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 struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
878 struct isl_upoly *res;
886 res = isl_upoly_copy(up);
888 res = isl_upoly_one(up->ctx);
890 while (power >>= 1) {
891 up = isl_upoly_mul(up, isl_upoly_copy(up));
893 res = isl_upoly_mul(res, isl_upoly_copy(up));
900 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
901 unsigned n_div, __isl_take struct isl_upoly *up)
903 struct isl_qpolynomial *qp = NULL;
909 total = isl_dim_total(dim);
911 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
916 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
927 isl_qpolynomial_free(qp);
931 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
940 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
942 struct isl_qpolynomial *dup;
947 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
948 isl_upoly_copy(qp->upoly));
951 isl_mat_free(dup->div);
952 dup->div = isl_mat_copy(qp->div);
958 isl_qpolynomial_free(dup);
962 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
970 return isl_qpolynomial_dup(qp);
973 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
981 isl_dim_free(qp->dim);
982 isl_mat_free(qp->div);
983 isl_upoly_free(qp->upoly);
988 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
991 struct isl_upoly *up;
992 struct isl_upoly_rec *rec;
993 struct isl_upoly_cst *cst;
995 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
998 for (i = 0; i < 1 + power; ++i) {
999 rec->p[i] = isl_upoly_zero(ctx);
1004 cst = isl_upoly_as_cst(rec->p[power]);
1005 isl_int_set_si(cst->n, 1);
1009 isl_upoly_free(&rec->up);
1013 /* r array maps original positions to new positions.
1015 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1019 struct isl_upoly_rec *rec;
1020 struct isl_upoly *base;
1021 struct isl_upoly *res;
1023 if (isl_upoly_is_cst(up))
1026 rec = isl_upoly_as_rec(up);
1030 isl_assert(up->ctx, rec->n >= 1, goto error);
1032 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1033 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1035 for (i = rec->n - 2; i >= 0; --i) {
1036 res = isl_upoly_mul(res, isl_upoly_copy(base));
1037 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1040 isl_upoly_free(base);
1049 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1054 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1055 div1->n_col >= div2->n_col, return -1);
1057 if (div1->n_row == div2->n_row)
1058 return isl_mat_is_equal(div1, div2);
1060 n_row = div1->n_row;
1061 n_col = div1->n_col;
1062 div1->n_row = div2->n_row;
1063 div1->n_col = div2->n_col;
1065 equal = isl_mat_is_equal(div1, div2);
1067 div1->n_row = n_row;
1068 div1->n_col = n_col;
1073 static void expand_row(__isl_keep isl_mat *dst, int d,
1074 __isl_keep isl_mat *src, int s, int *exp)
1077 unsigned c = src->n_col - src->n_row;
1079 isl_seq_cpy(dst->row[d], src->row[s], c);
1080 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
1082 for (i = 0; i < s; ++i)
1083 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
1086 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1090 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1091 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1096 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1099 struct isl_div_sort_info {
1104 static int div_sort_cmp(const void *p1, const void *p2)
1106 const struct isl_div_sort_info *i1, *i2;
1107 i1 = (const struct isl_div_sort_info *) p1;
1108 i2 = (const struct isl_div_sort_info *) p2;
1110 return cmp_row(i1->div, i1->row, i2->row);
1113 /* Sort divs and remove duplicates.
1115 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1120 struct isl_div_sort_info *array = NULL;
1121 int *pos = NULL, *at = NULL;
1122 int *reordering = NULL;
1127 if (qp->div->n_row <= 1)
1130 div_pos = isl_dim_total(qp->dim);
1132 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1134 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1135 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1136 len = qp->div->n_col - 2;
1137 reordering = isl_alloc_array(qp->div->ctx, int, len);
1138 if (!array || !pos || !at || !reordering)
1141 for (i = 0; i < qp->div->n_row; ++i) {
1142 array[i].div = qp->div;
1148 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1151 for (i = 0; i < div_pos; ++i)
1154 for (i = 0; i < qp->div->n_row; ++i) {
1155 if (pos[array[i].row] == i)
1157 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1158 pos[at[i]] = pos[array[i].row];
1159 at[pos[array[i].row]] = at[i];
1160 at[i] = array[i].row;
1161 pos[array[i].row] = i;
1165 for (i = 0; i < len - div_pos; ++i) {
1167 isl_seq_eq(qp->div->row[i - skip - 1],
1168 qp->div->row[i - skip], qp->div->n_col)) {
1169 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1170 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1171 2 + div_pos + i - skip);
1172 qp->div = isl_mat_drop_cols(qp->div,
1173 2 + div_pos + i - skip, 1);
1176 reordering[div_pos + array[i].row] = div_pos + i - skip;
1179 qp->upoly = reorder(qp->upoly, reordering);
1181 if (!qp->upoly || !qp->div)
1195 isl_qpolynomial_free(qp);
1199 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1200 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1203 isl_mat *div = NULL;
1204 unsigned d = div1->n_col - div1->n_row;
1206 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1207 d + div1->n_row + div2->n_row);
1211 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1214 expand_row(div, k, div1, i, exp1);
1215 expand_row(div, k + 1, div2, j, exp2);
1217 cmp = cmp_row(div, k, k + 1);
1221 } else if (cmp < 0) {
1225 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1228 for (; i < div1->n_row; ++i, ++k) {
1229 expand_row(div, k, div1, i, exp1);
1232 for (; j < div2->n_row; ++j, ++k) {
1233 expand_row(div, k, div2, j, exp2);
1243 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1244 int *exp, int first)
1247 struct isl_upoly_rec *rec;
1249 if (isl_upoly_is_cst(up))
1252 if (up->var < first)
1255 if (exp[up->var - first] == up->var - first)
1258 up = isl_upoly_cow(up);
1262 up->var = exp[up->var - first] + first;
1264 rec = isl_upoly_as_rec(up);
1268 for (i = 0; i < rec->n; ++i) {
1269 rec->p[i] = expand(rec->p[i], exp, first);
1280 static __isl_give isl_qpolynomial *with_merged_divs(
1281 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1282 __isl_take isl_qpolynomial *qp2),
1283 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1287 isl_mat *div = NULL;
1289 qp1 = isl_qpolynomial_cow(qp1);
1290 qp2 = isl_qpolynomial_cow(qp2);
1295 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1296 qp1->div->n_col >= qp2->div->n_col, goto error);
1298 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1299 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1303 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1307 isl_mat_free(qp1->div);
1308 qp1->div = isl_mat_copy(div);
1309 isl_mat_free(qp2->div);
1310 qp2->div = isl_mat_copy(div);
1312 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1313 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1315 if (!qp1->upoly || !qp2->upoly)
1322 return fn(qp1, qp2);
1327 isl_qpolynomial_free(qp1);
1328 isl_qpolynomial_free(qp2);
1332 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1333 __isl_take isl_qpolynomial *qp2)
1335 qp1 = isl_qpolynomial_cow(qp1);
1340 if (qp1->div->n_row < qp2->div->n_row)
1341 return isl_qpolynomial_add(qp2, qp1);
1343 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1344 if (!compatible_divs(qp1->div, qp2->div))
1345 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1347 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1351 isl_qpolynomial_free(qp2);
1355 isl_qpolynomial_free(qp1);
1356 isl_qpolynomial_free(qp2);
1360 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1361 __isl_keep isl_set *dom,
1362 __isl_take isl_qpolynomial *qp1,
1363 __isl_take isl_qpolynomial *qp2)
1365 return isl_qpolynomial_add(qp1, qp2);
1368 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1369 __isl_take isl_qpolynomial *qp2)
1371 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1374 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1376 qp = isl_qpolynomial_cow(qp);
1381 qp->upoly = isl_upoly_neg(qp->upoly);
1387 isl_qpolynomial_free(qp);
1391 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1392 __isl_take isl_qpolynomial *qp2)
1394 qp1 = isl_qpolynomial_cow(qp1);
1399 if (qp1->div->n_row < qp2->div->n_row)
1400 return isl_qpolynomial_mul(qp2, qp1);
1402 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1403 if (!compatible_divs(qp1->div, qp2->div))
1404 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1406 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1410 isl_qpolynomial_free(qp2);
1414 isl_qpolynomial_free(qp1);
1415 isl_qpolynomial_free(qp2);
1419 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1422 qp = isl_qpolynomial_cow(qp);
1427 qp->upoly = isl_upoly_pow(qp->upoly, power);
1433 isl_qpolynomial_free(qp);
1437 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1439 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1442 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1444 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1447 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1449 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1452 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1454 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1457 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1459 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1462 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1465 struct isl_qpolynomial *qp;
1466 struct isl_upoly_cst *cst;
1468 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1472 cst = isl_upoly_as_cst(qp->upoly);
1473 isl_int_set(cst->n, v);
1478 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1479 isl_int *n, isl_int *d)
1481 struct isl_upoly_cst *cst;
1486 if (!isl_upoly_is_cst(qp->upoly))
1489 cst = isl_upoly_as_cst(qp->upoly);
1494 isl_int_set(*n, cst->n);
1496 isl_int_set(*d, cst->d);
1501 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1504 struct isl_upoly_rec *rec;
1512 rec = isl_upoly_as_rec(up);
1519 isl_assert(up->ctx, rec->n > 1, return -1);
1521 is_cst = isl_upoly_is_cst(rec->p[1]);
1527 return isl_upoly_is_affine(rec->p[0]);
1530 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1535 if (qp->div->n_row > 0)
1538 return isl_upoly_is_affine(qp->upoly);
1541 static void update_coeff(__isl_keep isl_vec *aff,
1542 __isl_keep struct isl_upoly_cst *cst, int pos)
1547 if (isl_int_is_zero(cst->n))
1552 isl_int_gcd(gcd, cst->d, aff->el[0]);
1553 isl_int_divexact(f, cst->d, gcd);
1554 isl_int_divexact(gcd, aff->el[0], gcd);
1555 isl_seq_scale(aff->el, aff->el, f, aff->size);
1556 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1561 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1562 __isl_keep isl_vec *aff)
1564 struct isl_upoly_cst *cst;
1565 struct isl_upoly_rec *rec;
1571 struct isl_upoly_cst *cst;
1573 cst = isl_upoly_as_cst(up);
1576 update_coeff(aff, cst, 0);
1580 rec = isl_upoly_as_rec(up);
1583 isl_assert(up->ctx, rec->n == 2, return -1);
1585 cst = isl_upoly_as_cst(rec->p[1]);
1588 update_coeff(aff, cst, 1 + up->var);
1590 return isl_upoly_update_affine(rec->p[0], aff);
1593 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1594 __isl_keep isl_qpolynomial *qp)
1602 isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1603 d = isl_dim_total(qp->dim);
1604 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1608 isl_seq_clr(aff->el + 1, 1 + d);
1609 isl_int_set_si(aff->el[0], 1);
1611 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1620 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1621 __isl_keep isl_qpolynomial *qp2)
1626 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1629 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1632 struct isl_upoly_rec *rec;
1634 if (isl_upoly_is_cst(up)) {
1635 struct isl_upoly_cst *cst;
1636 cst = isl_upoly_as_cst(up);
1639 isl_int_lcm(*d, *d, cst->d);
1643 rec = isl_upoly_as_rec(up);
1647 for (i = 0; i < rec->n; ++i)
1648 upoly_update_den(rec->p[i], d);
1651 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1653 isl_int_set_si(*d, 1);
1656 upoly_update_den(qp->upoly, d);
1659 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1662 struct isl_ctx *ctx;
1669 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1672 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1673 enum isl_dim_type type, unsigned pos)
1678 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1679 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1681 if (type == isl_dim_set)
1682 pos += isl_dim_size(dim, isl_dim_param);
1684 return isl_qpolynomial_var_pow(dim, pos, 1);
1690 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1691 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1694 struct isl_upoly_rec *rec;
1695 struct isl_upoly *base, *res;
1700 if (isl_upoly_is_cst(up))
1703 if (up->var < first)
1706 rec = isl_upoly_as_rec(up);
1710 isl_assert(up->ctx, rec->n >= 1, goto error);
1712 if (up->var >= first + n)
1713 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1715 base = isl_upoly_copy(subs[up->var - first]);
1717 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1718 for (i = rec->n - 2; i >= 0; --i) {
1719 struct isl_upoly *t;
1720 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1721 res = isl_upoly_mul(res, isl_upoly_copy(base));
1722 res = isl_upoly_sum(res, t);
1725 isl_upoly_free(base);
1734 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1735 isl_int denom, unsigned len)
1738 struct isl_upoly *up;
1740 isl_assert(ctx, len >= 1, return NULL);
1742 up = isl_upoly_rat_cst(ctx, f[0], denom);
1743 for (i = 0; i < len - 1; ++i) {
1744 struct isl_upoly *t;
1745 struct isl_upoly *c;
1747 if (isl_int_is_zero(f[1 + i]))
1750 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1751 t = isl_upoly_var_pow(ctx, i, 1);
1752 t = isl_upoly_mul(c, t);
1753 up = isl_upoly_sum(up, t);
1759 /* Remove common factor of non-constant terms and denominator.
1761 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1763 isl_ctx *ctx = qp->div->ctx;
1764 unsigned total = qp->div->n_col - 2;
1766 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1767 isl_int_gcd(ctx->normalize_gcd,
1768 ctx->normalize_gcd, qp->div->row[div][0]);
1769 if (isl_int_is_one(ctx->normalize_gcd))
1772 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1773 ctx->normalize_gcd, total);
1774 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1775 ctx->normalize_gcd);
1776 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1777 ctx->normalize_gcd);
1780 /* Replace the integer division identified by "div" by the polynomial "s".
1781 * The integer division is assumed not to appear in the definition
1782 * of any other integer divisions.
1784 static __isl_give isl_qpolynomial *substitute_div(
1785 __isl_take isl_qpolynomial *qp,
1786 int div, __isl_take struct isl_upoly *s)
1795 qp = isl_qpolynomial_cow(qp);
1799 total = isl_dim_total(qp->dim);
1800 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1804 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1807 for (i = 0; i < total + div; ++i)
1809 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1810 reordering[i] = i - 1;
1811 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1812 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1813 qp->upoly = reorder(qp->upoly, reordering);
1816 if (!qp->upoly || !qp->div)
1822 isl_qpolynomial_free(qp);
1827 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1828 * divisions because d is equal to 1 by their definition, i.e., e.
1830 static __isl_give isl_qpolynomial *substitute_non_divs(
1831 __isl_take isl_qpolynomial *qp)
1835 struct isl_upoly *s;
1840 total = isl_dim_total(qp->dim);
1841 for (i = 0; qp && i < qp->div->n_row; ++i) {
1842 if (!isl_int_is_one(qp->div->row[i][0]))
1844 for (j = i + 1; j < qp->div->n_row; ++j) {
1845 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1847 isl_seq_combine(qp->div->row[j] + 1,
1848 qp->div->ctx->one, qp->div->row[j] + 1,
1849 qp->div->row[j][2 + total + i],
1850 qp->div->row[i] + 1, 1 + total + i);
1851 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1852 normalize_div(qp, j);
1854 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1855 qp->div->row[i][0], qp->div->n_col - 1);
1856 qp = substitute_div(qp, i, s);
1863 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1864 * with d the denominator. When replacing the coefficient e of x by
1865 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1866 * inside the division, so we need to add floor(e/d) * x outside.
1867 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1868 * to adjust the coefficient of x in each later div that depends on the
1869 * current div "div" and also in the affine expression "aff"
1870 * (if it too depends on "div").
1872 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1873 __isl_keep isl_vec *aff)
1877 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1880 for (i = 0; i < 1 + total + div; ++i) {
1881 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1882 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1884 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1885 isl_int_fdiv_r(qp->div->row[div][1 + i],
1886 qp->div->row[div][1 + i], qp->div->row[div][0]);
1887 if (!isl_int_is_zero(aff->el[1 + total + div]))
1888 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1889 for (j = div + 1; j < qp->div->n_row; ++j) {
1890 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1892 isl_int_addmul(qp->div->row[j][1 + i],
1893 v, qp->div->row[j][2 + total + div]);
1899 /* Check if the last non-zero coefficient is bigger that half of the
1900 * denominator. If so, we will invert the div to further reduce the number
1901 * of distinct divs that may appear.
1902 * If the last non-zero coefficient is exactly half the denominator,
1903 * then we continue looking for earlier coefficients that are bigger
1904 * than half the denominator.
1906 static int needs_invert(__isl_keep isl_mat *div, int row)
1911 for (i = div->n_col - 1; i >= 1; --i) {
1912 if (isl_int_is_zero(div->row[row][i]))
1914 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1915 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1916 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1926 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1927 * We only invert the coefficients of e (and the coefficient of q in
1928 * later divs and in "aff"). After calling this function, the
1929 * coefficients of e should be reduced again.
1931 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1932 __isl_keep isl_vec *aff)
1934 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1936 isl_seq_neg(qp->div->row[div] + 1,
1937 qp->div->row[div] + 1, qp->div->n_col - 1);
1938 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
1939 isl_int_add(qp->div->row[div][1],
1940 qp->div->row[div][1], qp->div->row[div][0]);
1941 if (!isl_int_is_zero(aff->el[1 + total + div]))
1942 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
1943 isl_mat_col_mul(qp->div, 2 + total + div,
1944 qp->div->ctx->negone, 2 + total + div);
1947 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
1948 * in the interval [0, d-1], with d the denominator and such that the
1949 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
1951 * After the reduction, some divs may have become redundant or identical,
1952 * so we call substitute_non_divs and sort_divs. If these functions
1953 * eliminate divs of merge * two or more divs into one, the coefficients
1954 * of the enclosing divs may have to be reduced again, so we call
1955 * ourselves recursively if the number of divs decreases.
1957 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
1960 isl_vec *aff = NULL;
1961 struct isl_upoly *s;
1967 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
1968 aff = isl_vec_clr(aff);
1972 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
1974 for (i = 0; i < qp->div->n_row; ++i) {
1975 normalize_div(qp, i);
1976 reduce_div(qp, i, aff);
1977 if (needs_invert(qp->div, i)) {
1978 invert_div(qp, i, aff);
1979 reduce_div(qp, i, aff);
1983 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
1984 qp->div->ctx->one, aff->size);
1985 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
1992 n_div = qp->div->n_row;
1993 qp = substitute_non_divs(qp);
1995 if (qp && qp->div->n_row < n_div)
1996 return reduce_divs(qp);
2000 isl_qpolynomial_free(qp);
2005 /* Assumes each div only depends on earlier divs.
2007 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2010 struct isl_qpolynomial *qp = NULL;
2011 struct isl_upoly_rec *rec;
2012 struct isl_upoly_cst *cst;
2019 d = div->line - div->bmap->div;
2021 pos = isl_dim_total(div->bmap->dim) + d;
2022 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2023 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2024 div->bmap->n_div, &rec->up);
2028 for (i = 0; i < div->bmap->n_div; ++i)
2029 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2031 for (i = 0; i < 1 + power; ++i) {
2032 rec->p[i] = isl_upoly_zero(div->ctx);
2037 cst = isl_upoly_as_cst(rec->p[power]);
2038 isl_int_set_si(cst->n, 1);
2042 qp = reduce_divs(qp);
2046 isl_qpolynomial_free(qp);
2051 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2053 return isl_qpolynomial_div_pow(div, 1);
2056 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2057 const isl_int n, const isl_int d)
2059 struct isl_qpolynomial *qp;
2060 struct isl_upoly_cst *cst;
2062 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2066 cst = isl_upoly_as_cst(qp->upoly);
2067 isl_int_set(cst->n, n);
2068 isl_int_set(cst->d, d);
2073 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2075 struct isl_upoly_rec *rec;
2081 if (isl_upoly_is_cst(up))
2085 active[up->var] = 1;
2087 rec = isl_upoly_as_rec(up);
2088 for (i = 0; i < rec->n; ++i)
2089 if (up_set_active(rec->p[i], active, d) < 0)
2095 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2098 int d = isl_dim_total(qp->dim);
2103 for (i = 0; i < d; ++i)
2104 for (j = 0; j < qp->div->n_row; ++j) {
2105 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2111 return up_set_active(qp->upoly, active, d);
2114 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2115 enum isl_dim_type type, unsigned first, unsigned n)
2126 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2128 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2129 type == isl_dim_set, return -1);
2131 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
2132 if (set_active(qp, active) < 0)
2135 if (type == isl_dim_set)
2136 first += isl_dim_size(qp->dim, isl_dim_param);
2137 for (i = 0; i < n; ++i)
2138 if (active[first + i]) {
2151 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2152 unsigned first, unsigned n)
2155 struct isl_upoly_rec *rec;
2159 if (n == 0 || up->var < 0 || up->var < first)
2161 if (up->var < first + n) {
2162 up = replace_by_constant_term(up);
2163 return isl_upoly_drop(up, first, n);
2165 up = isl_upoly_cow(up);
2169 rec = isl_upoly_as_rec(up);
2173 for (i = 0; i < rec->n; ++i) {
2174 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2185 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2186 __isl_take isl_qpolynomial *qp,
2187 enum isl_dim_type type, unsigned pos, const char *s)
2189 qp = isl_qpolynomial_cow(qp);
2192 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2197 isl_qpolynomial_free(qp);
2201 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2202 __isl_take isl_qpolynomial *qp,
2203 enum isl_dim_type type, unsigned first, unsigned n)
2207 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
2210 qp = isl_qpolynomial_cow(qp);
2214 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2216 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2217 type == isl_dim_set, goto error);
2219 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2223 if (type == isl_dim_set)
2224 first += isl_dim_size(qp->dim, isl_dim_param);
2226 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2230 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2236 isl_qpolynomial_free(qp);
2240 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2241 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2247 struct isl_upoly *up;
2251 if (eq->n_eq == 0) {
2252 isl_basic_set_free(eq);
2256 qp = isl_qpolynomial_cow(qp);
2259 qp->div = isl_mat_cow(qp->div);
2263 total = 1 + isl_dim_total(eq->dim);
2265 isl_int_init(denom);
2266 for (i = 0; i < eq->n_eq; ++i) {
2267 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2268 if (j < 0 || j == 0 || j >= total)
2271 for (k = 0; k < qp->div->n_row; ++k) {
2272 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2274 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2275 &qp->div->row[k][0]);
2276 normalize_div(qp, k);
2279 if (isl_int_is_pos(eq->eq[i][j]))
2280 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2281 isl_int_abs(denom, eq->eq[i][j]);
2282 isl_int_set_si(eq->eq[i][j], 0);
2284 up = isl_upoly_from_affine(qp->dim->ctx,
2285 eq->eq[i], denom, total);
2286 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2289 isl_int_clear(denom);
2294 isl_basic_set_free(eq);
2296 qp = substitute_non_divs(qp);
2301 isl_basic_set_free(eq);
2302 isl_qpolynomial_free(qp);
2306 static __isl_give isl_basic_set *add_div_constraints(
2307 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2315 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2318 total = isl_basic_set_total_dim(bset);
2319 for (i = 0; i < div->n_row; ++i)
2320 if (isl_basic_set_add_div_constraints_var(bset,
2321 total - div->n_row + i, div->row[i]) < 0)
2328 isl_basic_set_free(bset);
2332 /* Look for equalities among the variables shared by context and qp
2333 * and the integer divisions of qp, if any.
2334 * The equalities are then used to eliminate variables and/or integer
2335 * divisions from qp.
2337 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2338 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2344 if (qp->div->n_row > 0) {
2345 isl_basic_set *bset;
2346 context = isl_set_add_dims(context, isl_dim_set,
2348 bset = isl_basic_set_universe(isl_set_get_dim(context));
2349 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2350 context = isl_set_intersect(context,
2351 isl_set_from_basic_set(bset));
2354 aff = isl_set_affine_hull(context);
2355 return isl_qpolynomial_substitute_equalities(qp, aff);
2357 isl_qpolynomial_free(qp);
2358 isl_set_free(context);
2363 #define PW isl_pw_qpolynomial
2365 #define EL isl_qpolynomial
2367 #define IS_ZERO is_zero
2371 #include <isl_pw_templ.c>
2374 #define UNION isl_union_pw_qpolynomial
2376 #define PART isl_pw_qpolynomial
2378 #define PARTS pw_qpolynomial
2380 #include <isl_union_templ.c>
2382 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2390 if (!isl_set_fast_is_universe(pwqp->p[0].set))
2393 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2396 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2397 __isl_take isl_pw_qpolynomial *pwqp1,
2398 __isl_take isl_pw_qpolynomial *pwqp2)
2401 struct isl_pw_qpolynomial *res;
2404 if (!pwqp1 || !pwqp2)
2407 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2410 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2411 isl_pw_qpolynomial_free(pwqp2);
2415 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2416 isl_pw_qpolynomial_free(pwqp1);
2420 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2421 isl_pw_qpolynomial_free(pwqp1);
2425 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2426 isl_pw_qpolynomial_free(pwqp2);
2430 n = pwqp1->n * pwqp2->n;
2431 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2433 for (i = 0; i < pwqp1->n; ++i) {
2434 for (j = 0; j < pwqp2->n; ++j) {
2435 struct isl_set *common;
2436 struct isl_qpolynomial *prod;
2437 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2438 isl_set_copy(pwqp2->p[j].set));
2439 if (isl_set_fast_is_empty(common)) {
2440 isl_set_free(common);
2444 prod = isl_qpolynomial_mul(
2445 isl_qpolynomial_copy(pwqp1->p[i].qp),
2446 isl_qpolynomial_copy(pwqp2->p[j].qp));
2448 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2452 isl_pw_qpolynomial_free(pwqp1);
2453 isl_pw_qpolynomial_free(pwqp2);
2457 isl_pw_qpolynomial_free(pwqp1);
2458 isl_pw_qpolynomial_free(pwqp2);
2462 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2463 __isl_take isl_pw_qpolynomial *pwqp)
2470 if (isl_pw_qpolynomial_is_zero(pwqp))
2473 pwqp = isl_pw_qpolynomial_cow(pwqp);
2477 for (i = 0; i < pwqp->n; ++i) {
2478 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2485 isl_pw_qpolynomial_free(pwqp);
2489 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2490 __isl_take isl_pw_qpolynomial *pwqp1,
2491 __isl_take isl_pw_qpolynomial *pwqp2)
2493 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2496 __isl_give struct isl_upoly *isl_upoly_eval(
2497 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2500 struct isl_upoly_rec *rec;
2501 struct isl_upoly *res;
2502 struct isl_upoly *base;
2504 if (isl_upoly_is_cst(up)) {
2509 rec = isl_upoly_as_rec(up);
2513 isl_assert(up->ctx, rec->n >= 1, goto error);
2515 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2517 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2520 for (i = rec->n - 2; i >= 0; --i) {
2521 res = isl_upoly_mul(res, isl_upoly_copy(base));
2522 res = isl_upoly_sum(res,
2523 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2524 isl_vec_copy(vec)));
2527 isl_upoly_free(base);
2537 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2538 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2541 struct isl_upoly *up;
2546 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2548 if (qp->div->n_row == 0)
2549 ext = isl_vec_copy(pnt->vec);
2552 unsigned dim = isl_dim_total(qp->dim);
2553 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2557 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2558 for (i = 0; i < qp->div->n_row; ++i) {
2559 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2560 1 + dim + i, &ext->el[1+dim+i]);
2561 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2562 qp->div->row[i][0]);
2566 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2570 dim = isl_dim_copy(qp->dim);
2571 isl_qpolynomial_free(qp);
2572 isl_point_free(pnt);
2574 return isl_qpolynomial_alloc(dim, 0, up);
2576 isl_qpolynomial_free(qp);
2577 isl_point_free(pnt);
2581 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2582 __isl_keep struct isl_upoly_cst *cst2)
2587 isl_int_mul(t, cst1->n, cst2->d);
2588 isl_int_submul(t, cst2->n, cst1->d);
2589 cmp = isl_int_sgn(t);
2594 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2595 __isl_keep isl_qpolynomial *qp2)
2597 struct isl_upoly_cst *cst1, *cst2;
2601 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2602 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2603 if (isl_qpolynomial_is_nan(qp1))
2605 if (isl_qpolynomial_is_nan(qp2))
2607 cst1 = isl_upoly_as_cst(qp1->upoly);
2608 cst2 = isl_upoly_as_cst(qp2->upoly);
2610 return isl_upoly_cmp(cst1, cst2) <= 0;
2613 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2614 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2616 struct isl_upoly_cst *cst1, *cst2;
2621 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2622 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2623 cst1 = isl_upoly_as_cst(qp1->upoly);
2624 cst2 = isl_upoly_as_cst(qp2->upoly);
2625 cmp = isl_upoly_cmp(cst1, cst2);
2628 isl_qpolynomial_free(qp2);
2630 isl_qpolynomial_free(qp1);
2635 isl_qpolynomial_free(qp1);
2636 isl_qpolynomial_free(qp2);
2640 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2641 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2643 struct isl_upoly_cst *cst1, *cst2;
2648 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2649 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2650 cst1 = isl_upoly_as_cst(qp1->upoly);
2651 cst2 = isl_upoly_as_cst(qp2->upoly);
2652 cmp = isl_upoly_cmp(cst1, cst2);
2655 isl_qpolynomial_free(qp2);
2657 isl_qpolynomial_free(qp1);
2662 isl_qpolynomial_free(qp1);
2663 isl_qpolynomial_free(qp2);
2667 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2668 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2669 unsigned first, unsigned n)
2678 qp = isl_qpolynomial_cow(qp);
2682 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2685 g_pos = pos(qp->dim, type) + first;
2687 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2691 total = qp->div->n_col - 2;
2692 if (total > g_pos) {
2694 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2697 for (i = 0; i < total - g_pos; ++i)
2699 qp->upoly = expand(qp->upoly, exp, g_pos);
2705 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2711 isl_qpolynomial_free(qp);
2715 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2716 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2720 pos = isl_qpolynomial_dim(qp, type);
2722 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2725 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2726 __isl_take isl_pw_qpolynomial *pwqp,
2727 enum isl_dim_type type, unsigned n)
2731 pos = isl_pw_qpolynomial_dim(pwqp, type);
2733 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2736 static int *reordering_move(isl_ctx *ctx,
2737 unsigned len, unsigned dst, unsigned src, unsigned n)
2742 reordering = isl_alloc_array(ctx, int, len);
2747 for (i = 0; i < dst; ++i)
2749 for (i = 0; i < n; ++i)
2750 reordering[src + i] = dst + i;
2751 for (i = 0; i < src - dst; ++i)
2752 reordering[dst + i] = dst + n + i;
2753 for (i = 0; i < len - src - n; ++i)
2754 reordering[src + n + i] = src + n + i;
2756 for (i = 0; i < src; ++i)
2758 for (i = 0; i < n; ++i)
2759 reordering[src + i] = dst + i;
2760 for (i = 0; i < dst - src; ++i)
2761 reordering[src + n + i] = src + i;
2762 for (i = 0; i < len - dst - n; ++i)
2763 reordering[dst + n + i] = dst + n + i;
2769 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2770 __isl_take isl_qpolynomial *qp,
2771 enum isl_dim_type dst_type, unsigned dst_pos,
2772 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2778 qp = isl_qpolynomial_cow(qp);
2782 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2785 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2786 g_src_pos = pos(qp->dim, src_type) + src_pos;
2787 if (dst_type > src_type)
2790 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2797 reordering = reordering_move(qp->dim->ctx,
2798 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2802 qp->upoly = reorder(qp->upoly, reordering);
2807 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2813 isl_qpolynomial_free(qp);
2817 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2818 isl_int *f, isl_int denom)
2820 struct isl_upoly *up;
2825 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2827 return isl_qpolynomial_alloc(dim, 0, up);
2830 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2831 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2835 struct isl_upoly *up;
2836 isl_qpolynomial *qp;
2842 isl_int_init(denom);
2844 isl_constraint_get_coefficient(c, type, pos, &denom);
2845 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2846 sgn = isl_int_sgn(denom);
2847 isl_int_abs(denom, denom);
2848 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2849 1 + isl_constraint_dim(c, isl_dim_all));
2851 isl_int_neg(denom, denom);
2852 isl_constraint_set_coefficient(c, type, pos, denom);
2854 dim = isl_dim_copy(c->bmap->dim);
2856 isl_int_clear(denom);
2857 isl_constraint_free(c);
2859 qp = isl_qpolynomial_alloc(dim, 0, up);
2861 qp = isl_qpolynomial_neg(qp);
2865 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2866 * in "qp" by subs[i].
2868 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2869 __isl_take isl_qpolynomial *qp,
2870 enum isl_dim_type type, unsigned first, unsigned n,
2871 __isl_keep isl_qpolynomial **subs)
2874 struct isl_upoly **ups;
2879 qp = isl_qpolynomial_cow(qp);
2882 for (i = 0; i < n; ++i)
2886 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2889 for (i = 0; i < n; ++i)
2890 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2893 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2894 for (i = 0; i < n; ++i)
2895 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2897 first += pos(qp->dim, type);
2899 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2902 for (i = 0; i < n; ++i)
2903 ups[i] = subs[i]->upoly;
2905 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2914 isl_qpolynomial_free(qp);
2918 /* Extend "bset" with extra set dimensions for each integer division
2919 * in "qp" and then call "fn" with the extended bset and the polynomial
2920 * that results from replacing each of the integer divisions by the
2921 * corresponding extra set dimension.
2923 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2924 __isl_keep isl_basic_set *bset,
2925 int (*fn)(__isl_take isl_basic_set *bset,
2926 __isl_take isl_qpolynomial *poly, void *user), void *user)
2930 isl_qpolynomial *poly;
2934 if (qp->div->n_row == 0)
2935 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
2938 div = isl_mat_copy(qp->div);
2939 dim = isl_dim_copy(qp->dim);
2940 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
2941 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
2942 bset = isl_basic_set_copy(bset);
2943 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
2944 bset = add_div_constraints(bset, div);
2946 return fn(bset, poly, user);
2951 /* Return total degree in variables first (inclusive) up to last (exclusive).
2953 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
2957 struct isl_upoly_rec *rec;
2961 if (isl_upoly_is_zero(up))
2963 if (isl_upoly_is_cst(up) || up->var < first)
2966 rec = isl_upoly_as_rec(up);
2970 for (i = 0; i < rec->n; ++i) {
2973 if (isl_upoly_is_zero(rec->p[i]))
2975 d = isl_upoly_degree(rec->p[i], first, last);
2985 /* Return total degree in set variables.
2987 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
2995 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2996 nvar = isl_dim_size(poly->dim, isl_dim_set);
2997 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3000 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3001 unsigned pos, int deg)
3004 struct isl_upoly_rec *rec;
3009 if (isl_upoly_is_cst(up) || up->var < pos) {
3011 return isl_upoly_copy(up);
3013 return isl_upoly_zero(up->ctx);
3016 rec = isl_upoly_as_rec(up);
3020 if (up->var == pos) {
3022 return isl_upoly_copy(rec->p[deg]);
3024 return isl_upoly_zero(up->ctx);
3027 up = isl_upoly_copy(up);
3028 up = isl_upoly_cow(up);
3029 rec = isl_upoly_as_rec(up);
3033 for (i = 0; i < rec->n; ++i) {
3034 struct isl_upoly *t;
3035 t = isl_upoly_coeff(rec->p[i], pos, deg);
3038 isl_upoly_free(rec->p[i]);
3048 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3050 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3051 __isl_keep isl_qpolynomial *qp,
3052 enum isl_dim_type type, unsigned t_pos, int deg)
3055 struct isl_upoly *up;
3061 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3064 g_pos = pos(qp->dim, type) + t_pos;
3065 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3067 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3070 isl_mat_free(c->div);
3071 c->div = isl_mat_copy(qp->div);
3076 isl_qpolynomial_free(c);
3080 /* Homogenize the polynomial in the variables first (inclusive) up to
3081 * last (exclusive) by inserting powers of variable first.
3082 * Variable first is assumed not to appear in the input.
3084 __isl_give struct isl_upoly *isl_upoly_homogenize(
3085 __isl_take struct isl_upoly *up, int deg, int target,
3086 int first, int last)
3089 struct isl_upoly_rec *rec;
3093 if (isl_upoly_is_zero(up))
3097 if (isl_upoly_is_cst(up) || up->var < first) {
3098 struct isl_upoly *hom;
3100 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3103 rec = isl_upoly_as_rec(hom);
3104 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3109 up = isl_upoly_cow(up);
3110 rec = isl_upoly_as_rec(up);
3114 for (i = 0; i < rec->n; ++i) {
3115 if (isl_upoly_is_zero(rec->p[i]))
3117 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3118 up->var < last ? deg + i : i, target,
3130 /* Homogenize the polynomial in the set variables by introducing
3131 * powers of an extra set variable at position 0.
3133 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3134 __isl_take isl_qpolynomial *poly)
3138 int deg = isl_qpolynomial_degree(poly);
3143 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3144 poly = isl_qpolynomial_cow(poly);
3148 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3149 nvar = isl_dim_size(poly->dim, isl_dim_set);
3150 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3157 isl_qpolynomial_free(poly);
3161 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3162 __isl_take isl_mat *div)
3170 n = isl_dim_total(dim) + div->n_row;
3172 term = isl_calloc(dim->ctx, struct isl_term,
3173 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3180 isl_int_init(term->n);
3181 isl_int_init(term->d);
3190 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3199 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3208 total = isl_dim_total(term->dim) + term->div->n_row;
3210 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3214 isl_int_set(dup->n, term->n);
3215 isl_int_set(dup->d, term->d);
3217 for (i = 0; i < total; ++i)
3218 dup->pow[i] = term->pow[i];
3223 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3231 return isl_term_dup(term);
3234 void isl_term_free(__isl_take isl_term *term)
3239 if (--term->ref > 0)
3242 isl_dim_free(term->dim);
3243 isl_mat_free(term->div);
3244 isl_int_clear(term->n);
3245 isl_int_clear(term->d);
3249 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3257 case isl_dim_out: return isl_dim_size(term->dim, type);
3258 case isl_dim_div: return term->div->n_row;
3259 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3264 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3266 return term ? term->dim->ctx : NULL;
3269 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3273 isl_int_set(*n, term->n);
3276 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3280 isl_int_set(*d, term->d);
3283 int isl_term_get_exp(__isl_keep isl_term *term,
3284 enum isl_dim_type type, unsigned pos)
3289 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3291 if (type >= isl_dim_set)
3292 pos += isl_dim_size(term->dim, isl_dim_param);
3293 if (type >= isl_dim_div)
3294 pos += isl_dim_size(term->dim, isl_dim_set);
3296 return term->pow[pos];
3299 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3301 isl_basic_map *bmap;
3308 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3311 total = term->div->n_col - term->div->n_row - 2;
3312 /* No nested divs for now */
3313 isl_assert(term->dim->ctx,
3314 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3315 term->div->n_row) == -1,
3318 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3319 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3322 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3324 return isl_basic_map_div(bmap, k);
3326 isl_basic_map_free(bmap);
3330 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3331 int (*fn)(__isl_take isl_term *term, void *user),
3332 __isl_take isl_term *term, void *user)
3335 struct isl_upoly_rec *rec;
3340 if (isl_upoly_is_zero(up))
3343 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3344 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3345 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3347 if (isl_upoly_is_cst(up)) {
3348 struct isl_upoly_cst *cst;
3349 cst = isl_upoly_as_cst(up);
3352 term = isl_term_cow(term);
3355 isl_int_set(term->n, cst->n);
3356 isl_int_set(term->d, cst->d);
3357 if (fn(isl_term_copy(term), user) < 0)
3362 rec = isl_upoly_as_rec(up);
3366 for (i = 0; i < rec->n; ++i) {
3367 term = isl_term_cow(term);
3370 term->pow[up->var] = i;
3371 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3375 term->pow[up->var] = 0;
3379 isl_term_free(term);
3383 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3384 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3391 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3395 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3397 isl_term_free(term);
3399 return term ? 0 : -1;
3402 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3404 struct isl_upoly *up;
3405 isl_qpolynomial *qp;
3411 n = isl_dim_total(term->dim) + term->div->n_row;
3413 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3414 for (i = 0; i < n; ++i) {
3417 up = isl_upoly_mul(up,
3418 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3421 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3424 isl_mat_free(qp->div);
3425 qp->div = isl_mat_copy(term->div);
3429 isl_term_free(term);
3432 isl_qpolynomial_free(qp);
3433 isl_term_free(term);
3437 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3438 __isl_take isl_dim *dim)
3447 if (isl_dim_equal(qp->dim, dim)) {
3452 qp = isl_qpolynomial_cow(qp);
3456 extra = isl_dim_size(dim, isl_dim_set) -
3457 isl_dim_size(qp->dim, isl_dim_set);
3458 total = isl_dim_total(qp->dim);
3459 if (qp->div->n_row) {
3462 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3465 for (i = 0; i < qp->div->n_row; ++i)
3467 qp->upoly = expand(qp->upoly, exp, total);
3472 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3475 for (i = 0; i < qp->div->n_row; ++i)
3476 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3478 isl_dim_free(qp->dim);
3484 isl_qpolynomial_free(qp);
3488 /* For each parameter or variable that does not appear in qp,
3489 * first eliminate the variable from all constraints and then set it to zero.
3491 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3492 __isl_keep isl_qpolynomial *qp)
3503 d = isl_dim_total(set->dim);
3504 active = isl_calloc_array(set->ctx, int, d);
3505 if (set_active(qp, active) < 0)
3508 for (i = 0; i < d; ++i)
3517 nparam = isl_dim_size(set->dim, isl_dim_param);
3518 nvar = isl_dim_size(set->dim, isl_dim_set);
3519 for (i = 0; i < nparam; ++i) {
3522 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3523 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3525 for (i = 0; i < nvar; ++i) {
3526 if (active[nparam + i])
3528 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3529 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3541 struct isl_opt_data {
3542 isl_qpolynomial *qp;
3544 isl_qpolynomial *opt;
3548 static int opt_fn(__isl_take isl_point *pnt, void *user)
3550 struct isl_opt_data *data = (struct isl_opt_data *)user;
3551 isl_qpolynomial *val;
3553 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3557 } else if (data->max) {
3558 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3560 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3566 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3567 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3569 struct isl_opt_data data = { NULL, 1, NULL, max };
3574 if (isl_upoly_is_cst(qp->upoly)) {
3579 set = fix_inactive(set, qp);
3582 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3586 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3589 isl_qpolynomial_free(qp);
3593 isl_qpolynomial_free(qp);
3594 isl_qpolynomial_free(data.opt);
3598 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3599 __isl_take isl_morph *morph)
3604 struct isl_upoly *up;
3606 struct isl_upoly **subs;
3609 qp = isl_qpolynomial_cow(qp);
3614 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3616 n_sub = morph->inv->n_row - 1;
3617 if (morph->inv->n_row != morph->inv->n_col)
3618 n_sub += qp->div->n_row;
3619 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3623 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3624 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3625 morph->inv->row[0][0], morph->inv->n_col);
3626 if (morph->inv->n_row != morph->inv->n_col)
3627 for (i = 0; i < qp->div->n_row; ++i)
3628 subs[morph->inv->n_row - 1 + i] =
3629 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3631 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3633 for (i = 0; i < n_sub; ++i)
3634 isl_upoly_free(subs[i]);
3637 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3638 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3639 qp->div = isl_mat_product(qp->div, mat);
3640 isl_dim_free(qp->dim);
3641 qp->dim = isl_dim_copy(morph->ran->dim);
3643 if (!qp->upoly || !qp->div || !qp->dim)
3646 isl_morph_free(morph);
3650 isl_qpolynomial_free(qp);
3651 isl_morph_free(morph);
3655 static int neg_entry(void **entry, void *user)
3657 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3659 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3661 return *pwqp ? 0 : -1;
3664 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3665 __isl_take isl_union_pw_qpolynomial *upwqp)
3667 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3671 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3672 &neg_entry, NULL) < 0)
3677 isl_union_pw_qpolynomial_free(upwqp);
3681 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3682 __isl_take isl_union_pw_qpolynomial *upwqp1,
3683 __isl_take isl_union_pw_qpolynomial *upwqp2)
3685 return isl_union_pw_qpolynomial_add(upwqp1,
3686 isl_union_pw_qpolynomial_neg(upwqp2));
3689 static int mul_entry(void **entry, void *user)
3691 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3693 struct isl_hash_table_entry *entry2;
3694 isl_pw_qpolynomial *pwpq = *entry;
3697 hash = isl_dim_get_hash(pwpq->dim);
3698 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3699 hash, &has_dim, pwpq->dim, 0);
3703 pwpq = isl_pw_qpolynomial_copy(pwpq);
3704 pwpq = isl_pw_qpolynomial_mul(pwpq,
3705 isl_pw_qpolynomial_copy(entry2->data));
3707 empty = isl_pw_qpolynomial_is_zero(pwpq);
3709 isl_pw_qpolynomial_free(pwpq);
3713 isl_pw_qpolynomial_free(pwpq);
3717 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3722 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3723 __isl_take isl_union_pw_qpolynomial *upwqp1,
3724 __isl_take isl_union_pw_qpolynomial *upwqp2)
3726 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3729 /* Reorder the columns of the given div definitions according to the
3732 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3733 __isl_take isl_reordering *r)
3742 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3743 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3747 for (i = 0; i < div->n_row; ++i) {
3748 isl_seq_cpy(mat->row[i], div->row[i], 2);
3749 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3750 for (j = 0; j < r->len; ++j)
3751 isl_int_set(mat->row[i][2 + r->pos[j]],
3752 div->row[i][2 + j]);
3755 isl_reordering_free(r);
3759 isl_reordering_free(r);
3764 /* Reorder the dimension of "qp" according to the given reordering.
3766 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3767 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3769 qp = isl_qpolynomial_cow(qp);
3773 r = isl_reordering_extend(r, qp->div->n_row);
3777 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3781 qp->upoly = reorder(qp->upoly, r->pos);
3785 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3787 isl_reordering_free(r);
3790 isl_qpolynomial_free(qp);
3791 isl_reordering_free(r);
3795 struct isl_split_periods_data {
3797 isl_pw_qpolynomial *res;
3800 /* Create a slice where the integer division "div" has the fixed value "v".
3801 * In particular, if "div" refers to floor(f/m), then create a slice
3803 * m v <= f <= m v + (m - 1)
3808 * -f + m v + (m - 1) >= 0
3810 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3811 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3814 isl_basic_set *bset = NULL;
3820 total = isl_dim_total(dim);
3821 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3823 k = isl_basic_set_alloc_inequality(bset);
3826 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3827 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3829 k = isl_basic_set_alloc_inequality(bset);
3832 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3833 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3834 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3835 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3838 return isl_set_from_basic_set(bset);
3840 isl_basic_set_free(bset);
3845 static int split_periods(__isl_take isl_set *set,
3846 __isl_take isl_qpolynomial *qp, void *user);
3848 /* Create a slice of the domain "set" such that integer division "div"
3849 * has the fixed value "v" and add the results to data->res,
3850 * replacing the integer division by "v" in "qp".
3852 static int set_div(__isl_take isl_set *set,
3853 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3854 struct isl_split_periods_data *data)
3859 struct isl_upoly *cst;
3861 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3862 set = isl_set_intersect(set, slice);
3867 total = isl_dim_total(qp->dim);
3869 for (i = div + 1; i < qp->div->n_row; ++i) {
3870 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3872 isl_int_addmul(qp->div->row[i][1],
3873 qp->div->row[i][2 + total + div], v);
3874 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3877 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3878 qp = substitute_div(qp, div, cst);
3880 return split_periods(set, qp, data);
3883 isl_qpolynomial_free(qp);
3887 /* Split the domain "set" such that integer division "div"
3888 * has a fixed value (ranging from "min" to "max") on each slice
3889 * and add the results to data->res.
3891 static int split_div(__isl_take isl_set *set,
3892 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
3893 struct isl_split_periods_data *data)
3895 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
3896 isl_set *set_i = isl_set_copy(set);
3897 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
3899 if (set_div(set_i, qp_i, div, min, data) < 0)
3903 isl_qpolynomial_free(qp);
3907 isl_qpolynomial_free(qp);
3911 /* If "qp" refers to any integer division
3912 * that can only attain "max_periods" distinct values on "set"
3913 * then split the domain along those distinct values.
3914 * Add the results (or the original if no splitting occurs)
3917 static int split_periods(__isl_take isl_set *set,
3918 __isl_take isl_qpolynomial *qp, void *user)
3921 isl_pw_qpolynomial *pwqp;
3922 struct isl_split_periods_data *data;
3927 data = (struct isl_split_periods_data *)user;
3932 if (qp->div->n_row == 0) {
3933 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3934 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3940 total = isl_dim_total(qp->dim);
3941 for (i = 0; i < qp->div->n_row; ++i) {
3942 enum isl_lp_result lp_res;
3944 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
3945 qp->div->n_row) != -1)
3948 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
3949 set->ctx->one, &min, NULL, NULL);
3950 if (lp_res == isl_lp_error)
3952 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3954 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
3956 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
3957 set->ctx->one, &max, NULL, NULL);
3958 if (lp_res == isl_lp_error)
3960 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
3962 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
3964 isl_int_sub(max, max, min);
3965 if (isl_int_cmp_si(max, data->max_periods) < 0) {
3966 isl_int_add(max, max, min);
3971 if (i < qp->div->n_row) {
3972 r = split_div(set, qp, i, min, max, data);
3974 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3975 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3987 isl_qpolynomial_free(qp);
3991 /* If any quasi-polynomial in pwqp refers to any integer division
3992 * that can only attain "max_periods" distinct values on its domain
3993 * then split the domain along those distinct values.
3995 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
3996 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
3998 struct isl_split_periods_data data;
4000 data.max_periods = max_periods;
4001 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4003 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4006 isl_pw_qpolynomial_free(pwqp);
4010 isl_pw_qpolynomial_free(data.res);
4011 isl_pw_qpolynomial_free(pwqp);
4015 /* Construct a piecewise quasipolynomial that is constant on the given
4016 * domain. In particular, it is
4019 * infinity if cst == -1
4021 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4022 __isl_take isl_basic_set *bset, int cst)
4025 isl_qpolynomial *qp;
4030 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4031 dim = isl_basic_set_get_dim(bset);
4033 qp = isl_qpolynomial_infty(dim);
4035 qp = isl_qpolynomial_zero(dim);
4037 qp = isl_qpolynomial_one(dim);
4038 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4041 /* Factor bset, call fn on each of the factors and return the product.
4043 * If no factors can be found, simply call fn on the input.
4044 * Otherwise, construct the factors based on the factorizer,
4045 * call fn on each factor and compute the product.
4047 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4048 __isl_take isl_basic_set *bset,
4049 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4055 isl_qpolynomial *qp;
4056 isl_pw_qpolynomial *pwqp;
4060 f = isl_basic_set_factorizer(bset);
4063 if (f->n_group == 0) {
4064 isl_factorizer_free(f);
4068 nparam = isl_basic_set_dim(bset, isl_dim_param);
4069 nvar = isl_basic_set_dim(bset, isl_dim_set);
4071 dim = isl_basic_set_get_dim(bset);
4072 dim = isl_dim_domain(dim);
4073 set = isl_set_universe(isl_dim_copy(dim));
4074 qp = isl_qpolynomial_one(dim);
4075 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4077 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4079 for (i = 0, n = 0; i < f->n_group; ++i) {
4080 isl_basic_set *bset_i;
4081 isl_pw_qpolynomial *pwqp_i;
4083 bset_i = isl_basic_set_copy(bset);
4084 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4085 nparam + n + f->len[i], nvar - n - f->len[i]);
4086 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4088 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4089 n + f->len[i], nvar - n - f->len[i]);
4090 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4092 pwqp_i = fn(bset_i);
4093 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4098 isl_basic_set_free(bset);
4099 isl_factorizer_free(f);
4103 isl_basic_set_free(bset);
4107 /* Factor bset, call fn on each of the factors and return the product.
4108 * The function is assumed to evaluate to zero on empty domains,
4109 * to one on zero-dimensional domains and to infinity on unbounded domains
4110 * and will not be called explicitly on zero-dimensional or unbounded domains.
4112 * We first check for some special cases and remove all equalities.
4113 * Then we hand over control to compressed_multiplicative_call.
4115 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4116 __isl_take isl_basic_set *bset,
4117 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4121 isl_pw_qpolynomial *pwqp;
4122 unsigned orig_nvar, final_nvar;
4127 if (isl_basic_set_fast_is_empty(bset))
4128 return constant_on_domain(bset, 0);
4130 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4133 return constant_on_domain(bset, 1);
4135 bounded = isl_basic_set_is_bounded(bset);
4139 return constant_on_domain(bset, -1);
4141 if (bset->n_eq == 0)
4142 return compressed_multiplicative_call(bset, fn);
4144 morph = isl_basic_set_full_compression(bset);
4145 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4147 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4149 pwqp = compressed_multiplicative_call(bset, fn);
4151 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4152 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4153 morph = isl_morph_inverse(morph);
4155 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4159 isl_basic_set_free(bset);
4163 /* Drop all floors in "qp", turning each integer division [a/m] into
4164 * a rational division a/m. If "down" is set, then the integer division
4165 * is replaces by (a-(m-1))/m instead.
4167 static __isl_give isl_qpolynomial *qp_drop_floors(
4168 __isl_take isl_qpolynomial *qp, int down)
4171 struct isl_upoly *s;
4175 if (qp->div->n_row == 0)
4178 qp = isl_qpolynomial_cow(qp);
4182 for (i = qp->div->n_row - 1; i >= 0; --i) {
4184 isl_int_sub(qp->div->row[i][1],
4185 qp->div->row[i][1], qp->div->row[i][0]);
4186 isl_int_add_ui(qp->div->row[i][1],
4187 qp->div->row[i][1], 1);
4189 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4190 qp->div->row[i][0], qp->div->n_col - 1);
4191 qp = substitute_div(qp, i, s);
4199 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4200 * a rational division a/m.
4202 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4203 __isl_take isl_pw_qpolynomial *pwqp)
4210 if (isl_pw_qpolynomial_is_zero(pwqp))
4213 pwqp = isl_pw_qpolynomial_cow(pwqp);
4217 for (i = 0; i < pwqp->n; ++i) {
4218 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4225 isl_pw_qpolynomial_free(pwqp);
4229 /* Adjust all the integer divisions in "qp" such that they are at least
4230 * one over the given orthant (identified by "signs"). This ensures
4231 * that they will still be non-negative even after subtracting (m-1)/m.
4233 * In particular, f is replaced by f' + v, changing f = [a/m]
4234 * to f' = [(a - m v)/m].
4235 * If the constant term k in a is smaller than m,
4236 * the constant term of v is set to floor(k/m) - 1.
4237 * For any other term, if the coefficient c and the variable x have
4238 * the same sign, then no changes are needed.
4239 * Otherwise, if the variable is positive (and c is negative),
4240 * then the coefficient of x in v is set to floor(c/m).
4241 * If the variable is negative (and c is positive),
4242 * then the coefficient of x in v is set to ceil(c/m).
4244 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4250 struct isl_upoly *s;
4252 qp = isl_qpolynomial_cow(qp);
4255 qp->div = isl_mat_cow(qp->div);
4259 total = isl_dim_total(qp->dim);
4260 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4262 for (i = 0; i < qp->div->n_row; ++i) {
4263 isl_int *row = qp->div->row[i];
4267 if (isl_int_lt(row[1], row[0])) {
4268 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4269 isl_int_sub_ui(v->el[0], v->el[0], 1);
4270 isl_int_submul(row[1], row[0], v->el[0]);
4272 for (j = 0; j < total; ++j) {
4273 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4276 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4278 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4279 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4281 for (j = 0; j < i; ++j) {
4282 if (isl_int_sgn(row[2 + total + j]) >= 0)
4284 isl_int_fdiv_q(v->el[1 + total + j],
4285 row[2 + total + j], row[0]);
4286 isl_int_submul(row[2 + total + j],
4287 row[0], v->el[1 + total + j]);
4289 for (j = i + 1; j < qp->div->n_row; ++j) {
4290 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4292 isl_seq_combine(qp->div->row[j] + 1,
4293 qp->div->ctx->one, qp->div->row[j] + 1,
4294 qp->div->row[j][2 + total + i], v->el, v->size);
4296 isl_int_set_si(v->el[1 + total + i], 1);
4297 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4298 qp->div->ctx->one, v->size);
4299 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4309 isl_qpolynomial_free(qp);
4313 struct isl_to_poly_data {
4315 isl_pw_qpolynomial *res;
4316 isl_qpolynomial *qp;
4319 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4320 * We first make all integer divisions positive and then split the
4321 * quasipolynomials into terms with sign data->sign (the direction
4322 * of the requested approximation) and terms with the opposite sign.
4323 * In the first set of terms, each integer division [a/m] is
4324 * overapproximated by a/m, while in the second it is underapproximated
4327 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4330 struct isl_to_poly_data *data = user;
4331 isl_pw_qpolynomial *t;
4332 isl_qpolynomial *qp, *up, *down;
4334 qp = isl_qpolynomial_copy(data->qp);
4335 qp = make_divs_pos(qp, signs);
4337 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4338 up = qp_drop_floors(up, 0);
4339 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4340 down = qp_drop_floors(down, 1);
4342 isl_qpolynomial_free(qp);
4343 qp = isl_qpolynomial_add(up, down);
4345 t = isl_pw_qpolynomial_alloc(orthant, qp);
4346 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4351 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4352 * the polynomial will be an overapproximation. If "sign" is negative,
4353 * it will be an underapproximation. If "sign" is zero, the approximation
4354 * will lie somewhere in between.
4356 * In particular, is sign == 0, we simply drop the floors, turning
4357 * the integer divisions into rational divisions.
4358 * Otherwise, we split the domains into orthants, make all integer divisions
4359 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4360 * depending on the requested sign and the sign of the term in which
4361 * the integer division appears.
4363 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4364 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4367 struct isl_to_poly_data data;
4370 return pwqp_drop_floors(pwqp);
4376 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4378 for (i = 0; i < pwqp->n; ++i) {
4379 if (pwqp->p[i].qp->div->n_row == 0) {
4380 isl_pw_qpolynomial *t;
4381 t = isl_pw_qpolynomial_alloc(
4382 isl_set_copy(pwqp->p[i].set),
4383 isl_qpolynomial_copy(pwqp->p[i].qp));
4384 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4387 data.qp = pwqp->p[i].qp;
4388 if (isl_set_foreach_orthant(pwqp->p[i].set,
4389 &to_polynomial_on_orthant, &data) < 0)
4393 isl_pw_qpolynomial_free(pwqp);
4397 isl_pw_qpolynomial_free(pwqp);
4398 isl_pw_qpolynomial_free(data.res);
4402 static int poly_entry(void **entry, void *user)
4405 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4407 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4409 return *pwqp ? 0 : -1;
4412 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4413 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4415 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4419 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4420 &poly_entry, &sign) < 0)
4425 isl_union_pw_qpolynomial_free(upwqp);