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_factorization.h>
15 #include <isl_union_map_private.h>
16 #include <isl_polynomial_private.h>
17 #include <isl_point_private.h>
18 #include <isl_dim_private.h>
19 #include <isl_map_private.h>
20 #include <isl_mat_private.h>
21 #include <isl_range.h>
23 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
26 case isl_dim_param: return 0;
27 case isl_dim_in: return dim->nparam;
28 case isl_dim_out: return dim->nparam + dim->n_in;
33 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
41 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
46 isl_assert(up->ctx, up->var < 0, return NULL);
48 return (struct isl_upoly_cst *)up;
51 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
56 isl_assert(up->ctx, up->var >= 0, return NULL);
58 return (struct isl_upoly_rec *)up;
61 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
62 __isl_keep struct isl_upoly *up2)
65 struct isl_upoly_rec *rec1, *rec2;
71 if (up1->var != up2->var)
73 if (isl_upoly_is_cst(up1)) {
74 struct isl_upoly_cst *cst1, *cst2;
75 cst1 = isl_upoly_as_cst(up1);
76 cst2 = isl_upoly_as_cst(up2);
79 return isl_int_eq(cst1->n, cst2->n) &&
80 isl_int_eq(cst1->d, cst2->d);
83 rec1 = isl_upoly_as_rec(up1);
84 rec2 = isl_upoly_as_rec(up2);
88 if (rec1->n != rec2->n)
91 for (i = 0; i < rec1->n; ++i) {
92 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
100 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
102 struct isl_upoly_cst *cst;
106 if (!isl_upoly_is_cst(up))
109 cst = isl_upoly_as_cst(up);
113 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
116 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
118 struct isl_upoly_cst *cst;
122 if (!isl_upoly_is_cst(up))
125 cst = isl_upoly_as_cst(up);
129 return isl_int_sgn(cst->n);
132 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
134 struct isl_upoly_cst *cst;
138 if (!isl_upoly_is_cst(up))
141 cst = isl_upoly_as_cst(up);
145 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
148 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
150 struct isl_upoly_cst *cst;
154 if (!isl_upoly_is_cst(up))
157 cst = isl_upoly_as_cst(up);
161 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
164 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
166 struct isl_upoly_cst *cst;
170 if (!isl_upoly_is_cst(up))
173 cst = isl_upoly_as_cst(up);
177 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
180 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
182 struct isl_upoly_cst *cst;
186 if (!isl_upoly_is_cst(up))
189 cst = isl_upoly_as_cst(up);
193 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
196 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
198 struct isl_upoly_cst *cst;
202 if (!isl_upoly_is_cst(up))
205 cst = isl_upoly_as_cst(up);
209 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
212 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
214 struct isl_upoly_cst *cst;
216 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
225 isl_int_init(cst->n);
226 isl_int_init(cst->d);
231 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
233 struct isl_upoly_cst *cst;
235 cst = isl_upoly_cst_alloc(ctx);
239 isl_int_set_si(cst->n, 0);
240 isl_int_set_si(cst->d, 1);
245 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
247 struct isl_upoly_cst *cst;
249 cst = isl_upoly_cst_alloc(ctx);
253 isl_int_set_si(cst->n, 1);
254 isl_int_set_si(cst->d, 1);
259 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
261 struct isl_upoly_cst *cst;
263 cst = isl_upoly_cst_alloc(ctx);
267 isl_int_set_si(cst->n, 1);
268 isl_int_set_si(cst->d, 0);
273 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
275 struct isl_upoly_cst *cst;
277 cst = isl_upoly_cst_alloc(ctx);
281 isl_int_set_si(cst->n, -1);
282 isl_int_set_si(cst->d, 0);
287 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
289 struct isl_upoly_cst *cst;
291 cst = isl_upoly_cst_alloc(ctx);
295 isl_int_set_si(cst->n, 0);
296 isl_int_set_si(cst->d, 0);
301 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
302 isl_int n, isl_int d)
304 struct isl_upoly_cst *cst;
306 cst = isl_upoly_cst_alloc(ctx);
310 isl_int_set(cst->n, n);
311 isl_int_set(cst->d, d);
316 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
319 struct isl_upoly_rec *rec;
321 isl_assert(ctx, var >= 0, return NULL);
322 isl_assert(ctx, size >= 0, return NULL);
323 rec = isl_calloc(ctx, struct isl_upoly_rec,
324 sizeof(struct isl_upoly_rec) +
325 (size - 1) * sizeof(struct isl_upoly *));
340 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
341 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
343 qp = isl_qpolynomial_cow(qp);
347 isl_dim_free(qp->dim);
352 isl_qpolynomial_free(qp);
357 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
359 return qp ? qp->dim->ctx : NULL;
362 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
364 return qp ? isl_dim_copy(qp->dim) : NULL;
367 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
368 enum isl_dim_type type)
370 return qp ? isl_dim_size(qp->dim, type) : 0;
373 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
375 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
378 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
380 return qp ? isl_upoly_is_one(qp->upoly) : -1;
383 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
385 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
388 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
390 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
393 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
395 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
398 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
400 return qp ? isl_upoly_sgn(qp->upoly) : 0;
403 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
405 isl_int_clear(cst->n);
406 isl_int_clear(cst->d);
409 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
413 for (i = 0; i < rec->n; ++i)
414 isl_upoly_free(rec->p[i]);
417 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
426 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
428 struct isl_upoly_cst *cst;
429 struct isl_upoly_cst *dup;
431 cst = isl_upoly_as_cst(up);
435 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
438 isl_int_set(dup->n, cst->n);
439 isl_int_set(dup->d, cst->d);
444 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
447 struct isl_upoly_rec *rec;
448 struct isl_upoly_rec *dup;
450 rec = isl_upoly_as_rec(up);
454 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
458 for (i = 0; i < rec->n; ++i) {
459 dup->p[i] = isl_upoly_copy(rec->p[i]);
467 isl_upoly_free(&dup->up);
471 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
473 struct isl_upoly *dup;
478 if (isl_upoly_is_cst(up))
479 return isl_upoly_dup_cst(up);
481 return isl_upoly_dup_rec(up);
484 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
492 return isl_upoly_dup(up);
495 void isl_upoly_free(__isl_take struct isl_upoly *up)
504 upoly_free_cst((struct isl_upoly_cst *)up);
506 upoly_free_rec((struct isl_upoly_rec *)up);
508 isl_ctx_deref(up->ctx);
512 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
517 isl_int_gcd(gcd, cst->n, cst->d);
518 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
519 isl_int_divexact(cst->n, cst->n, gcd);
520 isl_int_divexact(cst->d, cst->d, gcd);
525 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
526 __isl_take struct isl_upoly *up2)
528 struct isl_upoly_cst *cst1;
529 struct isl_upoly_cst *cst2;
531 up1 = isl_upoly_cow(up1);
535 cst1 = isl_upoly_as_cst(up1);
536 cst2 = isl_upoly_as_cst(up2);
538 if (isl_int_eq(cst1->d, cst2->d))
539 isl_int_add(cst1->n, cst1->n, cst2->n);
541 isl_int_mul(cst1->n, cst1->n, cst2->d);
542 isl_int_addmul(cst1->n, cst2->n, cst1->d);
543 isl_int_mul(cst1->d, cst1->d, cst2->d);
546 isl_upoly_cst_reduce(cst1);
556 static __isl_give struct isl_upoly *replace_by_zero(
557 __isl_take struct isl_upoly *up)
565 return isl_upoly_zero(ctx);
568 static __isl_give struct isl_upoly *replace_by_constant_term(
569 __isl_take struct isl_upoly *up)
571 struct isl_upoly_rec *rec;
572 struct isl_upoly *cst;
577 rec = isl_upoly_as_rec(up);
580 cst = isl_upoly_copy(rec->p[0]);
588 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
589 __isl_take struct isl_upoly *up2)
592 struct isl_upoly_rec *rec1, *rec2;
597 if (isl_upoly_is_nan(up1)) {
602 if (isl_upoly_is_nan(up2)) {
607 if (isl_upoly_is_zero(up1)) {
612 if (isl_upoly_is_zero(up2)) {
617 if (up1->var < up2->var)
618 return isl_upoly_sum(up2, up1);
620 if (up2->var < up1->var) {
621 struct isl_upoly_rec *rec;
622 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
626 up1 = isl_upoly_cow(up1);
627 rec = isl_upoly_as_rec(up1);
630 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
632 up1 = replace_by_constant_term(up1);
636 if (isl_upoly_is_cst(up1))
637 return isl_upoly_sum_cst(up1, up2);
639 rec1 = isl_upoly_as_rec(up1);
640 rec2 = isl_upoly_as_rec(up2);
644 if (rec1->n < rec2->n)
645 return isl_upoly_sum(up2, up1);
647 up1 = isl_upoly_cow(up1);
648 rec1 = isl_upoly_as_rec(up1);
652 for (i = rec2->n - 1; i >= 0; --i) {
653 rec1->p[i] = isl_upoly_sum(rec1->p[i],
654 isl_upoly_copy(rec2->p[i]));
657 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
658 isl_upoly_free(rec1->p[i]);
664 up1 = replace_by_zero(up1);
665 else if (rec1->n == 1)
666 up1 = replace_by_constant_term(up1);
677 __isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up)
679 struct isl_upoly_cst *cst;
681 if (isl_upoly_is_zero(up))
684 up = isl_upoly_cow(up);
688 cst = isl_upoly_as_cst(up);
690 isl_int_neg(cst->n, cst->n);
695 __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up)
698 struct isl_upoly_rec *rec;
703 if (isl_upoly_is_cst(up))
704 return isl_upoly_neg_cst(up);
706 up = isl_upoly_cow(up);
707 rec = isl_upoly_as_rec(up);
711 for (i = 0; i < rec->n; ++i) {
712 rec->p[i] = isl_upoly_neg(rec->p[i]);
723 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
724 __isl_take struct isl_upoly *up2)
726 struct isl_upoly_cst *cst1;
727 struct isl_upoly_cst *cst2;
729 up1 = isl_upoly_cow(up1);
733 cst1 = isl_upoly_as_cst(up1);
734 cst2 = isl_upoly_as_cst(up2);
736 isl_int_mul(cst1->n, cst1->n, cst2->n);
737 isl_int_mul(cst1->d, cst1->d, cst2->d);
739 isl_upoly_cst_reduce(cst1);
749 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
750 __isl_take struct isl_upoly *up2)
752 struct isl_upoly_rec *rec1;
753 struct isl_upoly_rec *rec2;
754 struct isl_upoly_rec *res;
758 rec1 = isl_upoly_as_rec(up1);
759 rec2 = isl_upoly_as_rec(up2);
762 size = rec1->n + rec2->n - 1;
763 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
767 for (i = 0; i < rec1->n; ++i) {
768 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
769 isl_upoly_copy(rec1->p[i]));
774 for (; i < size; ++i) {
775 res->p[i] = isl_upoly_zero(up1->ctx);
780 for (i = 0; i < rec1->n; ++i) {
781 for (j = 1; j < rec2->n; ++j) {
782 struct isl_upoly *up;
783 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
784 isl_upoly_copy(rec1->p[i]));
785 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
798 isl_upoly_free(&res->up);
802 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
803 __isl_take struct isl_upoly *up2)
808 if (isl_upoly_is_nan(up1)) {
813 if (isl_upoly_is_nan(up2)) {
818 if (isl_upoly_is_zero(up1)) {
823 if (isl_upoly_is_zero(up2)) {
828 if (isl_upoly_is_one(up1)) {
833 if (isl_upoly_is_one(up2)) {
838 if (up1->var < up2->var)
839 return isl_upoly_mul(up2, up1);
841 if (up2->var < up1->var) {
843 struct isl_upoly_rec *rec;
844 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
845 isl_ctx *ctx = up1->ctx;
848 return isl_upoly_nan(ctx);
850 up1 = isl_upoly_cow(up1);
851 rec = isl_upoly_as_rec(up1);
855 for (i = 0; i < rec->n; ++i) {
856 rec->p[i] = isl_upoly_mul(rec->p[i],
857 isl_upoly_copy(up2));
865 if (isl_upoly_is_cst(up1))
866 return isl_upoly_mul_cst(up1, up2);
868 return isl_upoly_mul_rec(up1, up2);
875 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
876 unsigned n_div, __isl_take struct isl_upoly *up)
878 struct isl_qpolynomial *qp = NULL;
884 total = isl_dim_total(dim);
886 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
891 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
902 isl_qpolynomial_free(qp);
906 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
915 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
917 struct isl_qpolynomial *dup;
922 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
923 isl_upoly_copy(qp->upoly));
926 isl_mat_free(dup->div);
927 dup->div = isl_mat_copy(qp->div);
933 isl_qpolynomial_free(dup);
937 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
945 return isl_qpolynomial_dup(qp);
948 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
956 isl_dim_free(qp->dim);
957 isl_mat_free(qp->div);
958 isl_upoly_free(qp->upoly);
963 __isl_give struct isl_upoly *isl_upoly_pow(isl_ctx *ctx, int pos, int power)
966 struct isl_upoly *up;
967 struct isl_upoly_rec *rec;
968 struct isl_upoly_cst *cst;
970 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
973 for (i = 0; i < 1 + power; ++i) {
974 rec->p[i] = isl_upoly_zero(ctx);
979 cst = isl_upoly_as_cst(rec->p[power]);
980 isl_int_set_si(cst->n, 1);
984 isl_upoly_free(&rec->up);
988 /* r array maps original positions to new positions.
990 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
994 struct isl_upoly_rec *rec;
995 struct isl_upoly *base;
996 struct isl_upoly *res;
998 if (isl_upoly_is_cst(up))
1001 rec = isl_upoly_as_rec(up);
1005 isl_assert(up->ctx, rec->n >= 1, goto error);
1007 base = isl_upoly_pow(up->ctx, r[up->var], 1);
1008 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1010 for (i = rec->n - 2; i >= 0; --i) {
1011 res = isl_upoly_mul(res, isl_upoly_copy(base));
1012 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1015 isl_upoly_free(base);
1024 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1029 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1030 div1->n_col >= div2->n_col, return -1);
1032 if (div1->n_row == div2->n_row)
1033 return isl_mat_is_equal(div1, div2);
1035 n_row = div1->n_row;
1036 n_col = div1->n_col;
1037 div1->n_row = div2->n_row;
1038 div1->n_col = div2->n_col;
1040 equal = isl_mat_is_equal(div1, div2);
1042 div1->n_row = n_row;
1043 div1->n_col = n_col;
1048 static void expand_row(__isl_keep isl_mat *dst, int d,
1049 __isl_keep isl_mat *src, int s, int *exp)
1052 unsigned c = src->n_col - src->n_row;
1054 isl_seq_cpy(dst->row[d], src->row[s], c);
1055 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
1057 for (i = 0; i < s; ++i)
1058 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
1061 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1065 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1066 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1071 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1074 struct isl_div_sort_info {
1079 static int div_sort_cmp(const void *p1, const void *p2)
1081 const struct isl_div_sort_info *i1, *i2;
1082 i1 = (const struct isl_div_sort_info *) p1;
1083 i2 = (const struct isl_div_sort_info *) p2;
1085 return cmp_row(i1->div, i1->row, i2->row);
1088 /* Sort divs and remove duplicates.
1090 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1095 struct isl_div_sort_info *array = NULL;
1096 int *pos = NULL, *at = NULL;
1097 int *reordering = NULL;
1102 if (qp->div->n_row <= 1)
1105 div_pos = isl_dim_total(qp->dim);
1107 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1109 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1110 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1111 len = qp->div->n_col - 2;
1112 reordering = isl_alloc_array(qp->div->ctx, int, len);
1113 if (!array || !pos || !at || !reordering)
1116 for (i = 0; i < qp->div->n_row; ++i) {
1117 array[i].div = qp->div;
1123 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1126 for (i = 0; i < div_pos; ++i)
1129 for (i = 0; i < qp->div->n_row; ++i) {
1130 if (pos[array[i].row] == i)
1132 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1133 pos[at[i]] = pos[array[i].row];
1134 at[pos[array[i].row]] = at[i];
1135 at[i] = array[i].row;
1136 pos[array[i].row] = i;
1140 for (i = 0; i < len - div_pos; ++i) {
1142 isl_seq_eq(qp->div->row[i - skip - 1],
1143 qp->div->row[i - skip], qp->div->n_col)) {
1144 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1145 qp->div = isl_mat_drop_cols(qp->div,
1146 2 + div_pos + i - skip, 1);
1149 reordering[div_pos + array[i].row] = div_pos + i - skip;
1152 qp->upoly = reorder(qp->upoly, reordering);
1154 if (!qp->upoly || !qp->div)
1168 isl_qpolynomial_free(qp);
1172 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1173 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1176 isl_mat *div = NULL;
1177 unsigned d = div1->n_col - div1->n_row;
1179 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1180 d + div1->n_row + div2->n_row);
1184 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1187 expand_row(div, k, div1, i, exp1);
1188 expand_row(div, k + 1, div2, j, exp2);
1190 cmp = cmp_row(div, k, k + 1);
1194 } else if (cmp < 0) {
1198 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1201 for (; i < div1->n_row; ++i, ++k) {
1202 expand_row(div, k, div1, i, exp1);
1205 for (; j < div2->n_row; ++j, ++k) {
1206 expand_row(div, k, div2, j, exp2);
1216 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1217 int *exp, int first)
1220 struct isl_upoly_rec *rec;
1222 if (isl_upoly_is_cst(up))
1225 if (up->var < first)
1228 if (exp[up->var - first] == up->var - first)
1231 up = isl_upoly_cow(up);
1235 up->var = exp[up->var - first] + first;
1237 rec = isl_upoly_as_rec(up);
1241 for (i = 0; i < rec->n; ++i) {
1242 rec->p[i] = expand(rec->p[i], exp, first);
1253 static __isl_give isl_qpolynomial *with_merged_divs(
1254 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1255 __isl_take isl_qpolynomial *qp2),
1256 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1260 isl_mat *div = NULL;
1262 qp1 = isl_qpolynomial_cow(qp1);
1263 qp2 = isl_qpolynomial_cow(qp2);
1268 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1269 qp1->div->n_col >= qp2->div->n_col, goto error);
1271 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1272 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1276 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1280 isl_mat_free(qp1->div);
1281 qp1->div = isl_mat_copy(div);
1282 isl_mat_free(qp2->div);
1283 qp2->div = isl_mat_copy(div);
1285 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1286 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1288 if (!qp1->upoly || !qp2->upoly)
1295 return fn(qp1, qp2);
1300 isl_qpolynomial_free(qp1);
1301 isl_qpolynomial_free(qp2);
1305 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1306 __isl_take isl_qpolynomial *qp2)
1308 qp1 = isl_qpolynomial_cow(qp1);
1313 if (qp1->div->n_row < qp2->div->n_row)
1314 return isl_qpolynomial_add(qp2, qp1);
1316 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1317 if (!compatible_divs(qp1->div, qp2->div))
1318 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1320 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1324 isl_qpolynomial_free(qp2);
1328 isl_qpolynomial_free(qp1);
1329 isl_qpolynomial_free(qp2);
1333 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1334 __isl_keep isl_set *dom,
1335 __isl_take isl_qpolynomial *qp1,
1336 __isl_take isl_qpolynomial *qp2)
1338 return isl_qpolynomial_add(qp1, qp2);
1341 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1342 __isl_take isl_qpolynomial *qp2)
1344 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1347 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1349 qp = isl_qpolynomial_cow(qp);
1354 qp->upoly = isl_upoly_neg(qp->upoly);
1360 isl_qpolynomial_free(qp);
1364 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1365 __isl_take isl_qpolynomial *qp2)
1367 qp1 = isl_qpolynomial_cow(qp1);
1372 if (qp1->div->n_row < qp2->div->n_row)
1373 return isl_qpolynomial_mul(qp2, qp1);
1375 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1376 if (!compatible_divs(qp1->div, qp2->div))
1377 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1379 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1383 isl_qpolynomial_free(qp2);
1387 isl_qpolynomial_free(qp1);
1388 isl_qpolynomial_free(qp2);
1392 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1394 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1397 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1399 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1402 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1404 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1407 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1409 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1412 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1414 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1417 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1420 struct isl_qpolynomial *qp;
1421 struct isl_upoly_cst *cst;
1423 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1427 cst = isl_upoly_as_cst(qp->upoly);
1428 isl_int_set(cst->n, v);
1433 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1434 isl_int *n, isl_int *d)
1436 struct isl_upoly_cst *cst;
1441 if (!isl_upoly_is_cst(qp->upoly))
1444 cst = isl_upoly_as_cst(qp->upoly);
1449 isl_int_set(*n, cst->n);
1451 isl_int_set(*d, cst->d);
1456 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1459 struct isl_upoly_rec *rec;
1467 rec = isl_upoly_as_rec(up);
1474 isl_assert(up->ctx, rec->n > 1, return -1);
1476 is_cst = isl_upoly_is_cst(rec->p[1]);
1482 return isl_upoly_is_affine(rec->p[0]);
1485 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1490 if (qp->div->n_row > 0)
1493 return isl_upoly_is_affine(qp->upoly);
1496 static void update_coeff(__isl_keep isl_vec *aff,
1497 __isl_keep struct isl_upoly_cst *cst, int pos)
1502 if (isl_int_is_zero(cst->n))
1507 isl_int_gcd(gcd, cst->d, aff->el[0]);
1508 isl_int_divexact(f, cst->d, gcd);
1509 isl_int_divexact(gcd, aff->el[0], gcd);
1510 isl_seq_scale(aff->el, aff->el, f, aff->size);
1511 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1516 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1517 __isl_keep isl_vec *aff)
1519 struct isl_upoly_cst *cst;
1520 struct isl_upoly_rec *rec;
1526 struct isl_upoly_cst *cst;
1528 cst = isl_upoly_as_cst(up);
1531 update_coeff(aff, cst, 0);
1535 rec = isl_upoly_as_rec(up);
1538 isl_assert(up->ctx, rec->n == 2, return -1);
1540 cst = isl_upoly_as_cst(rec->p[1]);
1543 update_coeff(aff, cst, 1 + up->var);
1545 return isl_upoly_update_affine(rec->p[0], aff);
1548 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1549 __isl_keep isl_qpolynomial *qp)
1557 isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1558 d = isl_dim_total(qp->dim);
1559 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1563 isl_seq_clr(aff->el + 1, 1 + d);
1564 isl_int_set_si(aff->el[0], 1);
1566 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1575 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1576 __isl_keep isl_qpolynomial *qp2)
1581 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1584 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1587 struct isl_upoly_rec *rec;
1589 if (isl_upoly_is_cst(up)) {
1590 struct isl_upoly_cst *cst;
1591 cst = isl_upoly_as_cst(up);
1594 isl_int_lcm(*d, *d, cst->d);
1598 rec = isl_upoly_as_rec(up);
1602 for (i = 0; i < rec->n; ++i)
1603 upoly_update_den(rec->p[i], d);
1606 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1608 isl_int_set_si(*d, 1);
1611 upoly_update_den(qp->upoly, d);
1614 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_dim *dim,
1617 struct isl_ctx *ctx;
1624 return isl_qpolynomial_alloc(dim, 0, isl_upoly_pow(ctx, pos, power));
1627 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1628 enum isl_dim_type type, unsigned pos)
1633 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1634 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1636 if (type == isl_dim_set)
1637 pos += isl_dim_size(dim, isl_dim_param);
1639 return isl_qpolynomial_pow(dim, pos, 1);
1645 /* Remove common factor of non-constant terms and denominator.
1647 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1649 isl_ctx *ctx = qp->div->ctx;
1650 unsigned total = qp->div->n_col - 2;
1652 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1653 isl_int_gcd(ctx->normalize_gcd,
1654 ctx->normalize_gcd, qp->div->row[div][0]);
1655 if (isl_int_is_one(ctx->normalize_gcd))
1658 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1659 ctx->normalize_gcd, total);
1660 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1661 ctx->normalize_gcd);
1662 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1663 ctx->normalize_gcd);
1666 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
1669 struct isl_qpolynomial *qp = NULL;
1670 struct isl_upoly_rec *rec;
1671 struct isl_upoly_cst *cst;
1678 d = div->line - div->bmap->div;
1680 pos = isl_dim_total(div->bmap->dim) + d;
1681 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
1682 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
1683 div->bmap->n_div, &rec->up);
1687 for (i = 0; i < div->bmap->n_div; ++i) {
1688 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
1689 normalize_div(qp, i);
1692 for (i = 0; i < 1 + power; ++i) {
1693 rec->p[i] = isl_upoly_zero(div->ctx);
1698 cst = isl_upoly_as_cst(rec->p[power]);
1699 isl_int_set_si(cst->n, 1);
1705 isl_qpolynomial_free(qp);
1710 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
1712 return isl_qpolynomial_div_pow(div, 1);
1715 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
1716 const isl_int n, const isl_int d)
1718 struct isl_qpolynomial *qp;
1719 struct isl_upoly_cst *cst;
1721 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1725 cst = isl_upoly_as_cst(qp->upoly);
1726 isl_int_set(cst->n, n);
1727 isl_int_set(cst->d, d);
1732 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
1734 struct isl_upoly_rec *rec;
1740 if (isl_upoly_is_cst(up))
1744 active[up->var] = 1;
1746 rec = isl_upoly_as_rec(up);
1747 for (i = 0; i < rec->n; ++i)
1748 if (up_set_active(rec->p[i], active, d) < 0)
1754 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
1757 int d = isl_dim_total(qp->dim);
1762 for (i = 0; i < d; ++i)
1763 for (j = 0; j < qp->div->n_row; ++j) {
1764 if (isl_int_is_zero(qp->div->row[j][2 + i]))
1770 return up_set_active(qp->upoly, active, d);
1773 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
1774 enum isl_dim_type type, unsigned first, unsigned n)
1785 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1787 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1788 type == isl_dim_set, return -1);
1790 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
1791 if (set_active(qp, active) < 0)
1794 if (type == isl_dim_set)
1795 first += isl_dim_size(qp->dim, isl_dim_param);
1796 for (i = 0; i < n; ++i)
1797 if (active[first + i]) {
1810 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
1811 unsigned first, unsigned n)
1814 struct isl_upoly_rec *rec;
1818 if (n == 0 || up->var < 0 || up->var < first)
1820 if (up->var < first + n) {
1821 up = replace_by_constant_term(up);
1822 return isl_upoly_drop(up, first, n);
1824 up = isl_upoly_cow(up);
1828 rec = isl_upoly_as_rec(up);
1832 for (i = 0; i < rec->n; ++i) {
1833 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
1844 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1845 __isl_take isl_qpolynomial *qp,
1846 enum isl_dim_type type, unsigned pos, const char *s)
1848 qp = isl_qpolynomial_cow(qp);
1851 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
1856 isl_qpolynomial_free(qp);
1860 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
1861 __isl_take isl_qpolynomial *qp,
1862 enum isl_dim_type type, unsigned first, unsigned n)
1866 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
1869 qp = isl_qpolynomial_cow(qp);
1873 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1875 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1876 type == isl_dim_set, goto error);
1878 qp->dim = isl_dim_drop(qp->dim, type, first, n);
1882 if (type == isl_dim_set)
1883 first += isl_dim_size(qp->dim, isl_dim_param);
1885 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
1889 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
1895 isl_qpolynomial_free(qp);
1899 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1900 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1903 struct isl_upoly_rec *rec;
1904 struct isl_upoly *base, *res;
1909 if (isl_upoly_is_cst(up))
1912 if (up->var < first)
1915 rec = isl_upoly_as_rec(up);
1919 isl_assert(up->ctx, rec->n >= 1, goto error);
1921 if (up->var >= first + n)
1922 base = isl_upoly_pow(up->ctx, up->var, 1);
1924 base = isl_upoly_copy(subs[up->var - first]);
1926 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1927 for (i = rec->n - 2; i >= 0; --i) {
1928 struct isl_upoly *t;
1929 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1930 res = isl_upoly_mul(res, isl_upoly_copy(base));
1931 res = isl_upoly_sum(res, t);
1934 isl_upoly_free(base);
1943 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1944 isl_int denom, unsigned len)
1947 struct isl_upoly *up;
1949 isl_assert(ctx, len >= 1, return NULL);
1951 up = isl_upoly_rat_cst(ctx, f[0], denom);
1952 for (i = 0; i < len - 1; ++i) {
1953 struct isl_upoly *t;
1954 struct isl_upoly *c;
1956 if (isl_int_is_zero(f[1 + i]))
1959 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1960 t = isl_upoly_pow(ctx, i, 1);
1961 t = isl_upoly_mul(c, t);
1962 up = isl_upoly_sum(up, t);
1968 /* Replace the integer division identified by "div" by the polynomial "s".
1969 * The integer division is assumed not to appear in the definition
1970 * of any other integer divisions.
1972 static __isl_give isl_qpolynomial *substitute_div(
1973 __isl_take isl_qpolynomial *qp,
1974 int div, __isl_take struct isl_upoly *s)
1983 qp = isl_qpolynomial_cow(qp);
1987 total = isl_dim_total(qp->dim);
1988 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1992 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1995 for (i = 0; i < total + div; ++i)
1997 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1998 reordering[i] = i - 1;
1999 qp->div = isl_mat_drop_rows(qp->div, div, 1);
2000 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
2001 qp->upoly = reorder(qp->upoly, reordering);
2004 if (!qp->upoly || !qp->div)
2010 isl_qpolynomial_free(qp);
2015 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2016 * divisions because d is equal to 1 by their definition, i.e., e.
2018 static __isl_give isl_qpolynomial *substitute_non_divs(
2019 __isl_take isl_qpolynomial *qp)
2023 struct isl_upoly *s;
2028 total = isl_dim_total(qp->dim);
2029 for (i = 0; qp && i < qp->div->n_row; ++i) {
2030 if (!isl_int_is_one(qp->div->row[i][0]))
2032 for (j = i + 1; j < qp->div->n_row; ++j) {
2033 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
2035 isl_seq_combine(qp->div->row[j] + 1,
2036 qp->div->ctx->one, qp->div->row[j] + 1,
2037 qp->div->row[j][2 + total + i],
2038 qp->div->row[i] + 1, 1 + total + i);
2039 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
2040 normalize_div(qp, j);
2042 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
2043 qp->div->row[i][0], qp->div->n_col - 1);
2044 qp = substitute_div(qp, i, s);
2051 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2052 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2058 struct isl_upoly *up;
2062 if (eq->n_eq == 0) {
2063 isl_basic_set_free(eq);
2067 qp = isl_qpolynomial_cow(qp);
2070 qp->div = isl_mat_cow(qp->div);
2074 total = 1 + isl_dim_total(eq->dim);
2076 isl_int_init(denom);
2077 for (i = 0; i < eq->n_eq; ++i) {
2078 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2079 if (j < 0 || j == 0 || j >= total)
2082 for (k = 0; k < qp->div->n_row; ++k) {
2083 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2085 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2086 &qp->div->row[k][0]);
2087 normalize_div(qp, k);
2090 if (isl_int_is_pos(eq->eq[i][j]))
2091 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2092 isl_int_abs(denom, eq->eq[i][j]);
2093 isl_int_set_si(eq->eq[i][j], 0);
2095 up = isl_upoly_from_affine(qp->dim->ctx,
2096 eq->eq[i], denom, total);
2097 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2100 isl_int_clear(denom);
2105 isl_basic_set_free(eq);
2107 qp = substitute_non_divs(qp);
2112 isl_basic_set_free(eq);
2113 isl_qpolynomial_free(qp);
2117 static __isl_give isl_basic_set *add_div_constraints(
2118 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2126 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2129 total = isl_basic_set_total_dim(bset);
2130 for (i = 0; i < div->n_row; ++i)
2131 if (isl_basic_set_add_div_constraints_var(bset,
2132 total - div->n_row + i, div->row[i]) < 0)
2139 isl_basic_set_free(bset);
2143 /* Look for equalities among the variables shared by context and qp
2144 * and the integer divisions of qp, if any.
2145 * The equalities are then used to eliminate variables and/or integer
2146 * divisions from qp.
2148 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2149 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2155 if (qp->div->n_row > 0) {
2156 isl_basic_set *bset;
2157 context = isl_set_add_dims(context, isl_dim_set,
2159 bset = isl_basic_set_universe(isl_set_get_dim(context));
2160 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2161 context = isl_set_intersect(context,
2162 isl_set_from_basic_set(bset));
2165 aff = isl_set_affine_hull(context);
2166 return isl_qpolynomial_substitute_equalities(qp, aff);
2168 isl_qpolynomial_free(qp);
2169 isl_set_free(context);
2174 #define PW isl_pw_qpolynomial
2176 #define EL isl_qpolynomial
2178 #define IS_ZERO is_zero
2182 #include <isl_pw_templ.c>
2185 #define UNION isl_union_pw_qpolynomial
2187 #define PART isl_pw_qpolynomial
2189 #define PARTS pw_qpolynomial
2191 #include <isl_union_templ.c>
2193 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2201 if (!isl_set_fast_is_universe(pwqp->p[0].set))
2204 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2207 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2208 __isl_take isl_pw_qpolynomial *pwqp1,
2209 __isl_take isl_pw_qpolynomial *pwqp2)
2212 struct isl_pw_qpolynomial *res;
2215 if (!pwqp1 || !pwqp2)
2218 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2221 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2222 isl_pw_qpolynomial_free(pwqp2);
2226 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2227 isl_pw_qpolynomial_free(pwqp1);
2231 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2232 isl_pw_qpolynomial_free(pwqp1);
2236 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2237 isl_pw_qpolynomial_free(pwqp2);
2241 n = pwqp1->n * pwqp2->n;
2242 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2244 for (i = 0; i < pwqp1->n; ++i) {
2245 for (j = 0; j < pwqp2->n; ++j) {
2246 struct isl_set *common;
2247 struct isl_qpolynomial *prod;
2248 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2249 isl_set_copy(pwqp2->p[j].set));
2250 if (isl_set_fast_is_empty(common)) {
2251 isl_set_free(common);
2255 prod = isl_qpolynomial_mul(
2256 isl_qpolynomial_copy(pwqp1->p[i].qp),
2257 isl_qpolynomial_copy(pwqp2->p[j].qp));
2259 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2263 isl_pw_qpolynomial_free(pwqp1);
2264 isl_pw_qpolynomial_free(pwqp2);
2268 isl_pw_qpolynomial_free(pwqp1);
2269 isl_pw_qpolynomial_free(pwqp2);
2273 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2274 __isl_take isl_pw_qpolynomial *pwqp)
2281 if (isl_pw_qpolynomial_is_zero(pwqp))
2284 pwqp = isl_pw_qpolynomial_cow(pwqp);
2288 for (i = 0; i < pwqp->n; ++i) {
2289 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2296 isl_pw_qpolynomial_free(pwqp);
2300 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2301 __isl_take isl_pw_qpolynomial *pwqp1,
2302 __isl_take isl_pw_qpolynomial *pwqp2)
2304 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2307 __isl_give struct isl_upoly *isl_upoly_eval(
2308 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2311 struct isl_upoly_rec *rec;
2312 struct isl_upoly *res;
2313 struct isl_upoly *base;
2315 if (isl_upoly_is_cst(up)) {
2320 rec = isl_upoly_as_rec(up);
2324 isl_assert(up->ctx, rec->n >= 1, goto error);
2326 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2328 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2331 for (i = rec->n - 2; i >= 0; --i) {
2332 res = isl_upoly_mul(res, isl_upoly_copy(base));
2333 res = isl_upoly_sum(res,
2334 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2335 isl_vec_copy(vec)));
2338 isl_upoly_free(base);
2348 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2349 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2352 struct isl_upoly *up;
2357 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2359 if (qp->div->n_row == 0)
2360 ext = isl_vec_copy(pnt->vec);
2363 unsigned dim = isl_dim_total(qp->dim);
2364 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2368 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2369 for (i = 0; i < qp->div->n_row; ++i) {
2370 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2371 1 + dim + i, &ext->el[1+dim+i]);
2372 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2373 qp->div->row[i][0]);
2377 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2381 dim = isl_dim_copy(qp->dim);
2382 isl_qpolynomial_free(qp);
2383 isl_point_free(pnt);
2385 return isl_qpolynomial_alloc(dim, 0, up);
2387 isl_qpolynomial_free(qp);
2388 isl_point_free(pnt);
2392 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2393 __isl_keep struct isl_upoly_cst *cst2)
2398 isl_int_mul(t, cst1->n, cst2->d);
2399 isl_int_submul(t, cst2->n, cst1->d);
2400 cmp = isl_int_sgn(t);
2405 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2406 __isl_keep isl_qpolynomial *qp2)
2408 struct isl_upoly_cst *cst1, *cst2;
2412 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2413 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2414 if (isl_qpolynomial_is_nan(qp1))
2416 if (isl_qpolynomial_is_nan(qp2))
2418 cst1 = isl_upoly_as_cst(qp1->upoly);
2419 cst2 = isl_upoly_as_cst(qp2->upoly);
2421 return isl_upoly_cmp(cst1, cst2) <= 0;
2424 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2425 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2427 struct isl_upoly_cst *cst1, *cst2;
2432 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2433 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2434 cst1 = isl_upoly_as_cst(qp1->upoly);
2435 cst2 = isl_upoly_as_cst(qp2->upoly);
2436 cmp = isl_upoly_cmp(cst1, cst2);
2439 isl_qpolynomial_free(qp2);
2441 isl_qpolynomial_free(qp1);
2446 isl_qpolynomial_free(qp1);
2447 isl_qpolynomial_free(qp2);
2451 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2452 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2454 struct isl_upoly_cst *cst1, *cst2;
2459 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2460 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2461 cst1 = isl_upoly_as_cst(qp1->upoly);
2462 cst2 = isl_upoly_as_cst(qp2->upoly);
2463 cmp = isl_upoly_cmp(cst1, cst2);
2466 isl_qpolynomial_free(qp2);
2468 isl_qpolynomial_free(qp1);
2473 isl_qpolynomial_free(qp1);
2474 isl_qpolynomial_free(qp2);
2478 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2479 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2480 unsigned first, unsigned n)
2489 qp = isl_qpolynomial_cow(qp);
2493 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2496 g_pos = pos(qp->dim, type) + first;
2498 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2502 total = qp->div->n_col - 2;
2503 if (total > g_pos) {
2505 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2508 for (i = 0; i < total - g_pos; ++i)
2510 qp->upoly = expand(qp->upoly, exp, g_pos);
2516 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2522 isl_qpolynomial_free(qp);
2526 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2527 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2531 pos = isl_qpolynomial_dim(qp, type);
2533 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2536 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2537 __isl_take isl_pw_qpolynomial *pwqp,
2538 enum isl_dim_type type, unsigned n)
2542 pos = isl_pw_qpolynomial_dim(pwqp, type);
2544 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2547 static int *reordering_move(isl_ctx *ctx,
2548 unsigned len, unsigned dst, unsigned src, unsigned n)
2553 reordering = isl_alloc_array(ctx, int, len);
2558 for (i = 0; i < dst; ++i)
2560 for (i = 0; i < n; ++i)
2561 reordering[src + i] = dst + i;
2562 for (i = 0; i < src - dst; ++i)
2563 reordering[dst + i] = dst + n + i;
2564 for (i = 0; i < len - src - n; ++i)
2565 reordering[src + n + i] = src + n + i;
2567 for (i = 0; i < src; ++i)
2569 for (i = 0; i < n; ++i)
2570 reordering[src + i] = dst + i;
2571 for (i = 0; i < dst - src; ++i)
2572 reordering[src + n + i] = src + i;
2573 for (i = 0; i < len - dst - n; ++i)
2574 reordering[dst + n + i] = dst + n + i;
2580 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2581 __isl_take isl_qpolynomial *qp,
2582 enum isl_dim_type dst_type, unsigned dst_pos,
2583 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2589 qp = isl_qpolynomial_cow(qp);
2593 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2596 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2597 g_src_pos = pos(qp->dim, src_type) + src_pos;
2598 if (dst_type > src_type)
2601 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2608 reordering = reordering_move(qp->dim->ctx,
2609 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2613 qp->upoly = reorder(qp->upoly, reordering);
2618 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2624 isl_qpolynomial_free(qp);
2628 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2629 isl_int *f, isl_int denom)
2631 struct isl_upoly *up;
2636 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2638 return isl_qpolynomial_alloc(dim, 0, up);
2641 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2642 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2646 struct isl_upoly *up;
2647 isl_qpolynomial *qp;
2653 isl_int_init(denom);
2655 isl_constraint_get_coefficient(c, type, pos, &denom);
2656 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2657 sgn = isl_int_sgn(denom);
2658 isl_int_abs(denom, denom);
2659 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2660 1 + isl_constraint_dim(c, isl_dim_all));
2662 isl_int_neg(denom, denom);
2663 isl_constraint_set_coefficient(c, type, pos, denom);
2665 dim = isl_dim_copy(c->bmap->dim);
2667 isl_int_clear(denom);
2668 isl_constraint_free(c);
2670 qp = isl_qpolynomial_alloc(dim, 0, up);
2672 qp = isl_qpolynomial_neg(qp);
2676 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2677 * in "qp" by subs[i].
2679 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2680 __isl_take isl_qpolynomial *qp,
2681 enum isl_dim_type type, unsigned first, unsigned n,
2682 __isl_keep isl_qpolynomial **subs)
2685 struct isl_upoly **ups;
2690 qp = isl_qpolynomial_cow(qp);
2693 for (i = 0; i < n; ++i)
2697 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2700 for (i = 0; i < n; ++i)
2701 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2704 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2705 for (i = 0; i < n; ++i)
2706 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2708 first += pos(qp->dim, type);
2710 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2713 for (i = 0; i < n; ++i)
2714 ups[i] = subs[i]->upoly;
2716 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2725 isl_qpolynomial_free(qp);
2729 /* Extend "bset" with extra set dimensions for each integer division
2730 * in "qp" and then call "fn" with the extended bset and the polynomial
2731 * that results from replacing each of the integer divisions by the
2732 * corresponding extra set dimension.
2734 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2735 __isl_keep isl_basic_set *bset,
2736 int (*fn)(__isl_take isl_basic_set *bset,
2737 __isl_take isl_qpolynomial *poly, void *user), void *user)
2741 isl_qpolynomial *poly;
2745 if (qp->div->n_row == 0)
2746 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
2749 div = isl_mat_copy(qp->div);
2750 dim = isl_dim_copy(qp->dim);
2751 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
2752 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
2753 bset = isl_basic_set_copy(bset);
2754 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
2755 bset = add_div_constraints(bset, div);
2757 return fn(bset, poly, user);
2762 /* Return total degree in variables first (inclusive) up to last (exclusive).
2764 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
2768 struct isl_upoly_rec *rec;
2772 if (isl_upoly_is_zero(up))
2774 if (isl_upoly_is_cst(up) || up->var < first)
2777 rec = isl_upoly_as_rec(up);
2781 for (i = 0; i < rec->n; ++i) {
2784 if (isl_upoly_is_zero(rec->p[i]))
2786 d = isl_upoly_degree(rec->p[i], first, last);
2796 /* Return total degree in set variables.
2798 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
2806 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2807 nvar = isl_dim_size(poly->dim, isl_dim_set);
2808 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
2811 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
2812 unsigned pos, int deg)
2815 struct isl_upoly_rec *rec;
2820 if (isl_upoly_is_cst(up) || up->var < pos) {
2822 return isl_upoly_copy(up);
2824 return isl_upoly_zero(up->ctx);
2827 rec = isl_upoly_as_rec(up);
2831 if (up->var == pos) {
2833 return isl_upoly_copy(rec->p[deg]);
2835 return isl_upoly_zero(up->ctx);
2838 up = isl_upoly_copy(up);
2839 up = isl_upoly_cow(up);
2840 rec = isl_upoly_as_rec(up);
2844 for (i = 0; i < rec->n; ++i) {
2845 struct isl_upoly *t;
2846 t = isl_upoly_coeff(rec->p[i], pos, deg);
2849 isl_upoly_free(rec->p[i]);
2859 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
2861 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
2862 __isl_keep isl_qpolynomial *qp,
2863 enum isl_dim_type type, unsigned t_pos, int deg)
2866 struct isl_upoly *up;
2872 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
2875 g_pos = pos(qp->dim, type) + t_pos;
2876 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
2878 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
2881 isl_mat_free(c->div);
2882 c->div = isl_mat_copy(qp->div);
2887 isl_qpolynomial_free(c);
2891 /* Homogenize the polynomial in the variables first (inclusive) up to
2892 * last (exclusive) by inserting powers of variable first.
2893 * Variable first is assumed not to appear in the input.
2895 __isl_give struct isl_upoly *isl_upoly_homogenize(
2896 __isl_take struct isl_upoly *up, int deg, int target,
2897 int first, int last)
2900 struct isl_upoly_rec *rec;
2904 if (isl_upoly_is_zero(up))
2908 if (isl_upoly_is_cst(up) || up->var < first) {
2909 struct isl_upoly *hom;
2911 hom = isl_upoly_pow(up->ctx, first, target - deg);
2914 rec = isl_upoly_as_rec(hom);
2915 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
2920 up = isl_upoly_cow(up);
2921 rec = isl_upoly_as_rec(up);
2925 for (i = 0; i < rec->n; ++i) {
2926 if (isl_upoly_is_zero(rec->p[i]))
2928 rec->p[i] = isl_upoly_homogenize(rec->p[i],
2929 up->var < last ? deg + i : i, target,
2941 /* Homogenize the polynomial in the set variables by introducing
2942 * powers of an extra set variable at position 0.
2944 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
2945 __isl_take isl_qpolynomial *poly)
2949 int deg = isl_qpolynomial_degree(poly);
2954 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
2955 poly = isl_qpolynomial_cow(poly);
2959 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2960 nvar = isl_dim_size(poly->dim, isl_dim_set);
2961 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
2968 isl_qpolynomial_free(poly);
2972 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
2973 __isl_take isl_mat *div)
2981 n = isl_dim_total(dim) + div->n_row;
2983 term = isl_calloc(dim->ctx, struct isl_term,
2984 sizeof(struct isl_term) + (n - 1) * sizeof(int));
2991 isl_int_init(term->n);
2992 isl_int_init(term->d);
3001 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3010 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3019 total = isl_dim_total(term->dim) + term->div->n_row;
3021 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3025 isl_int_set(dup->n, term->n);
3026 isl_int_set(dup->d, term->d);
3028 for (i = 0; i < total; ++i)
3029 dup->pow[i] = term->pow[i];
3034 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3042 return isl_term_dup(term);
3045 void isl_term_free(__isl_take isl_term *term)
3050 if (--term->ref > 0)
3053 isl_dim_free(term->dim);
3054 isl_mat_free(term->div);
3055 isl_int_clear(term->n);
3056 isl_int_clear(term->d);
3060 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3068 case isl_dim_out: return isl_dim_size(term->dim, type);
3069 case isl_dim_div: return term->div->n_row;
3070 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3075 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3077 return term ? term->dim->ctx : NULL;
3080 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3084 isl_int_set(*n, term->n);
3087 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3091 isl_int_set(*d, term->d);
3094 int isl_term_get_exp(__isl_keep isl_term *term,
3095 enum isl_dim_type type, unsigned pos)
3100 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3102 if (type >= isl_dim_set)
3103 pos += isl_dim_size(term->dim, isl_dim_param);
3104 if (type >= isl_dim_div)
3105 pos += isl_dim_size(term->dim, isl_dim_set);
3107 return term->pow[pos];
3110 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3112 isl_basic_map *bmap;
3119 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3122 total = term->div->n_col - term->div->n_row - 2;
3123 /* No nested divs for now */
3124 isl_assert(term->dim->ctx,
3125 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3126 term->div->n_row) == -1,
3129 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3130 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3133 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3135 return isl_basic_map_div(bmap, k);
3137 isl_basic_map_free(bmap);
3141 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3142 int (*fn)(__isl_take isl_term *term, void *user),
3143 __isl_take isl_term *term, void *user)
3146 struct isl_upoly_rec *rec;
3151 if (isl_upoly_is_zero(up))
3154 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3155 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3156 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3158 if (isl_upoly_is_cst(up)) {
3159 struct isl_upoly_cst *cst;
3160 cst = isl_upoly_as_cst(up);
3163 term = isl_term_cow(term);
3166 isl_int_set(term->n, cst->n);
3167 isl_int_set(term->d, cst->d);
3168 if (fn(isl_term_copy(term), user) < 0)
3173 rec = isl_upoly_as_rec(up);
3177 for (i = 0; i < rec->n; ++i) {
3178 term = isl_term_cow(term);
3181 term->pow[up->var] = i;
3182 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3186 term->pow[up->var] = 0;
3190 isl_term_free(term);
3194 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3195 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3202 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3206 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3208 isl_term_free(term);
3210 return term ? 0 : -1;
3213 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3215 struct isl_upoly *up;
3216 isl_qpolynomial *qp;
3222 n = isl_dim_total(term->dim) + term->div->n_row;
3224 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3225 for (i = 0; i < n; ++i) {
3228 up = isl_upoly_mul(up,
3229 isl_upoly_pow(term->dim->ctx, i, term->pow[i]));
3232 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3235 isl_mat_free(qp->div);
3236 qp->div = isl_mat_copy(term->div);
3240 isl_term_free(term);
3243 isl_qpolynomial_free(qp);
3244 isl_term_free(term);
3248 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3249 __isl_take isl_dim *dim)
3258 if (isl_dim_equal(qp->dim, dim)) {
3263 qp = isl_qpolynomial_cow(qp);
3267 extra = isl_dim_size(dim, isl_dim_set) -
3268 isl_dim_size(qp->dim, isl_dim_set);
3269 total = isl_dim_total(qp->dim);
3270 if (qp->div->n_row) {
3273 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3276 for (i = 0; i < qp->div->n_row; ++i)
3278 qp->upoly = expand(qp->upoly, exp, total);
3283 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3286 for (i = 0; i < qp->div->n_row; ++i)
3287 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3289 isl_dim_free(qp->dim);
3295 isl_qpolynomial_free(qp);
3299 /* For each parameter or variable that does not appear in qp,
3300 * first eliminate the variable from all constraints and then set it to zero.
3302 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3303 __isl_keep isl_qpolynomial *qp)
3314 d = isl_dim_total(set->dim);
3315 active = isl_calloc_array(set->ctx, int, d);
3316 if (set_active(qp, active) < 0)
3319 for (i = 0; i < d; ++i)
3328 nparam = isl_dim_size(set->dim, isl_dim_param);
3329 nvar = isl_dim_size(set->dim, isl_dim_set);
3330 for (i = 0; i < nparam; ++i) {
3333 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3334 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3336 for (i = 0; i < nvar; ++i) {
3337 if (active[nparam + i])
3339 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3340 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3352 struct isl_opt_data {
3353 isl_qpolynomial *qp;
3355 isl_qpolynomial *opt;
3359 static int opt_fn(__isl_take isl_point *pnt, void *user)
3361 struct isl_opt_data *data = (struct isl_opt_data *)user;
3362 isl_qpolynomial *val;
3364 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3368 } else if (data->max) {
3369 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3371 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3377 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3378 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3380 struct isl_opt_data data = { NULL, 1, NULL, max };
3385 if (isl_upoly_is_cst(qp->upoly)) {
3390 set = fix_inactive(set, qp);
3393 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3397 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3400 isl_qpolynomial_free(qp);
3404 isl_qpolynomial_free(qp);
3405 isl_qpolynomial_free(data.opt);
3409 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3410 __isl_take isl_morph *morph)
3415 struct isl_upoly *up;
3417 struct isl_upoly **subs;
3420 qp = isl_qpolynomial_cow(qp);
3425 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3427 n_sub = morph->inv->n_row - 1;
3428 if (morph->inv->n_row != morph->inv->n_col)
3429 n_sub += qp->div->n_row;
3430 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3434 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3435 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3436 morph->inv->row[0][0], morph->inv->n_col);
3437 if (morph->inv->n_row != morph->inv->n_col)
3438 for (i = 0; i < qp->div->n_row; ++i)
3439 subs[morph->inv->n_row - 1 + i] =
3440 isl_upoly_pow(ctx, morph->inv->n_col - 1 + i, 1);
3442 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3444 for (i = 0; i < n_sub; ++i)
3445 isl_upoly_free(subs[i]);
3448 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3449 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3450 qp->div = isl_mat_product(qp->div, mat);
3451 isl_dim_free(qp->dim);
3452 qp->dim = isl_dim_copy(morph->ran->dim);
3454 if (!qp->upoly || !qp->div || !qp->dim)
3457 isl_morph_free(morph);
3461 isl_qpolynomial_free(qp);
3462 isl_morph_free(morph);
3466 static int neg_entry(void **entry, void *user)
3468 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3470 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3472 return *pwqp ? 0 : -1;
3475 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3476 __isl_take isl_union_pw_qpolynomial *upwqp)
3478 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3482 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3483 &neg_entry, NULL) < 0)
3488 isl_union_pw_qpolynomial_free(upwqp);
3492 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3493 __isl_take isl_union_pw_qpolynomial *upwqp1,
3494 __isl_take isl_union_pw_qpolynomial *upwqp2)
3496 return isl_union_pw_qpolynomial_add(upwqp1,
3497 isl_union_pw_qpolynomial_neg(upwqp2));
3500 static int mul_entry(void **entry, void *user)
3502 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3504 struct isl_hash_table_entry *entry2;
3505 isl_pw_qpolynomial *pwpq = *entry;
3508 hash = isl_dim_get_hash(pwpq->dim);
3509 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3510 hash, &has_dim, pwpq->dim, 0);
3514 pwpq = isl_pw_qpolynomial_copy(pwpq);
3515 pwpq = isl_pw_qpolynomial_mul(pwpq,
3516 isl_pw_qpolynomial_copy(entry2->data));
3518 empty = isl_pw_qpolynomial_is_zero(pwpq);
3520 isl_pw_qpolynomial_free(pwpq);
3524 isl_pw_qpolynomial_free(pwpq);
3528 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3533 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3534 __isl_take isl_union_pw_qpolynomial *upwqp1,
3535 __isl_take isl_union_pw_qpolynomial *upwqp2)
3537 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3540 /* Reorder the columns of the given div definitions according to the
3543 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3544 __isl_take isl_reordering *r)
3553 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3554 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3558 for (i = 0; i < div->n_row; ++i) {
3559 isl_seq_cpy(mat->row[i], div->row[i], 2);
3560 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3561 for (j = 0; j < r->len; ++j)
3562 isl_int_set(mat->row[i][2 + r->pos[j]],
3563 div->row[i][2 + j]);
3566 isl_reordering_free(r);
3570 isl_reordering_free(r);
3575 /* Reorder the dimension of "qp" according to the given reordering.
3577 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3578 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3580 qp = isl_qpolynomial_cow(qp);
3584 r = isl_reordering_extend(r, qp->div->n_row);
3588 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3592 qp->upoly = reorder(qp->upoly, r->pos);
3596 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3598 isl_reordering_free(r);
3601 isl_qpolynomial_free(qp);
3602 isl_reordering_free(r);
3606 struct isl_split_periods_data {
3608 isl_pw_qpolynomial *res;
3611 /* Create a slice where the integer division "div" has the fixed value "v".
3612 * In particular, if "div" refers to floor(f/m), then create a slice
3614 * m v <= f <= m v + (m - 1)
3619 * -f + m v + (m - 1) >= 0
3621 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3622 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3625 isl_basic_set *bset = NULL;
3631 total = isl_dim_total(dim);
3632 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3634 k = isl_basic_set_alloc_inequality(bset);
3637 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3638 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3640 k = isl_basic_set_alloc_inequality(bset);
3643 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3644 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3645 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3646 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3649 return isl_set_from_basic_set(bset);
3651 isl_basic_set_free(bset);
3656 static int split_periods(__isl_take isl_set *set,
3657 __isl_take isl_qpolynomial *qp, void *user);
3659 /* Create a slice of the domain "set" such that integer division "div"
3660 * has the fixed value "v" and add the results to data->res,
3661 * replacing the integer division by "v" in "qp".
3663 static int set_div(__isl_take isl_set *set,
3664 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3665 struct isl_split_periods_data *data)
3670 struct isl_upoly *cst;
3672 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3673 set = isl_set_intersect(set, slice);
3678 total = isl_dim_total(qp->dim);
3680 for (i = div + 1; i < qp->div->n_row; ++i) {
3681 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3683 isl_int_addmul(qp->div->row[i][1],
3684 qp->div->row[i][2 + total + div], v);
3685 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3688 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3689 qp = substitute_div(qp, div, cst);
3691 return split_periods(set, qp, data);
3694 isl_qpolynomial_free(qp);
3698 /* Split the domain "set" such that integer division "div"
3699 * has a fixed value (ranging from "min" to "max") on each slice
3700 * and add the results to data->res.
3702 static int split_div(__isl_take isl_set *set,
3703 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
3704 struct isl_split_periods_data *data)
3706 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
3707 isl_set *set_i = isl_set_copy(set);
3708 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
3710 if (set_div(set_i, qp_i, div, min, data) < 0)
3714 isl_qpolynomial_free(qp);
3718 isl_qpolynomial_free(qp);
3722 /* If "qp" refers to any integer division
3723 * that can only attain "max_periods" distinct values on "set"
3724 * then split the domain along those distinct values.
3725 * Add the results (or the original if no splitting occurs)
3728 static int split_periods(__isl_take isl_set *set,
3729 __isl_take isl_qpolynomial *qp, void *user)
3732 isl_pw_qpolynomial *pwqp;
3733 struct isl_split_periods_data *data;
3738 data = (struct isl_split_periods_data *)user;
3743 if (qp->div->n_row == 0) {
3744 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3745 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3751 total = isl_dim_total(qp->dim);
3752 for (i = 0; i < qp->div->n_row; ++i) {
3753 enum isl_lp_result lp_res;
3755 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
3756 qp->div->n_row) != -1)
3759 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
3760 set->ctx->one, &min, NULL, NULL);
3761 if (lp_res == isl_lp_error)
3763 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3765 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
3767 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
3768 set->ctx->one, &max, NULL, NULL);
3769 if (lp_res == isl_lp_error)
3771 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3773 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
3775 isl_int_sub(max, max, min);
3776 if (isl_int_cmp_si(max, data->max_periods) < 0) {
3777 isl_int_add(max, max, min);
3782 if (i < qp->div->n_row) {
3783 r = split_div(set, qp, i, min, max, data);
3785 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3786 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3798 isl_qpolynomial_free(qp);
3802 /* If any quasi-polynomial in pwqp refers to any integer division
3803 * that can only attain "max_periods" distinct values on its domain
3804 * then split the domain along those distinct values.
3806 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
3807 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
3809 struct isl_split_periods_data data;
3811 data.max_periods = max_periods;
3812 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
3814 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
3817 isl_pw_qpolynomial_free(pwqp);
3821 isl_pw_qpolynomial_free(data.res);
3822 isl_pw_qpolynomial_free(pwqp);
3826 /* Construct a piecewise quasipolynomial that is constant on the given
3827 * domain. In particular, it is
3830 * infinity if cst == -1
3832 static __isl_give isl_pw_qpolynomial *constant_on_domain(
3833 __isl_take isl_basic_set *bset, int cst)
3836 isl_qpolynomial *qp;
3841 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
3842 dim = isl_basic_set_get_dim(bset);
3844 qp = isl_qpolynomial_infty(dim);
3846 qp = isl_qpolynomial_zero(dim);
3848 qp = isl_qpolynomial_one(dim);
3849 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
3852 /* Factor bset, call fn on each of the factors and return the product.
3854 * If no factors can be found, simply call fn on the input.
3855 * Otherwise, construct the factors based on the factorizer,
3856 * call fn on each factor and compute the product.
3858 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
3859 __isl_take isl_basic_set *bset,
3860 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
3866 isl_qpolynomial *qp;
3867 isl_pw_qpolynomial *pwqp;
3871 f = isl_basic_set_factorizer(bset);
3874 if (f->n_group == 0) {
3875 isl_factorizer_free(f);
3879 nparam = isl_basic_set_dim(bset, isl_dim_param);
3880 nvar = isl_basic_set_dim(bset, isl_dim_set);
3882 dim = isl_basic_set_get_dim(bset);
3883 dim = isl_dim_domain(dim);
3884 set = isl_set_universe(isl_dim_copy(dim));
3885 qp = isl_qpolynomial_one(dim);
3886 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3888 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
3890 for (i = 0, n = 0; i < f->n_group; ++i) {
3891 isl_basic_set *bset_i;
3892 isl_pw_qpolynomial *pwqp_i;
3894 bset_i = isl_basic_set_copy(bset);
3895 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
3896 nparam + n + f->len[i], nvar - n - f->len[i]);
3897 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
3899 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
3900 n + f->len[i], nvar - n - f->len[i]);
3901 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
3903 pwqp_i = fn(bset_i);
3904 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
3909 isl_basic_set_free(bset);
3910 isl_factorizer_free(f);
3914 isl_basic_set_free(bset);
3918 /* Factor bset, call fn on each of the factors and return the product.
3919 * The function is assumed to evaluate to zero on empty domains,
3920 * to one on zero-dimensional domains and to infinity on unbounded domains
3921 * and will not be called explicitly on zero-dimensional or unbounded domains.
3923 * We first check for some special cases and remove all equalities.
3924 * Then we hand over control to compressed_multiplicative_call.
3926 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
3927 __isl_take isl_basic_set *bset,
3928 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
3932 isl_pw_qpolynomial *pwqp;
3933 unsigned orig_nvar, final_nvar;
3938 if (isl_basic_set_fast_is_empty(bset))
3939 return constant_on_domain(bset, 0);
3941 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
3944 return constant_on_domain(bset, 1);
3946 bounded = isl_basic_set_is_bounded(bset);
3950 return constant_on_domain(bset, -1);
3952 if (bset->n_eq == 0)
3953 return compressed_multiplicative_call(bset, fn);
3955 morph = isl_basic_set_full_compression(bset);
3956 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
3958 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
3960 pwqp = compressed_multiplicative_call(bset, fn);
3962 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
3963 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
3964 morph = isl_morph_inverse(morph);
3966 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
3970 isl_basic_set_free(bset);
3974 /* Drop all floors in "qp", turning each integer division [a/m] into
3975 * a rational division a/m. If "down" is set, then the integer division
3976 * is replaces by (a-(m-1))/m instead.
3978 static __isl_give isl_qpolynomial *qp_drop_floors(
3979 __isl_take isl_qpolynomial *qp, int down)
3982 struct isl_upoly *s;
3986 if (qp->div->n_row == 0)
3989 qp = isl_qpolynomial_cow(qp);
3993 for (i = qp->div->n_row - 1; i >= 0; --i) {
3995 isl_int_sub(qp->div->row[i][1],
3996 qp->div->row[i][1], qp->div->row[i][0]);
3997 isl_int_add_ui(qp->div->row[i][1],
3998 qp->div->row[i][1], 1);
4000 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4001 qp->div->row[i][0], qp->div->n_col - 1);
4002 qp = substitute_div(qp, i, s);
4010 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4011 * a rational division a/m.
4013 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4014 __isl_take isl_pw_qpolynomial *pwqp)
4021 if (isl_pw_qpolynomial_is_zero(pwqp))
4024 pwqp = isl_pw_qpolynomial_cow(pwqp);
4028 for (i = 0; i < pwqp->n; ++i) {
4029 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4036 isl_pw_qpolynomial_free(pwqp);
4040 /* Adjust all the integer divisions in "qp" such that they are at least
4041 * one over the given orthant (identified by "signs"). This ensures
4042 * that they will still be non-negative even after subtracting (m-1)/m.
4044 * In particular, f is replaced by f' + v, changing f = [a/m]
4045 * to f' = [(a - m v)/m].
4046 * If the constant term k in a is smaller than m,
4047 * the constant term of v is set to floor(k/m) - 1.
4048 * For any other term, if the coefficient c and the variable x have
4049 * the same sign, then no changes are needed.
4050 * Otherwise, if the variable is positive (and c is negative),
4051 * then the coefficient of x in v is set to floor(c/m).
4052 * If the variable is negative (and c is positive),
4053 * then the coefficient of x in v is set to ceil(c/m).
4055 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4061 struct isl_upoly *s;
4063 qp = isl_qpolynomial_cow(qp);
4066 qp->div = isl_mat_cow(qp->div);
4070 total = isl_dim_total(qp->dim);
4071 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4073 for (i = 0; i < qp->div->n_row; ++i) {
4074 isl_int *row = qp->div->row[i];
4078 if (isl_int_lt(row[1], row[0])) {
4079 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4080 isl_int_sub_ui(v->el[0], v->el[0], 1);
4081 isl_int_submul(row[1], row[0], v->el[0]);
4083 for (j = 0; j < total; ++j) {
4084 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4087 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4089 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4090 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4092 for (j = 0; j < i; ++j) {
4093 if (isl_int_sgn(row[2 + total + j]) >= 0)
4095 isl_int_fdiv_q(v->el[1 + total + j],
4096 row[2 + total + j], row[0]);
4097 isl_int_submul(row[2 + total + j],
4098 row[0], v->el[1 + total + j]);
4100 for (j = i + 1; j < qp->div->n_row; ++j) {
4101 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4103 isl_seq_combine(qp->div->row[j] + 1,
4104 qp->div->ctx->one, qp->div->row[j] + 1,
4105 qp->div->row[j][2 + total + i], v->el, v->size);
4107 isl_int_set_si(v->el[1 + total + i], 1);
4108 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4109 qp->div->ctx->one, v->size);
4110 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4120 isl_qpolynomial_free(qp);
4124 struct isl_to_poly_data {
4126 isl_pw_qpolynomial *res;
4127 isl_qpolynomial *qp;
4130 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4131 * We first make all integer divisions positive and then split the
4132 * quasipolynomials into terms with sign data->sign (the direction
4133 * of the requested approximation) and terms with the opposite sign.
4134 * In the first set of terms, each integer division [a/m] is
4135 * overapproximated by a/m, while in the second it is underapproximated
4138 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4141 struct isl_to_poly_data *data = user;
4142 isl_pw_qpolynomial *t;
4143 isl_qpolynomial *qp, *up, *down;
4145 qp = isl_qpolynomial_copy(data->qp);
4146 qp = make_divs_pos(qp, signs);
4148 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4149 up = qp_drop_floors(up, 0);
4150 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4151 down = qp_drop_floors(down, 1);
4153 isl_qpolynomial_free(qp);
4154 qp = isl_qpolynomial_add(up, down);
4156 t = isl_pw_qpolynomial_alloc(orthant, qp);
4157 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4162 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4163 * the polynomial will be an overapproximation. If "sign" is negative,
4164 * it will be an underapproximation. If "sign" is zero, the approximation
4165 * will lie somewhere in between.
4167 * In particular, is sign == 0, we simply drop the floors, turning
4168 * the integer divisions into rational divisions.
4169 * Otherwise, we split the domains into orthants, make all integer divisions
4170 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4171 * depending on the requested sign and the sign of the term in which
4172 * the integer division appears.
4174 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4175 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4178 struct isl_to_poly_data data;
4181 return pwqp_drop_floors(pwqp);
4187 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4189 for (i = 0; i < pwqp->n; ++i) {
4190 if (pwqp->p[i].qp->div->n_row == 0) {
4191 isl_pw_qpolynomial *t;
4192 t = isl_pw_qpolynomial_alloc(
4193 isl_set_copy(pwqp->p[i].set),
4194 isl_qpolynomial_copy(pwqp->p[i].qp));
4195 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4198 data.qp = pwqp->p[i].qp;
4199 if (isl_set_foreach_orthant(pwqp->p[i].set,
4200 &to_polynomial_on_orthant, &data) < 0)
4204 isl_pw_qpolynomial_free(pwqp);
4208 isl_pw_qpolynomial_free(pwqp);
4209 isl_pw_qpolynomial_free(data.res);
4213 static int poly_entry(void **entry, void *user)
4216 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4218 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4220 return *pwqp ? 0 : -1;
4223 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4224 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4226 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4230 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4231 &poly_entry, &sign) < 0)
4236 isl_union_pw_qpolynomial_free(upwqp);