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,
13 #include <isl_polynomial_private.h>
14 #include <isl_point_private.h>
15 #include <isl_dim_private.h>
16 #include <isl_map_private.h>
18 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
21 case isl_dim_param: return 0;
22 case isl_dim_in: return dim->nparam;
23 case isl_dim_out: return dim->nparam + dim->n_in;
28 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
36 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
41 isl_assert(up->ctx, up->var < 0, return NULL);
43 return (struct isl_upoly_cst *)up;
46 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
51 isl_assert(up->ctx, up->var >= 0, return NULL);
53 return (struct isl_upoly_rec *)up;
56 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
57 __isl_keep struct isl_upoly *up2)
60 struct isl_upoly_rec *rec1, *rec2;
66 if (up1->var != up2->var)
68 if (isl_upoly_is_cst(up1)) {
69 struct isl_upoly_cst *cst1, *cst2;
70 cst1 = isl_upoly_as_cst(up1);
71 cst2 = isl_upoly_as_cst(up2);
74 return isl_int_eq(cst1->n, cst2->n) &&
75 isl_int_eq(cst1->d, cst2->d);
78 rec1 = isl_upoly_as_rec(up1);
79 rec2 = isl_upoly_as_rec(up2);
83 if (rec1->n != rec2->n)
86 for (i = 0; i < rec1->n; ++i) {
87 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
95 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
97 struct isl_upoly_cst *cst;
101 if (!isl_upoly_is_cst(up))
104 cst = isl_upoly_as_cst(up);
108 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
111 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
113 struct isl_upoly_cst *cst;
117 if (!isl_upoly_is_cst(up))
120 cst = isl_upoly_as_cst(up);
124 return isl_int_sgn(cst->n);
127 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
129 struct isl_upoly_cst *cst;
133 if (!isl_upoly_is_cst(up))
136 cst = isl_upoly_as_cst(up);
140 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
143 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
145 struct isl_upoly_cst *cst;
149 if (!isl_upoly_is_cst(up))
152 cst = isl_upoly_as_cst(up);
156 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
159 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
161 struct isl_upoly_cst *cst;
165 if (!isl_upoly_is_cst(up))
168 cst = isl_upoly_as_cst(up);
172 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
175 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
177 struct isl_upoly_cst *cst;
181 if (!isl_upoly_is_cst(up))
184 cst = isl_upoly_as_cst(up);
188 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
191 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
193 struct isl_upoly_cst *cst;
197 if (!isl_upoly_is_cst(up))
200 cst = isl_upoly_as_cst(up);
204 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
207 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
209 struct isl_upoly_cst *cst;
211 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
220 isl_int_init(cst->n);
221 isl_int_init(cst->d);
226 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
228 struct isl_upoly_cst *cst;
230 cst = isl_upoly_cst_alloc(ctx);
234 isl_int_set_si(cst->n, 0);
235 isl_int_set_si(cst->d, 1);
240 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
242 struct isl_upoly_cst *cst;
244 cst = isl_upoly_cst_alloc(ctx);
248 isl_int_set_si(cst->n, 1);
249 isl_int_set_si(cst->d, 0);
254 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
256 struct isl_upoly_cst *cst;
258 cst = isl_upoly_cst_alloc(ctx);
262 isl_int_set_si(cst->n, -1);
263 isl_int_set_si(cst->d, 0);
268 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
270 struct isl_upoly_cst *cst;
272 cst = isl_upoly_cst_alloc(ctx);
276 isl_int_set_si(cst->n, 0);
277 isl_int_set_si(cst->d, 0);
282 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
283 isl_int n, isl_int d)
285 struct isl_upoly_cst *cst;
287 cst = isl_upoly_cst_alloc(ctx);
291 isl_int_set(cst->n, n);
292 isl_int_set(cst->d, d);
297 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
300 struct isl_upoly_rec *rec;
302 isl_assert(ctx, var >= 0, return NULL);
303 isl_assert(ctx, size >= 0, return NULL);
304 rec = isl_calloc(ctx, struct isl_upoly_rec,
305 sizeof(struct isl_upoly_rec) +
306 (size - 1) * sizeof(struct isl_upoly *));
321 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
323 return qp ? qp->dim->ctx : NULL;
326 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
328 return qp ? isl_dim_copy(qp->dim) : NULL;
331 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
332 enum isl_dim_type type)
334 return qp ? isl_dim_size(qp->dim, type) : 0;
337 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
339 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
342 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
344 return qp ? isl_upoly_is_one(qp->upoly) : -1;
347 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
349 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
352 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
354 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
357 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
359 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
362 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
364 return qp ? isl_upoly_sgn(qp->upoly) : 0;
367 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
369 isl_int_clear(cst->n);
370 isl_int_clear(cst->d);
373 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
377 for (i = 0; i < rec->n; ++i)
378 isl_upoly_free(rec->p[i]);
381 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
390 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
392 struct isl_upoly_cst *cst;
393 struct isl_upoly_cst *dup;
395 cst = isl_upoly_as_cst(up);
399 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
402 isl_int_set(dup->n, cst->n);
403 isl_int_set(dup->d, cst->d);
408 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
411 struct isl_upoly_rec *rec;
412 struct isl_upoly_rec *dup;
414 rec = isl_upoly_as_rec(up);
418 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
422 for (i = 0; i < rec->n; ++i) {
423 dup->p[i] = isl_upoly_copy(rec->p[i]);
431 isl_upoly_free(&dup->up);
435 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
437 struct isl_upoly *dup;
442 if (isl_upoly_is_cst(up))
443 return isl_upoly_dup_cst(up);
445 return isl_upoly_dup_rec(up);
448 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
456 return isl_upoly_dup(up);
459 void isl_upoly_free(__isl_take struct isl_upoly *up)
468 upoly_free_cst((struct isl_upoly_cst *)up);
470 upoly_free_rec((struct isl_upoly_rec *)up);
472 isl_ctx_deref(up->ctx);
476 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
481 isl_int_gcd(gcd, cst->n, cst->d);
482 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
483 isl_int_divexact(cst->n, cst->n, gcd);
484 isl_int_divexact(cst->d, cst->d, gcd);
489 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
490 __isl_take struct isl_upoly *up2)
492 struct isl_upoly_cst *cst1;
493 struct isl_upoly_cst *cst2;
495 up1 = isl_upoly_cow(up1);
499 cst1 = isl_upoly_as_cst(up1);
500 cst2 = isl_upoly_as_cst(up2);
502 if (isl_int_eq(cst1->d, cst2->d))
503 isl_int_add(cst1->n, cst1->n, cst2->n);
505 isl_int_mul(cst1->n, cst1->n, cst2->d);
506 isl_int_addmul(cst1->n, cst2->n, cst1->d);
507 isl_int_mul(cst1->d, cst1->d, cst2->d);
510 isl_upoly_cst_reduce(cst1);
520 static __isl_give struct isl_upoly *replace_by_zero(
521 __isl_take struct isl_upoly *up)
529 return isl_upoly_zero(ctx);
532 static __isl_give struct isl_upoly *replace_by_constant_term(
533 __isl_take struct isl_upoly *up)
535 struct isl_upoly_rec *rec;
536 struct isl_upoly *cst;
541 rec = isl_upoly_as_rec(up);
544 cst = isl_upoly_copy(rec->p[0]);
552 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
553 __isl_take struct isl_upoly *up2)
556 struct isl_upoly_rec *rec1, *rec2;
561 if (isl_upoly_is_nan(up1)) {
566 if (isl_upoly_is_nan(up2)) {
571 if (isl_upoly_is_zero(up1)) {
576 if (isl_upoly_is_zero(up2)) {
581 if (up1->var < up2->var)
582 return isl_upoly_sum(up2, up1);
584 if (up2->var < up1->var) {
585 struct isl_upoly_rec *rec;
586 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
590 up1 = isl_upoly_cow(up1);
591 rec = isl_upoly_as_rec(up1);
594 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
596 up1 = replace_by_constant_term(up1);
600 if (isl_upoly_is_cst(up1))
601 return isl_upoly_sum_cst(up1, up2);
603 rec1 = isl_upoly_as_rec(up1);
604 rec2 = isl_upoly_as_rec(up2);
608 if (rec1->n < rec2->n)
609 return isl_upoly_sum(up2, up1);
611 up1 = isl_upoly_cow(up1);
612 rec1 = isl_upoly_as_rec(up1);
616 for (i = rec2->n - 1; i >= 0; --i) {
617 rec1->p[i] = isl_upoly_sum(rec1->p[i],
618 isl_upoly_copy(rec2->p[i]));
621 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
622 isl_upoly_free(rec1->p[i]);
628 up1 = replace_by_zero(up1);
629 else if (rec1->n == 1)
630 up1 = replace_by_constant_term(up1);
641 __isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up)
643 struct isl_upoly_cst *cst;
645 if (isl_upoly_is_zero(up))
648 up = isl_upoly_cow(up);
652 cst = isl_upoly_as_cst(up);
654 isl_int_neg(cst->n, cst->n);
659 __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up)
662 struct isl_upoly_rec *rec;
667 if (isl_upoly_is_cst(up))
668 return isl_upoly_neg_cst(up);
670 up = isl_upoly_cow(up);
671 rec = isl_upoly_as_rec(up);
675 for (i = 0; i < rec->n; ++i) {
676 rec->p[i] = isl_upoly_neg(rec->p[i]);
687 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
688 __isl_take struct isl_upoly *up2)
690 struct isl_upoly_cst *cst1;
691 struct isl_upoly_cst *cst2;
693 up1 = isl_upoly_cow(up1);
697 cst1 = isl_upoly_as_cst(up1);
698 cst2 = isl_upoly_as_cst(up2);
700 isl_int_mul(cst1->n, cst1->n, cst2->n);
701 isl_int_mul(cst1->d, cst1->d, cst2->d);
703 isl_upoly_cst_reduce(cst1);
713 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
714 __isl_take struct isl_upoly *up2)
716 struct isl_upoly_rec *rec1;
717 struct isl_upoly_rec *rec2;
718 struct isl_upoly_rec *res;
722 rec1 = isl_upoly_as_rec(up1);
723 rec2 = isl_upoly_as_rec(up2);
726 size = rec1->n + rec2->n - 1;
727 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
731 for (i = 0; i < rec1->n; ++i) {
732 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
733 isl_upoly_copy(rec1->p[i]));
738 for (; i < size; ++i) {
739 res->p[i] = isl_upoly_zero(up1->ctx);
744 for (i = 0; i < rec1->n; ++i) {
745 for (j = 1; j < rec2->n; ++j) {
746 struct isl_upoly *up;
747 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
748 isl_upoly_copy(rec1->p[i]));
749 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
762 isl_upoly_free(&res->up);
766 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
767 __isl_take struct isl_upoly *up2)
772 if (isl_upoly_is_nan(up1)) {
777 if (isl_upoly_is_nan(up2)) {
782 if (isl_upoly_is_zero(up1)) {
787 if (isl_upoly_is_zero(up2)) {
792 if (isl_upoly_is_one(up1)) {
797 if (isl_upoly_is_one(up2)) {
802 if (up1->var < up2->var)
803 return isl_upoly_mul(up2, up1);
805 if (up2->var < up1->var) {
807 struct isl_upoly_rec *rec;
808 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
809 isl_ctx *ctx = up1->ctx;
812 return isl_upoly_nan(ctx);
814 up1 = isl_upoly_cow(up1);
815 rec = isl_upoly_as_rec(up1);
819 for (i = 0; i < rec->n; ++i) {
820 rec->p[i] = isl_upoly_mul(rec->p[i],
821 isl_upoly_copy(up2));
829 if (isl_upoly_is_cst(up1))
830 return isl_upoly_mul_cst(up1, up2);
832 return isl_upoly_mul_rec(up1, up2);
839 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
840 unsigned n_div, __isl_take struct isl_upoly *up)
842 struct isl_qpolynomial *qp = NULL;
848 total = isl_dim_total(dim);
850 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
855 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
866 isl_qpolynomial_free(qp);
870 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
879 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
881 struct isl_qpolynomial *dup;
886 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
887 isl_upoly_copy(qp->upoly));
890 isl_mat_free(dup->div);
891 dup->div = isl_mat_copy(qp->div);
897 isl_qpolynomial_free(dup);
901 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
909 return isl_qpolynomial_dup(qp);
912 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
920 isl_dim_free(qp->dim);
921 isl_mat_free(qp->div);
922 isl_upoly_free(qp->upoly);
927 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
932 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
933 div1->n_col >= div2->n_col, return -1);
935 if (div1->n_row == div2->n_row)
936 return isl_mat_is_equal(div1, div2);
940 div1->n_row = div2->n_row;
941 div1->n_col = div2->n_col;
943 equal = isl_mat_is_equal(div1, div2);
951 static void expand_row(__isl_keep isl_mat *dst, int d,
952 __isl_keep isl_mat *src, int s, int *exp)
955 unsigned c = src->n_col - src->n_row;
957 isl_seq_cpy(dst->row[d], src->row[s], c);
958 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
960 for (i = 0; i < s; ++i)
961 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
964 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
968 li = isl_seq_last_non_zero(div->row[i], div->n_col);
969 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
974 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
977 struct isl_div_sort_info {
982 static int div_sort_cmp(const void *p1, const void *p2)
984 const struct isl_div_sort_info *i1, *i2;
985 i1 = (const struct isl_div_sort_info *) p1;
986 i2 = (const struct isl_div_sort_info *) p2;
988 return cmp_row(i1->div, i1->row, i2->row);
991 static __isl_give isl_mat *sort_divs(__isl_take isl_mat *div)
994 struct isl_div_sort_info *array = NULL;
1002 array = isl_alloc_array(div->ctx, struct isl_div_sort_info, div->n_row);
1003 pos = isl_alloc_array(div->ctx, int, div->n_row);
1007 for (i = 0; i < div->n_row; ++i) {
1013 qsort(array, div->n_row, sizeof(struct isl_div_sort_info),
1016 for (i = 0; i < div->n_row; ++i) {
1018 if (pos[array[i].row] == i)
1020 div = isl_mat_cow(div);
1021 div = isl_mat_swap_rows(div, i, pos[array[i].row]);
1022 t = pos[array[i].row];
1023 pos[array[i].row] = pos[i];
1037 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1038 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1041 isl_mat *div = NULL;
1042 unsigned d = div1->n_col - div1->n_row;
1044 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1045 d + div1->n_row + div2->n_row);
1049 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1052 expand_row(div, k, div1, i, exp1);
1053 expand_row(div, k + 1, div2, j, exp2);
1055 cmp = cmp_row(div, k, k + 1);
1059 } else if (cmp < 0) {
1063 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1066 for (; i < div1->n_row; ++i, ++k) {
1067 expand_row(div, k, div1, i, exp1);
1070 for (; j < div2->n_row; ++j, ++k) {
1071 expand_row(div, k, div2, j, exp2);
1081 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1082 int *exp, int first)
1085 struct isl_upoly_rec *rec;
1087 if (isl_upoly_is_cst(up))
1090 if (up->var < first)
1093 if (exp[up->var - first] == up->var - first)
1096 up = isl_upoly_cow(up);
1100 up->var = exp[up->var - first] + first;
1102 rec = isl_upoly_as_rec(up);
1106 for (i = 0; i < rec->n; ++i) {
1107 rec->p[i] = expand(rec->p[i], exp, first);
1118 static __isl_give isl_qpolynomial *with_merged_divs(
1119 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1120 __isl_take isl_qpolynomial *qp2),
1121 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1125 isl_mat *div = NULL;
1127 qp1 = isl_qpolynomial_cow(qp1);
1128 qp2 = isl_qpolynomial_cow(qp2);
1133 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1134 qp1->div->n_col >= qp2->div->n_col, goto error);
1136 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1137 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1141 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1145 isl_mat_free(qp1->div);
1146 qp1->div = isl_mat_copy(div);
1147 isl_mat_free(qp2->div);
1148 qp2->div = isl_mat_copy(div);
1150 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1151 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1153 if (!qp1->upoly || !qp2->upoly)
1160 return fn(qp1, qp2);
1165 isl_qpolynomial_free(qp1);
1166 isl_qpolynomial_free(qp2);
1170 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1171 __isl_take isl_qpolynomial *qp2)
1173 qp1 = isl_qpolynomial_cow(qp1);
1178 if (qp1->div->n_row < qp2->div->n_row)
1179 return isl_qpolynomial_add(qp2, qp1);
1181 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1182 if (!compatible_divs(qp1->div, qp2->div))
1183 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1185 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1189 isl_qpolynomial_free(qp2);
1193 isl_qpolynomial_free(qp1);
1194 isl_qpolynomial_free(qp2);
1198 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1199 __isl_take isl_qpolynomial *qp2)
1201 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1204 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1206 qp = isl_qpolynomial_cow(qp);
1211 qp->upoly = isl_upoly_neg(qp->upoly);
1217 isl_qpolynomial_free(qp);
1221 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1222 __isl_take isl_qpolynomial *qp2)
1224 qp1 = isl_qpolynomial_cow(qp1);
1229 if (qp1->div->n_row < qp2->div->n_row)
1230 return isl_qpolynomial_mul(qp2, qp1);
1232 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1233 if (!compatible_divs(qp1->div, qp2->div))
1234 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1236 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1240 isl_qpolynomial_free(qp2);
1244 isl_qpolynomial_free(qp1);
1245 isl_qpolynomial_free(qp2);
1249 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1251 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1254 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1256 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1259 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1261 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1264 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1266 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1269 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1272 struct isl_qpolynomial *qp;
1273 struct isl_upoly_cst *cst;
1275 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1279 cst = isl_upoly_as_cst(qp->upoly);
1280 isl_int_set(cst->n, v);
1285 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1286 isl_int *n, isl_int *d)
1288 struct isl_upoly_cst *cst;
1293 if (!isl_upoly_is_cst(qp->upoly))
1296 cst = isl_upoly_as_cst(qp->upoly);
1301 isl_int_set(*n, cst->n);
1303 isl_int_set(*d, cst->d);
1308 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1311 struct isl_upoly_rec *rec;
1319 rec = isl_upoly_as_rec(up);
1326 isl_assert(up->ctx, rec->n > 1, return -1);
1328 is_cst = isl_upoly_is_cst(rec->p[1]);
1334 return isl_upoly_is_affine(rec->p[0]);
1337 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1342 if (qp->div->n_row > 0)
1345 return isl_upoly_is_affine(qp->upoly);
1348 static void update_coeff(__isl_keep isl_vec *aff,
1349 __isl_keep struct isl_upoly_cst *cst, int pos)
1354 if (isl_int_is_zero(cst->n))
1359 isl_int_gcd(gcd, cst->d, aff->el[0]);
1360 isl_int_divexact(f, cst->d, gcd);
1361 isl_int_divexact(gcd, aff->el[0], gcd);
1362 isl_seq_scale(aff->el, aff->el, f, aff->size);
1363 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1368 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1369 __isl_keep isl_vec *aff)
1371 struct isl_upoly_cst *cst;
1372 struct isl_upoly_rec *rec;
1378 struct isl_upoly_cst *cst;
1380 cst = isl_upoly_as_cst(up);
1383 update_coeff(aff, cst, 0);
1387 rec = isl_upoly_as_rec(up);
1390 isl_assert(up->ctx, rec->n == 2, return -1);
1392 cst = isl_upoly_as_cst(rec->p[1]);
1395 update_coeff(aff, cst, 1 + up->var);
1397 return isl_upoly_update_affine(rec->p[0], aff);
1400 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1401 __isl_keep isl_qpolynomial *qp)
1409 isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1410 d = isl_dim_total(qp->dim);
1411 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1415 isl_seq_clr(aff->el + 1, 1 + d);
1416 isl_int_set_si(aff->el[0], 1);
1418 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1427 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1428 __isl_keep isl_qpolynomial *qp2)
1433 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1436 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1439 struct isl_upoly_rec *rec;
1441 if (isl_upoly_is_cst(up)) {
1442 struct isl_upoly_cst *cst;
1443 cst = isl_upoly_as_cst(up);
1446 isl_int_lcm(*d, *d, cst->d);
1450 rec = isl_upoly_as_rec(up);
1454 for (i = 0; i < rec->n; ++i)
1455 upoly_update_den(rec->p[i], d);
1458 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1460 isl_int_set_si(*d, 1);
1463 upoly_update_den(qp->upoly, d);
1466 __isl_give struct isl_upoly *isl_upoly_pow(isl_ctx *ctx, int pos, int power)
1469 struct isl_upoly *up;
1470 struct isl_upoly_rec *rec;
1471 struct isl_upoly_cst *cst;
1473 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1476 for (i = 0; i < 1 + power; ++i) {
1477 rec->p[i] = isl_upoly_zero(ctx);
1482 cst = isl_upoly_as_cst(rec->p[power]);
1483 isl_int_set_si(cst->n, 1);
1487 isl_upoly_free(&rec->up);
1491 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_dim *dim,
1494 struct isl_ctx *ctx;
1501 return isl_qpolynomial_alloc(dim, 0, isl_upoly_pow(ctx, pos, power));
1504 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1505 enum isl_dim_type type, unsigned pos)
1510 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1511 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1513 if (type == isl_dim_set)
1514 pos += isl_dim_size(dim, isl_dim_param);
1516 return isl_qpolynomial_pow(dim, pos, 1);
1522 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
1525 struct isl_qpolynomial *qp = NULL;
1526 struct isl_upoly_rec *rec;
1527 struct isl_upoly_cst *cst;
1533 isl_assert(div->ctx, div->bmap->n_div == 1, goto error);
1535 pos = isl_dim_total(div->bmap->dim);
1536 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
1537 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap), 1,
1542 isl_seq_cpy(qp->div->row[0], div->line[0], qp->div->n_col - 1);
1543 isl_int_set_si(qp->div->row[0][qp->div->n_col - 1], 0);
1545 for (i = 0; i < 1 + power; ++i) {
1546 rec->p[i] = isl_upoly_zero(div->ctx);
1551 cst = isl_upoly_as_cst(rec->p[power]);
1552 isl_int_set_si(cst->n, 1);
1558 isl_qpolynomial_free(qp);
1563 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
1565 return isl_qpolynomial_div_pow(div, 1);
1568 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
1569 const isl_int n, const isl_int d)
1571 struct isl_qpolynomial *qp;
1572 struct isl_upoly_cst *cst;
1574 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1578 cst = isl_upoly_as_cst(qp->upoly);
1579 isl_int_set(cst->n, n);
1580 isl_int_set(cst->d, d);
1585 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
1587 struct isl_upoly_rec *rec;
1593 if (isl_upoly_is_cst(up))
1597 active[up->var] = 1;
1599 rec = isl_upoly_as_rec(up);
1600 for (i = 0; i < rec->n; ++i)
1601 if (up_set_active(rec->p[i], active, d) < 0)
1607 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
1610 int d = isl_dim_total(qp->dim);
1615 for (i = 0; i < d; ++i)
1616 for (j = 0; j < qp->div->n_row; ++j) {
1617 if (isl_int_is_zero(qp->div->row[j][2 + i]))
1623 return up_set_active(qp->upoly, active, d);
1626 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
1627 enum isl_dim_type type, unsigned first, unsigned n)
1638 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1640 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1641 type == isl_dim_set, return -1);
1643 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
1644 if (set_active(qp, active) < 0)
1647 if (type == isl_dim_set)
1648 first += isl_dim_size(qp->dim, isl_dim_param);
1649 for (i = 0; i < n; ++i)
1650 if (active[first + i]) {
1663 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
1664 unsigned first, unsigned n)
1667 struct isl_upoly_rec *rec;
1671 if (n == 0 || up->var < 0 || up->var < first)
1673 if (up->var < first + n) {
1674 up = replace_by_constant_term(up);
1675 return isl_upoly_drop(up, first, n);
1677 up = isl_upoly_cow(up);
1681 rec = isl_upoly_as_rec(up);
1685 for (i = 0; i < rec->n; ++i) {
1686 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
1697 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
1698 __isl_take isl_qpolynomial *qp,
1699 enum isl_dim_type type, unsigned first, unsigned n)
1706 qp = isl_qpolynomial_cow(qp);
1710 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1712 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1713 type == isl_dim_set, goto error);
1715 qp->dim = isl_dim_drop(qp->dim, type, first, n);
1719 if (type == isl_dim_set)
1720 first += isl_dim_size(qp->dim, isl_dim_param);
1722 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
1726 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
1732 isl_qpolynomial_free(qp);
1737 #define PW isl_pw_qpolynomial
1739 #define EL isl_qpolynomial
1741 #define IS_ZERO is_zero
1745 #define ADD(d,e1,e2) isl_qpolynomial_add(e1,e2)
1747 #include <isl_pw_templ.c>
1749 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
1757 if (!isl_set_fast_is_universe(pwqp->p[0].set))
1760 return isl_qpolynomial_is_one(pwqp->p[0].qp);
1763 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1764 __isl_take isl_pw_qpolynomial *pwqp1,
1765 __isl_take isl_pw_qpolynomial *pwqp2)
1768 struct isl_pw_qpolynomial *res;
1771 if (!pwqp1 || !pwqp2)
1774 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
1777 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
1778 isl_pw_qpolynomial_free(pwqp2);
1782 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
1783 isl_pw_qpolynomial_free(pwqp1);
1787 if (isl_pw_qpolynomial_is_one(pwqp1)) {
1788 isl_pw_qpolynomial_free(pwqp1);
1792 if (isl_pw_qpolynomial_is_one(pwqp2)) {
1793 isl_pw_qpolynomial_free(pwqp2);
1797 n = pwqp1->n * pwqp2->n;
1798 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
1800 for (i = 0; i < pwqp1->n; ++i) {
1801 for (j = 0; j < pwqp2->n; ++j) {
1802 struct isl_set *common;
1803 struct isl_qpolynomial *prod;
1804 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
1805 isl_set_copy(pwqp2->p[j].set));
1806 if (isl_set_fast_is_empty(common)) {
1807 isl_set_free(common);
1811 prod = isl_qpolynomial_mul(
1812 isl_qpolynomial_copy(pwqp1->p[i].qp),
1813 isl_qpolynomial_copy(pwqp2->p[j].qp));
1815 res = isl_pw_qpolynomial_add_piece(res, common, prod);
1819 isl_pw_qpolynomial_free(pwqp1);
1820 isl_pw_qpolynomial_free(pwqp2);
1824 isl_pw_qpolynomial_free(pwqp1);
1825 isl_pw_qpolynomial_free(pwqp2);
1829 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1830 __isl_take isl_pw_qpolynomial *pwqp)
1833 struct isl_pw_qpolynomial *res;
1839 if (isl_pw_qpolynomial_is_zero(pwqp))
1842 pwqp = isl_pw_qpolynomial_cow(pwqp);
1844 for (i = 0; i < pwqp->n; ++i) {
1845 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
1852 isl_pw_qpolynomial_free(pwqp);
1856 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1857 __isl_take isl_pw_qpolynomial *pwqp1,
1858 __isl_take isl_pw_qpolynomial *pwqp2)
1860 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
1863 __isl_give struct isl_upoly *isl_upoly_eval(
1864 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
1867 struct isl_upoly_rec *rec;
1868 struct isl_upoly *res;
1869 struct isl_upoly *base;
1871 if (isl_upoly_is_cst(up)) {
1876 rec = isl_upoly_as_rec(up);
1880 isl_assert(up->ctx, rec->n >= 1, goto error);
1882 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
1884 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
1887 for (i = rec->n - 2; i >= 0; --i) {
1888 res = isl_upoly_mul(res, isl_upoly_copy(base));
1889 res = isl_upoly_sum(res,
1890 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
1891 isl_vec_copy(vec)));
1894 isl_upoly_free(base);
1904 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
1905 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
1908 struct isl_upoly *up;
1913 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
1915 if (qp->div->n_row == 0)
1916 ext = isl_vec_copy(pnt->vec);
1919 unsigned dim = isl_dim_total(qp->dim);
1920 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
1924 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
1925 for (i = 0; i < qp->div->n_row; ++i) {
1926 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
1927 1 + dim + i, &ext->el[1+dim+i]);
1928 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
1929 qp->div->row[i][0]);
1933 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
1937 dim = isl_dim_copy(qp->dim);
1938 isl_qpolynomial_free(qp);
1939 isl_point_free(pnt);
1941 return isl_qpolynomial_alloc(dim, 0, up);
1943 isl_qpolynomial_free(qp);
1944 isl_point_free(pnt);
1948 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
1949 __isl_keep struct isl_upoly_cst *cst2)
1954 isl_int_mul(t, cst1->n, cst2->d);
1955 isl_int_submul(t, cst2->n, cst1->d);
1956 cmp = isl_int_sgn(t);
1961 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
1962 __isl_keep isl_qpolynomial *qp2)
1964 struct isl_upoly_cst *cst1, *cst2;
1968 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
1969 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
1970 if (isl_qpolynomial_is_nan(qp1))
1972 if (isl_qpolynomial_is_nan(qp2))
1974 cst1 = isl_upoly_as_cst(qp1->upoly);
1975 cst2 = isl_upoly_as_cst(qp2->upoly);
1977 return isl_upoly_cmp(cst1, cst2) <= 0;
1980 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
1981 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1983 struct isl_upoly_cst *cst1, *cst2;
1988 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
1989 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
1990 cst1 = isl_upoly_as_cst(qp1->upoly);
1991 cst2 = isl_upoly_as_cst(qp2->upoly);
1992 cmp = isl_upoly_cmp(cst1, cst2);
1995 isl_qpolynomial_free(qp2);
1997 isl_qpolynomial_free(qp1);
2002 isl_qpolynomial_free(qp1);
2003 isl_qpolynomial_free(qp2);
2007 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2008 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2010 struct isl_upoly_cst *cst1, *cst2;
2015 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2016 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2017 cst1 = isl_upoly_as_cst(qp1->upoly);
2018 cst2 = isl_upoly_as_cst(qp2->upoly);
2019 cmp = isl_upoly_cmp(cst1, cst2);
2022 isl_qpolynomial_free(qp2);
2024 isl_qpolynomial_free(qp1);
2029 isl_qpolynomial_free(qp1);
2030 isl_qpolynomial_free(qp2);
2034 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2035 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2036 unsigned first, unsigned n)
2045 qp = isl_qpolynomial_cow(qp);
2049 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2052 g_pos = pos(qp->dim, type) + first;
2054 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2058 total = qp->div->n_col - 2;
2059 if (total > g_pos) {
2061 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2064 for (i = 0; i < total - g_pos; ++i)
2066 qp->upoly = expand(qp->upoly, exp, g_pos);
2072 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2078 isl_qpolynomial_free(qp);
2082 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2083 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2087 pos = isl_qpolynomial_dim(qp, type);
2089 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2092 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2093 __isl_take isl_pw_qpolynomial *pwqp,
2094 enum isl_dim_type type, unsigned n)
2101 pwqp = isl_pw_qpolynomial_cow(pwqp);
2105 pwqp->dim = isl_dim_add(pwqp->dim, type, n);
2109 for (i = 0; i < pwqp->n; ++i) {
2110 pwqp->p[i].set = isl_set_add(pwqp->p[i].set, type, n);
2111 if (!pwqp->p[i].set)
2113 pwqp->p[i].qp = isl_qpolynomial_add_dims(pwqp->p[i].qp, type, n);
2120 isl_pw_qpolynomial_free(pwqp);
2124 static int *reordering_move(isl_ctx *ctx,
2125 unsigned len, unsigned dst, unsigned src, unsigned n)
2130 reordering = isl_alloc_array(ctx, int, len);
2135 for (i = 0; i < dst; ++i)
2137 for (i = 0; i < n; ++i)
2138 reordering[src + i] = dst + i;
2139 for (i = 0; i < src - dst; ++i)
2140 reordering[dst + i] = dst + n + i;
2141 for (i = 0; i < len - src - n; ++i)
2142 reordering[src + n + i] = src + n + i;
2144 for (i = 0; i < src; ++i)
2146 for (i = 0; i < n; ++i)
2147 reordering[src + i] = dst + i;
2148 for (i = 0; i < dst - src; ++i)
2149 reordering[src + n + i] = src + i;
2150 for (i = 0; i < len - dst - n; ++i)
2151 reordering[dst + n + i] = dst + n + i;
2157 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
2161 struct isl_upoly_rec *rec;
2162 struct isl_upoly *base;
2163 struct isl_upoly *res;
2165 if (isl_upoly_is_cst(up))
2168 rec = isl_upoly_as_rec(up);
2172 isl_assert(up->ctx, rec->n >= 1, goto error);
2174 base = isl_upoly_pow(up->ctx, r[up->var], 1);
2175 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
2177 for (i = rec->n - 2; i >= 0; --i) {
2178 res = isl_upoly_mul(res, isl_upoly_copy(base));
2179 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
2182 isl_upoly_free(base);
2191 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2192 __isl_take isl_qpolynomial *qp,
2193 enum isl_dim_type dst_type, unsigned dst_pos,
2194 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2200 qp = isl_qpolynomial_cow(qp);
2204 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2207 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2208 g_src_pos = pos(qp->dim, src_type) + src_pos;
2209 if (dst_type > src_type)
2212 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2213 qp->div = sort_divs(qp->div);
2217 reordering = reordering_move(qp->dim->ctx,
2218 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2222 qp->upoly = reorder(qp->upoly, reordering);
2227 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2233 isl_qpolynomial_free(qp);
2237 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
2238 isl_int denom, unsigned len)
2241 struct isl_upoly *up;
2243 isl_assert(ctx, len >= 1, return NULL);
2245 up = isl_upoly_rat_cst(ctx, f[0], denom);
2246 for (i = 0; i < len - 1; ++i) {
2247 struct isl_upoly *t;
2248 struct isl_upoly *c;
2250 if (isl_int_is_zero(f[1 + i]))
2253 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
2254 t = isl_upoly_pow(ctx, i, 1);
2255 t = isl_upoly_mul(c, t);
2256 up = isl_upoly_sum(up, t);
2262 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2263 isl_int *f, isl_int denom)
2265 struct isl_upoly *up;
2270 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2272 return isl_qpolynomial_alloc(dim, 0, up);
2275 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2276 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2280 struct isl_upoly *up;
2281 isl_qpolynomial *qp;
2287 isl_int_init(denom);
2289 isl_constraint_get_coefficient(c, type, pos, &denom);
2290 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2291 sgn = isl_int_sgn(denom);
2292 isl_int_abs(denom, denom);
2293 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2294 1 + isl_constraint_dim(c, isl_dim_all));
2296 isl_int_neg(denom, denom);
2297 isl_constraint_set_coefficient(c, type, pos, denom);
2299 dim = isl_dim_copy(c->bmap->dim);
2301 isl_int_clear(denom);
2302 isl_constraint_free(c);
2304 qp = isl_qpolynomial_alloc(dim, 0, up);
2306 qp = isl_qpolynomial_neg(qp);
2310 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
2311 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
2314 struct isl_upoly_rec *rec;
2315 struct isl_upoly *base, *res;
2320 if (isl_upoly_is_cst(up))
2323 if (up->var < first)
2326 rec = isl_upoly_as_rec(up);
2330 isl_assert(up->ctx, rec->n >= 1, goto error);
2332 if (up->var >= first + n)
2333 base = isl_upoly_pow(up->ctx, up->var, 1);
2335 base = isl_upoly_copy(subs[up->var - first]);
2337 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
2338 for (i = rec->n - 2; i >= 0; --i) {
2339 struct isl_upoly *t;
2340 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
2341 res = isl_upoly_mul(res, isl_upoly_copy(base));
2342 res = isl_upoly_sum(res, t);
2345 isl_upoly_free(base);
2354 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2355 * in "qp" by subs[i].
2357 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2358 __isl_take isl_qpolynomial *qp,
2359 enum isl_dim_type type, unsigned first, unsigned n,
2360 __isl_keep isl_qpolynomial **subs)
2363 struct isl_upoly **ups;
2368 qp = isl_qpolynomial_cow(qp);
2371 for (i = 0; i < n; ++i)
2375 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2378 for (i = 0; i < n; ++i)
2379 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2382 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2383 for (i = 0; i < n; ++i)
2384 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2386 first += pos(qp->dim, type);
2388 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2391 for (i = 0; i < n; ++i)
2392 ups[i] = subs[i]->upoly;
2394 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2403 isl_qpolynomial_free(qp);
2407 __isl_give isl_basic_set *add_div_constraints(__isl_take isl_basic_set *bset,
2408 __isl_take isl_mat *div)
2416 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2419 total = isl_basic_set_total_dim(bset);
2420 for (i = 0; i < div->n_row; ++i)
2421 if (isl_basic_set_add_div_constraints_var(bset,
2422 total - div->n_row + i, div->row[i]) < 0)
2429 isl_basic_set_free(bset);
2433 /* Extend "bset" with extra set dimensions for each integer division
2434 * in "qp" and then call "fn" with the extended bset and the polynomial
2435 * that results from replacing each of the integer divisions by the
2436 * corresponding extra set dimension.
2438 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2439 __isl_keep isl_basic_set *bset,
2440 int (*fn)(__isl_take isl_basic_set *bset,
2441 __isl_take isl_qpolynomial *poly, void *user), void *user)
2445 isl_qpolynomial *poly;
2449 if (qp->div->n_row == 0)
2450 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
2453 div = isl_mat_copy(qp->div);
2454 dim = isl_dim_copy(qp->dim);
2455 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
2456 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
2457 bset = isl_basic_set_copy(bset);
2458 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
2459 bset = add_div_constraints(bset, div);
2461 return fn(bset, poly, user);
2466 /* Return total degree in variables first (inclusive) up to last (exclusive).
2468 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
2472 struct isl_upoly_rec *rec;
2476 if (isl_upoly_is_zero(up))
2478 if (isl_upoly_is_cst(up) || up->var < first)
2481 rec = isl_upoly_as_rec(up);
2485 for (i = 0; i < rec->n; ++i) {
2488 if (isl_upoly_is_zero(rec->p[i]))
2490 d = isl_upoly_degree(rec->p[i], first, last);
2500 /* Return total degree in set variables.
2502 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
2510 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2511 nvar = isl_dim_size(poly->dim, isl_dim_set);
2512 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
2515 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
2516 unsigned pos, int deg)
2519 struct isl_upoly_rec *rec;
2524 if (isl_upoly_is_cst(up) || up->var < pos) {
2526 return isl_upoly_copy(up);
2528 return isl_upoly_zero(up->ctx);
2531 rec = isl_upoly_as_rec(up);
2535 if (up->var == pos) {
2537 return isl_upoly_copy(rec->p[deg]);
2539 return isl_upoly_zero(up->ctx);
2542 up = isl_upoly_copy(up);
2543 up = isl_upoly_cow(up);
2544 rec = isl_upoly_as_rec(up);
2548 for (i = 0; i < rec->n; ++i) {
2549 struct isl_upoly *t;
2550 t = isl_upoly_coeff(rec->p[i], pos, deg);
2553 isl_upoly_free(rec->p[i]);
2563 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
2565 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
2566 __isl_keep isl_qpolynomial *qp,
2567 enum isl_dim_type type, unsigned t_pos, int deg)
2570 struct isl_upoly *up;
2576 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
2579 g_pos = pos(qp->dim, type) + t_pos;
2580 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
2582 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
2585 isl_mat_free(c->div);
2586 c->div = isl_mat_copy(qp->div);
2591 isl_qpolynomial_free(c);
2595 /* Homogenize the polynomial in the variables first (inclusive) up to
2596 * last (exclusive) by inserting powers of variable first.
2597 * Variable first is assumed not to appear in the input.
2599 __isl_give struct isl_upoly *isl_upoly_homogenize(
2600 __isl_take struct isl_upoly *up, int deg, int target,
2601 int first, int last)
2604 struct isl_upoly_rec *rec;
2608 if (isl_upoly_is_zero(up))
2612 if (isl_upoly_is_cst(up) || up->var < first) {
2613 struct isl_upoly *hom;
2615 hom = isl_upoly_pow(up->ctx, first, target - deg);
2618 rec = isl_upoly_as_rec(hom);
2619 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
2624 up = isl_upoly_cow(up);
2625 rec = isl_upoly_as_rec(up);
2629 for (i = 0; i < rec->n; ++i) {
2630 if (isl_upoly_is_zero(rec->p[i]))
2632 rec->p[i] = isl_upoly_homogenize(rec->p[i],
2633 up->var < last ? deg + i : i, target,
2645 /* Homogenize the polynomial in the set variables by introducing
2646 * powers of an extra set variable at position 0.
2648 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
2649 __isl_take isl_qpolynomial *poly)
2653 int deg = isl_qpolynomial_degree(poly);
2658 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
2659 poly = isl_qpolynomial_cow(poly);
2663 ovar = isl_dim_offset(poly->dim, isl_dim_set);
2664 nvar = isl_dim_size(poly->dim, isl_dim_set);
2665 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
2672 isl_qpolynomial_free(poly);
2676 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
2677 __isl_take isl_mat *div)
2685 n = isl_dim_total(dim) + div->n_row;
2687 term = isl_calloc(dim->ctx, struct isl_term,
2688 sizeof(struct isl_term) + (n - 1) * sizeof(int));
2695 isl_int_init(term->n);
2696 isl_int_init(term->d);
2705 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
2714 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
2723 total = isl_dim_total(term->dim) + term->div->n_row;
2725 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
2729 isl_int_set(dup->n, term->n);
2730 isl_int_set(dup->d, term->d);
2732 for (i = 0; i < total; ++i)
2733 dup->pow[i] = term->pow[i];
2738 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
2746 return isl_term_dup(term);
2749 void isl_term_free(__isl_take isl_term *term)
2754 if (--term->ref > 0)
2757 isl_dim_free(term->dim);
2758 isl_mat_free(term->div);
2759 isl_int_clear(term->n);
2760 isl_int_clear(term->d);
2764 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
2772 case isl_dim_out: return isl_dim_size(term->dim, type);
2773 case isl_dim_div: return term->div->n_row;
2774 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
2779 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
2781 return term ? term->dim->ctx : NULL;
2784 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
2788 isl_int_set(*n, term->n);
2791 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
2795 isl_int_set(*d, term->d);
2798 int isl_term_get_exp(__isl_keep isl_term *term,
2799 enum isl_dim_type type, unsigned pos)
2804 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
2806 if (type >= isl_dim_set)
2807 pos += isl_dim_size(term->dim, isl_dim_param);
2808 if (type >= isl_dim_div)
2809 pos += isl_dim_size(term->dim, isl_dim_set);
2811 return term->pow[pos];
2814 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
2816 isl_basic_map *bmap;
2823 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
2826 total = term->div->n_col - term->div->n_row - 2;
2827 /* No nested divs for now */
2828 isl_assert(term->dim->ctx,
2829 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
2830 term->div->n_row) == -1,
2833 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
2834 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
2837 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
2839 return isl_basic_map_div(bmap, k);
2841 isl_basic_map_free(bmap);
2845 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
2846 int (*fn)(__isl_take isl_term *term, void *user),
2847 __isl_take isl_term *term, void *user)
2850 struct isl_upoly_rec *rec;
2855 if (isl_upoly_is_zero(up))
2858 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
2859 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
2860 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
2862 if (isl_upoly_is_cst(up)) {
2863 struct isl_upoly_cst *cst;
2864 cst = isl_upoly_as_cst(up);
2867 term = isl_term_cow(term);
2870 isl_int_set(term->n, cst->n);
2871 isl_int_set(term->d, cst->d);
2872 if (fn(isl_term_copy(term), user) < 0)
2877 rec = isl_upoly_as_rec(up);
2881 for (i = 0; i < rec->n; ++i) {
2882 term = isl_term_cow(term);
2885 term->pow[up->var] = i;
2886 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
2890 term->pow[up->var] = 0;
2894 isl_term_free(term);
2898 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
2899 int (*fn)(__isl_take isl_term *term, void *user), void *user)
2906 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
2910 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
2912 isl_term_free(term);
2914 return term ? 0 : -1;
2917 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
2919 struct isl_upoly *up;
2920 isl_qpolynomial *qp;
2926 n = isl_dim_total(term->dim) + term->div->n_row;
2928 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
2929 for (i = 0; i < n; ++i) {
2932 up = isl_upoly_mul(up,
2933 isl_upoly_pow(term->dim->ctx, i, term->pow[i]));
2936 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
2939 isl_mat_free(qp->div);
2940 qp->div = isl_mat_copy(term->div);
2944 isl_term_free(term);
2947 isl_qpolynomial_free(qp);
2948 isl_term_free(term);
2952 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
2953 __isl_take isl_dim *dim)
2962 if (isl_dim_equal(qp->dim, dim)) {
2967 qp = isl_qpolynomial_cow(qp);
2971 extra = isl_dim_size(dim, isl_dim_set) -
2972 isl_dim_size(qp->dim, isl_dim_set);
2973 total = isl_dim_total(qp->dim);
2974 if (qp->div->n_row) {
2977 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
2980 for (i = 0; i < qp->div->n_row; ++i)
2982 qp->upoly = expand(qp->upoly, exp, total);
2987 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
2990 for (i = 0; i < qp->div->n_row; ++i)
2991 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
2993 isl_dim_free(qp->dim);
2999 isl_qpolynomial_free(qp);
3003 /* For each parameter or variable that does not appear in qp,
3004 * first eliminate the variable from all constraints and then set it to zero.
3006 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3007 __isl_keep isl_qpolynomial *qp)
3018 d = isl_dim_total(set->dim);
3019 active = isl_calloc_array(set->ctx, int, d);
3020 if (set_active(qp, active) < 0)
3023 for (i = 0; i < d; ++i)
3032 nparam = isl_dim_size(set->dim, isl_dim_param);
3033 nvar = isl_dim_size(set->dim, isl_dim_set);
3034 for (i = 0; i < nparam; ++i) {
3037 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3038 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3040 for (i = 0; i < nvar; ++i) {
3041 if (active[nparam + i])
3043 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3044 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3056 struct isl_opt_data {
3057 isl_qpolynomial *qp;
3059 isl_qpolynomial *opt;
3063 static int opt_fn(__isl_take isl_point *pnt, void *user)
3065 struct isl_opt_data *data = (struct isl_opt_data *)user;
3066 isl_qpolynomial *val;
3068 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3072 } else if (data->max) {
3073 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3075 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3081 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3082 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3084 struct isl_opt_data data = { NULL, 1, NULL, max };
3089 if (isl_upoly_is_cst(qp->upoly)) {
3094 set = fix_inactive(set, qp);
3097 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3101 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3104 isl_qpolynomial_free(qp);
3108 isl_qpolynomial_free(qp);
3109 isl_qpolynomial_free(data.opt);
3113 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3114 __isl_take isl_morph *morph)
3118 struct isl_upoly *up;
3120 struct isl_upoly **subs;
3123 qp = isl_qpolynomial_cow(qp);
3128 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3130 subs = isl_calloc_array(ctx, struct isl_upoly *, morph->inv->n_row - 1);
3134 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3135 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3136 morph->inv->row[0][0], morph->inv->n_col);
3138 qp->upoly = isl_upoly_subs(qp->upoly, 0, morph->inv->n_row - 1, subs);
3140 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3141 isl_upoly_free(subs[i]);
3144 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3145 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3146 qp->div = isl_mat_product(qp->div, mat);
3147 isl_dim_free(qp->dim);
3148 qp->dim = isl_dim_copy(morph->ran->dim);
3150 if (!qp->upoly || !qp->div || !qp->dim)
3153 isl_morph_free(morph);
3157 isl_qpolynomial_free(qp);
3158 isl_morph_free(morph);