int j = isl_basic_map_alloc_inequality(bmap);
231 bmap->ineq[0] = bmap->ineq[j];
239 int isl_basic_set_alloc_equality(struct isl_basic_set *bset)
241 return isl_basic_map_alloc_equality((struct isl_basic_map *)bset);
244 int isl_basic_map_free_equality(struct isl_basic_map *bmap, unsigned n)
248 isl_assert(bmap->ctx, n <= bmap->n_eq, return -1);
253 int isl_basic_map_drop_equality(struct isl_basic_map *bmap, unsigned pos)
258 isl_assert(bmap->ctx, pos < bmap->n_eq, return -1);
260 if (pos != bmap->n_eq - 1) {
262 bmap->eq[pos] = bmap->eq[bmap->n_eq - 1];
263 bmap->eq[bmap->n_eq - 1] = t;
269 int isl_basic_set_drop_equality(struct isl_basic_set *bset, unsigned pos)
271 return isl_basic_map_drop_equality((struct isl_basic_map *)bset, pos);
274 void isl_basic_map_inequality_to_equality(
275 struct isl_basic_map *bmap, unsigned pos)
280 bmap->ineq[pos] = bmap->ineq[0];
281 bmap->ineq[0] = bmap->eq[bmap->n_eq];
282 bmap->eq[bmap->n_eq] = t;
286 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
289 int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
295 isl_assert(ctx, (bmap->ineq - bmap->eq) + bmap->n_ineq < bmap->c_size,
297 F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
298 F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
299 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
300 return bmap->n_ineq++;
303 int isl_basic_set_alloc_inequality(struct isl_basic_set *bset)
305 return isl_basic_map_alloc_inequality((struct isl_basic_map *)bset);
308 int isl_basic_map_free_inequality(struct isl_basic_map *bmap, unsigned n)
312 isl_assert(bmap->ctx, n <= bmap->n_ineq, return -1);
317 int isl_basic_set_free_inequality(struct isl_basic_set *bset, unsigned n)
319 return isl_basic_map_free_inequality((struct isl_basic_map *)bset, n);
322 int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
327 isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
329 if (pos != bmap->n_ineq - 1) {
331 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
332 bmap->ineq[bmap->n_ineq - 1] = t;
333 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
339 int isl_basic_set_drop_inequality(struct isl_basic_set *bset, unsigned pos)
341 return isl_basic_map_drop_inequality((struct isl_basic_map *)bset, pos);
344 int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
348 isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
349 return bmap->n_div++;
352 int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
356 isl_assert(bmap->ctx, n <= bmap->n_div, return -1);
361 /* Copy constraint from src to dst, putting the vars of src at offset
362 * dim_off in dst and the divs of src at offset div_off in dst.
363 * If both sets are actually map, then dim_off applies to the input
366 static void copy_constraint(struct isl_basic_map *dst_map, isl_int *dst,
367 struct isl_basic_map *src_map, isl_int *src,
368 unsigned in_off, unsigned out_off, unsigned div_off)
370 isl_int_set(dst[0], src[0]);
371 isl_seq_cpy(dst+1, src+1, isl_min(dst_map->nparam, src_map->nparam));
372 if (dst_map->nparam > src_map->nparam)
373 isl_seq_clr(dst+1+src_map->nparam,
374 dst_map->nparam - src_map->nparam);
375 isl_seq_clr(dst+1+dst_map->nparam, in_off);
376 isl_seq_cpy(dst+1+dst_map->nparam+in_off,
377 src+1+src_map->nparam,
378 isl_min(dst_map->n_in-in_off, src_map->n_in));
379 if (dst_map->n_in-in_off > src_map->n_in)
380 isl_seq_clr(dst+1+dst_map->nparam+in_off+src_map->n_in,
381 dst_map->n_in - in_off - src_map->n_in);
382 isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in, out_off);
383 isl_seq_cpy(dst+1+dst_map->nparam+dst_map->n_in+out_off,
384 src+1+src_map->nparam+src_map->n_in,
385 isl_min(dst_map->n_out-out_off, src_map->n_out));
386 if (dst_map->n_out-out_off > src_map->n_out)
387 isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in+out_off+src_map->n_out,
388 dst_map->n_out - out_off - src_map->n_out);
389 isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in+dst_map->n_out, div_off);
390 isl_seq_cpy(dst+1+dst_map->nparam+dst_map->n_in+dst_map->n_out+div_off,
391 src+1+src_map->nparam+src_map->n_in+src_map->n_out,
392 isl_min(dst_map->extra-div_off, src_map->extra));
393 if (dst_map->extra-div_off > src_map->extra)
394 isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in+dst_map->n_out+
395 div_off+src_map->extra,
396 dst_map->extra - div_off - src_map->extra);
399 static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
400 struct isl_basic_map *src_map, isl_int *src,
401 unsigned in_off, unsigned out_off, unsigned div_off)
403 isl_int_set(dst[0], src[0]);
404 copy_constraint(dst_map, dst+1, src_map, src+1, in_off, out_off, div_off);
407 static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
408 struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
413 if (!bmap1 || !bmap2)
416 div_off = bmap1->n_div;
418 for (i = 0; i < bmap2->n_eq; ++i) {
419 int i1 = isl_basic_map_alloc_equality(bmap1);
422 copy_constraint(bmap1, bmap1->eq[i1], bmap2, bmap2->eq[i],
423 i_pos, o_pos, div_off);
426 for (i = 0; i < bmap2->n_ineq; ++i) {
427 int i1 = isl_basic_map_alloc_inequality(bmap1);
430 copy_constraint(bmap1, bmap1->ineq[i1], bmap2, bmap2->ineq[i],
431 i_pos, o_pos, div_off);
434 for (i = 0; i < bmap2->n_div; ++i) {
435 int i1 = isl_basic_map_alloc_div(bmap1);
438 copy_div(bmap1, bmap1->div[i1], bmap2, bmap2->div[i],
439 i_pos, o_pos, div_off);
442 isl_basic_map_free(bmap2);
447 isl_basic_map_free(bmap1);
448 isl_basic_map_free(bmap2);
452 static struct isl_basic_set *set_add_constraints(struct isl_basic_set *bset1,
453 struct isl_basic_set *bset2, unsigned pos)
455 return (struct isl_basic_set *)
456 add_constraints((struct isl_basic_map *)bset1,
457 (struct isl_basic_map *)bset2, 0, pos);
460 struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
461 unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
462 unsigned n_eq, unsigned n_ineq)
464 struct isl_basic_map *ext;
468 base = isl_basic_map_cow(base);
472 dims_ok = base && base->nparam == nparam &&
473 base->n_in == n_in && base->n_out == n_out &&
474 base->extra >= base->n_div + extra;
476 if (dims_ok && n_eq == 0 && n_ineq == 0)
479 isl_assert(base->ctx, base->nparam <= nparam, goto error);
480 isl_assert(base->ctx, base->n_in <= n_in, goto error);
481 isl_assert(base->ctx, base->n_out <= n_out, goto error);
482 extra += base->extra;
484 n_ineq += base->n_ineq;
486 ext = isl_basic_map_alloc(base->ctx, nparam, n_in, n_out,
487 extra, n_eq, n_ineq);
494 ext = add_constraints(ext, base, 0, 0);
497 F_CLR(ext, ISL_BASIC_SET_FINAL);
503 isl_basic_map_free(base);
507 struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
508 unsigned nparam, unsigned dim, unsigned extra,
509 unsigned n_eq, unsigned n_ineq)
511 return (struct isl_basic_set *)
512 isl_basic_map_extend((struct isl_basic_map *)base,
513 nparam, 0, dim, extra, n_eq, n_ineq);
516 struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
518 return (struct isl_basic_set *)
519 isl_basic_map_cow((struct isl_basic_map *)bset);
522 struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
529 bmap = isl_basic_map_dup(bmap);
531 F_CLR(bmap, ISL_BASIC_SET_FINAL);
535 struct isl_set *isl_set_cow(struct isl_set *set)
543 return isl_set_dup(set);
546 struct isl_map *isl_map_cow(struct isl_map *map)
554 return isl_map_dup(map);
557 static void swap_vars(struct isl_blk blk, isl_int *a,
558 unsigned a_len, unsigned b_len)
560 isl_seq_cpy(blk.data, a+a_len, b_len);
561 isl_seq_cpy(blk.data+b_len, a, a_len);
562 isl_seq_cpy(a, blk.data, b_len+a_len);
565 struct isl_basic_set *isl_basic_set_swap_vars(
566 struct isl_basic_set *bset, unsigned n)
574 isl_assert(bset->ctx, n <= bset->dim, goto error);
579 bset = isl_basic_set_cow(bset);
583 blk = isl_blk_alloc(bset->ctx, bset->dim);
584 if (isl_blk_is_error(blk))
587 for (i = 0; i < bset->n_eq; ++i)
589 bset->eq[i]+1+bset->nparam, n, bset->dim - n);
591 for (i = 0; i < bset->n_ineq; ++i)
593 bset->ineq[i]+1+bset->nparam, n, bset->dim - n);
595 for (i = 0; i < bset->n_div; ++i)
597 bset->div[i]+1+1+bset->nparam, n, bset->dim - n);
599 isl_blk_free(bset->ctx, blk);
601 F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
605 isl_basic_set_free(bset);
609 struct isl_set *isl_set_swap_vars(struct isl_set *set, unsigned n)
612 set = isl_set_cow(set);
616 for (i = 0; i < set->n; ++i) {
617 set->p[i] = isl_basic_set_swap_vars(set->p[i], n);
623 F_CLR(set, ISL_SET_NORMALIZED);
627 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
629 isl_seq_cpy(c, c + n, rem);
630 isl_seq_clr(c + rem, n);
633 struct isl_basic_set *isl_basic_set_drop_dims(
634 struct isl_basic_set *bset, unsigned first, unsigned n)
641 isl_assert(bset->ctx, first + n <= bset->dim, goto error);
646 bset = isl_basic_set_cow(bset);
650 for (i = 0; i < bset->n_eq; ++i)
651 constraint_drop_vars(bset->eq[i]+1+bset->nparam+first, n,
652 (bset->dim-first-n)+bset->extra);
654 for (i = 0; i < bset->n_ineq; ++i)
655 constraint_drop_vars(bset->ineq[i]+1+bset->nparam+first, n,
656 (bset->dim-first-n)+bset->extra);
658 for (i = 0; i < bset->n_div; ++i)
659 constraint_drop_vars(bset->div[i]+1+1+bset->nparam+first, n,
660 (bset->dim-first-n)+bset->extra);
665 F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
666 bset = isl_basic_set_simplify(bset);
667 return isl_basic_set_finalize(bset);
669 isl_basic_set_free(bset);
673 static struct isl_set *isl_set_drop_dims(
674 struct isl_set *set, unsigned first, unsigned n)
681 isl_assert(set->ctx, first + n <= set->dim, goto error);
685 set = isl_set_cow(set);
689 for (i = 0; i < set->n; ++i) {
690 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
696 F_CLR(set, ISL_SET_NORMALIZED);
703 struct isl_basic_map *isl_basic_map_drop_inputs(
704 struct isl_basic_map *bmap, unsigned first, unsigned n)
711 isl_assert(bmap->ctx, first + n <= bmap->n_in, goto error);
716 bmap = isl_basic_map_cow(bmap);
720 for (i = 0; i < bmap->n_eq; ++i)
721 constraint_drop_vars(bmap->eq[i]+1+bmap->nparam+first, n,
722 (bmap->n_in-first-n)+bmap->n_out+bmap->extra);
724 for (i = 0; i < bmap->n_ineq; ++i)
725 constraint_drop_vars(bmap->ineq[i]+1+bmap->nparam+first, n,
726 (bmap->n_in-first-n)+bmap->n_out+bmap->extra);
728 for (i = 0; i < bmap->n_div; ++i)
729 constraint_drop_vars(bmap->div[i]+1+1+bmap->nparam+first, n,
730 (bmap->n_in-first-n)+bmap->n_out+bmap->extra);
735 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
736 bmap = isl_basic_map_simplify(bmap);
737 return isl_basic_map_finalize(bmap);
739 isl_basic_map_free(bmap);
743 static struct isl_map *isl_map_drop_inputs(
744 struct isl_map *map, unsigned first, unsigned n)
751 isl_assert(map->ctx, first + n <= map->n_in, goto error);
755 map = isl_map_cow(map);
759 for (i = 0; i < map->n; ++i) {
760 map->p[i] = isl_basic_map_drop_inputs(map->p[i], first, n);
765 F_CLR(map, ISL_MAP_NORMALIZED);
774 * We don't cow, as the div is assumed to be redundant.
776 static struct isl_basic_map *isl_basic_map_drop_div(
777 struct isl_basic_map *bmap, unsigned div)
785 pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
787 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
789 for (i = 0; i < bmap->n_eq; ++i)
790 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
792 for (i = 0; i < bmap->n_ineq; ++i) {
793 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
794 isl_basic_map_drop_inequality(bmap, i);
798 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
801 for (i = 0; i < bmap->n_div; ++i)
802 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
804 if (div != bmap->n_div - 1) {
806 isl_int *t = bmap->div[div];
808 for (j = div; j < bmap->n_div - 1; ++j)
809 bmap->div[j] = bmap->div[j+1];
811 bmap->div[bmap->n_div - 1] = t;
813 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
814 isl_basic_map_free_div(bmap, 1);
818 isl_basic_map_free(bmap);
822 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
825 unsigned pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
827 len = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
829 for (i = 0; i < bmap->n_eq; ++i)
830 if (bmap->eq[i] != eq)
831 isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
833 for (i = 0; i < bmap->n_ineq; ++i)
834 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
836 /* We need to be careful about circular definitions,
837 * so for now we just remove the definitions of other divs that
838 * depend on this div and (possibly) recompute them later.
840 for (i = 0; i < bmap->n_div; ++i)
841 if (!isl_int_is_zero(bmap->div[i][0]) &&
842 !isl_int_is_zero(bmap->div[i][1 + pos]))
843 isl_seq_clr(bmap->div[i], 1 + len);
845 isl_basic_map_drop_div(bmap, div);
848 struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
854 total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra;
855 isl_basic_map_free_div(bmap, bmap->n_div);
856 isl_basic_map_free_inequality(bmap, bmap->n_ineq);
858 isl_basic_map_free_equality(bmap, bmap->n_eq-1);
860 isl_basic_map_alloc_equality(bmap);
864 isl_int_set_si(bmap->eq[i][0], 1);
865 isl_seq_clr(bmap->eq[i]+1, total);
866 F_SET(bmap, ISL_BASIC_MAP_EMPTY);
867 return isl_basic_map_finalize(bmap);
869 isl_basic_map_free(bmap);
873 struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
875 return (struct isl_basic_set *)
876 isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
879 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
881 isl_int *t = bmap->eq[a];
882 bmap->eq[a] = bmap->eq[b];
886 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
889 isl_int *t = bmap->ineq[a];
890 bmap->ineq[a] = bmap->ineq[b];
895 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
897 swap_inequality((struct isl_basic_map *)bset, a, b);
900 static void swap_div(struct isl_basic_map *bmap, int a, int b)
903 unsigned off = bmap->nparam + bmap->n_in + bmap->n_out;
904 isl_int *t = bmap->div[a];
905 bmap->div[a] = bmap->div[b];
908 for (i = 0; i < bmap->n_eq; ++i)
909 isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);
911 for (i = 0; i < bmap->n_ineq; ++i)
912 isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);
914 for (i = 0; i < bmap->n_div; ++i)
915 isl_int_swap(bmap->div[i][1+1+off+a], bmap->div[i][1+1+off+b]);
916 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
919 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
920 unsigned pos, isl_int *eq, int *progress)
925 total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
926 for (k = 0; k < bmap->n_eq; ++k) {
927 if (bmap->eq[k] == eq)
929 if (isl_int_is_zero(bmap->eq[k][1+pos]))
933 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
936 for (k = 0; k < bmap->n_ineq; ++k) {
937 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
941 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
942 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
945 for (k = 0; k < bmap->n_div; ++k) {
946 if (isl_int_is_zero(bmap->div[k][0]))
948 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
952 isl_seq_elim(bmap->div[k]+1, eq,
953 1+pos, 1+total, &bmap->div[k][0]);
954 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
959 struct isl_basic_map *isl_basic_map_gauss(
960 struct isl_basic_map *bmap, int *progress)
971 total_var = bmap->nparam + bmap->n_in + bmap->n_out;
972 total = total_var + bmap->n_div;
974 last_var = total - 1;
975 for (done = 0; done < bmap->n_eq; ++done) {
976 for (; last_var >= 0; --last_var) {
977 for (k = done; k < bmap->n_eq; ++k)
978 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
986 swap_equality(bmap, k, done);
987 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
988 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
990 eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
993 if (last_var >= total_var &&
994 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
995 unsigned div = last_var - total_var;
996 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
997 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
998 isl_int_set(bmap->div[div][0],
999 bmap->eq[done][1+last_var]);
1000 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1003 if (done == bmap->n_eq)
1005 for (k = done; k < bmap->n_eq; ++k) {
1006 if (isl_int_is_zero(bmap->eq[k][0]))
1008 return isl_basic_map_set_to_empty(bmap);
1010 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
1014 struct isl_basic_set *isl_basic_set_gauss(
1015 struct isl_basic_set *bset, int *progress)
1017 return (struct isl_basic_set*)isl_basic_map_gauss(
1018 (struct isl_basic_map *)bset, progress);
1021 static unsigned int round_up(unsigned int v)
1032 static int hash_index(int *index, unsigned int size, int bits,
1033 struct isl_basic_map *bmap, int k)
1036 unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1037 u_int32_t hash = isl_seq_hash(bmap->ineq[k]+1, total, bits);
1038 for (h = hash; index[h]; h = (h+1) % size)
1039 if (k != index[h]-1 &&
1040 isl_seq_eq(bmap->ineq[k]+1,
1041 bmap->ineq[index[h]-1]+1, total))
1046 static struct isl_basic_map *remove_duplicate_constraints(
1047 struct isl_basic_map *bmap, int *progress)
1053 unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1056 if (bmap->n_ineq <= 1)
1059 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1060 bits = ffs(size) - 1;
1061 index = isl_alloc_array(ctx, int, size);
1062 memset(index, 0, size * sizeof(int));
1066 index[isl_seq_hash(bmap->ineq[0]+1, total, bits)] = 1;
1067 for (k = 1; k < bmap->n_ineq; ++k) {
1068 h = hash_index(index, size, bits, bmap, k);
1076 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1077 swap_inequality(bmap, k, l);
1078 isl_basic_map_drop_inequality(bmap, k);
1082 for (k = 0; k < bmap->n_ineq-1; ++k) {
1083 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1084 h = hash_index(index, size, bits, bmap, k);
1085 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1089 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1090 if (isl_int_is_pos(sum))
1092 if (isl_int_is_zero(sum)) {
1093 /* We need to break out of the loop after these
1094 * changes since the contents of the hash
1095 * will no longer be valid.
1096 * Plus, we probably we want to regauss first.
1098 isl_basic_map_drop_inequality(bmap, l);
1099 isl_basic_map_inequality_to_equality(bmap, k);
1101 bmap = isl_basic_map_set_to_empty(bmap);
1110 static struct isl_basic_map *remove_duplicate_divs(
1111 struct isl_basic_map *bmap, int *progress)
1118 unsigned total_var = bmap->nparam + bmap->n_in + bmap->n_out;
1119 unsigned total = total_var + bmap->n_div;
1120 struct isl_ctx *ctx;
1122 if (bmap->n_div <= 1)
1126 for (k = bmap->n_div - 1; k >= 0; --k)
1127 if (!isl_int_is_zero(bmap->div[k][0]))
1132 size = round_up(4 * bmap->n_div / 3 - 1);
1133 bits = ffs(size) - 1;
1134 index = isl_alloc_array(ctx, int, size);
1135 memset(index, 0, size * sizeof(int));
1138 eq = isl_blk_alloc(ctx, 1+total);
1139 if (isl_blk_is_error(eq))
1142 isl_seq_clr(eq.data, 1+total);
1143 index[isl_seq_hash(bmap->div[k], 2+total, bits)] = k + 1;
1144 for (--k; k >= 0; --k) {
1147 if (isl_int_is_zero(bmap->div[k][0]))
1150 hash = isl_seq_hash(bmap->div[k], 2+total, bits);
1151 for (h = hash; index[h]; h = (h+1) % size)
1152 if (isl_seq_eq(bmap->div[k],
1153 bmap->div[index[h]-1], 2+total))
1158 isl_int_set_si(eq.data[1+total_var+k], -1);
1159 isl_int_set_si(eq.data[1+total_var+l], 1);
1160 eliminate_div(bmap, eq.data, l);
1161 isl_int_set_si(eq.data[1+total_var+k], 0);
1162 isl_int_set_si(eq.data[1+total_var+l], 0);
1167 isl_blk_free(ctx, eq);
1173 /* Elimininate divs based on equalities
1175 static struct isl_basic_map *eliminate_divs_eq(
1176 struct isl_basic_map *bmap, int *progress)
1186 off = 1 + bmap->nparam + bmap->n_in + bmap->n_out;
1188 for (d = bmap->n_div - 1; d >= 0 ; --d) {
1189 for (i = 0; i < bmap->n_eq; ++i) {
1190 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
1191 !isl_int_is_negone(bmap->eq[i][off + d]))
1195 eliminate_div(bmap, bmap->eq[i], d);
1196 isl_basic_map_drop_equality(bmap, i);
1201 return eliminate_divs_eq(bmap, progress);
1205 static struct isl_basic_map *normalize_constraints(struct isl_basic_map *bmap)
1209 unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1212 for (i = bmap->n_eq - 1; i >= 0; --i) {
1213 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
1214 if (isl_int_is_zero(gcd)) {
1215 if (!isl_int_is_zero(bmap->eq[i][0])) {
1216 bmap = isl_basic_map_set_to_empty(bmap);
1219 isl_basic_map_drop_equality(bmap, i);
1222 if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
1223 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
1224 if (isl_int_is_one(gcd))
1226 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
1227 bmap = isl_basic_map_set_to_empty(bmap);
1230 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
1233 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1234 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
1235 if (isl_int_is_zero(gcd)) {
1236 if (isl_int_is_neg(bmap->ineq[i][0])) {
1237 bmap = isl_basic_map_set_to_empty(bmap);
1240 isl_basic_map_drop_inequality(bmap, i);
1243 if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
1244 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
1245 if (isl_int_is_one(gcd))
1247 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
1248 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
1256 /* Eliminate the specified variables from the constraints using
1257 * Fourier-Motzkin. The variables themselves are not removed.
1259 struct isl_basic_map *isl_basic_map_eliminate_vars(
1260 struct isl_basic_map *bmap, int pos, unsigned n)
1269 total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1270 extra = bmap->extra - bmap->n_div;
1272 bmap = isl_basic_map_cow(bmap);
1273 for (d = pos + n - 1; d >= pos; --d) {
1274 int n_lower, n_upper;
1277 for (i = 0; i < bmap->n_eq; ++i) {
1278 if (isl_int_is_zero(bmap->eq[i][1+d]))
1280 eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1281 isl_basic_map_drop_equality(bmap, i);
1288 for (i = 0; i < bmap->n_ineq; ++i) {
1289 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1291 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1294 bmap = isl_basic_map_extend(bmap,
1295 bmap->nparam, bmap->n_in, bmap->n_out, 0,
1296 0, n_lower * n_upper);
1297 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1299 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1302 for (j = 0; j < i; ++j) {
1303 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1306 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1307 isl_int_sgn(bmap->ineq[j][1+d]))
1309 k = isl_basic_map_alloc_inequality(bmap);
1312 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1314 isl_seq_clr(bmap->ineq[k]+1+total, extra);
1315 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1316 1+d, 1+total, NULL);
1318 isl_basic_map_drop_inequality(bmap, i);
1321 if (n_lower > 0 && n_upper > 0) {
1322 bmap = normalize_constraints(bmap);
1323 bmap = remove_duplicate_constraints(bmap, NULL);
1324 bmap = isl_basic_map_gauss(bmap, NULL);
1325 bmap = isl_basic_map_convex_hull(bmap);
1328 if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1332 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1335 isl_basic_map_free(bmap);
1339 struct isl_basic_set *isl_basic_set_eliminate_vars(
1340 struct isl_basic_set *bset, unsigned pos, unsigned n)
1342 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1343 (struct isl_basic_map *)bset, pos, n);
1346 /* Project out n dimensions starting at first using Fourier-Motzkin */
1347 struct isl_set *isl_set_remove_dims(struct isl_set *set,
1348 unsigned first, unsigned n)
1355 set = isl_set_cow(set);
1358 isl_assert(set->ctx, first+n <= set->dim, goto error);
1360 for (i = 0; i < set->n; ++i) {
1361 set->p[i] = isl_basic_set_eliminate_vars(set->p[i],
1362 set->nparam + first, n);
1366 set = isl_set_drop_dims(set, first, n);
1373 /* Project out n inputs starting at first using Fourier-Motzkin */
1374 struct isl_map *isl_map_remove_inputs(struct isl_map *map,
1375 unsigned first, unsigned n)
1382 map = isl_map_cow(map);
1385 isl_assert(map->ctx, first+n <= map->n_in, goto error);
1387 for (i = 0; i < map->n; ++i) {
1388 map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
1389 map->nparam + first, n);
1393 map = isl_map_drop_inputs(map, first, n);
1400 /* Project out n dimensions starting at first using Fourier-Motzkin */
1401 struct isl_basic_set *isl_basic_set_remove_dims(struct isl_basic_set *bset,
1402 unsigned first, unsigned n)
1404 bset = isl_basic_set_eliminate_vars(bset, bset->nparam + first, n);
1405 bset = isl_basic_set_drop_dims(bset, first, n);
1409 /* Elimininate divs based on inequalities
1411 static struct isl_basic_map *eliminate_divs_ineq(
1412 struct isl_basic_map *bmap, int *progress)
1417 struct isl_ctx *ctx;
1423 off = 1 + bmap->nparam + bmap->n_in + bmap->n_out;
1425 for (d = bmap->n_div - 1; d >= 0 ; --d) {
1426 for (i = 0; i < bmap->n_eq; ++i)
1427 if (!isl_int_is_zero(bmap->eq[i][off + d]))
1431 for (i = 0; i < bmap->n_ineq; ++i)
1432 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
1434 if (i < bmap->n_ineq)
1437 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
1438 if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1440 bmap = isl_basic_map_drop_div(bmap, d);
1447 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1454 bmap = normalize_constraints(bmap);
1455 bmap = eliminate_divs_eq(bmap, &progress);
1456 bmap = eliminate_divs_ineq(bmap, &progress);
1457 bmap = isl_basic_map_gauss(bmap, &progress);
1458 bmap = remove_duplicate_divs(bmap, &progress);
1459 bmap = remove_duplicate_constraints(bmap, &progress);
1464 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1466 return (struct isl_basic_set *)
1467 isl_basic_map_simplify((struct isl_basic_map *)bset);
1470 static void dump_term(struct isl_basic_map *bmap,
1471 isl_int c, int pos, FILE *out)
1473 unsigned in = bmap->n_in;
1474 unsigned dim = bmap->n_in + bmap->n_out;
1476 isl_int_print(out, c);
1478 if (!isl_int_is_one(c))
1479 isl_int_print(out, c);
1480 if (pos < 1 + bmap->nparam)
1481 fprintf(out, "p%d", pos - 1);
1482 else if (pos < 1 + bmap->nparam + in)
1483 fprintf(out, "i%d", pos - 1 - bmap->nparam);
1484 else if (pos < 1 + bmap->nparam + dim)
1485 fprintf(out, "o%d", pos - 1 - bmap->nparam - in);
1487 fprintf(out, "e%d", pos - 1 - bmap->nparam - dim);
1491 static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
1492 int sign, FILE *out)
1496 unsigned len = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1500 for (i = 0, first = 1; i < len; ++i) {
1501 if (isl_int_sgn(c[i]) * sign <= 0)
1504 fprintf(out, " + ");
1506 isl_int_abs(v, c[i]);
1507 dump_term(bmap, v, i, out);
1514 static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
1515 const char *op, FILE *out, int indent)
1519 fprintf(out, "%*s", indent, "");
1521 dump_constraint_sign(bmap, c, 1, out);
1522 fprintf(out, " %s ", op);
1523 dump_constraint_sign(bmap, c, -1, out);
1527 for (i = bmap->n_div; i < bmap->extra; ++i) {
1528 if (isl_int_is_zero(c[1+bmap->nparam+bmap->n_in+bmap->n_out+i]))
1530 fprintf(out, "%*s", indent, "");
1531 fprintf(out, "ERROR: unused div coefficient not zero\n");
1535 static void dump_constraints(struct isl_basic_map *bmap,
1536 isl_int **c, unsigned n,
1537 const char *op, FILE *out, int indent)
1541 for (i = 0; i < n; ++i)
1542 dump_constraint(bmap, c[i], op, out, indent);
1545 static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
1549 unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1551 for (j = 0; j < 1 + total; ++j) {
1552 if (isl_int_is_zero(exp[j]))
1554 if (!first && isl_int_is_pos(exp[j]))
1556 dump_term(bmap, exp[j], j, out);
1561 static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
1565 dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
1566 dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
1568 for (i = 0; i < bmap->n_div; ++i) {
1569 fprintf(out, "%*s", indent, "");
1570 fprintf(out, "e%d = [(", i);
1571 dump_affine(bmap, bmap->div[i]+1, out);
1573 isl_int_print(out, bmap->div[i][0]);
1574 fprintf(out, "]\n");
1578 void isl_basic_set_dump(struct isl_basic_set *bset, FILE *out, int indent)
1581 fprintf(out, "null basic set\n");
1585 fprintf(out, "%*s", indent, "");
1586 fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
1587 bset->ref, bset->nparam, bset->dim, bset->extra,
1589 dump((struct isl_basic_map *)bset, out, indent);
1592 void isl_basic_map_dump(struct isl_basic_map *bmap, FILE *out, int indent)
1595 fprintf(out, "null basic map\n");
1599 fprintf(out, "%*s", indent, "");
1600 fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, flags: %x\n",
1602 bmap->nparam, bmap->n_in, bmap->n_out, bmap->extra, bmap->flags);
1603 dump(bmap, out, indent);
1606 int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
1608 unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1611 isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
1612 isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
1613 isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
1614 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1618 struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
1619 unsigned nparam, unsigned dim, int n, unsigned flags)
1621 struct isl_set *set;
1623 isl_assert(ctx, n >= 0, return NULL);
1624 set = isl_alloc(ctx, struct isl_set,
1625 sizeof(struct isl_set) +
1626 n * sizeof(struct isl_basic_set *));
1635 set->nparam = nparam;
1642 struct isl_set *isl_set_dup(struct isl_set *set)
1645 struct isl_set *dup;
1650 dup = isl_set_alloc(set->ctx, set->nparam, set->dim, set->n, set->flags);
1653 for (i = 0; i < set->n; ++i)
1654 dup = isl_set_add(dup,
1655 isl_basic_set_dup(set->p[i]));
1659 struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
1661 struct isl_set *set;
1666 set = isl_set_alloc(bset->ctx, bset->nparam, bset->dim, 1, ISL_MAP_DISJOINT);
1668 isl_basic_set_free(bset);
1671 return isl_set_add(set, bset);
1674 struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
1676 struct isl_map *map;
1681 map = isl_map_alloc(bmap->ctx, bmap->nparam, bmap->n_in, bmap->n_out, 1,
1684 isl_basic_map_free(bmap);
1687 return isl_map_add(map, bmap);
1690 struct isl_set *isl_set_add(struct isl_set *set, struct isl_basic_set *bset)
1694 isl_assert(set->ctx, set->nparam == bset->nparam, goto error);
1695 isl_assert(set->ctx, set->dim == bset->dim, goto error);
1696 isl_assert(set->ctx, set->n < set->size, goto error);
1697 set->p[set->n] = bset;
1704 isl_basic_set_free(bset);
1708 void isl_set_free(struct isl_set *set)
1718 isl_ctx_deref(set->ctx);
1719 for (i = 0; i < set->n; ++i)
1720 isl_basic_set_free(set->p[i]);
1724 void isl_set_dump(struct isl_set *set, FILE *out, int indent)
1729 fprintf(out, "null set\n");
1733 fprintf(out, "%*s", indent, "");
1734 fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
1735 set->ref, set->n, set->nparam, set->dim, set->flags);
1736 for (i = 0; i < set->n; ++i) {
1737 fprintf(out, "%*s", indent, "");
1738 fprintf(out, "basic set %d:\n", i);
1739 isl_basic_set_dump(set->p[i], out, indent+4);
1743 void isl_map_dump(struct isl_map *map, FILE *out, int indent)
1748 fprintf(out, "null map\n");
1752 fprintf(out, "%*s", indent, "");
1753 fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, flags: %x\n",
1754 map->ref, map->n, map->nparam, map->n_in, map->n_out,
1756 for (i = 0; i < map->n; ++i) {
1757 fprintf(out, "%*s", indent, "");
1758 fprintf(out, "basic map %d:\n", i);
1759 isl_basic_map_dump(map->p[i], out, indent+4);
1763 struct isl_basic_map *isl_basic_map_intersect_domain(
1764 struct isl_basic_map *bmap, struct isl_basic_set *bset)
1766 struct isl_basic_map *bmap_domain;
1771 isl_assert(bset->ctx, bset->dim == bmap->n_in, goto error);
1772 isl_assert(bset->ctx, bset->nparam == bmap->nparam, goto error);
1774 bmap = isl_basic_map_extend(bmap,
1775 bset->nparam, bmap->n_in, bmap->n_out,
1776 bset->n_div, bset->n_eq, bset->n_ineq);
1779 bmap_domain = isl_basic_map_from_basic_set(bset,
1781 bmap = add_constraints(bmap, bmap_domain, 0, 0);
1783 bmap = isl_basic_map_simplify(bmap);
1784 return isl_basic_map_finalize(bmap);
1786 isl_basic_map_free(bmap);
1787 isl_basic_set_free(bset);
1791 struct isl_basic_map *isl_basic_map_intersect_range(
1792 struct isl_basic_map *bmap, struct isl_basic_set *bset)
1794 struct isl_basic_map *bmap_range;
1799 isl_assert(bset->ctx, bset->dim == bmap->n_out, goto error);
1800 isl_assert(bset->ctx, bset->nparam == bmap->nparam, goto error);
1802 bmap = isl_basic_map_extend(bmap,
1803 bset->nparam, bmap->n_in, bmap->n_out,
1804 bset->n_div, bset->n_eq, bset->n_ineq);
1807 bmap_range = isl_basic_map_from_basic_set(bset,
1809 bmap = add_constraints(bmap, bmap_range, 0, 0);
1811 bmap = isl_basic_map_simplify(bmap);
1812 return isl_basic_map_finalize(bmap);
1814 isl_basic_map_free(bmap);
1815 isl_basic_set_free(bset);
1819 struct isl_basic_map *isl_basic_map_intersect(
1820 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1822 if (!bmap1 || !bmap2)
1825 isl_assert(bmap1->ctx, bmap1->nparam == bmap2->nparam, goto error);
1826 isl_assert(bmap1->ctx, bmap1->n_in == bmap2->n_in, goto error);
1827 isl_assert(bmap1->ctx, bmap1->n_out == bmap2->n_out, goto error);
1829 bmap1 = isl_basic_map_extend(bmap1,
1830 bmap1->nparam, bmap1->n_in, bmap1->n_out,
1831 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
1834 bmap1 = add_constraints(bmap1, bmap2, 0, 0);
1836 bmap1 = isl_basic_map_simplify(bmap1);
1837 return isl_basic_map_finalize(bmap1);
1839 isl_basic_map_free(bmap1);
1840 isl_basic_map_free(bmap2);
1844 struct isl_basic_set *isl_basic_set_intersect(
1845 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
1847 return (struct isl_basic_set *)
1848 isl_basic_map_intersect(
1849 (struct isl_basic_map *)bset1,
1850 (struct isl_basic_map *)bset2);
1853 struct isl_map *isl_map_intersect(struct isl_map *map1, struct isl_map *map2)
1856 struct isl_map *result;
1862 if (F_ISSET(map1, ISL_MAP_DISJOINT) &&
1863 F_ISSET(map2, ISL_MAP_DISJOINT))
1864 FL_SET(flags, ISL_MAP_DISJOINT);
1866 result = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map1->n_out,
1867 map1->n * map2->n, flags);
1870 for (i = 0; i < map1->n; ++i)
1871 for (j = 0; j < map2->n; ++j) {
1872 struct isl_basic_map *part;
1873 part = isl_basic_map_intersect(
1874 isl_basic_map_copy(map1->p[i]),
1875 isl_basic_map_copy(map2->p[j]));
1876 if (isl_basic_map_is_empty(part))
1877 isl_basic_map_free(part);
1879 result = isl_map_add(result, part);
1892 struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
1894 return (struct isl_set *)
1895 isl_map_intersect((struct isl_map *)set1,
1896 (struct isl_map *)set2);
1899 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
1901 struct isl_basic_set *bset;
1906 bmap = isl_basic_map_cow(bmap);
1910 bset = isl_basic_set_from_basic_map(bmap);
1911 bset = isl_basic_set_swap_vars(bset, in);
1912 return isl_basic_map_from_basic_set(bset, bset->dim-in, in);
1915 /* Turn final n dimensions into existentially quantified variables.
1917 struct isl_basic_set *isl_basic_set_project_out(
1918 struct isl_basic_set *bset, unsigned n, unsigned flags)
1928 isl_assert(bset->ctx, n <= bset->dim, goto error);
1933 bset = isl_basic_set_cow(bset);
1935 row_size = 1 + bset->nparam + bset->dim + bset->extra;
1936 old = bset->block2.data;
1937 bset->block2 = isl_blk_extend(bset->ctx, bset->block2,
1938 (bset->extra + n) * (1 + row_size));
1939 if (!bset->block2.data)
1941 new_div = isl_alloc_array(ctx, isl_int *, bset->extra + n);
1944 for (i = 0; i < n; ++i) {
1945 new_div[i] = bset->block2.data +
1946 (bset->extra + i) * (1 + row_size);
1947 isl_seq_clr(new_div[i], 1 + row_size);
1949 for (i = 0; i < bset->extra; ++i)
1950 new_div[n + i] = bset->block2.data + (bset->div[i] - old);
1952 bset->div = new_div;
1956 bset = isl_basic_set_simplify(bset);
1957 return isl_basic_set_finalize(bset);
1959 isl_basic_set_free(bset);
1963 struct isl_basic_map *isl_basic_map_apply_range(
1964 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1966 struct isl_basic_set *bset;
1967 unsigned n_in, n_out;
1969 if (!bmap1 || !bmap2)
1972 isl_assert(bmap->ctx, bmap1->n_out == bmap2->n_in, goto error);
1973 isl_assert(bmap->ctx, bmap1->nparam == bmap2->nparam, goto error);
1976 n_out = bmap2->n_out;
1978 bmap2 = isl_basic_map_reverse(bmap2);
1981 bmap1 = isl_basic_map_extend(bmap1, bmap1->nparam,
1982 bmap1->n_in + bmap2->n_in, bmap1->n_out,
1983 bmap2->extra, bmap2->n_eq, bmap2->n_ineq);
1986 bmap1 = add_constraints(bmap1, bmap2, bmap1->n_in - bmap2->n_in, 0);
1987 bmap1 = isl_basic_map_simplify(bmap1);
1988 bset = isl_basic_set_from_basic_map(bmap1);
1989 bset = isl_basic_set_project_out(bset,
1990 bset->dim - (n_in + n_out), 0);
1991 return isl_basic_map_from_basic_set(bset, n_in, n_out);
1993 isl_basic_map_free(bmap1);
1994 isl_basic_map_free(bmap2);
1998 struct isl_basic_set *isl_basic_set_apply(
1999 struct isl_basic_set *bset, struct isl_basic_map *bmap)
2004 isl_assert(bset->ctx, bset->dim == bmap->n_in, goto error);
2006 return (struct isl_basic_set *)
2007 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
2009 isl_basic_set_free(bset);
2010 isl_basic_map_free(bmap);
2014 struct isl_basic_map *isl_basic_map_apply_domain(
2015 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
2017 if (!bmap1 || !bmap2)
2020 isl_assert(ctx, bmap1->n_in == bmap2->n_in, goto error);
2021 isl_assert(ctx, bmap1->nparam == bmap2->nparam, goto error);
2023 bmap1 = isl_basic_map_reverse(bmap1);
2024 bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
2025 return isl_basic_map_reverse(bmap1);
2027 isl_basic_map_free(bmap1);
2028 isl_basic_map_free(bmap2);
2032 static struct isl_basic_map *var_equal(struct isl_ctx *ctx,
2033 struct isl_basic_map *bmap, unsigned pos)
2036 i = isl_basic_map_alloc_equality(bmap);
2039 isl_seq_clr(bmap->eq[i],
2040 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
2041 isl_int_set_si(bmap->eq[i][1+bmap->nparam+pos], -1);
2042 isl_int_set_si(bmap->eq[i][1+bmap->nparam+bmap->n_in+pos], 1);
2043 return isl_basic_map_finalize(bmap);
2045 isl_basic_map_free(bmap);
2049 static struct isl_basic_map *var_more(struct isl_ctx *ctx,
2050 struct isl_basic_map *bmap, unsigned pos)
2053 i = isl_basic_map_alloc_inequality(bmap);
2056 isl_seq_clr(bmap->ineq[i],
2057 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
2058 isl_int_set_si(bmap->ineq[i][0], -1);
2059 isl_int_set_si(bmap->ineq[i][1+bmap->nparam+pos], -1);
2060 isl_int_set_si(bmap->ineq[i][1+bmap->nparam+bmap->n_in+pos], 1);
2061 return isl_basic_map_finalize(bmap);
2063 isl_basic_map_free(bmap);
2067 static struct isl_basic_map *var_less(struct isl_ctx *ctx,
2068 struct isl_basic_map *bmap, unsigned pos)
2071 i = isl_basic_map_alloc_inequality(bmap);
2074 isl_seq_clr(bmap->ineq[i],
2075 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
2076 isl_int_set_si(bmap->ineq[i][0], -1);
2077 isl_int_set_si(bmap->ineq[i][1+bmap->nparam+pos], 1);
2078 isl_int_set_si(bmap->ineq[i][1+bmap->nparam+bmap->n_in+pos], -1);
2079 return isl_basic_map_finalize(bmap);
2081 isl_basic_map_free(bmap);
2085 struct isl_basic_map *isl_basic_map_equal(struct isl_ctx *ctx,
2086 unsigned nparam, unsigned in, unsigned out, unsigned n_equal)
2089 struct isl_basic_map *bmap;
2090 bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, n_equal, 0);
2093 for (i = 0; i < n_equal && bmap; ++i)
2094 bmap = var_equal(ctx, bmap, i);
2095 return isl_basic_map_finalize(bmap);
2098 struct isl_basic_map *isl_basic_map_less_at(struct isl_ctx *ctx,
2099 unsigned nparam, unsigned in, unsigned out, unsigned pos)
2102 struct isl_basic_map *bmap;
2103 bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, pos, 1);
2106 for (i = 0; i < pos && bmap; ++i)
2107 bmap = var_equal(ctx, bmap, i);
2109 bmap = var_less(ctx, bmap, pos);
2110 return isl_basic_map_finalize(bmap);
2113 struct isl_basic_map *isl_basic_map_more_at(struct isl_ctx *ctx,
2114 unsigned nparam, unsigned in, unsigned out, unsigned pos)
2117 struct isl_basic_map *bmap;
2118 bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, pos, 1);
2121 for (i = 0; i < pos && bmap; ++i)
2122 bmap = var_equal(ctx, bmap, i);
2124 bmap = var_more(ctx, bmap, pos);
2125 return isl_basic_map_finalize(bmap);
2128 struct isl_basic_map *isl_basic_map_from_basic_set(
2129 struct isl_basic_set *bset, unsigned n_in, unsigned n_out)
2131 struct isl_basic_map *bmap;
2133 bset = isl_basic_set_cow(bset);
2137 isl_assert(ctx, bset->dim == n_in + n_out, goto error);
2138 bmap = (struct isl_basic_map *) bset;
2140 bmap->n_out = n_out;
2141 return isl_basic_map_finalize(bmap);
2143 isl_basic_set_free(bset);
2147 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
2151 if (bmap->n_in == 0)
2152 return (struct isl_basic_set *)bmap;
2153 bmap = isl_basic_map_cow(bmap);
2156 bmap->n_out += bmap->n_in;
2158 bmap = isl_basic_map_finalize(bmap);
2159 return (struct isl_basic_set *)bmap;
2164 /* For a div d = floor(f/m), add the constraints
2167 * -(f-(n-1)) + m d >= 0
2169 * Note that the second constraint is the negation of
2173 static int add_div_constraints(struct isl_basic_map *bmap, unsigned div)
2176 unsigned div_pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
2177 unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra;
2179 i = isl_basic_map_alloc_inequality(bmap);
2182 isl_seq_cpy(bmap->ineq[i], bmap->div[div]+1, 1+total);
2183 isl_int_neg(bmap->ineq[i][div_pos], bmap->div[div][0]);
2185 j = isl_basic_map_alloc_inequality(bmap);
2188 isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
2189 isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][div_pos]);
2190 isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
2194 struct isl_basic_set *isl_basic_map_underlying_set(
2195 struct isl_basic_map *bmap)
2199 if (bmap->nparam == 0 && bmap->n_in == 0 && bmap->n_div == 0)
2200 return (struct isl_basic_set *)bmap;
2201 bmap = isl_basic_map_cow(bmap);
2204 bmap->n_out += bmap->nparam + bmap->n_in + bmap->n_div;
2207 bmap->extra -= bmap->n_div;
2209 bmap = isl_basic_map_finalize(bmap);
2210 return (struct isl_basic_set *)bmap;
2215 struct isl_basic_map *isl_basic_map_overlying_set(
2216 struct isl_basic_set *bset, struct isl_basic_map *like)
2218 struct isl_basic_map *bmap;
2219 struct isl_ctx *ctx;
2226 isl_assert(ctx, bset->dim ==
2227 like->nparam + like->n_in + like->n_out + like->n_div,
2229 if (like->nparam == 0 && like->n_in == 0 && like->n_div == 0) {
2230 isl_basic_map_free(like);
2231 return (struct isl_basic_map *)bset;
2233 bset = isl_basic_set_cow(bset);
2236 total = bset->dim + bset->extra;
2237 bmap = (struct isl_basic_map *)bset;
2238 bmap->nparam = like->nparam;
2239 bmap->n_in = like->n_in;
2240 bmap->n_out = like->n_out;
2241 bmap->extra += like->n_div;
2244 ltotal = total - bmap->extra + like->extra;
2247 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
2248 bmap->extra * (1 + 1 + total));
2249 if (isl_blk_is_error(bmap->block2))
2251 bmap->div = isl_realloc_array(ctx, bmap->div, isl_int *,
2255 bmap = isl_basic_map_extend(bmap, bmap->nparam,
2256 bmap->n_in, bmap->n_out, 0, 0, 2 * like->n_div);
2257 for (i = 0; i < like->n_div; ++i) {
2258 k = isl_basic_map_alloc_div(bmap);
2261 isl_seq_cpy(bmap->div[k], like->div[i], 1 + 1 + ltotal);
2262 isl_seq_clr(bmap->div[k]+1+1+ltotal, total - ltotal);
2263 if (add_div_constraints(bmap, k) < 0)
2267 isl_basic_map_free(like);
2268 bmap = isl_basic_map_finalize(bmap);
2271 isl_basic_map_free(like);
2272 isl_basic_set_free(bset);
2276 struct isl_basic_set *isl_basic_set_from_underlying_set(
2277 struct isl_basic_set *bset, struct isl_basic_set *like)
2279 return (struct isl_basic_set *)
2280 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
2283 struct isl_set *isl_set_from_underlying_set(
2284 struct isl_set *set, struct isl_basic_set *like)
2290 isl_assert(set->ctx, set->dim == like->nparam + like->dim + like->n_div,
2292 if (like->nparam == 0 && like->n_div == 0) {
2293 isl_basic_set_free(like);
2296 set = isl_set_cow(set);
2299 for (i = 0; i < set->n; ++i) {
2300 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
2301 isl_basic_set_copy(like));
2305 set->nparam = like->nparam;
2306 set->dim = like->dim;
2307 isl_basic_set_free(like);
2310 isl_basic_set_free(like);
2315 struct isl_set *isl_map_underlying_set(struct isl_map *map)
2319 map = isl_map_align_divs(map);
2320 map = isl_map_cow(map);
2324 for (i = 0; i < map->n; ++i) {
2325 map->p[i] = (struct isl_basic_map *)
2326 isl_basic_map_underlying_set(map->p[i]);
2331 map->n_out += map->nparam + map->n_in;
2333 map->n_out = map->p[0]->n_out;
2336 return (struct isl_set *)map;
2342 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
2344 return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
2347 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
2349 struct isl_basic_set *domain;
2353 n_out = bmap->n_out;
2354 domain = isl_basic_set_from_basic_map(bmap);
2355 return isl_basic_set_project_out(domain, n_out, 0);
2358 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
2360 return isl_basic_map_domain(isl_basic_map_reverse(bmap));
2363 struct isl_set *isl_map_range(struct isl_map *map)
2366 struct isl_set *set;
2370 map = isl_map_cow(map);
2374 set = (struct isl_set *) map;
2376 for (i = 0; i < map->n; ++i) {
2377 set->p[i] = isl_basic_map_range(map->p[i]);
2381 F_CLR(set, ISL_MAP_DISJOINT);
2382 F_CLR(set, ISL_SET_NORMALIZED);
2389 struct isl_map *isl_map_from_set(struct isl_set *set,
2390 unsigned n_in, unsigned n_out)
2393 struct isl_map *map = NULL;
2397 isl_assert(set->ctx, set->dim == n_in + n_out, goto error);
2398 set = isl_set_cow(set);
2401 map = (struct isl_map *)set;
2402 for (i = 0; i < set->n; ++i) {
2403 map->p[i] = isl_basic_map_from_basic_set(
2404 set->p[i], n_in, n_out);
2416 struct isl_set *isl_set_from_map(struct isl_map *map)
2419 struct isl_set *set = NULL;
2423 map = isl_map_cow(map);
2426 map->n_out += map->n_in;
2428 set = (struct isl_set *)map;
2429 for (i = 0; i < map->n; ++i) {
2430 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
2440 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
2441 unsigned nparam, unsigned in, unsigned out, int n,
2444 struct isl_map *map;
2446 map = isl_alloc(ctx, struct isl_map,
2447 sizeof(struct isl_map) +
2448 n * sizeof(struct isl_basic_map *));
2457 map->nparam = nparam;
2464 struct isl_basic_map *isl_basic_map_empty(struct isl_ctx *ctx,
2465 unsigned nparam, unsigned in, unsigned out)
2467 struct isl_basic_map *bmap;
2468 bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 1, 0);
2469 bmap = isl_basic_map_set_to_empty(bmap);
2473 struct isl_basic_set *isl_basic_set_empty(struct isl_ctx *ctx,
2474 unsigned nparam, unsigned dim)
2476 struct isl_basic_set *bset;
2477 bset = isl_basic_set_alloc(ctx, nparam, dim, 0, 1, 0);
2478 bset = isl_basic_set_set_to_empty(bset);
2482 struct isl_basic_map *isl_basic_map_universe(struct isl_ctx *ctx,
2483 unsigned nparam, unsigned in, unsigned out)
2485 struct isl_basic_map *bmap;
2486 bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 0, 0);
2490 struct isl_basic_set *isl_basic_set_universe(struct isl_ctx *ctx,
2491 unsigned nparam, unsigned dim)
2493 struct isl_basic_set *bset;
2494 bset = isl_basic_set_alloc(ctx, nparam, dim, 0, 0, 0);
2498 struct isl_map *isl_map_empty(struct isl_ctx *ctx,
2499 unsigned nparam, unsigned in, unsigned out)
2501 return isl_map_alloc(ctx, nparam, in, out, 0, ISL_MAP_DISJOINT);
2504 struct isl_set *isl_set_empty(struct isl_ctx *ctx,
2505 unsigned nparam, unsigned dim)
2507 return isl_set_alloc(ctx, nparam, dim, 0, ISL_MAP_DISJOINT);
2510 struct isl_map *isl_map_dup(struct isl_map *map)
2513 struct isl_map *dup;
2517 dup = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out, map->n,
2519 for (i = 0; i < map->n; ++i)
2520 dup = isl_map_add(dup,
2521 isl_basic_map_dup(map->p[i]));
2525 struct isl_map *isl_map_add(struct isl_map *map, struct isl_basic_map *bmap)
2529 isl_assert(map->ctx, map->nparam == bmap->nparam, goto error);
2530 isl_assert(map->ctx, map->n_in == bmap->n_in, goto error);
2531 isl_assert(map->ctx, map->n_out == bmap->n_out, goto error);
2532 isl_assert(map->ctx, map->n < map->size, goto error);
2533 map->p[map->n] = bmap;
2535 F_CLR(map, ISL_MAP_NORMALIZED);
2541 isl_basic_map_free(bmap);
2545 void isl_map_free(struct isl_map *map)
2555 isl_ctx_deref(map->ctx);
2556 for (i = 0; i < map->n; ++i)
2557 isl_basic_map_free(map->p[i]);
2561 struct isl_map *isl_map_extend(struct isl_map *base,
2562 unsigned nparam, unsigned n_in, unsigned n_out)
2566 base = isl_map_cow(base);
2570 isl_assert(base->ctx, base->nparam <= nparam, goto error);
2571 isl_assert(base->ctx, base->n_in <= n_in, goto error);
2572 isl_assert(base->ctx, base->n_out <= n_out, goto error);
2573 base->nparam = nparam;
2575 base->n_out = n_out;
2576 for (i = 0; i < base->n; ++i) {
2577 base->p[i] = isl_basic_map_extend(base->p[i],
2578 nparam, n_in, n_out, 0, 0, 0);
2588 struct isl_set *isl_set_extend(struct isl_set *base,
2589 unsigned nparam, unsigned dim)
2591 return (struct isl_set *)isl_map_extend((struct isl_map *)base,
2595 static struct isl_basic_map *isl_basic_map_fix_var(struct isl_basic_map *bmap,
2596 unsigned var, int value)
2600 bmap = isl_basic_map_cow(bmap);
2601 bmap = isl_basic_map_extend(bmap,
2602 bmap->nparam, bmap->n_in, bmap->n_out, 0, 1, 0);
2603 j = isl_basic_map_alloc_equality(bmap);
2606 isl_seq_clr(bmap->eq[j],
2607 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
2608 isl_int_set_si(bmap->eq[j][1 + var], -1);
2609 isl_int_set_si(bmap->eq[j][0], value);
2610 bmap = isl_basic_map_simplify(bmap);
2611 return isl_basic_map_finalize(bmap);
2613 isl_basic_map_free(bmap);
2617 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
2618 unsigned input, int value)
2622 isl_assert(bmap->ctx, input < bmap->n_in, goto error);
2623 return isl_basic_map_fix_var(bmap, bmap->nparam + input, value);
2625 isl_basic_map_free(bmap);
2629 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
2630 unsigned dim, int value)
2634 isl_assert(bset->ctx, dim < bset->dim, goto error);
2635 return (struct isl_basic_set *)
2636 isl_basic_map_fix_var((struct isl_basic_map *)bset,
2637 bset->nparam + dim, value);
2639 isl_basic_set_free(bset);
2643 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
2644 unsigned input, int value)
2648 map = isl_map_cow(map);
2652 isl_assert(ctx, input < map->n_in, goto error);
2653 for (i = 0; i < map->n; ++i) {
2654 map->p[i] = isl_basic_map_fix_input_si(map->p[i], input, value);
2658 F_CLR(map, ISL_MAP_NORMALIZED);
2665 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
2669 set = isl_set_cow(set);
2673 isl_assert(set->ctx, dim < set->dim, goto error);
2674 for (i = 0; i < set->n; ++i) {
2675 set->p[i] = isl_basic_set_fix_dim_si(set->p[i], dim, value);
2685 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
2686 unsigned dim, isl_int value)
2690 bset = isl_basic_set_cow(bset);
2691 bset = isl_basic_set_extend(bset, bset->nparam, bset->dim, 0, 0, 1);
2692 j = isl_basic_set_alloc_inequality(bset);
2695 isl_seq_clr(bset->ineq[j], 1 + bset->nparam + bset->dim + bset->extra);
2696 isl_int_set_si(bset->ineq[j][1 + bset->nparam + dim], 1);
2697 isl_int_neg(bset->ineq[j][0], value);
2698 bset = isl_basic_set_simplify(bset);
2699 return isl_basic_set_finalize(bset);
2701 isl_basic_set_free(bset);
2705 struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
2710 set = isl_set_cow(set);
2714 isl_assert(set->ctx, dim < set->dim, goto error);
2715 for (i = 0; i < set->n; ++i) {
2716 set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
2726 struct isl_map *isl_map_reverse(struct isl_map *map)
2731 map = isl_map_cow(map);
2736 map->n_in = map->n_out;
2738 for (i = 0; i < map->n; ++i) {
2739 map->p[i] = isl_basic_map_reverse(map->p[i]);
2743 F_CLR(map, ISL_MAP_NORMALIZED);
2750 struct isl_map *isl_basic_map_lexmax(
2751 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2752 struct isl_set **empty)
2754 return isl_pip_basic_map_lexmax(bmap, dom, empty);
2757 struct isl_map *isl_basic_map_lexmin(
2758 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2759 struct isl_set **empty)
2761 return isl_pip_basic_map_lexmin(bmap, dom, empty);
2764 struct isl_set *isl_basic_set_lexmin(struct isl_basic_set *bset)
2766 struct isl_basic_map *bmap = NULL;
2767 struct isl_basic_set *dom = NULL;
2768 struct isl_map *min;
2772 bmap = isl_basic_map_from_basic_set(bset, 0, bset->dim);
2775 dom = isl_basic_set_alloc(bmap->ctx, bmap->nparam, 0, 0, 0, 0);
2778 min = isl_basic_map_lexmin(bmap, dom, NULL);
2779 return isl_map_range(min);
2781 isl_basic_map_free(bmap);
2785 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
2789 if (bmap->n_div == 0)
2790 return isl_map_from_basic_map(bmap);
2791 return isl_pip_basic_map_compute_divs(bmap);
2794 struct isl_map *isl_map_compute_divs(struct isl_map *map)
2797 struct isl_map *res;
2803 res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
2804 for (i = 1 ; i < map->n; ++i) {
2806 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
2807 if (F_ISSET(map, ISL_MAP_DISJOINT))
2808 res = isl_map_union_disjoint(res, r2);
2810 res = isl_map_union(res, r2);
2817 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
2819 return (struct isl_set *)
2820 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
2823 struct isl_set *isl_set_compute_divs(struct isl_set *set)
2825 return (struct isl_set *)
2826 isl_map_compute_divs((struct isl_map *)set);
2829 struct isl_set *isl_map_domain(struct isl_map *map)
2832 struct isl_set *set;
2837 map = isl_map_cow(map);
2841 set = (struct isl_set *)map;
2842 set->dim = map->n_in;
2844 for (i = 0; i < map->n; ++i) {
2845 set->p[i] = isl_basic_map_domain(map->p[i]);
2849 F_CLR(set, ISL_MAP_DISJOINT);
2850 F_CLR(set, ISL_SET_NORMALIZED);
2857 struct isl_map *isl_map_union_disjoint(
2858 struct isl_map *map1, struct isl_map *map2)
2862 struct isl_map *map = NULL;
2876 isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
2877 isl_assert(map1->ctx, map1->n_in == map2->n_in, goto error);
2878 isl_assert(map1->ctx, map1->n_out == map2->n_out, goto error);
2880 if (F_ISSET(map1, ISL_MAP_DISJOINT) &&
2881 F_ISSET(map2, ISL_MAP_DISJOINT))
2882 FL_SET(flags, ISL_MAP_DISJOINT);
2884 map = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map1->n_out,
2885 map1->n + map2->n, flags);
2888 for (i = 0; i < map1->n; ++i) {
2889 map = isl_map_add(map,
2890 isl_basic_map_copy(map1->p[i]));
2894 for (i = 0; i < map2->n; ++i) {
2895 map = isl_map_add(map,
2896 isl_basic_map_copy(map2->p[i]));
2910 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
2912 map1 = isl_map_union_disjoint(map1, map2);
2916 F_CLR(map1, ISL_MAP_DISJOINT);
2920 struct isl_set *isl_set_union_disjoint(
2921 struct isl_set *set1, struct isl_set *set2)
2923 return (struct isl_set *)
2924 isl_map_union_disjoint(
2925 (struct isl_map *)set1, (struct isl_map *)set2);
2928 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
2930 return (struct isl_set *)
2931 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
2934 struct isl_map *isl_map_intersect_range(
2935 struct isl_map *map, struct isl_set *set)
2938 struct isl_map *result;
2944 if (F_ISSET(map, ISL_MAP_DISJOINT) &&
2945 F_ISSET(set, ISL_MAP_DISJOINT))
2946 FL_SET(flags, ISL_MAP_DISJOINT);
2948 result = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out,
2949 map->n * set->n, flags);
2952 for (i = 0; i < map->n; ++i)
2953 for (j = 0; j < set->n; ++j) {
2954 result = isl_map_add(result,
2955 isl_basic_map_intersect_range(
2956 isl_basic_map_copy(map->p[i]),
2957 isl_basic_set_copy(set->p[j])));
2970 struct isl_map *isl_map_intersect_domain(
2971 struct isl_map *map, struct isl_set *set)
2973 return isl_map_reverse(
2974 isl_map_intersect_range(isl_map_reverse(map), set));
2977 struct isl_map *isl_map_apply_domain(
2978 struct isl_map *map1, struct isl_map *map2)
2982 map1 = isl_map_reverse(map1);
2983 map1 = isl_map_apply_range(map1, map2);
2984 return isl_map_reverse(map1);
2991 struct isl_map *isl_map_apply_range(
2992 struct isl_map *map1, struct isl_map *map2)
2994 struct isl_map *result;
3000 isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
3001 isl_assert(map1->ctx, map1->n_out == map2->n_in, goto error);
3003 result = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map2->n_out,
3004 map1->n * map2->n, 0);
3007 for (i = 0; i < map1->n; ++i)
3008 for (j = 0; j < map2->n; ++j) {
3009 result = isl_map_add(result,
3010 isl_basic_map_apply_range(
3011 isl_basic_map_copy(map1->p[i]),
3012 isl_basic_map_copy(map2->p[j])));
3018 if (result && result->n <= 1)
3019 F_SET(result, ISL_MAP_DISJOINT);
3028 * returns range - domain
3030 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
3032 struct isl_basic_set *bset;
3038 isl_assert(bmap->ctx, bmap->n_in == bmap->n_out, goto error);
3040 bset = isl_basic_set_from_basic_map(bmap);
3041 bset = isl_basic_set_extend(bset, bset->nparam, 3*dim, 0,
3043 bset = isl_basic_set_swap_vars(bset, 2*dim);
3044 for (i = 0; i < dim; ++i) {
3045 int j = isl_basic_map_alloc_equality(
3046 (struct isl_basic_map *)bset);
3049 isl_seq_clr(bset->eq[j],
3050 1 + bset->nparam + bset->dim + bset->extra);
3051 isl_int_set_si(bset->eq[j][1+bset->nparam+i], 1);
3052 isl_int_set_si(bset->eq[j][1+bset->nparam+dim+i], 1);
3053 isl_int_set_si(bset->eq[j][1+bset->nparam+2*dim+i], -1);
3055 return isl_basic_set_project_out(bset, 2*dim, 0);
3057 isl_basic_map_free(bmap);
3062 * returns range - domain
3064 struct isl_set *isl_map_deltas(struct isl_map *map)
3067 struct isl_set *result;
3072 isl_assert(map->ctx, map->n_in == map->n_out, goto error);
3073 result = isl_set_alloc(map->ctx, map->nparam, map->n_in, map->n, map->flags);
3076 for (i = 0; i < map->n; ++i)
3077 result = isl_set_add(result,
3078 isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
3086 /* If the only constraints a div d=floor(f/m)
3087 * appears in are its two defining constraints
3090 * -(f - (m - 1)) + m d >= 0
3092 * then it can safely be removed.
3094 static int div_is_redundant(struct isl_basic_map *bmap, int div)
3097 unsigned pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
3099 for (i = 0; i < bmap->n_eq; ++i)
3100 if (!isl_int_is_zero(bmap->eq[i][pos]))
3103 for (i = 0; i < bmap->n_ineq; ++i) {
3104 if (isl_int_is_zero(bmap->ineq[i][pos]))
3106 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
3108 isl_int_sub(bmap->div[div][1],
3109 bmap->div[div][1], bmap->div[div][0]);
3110 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
3111 neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
3112 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
3113 isl_int_add(bmap->div[div][1],
3114 bmap->div[div][1], bmap->div[div][0]);
3117 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
3118 bmap->n_div-div-1) != -1)
3120 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
3121 if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
3123 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
3124 bmap->n_div-div-1) != -1)
3130 for (i = 0; i < bmap->n_div; ++i)
3131 if (!isl_int_is_zero(bmap->div[i][1+pos]))
3138 * Remove divs that don't occur in any of the constraints or other divs.
3139 * These can arise when dropping some of the variables in a quast
3140 * returned by piplib.
3142 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
3149 for (i = bmap->n_div-1; i >= 0; --i) {
3150 if (!div_is_redundant(bmap, i))
3152 bmap = isl_basic_map_drop_div(bmap, i);
3157 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
3159 bmap = remove_redundant_divs(bmap);
3162 F_SET(bmap, ISL_BASIC_SET_FINAL);
3166 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
3168 return (struct isl_basic_set *)
3169 isl_basic_map_finalize((struct isl_basic_map *)bset);
3172 struct isl_set *isl_set_finalize(struct isl_set *set)
3178 for (i = 0; i < set->n; ++i) {
3179 set->p[i] = isl_basic_set_finalize(set->p[i]);
3189 struct isl_map *isl_map_finalize(struct isl_map *map)
3195 for (i = 0; i < map->n; ++i) {
3196 map->p[i] = isl_basic_map_finalize(map->p[i]);
3200 F_CLR(map, ISL_MAP_NORMALIZED);
3207 struct isl_basic_map *isl_basic_map_identity(struct isl_ctx *ctx,
3208 unsigned nparam, unsigned dim)
3210 struct isl_basic_map *bmap;
3213 bmap = isl_basic_map_alloc(ctx, nparam, dim, dim, 0, dim, 0);
3217 for (i = 0; i < dim; ++i) {
3218 int j = isl_basic_map_alloc_equality(bmap);
3221 isl_seq_clr(bmap->eq[j],
3222 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
3223 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
3224 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
3226 return isl_basic_map_finalize(bmap);
3228 isl_basic_map_free(bmap);
3232 struct isl_map *isl_map_identity(struct isl_ctx *ctx,
3233 unsigned nparam, unsigned dim)
3235 struct isl_map *map = isl_map_alloc(ctx, nparam, dim, dim, 1,
3239 map = isl_map_add(map,
3240 isl_basic_map_identity(ctx, nparam, dim));
3247 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
3249 return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
3252 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
3254 return isl_map_is_subset(
3255 (struct isl_map *)set1, (struct isl_map *)set2);
3258 int isl_basic_map_is_subset(
3259 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3262 struct isl_map *map1;
3263 struct isl_map *map2;
3265 if (!bmap1 || !bmap2)
3268 map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
3269 map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
3271 is_subset = isl_map_is_subset(map1, map2);
3279 int isl_basic_map_is_equal(
3280 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3284 if (!bmap1 || !bmap2)
3286 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3289 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3293 int isl_basic_set_is_equal(
3294 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
3296 return isl_basic_map_is_equal(
3297 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
3300 int isl_map_is_empty(struct isl_map *map)
3307 for (i = 0; i < map->n; ++i) {
3308 is_empty = isl_basic_map_is_empty(map->p[i]);
3317 int isl_set_is_empty(struct isl_set *set)
3319 return isl_map_is_empty((struct isl_map *)set);
3322 int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
3326 struct isl_map *diff;
3331 if (isl_map_is_empty(map1))
3334 if (isl_map_is_empty(map2))
3337 diff = isl_map_subtract(isl_map_copy(map1), isl_map_copy(map2));
3341 is_subset = isl_map_is_empty(diff);
3347 int isl_map_is_equal(struct isl_map *map1, struct isl_map *map2)
3353 is_subset = isl_map_is_subset(map1, map2);
3356 is_subset = isl_map_is_subset(map2, map1);
3360 int isl_basic_map_is_strict_subset(
3361 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3365 if (!bmap1 || !bmap2)
3367 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3370 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3371 if (is_subset == -1)
3376 static int basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
3382 total = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
3383 if (total != vec->size)
3388 for (i = 0; i < bmap->n_eq; ++i) {
3389 isl_seq_inner_product(vec->block.data, bmap->eq[i], total, &s);
3390 if (!isl_int_is_zero(s)) {
3396 for (i = 0; i < bmap->n_ineq; ++i) {
3397 isl_seq_inner_product(vec->block.data, bmap->ineq[i], total, &s);
3398 if (isl_int_is_neg(s)) {
3409 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
3413 return bmap->n_eq == 0 && bmap->n_ineq == 0;
3416 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
3418 struct isl_basic_set *bset = NULL;
3419 struct isl_vec *sample = NULL;
3426 if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
3429 if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
3430 struct isl_basic_map *copy = isl_basic_map_copy(bmap);
3431 copy = isl_basic_map_convex_hull(copy);
3432 empty = F_ISSET(copy, ISL_BASIC_MAP_EMPTY);
3433 isl_basic_map_free(copy);
3437 total = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
3438 if (bmap->sample && bmap->sample->size == total) {
3439 int contains = basic_map_contains(bmap, bmap->sample);
3445 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
3448 sample = isl_basic_set_sample(bset);
3451 empty = sample->size == 0;
3453 isl_vec_free(bmap->ctx, bmap->sample);
3454 bmap->sample = sample;
3459 struct isl_map *isl_basic_map_union(
3460 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3462 struct isl_map *map;
3463 if (!bmap1 || !bmap2)
3466 isl_assert(bmap1->ctx, bmap1->nparam == bmap2->nparam, goto error);
3467 isl_assert(bmap1->ctx, bmap1->n_in == bmap2->n_in, goto error);
3468 isl_assert(bmap1->ctx, bmap1->n_out == bmap2->n_out, goto error);
3470 map = isl_map_alloc(bmap1->ctx, bmap1->nparam,
3471 bmap1->n_in, bmap1->n_out, 2, 0);
3474 map = isl_map_add(map, bmap1);
3475 map = isl_map_add(map, bmap2);
3478 isl_basic_map_free(bmap1);
3479 isl_basic_map_free(bmap2);
3483 struct isl_set *isl_basic_set_union(
3484 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
3486 return (struct isl_set *)isl_basic_map_union(
3487 (struct isl_basic_map *)bset1,
3488 (struct isl_basic_map *)bset2);
3491 /* Order divs such that any div only depends on previous divs */
3492 static struct isl_basic_map *order_divs(struct isl_basic_map *bmap)
3495 unsigned off = bmap->nparam + bmap->n_in + bmap->n_out;
3497 for (i = 0; i < bmap->n_div; ++i) {
3499 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
3503 swap_div(bmap, i, pos);
3509 static int find_div(struct isl_basic_map *dst,
3510 struct isl_basic_map *src, unsigned div)
3514 unsigned total = src->nparam + src->n_in + src->n_out + src->n_div;
3516 for (i = 0; i < dst->n_div; ++i)
3517 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total) &&
3518 isl_seq_first_non_zero(dst->div[i]+1+1+total,
3519 dst->n_div - src->n_div) == -1)
3524 struct isl_basic_map *isl_basic_map_align_divs(
3525 struct isl_basic_map *dst, struct isl_basic_map *src)
3528 unsigned total = src->nparam + src->n_in + src->n_out + src->n_div;
3530 if (src->n_div == 0)
3533 src = order_divs(src);
3534 dst = isl_basic_map_extend(dst, dst->nparam, dst->n_in,
3535 dst->n_out, src->n_div, 0, 2 * src->n_div);
3538 for (i = 0; i < src->n_div; ++i) {
3539 int j = find_div(dst, src, i);
3541 j = isl_basic_map_alloc_div(dst);
3544 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
3545 isl_seq_clr(dst->div[j]+1+1+total,
3546 dst->extra - src->n_div);
3547 if (add_div_constraints(dst, j) < 0)
3551 swap_div(dst, i, j);
3555 isl_basic_map_free(dst);
3559 struct isl_map *isl_map_align_divs(struct isl_map *map)
3563 map = isl_map_compute_divs(map);
3564 map = isl_map_cow(map);
3568 for (i = 1; i < map->n; ++i)
3569 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
3570 for (i = 1; i < map->n; ++i)
3571 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
3573 F_CLR(map, ISL_MAP_NORMALIZED);
3577 static struct isl_map *add_cut_constraint(struct isl_map *dst,
3578 struct isl_basic_map *src, isl_int *c,
3579 unsigned len, int oppose)
3581 struct isl_basic_map *copy = NULL;
3586 copy = isl_basic_map_copy(src);
3587 copy = isl_basic_map_cow(copy);
3590 copy = isl_basic_map_extend(copy,
3591 copy->nparam, copy->n_in, copy->n_out, 0, 0, 1);
3592 k = isl_basic_map_alloc_inequality(copy);
3596 isl_seq_neg(copy->ineq[k], c, len);
3598 isl_seq_cpy(copy->ineq[k], c, len);
3599 total = 1 + copy->nparam + copy->n_in + copy->n_out + copy->extra;
3600 isl_seq_clr(copy->ineq[k]+len, total - len);
3601 isl_inequality_negate(copy, k);
3602 copy = isl_basic_map_simplify(copy);
3603 copy = isl_basic_map_finalize(copy);
3604 is_empty = isl_basic_map_is_empty(copy);
3608 dst = isl_map_add(dst, copy);
3610 isl_basic_map_free(copy);
3613 isl_basic_map_free(copy);
3618 static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
3622 struct isl_map *rest = NULL;
3624 unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
3631 if (F_ISSET(map, ISL_MAP_DISJOINT))
3632 FL_SET(flags, ISL_MAP_DISJOINT);
3634 max = map->n * (2 * bmap->n_eq + bmap->n_ineq);
3635 rest = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out,
3640 for (i = 0; i < map->n; ++i) {
3641 map->p[i] = isl_basic_map_align_divs(map->p[i], bmap);
3646 for (j = 0; j < map->n; ++j)
3647 map->p[j] = isl_basic_map_cow(map->p[j]);
3649 for (i = 0; i < bmap->n_eq; ++i) {
3650 for (j = 0; j < map->n; ++j) {
3651 rest = add_cut_constraint(rest,
3652 map->p[j], bmap->eq[i], 1+total, 0);
3656 rest = add_cut_constraint(rest,
3657 map->p[j], bmap->eq[i], 1+total, 1);
3661 map->p[j] = isl_basic_map_extend(map->p[j],
3662 map->p[j]->nparam, map->p[j]->n_in,
3663 map->p[j]->n_out, 0, 1, 0);
3666 k = isl_basic_map_alloc_equality(map->p[j]);
3669 isl_seq_cpy(map->p[j]->eq[k], bmap->eq[i], 1+total);
3670 isl_seq_clr(map->p[j]->eq[k]+1+total,
3671 map->p[j]->extra - bmap->n_div);
3675 for (i = 0; i < bmap->n_ineq; ++i) {
3676 for (j = 0; j < map->n; ++j) {
3677 rest = add_cut_constraint(rest,
3678 map->p[j], bmap->ineq[i], 1+total, 0);
3682 map->p[j] = isl_basic_map_extend(map->p[j],
3683 map->p[j]->nparam, map->p[j]->n_in,
3684 map->p[j]->n_out, 0, 0, 1);
3687 k = isl_basic_map_alloc_inequality(map->p[j]);
3690 isl_seq_cpy(map->p[j]->ineq[k], bmap->ineq[i], 1+total);
3691 isl_seq_clr(map->p[j]->ineq[k]+1+total,
3692 map->p[j]->extra - bmap->n_div);
3704 struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
3710 isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
3711 isl_assert(map1->ctx, map1->n_in == map2->n_in, goto error);
3712 isl_assert(map1->ctx, map1->n_out == map2->n_out, goto error);
3714 if (isl_map_is_empty(map2)) {
3719 map1 = isl_map_compute_divs(map1);
3720 map2 = isl_map_compute_divs(map2);
3724 for (i = 0; map1 && i < map2->n; ++i)
3725 map1 = subtract(map1, map2->p[i]);
3735 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
3737 return (struct isl_set *)
3739 (struct isl_map *)set1, (struct isl_map *)set2);
3742 struct isl_set *isl_set_apply(struct isl_set *set, struct isl_map *map)
3746 isl_assert(set->ctx, set->dim == map->n_in, goto error);
3747 map = isl_map_intersect_domain(map, set);
3748 set = isl_map_range(map);
3756 /* There is no need to cow as removing empty parts doesn't change
3757 * the meaning of the set.
3759 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
3766 for (i = map->n-1; i >= 0; --i) {
3767 if (!F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
3769 isl_basic_map_free(map->p[i]);
3770 if (i != map->n-1) {
3771 F_CLR(map, ISL_MAP_NORMALIZED);
3772 map->p[i] = map->p[map->n-1];
3780 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
3782 return (struct isl_set *)
3783 isl_map_remove_empty_parts((struct isl_map *)set);
3786 struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
3788 struct isl_basic_set *bset;
3789 if (!set || set->n == 0)
3791 bset = set->p[set->n-1];
3792 isl_assert(set->ctx, F_ISSET(bset, ISL_BASIC_SET_FINAL), return NULL);
3793 return isl_basic_set_copy(bset);
3796 struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
3797 struct isl_basic_set *bset)
3803 for (i = set->n-1; i >= 0; --i) {
3804 if (set->p[i] != bset)
3806 set = isl_set_cow(set);
3809 isl_basic_set_free(set->p[i]);
3810 if (i != set->n-1) {
3811 F_CLR(set, ISL_SET_NORMALIZED);
3812 set->p[i] = set->p[set->n-1];
3817 isl_basic_set_free(bset);
3821 isl_basic_set_free(bset);
3825 /* Given two _disjoint_ basic sets bset1 and bset2, check whether
3826 * for any common value of the parameters and dimensions preceding dim
3827 * in both basic sets, the values of dimension pos in bset1 are
3828 * smaller or larger then those in bset2.
3831 * 1 if bset1 follows bset2
3832 * -1 if bset1 precedes bset2
3833 * 0 if bset1 and bset2 are incomparable
3834 * -2 if some error occurred.
3836 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
3837 struct isl_basic_set *bset2, int pos)
3839 struct isl_basic_map *bmap1 = NULL;
3840 struct isl_basic_map *bmap2 = NULL;
3841 struct isl_ctx *ctx;
3842 struct isl_vec *obj;
3845 enum isl_lp_result res;
3848 if (!bset1 || !bset2)
3851 bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1),
3852 pos, bset1->dim - pos);
3853 bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2),
3854 pos, bset2->dim - pos);
3855 if (!bmap1 || !bmap2)
3857 bmap1 = isl_basic_map_extend(bmap1, bmap1->nparam,
3858 bmap1->n_in, bmap1->n_out + bmap2->n_out,
3859 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
3862 total = bmap1->nparam + bmap1->n_in + bmap1->n_out + bmap1->n_div;
3864 obj = isl_vec_alloc(ctx, total);
3865 isl_seq_clr(obj->block.data, total);
3866 isl_int_set_si(obj->block.data[bmap1->nparam+bmap1->n_in], 1);
3867 isl_int_set_si(obj->block.data[bmap1->nparam+bmap1->n_in+
3868 bmap1->n_out-bmap2->n_out], -1);
3871 bmap1 = add_constraints(bmap1, bmap2, 0, bmap1->n_out - bmap2->n_out);
3874 res = isl_solve_lp(bmap1, 0, obj->block.data, ctx->one, &num, &den);
3875 if (res == isl_lp_empty)
3877 else if (res == isl_lp_ok && isl_int_is_pos(num))
3879 else if ((res == isl_lp_ok && isl_int_is_neg(num)) ||
3880 res == isl_lp_unbounded)
3886 isl_basic_map_free(bmap1);
3887 isl_vec_free(ctx, obj);
3890 isl_basic_map_free(bmap1);
3891 isl_basic_map_free(bmap2);
3895 static int isl_basic_map_fast_has_fixed_var(struct isl_basic_map *bmap,
3896 unsigned pos, isl_int *val)
3904 total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
3905 for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
3906 for (; d+1 > pos; --d)
3907 if (!isl_int_is_zero(bmap->eq[i][1+d]))
3911 if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
3913 if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
3915 if (!isl_int_is_one(bmap->eq[i][1+d]))
3918 isl_int_neg(*val, bmap->eq[i][0]);
3924 static int isl_map_fast_has_fixed_var(struct isl_map *map,
3925 unsigned pos, isl_int *val)
3937 return isl_basic_map_fast_has_fixed_var(map->p[0], pos, val);
3940 fixed = isl_basic_map_fast_has_fixed_var(map->p[0], pos, &v);
3941 for (i = 1; fixed == 1 && i < map->n; ++i) {
3942 fixed = isl_basic_map_fast_has_fixed_var(map->p[i], pos, &tmp);
3943 if (fixed == 1 && isl_int_ne(tmp, v))
3947 isl_int_set(*val, v);
3953 static int isl_set_fast_has_fixed_var(struct isl_set *set, unsigned pos,
3956 return isl_map_fast_has_fixed_var((struct isl_map *)set, pos, val);
3959 /* Check if dimension dim has fixed value and if so and if val is not NULL,
3960 * then return this fixed value in *val.
3962 int isl_set_fast_dim_is_fixed(struct isl_set *set, unsigned dim, isl_int *val)
3964 return isl_set_fast_has_fixed_var(set, set->nparam + dim, val);
3967 /* Check if input variable in has fixed value and if so and if val is not NULL,
3968 * then return this fixed value in *val.
3970 int isl_map_fast_input_is_fixed(struct isl_map *map, unsigned in, isl_int *val)
3972 return isl_map_fast_has_fixed_var(map, map->nparam + in, val);
3975 /* Check if dimension dim has an (obvious) fixed lower bound and if so
3976 * and if val is not NULL, then return this lower bound in *val.
3978 int isl_basic_set_fast_dim_has_fixed_lower_bound(struct isl_basic_set *bset,
3979 unsigned dim, isl_int *val)
3981 int i, i_eq = -1, i_ineq = -1;
3987 total = bset->nparam + bset->dim + bset->n_div;
3988 for (i = 0; i < bset->n_eq; ++i) {
3989 if (isl_int_is_zero(bset->eq[i][1+bset->nparam+dim]))
3995 for (i = 0; i < bset->n_ineq; ++i) {
3996 if (!isl_int_is_pos(bset->ineq[i][1+bset->nparam+dim]))
3998 if (i_eq != -1 || i_ineq != -1)
4002 if (i_eq == -1 && i_ineq == -1)
4004 c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
4005 /* The coefficient should always be one due to normalization. */
4006 if (!isl_int_is_one(c[1+bset->nparam+dim]))
4008 if (isl_seq_first_non_zero(c+1, bset->nparam+dim) != -1)
4010 if (isl_seq_first_non_zero(c+1+bset->nparam+dim+1,
4011 total - bset->nparam - dim - 1) != -1)
4014 isl_int_neg(*val, c[0]);
4018 int isl_set_fast_dim_has_fixed_lower_bound(struct isl_set *set,
4019 unsigned dim, isl_int *val)
4031 return isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
4035 fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
4037 for (i = 1; fixed == 1 && i < set->n; ++i) {
4038 fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[i],
4040 if (fixed == 1 && isl_int_ne(tmp, v))
4044 isl_int_set(*val, v);
4050 /* Remove all information from bset that is redundant in the context
4051 * of context. In particular, equalities that are linear combinations
4052 * of those in context are remobed. Then the inequalities that are
4053 * redundant in the context of the equalities and inequalities of
4054 * context are removed.
4056 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
4057 struct isl_basic_set *context)
4061 struct isl_basic_set *combined;
4062 struct isl_ctx *ctx;
4063 enum isl_lp_result res = isl_lp_ok;
4065 if (!bset || !context)
4068 if (context->n_eq > 0) {
4071 struct isl_ctx *ctx = context->ctx;
4072 context = isl_basic_set_remove_equalities(context, &T, &T2);
4075 bset = isl_basic_set_preimage(ctx, bset, T);
4076 bset = uset_gist(bset, context);
4077 bset = isl_basic_set_preimage(ctx, bset, T2);
4080 combined = isl_basic_set_extend(isl_basic_set_copy(bset),
4081 0, bset->dim, 0, context->n_eq, context->n_ineq);
4082 context = set_add_constraints(combined, context, 0);
4087 for (i = bset->n_ineq-1; i >= 0; --i) {
4088 set_swap_inequality(context, i, context->n_ineq-1);
4090 res = isl_solve_lp((struct isl_basic_map *)context, 0,
4091 context->ineq[context->n_ineq]+1, ctx->one, &opt, NULL);
4093 set_swap_inequality(context, i, context->n_ineq-1);
4094 if (res == isl_lp_unbounded)
4096 if (res == isl_lp_error)
4098 if (res == isl_lp_empty) {
4099 bset = isl_basic_set_set_to_empty(bset);
4102 isl_int_add(opt, opt, context->ineq[i][0]);
4103 if (!isl_int_is_neg(opt)) {
4104 isl_basic_set_drop_inequality(context, i);
4105 isl_basic_set_drop_inequality(bset, i);
4109 if (res == isl_lp_error)
4111 isl_basic_set_free(context);
4114 isl_basic_set_free(context);
4115 isl_basic_set_free(bset);
4119 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
4120 struct isl_basic_map *context)
4122 struct isl_basic_set *bset;
4124 if (!bmap || !context)
4127 context = isl_basic_map_align_divs(context, bmap);
4128 bmap = isl_basic_map_align_divs(bmap, context);
4130 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
4131 isl_basic_map_underlying_set(context));
4133 return isl_basic_map_overlying_set(bset, bmap);
4135 isl_basic_map_free(bmap);
4136 isl_basic_map_free(context);
4140 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
4144 map = isl_map_cow(map);
4145 if (!map || !context)
4147 isl_assert(map->ctx, map->nparam == context->nparam, goto error);
4148 isl_assert(map->ctx, map->n_in == context->n_in, goto error);
4149 isl_assert(map->ctx, map->n_out == context->n_out, goto error);
4150 for (i = 0; i < map->n; ++i)
4151 context = isl_basic_map_align_divs(context, map->p[i]);
4152 for (i = 0; i < map->n; ++i) {
4153 map->p[i] = isl_basic_map_gist(map->p[i],
4154 isl_basic_map_copy(context));
4158 isl_basic_map_free(context);
4159 F_CLR(map, ISL_MAP_NORMALIZED);
4163 isl_basic_map_free(context);
4167 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
4169 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
4170 (struct isl_basic_map *)context);
4178 static int qsort_constraint_cmp(const void *p1, const void *p2)
4180 const struct constraint *c1 = (const struct constraint *)p1;
4181 const struct constraint *c2 = (const struct constraint *)p2;
4182 unsigned size = isl_min(c1->size, c2->size);
4183 return isl_seq_cmp(c1->c, c2->c, size);
4186 static struct isl_basic_map *isl_basic_map_sort_constraints(
4187 struct isl_basic_map *bmap)
4190 struct constraint *c;
4195 total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
4196 c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
4199 for (i = 0; i < bmap->n_ineq; ++i) {
4201 c[i].c = bmap->ineq[i];
4203 qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
4204 for (i = 0; i < bmap->n_ineq; ++i)
4205 bmap->ineq[i] = c[i].c;
4209 isl_basic_map_free(bmap);
4213 struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
4217 if (F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
4219 bmap = isl_basic_map_convex_hull(bmap);
4220 bmap = isl_basic_map_sort_constraints(bmap);
4221 F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
4225 static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
4226 const struct isl_basic_map *bmap2)
4233 if (bmap1->nparam != bmap2->nparam)
4234 return bmap1->nparam - bmap2->nparam;
4235 if (bmap1->n_in != bmap2->n_in)
4236 return bmap1->n_in - bmap2->n_in;
4237 if (bmap1->n_out != bmap2->n_out)
4238 return bmap1->n_out - bmap2->n_out;
4239 if (F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
4240 F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
4242 if (F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
4244 if (F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
4246 if (bmap1->n_eq != bmap2->n_eq)
4247 return bmap1->n_eq - bmap2->n_eq;
4248 if (bmap1->n_ineq != bmap2->n_ineq)
4249 return bmap1->n_ineq - bmap2->n_ineq;
4250 if (bmap1->n_div != bmap2->n_div)
4251 return bmap1->n_div - bmap2->n_div;
4252 total = bmap1->nparam + bmap1->n_in + bmap1->n_out + bmap1->n_div;
4253 for (i = 0; i < bmap1->n_eq; ++i) {
4254 cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
4258 for (i = 0; i < bmap1->n_ineq; ++i) {
4259 cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
4263 for (i = 0; i < bmap1->n_div; ++i) {
4264 cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
4271 static int isl_basic_map_fast_is_equal(struct isl_basic_map *bmap1,
4272 struct isl_basic_map *bmap2)
4274 return isl_basic_map_fast_cmp(bmap1, bmap2) == 0;
4277 static int qsort_bmap_cmp(const void *p1, const void *p2)
4279 const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
4280 const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
4282 return isl_basic_map_fast_cmp(bmap1, bmap2);
4285 /* We normalize in place, but if anything goes wrong we need
4286 * to return NULL, so we need to make sure we don't change the
4287 * meaning of any possible other copies of map.
4289 struct isl_map *isl_map_normalize(struct isl_map *map)
4292 struct isl_basic_map *bmap;
4296 if (F_ISSET(map, ISL_MAP_NORMALIZED))
4298 for (i = 0; i < map->n; ++i) {
4299 bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
4302 isl_basic_map_free(map->p[i]);
4305 qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
4306 F_SET(map, ISL_MAP_NORMALIZED);
4307 map = isl_map_remove_empty_parts(map);
4310 for (i = map->n - 1; i >= 1; --i) {
4311 if (!isl_basic_map_fast_is_equal(map->p[i-1], map->p[i]))
4313 isl_basic_map_free(map->p[i-1]);
4314 for (j = i; j < map->n; ++j)
4315 map->p[j-1] = map->p[j];
4325 struct isl_set *isl_set_normalize(struct isl_set *set)
4327 return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
4330 int isl_map_fast_is_equal(struct isl_map *map1, struct isl_map *map2)
4340 if (map1->nparam != map2->nparam)
4342 if (map1->n_in != map2->n_in)
4344 if (map1->n_out != map2->n_out)
4347 map1 = isl_map_copy(map1);
4348 map2 = isl_map_copy(map2);
4349 map1 = isl_map_normalize(map1);
4350 map2 = isl_map_normalize(map2);
4353 equal = map1->n == map2->n;
4354 for (i = 0; equal && i < map1->n; ++i) {
4355 equal = isl_basic_map_fast_is_equal(map1->p[i], map2->p[i]);
4368 int isl_set_fast_is_equal(struct isl_set *set1, struct isl_set *set2)
4370 return isl_map_fast_is_equal((struct isl_map *)set1,
4371 (struct isl_map *)set2);