2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_factorization.h>
17 #include <isl_union_map_private.h>
18 #include <isl_polynomial_private.h>
19 #include <isl_point_private.h>
20 #include <isl_dim_private.h>
21 #include <isl_div_private.h>
22 #include <isl_mat_private.h>
23 #include <isl_range.h>
24 #include <isl_local_space_private.h>
25 #include <isl_aff_private.h>
27 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
30 case isl_dim_param: return 0;
31 case isl_dim_in: return dim->nparam;
32 case isl_dim_out: return dim->nparam + dim->n_in;
37 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
45 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
50 isl_assert(up->ctx, up->var < 0, return NULL);
52 return (struct isl_upoly_cst *)up;
55 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
60 isl_assert(up->ctx, up->var >= 0, return NULL);
62 return (struct isl_upoly_rec *)up;
65 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
66 __isl_keep struct isl_upoly *up2)
69 struct isl_upoly_rec *rec1, *rec2;
75 if (up1->var != up2->var)
77 if (isl_upoly_is_cst(up1)) {
78 struct isl_upoly_cst *cst1, *cst2;
79 cst1 = isl_upoly_as_cst(up1);
80 cst2 = isl_upoly_as_cst(up2);
83 return isl_int_eq(cst1->n, cst2->n) &&
84 isl_int_eq(cst1->d, cst2->d);
87 rec1 = isl_upoly_as_rec(up1);
88 rec2 = isl_upoly_as_rec(up2);
92 if (rec1->n != rec2->n)
95 for (i = 0; i < rec1->n; ++i) {
96 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
104 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
106 struct isl_upoly_cst *cst;
110 if (!isl_upoly_is_cst(up))
113 cst = isl_upoly_as_cst(up);
117 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
120 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
122 struct isl_upoly_cst *cst;
126 if (!isl_upoly_is_cst(up))
129 cst = isl_upoly_as_cst(up);
133 return isl_int_sgn(cst->n);
136 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
138 struct isl_upoly_cst *cst;
142 if (!isl_upoly_is_cst(up))
145 cst = isl_upoly_as_cst(up);
149 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
152 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
154 struct isl_upoly_cst *cst;
158 if (!isl_upoly_is_cst(up))
161 cst = isl_upoly_as_cst(up);
165 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
168 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
170 struct isl_upoly_cst *cst;
174 if (!isl_upoly_is_cst(up))
177 cst = isl_upoly_as_cst(up);
181 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
184 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
186 struct isl_upoly_cst *cst;
190 if (!isl_upoly_is_cst(up))
193 cst = isl_upoly_as_cst(up);
197 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
200 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
202 struct isl_upoly_cst *cst;
206 if (!isl_upoly_is_cst(up))
209 cst = isl_upoly_as_cst(up);
213 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
216 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
218 struct isl_upoly_cst *cst;
220 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
229 isl_int_init(cst->n);
230 isl_int_init(cst->d);
235 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
237 struct isl_upoly_cst *cst;
239 cst = isl_upoly_cst_alloc(ctx);
243 isl_int_set_si(cst->n, 0);
244 isl_int_set_si(cst->d, 1);
249 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
251 struct isl_upoly_cst *cst;
253 cst = isl_upoly_cst_alloc(ctx);
257 isl_int_set_si(cst->n, 1);
258 isl_int_set_si(cst->d, 1);
263 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
265 struct isl_upoly_cst *cst;
267 cst = isl_upoly_cst_alloc(ctx);
271 isl_int_set_si(cst->n, 1);
272 isl_int_set_si(cst->d, 0);
277 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
279 struct isl_upoly_cst *cst;
281 cst = isl_upoly_cst_alloc(ctx);
285 isl_int_set_si(cst->n, -1);
286 isl_int_set_si(cst->d, 0);
291 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
293 struct isl_upoly_cst *cst;
295 cst = isl_upoly_cst_alloc(ctx);
299 isl_int_set_si(cst->n, 0);
300 isl_int_set_si(cst->d, 0);
305 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
306 isl_int n, isl_int d)
308 struct isl_upoly_cst *cst;
310 cst = isl_upoly_cst_alloc(ctx);
314 isl_int_set(cst->n, n);
315 isl_int_set(cst->d, d);
320 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
323 struct isl_upoly_rec *rec;
325 isl_assert(ctx, var >= 0, return NULL);
326 isl_assert(ctx, size >= 0, return NULL);
327 rec = isl_calloc(ctx, struct isl_upoly_rec,
328 sizeof(struct isl_upoly_rec) +
329 (size - 1) * sizeof(struct isl_upoly *));
344 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
345 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
347 qp = isl_qpolynomial_cow(qp);
351 isl_dim_free(qp->dim);
356 isl_qpolynomial_free(qp);
361 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
363 return qp ? qp->dim->ctx : NULL;
366 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
368 return qp ? isl_dim_copy(qp->dim) : NULL;
371 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
372 enum isl_dim_type type)
374 return qp ? isl_dim_size(qp->dim, type) : 0;
377 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
379 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
382 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
384 return qp ? isl_upoly_is_one(qp->upoly) : -1;
387 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
389 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
392 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
394 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
397 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
399 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
402 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
404 return qp ? isl_upoly_sgn(qp->upoly) : 0;
407 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
409 isl_int_clear(cst->n);
410 isl_int_clear(cst->d);
413 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
417 for (i = 0; i < rec->n; ++i)
418 isl_upoly_free(rec->p[i]);
421 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
430 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
432 struct isl_upoly_cst *cst;
433 struct isl_upoly_cst *dup;
435 cst = isl_upoly_as_cst(up);
439 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
442 isl_int_set(dup->n, cst->n);
443 isl_int_set(dup->d, cst->d);
448 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
451 struct isl_upoly_rec *rec;
452 struct isl_upoly_rec *dup;
454 rec = isl_upoly_as_rec(up);
458 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
462 for (i = 0; i < rec->n; ++i) {
463 dup->p[i] = isl_upoly_copy(rec->p[i]);
471 isl_upoly_free(&dup->up);
475 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
477 struct isl_upoly *dup;
482 if (isl_upoly_is_cst(up))
483 return isl_upoly_dup_cst(up);
485 return isl_upoly_dup_rec(up);
488 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
496 return isl_upoly_dup(up);
499 void isl_upoly_free(__isl_take struct isl_upoly *up)
508 upoly_free_cst((struct isl_upoly_cst *)up);
510 upoly_free_rec((struct isl_upoly_rec *)up);
512 isl_ctx_deref(up->ctx);
516 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
521 isl_int_gcd(gcd, cst->n, cst->d);
522 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
523 isl_int_divexact(cst->n, cst->n, gcd);
524 isl_int_divexact(cst->d, cst->d, gcd);
529 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
530 __isl_take struct isl_upoly *up2)
532 struct isl_upoly_cst *cst1;
533 struct isl_upoly_cst *cst2;
535 up1 = isl_upoly_cow(up1);
539 cst1 = isl_upoly_as_cst(up1);
540 cst2 = isl_upoly_as_cst(up2);
542 if (isl_int_eq(cst1->d, cst2->d))
543 isl_int_add(cst1->n, cst1->n, cst2->n);
545 isl_int_mul(cst1->n, cst1->n, cst2->d);
546 isl_int_addmul(cst1->n, cst2->n, cst1->d);
547 isl_int_mul(cst1->d, cst1->d, cst2->d);
550 isl_upoly_cst_reduce(cst1);
560 static __isl_give struct isl_upoly *replace_by_zero(
561 __isl_take struct isl_upoly *up)
569 return isl_upoly_zero(ctx);
572 static __isl_give struct isl_upoly *replace_by_constant_term(
573 __isl_take struct isl_upoly *up)
575 struct isl_upoly_rec *rec;
576 struct isl_upoly *cst;
581 rec = isl_upoly_as_rec(up);
584 cst = isl_upoly_copy(rec->p[0]);
592 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
593 __isl_take struct isl_upoly *up2)
596 struct isl_upoly_rec *rec1, *rec2;
601 if (isl_upoly_is_nan(up1)) {
606 if (isl_upoly_is_nan(up2)) {
611 if (isl_upoly_is_zero(up1)) {
616 if (isl_upoly_is_zero(up2)) {
621 if (up1->var < up2->var)
622 return isl_upoly_sum(up2, up1);
624 if (up2->var < up1->var) {
625 struct isl_upoly_rec *rec;
626 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
630 up1 = isl_upoly_cow(up1);
631 rec = isl_upoly_as_rec(up1);
634 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
636 up1 = replace_by_constant_term(up1);
640 if (isl_upoly_is_cst(up1))
641 return isl_upoly_sum_cst(up1, up2);
643 rec1 = isl_upoly_as_rec(up1);
644 rec2 = isl_upoly_as_rec(up2);
648 if (rec1->n < rec2->n)
649 return isl_upoly_sum(up2, up1);
651 up1 = isl_upoly_cow(up1);
652 rec1 = isl_upoly_as_rec(up1);
656 for (i = rec2->n - 1; i >= 0; --i) {
657 rec1->p[i] = isl_upoly_sum(rec1->p[i],
658 isl_upoly_copy(rec2->p[i]));
661 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
662 isl_upoly_free(rec1->p[i]);
668 up1 = replace_by_zero(up1);
669 else if (rec1->n == 1)
670 up1 = replace_by_constant_term(up1);
681 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
682 __isl_take struct isl_upoly *up, isl_int v)
684 struct isl_upoly_cst *cst;
686 up = isl_upoly_cow(up);
690 cst = isl_upoly_as_cst(up);
692 isl_int_addmul(cst->n, cst->d, v);
697 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
698 __isl_take struct isl_upoly *up, isl_int v)
700 struct isl_upoly_rec *rec;
705 if (isl_upoly_is_cst(up))
706 return isl_upoly_cst_add_isl_int(up, v);
708 up = isl_upoly_cow(up);
709 rec = isl_upoly_as_rec(up);
713 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
723 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
724 __isl_take struct isl_upoly *up, isl_int v)
726 struct isl_upoly_cst *cst;
728 if (isl_upoly_is_zero(up))
731 up = isl_upoly_cow(up);
735 cst = isl_upoly_as_cst(up);
737 isl_int_mul(cst->n, cst->n, v);
742 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
743 __isl_take struct isl_upoly *up, isl_int v)
746 struct isl_upoly_rec *rec;
751 if (isl_upoly_is_cst(up))
752 return isl_upoly_cst_mul_isl_int(up, v);
754 up = isl_upoly_cow(up);
755 rec = isl_upoly_as_rec(up);
759 for (i = 0; i < rec->n; ++i) {
760 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
771 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
772 __isl_take struct isl_upoly *up2)
774 struct isl_upoly_cst *cst1;
775 struct isl_upoly_cst *cst2;
777 up1 = isl_upoly_cow(up1);
781 cst1 = isl_upoly_as_cst(up1);
782 cst2 = isl_upoly_as_cst(up2);
784 isl_int_mul(cst1->n, cst1->n, cst2->n);
785 isl_int_mul(cst1->d, cst1->d, cst2->d);
787 isl_upoly_cst_reduce(cst1);
797 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
798 __isl_take struct isl_upoly *up2)
800 struct isl_upoly_rec *rec1;
801 struct isl_upoly_rec *rec2;
802 struct isl_upoly_rec *res;
806 rec1 = isl_upoly_as_rec(up1);
807 rec2 = isl_upoly_as_rec(up2);
810 size = rec1->n + rec2->n - 1;
811 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
815 for (i = 0; i < rec1->n; ++i) {
816 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
817 isl_upoly_copy(rec1->p[i]));
822 for (; i < size; ++i) {
823 res->p[i] = isl_upoly_zero(up1->ctx);
828 for (i = 0; i < rec1->n; ++i) {
829 for (j = 1; j < rec2->n; ++j) {
830 struct isl_upoly *up;
831 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
832 isl_upoly_copy(rec1->p[i]));
833 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
846 isl_upoly_free(&res->up);
850 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
851 __isl_take struct isl_upoly *up2)
856 if (isl_upoly_is_nan(up1)) {
861 if (isl_upoly_is_nan(up2)) {
866 if (isl_upoly_is_zero(up1)) {
871 if (isl_upoly_is_zero(up2)) {
876 if (isl_upoly_is_one(up1)) {
881 if (isl_upoly_is_one(up2)) {
886 if (up1->var < up2->var)
887 return isl_upoly_mul(up2, up1);
889 if (up2->var < up1->var) {
891 struct isl_upoly_rec *rec;
892 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
893 isl_ctx *ctx = up1->ctx;
896 return isl_upoly_nan(ctx);
898 up1 = isl_upoly_cow(up1);
899 rec = isl_upoly_as_rec(up1);
903 for (i = 0; i < rec->n; ++i) {
904 rec->p[i] = isl_upoly_mul(rec->p[i],
905 isl_upoly_copy(up2));
913 if (isl_upoly_is_cst(up1))
914 return isl_upoly_mul_cst(up1, up2);
916 return isl_upoly_mul_rec(up1, up2);
923 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
926 struct isl_upoly *res;
934 res = isl_upoly_copy(up);
936 res = isl_upoly_one(up->ctx);
938 while (power >>= 1) {
939 up = isl_upoly_mul(up, isl_upoly_copy(up));
941 res = isl_upoly_mul(res, isl_upoly_copy(up));
948 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
949 unsigned n_div, __isl_take struct isl_upoly *up)
951 struct isl_qpolynomial *qp = NULL;
957 total = isl_dim_total(dim);
959 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
964 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
975 isl_qpolynomial_free(qp);
979 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
988 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
990 struct isl_qpolynomial *dup;
995 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
996 isl_upoly_copy(qp->upoly));
999 isl_mat_free(dup->div);
1000 dup->div = isl_mat_copy(qp->div);
1006 isl_qpolynomial_free(dup);
1010 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1018 return isl_qpolynomial_dup(qp);
1021 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1029 isl_dim_free(qp->dim);
1030 isl_mat_free(qp->div);
1031 isl_upoly_free(qp->upoly);
1036 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1039 struct isl_upoly *up;
1040 struct isl_upoly_rec *rec;
1041 struct isl_upoly_cst *cst;
1043 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1046 for (i = 0; i < 1 + power; ++i) {
1047 rec->p[i] = isl_upoly_zero(ctx);
1052 cst = isl_upoly_as_cst(rec->p[power]);
1053 isl_int_set_si(cst->n, 1);
1057 isl_upoly_free(&rec->up);
1061 /* r array maps original positions to new positions.
1063 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1067 struct isl_upoly_rec *rec;
1068 struct isl_upoly *base;
1069 struct isl_upoly *res;
1071 if (isl_upoly_is_cst(up))
1074 rec = isl_upoly_as_rec(up);
1078 isl_assert(up->ctx, rec->n >= 1, goto error);
1080 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1081 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1083 for (i = rec->n - 2; i >= 0; --i) {
1084 res = isl_upoly_mul(res, isl_upoly_copy(base));
1085 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1088 isl_upoly_free(base);
1097 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1102 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1103 div1->n_col >= div2->n_col, return -1);
1105 if (div1->n_row == div2->n_row)
1106 return isl_mat_is_equal(div1, div2);
1108 n_row = div1->n_row;
1109 n_col = div1->n_col;
1110 div1->n_row = div2->n_row;
1111 div1->n_col = div2->n_col;
1113 equal = isl_mat_is_equal(div1, div2);
1115 div1->n_row = n_row;
1116 div1->n_col = n_col;
1121 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1125 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1126 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1131 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1134 struct isl_div_sort_info {
1139 static int div_sort_cmp(const void *p1, const void *p2)
1141 const struct isl_div_sort_info *i1, *i2;
1142 i1 = (const struct isl_div_sort_info *) p1;
1143 i2 = (const struct isl_div_sort_info *) p2;
1145 return cmp_row(i1->div, i1->row, i2->row);
1148 /* Sort divs and remove duplicates.
1150 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1155 struct isl_div_sort_info *array = NULL;
1156 int *pos = NULL, *at = NULL;
1157 int *reordering = NULL;
1162 if (qp->div->n_row <= 1)
1165 div_pos = isl_dim_total(qp->dim);
1167 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1169 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1170 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1171 len = qp->div->n_col - 2;
1172 reordering = isl_alloc_array(qp->div->ctx, int, len);
1173 if (!array || !pos || !at || !reordering)
1176 for (i = 0; i < qp->div->n_row; ++i) {
1177 array[i].div = qp->div;
1183 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1186 for (i = 0; i < div_pos; ++i)
1189 for (i = 0; i < qp->div->n_row; ++i) {
1190 if (pos[array[i].row] == i)
1192 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1193 pos[at[i]] = pos[array[i].row];
1194 at[pos[array[i].row]] = at[i];
1195 at[i] = array[i].row;
1196 pos[array[i].row] = i;
1200 for (i = 0; i < len - div_pos; ++i) {
1202 isl_seq_eq(qp->div->row[i - skip - 1],
1203 qp->div->row[i - skip], qp->div->n_col)) {
1204 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1205 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1206 2 + div_pos + i - skip);
1207 qp->div = isl_mat_drop_cols(qp->div,
1208 2 + div_pos + i - skip, 1);
1211 reordering[div_pos + array[i].row] = div_pos + i - skip;
1214 qp->upoly = reorder(qp->upoly, reordering);
1216 if (!qp->upoly || !qp->div)
1230 isl_qpolynomial_free(qp);
1234 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1235 int *exp, int first)
1238 struct isl_upoly_rec *rec;
1240 if (isl_upoly_is_cst(up))
1243 if (up->var < first)
1246 if (exp[up->var - first] == up->var - first)
1249 up = isl_upoly_cow(up);
1253 up->var = exp[up->var - first] + first;
1255 rec = isl_upoly_as_rec(up);
1259 for (i = 0; i < rec->n; ++i) {
1260 rec->p[i] = expand(rec->p[i], exp, first);
1271 static __isl_give isl_qpolynomial *with_merged_divs(
1272 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1273 __isl_take isl_qpolynomial *qp2),
1274 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1278 isl_mat *div = NULL;
1280 qp1 = isl_qpolynomial_cow(qp1);
1281 qp2 = isl_qpolynomial_cow(qp2);
1286 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1287 qp1->div->n_col >= qp2->div->n_col, goto error);
1289 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1290 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1294 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1298 isl_mat_free(qp1->div);
1299 qp1->div = isl_mat_copy(div);
1300 isl_mat_free(qp2->div);
1301 qp2->div = isl_mat_copy(div);
1303 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1304 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1306 if (!qp1->upoly || !qp2->upoly)
1313 return fn(qp1, qp2);
1318 isl_qpolynomial_free(qp1);
1319 isl_qpolynomial_free(qp2);
1323 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1324 __isl_take isl_qpolynomial *qp2)
1326 qp1 = isl_qpolynomial_cow(qp1);
1331 if (qp1->div->n_row < qp2->div->n_row)
1332 return isl_qpolynomial_add(qp2, qp1);
1334 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1335 if (!compatible_divs(qp1->div, qp2->div))
1336 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1338 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1342 isl_qpolynomial_free(qp2);
1346 isl_qpolynomial_free(qp1);
1347 isl_qpolynomial_free(qp2);
1351 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1352 __isl_keep isl_set *dom,
1353 __isl_take isl_qpolynomial *qp1,
1354 __isl_take isl_qpolynomial *qp2)
1356 qp1 = isl_qpolynomial_add(qp1, qp2);
1357 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1361 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1362 __isl_take isl_qpolynomial *qp2)
1364 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1367 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1368 __isl_take isl_qpolynomial *qp, isl_int v)
1370 if (isl_int_is_zero(v))
1373 qp = isl_qpolynomial_cow(qp);
1377 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1383 isl_qpolynomial_free(qp);
1388 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1393 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1396 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1397 __isl_take isl_qpolynomial *qp, isl_int v)
1399 if (isl_int_is_one(v))
1402 if (qp && isl_int_is_zero(v)) {
1403 isl_qpolynomial *zero;
1404 zero = isl_qpolynomial_zero(isl_dim_copy(qp->dim));
1405 isl_qpolynomial_free(qp);
1409 qp = isl_qpolynomial_cow(qp);
1413 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1419 isl_qpolynomial_free(qp);
1423 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1424 __isl_take isl_qpolynomial *qp2)
1426 qp1 = isl_qpolynomial_cow(qp1);
1431 if (qp1->div->n_row < qp2->div->n_row)
1432 return isl_qpolynomial_mul(qp2, qp1);
1434 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1435 if (!compatible_divs(qp1->div, qp2->div))
1436 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1438 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1442 isl_qpolynomial_free(qp2);
1446 isl_qpolynomial_free(qp1);
1447 isl_qpolynomial_free(qp2);
1451 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1454 qp = isl_qpolynomial_cow(qp);
1459 qp->upoly = isl_upoly_pow(qp->upoly, power);
1465 isl_qpolynomial_free(qp);
1469 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1473 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1476 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1480 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1483 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1487 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1490 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1494 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1497 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1501 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1504 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1507 struct isl_qpolynomial *qp;
1508 struct isl_upoly_cst *cst;
1513 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1517 cst = isl_upoly_as_cst(qp->upoly);
1518 isl_int_set(cst->n, v);
1523 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1524 isl_int *n, isl_int *d)
1526 struct isl_upoly_cst *cst;
1531 if (!isl_upoly_is_cst(qp->upoly))
1534 cst = isl_upoly_as_cst(qp->upoly);
1539 isl_int_set(*n, cst->n);
1541 isl_int_set(*d, cst->d);
1546 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1549 struct isl_upoly_rec *rec;
1557 rec = isl_upoly_as_rec(up);
1564 isl_assert(up->ctx, rec->n > 1, return -1);
1566 is_cst = isl_upoly_is_cst(rec->p[1]);
1572 return isl_upoly_is_affine(rec->p[0]);
1575 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1580 if (qp->div->n_row > 0)
1583 return isl_upoly_is_affine(qp->upoly);
1586 static void update_coeff(__isl_keep isl_vec *aff,
1587 __isl_keep struct isl_upoly_cst *cst, int pos)
1592 if (isl_int_is_zero(cst->n))
1597 isl_int_gcd(gcd, cst->d, aff->el[0]);
1598 isl_int_divexact(f, cst->d, gcd);
1599 isl_int_divexact(gcd, aff->el[0], gcd);
1600 isl_seq_scale(aff->el, aff->el, f, aff->size);
1601 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1606 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1607 __isl_keep isl_vec *aff)
1609 struct isl_upoly_cst *cst;
1610 struct isl_upoly_rec *rec;
1616 struct isl_upoly_cst *cst;
1618 cst = isl_upoly_as_cst(up);
1621 update_coeff(aff, cst, 0);
1625 rec = isl_upoly_as_rec(up);
1628 isl_assert(up->ctx, rec->n == 2, return -1);
1630 cst = isl_upoly_as_cst(rec->p[1]);
1633 update_coeff(aff, cst, 1 + up->var);
1635 return isl_upoly_update_affine(rec->p[0], aff);
1638 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1639 __isl_keep isl_qpolynomial *qp)
1647 d = isl_dim_total(qp->dim);
1648 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1652 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1653 isl_int_set_si(aff->el[0], 1);
1655 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1664 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1665 __isl_keep isl_qpolynomial *qp2)
1670 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1673 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1676 struct isl_upoly_rec *rec;
1678 if (isl_upoly_is_cst(up)) {
1679 struct isl_upoly_cst *cst;
1680 cst = isl_upoly_as_cst(up);
1683 isl_int_lcm(*d, *d, cst->d);
1687 rec = isl_upoly_as_rec(up);
1691 for (i = 0; i < rec->n; ++i)
1692 upoly_update_den(rec->p[i], d);
1695 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1697 isl_int_set_si(*d, 1);
1700 upoly_update_den(qp->upoly, d);
1703 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1706 struct isl_ctx *ctx;
1713 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1716 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1717 enum isl_dim_type type, unsigned pos)
1722 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1723 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1725 if (type == isl_dim_set)
1726 pos += isl_dim_size(dim, isl_dim_param);
1728 return isl_qpolynomial_var_pow(dim, pos, 1);
1734 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1735 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1738 struct isl_upoly_rec *rec;
1739 struct isl_upoly *base, *res;
1744 if (isl_upoly_is_cst(up))
1747 if (up->var < first)
1750 rec = isl_upoly_as_rec(up);
1754 isl_assert(up->ctx, rec->n >= 1, goto error);
1756 if (up->var >= first + n)
1757 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1759 base = isl_upoly_copy(subs[up->var - first]);
1761 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1762 for (i = rec->n - 2; i >= 0; --i) {
1763 struct isl_upoly *t;
1764 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1765 res = isl_upoly_mul(res, isl_upoly_copy(base));
1766 res = isl_upoly_sum(res, t);
1769 isl_upoly_free(base);
1778 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1779 isl_int denom, unsigned len)
1782 struct isl_upoly *up;
1784 isl_assert(ctx, len >= 1, return NULL);
1786 up = isl_upoly_rat_cst(ctx, f[0], denom);
1787 for (i = 0; i < len - 1; ++i) {
1788 struct isl_upoly *t;
1789 struct isl_upoly *c;
1791 if (isl_int_is_zero(f[1 + i]))
1794 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1795 t = isl_upoly_var_pow(ctx, i, 1);
1796 t = isl_upoly_mul(c, t);
1797 up = isl_upoly_sum(up, t);
1803 /* Remove common factor of non-constant terms and denominator.
1805 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1807 isl_ctx *ctx = qp->div->ctx;
1808 unsigned total = qp->div->n_col - 2;
1810 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1811 isl_int_gcd(ctx->normalize_gcd,
1812 ctx->normalize_gcd, qp->div->row[div][0]);
1813 if (isl_int_is_one(ctx->normalize_gcd))
1816 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1817 ctx->normalize_gcd, total);
1818 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1819 ctx->normalize_gcd);
1820 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1821 ctx->normalize_gcd);
1824 /* Replace the integer division identified by "div" by the polynomial "s".
1825 * The integer division is assumed not to appear in the definition
1826 * of any other integer divisions.
1828 static __isl_give isl_qpolynomial *substitute_div(
1829 __isl_take isl_qpolynomial *qp,
1830 int div, __isl_take struct isl_upoly *s)
1839 qp = isl_qpolynomial_cow(qp);
1843 total = isl_dim_total(qp->dim);
1844 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1848 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1851 for (i = 0; i < total + div; ++i)
1853 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1854 reordering[i] = i - 1;
1855 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1856 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1857 qp->upoly = reorder(qp->upoly, reordering);
1860 if (!qp->upoly || !qp->div)
1866 isl_qpolynomial_free(qp);
1871 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1872 * divisions because d is equal to 1 by their definition, i.e., e.
1874 static __isl_give isl_qpolynomial *substitute_non_divs(
1875 __isl_take isl_qpolynomial *qp)
1879 struct isl_upoly *s;
1884 total = isl_dim_total(qp->dim);
1885 for (i = 0; qp && i < qp->div->n_row; ++i) {
1886 if (!isl_int_is_one(qp->div->row[i][0]))
1888 for (j = i + 1; j < qp->div->n_row; ++j) {
1889 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1891 isl_seq_combine(qp->div->row[j] + 1,
1892 qp->div->ctx->one, qp->div->row[j] + 1,
1893 qp->div->row[j][2 + total + i],
1894 qp->div->row[i] + 1, 1 + total + i);
1895 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1896 normalize_div(qp, j);
1898 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1899 qp->div->row[i][0], qp->div->n_col - 1);
1900 qp = substitute_div(qp, i, s);
1907 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1908 * with d the denominator. When replacing the coefficient e of x by
1909 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1910 * inside the division, so we need to add floor(e/d) * x outside.
1911 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1912 * to adjust the coefficient of x in each later div that depends on the
1913 * current div "div" and also in the affine expression "aff"
1914 * (if it too depends on "div").
1916 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1917 __isl_keep isl_vec *aff)
1921 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1924 for (i = 0; i < 1 + total + div; ++i) {
1925 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1926 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1928 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1929 isl_int_fdiv_r(qp->div->row[div][1 + i],
1930 qp->div->row[div][1 + i], qp->div->row[div][0]);
1931 if (!isl_int_is_zero(aff->el[1 + total + div]))
1932 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1933 for (j = div + 1; j < qp->div->n_row; ++j) {
1934 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1936 isl_int_addmul(qp->div->row[j][1 + i],
1937 v, qp->div->row[j][2 + total + div]);
1943 /* Check if the last non-zero coefficient is bigger that half of the
1944 * denominator. If so, we will invert the div to further reduce the number
1945 * of distinct divs that may appear.
1946 * If the last non-zero coefficient is exactly half the denominator,
1947 * then we continue looking for earlier coefficients that are bigger
1948 * than half the denominator.
1950 static int needs_invert(__isl_keep isl_mat *div, int row)
1955 for (i = div->n_col - 1; i >= 1; --i) {
1956 if (isl_int_is_zero(div->row[row][i]))
1958 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1959 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1960 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1970 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1971 * We only invert the coefficients of e (and the coefficient of q in
1972 * later divs and in "aff"). After calling this function, the
1973 * coefficients of e should be reduced again.
1975 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1976 __isl_keep isl_vec *aff)
1978 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1980 isl_seq_neg(qp->div->row[div] + 1,
1981 qp->div->row[div] + 1, qp->div->n_col - 1);
1982 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
1983 isl_int_add(qp->div->row[div][1],
1984 qp->div->row[div][1], qp->div->row[div][0]);
1985 if (!isl_int_is_zero(aff->el[1 + total + div]))
1986 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
1987 isl_mat_col_mul(qp->div, 2 + total + div,
1988 qp->div->ctx->negone, 2 + total + div);
1991 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
1992 * in the interval [0, d-1], with d the denominator and such that the
1993 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
1995 * After the reduction, some divs may have become redundant or identical,
1996 * so we call substitute_non_divs and sort_divs. If these functions
1997 * eliminate divs or merge two or more divs into one, the coefficients
1998 * of the enclosing divs may have to be reduced again, so we call
1999 * ourselves recursively if the number of divs decreases.
2001 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2004 isl_vec *aff = NULL;
2005 struct isl_upoly *s;
2011 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2012 aff = isl_vec_clr(aff);
2016 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2018 for (i = 0; i < qp->div->n_row; ++i) {
2019 normalize_div(qp, i);
2020 reduce_div(qp, i, aff);
2021 if (needs_invert(qp->div, i)) {
2022 invert_div(qp, i, aff);
2023 reduce_div(qp, i, aff);
2027 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2028 qp->div->ctx->one, aff->size);
2029 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2036 n_div = qp->div->n_row;
2037 qp = substitute_non_divs(qp);
2039 if (qp && qp->div->n_row < n_div)
2040 return reduce_divs(qp);
2044 isl_qpolynomial_free(qp);
2049 /* Assumes each div only depends on earlier divs.
2051 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2054 struct isl_qpolynomial *qp = NULL;
2055 struct isl_upoly_rec *rec;
2056 struct isl_upoly_cst *cst;
2063 d = div->line - div->bmap->div;
2065 pos = isl_dim_total(div->bmap->dim) + d;
2066 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2067 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2068 div->bmap->n_div, &rec->up);
2072 for (i = 0; i < div->bmap->n_div; ++i)
2073 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2075 for (i = 0; i < 1 + power; ++i) {
2076 rec->p[i] = isl_upoly_zero(div->ctx);
2081 cst = isl_upoly_as_cst(rec->p[power]);
2082 isl_int_set_si(cst->n, 1);
2086 qp = reduce_divs(qp);
2090 isl_qpolynomial_free(qp);
2095 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2097 return isl_qpolynomial_div_pow(div, 1);
2100 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2101 const isl_int n, const isl_int d)
2103 struct isl_qpolynomial *qp;
2104 struct isl_upoly_cst *cst;
2106 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2110 cst = isl_upoly_as_cst(qp->upoly);
2111 isl_int_set(cst->n, n);
2112 isl_int_set(cst->d, d);
2117 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2119 struct isl_upoly_rec *rec;
2125 if (isl_upoly_is_cst(up))
2129 active[up->var] = 1;
2131 rec = isl_upoly_as_rec(up);
2132 for (i = 0; i < rec->n; ++i)
2133 if (up_set_active(rec->p[i], active, d) < 0)
2139 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2142 int d = isl_dim_total(qp->dim);
2147 for (i = 0; i < d; ++i)
2148 for (j = 0; j < qp->div->n_row; ++j) {
2149 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2155 return up_set_active(qp->upoly, active, d);
2158 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2159 enum isl_dim_type type, unsigned first, unsigned n)
2170 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2172 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2173 type == isl_dim_set, return -1);
2175 active = isl_calloc_array(qp->dim->ctx, int, isl_dim_total(qp->dim));
2176 if (set_active(qp, active) < 0)
2179 if (type == isl_dim_set)
2180 first += isl_dim_size(qp->dim, isl_dim_param);
2181 for (i = 0; i < n; ++i)
2182 if (active[first + i]) {
2195 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2196 * of the divs that do appear in the quasi-polynomial.
2198 static __isl_give isl_qpolynomial *remove_redundant_divs(
2199 __isl_take isl_qpolynomial *qp)
2206 int *reordering = NULL;
2212 if (qp->div->n_row == 0)
2215 d = isl_dim_total(qp->dim);
2216 len = qp->div->n_col - 2;
2217 active = isl_calloc_array(qp->ctx, int, len);
2221 if (up_set_active(qp->upoly, active, len) < 0)
2224 for (i = qp->div->n_row - 1; i >= 0; --i) {
2225 if (!active[d + i]) {
2229 for (j = 0; j < i; ++j) {
2230 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2242 reordering = isl_alloc_array(qp->div->ctx, int, len);
2246 for (i = 0; i < d; ++i)
2250 n_div = qp->div->n_row;
2251 for (i = 0; i < n_div; ++i) {
2252 if (!active[d + i]) {
2253 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2254 qp->div = isl_mat_drop_cols(qp->div,
2255 2 + d + i - skip, 1);
2258 reordering[d + i] = d + i - skip;
2261 qp->upoly = reorder(qp->upoly, reordering);
2263 if (!qp->upoly || !qp->div)
2273 isl_qpolynomial_free(qp);
2277 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2278 unsigned first, unsigned n)
2281 struct isl_upoly_rec *rec;
2285 if (n == 0 || up->var < 0 || up->var < first)
2287 if (up->var < first + n) {
2288 up = replace_by_constant_term(up);
2289 return isl_upoly_drop(up, first, n);
2291 up = isl_upoly_cow(up);
2295 rec = isl_upoly_as_rec(up);
2299 for (i = 0; i < rec->n; ++i) {
2300 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2311 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2312 __isl_take isl_qpolynomial *qp,
2313 enum isl_dim_type type, unsigned pos, const char *s)
2315 qp = isl_qpolynomial_cow(qp);
2318 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2323 isl_qpolynomial_free(qp);
2327 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2328 __isl_take isl_qpolynomial *qp,
2329 enum isl_dim_type type, unsigned first, unsigned n)
2333 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
2336 qp = isl_qpolynomial_cow(qp);
2340 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2342 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2343 type == isl_dim_set, goto error);
2345 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2349 if (type == isl_dim_set)
2350 first += isl_dim_size(qp->dim, isl_dim_param);
2352 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2356 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2362 isl_qpolynomial_free(qp);
2366 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2367 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2373 struct isl_upoly *up;
2377 if (eq->n_eq == 0) {
2378 isl_basic_set_free(eq);
2382 qp = isl_qpolynomial_cow(qp);
2385 qp->div = isl_mat_cow(qp->div);
2389 total = 1 + isl_dim_total(eq->dim);
2391 isl_int_init(denom);
2392 for (i = 0; i < eq->n_eq; ++i) {
2393 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2394 if (j < 0 || j == 0 || j >= total)
2397 for (k = 0; k < qp->div->n_row; ++k) {
2398 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2400 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2401 &qp->div->row[k][0]);
2402 normalize_div(qp, k);
2405 if (isl_int_is_pos(eq->eq[i][j]))
2406 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2407 isl_int_abs(denom, eq->eq[i][j]);
2408 isl_int_set_si(eq->eq[i][j], 0);
2410 up = isl_upoly_from_affine(qp->dim->ctx,
2411 eq->eq[i], denom, total);
2412 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2415 isl_int_clear(denom);
2420 isl_basic_set_free(eq);
2422 qp = substitute_non_divs(qp);
2427 isl_basic_set_free(eq);
2428 isl_qpolynomial_free(qp);
2432 static __isl_give isl_basic_set *add_div_constraints(
2433 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2441 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2444 total = isl_basic_set_total_dim(bset);
2445 for (i = 0; i < div->n_row; ++i)
2446 if (isl_basic_set_add_div_constraints_var(bset,
2447 total - div->n_row + i, div->row[i]) < 0)
2454 isl_basic_set_free(bset);
2458 /* Look for equalities among the variables shared by context and qp
2459 * and the integer divisions of qp, if any.
2460 * The equalities are then used to eliminate variables and/or integer
2461 * divisions from qp.
2463 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2464 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2470 if (qp->div->n_row > 0) {
2471 isl_basic_set *bset;
2472 context = isl_set_add_dims(context, isl_dim_set,
2474 bset = isl_basic_set_universe(isl_set_get_dim(context));
2475 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2476 context = isl_set_intersect(context,
2477 isl_set_from_basic_set(bset));
2480 aff = isl_set_affine_hull(context);
2481 return isl_qpolynomial_substitute_equalities(qp, aff);
2483 isl_qpolynomial_free(qp);
2484 isl_set_free(context);
2489 #define PW isl_pw_qpolynomial
2491 #define EL isl_qpolynomial
2493 #define IS_ZERO is_zero
2497 #include <isl_pw_templ.c>
2500 #define UNION isl_union_pw_qpolynomial
2502 #define PART isl_pw_qpolynomial
2504 #define PARTS pw_qpolynomial
2506 #include <isl_union_templ.c>
2508 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2516 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2519 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2522 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2523 __isl_take isl_pw_qpolynomial *pwqp1,
2524 __isl_take isl_pw_qpolynomial *pwqp2)
2527 struct isl_pw_qpolynomial *res;
2530 if (!pwqp1 || !pwqp2)
2533 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2536 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2537 isl_pw_qpolynomial_free(pwqp2);
2541 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2542 isl_pw_qpolynomial_free(pwqp1);
2546 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2547 isl_pw_qpolynomial_free(pwqp1);
2551 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2552 isl_pw_qpolynomial_free(pwqp2);
2556 n = pwqp1->n * pwqp2->n;
2557 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2559 for (i = 0; i < pwqp1->n; ++i) {
2560 for (j = 0; j < pwqp2->n; ++j) {
2561 struct isl_set *common;
2562 struct isl_qpolynomial *prod;
2563 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2564 isl_set_copy(pwqp2->p[j].set));
2565 if (isl_set_plain_is_empty(common)) {
2566 isl_set_free(common);
2570 prod = isl_qpolynomial_mul(
2571 isl_qpolynomial_copy(pwqp1->p[i].qp),
2572 isl_qpolynomial_copy(pwqp2->p[j].qp));
2574 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2578 isl_pw_qpolynomial_free(pwqp1);
2579 isl_pw_qpolynomial_free(pwqp2);
2583 isl_pw_qpolynomial_free(pwqp1);
2584 isl_pw_qpolynomial_free(pwqp2);
2588 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2589 __isl_take isl_pw_qpolynomial *pwqp)
2596 if (isl_pw_qpolynomial_is_zero(pwqp))
2599 pwqp = isl_pw_qpolynomial_cow(pwqp);
2603 for (i = 0; i < pwqp->n; ++i) {
2604 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2611 isl_pw_qpolynomial_free(pwqp);
2615 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2616 __isl_take isl_pw_qpolynomial *pwqp1,
2617 __isl_take isl_pw_qpolynomial *pwqp2)
2619 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2622 __isl_give struct isl_upoly *isl_upoly_eval(
2623 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2626 struct isl_upoly_rec *rec;
2627 struct isl_upoly *res;
2628 struct isl_upoly *base;
2630 if (isl_upoly_is_cst(up)) {
2635 rec = isl_upoly_as_rec(up);
2639 isl_assert(up->ctx, rec->n >= 1, goto error);
2641 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2643 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2646 for (i = rec->n - 2; i >= 0; --i) {
2647 res = isl_upoly_mul(res, isl_upoly_copy(base));
2648 res = isl_upoly_sum(res,
2649 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2650 isl_vec_copy(vec)));
2653 isl_upoly_free(base);
2663 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2664 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2667 struct isl_upoly *up;
2672 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2674 if (qp->div->n_row == 0)
2675 ext = isl_vec_copy(pnt->vec);
2678 unsigned dim = isl_dim_total(qp->dim);
2679 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2683 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2684 for (i = 0; i < qp->div->n_row; ++i) {
2685 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2686 1 + dim + i, &ext->el[1+dim+i]);
2687 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2688 qp->div->row[i][0]);
2692 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2696 dim = isl_dim_copy(qp->dim);
2697 isl_qpolynomial_free(qp);
2698 isl_point_free(pnt);
2700 return isl_qpolynomial_alloc(dim, 0, up);
2702 isl_qpolynomial_free(qp);
2703 isl_point_free(pnt);
2707 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2708 __isl_keep struct isl_upoly_cst *cst2)
2713 isl_int_mul(t, cst1->n, cst2->d);
2714 isl_int_submul(t, cst2->n, cst1->d);
2715 cmp = isl_int_sgn(t);
2720 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2721 __isl_keep isl_qpolynomial *qp2)
2723 struct isl_upoly_cst *cst1, *cst2;
2727 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2728 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2729 if (isl_qpolynomial_is_nan(qp1))
2731 if (isl_qpolynomial_is_nan(qp2))
2733 cst1 = isl_upoly_as_cst(qp1->upoly);
2734 cst2 = isl_upoly_as_cst(qp2->upoly);
2736 return isl_upoly_cmp(cst1, cst2) <= 0;
2739 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2740 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2742 struct isl_upoly_cst *cst1, *cst2;
2747 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2748 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2749 cst1 = isl_upoly_as_cst(qp1->upoly);
2750 cst2 = isl_upoly_as_cst(qp2->upoly);
2751 cmp = isl_upoly_cmp(cst1, cst2);
2754 isl_qpolynomial_free(qp2);
2756 isl_qpolynomial_free(qp1);
2761 isl_qpolynomial_free(qp1);
2762 isl_qpolynomial_free(qp2);
2766 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2767 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2769 struct isl_upoly_cst *cst1, *cst2;
2774 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2775 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2776 cst1 = isl_upoly_as_cst(qp1->upoly);
2777 cst2 = isl_upoly_as_cst(qp2->upoly);
2778 cmp = isl_upoly_cmp(cst1, cst2);
2781 isl_qpolynomial_free(qp2);
2783 isl_qpolynomial_free(qp1);
2788 isl_qpolynomial_free(qp1);
2789 isl_qpolynomial_free(qp2);
2793 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2794 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2795 unsigned first, unsigned n)
2804 qp = isl_qpolynomial_cow(qp);
2808 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2811 g_pos = pos(qp->dim, type) + first;
2813 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2817 total = qp->div->n_col - 2;
2818 if (total > g_pos) {
2820 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2823 for (i = 0; i < total - g_pos; ++i)
2825 qp->upoly = expand(qp->upoly, exp, g_pos);
2831 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2837 isl_qpolynomial_free(qp);
2841 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2842 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2846 pos = isl_qpolynomial_dim(qp, type);
2848 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2851 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2852 __isl_take isl_pw_qpolynomial *pwqp,
2853 enum isl_dim_type type, unsigned n)
2857 pos = isl_pw_qpolynomial_dim(pwqp, type);
2859 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2862 static int *reordering_move(isl_ctx *ctx,
2863 unsigned len, unsigned dst, unsigned src, unsigned n)
2868 reordering = isl_alloc_array(ctx, int, len);
2873 for (i = 0; i < dst; ++i)
2875 for (i = 0; i < n; ++i)
2876 reordering[src + i] = dst + i;
2877 for (i = 0; i < src - dst; ++i)
2878 reordering[dst + i] = dst + n + i;
2879 for (i = 0; i < len - src - n; ++i)
2880 reordering[src + n + i] = src + n + i;
2882 for (i = 0; i < src; ++i)
2884 for (i = 0; i < n; ++i)
2885 reordering[src + i] = dst + i;
2886 for (i = 0; i < dst - src; ++i)
2887 reordering[src + n + i] = src + i;
2888 for (i = 0; i < len - dst - n; ++i)
2889 reordering[dst + n + i] = dst + n + i;
2895 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2896 __isl_take isl_qpolynomial *qp,
2897 enum isl_dim_type dst_type, unsigned dst_pos,
2898 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2904 qp = isl_qpolynomial_cow(qp);
2908 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2911 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2912 g_src_pos = pos(qp->dim, src_type) + src_pos;
2913 if (dst_type > src_type)
2916 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2923 reordering = reordering_move(qp->dim->ctx,
2924 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2928 qp->upoly = reorder(qp->upoly, reordering);
2933 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2939 isl_qpolynomial_free(qp);
2943 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2944 isl_int *f, isl_int denom)
2946 struct isl_upoly *up;
2951 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2953 return isl_qpolynomial_alloc(dim, 0, up);
2956 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
2959 struct isl_upoly *up;
2960 isl_qpolynomial *qp;
2965 ctx = isl_aff_get_ctx(aff);
2966 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
2969 qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff),
2970 aff->ls->div->n_row, up);
2974 isl_mat_free(qp->div);
2975 qp->div = isl_mat_copy(aff->ls->div);
2976 qp->div = isl_mat_cow(qp->div);
2981 qp = reduce_divs(qp);
2982 qp = remove_redundant_divs(qp);
2989 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2990 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2994 struct isl_upoly *up;
2995 isl_qpolynomial *qp;
3001 isl_int_init(denom);
3003 isl_constraint_get_coefficient(c, type, pos, &denom);
3004 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
3005 sgn = isl_int_sgn(denom);
3006 isl_int_abs(denom, denom);
3007 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
3008 1 + isl_constraint_dim(c, isl_dim_all));
3010 isl_int_neg(denom, denom);
3011 isl_constraint_set_coefficient(c, type, pos, denom);
3013 dim = isl_dim_copy(c->bmap->dim);
3015 isl_int_clear(denom);
3016 isl_constraint_free(c);
3018 qp = isl_qpolynomial_alloc(dim, 0, up);
3020 qp = isl_qpolynomial_neg(qp);
3024 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3025 * in "qp" by subs[i].
3027 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3028 __isl_take isl_qpolynomial *qp,
3029 enum isl_dim_type type, unsigned first, unsigned n,
3030 __isl_keep isl_qpolynomial **subs)
3033 struct isl_upoly **ups;
3038 qp = isl_qpolynomial_cow(qp);
3041 for (i = 0; i < n; ++i)
3045 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
3048 for (i = 0; i < n; ++i)
3049 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3052 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3053 for (i = 0; i < n; ++i)
3054 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3056 first += pos(qp->dim, type);
3058 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3061 for (i = 0; i < n; ++i)
3062 ups[i] = subs[i]->upoly;
3064 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3073 isl_qpolynomial_free(qp);
3077 /* Extend "bset" with extra set dimensions for each integer division
3078 * in "qp" and then call "fn" with the extended bset and the polynomial
3079 * that results from replacing each of the integer divisions by the
3080 * corresponding extra set dimension.
3082 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3083 __isl_keep isl_basic_set *bset,
3084 int (*fn)(__isl_take isl_basic_set *bset,
3085 __isl_take isl_qpolynomial *poly, void *user), void *user)
3089 isl_qpolynomial *poly;
3093 if (qp->div->n_row == 0)
3094 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3097 div = isl_mat_copy(qp->div);
3098 dim = isl_dim_copy(qp->dim);
3099 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3100 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3101 bset = isl_basic_set_copy(bset);
3102 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3103 bset = add_div_constraints(bset, div);
3105 return fn(bset, poly, user);
3110 /* Return total degree in variables first (inclusive) up to last (exclusive).
3112 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3116 struct isl_upoly_rec *rec;
3120 if (isl_upoly_is_zero(up))
3122 if (isl_upoly_is_cst(up) || up->var < first)
3125 rec = isl_upoly_as_rec(up);
3129 for (i = 0; i < rec->n; ++i) {
3132 if (isl_upoly_is_zero(rec->p[i]))
3134 d = isl_upoly_degree(rec->p[i], first, last);
3144 /* Return total degree in set variables.
3146 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3154 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3155 nvar = isl_dim_size(poly->dim, isl_dim_set);
3156 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3159 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3160 unsigned pos, int deg)
3163 struct isl_upoly_rec *rec;
3168 if (isl_upoly_is_cst(up) || up->var < pos) {
3170 return isl_upoly_copy(up);
3172 return isl_upoly_zero(up->ctx);
3175 rec = isl_upoly_as_rec(up);
3179 if (up->var == pos) {
3181 return isl_upoly_copy(rec->p[deg]);
3183 return isl_upoly_zero(up->ctx);
3186 up = isl_upoly_copy(up);
3187 up = isl_upoly_cow(up);
3188 rec = isl_upoly_as_rec(up);
3192 for (i = 0; i < rec->n; ++i) {
3193 struct isl_upoly *t;
3194 t = isl_upoly_coeff(rec->p[i], pos, deg);
3197 isl_upoly_free(rec->p[i]);
3207 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3209 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3210 __isl_keep isl_qpolynomial *qp,
3211 enum isl_dim_type type, unsigned t_pos, int deg)
3214 struct isl_upoly *up;
3220 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3223 g_pos = pos(qp->dim, type) + t_pos;
3224 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3226 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3229 isl_mat_free(c->div);
3230 c->div = isl_mat_copy(qp->div);
3235 isl_qpolynomial_free(c);
3239 /* Homogenize the polynomial in the variables first (inclusive) up to
3240 * last (exclusive) by inserting powers of variable first.
3241 * Variable first is assumed not to appear in the input.
3243 __isl_give struct isl_upoly *isl_upoly_homogenize(
3244 __isl_take struct isl_upoly *up, int deg, int target,
3245 int first, int last)
3248 struct isl_upoly_rec *rec;
3252 if (isl_upoly_is_zero(up))
3256 if (isl_upoly_is_cst(up) || up->var < first) {
3257 struct isl_upoly *hom;
3259 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3262 rec = isl_upoly_as_rec(hom);
3263 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3268 up = isl_upoly_cow(up);
3269 rec = isl_upoly_as_rec(up);
3273 for (i = 0; i < rec->n; ++i) {
3274 if (isl_upoly_is_zero(rec->p[i]))
3276 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3277 up->var < last ? deg + i : i, target,
3289 /* Homogenize the polynomial in the set variables by introducing
3290 * powers of an extra set variable at position 0.
3292 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3293 __isl_take isl_qpolynomial *poly)
3297 int deg = isl_qpolynomial_degree(poly);
3302 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3303 poly = isl_qpolynomial_cow(poly);
3307 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3308 nvar = isl_dim_size(poly->dim, isl_dim_set);
3309 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3316 isl_qpolynomial_free(poly);
3320 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3321 __isl_take isl_mat *div)
3329 n = isl_dim_total(dim) + div->n_row;
3331 term = isl_calloc(dim->ctx, struct isl_term,
3332 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3339 isl_int_init(term->n);
3340 isl_int_init(term->d);
3349 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3358 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3367 total = isl_dim_total(term->dim) + term->div->n_row;
3369 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3373 isl_int_set(dup->n, term->n);
3374 isl_int_set(dup->d, term->d);
3376 for (i = 0; i < total; ++i)
3377 dup->pow[i] = term->pow[i];
3382 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3390 return isl_term_dup(term);
3393 void isl_term_free(__isl_take isl_term *term)
3398 if (--term->ref > 0)
3401 isl_dim_free(term->dim);
3402 isl_mat_free(term->div);
3403 isl_int_clear(term->n);
3404 isl_int_clear(term->d);
3408 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3416 case isl_dim_out: return isl_dim_size(term->dim, type);
3417 case isl_dim_div: return term->div->n_row;
3418 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3423 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3425 return term ? term->dim->ctx : NULL;
3428 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3432 isl_int_set(*n, term->n);
3435 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3439 isl_int_set(*d, term->d);
3442 int isl_term_get_exp(__isl_keep isl_term *term,
3443 enum isl_dim_type type, unsigned pos)
3448 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3450 if (type >= isl_dim_set)
3451 pos += isl_dim_size(term->dim, isl_dim_param);
3452 if (type >= isl_dim_div)
3453 pos += isl_dim_size(term->dim, isl_dim_set);
3455 return term->pow[pos];
3458 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3460 isl_basic_map *bmap;
3467 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3470 total = term->div->n_col - term->div->n_row - 2;
3471 /* No nested divs for now */
3472 isl_assert(term->dim->ctx,
3473 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3474 term->div->n_row) == -1,
3477 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3478 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3481 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3483 return isl_basic_map_div(bmap, k);
3485 isl_basic_map_free(bmap);
3489 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3490 int (*fn)(__isl_take isl_term *term, void *user),
3491 __isl_take isl_term *term, void *user)
3494 struct isl_upoly_rec *rec;
3499 if (isl_upoly_is_zero(up))
3502 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3503 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3504 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3506 if (isl_upoly_is_cst(up)) {
3507 struct isl_upoly_cst *cst;
3508 cst = isl_upoly_as_cst(up);
3511 term = isl_term_cow(term);
3514 isl_int_set(term->n, cst->n);
3515 isl_int_set(term->d, cst->d);
3516 if (fn(isl_term_copy(term), user) < 0)
3521 rec = isl_upoly_as_rec(up);
3525 for (i = 0; i < rec->n; ++i) {
3526 term = isl_term_cow(term);
3529 term->pow[up->var] = i;
3530 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3534 term->pow[up->var] = 0;
3538 isl_term_free(term);
3542 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3543 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3550 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3554 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3556 isl_term_free(term);
3558 return term ? 0 : -1;
3561 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3563 struct isl_upoly *up;
3564 isl_qpolynomial *qp;
3570 n = isl_dim_total(term->dim) + term->div->n_row;
3572 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3573 for (i = 0; i < n; ++i) {
3576 up = isl_upoly_mul(up,
3577 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3580 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3583 isl_mat_free(qp->div);
3584 qp->div = isl_mat_copy(term->div);
3588 isl_term_free(term);
3591 isl_qpolynomial_free(qp);
3592 isl_term_free(term);
3596 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3597 __isl_take isl_dim *dim)
3606 if (isl_dim_equal(qp->dim, dim)) {
3611 qp = isl_qpolynomial_cow(qp);
3615 extra = isl_dim_size(dim, isl_dim_set) -
3616 isl_dim_size(qp->dim, isl_dim_set);
3617 total = isl_dim_total(qp->dim);
3618 if (qp->div->n_row) {
3621 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3624 for (i = 0; i < qp->div->n_row; ++i)
3626 qp->upoly = expand(qp->upoly, exp, total);
3631 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3634 for (i = 0; i < qp->div->n_row; ++i)
3635 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3637 isl_dim_free(qp->dim);
3643 isl_qpolynomial_free(qp);
3647 /* For each parameter or variable that does not appear in qp,
3648 * first eliminate the variable from all constraints and then set it to zero.
3650 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3651 __isl_keep isl_qpolynomial *qp)
3662 d = isl_dim_total(set->dim);
3663 active = isl_calloc_array(set->ctx, int, d);
3664 if (set_active(qp, active) < 0)
3667 for (i = 0; i < d; ++i)
3676 nparam = isl_dim_size(set->dim, isl_dim_param);
3677 nvar = isl_dim_size(set->dim, isl_dim_set);
3678 for (i = 0; i < nparam; ++i) {
3681 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3682 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3684 for (i = 0; i < nvar; ++i) {
3685 if (active[nparam + i])
3687 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3688 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3700 struct isl_opt_data {
3701 isl_qpolynomial *qp;
3703 isl_qpolynomial *opt;
3707 static int opt_fn(__isl_take isl_point *pnt, void *user)
3709 struct isl_opt_data *data = (struct isl_opt_data *)user;
3710 isl_qpolynomial *val;
3712 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3716 } else if (data->max) {
3717 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3719 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3725 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3726 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3728 struct isl_opt_data data = { NULL, 1, NULL, max };
3733 if (isl_upoly_is_cst(qp->upoly)) {
3738 set = fix_inactive(set, qp);
3741 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3745 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3748 isl_qpolynomial_free(qp);
3752 isl_qpolynomial_free(qp);
3753 isl_qpolynomial_free(data.opt);
3757 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3758 __isl_take isl_morph *morph)
3763 struct isl_upoly *up;
3765 struct isl_upoly **subs;
3768 qp = isl_qpolynomial_cow(qp);
3773 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3775 n_sub = morph->inv->n_row - 1;
3776 if (morph->inv->n_row != morph->inv->n_col)
3777 n_sub += qp->div->n_row;
3778 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3782 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3783 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3784 morph->inv->row[0][0], morph->inv->n_col);
3785 if (morph->inv->n_row != morph->inv->n_col)
3786 for (i = 0; i < qp->div->n_row; ++i)
3787 subs[morph->inv->n_row - 1 + i] =
3788 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3790 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3792 for (i = 0; i < n_sub; ++i)
3793 isl_upoly_free(subs[i]);
3796 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3797 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3798 qp->div = isl_mat_product(qp->div, mat);
3799 isl_dim_free(qp->dim);
3800 qp->dim = isl_dim_copy(morph->ran->dim);
3802 if (!qp->upoly || !qp->div || !qp->dim)
3805 isl_morph_free(morph);
3809 isl_qpolynomial_free(qp);
3810 isl_morph_free(morph);
3814 static int neg_entry(void **entry, void *user)
3816 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3818 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3820 return *pwqp ? 0 : -1;
3823 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3824 __isl_take isl_union_pw_qpolynomial *upwqp)
3826 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3830 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3831 &neg_entry, NULL) < 0)
3836 isl_union_pw_qpolynomial_free(upwqp);
3840 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3841 __isl_take isl_union_pw_qpolynomial *upwqp1,
3842 __isl_take isl_union_pw_qpolynomial *upwqp2)
3844 return isl_union_pw_qpolynomial_add(upwqp1,
3845 isl_union_pw_qpolynomial_neg(upwqp2));
3848 static int mul_entry(void **entry, void *user)
3850 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3852 struct isl_hash_table_entry *entry2;
3853 isl_pw_qpolynomial *pwpq = *entry;
3856 hash = isl_dim_get_hash(pwpq->dim);
3857 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3858 hash, &has_dim, pwpq->dim, 0);
3862 pwpq = isl_pw_qpolynomial_copy(pwpq);
3863 pwpq = isl_pw_qpolynomial_mul(pwpq,
3864 isl_pw_qpolynomial_copy(entry2->data));
3866 empty = isl_pw_qpolynomial_is_zero(pwpq);
3868 isl_pw_qpolynomial_free(pwpq);
3872 isl_pw_qpolynomial_free(pwpq);
3876 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3881 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3882 __isl_take isl_union_pw_qpolynomial *upwqp1,
3883 __isl_take isl_union_pw_qpolynomial *upwqp2)
3885 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3888 /* Reorder the columns of the given div definitions according to the
3891 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3892 __isl_take isl_reordering *r)
3901 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3902 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3906 for (i = 0; i < div->n_row; ++i) {
3907 isl_seq_cpy(mat->row[i], div->row[i], 2);
3908 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3909 for (j = 0; j < r->len; ++j)
3910 isl_int_set(mat->row[i][2 + r->pos[j]],
3911 div->row[i][2 + j]);
3914 isl_reordering_free(r);
3918 isl_reordering_free(r);
3923 /* Reorder the dimension of "qp" according to the given reordering.
3925 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3926 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3928 qp = isl_qpolynomial_cow(qp);
3932 r = isl_reordering_extend(r, qp->div->n_row);
3936 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3940 qp->upoly = reorder(qp->upoly, r->pos);
3944 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3946 isl_reordering_free(r);
3949 isl_qpolynomial_free(qp);
3950 isl_reordering_free(r);
3954 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3955 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3960 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3961 isl_reordering *exp;
3963 model = isl_dim_drop(model, isl_dim_in,
3964 0, isl_dim_size(model, isl_dim_in));
3965 model = isl_dim_drop(model, isl_dim_out,
3966 0, isl_dim_size(model, isl_dim_out));
3967 exp = isl_parameter_alignment_reordering(qp->dim, model);
3968 exp = isl_reordering_extend_dim(exp,
3969 isl_qpolynomial_get_dim(qp));
3970 qp = isl_qpolynomial_realign(qp, exp);
3973 isl_dim_free(model);
3976 isl_dim_free(model);
3977 isl_qpolynomial_free(qp);
3981 struct isl_split_periods_data {
3983 isl_pw_qpolynomial *res;
3986 /* Create a slice where the integer division "div" has the fixed value "v".
3987 * In particular, if "div" refers to floor(f/m), then create a slice
3989 * m v <= f <= m v + (m - 1)
3994 * -f + m v + (m - 1) >= 0
3996 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3997 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4000 isl_basic_set *bset = NULL;
4006 total = isl_dim_total(dim);
4007 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
4009 k = isl_basic_set_alloc_inequality(bset);
4012 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4013 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4015 k = isl_basic_set_alloc_inequality(bset);
4018 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4019 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4020 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4021 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4024 return isl_set_from_basic_set(bset);
4026 isl_basic_set_free(bset);
4031 static int split_periods(__isl_take isl_set *set,
4032 __isl_take isl_qpolynomial *qp, void *user);
4034 /* Create a slice of the domain "set" such that integer division "div"
4035 * has the fixed value "v" and add the results to data->res,
4036 * replacing the integer division by "v" in "qp".
4038 static int set_div(__isl_take isl_set *set,
4039 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4040 struct isl_split_periods_data *data)
4045 struct isl_upoly *cst;
4047 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
4048 set = isl_set_intersect(set, slice);
4053 total = isl_dim_total(qp->dim);
4055 for (i = div + 1; i < qp->div->n_row; ++i) {
4056 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4058 isl_int_addmul(qp->div->row[i][1],
4059 qp->div->row[i][2 + total + div], v);
4060 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4063 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4064 qp = substitute_div(qp, div, cst);
4066 return split_periods(set, qp, data);
4069 isl_qpolynomial_free(qp);
4073 /* Split the domain "set" such that integer division "div"
4074 * has a fixed value (ranging from "min" to "max") on each slice
4075 * and add the results to data->res.
4077 static int split_div(__isl_take isl_set *set,
4078 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4079 struct isl_split_periods_data *data)
4081 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4082 isl_set *set_i = isl_set_copy(set);
4083 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4085 if (set_div(set_i, qp_i, div, min, data) < 0)
4089 isl_qpolynomial_free(qp);
4093 isl_qpolynomial_free(qp);
4097 /* If "qp" refers to any integer division
4098 * that can only attain "max_periods" distinct values on "set"
4099 * then split the domain along those distinct values.
4100 * Add the results (or the original if no splitting occurs)
4103 static int split_periods(__isl_take isl_set *set,
4104 __isl_take isl_qpolynomial *qp, void *user)
4107 isl_pw_qpolynomial *pwqp;
4108 struct isl_split_periods_data *data;
4113 data = (struct isl_split_periods_data *)user;
4118 if (qp->div->n_row == 0) {
4119 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4120 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4126 total = isl_dim_total(qp->dim);
4127 for (i = 0; i < qp->div->n_row; ++i) {
4128 enum isl_lp_result lp_res;
4130 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4131 qp->div->n_row) != -1)
4134 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4135 set->ctx->one, &min, NULL, NULL);
4136 if (lp_res == isl_lp_error)
4138 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4140 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4142 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4143 set->ctx->one, &max, NULL, NULL);
4144 if (lp_res == isl_lp_error)
4146 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4148 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4150 isl_int_sub(max, max, min);
4151 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4152 isl_int_add(max, max, min);
4157 if (i < qp->div->n_row) {
4158 r = split_div(set, qp, i, min, max, data);
4160 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4161 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4173 isl_qpolynomial_free(qp);
4177 /* If any quasi-polynomial in pwqp refers to any integer division
4178 * that can only attain "max_periods" distinct values on its domain
4179 * then split the domain along those distinct values.
4181 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4182 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4184 struct isl_split_periods_data data;
4186 data.max_periods = max_periods;
4187 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4189 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4192 isl_pw_qpolynomial_free(pwqp);
4196 isl_pw_qpolynomial_free(data.res);
4197 isl_pw_qpolynomial_free(pwqp);
4201 /* Construct a piecewise quasipolynomial that is constant on the given
4202 * domain. In particular, it is
4205 * infinity if cst == -1
4207 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4208 __isl_take isl_basic_set *bset, int cst)
4211 isl_qpolynomial *qp;
4216 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4217 dim = isl_basic_set_get_dim(bset);
4219 qp = isl_qpolynomial_infty(dim);
4221 qp = isl_qpolynomial_zero(dim);
4223 qp = isl_qpolynomial_one(dim);
4224 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4227 /* Factor bset, call fn on each of the factors and return the product.
4229 * If no factors can be found, simply call fn on the input.
4230 * Otherwise, construct the factors based on the factorizer,
4231 * call fn on each factor and compute the product.
4233 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4234 __isl_take isl_basic_set *bset,
4235 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4241 isl_qpolynomial *qp;
4242 isl_pw_qpolynomial *pwqp;
4246 f = isl_basic_set_factorizer(bset);
4249 if (f->n_group == 0) {
4250 isl_factorizer_free(f);
4254 nparam = isl_basic_set_dim(bset, isl_dim_param);
4255 nvar = isl_basic_set_dim(bset, isl_dim_set);
4257 dim = isl_basic_set_get_dim(bset);
4258 dim = isl_dim_domain(dim);
4259 set = isl_set_universe(isl_dim_copy(dim));
4260 qp = isl_qpolynomial_one(dim);
4261 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4263 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4265 for (i = 0, n = 0; i < f->n_group; ++i) {
4266 isl_basic_set *bset_i;
4267 isl_pw_qpolynomial *pwqp_i;
4269 bset_i = isl_basic_set_copy(bset);
4270 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4271 nparam + n + f->len[i], nvar - n - f->len[i]);
4272 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4274 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4275 n + f->len[i], nvar - n - f->len[i]);
4276 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4278 pwqp_i = fn(bset_i);
4279 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4284 isl_basic_set_free(bset);
4285 isl_factorizer_free(f);
4289 isl_basic_set_free(bset);
4293 /* Factor bset, call fn on each of the factors and return the product.
4294 * The function is assumed to evaluate to zero on empty domains,
4295 * to one on zero-dimensional domains and to infinity on unbounded domains
4296 * and will not be called explicitly on zero-dimensional or unbounded domains.
4298 * We first check for some special cases and remove all equalities.
4299 * Then we hand over control to compressed_multiplicative_call.
4301 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4302 __isl_take isl_basic_set *bset,
4303 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4307 isl_pw_qpolynomial *pwqp;
4308 unsigned orig_nvar, final_nvar;
4313 if (isl_basic_set_plain_is_empty(bset))
4314 return constant_on_domain(bset, 0);
4316 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4319 return constant_on_domain(bset, 1);
4321 bounded = isl_basic_set_is_bounded(bset);
4325 return constant_on_domain(bset, -1);
4327 if (bset->n_eq == 0)
4328 return compressed_multiplicative_call(bset, fn);
4330 morph = isl_basic_set_full_compression(bset);
4331 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4333 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4335 pwqp = compressed_multiplicative_call(bset, fn);
4337 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4338 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4339 morph = isl_morph_inverse(morph);
4341 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4345 isl_basic_set_free(bset);
4349 /* Drop all floors in "qp", turning each integer division [a/m] into
4350 * a rational division a/m. If "down" is set, then the integer division
4351 * is replaces by (a-(m-1))/m instead.
4353 static __isl_give isl_qpolynomial *qp_drop_floors(
4354 __isl_take isl_qpolynomial *qp, int down)
4357 struct isl_upoly *s;
4361 if (qp->div->n_row == 0)
4364 qp = isl_qpolynomial_cow(qp);
4368 for (i = qp->div->n_row - 1; i >= 0; --i) {
4370 isl_int_sub(qp->div->row[i][1],
4371 qp->div->row[i][1], qp->div->row[i][0]);
4372 isl_int_add_ui(qp->div->row[i][1],
4373 qp->div->row[i][1], 1);
4375 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4376 qp->div->row[i][0], qp->div->n_col - 1);
4377 qp = substitute_div(qp, i, s);
4385 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4386 * a rational division a/m.
4388 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4389 __isl_take isl_pw_qpolynomial *pwqp)
4396 if (isl_pw_qpolynomial_is_zero(pwqp))
4399 pwqp = isl_pw_qpolynomial_cow(pwqp);
4403 for (i = 0; i < pwqp->n; ++i) {
4404 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4411 isl_pw_qpolynomial_free(pwqp);
4415 /* Adjust all the integer divisions in "qp" such that they are at least
4416 * one over the given orthant (identified by "signs"). This ensures
4417 * that they will still be non-negative even after subtracting (m-1)/m.
4419 * In particular, f is replaced by f' + v, changing f = [a/m]
4420 * to f' = [(a - m v)/m].
4421 * If the constant term k in a is smaller than m,
4422 * the constant term of v is set to floor(k/m) - 1.
4423 * For any other term, if the coefficient c and the variable x have
4424 * the same sign, then no changes are needed.
4425 * Otherwise, if the variable is positive (and c is negative),
4426 * then the coefficient of x in v is set to floor(c/m).
4427 * If the variable is negative (and c is positive),
4428 * then the coefficient of x in v is set to ceil(c/m).
4430 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4436 struct isl_upoly *s;
4438 qp = isl_qpolynomial_cow(qp);
4441 qp->div = isl_mat_cow(qp->div);
4445 total = isl_dim_total(qp->dim);
4446 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4448 for (i = 0; i < qp->div->n_row; ++i) {
4449 isl_int *row = qp->div->row[i];
4453 if (isl_int_lt(row[1], row[0])) {
4454 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4455 isl_int_sub_ui(v->el[0], v->el[0], 1);
4456 isl_int_submul(row[1], row[0], v->el[0]);
4458 for (j = 0; j < total; ++j) {
4459 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4462 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4464 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4465 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4467 for (j = 0; j < i; ++j) {
4468 if (isl_int_sgn(row[2 + total + j]) >= 0)
4470 isl_int_fdiv_q(v->el[1 + total + j],
4471 row[2 + total + j], row[0]);
4472 isl_int_submul(row[2 + total + j],
4473 row[0], v->el[1 + total + j]);
4475 for (j = i + 1; j < qp->div->n_row; ++j) {
4476 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4478 isl_seq_combine(qp->div->row[j] + 1,
4479 qp->div->ctx->one, qp->div->row[j] + 1,
4480 qp->div->row[j][2 + total + i], v->el, v->size);
4482 isl_int_set_si(v->el[1 + total + i], 1);
4483 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4484 qp->div->ctx->one, v->size);
4485 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4495 isl_qpolynomial_free(qp);
4499 struct isl_to_poly_data {
4501 isl_pw_qpolynomial *res;
4502 isl_qpolynomial *qp;
4505 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4506 * We first make all integer divisions positive and then split the
4507 * quasipolynomials into terms with sign data->sign (the direction
4508 * of the requested approximation) and terms with the opposite sign.
4509 * In the first set of terms, each integer division [a/m] is
4510 * overapproximated by a/m, while in the second it is underapproximated
4513 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4516 struct isl_to_poly_data *data = user;
4517 isl_pw_qpolynomial *t;
4518 isl_qpolynomial *qp, *up, *down;
4520 qp = isl_qpolynomial_copy(data->qp);
4521 qp = make_divs_pos(qp, signs);
4523 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4524 up = qp_drop_floors(up, 0);
4525 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4526 down = qp_drop_floors(down, 1);
4528 isl_qpolynomial_free(qp);
4529 qp = isl_qpolynomial_add(up, down);
4531 t = isl_pw_qpolynomial_alloc(orthant, qp);
4532 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4537 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4538 * the polynomial will be an overapproximation. If "sign" is negative,
4539 * it will be an underapproximation. If "sign" is zero, the approximation
4540 * will lie somewhere in between.
4542 * In particular, is sign == 0, we simply drop the floors, turning
4543 * the integer divisions into rational divisions.
4544 * Otherwise, we split the domains into orthants, make all integer divisions
4545 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4546 * depending on the requested sign and the sign of the term in which
4547 * the integer division appears.
4549 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4550 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4553 struct isl_to_poly_data data;
4556 return pwqp_drop_floors(pwqp);
4562 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4564 for (i = 0; i < pwqp->n; ++i) {
4565 if (pwqp->p[i].qp->div->n_row == 0) {
4566 isl_pw_qpolynomial *t;
4567 t = isl_pw_qpolynomial_alloc(
4568 isl_set_copy(pwqp->p[i].set),
4569 isl_qpolynomial_copy(pwqp->p[i].qp));
4570 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4573 data.qp = pwqp->p[i].qp;
4574 if (isl_set_foreach_orthant(pwqp->p[i].set,
4575 &to_polynomial_on_orthant, &data) < 0)
4579 isl_pw_qpolynomial_free(pwqp);
4583 isl_pw_qpolynomial_free(pwqp);
4584 isl_pw_qpolynomial_free(data.res);
4588 static int poly_entry(void **entry, void *user)
4591 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4593 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4595 return *pwqp ? 0 : -1;
4598 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4599 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4601 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4605 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4606 &poly_entry, &sign) < 0)
4611 isl_union_pw_qpolynomial_free(upwqp);
4615 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4616 __isl_take isl_qpolynomial *qp)
4620 isl_vec *aff = NULL;
4621 isl_basic_map *bmap = NULL;
4627 if (!isl_upoly_is_affine(qp->upoly))
4628 isl_die(qp->dim->ctx, isl_error_invalid,
4629 "input quasi-polynomial not affine", goto error);
4630 aff = isl_qpolynomial_extract_affine(qp);
4633 dim = isl_qpolynomial_get_dim(qp);
4634 dim = isl_dim_from_domain(dim);
4635 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4636 dim = isl_dim_add(dim, isl_dim_out, 1);
4637 n_div = qp->div->n_row;
4638 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4640 for (i = 0; i < n_div; ++i) {
4641 k = isl_basic_map_alloc_div(bmap);
4644 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4645 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4646 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4649 k = isl_basic_map_alloc_equality(bmap);
4652 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4653 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4654 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4657 isl_qpolynomial_free(qp);
4658 bmap = isl_basic_map_finalize(bmap);
4662 isl_qpolynomial_free(qp);
4663 isl_basic_map_free(bmap);