2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the MIT 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_map_private.h>
12 #include <isl_morph.h>
14 #include <isl_mat_private.h>
15 #include <isl_space_private.h>
16 #include <isl_equalities.h>
18 __isl_give isl_morph *isl_morph_alloc(
19 __isl_take isl_basic_set *dom, __isl_take isl_basic_set *ran,
20 __isl_take isl_mat *map, __isl_take isl_mat *inv)
24 if (!dom || !ran || !map || !inv)
27 morph = isl_alloc_type(dom->ctx, struct isl_morph);
39 isl_basic_set_free(dom);
40 isl_basic_set_free(ran);
46 __isl_give isl_morph *isl_morph_copy(__isl_keep isl_morph *morph)
55 __isl_give isl_morph *isl_morph_dup(__isl_keep isl_morph *morph)
60 return isl_morph_alloc(isl_basic_set_copy(morph->dom),
61 isl_basic_set_copy(morph->ran),
62 isl_mat_copy(morph->map), isl_mat_copy(morph->inv));
65 __isl_give isl_morph *isl_morph_cow(__isl_take isl_morph *morph)
73 return isl_morph_dup(morph);
76 void isl_morph_free(__isl_take isl_morph *morph)
84 isl_basic_set_free(morph->dom);
85 isl_basic_set_free(morph->ran);
86 isl_mat_free(morph->map);
87 isl_mat_free(morph->inv);
91 __isl_give isl_space *isl_morph_get_ran_space(__isl_keep isl_morph *morph)
96 return isl_space_copy(morph->ran->dim);
99 unsigned isl_morph_dom_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
104 return isl_basic_set_dim(morph->dom, type);
107 unsigned isl_morph_ran_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
112 return isl_basic_set_dim(morph->ran, type);
115 __isl_give isl_morph *isl_morph_remove_dom_dims(__isl_take isl_morph *morph,
116 enum isl_dim_type type, unsigned first, unsigned n)
123 morph = isl_morph_cow(morph);
127 dom_offset = 1 + isl_space_offset(morph->dom->dim, type);
129 morph->dom = isl_basic_set_remove_dims(morph->dom, type, first, n);
131 morph->map = isl_mat_drop_cols(morph->map, dom_offset + first, n);
133 morph->inv = isl_mat_drop_rows(morph->inv, dom_offset + first, n);
135 if (morph->dom && morph->ran && morph->map && morph->inv)
138 isl_morph_free(morph);
142 __isl_give isl_morph *isl_morph_remove_ran_dims(__isl_take isl_morph *morph,
143 enum isl_dim_type type, unsigned first, unsigned n)
150 morph = isl_morph_cow(morph);
154 ran_offset = 1 + isl_space_offset(morph->ran->dim, type);
156 morph->ran = isl_basic_set_remove_dims(morph->ran, type, first, n);
158 morph->map = isl_mat_drop_rows(morph->map, ran_offset + first, n);
160 morph->inv = isl_mat_drop_cols(morph->inv, ran_offset + first, n);
162 if (morph->dom && morph->ran && morph->map && morph->inv)
165 isl_morph_free(morph);
169 /* Project domain of morph onto its parameter domain.
171 __isl_give isl_morph *isl_morph_dom_params(__isl_take isl_morph *morph)
175 morph = isl_morph_cow(morph);
178 n = isl_basic_set_dim(morph->dom, isl_dim_set);
179 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, n);
182 morph->dom = isl_basic_set_params(morph->dom);
186 isl_morph_free(morph);
190 /* Project range of morph onto its parameter domain.
192 __isl_give isl_morph *isl_morph_ran_params(__isl_take isl_morph *morph)
196 morph = isl_morph_cow(morph);
199 n = isl_basic_set_dim(morph->ran, isl_dim_set);
200 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, n);
203 morph->ran = isl_basic_set_params(morph->ran);
207 isl_morph_free(morph);
211 void isl_morph_print_internal(__isl_take isl_morph *morph, FILE *out)
216 isl_basic_set_print(morph->dom, out, 0, "", "", ISL_FORMAT_ISL);
217 isl_basic_set_print(morph->ran, out, 0, "", "", ISL_FORMAT_ISL);
218 isl_mat_print_internal(morph->map, out, 4);
219 isl_mat_print_internal(morph->inv, out, 4);
222 void isl_morph_dump(__isl_take isl_morph *morph)
224 isl_morph_print_internal(morph, stderr);
227 __isl_give isl_morph *isl_morph_identity(__isl_keep isl_basic_set *bset)
230 isl_basic_set *universe;
236 total = isl_basic_set_total_dim(bset);
237 id = isl_mat_identity(bset->ctx, 1 + total);
238 universe = isl_basic_set_universe(isl_space_copy(bset->dim));
240 return isl_morph_alloc(universe, isl_basic_set_copy(universe),
241 id, isl_mat_copy(id));
244 /* Create a(n identity) morphism between empty sets of the same dimension
247 __isl_give isl_morph *isl_morph_empty(__isl_keep isl_basic_set *bset)
250 isl_basic_set *empty;
256 total = isl_basic_set_total_dim(bset);
257 id = isl_mat_identity(bset->ctx, 1 + total);
258 empty = isl_basic_set_empty(isl_space_copy(bset->dim));
260 return isl_morph_alloc(empty, isl_basic_set_copy(empty),
261 id, isl_mat_copy(id));
264 /* Given a matrix that maps a (possibly) parametric domain to
265 * a parametric domain, add in rows that map the "nparam" parameters onto
268 static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat,
278 mat = isl_mat_insert_rows(mat, 1, nparam);
282 for (i = 0; i < nparam; ++i) {
283 isl_seq_clr(mat->row[1 + i], mat->n_col);
284 isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0]);
290 /* Construct a basic set described by the "n" equalities of "bset" starting
293 static __isl_give isl_basic_set *copy_equalities(__isl_keep isl_basic_set *bset,
294 unsigned first, unsigned n)
300 isl_assert(bset->ctx, bset->n_div == 0, return NULL);
302 total = isl_basic_set_total_dim(bset);
303 eq = isl_basic_set_alloc_space(isl_space_copy(bset->dim), 0, n, 0);
306 for (i = 0; i < n; ++i) {
307 k = isl_basic_set_alloc_equality(eq);
310 isl_seq_cpy(eq->eq[k], bset->eq[first + k], 1 + total);
315 isl_basic_set_free(eq);
319 /* Given a basic set, exploit the equalties in the basic set to construct
320 * a morphishm that maps the basic set to a lower-dimensional space.
321 * Specifically, the morphism reduces the number of dimensions of type "type".
323 * This function is a slight generalization of isl_mat_variable_compression
324 * in that it allows the input to be parametric and that it allows for the
325 * compression of either parameters or set variables.
327 * We first select the equalities of interest, that is those that involve
328 * variables of type "type" and no later variables.
329 * Denote those equalities as
333 * where C(p) depends on the parameters if type == isl_dim_set and
334 * is a constant if type == isl_dim_param.
336 * First compute the (left) Hermite normal form of M,
338 * M [U1 U2] = M U = H = [H1 0]
340 * M = H Q = [H1 0] [Q1]
343 * with U, Q unimodular, Q = U^{-1} (and H lower triangular).
344 * Define the transformed variables as
346 * x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
349 * The equalities then become
351 * -C(p) + H1 x1' = 0 or x1' = H1^{-1} C(p) = C'(p)
353 * If the denominator of the constant term does not divide the
354 * the common denominator of the parametric terms, then every
355 * integer point is mapped to a non-integer point and then the original set has no
356 * integer solutions (since the x' are a unimodular transformation
357 * of the x). In this case, an empty morphism is returned.
358 * Otherwise, the transformation is given by
360 * x = U1 H1^{-1} C(p) + U2 x2'
362 * The inverse transformation is simply
366 * Both matrices are extended to map the full original space to the full
369 __isl_give isl_morph *isl_basic_set_variable_compression(
370 __isl_keep isl_basic_set *bset, enum isl_dim_type type)
378 isl_mat *H, *U, *Q, *C = NULL, *H1, *U1, *U2;
379 isl_basic_set *dom, *ran;
384 if (isl_basic_set_plain_is_empty(bset))
385 return isl_morph_empty(bset);
387 isl_assert(bset->ctx, bset->n_div == 0, return NULL);
389 otype = 1 + isl_space_offset(bset->dim, type);
390 ntype = isl_basic_set_dim(bset, type);
391 orest = otype + ntype;
392 nrest = isl_basic_set_total_dim(bset) - (orest - 1);
394 for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)
395 if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)
397 for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)
398 if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)
401 return isl_morph_identity(bset);
403 H = isl_mat_sub_alloc6(bset->ctx, bset->eq, f_eq, n_eq, otype, ntype);
404 H = isl_mat_left_hermite(H, 0, &U, &Q);
407 Q = isl_mat_drop_rows(Q, 0, n_eq);
408 Q = isl_mat_diagonal(isl_mat_identity(bset->ctx, otype), Q);
409 Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
410 C = isl_mat_alloc(bset->ctx, 1 + n_eq, otype);
413 isl_int_set_si(C->row[0][0], 1);
414 isl_seq_clr(C->row[0] + 1, otype - 1);
415 isl_mat_sub_neg(C->ctx, C->row + 1, bset->eq + f_eq, n_eq, 0, 0, otype);
416 H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
417 H1 = isl_mat_lin_to_aff(H1);
418 C = isl_mat_inverse_product(H1, C);
423 if (!isl_int_is_one(C->row[0][0])) {
428 for (i = 0; i < n_eq; ++i) {
429 isl_seq_gcd(C->row[1 + i] + 1, otype - 1, &g);
430 isl_int_gcd(g, g, C->row[0][0]);
431 if (!isl_int_is_divisible_by(C->row[1 + i][0], g))
440 return isl_morph_empty(bset);
443 C = isl_mat_normalize(C);
446 U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, n_eq);
447 U1 = isl_mat_lin_to_aff(U1);
448 U2 = isl_mat_sub_alloc(U, 0, U->n_row, n_eq, U->n_row - n_eq);
449 U2 = isl_mat_lin_to_aff(U2);
452 C = isl_mat_product(U1, C);
453 C = isl_mat_aff_direct_sum(C, U2);
454 C = insert_parameter_rows(C, otype - 1);
455 C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));
457 dim = isl_space_copy(bset->dim);
458 dim = isl_space_drop_dims(dim, type, 0, ntype);
459 dim = isl_space_add_dims(dim, type, ntype - n_eq);
460 ran = isl_basic_set_universe(dim);
461 dom = copy_equalities(bset, f_eq, n_eq);
463 return isl_morph_alloc(dom, ran, Q, C);
472 /* Construct a parameter compression for "bset".
473 * We basically just call isl_mat_parameter_compression with the right input
474 * and then extend the resulting matrix to include the variables.
476 * The implementation assumes that "bset" does not have any equalities
477 * that only involve the parameters and that isl_basic_set_gauss has
478 * been applied to "bset".
480 * Let the equalities be given as
484 * and let [H 0] be the Hermite Normal Form of A, then
488 * needs to be integer, so we impose that each row is divisible by
491 __isl_give isl_morph *isl_basic_set_parameter_compression(
492 __isl_keep isl_basic_set *bset)
500 isl_basic_set *dom, *ran;
505 if (isl_basic_set_plain_is_empty(bset))
506 return isl_morph_empty(bset);
508 return isl_morph_identity(bset);
510 isl_assert(bset->ctx, bset->n_div == 0, return NULL);
513 nparam = isl_basic_set_dim(bset, isl_dim_param);
514 nvar = isl_basic_set_dim(bset, isl_dim_set);
516 if (isl_seq_first_non_zero(bset->eq[bset->n_eq - 1] + 1 + nparam,
518 isl_die(isl_basic_set_get_ctx(bset), isl_error_invalid,
519 "input not allowed to have parameter equalities",
522 isl_die(isl_basic_set_get_ctx(bset), isl_error_invalid,
523 "input not gaussed", return NULL);
525 d = isl_vec_alloc(bset->ctx, n_eq);
526 B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
527 H = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 1 + nparam, nvar);
528 H = isl_mat_left_hermite(H, 0, NULL, NULL);
529 H = isl_mat_drop_cols(H, n_eq, nvar - n_eq);
530 H = isl_mat_lin_to_aff(H);
531 H = isl_mat_right_inverse(H);
534 d = isl_vec_set(d, H->row[0][0]);
535 H = isl_mat_drop_rows(H, 0, 1);
536 H = isl_mat_drop_cols(H, 0, 1);
537 B = isl_mat_product(H, B);
538 inv = isl_mat_parameter_compression(B, d);
539 inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));
540 map = isl_mat_right_inverse(isl_mat_copy(inv));
542 dom = isl_basic_set_universe(isl_space_copy(bset->dim));
543 ran = isl_basic_set_universe(isl_space_copy(bset->dim));
545 return isl_morph_alloc(dom, ran, map, inv);
553 /* Add stride constraints to "bset" based on the inverse mapping
554 * that was plugged in. In particular, if morph maps x' to x,
555 * the the constraints of the original input
559 * have been rewritten to
563 * However, this substitution may loose information on the integrality of x',
564 * so we need to impose that
568 * is integral. If inv = B/d, this means that we need to impose that
574 * exists alpha in Z^m: B x = d alpha
577 static __isl_give isl_basic_set *add_strides(__isl_take isl_basic_set *bset,
578 __isl_keep isl_morph *morph)
583 if (isl_int_is_one(morph->inv->row[0][0]))
588 for (i = 0; 1 + i < morph->inv->n_row; ++i) {
589 isl_seq_gcd(morph->inv->row[1 + i], morph->inv->n_col, &gcd);
590 if (isl_int_is_divisible_by(gcd, morph->inv->row[0][0]))
592 div = isl_basic_set_alloc_div(bset);
595 isl_int_set_si(bset->div[div][0], 0);
596 k = isl_basic_set_alloc_equality(bset);
599 isl_seq_cpy(bset->eq[k], morph->inv->row[1 + i],
601 isl_seq_clr(bset->eq[k] + morph->inv->n_col, bset->n_div);
602 isl_int_set(bset->eq[k][morph->inv->n_col + div],
603 morph->inv->row[0][0]);
611 isl_basic_set_free(bset);
615 /* Apply the morphism to the basic set.
616 * We basically just compute the preimage of "bset" under the inverse mapping
617 * in morph, add in stride constraints and intersect with the range
620 __isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,
621 __isl_take isl_basic_set *bset)
623 isl_basic_set *res = NULL;
631 isl_assert(bset->ctx, isl_space_is_equal(bset->dim, morph->dom->dim),
634 max_stride = morph->inv->n_row - 1;
635 if (isl_int_is_one(morph->inv->row[0][0]))
637 res = isl_basic_set_alloc_space(isl_space_copy(morph->ran->dim),
638 bset->n_div + max_stride, bset->n_eq + max_stride, bset->n_ineq);
640 for (i = 0; i < bset->n_div; ++i)
641 if (isl_basic_set_alloc_div(res) < 0)
644 mat = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,
645 0, morph->inv->n_row);
646 mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
649 for (i = 0; i < bset->n_eq; ++i) {
650 k = isl_basic_set_alloc_equality(res);
653 isl_seq_cpy(res->eq[k], mat->row[i], mat->n_col);
654 isl_seq_scale(res->eq[k] + mat->n_col, bset->eq[i] + mat->n_col,
655 morph->inv->row[0][0], bset->n_div);
659 mat = isl_mat_sub_alloc6(bset->ctx, bset->ineq, 0, bset->n_ineq,
660 0, morph->inv->n_row);
661 mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
664 for (i = 0; i < bset->n_ineq; ++i) {
665 k = isl_basic_set_alloc_inequality(res);
668 isl_seq_cpy(res->ineq[k], mat->row[i], mat->n_col);
669 isl_seq_scale(res->ineq[k] + mat->n_col,
670 bset->ineq[i] + mat->n_col,
671 morph->inv->row[0][0], bset->n_div);
675 mat = isl_mat_sub_alloc6(bset->ctx, bset->div, 0, bset->n_div,
676 1, morph->inv->n_row);
677 mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
680 for (i = 0; i < bset->n_div; ++i) {
681 isl_int_mul(res->div[i][0],
682 morph->inv->row[0][0], bset->div[i][0]);
683 isl_seq_cpy(res->div[i] + 1, mat->row[i], mat->n_col);
684 isl_seq_scale(res->div[i] + 1 + mat->n_col,
685 bset->div[i] + 1 + mat->n_col,
686 morph->inv->row[0][0], bset->n_div);
690 res = add_strides(res, morph);
692 if (isl_basic_set_is_rational(bset))
693 res = isl_basic_set_set_rational(res);
695 res = isl_basic_set_simplify(res);
696 res = isl_basic_set_finalize(res);
698 res = isl_basic_set_intersect(res, isl_basic_set_copy(morph->ran));
700 isl_morph_free(morph);
701 isl_basic_set_free(bset);
705 isl_morph_free(morph);
706 isl_basic_set_free(bset);
707 isl_basic_set_free(res);
711 /* Apply the morphism to the set.
713 __isl_give isl_set *isl_morph_set(__isl_take isl_morph *morph,
714 __isl_take isl_set *set)
721 isl_assert(set->ctx, isl_space_is_equal(set->dim, morph->dom->dim), goto error);
723 set = isl_set_cow(set);
727 isl_space_free(set->dim);
728 set->dim = isl_space_copy(morph->ran->dim);
732 for (i = 0; i < set->n; ++i) {
733 set->p[i] = isl_morph_basic_set(isl_morph_copy(morph), set->p[i]);
738 isl_morph_free(morph);
740 ISL_F_CLR(set, ISL_SET_NORMALIZED);
745 isl_morph_free(morph);
749 /* Construct a morphism that first does morph2 and then morph1.
751 __isl_give isl_morph *isl_morph_compose(__isl_take isl_morph *morph1,
752 __isl_take isl_morph *morph2)
755 isl_basic_set *dom, *ran;
757 if (!morph1 || !morph2)
760 map = isl_mat_product(isl_mat_copy(morph1->map), isl_mat_copy(morph2->map));
761 inv = isl_mat_product(isl_mat_copy(morph2->inv), isl_mat_copy(morph1->inv));
762 dom = isl_morph_basic_set(isl_morph_inverse(isl_morph_copy(morph2)),
763 isl_basic_set_copy(morph1->dom));
764 dom = isl_basic_set_intersect(dom, isl_basic_set_copy(morph2->dom));
765 ran = isl_morph_basic_set(isl_morph_copy(morph1),
766 isl_basic_set_copy(morph2->ran));
767 ran = isl_basic_set_intersect(ran, isl_basic_set_copy(morph1->ran));
769 isl_morph_free(morph1);
770 isl_morph_free(morph2);
772 return isl_morph_alloc(dom, ran, map, inv);
774 isl_morph_free(morph1);
775 isl_morph_free(morph2);
779 __isl_give isl_morph *isl_morph_inverse(__isl_take isl_morph *morph)
784 morph = isl_morph_cow(morph);
789 morph->dom = morph->ran;
793 morph->map = morph->inv;
799 /* We detect all the equalities first to avoid implicit equalties
800 * being discovered during the computations. In particular,
801 * the compression on the variables could expose additional stride
802 * constraints on the parameters. This would result in existentially
803 * quantified variables after applying the resulting morph, which
804 * in turn could break invariants of the calling functions.
806 __isl_give isl_morph *isl_basic_set_full_compression(
807 __isl_keep isl_basic_set *bset)
809 isl_morph *morph, *morph2;
811 bset = isl_basic_set_copy(bset);
812 bset = isl_basic_set_detect_equalities(bset);
814 morph = isl_basic_set_variable_compression(bset, isl_dim_param);
815 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
817 morph2 = isl_basic_set_parameter_compression(bset);
818 bset = isl_morph_basic_set(isl_morph_copy(morph2), bset);
820 morph = isl_morph_compose(morph2, morph);
822 morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
823 isl_basic_set_free(bset);
825 morph = isl_morph_compose(morph2, morph);
830 __isl_give isl_vec *isl_morph_vec(__isl_take isl_morph *morph,
831 __isl_take isl_vec *vec)
836 vec = isl_mat_vec_product(isl_mat_copy(morph->map), vec);
838 isl_morph_free(morph);
841 isl_morph_free(morph);