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>
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(dim->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 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
333 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
336 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
338 return qp ? isl_upoly_is_one(qp->upoly) : -1;
341 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
343 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
346 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
348 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
351 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
353 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
356 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
358 return qp ? isl_upoly_sgn(qp->upoly) : 0;
361 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
363 isl_int_clear(cst->n);
364 isl_int_clear(cst->d);
367 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
371 for (i = 0; i < rec->n; ++i)
372 isl_upoly_free(rec->p[i]);
375 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
384 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
386 struct isl_upoly_cst *cst;
387 struct isl_upoly_cst *dup;
389 cst = isl_upoly_as_cst(up);
393 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
396 isl_int_set(dup->n, cst->n);
397 isl_int_set(dup->d, cst->d);
402 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
405 struct isl_upoly_rec *rec;
406 struct isl_upoly_rec *dup;
408 rec = isl_upoly_as_rec(up);
412 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
416 for (i = 0; i < rec->n; ++i) {
417 dup->p[i] = isl_upoly_copy(rec->p[i]);
425 isl_upoly_free(&dup->up);
429 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
431 struct isl_upoly *dup;
436 if (isl_upoly_is_cst(up))
437 return isl_upoly_dup_cst(up);
439 return isl_upoly_dup_rec(up);
442 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
450 return isl_upoly_dup(up);
453 void isl_upoly_free(__isl_take struct isl_upoly *up)
462 upoly_free_cst((struct isl_upoly_cst *)up);
464 upoly_free_rec((struct isl_upoly_rec *)up);
466 isl_ctx_deref(up->ctx);
470 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
475 isl_int_gcd(gcd, cst->n, cst->d);
476 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
477 isl_int_divexact(cst->n, cst->n, gcd);
478 isl_int_divexact(cst->d, cst->d, gcd);
483 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
484 __isl_take struct isl_upoly *up2)
486 struct isl_upoly_cst *cst1;
487 struct isl_upoly_cst *cst2;
489 up1 = isl_upoly_cow(up1);
493 cst1 = isl_upoly_as_cst(up1);
494 cst2 = isl_upoly_as_cst(up2);
496 if (isl_int_eq(cst1->d, cst2->d))
497 isl_int_add(cst1->n, cst1->n, cst2->n);
499 isl_int_mul(cst1->n, cst1->n, cst2->d);
500 isl_int_addmul(cst1->n, cst2->n, cst1->d);
501 isl_int_mul(cst1->d, cst1->d, cst2->d);
504 isl_upoly_cst_reduce(cst1);
514 static __isl_give struct isl_upoly *replace_by_zero(
515 __isl_take struct isl_upoly *up)
523 return isl_upoly_zero(ctx);
526 static __isl_give struct isl_upoly *replace_by_constant_term(
527 __isl_take struct isl_upoly *up)
529 struct isl_upoly_rec *rec;
530 struct isl_upoly *cst;
535 rec = isl_upoly_as_rec(up);
538 cst = isl_upoly_copy(rec->p[0]);
546 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
547 __isl_take struct isl_upoly *up2)
550 struct isl_upoly_rec *rec1, *rec2;
555 if (isl_upoly_is_nan(up1)) {
560 if (isl_upoly_is_nan(up2)) {
565 if (isl_upoly_is_zero(up1)) {
570 if (isl_upoly_is_zero(up2)) {
575 if (up1->var < up2->var)
576 return isl_upoly_sum(up2, up1);
578 if (up2->var < up1->var) {
579 struct isl_upoly_rec *rec;
580 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
584 up1 = isl_upoly_cow(up1);
585 rec = isl_upoly_as_rec(up1);
588 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
590 up1 = replace_by_constant_term(up1);
594 if (isl_upoly_is_cst(up1))
595 return isl_upoly_sum_cst(up1, up2);
597 rec1 = isl_upoly_as_rec(up1);
598 rec2 = isl_upoly_as_rec(up2);
602 if (rec1->n < rec2->n)
603 return isl_upoly_sum(up2, up1);
605 up1 = isl_upoly_cow(up1);
606 rec1 = isl_upoly_as_rec(up1);
610 for (i = rec2->n - 1; i >= 0; --i) {
611 rec1->p[i] = isl_upoly_sum(rec1->p[i],
612 isl_upoly_copy(rec2->p[i]));
615 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
616 isl_upoly_free(rec1->p[i]);
622 up1 = replace_by_zero(up1);
623 else if (rec1->n == 1)
624 up1 = replace_by_constant_term(up1);
635 __isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up)
637 struct isl_upoly_cst *cst;
639 if (isl_upoly_is_zero(up))
642 up = isl_upoly_cow(up);
646 cst = isl_upoly_as_cst(up);
648 isl_int_neg(cst->n, cst->n);
653 __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up)
656 struct isl_upoly_rec *rec;
661 if (isl_upoly_is_cst(up))
662 return isl_upoly_neg_cst(up);
664 up = isl_upoly_cow(up);
665 rec = isl_upoly_as_rec(up);
669 for (i = 0; i < rec->n; ++i) {
670 rec->p[i] = isl_upoly_neg(rec->p[i]);
681 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
682 __isl_take struct isl_upoly *up2)
684 struct isl_upoly_cst *cst1;
685 struct isl_upoly_cst *cst2;
687 up1 = isl_upoly_cow(up1);
691 cst1 = isl_upoly_as_cst(up1);
692 cst2 = isl_upoly_as_cst(up2);
694 isl_int_mul(cst1->n, cst1->n, cst2->n);
695 isl_int_mul(cst1->d, cst1->d, cst2->d);
697 isl_upoly_cst_reduce(cst1);
707 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
708 __isl_take struct isl_upoly *up2)
710 struct isl_upoly_rec *rec1;
711 struct isl_upoly_rec *rec2;
712 struct isl_upoly_rec *res;
716 rec1 = isl_upoly_as_rec(up1);
717 rec2 = isl_upoly_as_rec(up2);
720 size = rec1->n + rec2->n - 1;
721 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
725 for (i = 0; i < rec1->n; ++i) {
726 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
727 isl_upoly_copy(rec1->p[i]));
732 for (; i < size; ++i) {
733 res->p[i] = isl_upoly_zero(up1->ctx);
738 for (i = 0; i < rec1->n; ++i) {
739 for (j = 1; j < rec2->n; ++j) {
740 struct isl_upoly *up;
741 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
742 isl_upoly_copy(rec1->p[i]));
743 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
756 isl_upoly_free(&res->up);
760 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
761 __isl_take struct isl_upoly *up2)
766 if (isl_upoly_is_nan(up1)) {
771 if (isl_upoly_is_nan(up2)) {
776 if (isl_upoly_is_zero(up1)) {
781 if (isl_upoly_is_zero(up2)) {
786 if (isl_upoly_is_one(up1)) {
791 if (isl_upoly_is_one(up2)) {
796 if (up1->var < up2->var)
797 return isl_upoly_mul(up2, up1);
799 if (up2->var < up1->var) {
801 struct isl_upoly_rec *rec;
802 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
803 isl_ctx *ctx = up1->ctx;
806 return isl_upoly_nan(ctx);
808 up1 = isl_upoly_cow(up1);
809 rec = isl_upoly_as_rec(up1);
813 for (i = 0; i < rec->n; ++i) {
814 rec->p[i] = isl_upoly_mul(rec->p[i],
815 isl_upoly_copy(up2));
823 if (isl_upoly_is_cst(up1))
824 return isl_upoly_mul_cst(up1, up2);
826 return isl_upoly_mul_rec(up1, up2);
833 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
834 unsigned n_div, __isl_take struct isl_upoly *up)
836 struct isl_qpolynomial *qp = NULL;
842 total = isl_dim_total(dim);
844 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
849 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
860 isl_qpolynomial_free(qp);
864 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
873 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
875 struct isl_qpolynomial *dup;
880 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
881 isl_upoly_copy(qp->upoly));
884 isl_mat_free(dup->div);
885 dup->div = isl_mat_copy(qp->div);
891 isl_qpolynomial_free(dup);
895 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
903 return isl_qpolynomial_dup(qp);
906 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
914 isl_dim_free(qp->dim);
915 isl_mat_free(qp->div);
916 isl_upoly_free(qp->upoly);
921 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
926 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
927 div1->n_col >= div2->n_col, return -1);
929 if (div1->n_row == div2->n_row)
930 return isl_mat_is_equal(div1, div2);
934 div1->n_row = div2->n_row;
935 div1->n_col = div2->n_col;
937 equal = isl_mat_is_equal(div1, div2);
945 static void expand_row(__isl_keep isl_mat *dst, int d,
946 __isl_keep isl_mat *src, int s, int *exp)
949 unsigned c = src->n_col - src->n_row;
951 isl_seq_cpy(dst->row[d], src->row[s], c);
952 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
954 for (i = 0; i < s; ++i)
955 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
958 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
962 li = isl_seq_last_non_zero(div->row[i], div->n_col);
963 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
968 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
971 struct isl_div_sort_info {
976 static int div_sort_cmp(const void *p1, const void *p2)
978 const struct isl_div_sort_info *i1, *i2;
979 i1 = (const struct isl_div_sort_info *) p1;
980 i2 = (const struct isl_div_sort_info *) p2;
982 return cmp_row(i1->div, i1->row, i2->row);
985 static __isl_give isl_mat *sort_divs(__isl_take isl_mat *div)
988 struct isl_div_sort_info *array = NULL;
996 array = isl_alloc_array(div->ctx, struct isl_div_sort_info, div->n_row);
997 pos = isl_alloc_array(div->ctx, int, div->n_row);
1001 for (i = 0; i < div->n_row; ++i) {
1007 qsort(array, div->n_row, sizeof(struct isl_div_sort_info),
1010 for (i = 0; i < div->n_row; ++i) {
1012 if (pos[array[i].row] == i)
1014 div = isl_mat_cow(div);
1015 div = isl_mat_swap_rows(div, i, pos[array[i].row]);
1016 t = pos[array[i].row];
1017 pos[array[i].row] = pos[i];
1031 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1032 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1035 isl_mat *div = NULL;
1036 unsigned d = div1->n_col - div1->n_row;
1038 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1039 d + div1->n_row + div2->n_row);
1043 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1046 expand_row(div, k, div1, i, exp1);
1047 expand_row(div, k + 1, div2, j, exp2);
1049 cmp = cmp_row(div, k, k + 1);
1053 } else if (cmp < 0) {
1057 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1060 for (; i < div1->n_row; ++i, ++k) {
1061 expand_row(div, k, div1, i, exp1);
1064 for (; j < div2->n_row; ++j, ++k) {
1065 expand_row(div, k, div2, j, exp2);
1075 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1076 int *exp, int first)
1079 struct isl_upoly_rec *rec;
1081 if (isl_upoly_is_cst(up))
1084 if (up->var < first)
1087 if (exp[up->var - first] == up->var - first)
1090 up = isl_upoly_cow(up);
1094 up->var = exp[up->var - first] + first;
1096 rec = isl_upoly_as_rec(up);
1100 for (i = 0; i < rec->n; ++i) {
1101 rec->p[i] = expand(rec->p[i], exp, first);
1112 static __isl_give isl_qpolynomial *with_merged_divs(
1113 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1114 __isl_take isl_qpolynomial *qp2),
1115 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1119 isl_mat *div = NULL;
1121 qp1 = isl_qpolynomial_cow(qp1);
1122 qp2 = isl_qpolynomial_cow(qp2);
1127 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1128 qp1->div->n_col >= qp2->div->n_col, goto error);
1130 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1131 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1135 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1139 isl_mat_free(qp1->div);
1140 qp1->div = isl_mat_copy(div);
1141 isl_mat_free(qp2->div);
1142 qp2->div = isl_mat_copy(div);
1144 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1145 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1147 if (!qp1->upoly || !qp2->upoly)
1154 return fn(qp1, qp2);
1159 isl_qpolynomial_free(qp1);
1160 isl_qpolynomial_free(qp2);
1164 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1165 __isl_take isl_qpolynomial *qp2)
1167 qp1 = isl_qpolynomial_cow(qp1);
1172 if (qp1->div->n_row < qp2->div->n_row)
1173 return isl_qpolynomial_add(qp2, qp1);
1175 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1176 if (!compatible_divs(qp1->div, qp2->div))
1177 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1179 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1183 isl_qpolynomial_free(qp2);
1187 isl_qpolynomial_free(qp1);
1188 isl_qpolynomial_free(qp2);
1192 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1193 __isl_take isl_qpolynomial *qp2)
1195 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1198 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1200 qp = isl_qpolynomial_cow(qp);
1205 qp->upoly = isl_upoly_neg(qp->upoly);
1211 isl_qpolynomial_free(qp);
1215 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1216 __isl_take isl_qpolynomial *qp2)
1218 qp1 = isl_qpolynomial_cow(qp1);
1223 if (qp1->div->n_row < qp2->div->n_row)
1224 return isl_qpolynomial_mul(qp2, qp1);
1226 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1227 if (!compatible_divs(qp1->div, qp2->div))
1228 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1230 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1234 isl_qpolynomial_free(qp2);
1238 isl_qpolynomial_free(qp1);
1239 isl_qpolynomial_free(qp2);
1243 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1245 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1248 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1250 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1253 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1255 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1258 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1260 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1263 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1266 struct isl_qpolynomial *qp;
1267 struct isl_upoly_cst *cst;
1269 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1273 cst = isl_upoly_as_cst(qp->upoly);
1274 isl_int_set(cst->n, v);
1279 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1280 isl_int *n, isl_int *d)
1282 struct isl_upoly_cst *cst;
1287 if (!isl_upoly_is_cst(qp->upoly))
1290 cst = isl_upoly_as_cst(qp->upoly);
1295 isl_int_set(*n, cst->n);
1297 isl_int_set(*d, cst->d);
1302 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1305 struct isl_upoly_rec *rec;
1313 rec = isl_upoly_as_rec(up);
1320 isl_assert(up->ctx, rec->n > 1, return -1);
1322 is_cst = isl_upoly_is_cst(rec->p[1]);
1328 return isl_upoly_is_affine(rec->p[0]);
1331 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1336 if (qp->div->n_row > 0)
1339 return isl_upoly_is_affine(qp->upoly);
1342 static void update_coeff(__isl_keep isl_vec *aff,
1343 __isl_keep struct isl_upoly_cst *cst, int pos)
1348 if (isl_int_is_zero(cst->n))
1353 isl_int_gcd(gcd, cst->d, aff->el[0]);
1354 isl_int_divexact(f, cst->d, gcd);
1355 isl_int_divexact(gcd, aff->el[0], gcd);
1356 isl_seq_scale(aff->el, aff->el, f, aff->size);
1357 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1362 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1363 __isl_keep isl_vec *aff)
1365 struct isl_upoly_cst *cst;
1366 struct isl_upoly_rec *rec;
1372 struct isl_upoly_cst *cst;
1374 cst = isl_upoly_as_cst(up);
1377 update_coeff(aff, cst, 0);
1381 rec = isl_upoly_as_rec(up);
1384 isl_assert(up->ctx, rec->n == 2, return -1);
1386 cst = isl_upoly_as_cst(rec->p[1]);
1389 update_coeff(aff, cst, 1 + up->var);
1391 return isl_upoly_update_affine(rec->p[0], aff);
1394 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1395 __isl_keep isl_qpolynomial *qp)
1403 isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1404 d = isl_dim_total(qp->dim);
1405 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1409 isl_seq_clr(aff->el + 1, 1 + d);
1410 isl_int_set_si(aff->el[0], 1);
1412 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1421 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1422 __isl_keep isl_qpolynomial *qp2)
1427 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1430 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1433 struct isl_upoly_rec *rec;
1435 if (isl_upoly_is_cst(up)) {
1436 struct isl_upoly_cst *cst;
1437 cst = isl_upoly_as_cst(up);
1440 isl_int_lcm(*d, *d, cst->d);
1444 rec = isl_upoly_as_rec(up);
1448 for (i = 0; i < rec->n; ++i)
1449 upoly_update_den(rec->p[i], d);
1452 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1454 isl_int_set_si(*d, 1);
1457 upoly_update_den(qp->upoly, d);
1460 __isl_give struct isl_upoly *isl_upoly_pow(isl_ctx *ctx, int pos, int power)
1463 struct isl_upoly *up;
1464 struct isl_upoly_rec *rec;
1465 struct isl_upoly_cst *cst;
1467 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1470 for (i = 0; i < 1 + power; ++i) {
1471 rec->p[i] = isl_upoly_zero(ctx);
1476 cst = isl_upoly_as_cst(rec->p[power]);
1477 isl_int_set_si(cst->n, 1);
1481 isl_upoly_free(&rec->up);
1485 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_dim *dim,
1488 struct isl_ctx *ctx;
1495 return isl_qpolynomial_alloc(dim, 0, isl_upoly_pow(ctx, pos, power));
1498 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1499 enum isl_dim_type type, unsigned pos)
1504 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1505 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1507 if (type == isl_dim_set)
1508 pos += isl_dim_size(dim, isl_dim_param);
1510 return isl_qpolynomial_pow(dim, pos, 1);
1516 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
1519 struct isl_qpolynomial *qp = NULL;
1520 struct isl_upoly_rec *rec;
1521 struct isl_upoly_cst *cst;
1527 isl_assert(div->ctx, div->bmap->n_div == 1, goto error);
1529 pos = isl_dim_total(div->bmap->dim);
1530 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
1531 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap), 1,
1536 isl_seq_cpy(qp->div->row[0], div->line[0], qp->div->n_col - 1);
1537 isl_int_set_si(qp->div->row[0][qp->div->n_col - 1], 0);
1539 for (i = 0; i < 1 + power; ++i) {
1540 rec->p[i] = isl_upoly_zero(div->ctx);
1545 cst = isl_upoly_as_cst(rec->p[power]);
1546 isl_int_set_si(cst->n, 1);
1552 isl_qpolynomial_free(qp);
1557 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
1559 return isl_qpolynomial_div_pow(div, 1);
1562 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
1563 const isl_int n, const isl_int d)
1565 struct isl_qpolynomial *qp;
1566 struct isl_upoly_cst *cst;
1568 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1572 cst = isl_upoly_as_cst(qp->upoly);
1573 isl_int_set(cst->n, n);
1574 isl_int_set(cst->d, d);
1579 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
1581 struct isl_upoly_rec *rec;
1587 if (isl_upoly_is_cst(up))
1591 active[up->var] = 1;
1593 rec = isl_upoly_as_rec(up);
1594 for (i = 0; i < rec->n; ++i)
1595 if (up_set_active(rec->p[i], active, d) < 0)
1601 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
1604 int d = isl_dim_total(qp->dim);
1609 for (i = 0; i < d; ++i)
1610 for (j = 0; j < qp->div->n_row; ++j) {
1611 if (isl_int_is_zero(qp->div->row[j][2 + i]))
1617 return up_set_active(qp->upoly, active, d);
1620 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
1621 enum isl_dim_type type, unsigned first, unsigned n)
1632 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1634 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1635 type == isl_dim_set, return -1);
1637 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
1638 if (set_active(qp, active) < 0)
1641 if (type == isl_dim_set)
1642 first += isl_dim_size(qp->dim, isl_dim_param);
1643 for (i = 0; i < n; ++i)
1644 if (active[first + i]) {
1657 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
1658 unsigned first, unsigned n)
1661 struct isl_upoly_rec *rec;
1665 if (n == 0 || up->var < 0 || up->var < first)
1667 if (up->var < first + n) {
1668 up = replace_by_constant_term(up);
1669 return isl_upoly_drop(up, first, n);
1671 up = isl_upoly_cow(up);
1675 rec = isl_upoly_as_rec(up);
1679 for (i = 0; i < rec->n; ++i) {
1680 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
1691 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
1692 __isl_take isl_qpolynomial *qp,
1693 enum isl_dim_type type, unsigned first, unsigned n)
1700 qp = isl_qpolynomial_cow(qp);
1704 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1706 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1707 type == isl_dim_set, goto error);
1709 qp->dim = isl_dim_drop(qp->dim, type, first, n);
1713 if (type == isl_dim_set)
1714 first += isl_dim_size(qp->dim, isl_dim_param);
1716 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
1720 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
1726 isl_qpolynomial_free(qp);
1731 #define PW isl_pw_qpolynomial
1733 #define EL isl_qpolynomial
1735 #define IS_ZERO is_zero
1739 #define ADD(d,e1,e2) isl_qpolynomial_add(e1,e2)
1741 #include <isl_pw_templ.c>
1743 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
1751 if (!isl_set_fast_is_universe(pwqp->p[0].set))
1754 return isl_qpolynomial_is_one(pwqp->p[0].qp);
1757 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1758 __isl_take isl_pw_qpolynomial *pwqp1,
1759 __isl_take isl_pw_qpolynomial *pwqp2)
1762 struct isl_pw_qpolynomial *res;
1765 if (!pwqp1 || !pwqp2)
1768 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
1771 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
1772 isl_pw_qpolynomial_free(pwqp2);
1776 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
1777 isl_pw_qpolynomial_free(pwqp1);
1781 if (isl_pw_qpolynomial_is_one(pwqp1)) {
1782 isl_pw_qpolynomial_free(pwqp1);
1786 if (isl_pw_qpolynomial_is_one(pwqp2)) {
1787 isl_pw_qpolynomial_free(pwqp2);
1791 n = pwqp1->n * pwqp2->n;
1792 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
1794 for (i = 0; i < pwqp1->n; ++i) {
1795 for (j = 0; j < pwqp2->n; ++j) {
1796 struct isl_set *common;
1797 struct isl_qpolynomial *prod;
1798 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
1799 isl_set_copy(pwqp2->p[j].set));
1800 if (isl_set_fast_is_empty(common)) {
1801 isl_set_free(common);
1805 prod = isl_qpolynomial_mul(
1806 isl_qpolynomial_copy(pwqp1->p[i].qp),
1807 isl_qpolynomial_copy(pwqp2->p[j].qp));
1809 res = isl_pw_qpolynomial_add_piece(res, common, prod);
1813 isl_pw_qpolynomial_free(pwqp1);
1814 isl_pw_qpolynomial_free(pwqp2);
1818 isl_pw_qpolynomial_free(pwqp1);
1819 isl_pw_qpolynomial_free(pwqp2);
1823 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1824 __isl_take isl_pw_qpolynomial *pwqp)
1827 struct isl_pw_qpolynomial *res;
1833 if (isl_pw_qpolynomial_is_zero(pwqp))
1836 pwqp = isl_pw_qpolynomial_cow(pwqp);
1838 for (i = 0; i < pwqp->n; ++i) {
1839 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
1846 isl_pw_qpolynomial_free(pwqp);
1850 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1851 __isl_take isl_pw_qpolynomial *pwqp1,
1852 __isl_take isl_pw_qpolynomial *pwqp2)
1854 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
1857 __isl_give struct isl_upoly *isl_upoly_eval(
1858 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
1861 struct isl_upoly_rec *rec;
1862 struct isl_upoly *res;
1863 struct isl_upoly *base;
1865 if (isl_upoly_is_cst(up)) {
1870 rec = isl_upoly_as_rec(up);
1874 isl_assert(up->ctx, rec->n >= 1, goto error);
1876 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
1878 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
1881 for (i = rec->n - 2; i >= 0; --i) {
1882 res = isl_upoly_mul(res, isl_upoly_copy(base));
1883 res = isl_upoly_sum(res,
1884 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
1885 isl_vec_copy(vec)));
1888 isl_upoly_free(base);
1898 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
1899 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
1902 struct isl_upoly *up;
1907 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
1909 if (qp->div->n_row == 0)
1910 ext = isl_vec_copy(pnt->vec);
1913 unsigned dim = isl_dim_total(qp->dim);
1914 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
1918 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
1919 for (i = 0; i < qp->div->n_row; ++i) {
1920 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
1921 1 + dim + i, &ext->el[1+dim+i]);
1922 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
1923 qp->div->row[i][0]);
1927 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
1931 dim = isl_dim_copy(qp->dim);
1932 isl_qpolynomial_free(qp);
1933 isl_point_free(pnt);
1935 return isl_qpolynomial_alloc(dim, 0, up);
1937 isl_qpolynomial_free(qp);
1938 isl_point_free(pnt);
1942 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
1943 __isl_keep struct isl_upoly_cst *cst2)
1948 isl_int_mul(t, cst1->n, cst2->d);
1949 isl_int_submul(t, cst2->n, cst1->d);
1950 cmp = isl_int_sgn(t);
1955 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
1956 __isl_keep isl_qpolynomial *qp2)
1958 struct isl_upoly_cst *cst1, *cst2;
1962 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
1963 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
1964 if (isl_qpolynomial_is_nan(qp1))
1966 if (isl_qpolynomial_is_nan(qp2))
1968 cst1 = isl_upoly_as_cst(qp1->upoly);
1969 cst2 = isl_upoly_as_cst(qp2->upoly);
1971 return isl_upoly_cmp(cst1, cst2) <= 0;
1974 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
1975 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1977 struct isl_upoly_cst *cst1, *cst2;
1982 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
1983 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
1984 cst1 = isl_upoly_as_cst(qp1->upoly);
1985 cst2 = isl_upoly_as_cst(qp2->upoly);
1986 cmp = isl_upoly_cmp(cst1, cst2);
1989 isl_qpolynomial_free(qp2);
1991 isl_qpolynomial_free(qp1);
1996 isl_qpolynomial_free(qp1);
1997 isl_qpolynomial_free(qp2);
2001 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2002 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2004 struct isl_upoly_cst *cst1, *cst2;
2009 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2010 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2011 cst1 = isl_upoly_as_cst(qp1->upoly);
2012 cst2 = isl_upoly_as_cst(qp2->upoly);
2013 cmp = isl_upoly_cmp(cst1, cst2);
2016 isl_qpolynomial_free(qp2);
2018 isl_qpolynomial_free(qp1);
2023 isl_qpolynomial_free(qp1);
2024 isl_qpolynomial_free(qp2);
2028 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2029 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2038 qp = isl_qpolynomial_cow(qp);
2042 g_pos = pos(qp->dim, type) + isl_dim_size(qp->dim, type);
2044 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2048 total = qp->div->n_col - 2;
2049 if (total > g_pos) {
2051 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2054 for (i = 0; i < total - g_pos; ++i)
2056 qp->upoly = expand(qp->upoly, exp, g_pos);
2062 qp->dim = isl_dim_add(qp->dim, type, n);
2068 isl_qpolynomial_free(qp);
2072 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2073 __isl_take isl_pw_qpolynomial *pwqp,
2074 enum isl_dim_type type, unsigned n)
2081 pwqp = isl_pw_qpolynomial_cow(pwqp);
2085 pwqp->dim = isl_dim_add(pwqp->dim, type, n);
2089 for (i = 0; i < pwqp->n; ++i) {
2090 pwqp->p[i].set = isl_set_add(pwqp->p[i].set, type, n);
2091 if (!pwqp->p[i].set)
2093 pwqp->p[i].qp = isl_qpolynomial_add_dims(pwqp->p[i].qp, type, n);
2100 isl_pw_qpolynomial_free(pwqp);
2104 static int *reordering_move(isl_ctx *ctx,
2105 unsigned len, unsigned dst, unsigned src, unsigned n)
2110 reordering = isl_alloc_array(ctx, int, len);
2115 for (i = 0; i < dst; ++i)
2117 for (i = 0; i < n; ++i)
2118 reordering[src + i] = dst + i;
2119 for (i = 0; i < src - dst; ++i)
2120 reordering[dst + i] = dst + n + i;
2121 for (i = 0; i < len - src - n; ++i)
2122 reordering[src + n + i] = src + n + i;
2124 for (i = 0; i < src; ++i)
2126 for (i = 0; i < n; ++i)
2127 reordering[src + i] = dst + i;
2128 for (i = 0; i < dst - src; ++i)
2129 reordering[src + n + i] = src + i;
2130 for (i = 0; i < len - dst - n; ++i)
2131 reordering[dst + n + i] = dst + n + i;
2137 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
2141 struct isl_upoly_rec *rec;
2142 struct isl_upoly *base;
2143 struct isl_upoly *res;
2145 if (isl_upoly_is_cst(up))
2148 rec = isl_upoly_as_rec(up);
2152 isl_assert(up->ctx, rec->n >= 1, goto error);
2154 base = isl_upoly_pow(up->ctx, r[up->var], 1);
2155 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
2157 for (i = rec->n - 2; i >= 0; --i) {
2158 res = isl_upoly_mul(res, isl_upoly_copy(base));
2159 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
2162 isl_upoly_free(base);
2171 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2172 __isl_take isl_qpolynomial *qp,
2173 enum isl_dim_type dst_type, unsigned dst_pos,
2174 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2180 qp = isl_qpolynomial_cow(qp);
2184 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2187 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2188 g_src_pos = pos(qp->dim, src_type) + src_pos;
2189 if (dst_type > src_type)
2192 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2193 qp->div = sort_divs(qp->div);
2197 reordering = reordering_move(qp->dim->ctx,
2198 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2202 qp->upoly = reorder(qp->upoly, reordering);
2207 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2213 isl_qpolynomial_free(qp);
2217 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
2218 isl_int denom, unsigned len)
2221 struct isl_upoly *up;
2223 isl_assert(ctx, len >= 1, return NULL);
2225 up = isl_upoly_rat_cst(ctx, f[0], denom);
2226 for (i = 0; i < len - 1; ++i) {
2227 struct isl_upoly *t;
2228 struct isl_upoly *c;
2230 if (isl_int_is_zero(f[1 + i]))
2233 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
2234 t = isl_upoly_pow(ctx, i, 1);
2235 t = isl_upoly_mul(c, t);
2236 up = isl_upoly_sum(up, t);
2242 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2243 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2247 struct isl_upoly *up;
2248 isl_qpolynomial *qp;
2254 isl_int_init(denom);
2256 isl_constraint_get_coefficient(c, type, pos, &denom);
2257 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2258 sgn = isl_int_sgn(denom);
2259 isl_int_abs(denom, denom);
2260 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2261 1 + isl_constraint_dim(c, isl_dim_all));
2263 isl_int_neg(denom, denom);
2264 isl_constraint_set_coefficient(c, type, pos, denom);
2266 dim = isl_dim_copy(c->bmap->dim);
2268 isl_int_clear(denom);
2269 isl_constraint_free(c);
2271 qp = isl_qpolynomial_alloc(dim, 0, up);
2273 qp = isl_qpolynomial_neg(qp);
2277 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
2278 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
2281 struct isl_upoly_rec *rec;
2282 struct isl_upoly *base, *res;
2287 if (isl_upoly_is_cst(up))
2290 if (up->var < first)
2293 rec = isl_upoly_as_rec(up);
2297 isl_assert(up->ctx, rec->n >= 1, goto error);
2299 if (up->var >= first + n)
2300 base = isl_upoly_pow(up->ctx, up->var, 1);
2302 base = isl_upoly_copy(subs[up->var - first]);
2304 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
2305 for (i = rec->n - 2; i >= 0; --i) {
2306 struct isl_upoly *t;
2307 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
2308 res = isl_upoly_mul(res, isl_upoly_copy(base));
2309 res = isl_upoly_sum(res, t);
2312 isl_upoly_free(base);
2321 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2322 * in "qp" by subs[i].
2324 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2325 __isl_take isl_qpolynomial *qp,
2326 enum isl_dim_type type, unsigned first, unsigned n,
2327 __isl_keep isl_qpolynomial **subs)
2330 struct isl_upoly **ups;
2335 qp = isl_qpolynomial_cow(qp);
2338 for (i = 0; i < n; ++i)
2342 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2345 for (i = 0; i < n; ++i)
2346 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2349 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2350 for (i = 0; i < n; ++i)
2351 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2353 first += pos(qp->dim, type);
2355 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2358 for (i = 0; i < n; ++i)
2359 ups[i] = subs[i]->upoly;
2361 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2370 isl_qpolynomial_free(qp);
2374 __isl_give isl_basic_set *add_div_constraints(__isl_take isl_basic_set *bset,
2375 __isl_take isl_mat *div)
2383 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2386 total = isl_basic_set_total_dim(bset);
2387 for (i = 0; i < div->n_row; ++i)
2388 if (isl_basic_set_add_div_constraints_var(bset,
2389 total - div->n_row + i, div->row[i]) < 0)
2396 isl_basic_set_free(bset);
2400 /* Extend "bset" with extra set dimensions for each integer division
2401 * in "qp" and then call "fn" with the extended bset and the polynomial
2402 * that results from replacing each of the integer divisions by the
2403 * corresponding extra set dimension.
2405 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2406 __isl_keep isl_basic_set *bset,
2407 int (*fn)(__isl_take isl_basic_set *bset,
2408 __isl_take isl_qpolynomial *poly, void *user), void *user)
2412 isl_qpolynomial *poly;
2416 if (qp->div->n_row == 0)
2417 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
2420 div = isl_mat_copy(qp->div);
2421 dim = isl_dim_copy(qp->dim);
2422 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
2423 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
2424 bset = isl_basic_set_copy(bset);
2425 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
2426 bset = add_div_constraints(bset, div);
2428 return fn(bset, poly, user);
2433 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
2434 __isl_take isl_mat *div)
2442 n = isl_dim_total(dim) + div->n_row;
2444 term = isl_calloc(dim->ctx, struct isl_term,
2445 sizeof(struct isl_term) + (n - 1) * sizeof(int));
2452 isl_int_init(term->n);
2453 isl_int_init(term->d);
2462 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
2471 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
2480 total = isl_dim_total(term->dim) + term->div->n_row;
2482 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
2486 isl_int_set(dup->n, term->n);
2487 isl_int_set(dup->d, term->d);
2489 for (i = 0; i < total; ++i)
2490 dup->pow[i] = term->pow[i];
2495 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
2503 return isl_term_dup(term);
2506 void isl_term_free(__isl_take isl_term *term)
2511 if (--term->ref > 0)
2514 isl_dim_free(term->dim);
2515 isl_mat_free(term->div);
2516 isl_int_clear(term->n);
2517 isl_int_clear(term->d);
2521 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
2529 case isl_dim_out: return isl_dim_size(term->dim, type);
2530 case isl_dim_div: return term->div->n_row;
2531 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
2536 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
2538 return term ? term->dim->ctx : NULL;
2541 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
2545 isl_int_set(*n, term->n);
2548 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
2552 isl_int_set(*d, term->d);
2555 int isl_term_get_exp(__isl_keep isl_term *term,
2556 enum isl_dim_type type, unsigned pos)
2561 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
2563 if (type >= isl_dim_set)
2564 pos += isl_dim_size(term->dim, isl_dim_param);
2565 if (type >= isl_dim_div)
2566 pos += isl_dim_size(term->dim, isl_dim_set);
2568 return term->pow[pos];
2571 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
2573 isl_basic_map *bmap;
2580 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
2583 total = term->div->n_col - term->div->n_row - 2;
2584 /* No nested divs for now */
2585 isl_assert(term->dim->ctx,
2586 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
2587 term->div->n_row) == -1,
2590 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
2591 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
2594 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
2596 return isl_basic_map_div(bmap, k);
2598 isl_basic_map_free(bmap);
2602 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
2603 int (*fn)(__isl_take isl_term *term, void *user),
2604 __isl_take isl_term *term, void *user)
2607 struct isl_upoly_rec *rec;
2612 if (isl_upoly_is_zero(up))
2615 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
2616 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
2617 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
2619 if (isl_upoly_is_cst(up)) {
2620 struct isl_upoly_cst *cst;
2621 cst = isl_upoly_as_cst(up);
2624 term = isl_term_cow(term);
2627 isl_int_set(term->n, cst->n);
2628 isl_int_set(term->d, cst->d);
2629 if (fn(isl_term_copy(term), user) < 0)
2634 rec = isl_upoly_as_rec(up);
2638 for (i = 0; i < rec->n; ++i) {
2639 term = isl_term_cow(term);
2642 term->pow[up->var] = i;
2643 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
2647 term->pow[up->var] = 0;
2651 isl_term_free(term);
2655 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
2656 int (*fn)(__isl_take isl_term *term, void *user), void *user)
2663 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
2667 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
2669 isl_term_free(term);
2671 return term ? 0 : -1;
2674 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
2676 struct isl_upoly *up;
2677 isl_qpolynomial *qp;
2683 n = isl_dim_total(term->dim) + term->div->n_row;
2685 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
2686 for (i = 0; i < n; ++i) {
2689 up = isl_upoly_mul(up,
2690 isl_upoly_pow(term->dim->ctx, i, term->pow[i]));
2693 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
2696 isl_mat_free(qp->div);
2697 qp->div = isl_mat_copy(term->div);
2701 isl_term_free(term);
2704 isl_qpolynomial_free(qp);
2705 isl_term_free(term);
2709 int isl_pw_qpolynomial_foreach_piece(__isl_keep isl_pw_qpolynomial *pwqp,
2710 int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp,
2711 void *user), void *user)
2718 for (i = 0; i < pwqp->n; ++i)
2719 if (fn(isl_set_copy(pwqp->p[i].set),
2720 isl_qpolynomial_copy(pwqp->p[i].qp), user) < 0)
2726 static int any_divs(__isl_keep isl_set *set)
2733 for (i = 0; i < set->n; ++i)
2734 if (set->p[i]->n_div > 0)
2740 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
2741 __isl_take isl_dim *dim)
2746 if (isl_dim_equal(qp->dim, dim)) {
2751 qp = isl_qpolynomial_cow(qp);
2755 if (qp->div->n_row) {
2761 extra = isl_dim_size(dim, isl_dim_set) -
2762 isl_dim_size(qp->dim, isl_dim_set);
2763 total = isl_dim_total(qp->dim);
2764 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
2767 for (i = 0; i < qp->div->n_row; ++i)
2769 qp->upoly = expand(qp->upoly, exp, total);
2773 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
2776 for (i = 0; i < qp->div->n_row; ++i)
2777 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
2780 isl_dim_free(qp->dim);
2786 isl_qpolynomial_free(qp);
2790 static int foreach_lifted_subset(__isl_take isl_set *set,
2791 __isl_take isl_qpolynomial *qp,
2792 int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp,
2793 void *user), void *user)
2800 for (i = 0; i < set->n; ++i) {
2802 isl_qpolynomial *copy;
2804 lift = isl_set_from_basic_set(isl_basic_set_copy(set->p[i]));
2805 lift = isl_set_lift(lift);
2807 copy = isl_qpolynomial_copy(qp);
2808 copy = isl_qpolynomial_lift(copy, isl_set_get_dim(lift));
2810 if (fn(lift, copy, user) < 0)
2815 isl_qpolynomial_free(qp);
2820 isl_qpolynomial_free(qp);
2824 int isl_pw_qpolynomial_foreach_lifted_piece(__isl_keep isl_pw_qpolynomial *pwqp,
2825 int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp,
2826 void *user), void *user)
2833 for (i = 0; i < pwqp->n; ++i) {
2835 isl_qpolynomial *qp;
2837 set = isl_set_copy(pwqp->p[i].set);
2838 qp = isl_qpolynomial_copy(pwqp->p[i].qp);
2839 if (!any_divs(set)) {
2840 if (fn(set, qp, user) < 0)
2844 if (foreach_lifted_subset(set, qp, fn, user) < 0)
2851 /* For each parameter or variable that does not appear in qp,
2852 * first eliminate the variable from all constraints and then set it to zero.
2854 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
2855 __isl_keep isl_qpolynomial *qp)
2866 d = isl_dim_total(set->dim);
2867 active = isl_calloc_array(set->ctx, int, d);
2868 if (set_active(qp, active) < 0)
2871 for (i = 0; i < d; ++i)
2880 nparam = isl_dim_size(set->dim, isl_dim_param);
2881 nvar = isl_dim_size(set->dim, isl_dim_set);
2882 for (i = 0; i < nparam; ++i) {
2885 set = isl_set_eliminate(set, isl_dim_param, i, 1);
2886 set = isl_set_fix_si(set, isl_dim_param, i, 0);
2888 for (i = 0; i < nvar; ++i) {
2889 if (active[nparam + i])
2891 set = isl_set_eliminate(set, isl_dim_set, i, 1);
2892 set = isl_set_fix_si(set, isl_dim_set, i, 0);
2904 struct isl_opt_data {
2905 isl_qpolynomial *qp;
2907 isl_qpolynomial *opt;
2911 static int opt_fn(__isl_take isl_point *pnt, void *user)
2913 struct isl_opt_data *data = (struct isl_opt_data *)user;
2914 isl_qpolynomial *val;
2916 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
2920 } else if (data->max) {
2921 data->opt = isl_qpolynomial_max_cst(data->opt, val);
2923 data->opt = isl_qpolynomial_min_cst(data->opt, val);
2929 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
2930 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
2932 struct isl_opt_data data = { NULL, 1, NULL, max };
2937 if (isl_upoly_is_cst(qp->upoly)) {
2942 set = fix_inactive(set, qp);
2945 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
2949 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
2952 isl_qpolynomial_free(qp);
2956 isl_qpolynomial_free(qp);
2957 isl_qpolynomial_free(data.opt);
2961 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
2962 __isl_take isl_morph *morph)
2966 struct isl_upoly *up;
2968 struct isl_upoly **subs;
2971 qp = isl_qpolynomial_cow(qp);
2976 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
2978 subs = isl_calloc_array(ctx, struct isl_upoly *, morph->inv->n_row - 1);
2982 for (i = 0; 1 + i < morph->inv->n_row; ++i)
2983 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
2984 morph->inv->row[0][0], morph->inv->n_col);
2986 qp->upoly = isl_upoly_subs(qp->upoly, 0, morph->inv->n_row - 1, subs);
2988 for (i = 0; 1 + i < morph->inv->n_row; ++i)
2989 isl_upoly_free(subs[i]);
2992 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
2993 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
2994 qp->div = isl_mat_product(qp->div, mat);
2995 isl_dim_free(qp->dim);
2996 qp->dim = isl_dim_copy(morph->ran->dim);
2998 if (!qp->upoly || !qp->div || !qp->dim)
3001 isl_morph_free(morph);
3005 isl_qpolynomial_free(qp);
3006 isl_morph_free(morph);