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;
27 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
35 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
40 isl_assert(up->ctx, up->var < 0, return NULL);
42 return (struct isl_upoly_cst *)up;
45 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
50 isl_assert(up->ctx, up->var >= 0, return NULL);
52 return (struct isl_upoly_rec *)up;
55 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
56 __isl_keep struct isl_upoly *up2)
59 struct isl_upoly_rec *rec1, *rec2;
65 if (up1->var != up2->var)
67 if (isl_upoly_is_cst(up1)) {
68 struct isl_upoly_cst *cst1, *cst2;
69 cst1 = isl_upoly_as_cst(up1);
70 cst2 = isl_upoly_as_cst(up2);
73 return isl_int_eq(cst1->n, cst2->n) &&
74 isl_int_eq(cst1->d, cst2->d);
77 rec1 = isl_upoly_as_rec(up1);
78 rec2 = isl_upoly_as_rec(up2);
82 if (rec1->n != rec2->n)
85 for (i = 0; i < rec1->n; ++i) {
86 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
94 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
96 struct isl_upoly_cst *cst;
100 if (!isl_upoly_is_cst(up))
103 cst = isl_upoly_as_cst(up);
107 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
110 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
112 struct isl_upoly_cst *cst;
116 if (!isl_upoly_is_cst(up))
119 cst = isl_upoly_as_cst(up);
123 return isl_int_sgn(cst->n);
126 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
128 struct isl_upoly_cst *cst;
132 if (!isl_upoly_is_cst(up))
135 cst = isl_upoly_as_cst(up);
139 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
142 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
144 struct isl_upoly_cst *cst;
148 if (!isl_upoly_is_cst(up))
151 cst = isl_upoly_as_cst(up);
155 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
158 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
160 struct isl_upoly_cst *cst;
164 if (!isl_upoly_is_cst(up))
167 cst = isl_upoly_as_cst(up);
171 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
174 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
176 struct isl_upoly_cst *cst;
180 if (!isl_upoly_is_cst(up))
183 cst = isl_upoly_as_cst(up);
187 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
190 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
192 struct isl_upoly_cst *cst;
196 if (!isl_upoly_is_cst(up))
199 cst = isl_upoly_as_cst(up);
203 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
206 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
208 struct isl_upoly_cst *cst;
210 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
219 isl_int_init(cst->n);
220 isl_int_init(cst->d);
225 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
227 struct isl_upoly_cst *cst;
229 cst = isl_upoly_cst_alloc(ctx);
233 isl_int_set_si(cst->n, 0);
234 isl_int_set_si(cst->d, 1);
239 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
241 struct isl_upoly_cst *cst;
243 cst = isl_upoly_cst_alloc(ctx);
247 isl_int_set_si(cst->n, 1);
248 isl_int_set_si(cst->d, 0);
253 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
255 struct isl_upoly_cst *cst;
257 cst = isl_upoly_cst_alloc(ctx);
261 isl_int_set_si(cst->n, -1);
262 isl_int_set_si(cst->d, 0);
267 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
269 struct isl_upoly_cst *cst;
271 cst = isl_upoly_cst_alloc(ctx);
275 isl_int_set_si(cst->n, 0);
276 isl_int_set_si(cst->d, 0);
281 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
282 isl_int n, isl_int d)
284 struct isl_upoly_cst *cst;
286 cst = isl_upoly_cst_alloc(ctx);
290 isl_int_set(cst->n, n);
291 isl_int_set(cst->d, d);
296 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
299 struct isl_upoly_rec *rec;
301 isl_assert(ctx, var >= 0, return NULL);
302 isl_assert(ctx, size >= 0, return NULL);
303 rec = isl_calloc(dim->ctx, struct isl_upoly_rec,
304 sizeof(struct isl_upoly_rec) +
305 (size - 1) * sizeof(struct isl_upoly *));
319 isl_upoly_free(&rec->up);
323 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
325 return qp ? qp->dim->ctx : NULL;
328 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
330 return qp ? isl_dim_copy(qp->dim) : NULL;
333 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
335 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
338 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
340 return qp ? isl_upoly_is_one(qp->upoly) : -1;
343 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
345 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
348 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
350 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
353 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
355 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
358 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
360 return qp ? isl_upoly_sgn(qp->upoly) : 0;
363 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
365 isl_int_clear(cst->n);
366 isl_int_clear(cst->d);
369 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
373 for (i = 0; i < rec->n; ++i)
374 isl_upoly_free(rec->p[i]);
377 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
386 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
388 struct isl_upoly_cst *cst;
389 struct isl_upoly_cst *dup;
391 cst = isl_upoly_as_cst(up);
395 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
398 isl_int_set(dup->n, cst->n);
399 isl_int_set(dup->d, cst->d);
404 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
407 struct isl_upoly_rec *rec;
408 struct isl_upoly_rec *dup;
410 rec = isl_upoly_as_rec(up);
414 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
418 for (i = 0; i < rec->n; ++i) {
419 dup->p[i] = isl_upoly_copy(rec->p[i]);
427 isl_upoly_free(&dup->up);
431 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
433 struct isl_upoly *dup;
438 if (isl_upoly_is_cst(up))
439 return isl_upoly_dup_cst(up);
441 return isl_upoly_dup_rec(up);
444 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
452 return isl_upoly_dup(up);
455 void isl_upoly_free(__isl_take struct isl_upoly *up)
464 upoly_free_cst((struct isl_upoly_cst *)up);
466 upoly_free_rec((struct isl_upoly_rec *)up);
468 isl_ctx_deref(up->ctx);
472 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
477 isl_int_gcd(gcd, cst->n, cst->d);
478 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
479 isl_int_divexact(cst->n, cst->n, gcd);
480 isl_int_divexact(cst->d, cst->d, gcd);
485 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
486 __isl_take struct isl_upoly *up2)
488 struct isl_upoly_cst *cst1;
489 struct isl_upoly_cst *cst2;
491 up1 = isl_upoly_cow(up1);
495 cst1 = isl_upoly_as_cst(up1);
496 cst2 = isl_upoly_as_cst(up2);
498 if (isl_int_eq(cst1->d, cst2->d))
499 isl_int_add(cst1->n, cst1->n, cst2->n);
501 isl_int_mul(cst1->n, cst1->n, cst2->d);
502 isl_int_addmul(cst1->n, cst2->n, cst1->d);
503 isl_int_mul(cst1->d, cst1->d, cst2->d);
506 isl_upoly_cst_reduce(cst1);
516 static __isl_give struct isl_upoly *replace_by_zero(
517 __isl_take struct isl_upoly *up)
525 return isl_upoly_zero(ctx);
528 static __isl_give struct isl_upoly *replace_by_constant_term(
529 __isl_take struct isl_upoly *up)
531 struct isl_upoly_rec *rec;
532 struct isl_upoly *cst;
537 rec = isl_upoly_as_rec(up);
540 cst = isl_upoly_copy(rec->p[0]);
548 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
549 __isl_take struct isl_upoly *up2)
552 struct isl_upoly_rec *rec1, *rec2;
557 if (isl_upoly_is_nan(up1)) {
562 if (isl_upoly_is_nan(up2)) {
567 if (isl_upoly_is_zero(up1)) {
572 if (isl_upoly_is_zero(up2)) {
577 if (up1->var < up2->var)
578 return isl_upoly_sum(up2, up1);
580 if (up2->var < up1->var) {
581 struct isl_upoly_rec *rec;
582 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
586 up1 = isl_upoly_cow(up1);
587 rec = isl_upoly_as_rec(up1);
590 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
592 up1 = replace_by_constant_term(up1);
596 if (isl_upoly_is_cst(up1))
597 return isl_upoly_sum_cst(up1, up2);
599 rec1 = isl_upoly_as_rec(up1);
600 rec2 = isl_upoly_as_rec(up2);
604 if (rec1->n < rec2->n)
605 return isl_upoly_sum(up2, up1);
607 up1 = isl_upoly_cow(up1);
608 rec1 = isl_upoly_as_rec(up1);
612 for (i = rec2->n - 1; i >= 0; --i) {
613 rec1->p[i] = isl_upoly_sum(rec1->p[i],
614 isl_upoly_copy(rec2->p[i]));
617 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
618 isl_upoly_free(rec1->p[i]);
624 up1 = replace_by_zero(up1);
625 else if (rec1->n == 1)
626 up1 = replace_by_constant_term(up1);
637 __isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up)
639 struct isl_upoly_cst *cst;
641 if (isl_upoly_is_zero(up))
644 up = isl_upoly_cow(up);
648 cst = isl_upoly_as_cst(up);
650 isl_int_neg(cst->n, cst->n);
655 __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up)
658 struct isl_upoly_rec *rec;
663 if (isl_upoly_is_cst(up))
664 return isl_upoly_neg_cst(up);
666 up = isl_upoly_cow(up);
667 rec = isl_upoly_as_rec(up);
671 for (i = 0; i < rec->n; ++i) {
672 rec->p[i] = isl_upoly_neg(rec->p[i]);
683 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
684 __isl_take struct isl_upoly *up2)
686 struct isl_upoly_cst *cst1;
687 struct isl_upoly_cst *cst2;
689 up1 = isl_upoly_cow(up1);
693 cst1 = isl_upoly_as_cst(up1);
694 cst2 = isl_upoly_as_cst(up2);
696 isl_int_mul(cst1->n, cst1->n, cst2->n);
697 isl_int_mul(cst1->d, cst1->d, cst2->d);
699 isl_upoly_cst_reduce(cst1);
709 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
710 __isl_take struct isl_upoly *up2)
712 struct isl_upoly_rec *rec1;
713 struct isl_upoly_rec *rec2;
714 struct isl_upoly_rec *res;
718 rec1 = isl_upoly_as_rec(up1);
719 rec2 = isl_upoly_as_rec(up2);
722 size = rec1->n + rec2->n - 1;
723 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
727 for (i = 0; i < rec1->n; ++i) {
728 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
729 isl_upoly_copy(rec1->p[i]));
734 for (; i < size; ++i) {
735 res->p[i] = isl_upoly_zero(up1->ctx);
740 for (i = 0; i < rec1->n; ++i) {
741 for (j = 1; j < rec2->n; ++j) {
742 struct isl_upoly *up;
743 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
744 isl_upoly_copy(rec1->p[i]));
745 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
758 isl_upoly_free(&res->up);
762 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
763 __isl_take struct isl_upoly *up2)
768 if (isl_upoly_is_nan(up1)) {
773 if (isl_upoly_is_nan(up2)) {
778 if (isl_upoly_is_zero(up1)) {
783 if (isl_upoly_is_zero(up2)) {
788 if (isl_upoly_is_one(up1)) {
793 if (isl_upoly_is_one(up2)) {
798 if (up1->var < up2->var)
799 return isl_upoly_mul(up2, up1);
801 if (up2->var < up1->var) {
803 struct isl_upoly_rec *rec;
804 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
805 isl_ctx *ctx = up1->ctx;
808 return isl_upoly_nan(ctx);
810 up1 = isl_upoly_cow(up1);
811 rec = isl_upoly_as_rec(up1);
815 for (i = 0; i < rec->n; ++i) {
816 rec->p[i] = isl_upoly_mul(rec->p[i],
817 isl_upoly_copy(up2));
825 if (isl_upoly_is_cst(up1))
826 return isl_upoly_mul_cst(up1, up2);
828 return isl_upoly_mul_rec(up1, up2);
835 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
836 unsigned n_div, __isl_take struct isl_upoly *up)
838 struct isl_qpolynomial *qp = NULL;
844 total = isl_dim_total(dim);
846 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
851 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
862 isl_qpolynomial_free(qp);
866 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
875 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
877 struct isl_qpolynomial *dup;
882 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
883 isl_upoly_copy(qp->upoly));
886 isl_mat_free(dup->div);
887 dup->div = isl_mat_copy(qp->div);
893 isl_qpolynomial_free(dup);
897 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
905 return isl_qpolynomial_dup(qp);
908 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
916 isl_dim_free(qp->dim);
917 isl_mat_free(qp->div);
918 isl_upoly_free(qp->upoly);
923 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
928 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
929 div1->n_col >= div2->n_col, return -1);
931 if (div1->n_row == div2->n_row)
932 return isl_mat_is_equal(div1, div2);
936 div1->n_row = div2->n_row;
937 div1->n_col = div2->n_col;
939 equal = isl_mat_is_equal(div1, div2);
947 static void expand_row(__isl_keep isl_mat *dst, int d,
948 __isl_keep isl_mat *src, int s, int *exp)
951 unsigned c = src->n_col - src->n_row;
953 isl_seq_cpy(dst->row[d], src->row[s], c);
954 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
956 for (i = 0; i < s; ++i)
957 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
960 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
964 li = isl_seq_last_non_zero(div->row[i], div->n_col);
965 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
970 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
973 struct isl_div_sort_info {
978 static int div_sort_cmp(const void *p1, const void *p2)
980 const struct isl_div_sort_info *i1, *i2;
981 i1 = (const struct isl_div_sort_info *) p1;
982 i2 = (const struct isl_div_sort_info *) p2;
984 return cmp_row(i1->div, i1->row, i2->row);
987 static __isl_give isl_mat *sort_divs(__isl_take isl_mat *div)
990 struct isl_div_sort_info *array = NULL;
998 array = isl_alloc_array(div->ctx, struct isl_div_sort_info, div->n_row);
999 pos = isl_alloc_array(div->ctx, int, div->n_row);
1003 for (i = 0; i < div->n_row; ++i) {
1009 qsort(array, div->n_row, sizeof(struct isl_div_sort_info),
1012 for (i = 0; i < div->n_row; ++i) {
1014 if (pos[array[i].row] == i)
1016 div = isl_mat_cow(div);
1017 div = isl_mat_swap_rows(div, i, pos[array[i].row]);
1018 t = pos[array[i].row];
1019 pos[array[i].row] = pos[i];
1033 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1034 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1037 isl_mat *div = NULL;
1038 unsigned d = div1->n_col - div1->n_row;
1040 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1041 d + div1->n_row + div2->n_row);
1045 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1048 expand_row(div, k, div1, i, exp1);
1049 expand_row(div, k + 1, div2, j, exp2);
1051 cmp = cmp_row(div, k, k + 1);
1055 } else if (cmp < 0) {
1059 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1062 for (; i < div1->n_row; ++i, ++k) {
1063 expand_row(div, k, div1, i, exp1);
1066 for (; j < div2->n_row; ++j, ++k) {
1067 expand_row(div, k, div2, j, exp2);
1077 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1078 int *exp, int first)
1081 struct isl_upoly_rec *rec;
1083 if (isl_upoly_is_cst(up))
1086 if (up->var < first)
1089 if (exp[up->var - first] == up->var - first)
1092 up = isl_upoly_cow(up);
1096 up->var = exp[up->var - first] + first;
1098 rec = isl_upoly_as_rec(up);
1102 for (i = 0; i < rec->n; ++i) {
1103 rec->p[i] = expand(rec->p[i], exp, first);
1114 static __isl_give isl_qpolynomial *with_merged_divs(
1115 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1116 __isl_take isl_qpolynomial *qp2),
1117 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1121 isl_mat *div = NULL;
1123 qp1 = isl_qpolynomial_cow(qp1);
1124 qp2 = isl_qpolynomial_cow(qp2);
1129 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1130 qp1->div->n_col >= qp2->div->n_col, goto error);
1132 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1133 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1137 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1141 isl_mat_free(qp1->div);
1142 qp1->div = isl_mat_copy(div);
1143 isl_mat_free(qp2->div);
1144 qp2->div = isl_mat_copy(div);
1146 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1147 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1149 if (!qp1->upoly || !qp2->upoly)
1156 return fn(qp1, qp2);
1161 isl_qpolynomial_free(qp1);
1162 isl_qpolynomial_free(qp2);
1166 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1167 __isl_take isl_qpolynomial *qp2)
1169 qp1 = isl_qpolynomial_cow(qp1);
1174 if (qp1->div->n_row < qp2->div->n_row)
1175 return isl_qpolynomial_add(qp2, qp1);
1177 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1178 if (!compatible_divs(qp1->div, qp2->div))
1179 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1181 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1185 isl_qpolynomial_free(qp2);
1189 isl_qpolynomial_free(qp1);
1190 isl_qpolynomial_free(qp2);
1194 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1195 __isl_take isl_qpolynomial *qp2)
1197 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1200 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1202 qp = isl_qpolynomial_cow(qp);
1207 qp->upoly = isl_upoly_neg(qp->upoly);
1213 isl_qpolynomial_free(qp);
1217 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1218 __isl_take isl_qpolynomial *qp2)
1220 qp1 = isl_qpolynomial_cow(qp1);
1225 if (qp1->div->n_row < qp2->div->n_row)
1226 return isl_qpolynomial_mul(qp2, qp1);
1228 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1229 if (!compatible_divs(qp1->div, qp2->div))
1230 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1232 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1236 isl_qpolynomial_free(qp2);
1240 isl_qpolynomial_free(qp1);
1241 isl_qpolynomial_free(qp2);
1245 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1247 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1250 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1252 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1255 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1257 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1260 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1262 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1265 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1268 struct isl_qpolynomial *qp;
1269 struct isl_upoly_cst *cst;
1271 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1275 cst = isl_upoly_as_cst(qp->upoly);
1276 isl_int_set(cst->n, v);
1280 isl_qpolynomial_free(qp);
1284 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1285 isl_int *n, isl_int *d)
1287 struct isl_upoly_cst *cst;
1292 if (!isl_upoly_is_cst(qp->upoly))
1295 cst = isl_upoly_as_cst(qp->upoly);
1300 isl_int_set(*n, cst->n);
1302 isl_int_set(*d, cst->d);
1307 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1310 struct isl_upoly_rec *rec;
1318 rec = isl_upoly_as_rec(up);
1325 isl_assert(up->ctx, rec->n > 1, return -1);
1327 is_cst = isl_upoly_is_cst(rec->p[1]);
1333 return isl_upoly_is_affine(rec->p[0]);
1336 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1341 if (qp->div->n_row > 0)
1344 return isl_upoly_is_affine(qp->upoly);
1347 static void update_coeff(__isl_keep isl_vec *aff,
1348 __isl_keep struct isl_upoly_cst *cst, int pos)
1353 if (isl_int_is_zero(cst->n))
1358 isl_int_gcd(gcd, cst->d, aff->el[0]);
1359 isl_int_divexact(f, cst->d, gcd);
1360 isl_int_divexact(gcd, aff->el[0], gcd);
1361 isl_seq_scale(aff->el, aff->el, f, aff->size);
1362 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1367 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1368 __isl_keep isl_vec *aff)
1370 struct isl_upoly_cst *cst;
1371 struct isl_upoly_rec *rec;
1377 struct isl_upoly_cst *cst;
1379 cst = isl_upoly_as_cst(up);
1382 update_coeff(aff, cst, 0);
1386 rec = isl_upoly_as_rec(up);
1389 isl_assert(up->ctx, rec->n == 2, return -1);
1391 cst = isl_upoly_as_cst(rec->p[1]);
1394 update_coeff(aff, cst, 1 + up->var);
1396 return isl_upoly_update_affine(rec->p[0], aff);
1399 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1400 __isl_keep isl_qpolynomial *qp)
1408 isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1409 d = isl_dim_total(qp->dim);
1410 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1414 isl_seq_clr(aff->el + 1, 1 + d);
1415 isl_int_set_si(aff->el[0], 1);
1417 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1426 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1427 __isl_keep isl_qpolynomial *qp2)
1432 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1435 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1438 struct isl_upoly_rec *rec;
1440 if (isl_upoly_is_cst(up)) {
1441 struct isl_upoly_cst *cst;
1442 cst = isl_upoly_as_cst(up);
1445 isl_int_lcm(*d, *d, cst->d);
1449 rec = isl_upoly_as_rec(up);
1453 for (i = 0; i < rec->n; ++i)
1454 upoly_update_den(rec->p[i], d);
1457 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1459 isl_int_set_si(*d, 1);
1462 upoly_update_den(qp->upoly, d);
1465 __isl_give struct isl_upoly *isl_upoly_pow(isl_ctx *ctx, int pos, int power)
1468 struct isl_upoly *up;
1469 struct isl_upoly_rec *rec;
1470 struct isl_upoly_cst *cst;
1472 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1475 for (i = 0; i < 1 + power; ++i) {
1476 rec->p[i] = isl_upoly_zero(ctx);
1481 cst = isl_upoly_as_cst(rec->p[power]);
1482 isl_int_set_si(cst->n, 1);
1486 isl_upoly_free(&rec->up);
1490 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_dim *dim,
1493 struct isl_ctx *ctx;
1500 return isl_qpolynomial_alloc(dim, 0, isl_upoly_pow(ctx, pos, power));
1503 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1504 enum isl_dim_type type, unsigned pos)
1509 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1510 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1512 if (type == isl_dim_set)
1513 pos += isl_dim_size(dim, isl_dim_param);
1515 return isl_qpolynomial_pow(dim, pos, 1);
1521 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
1524 struct isl_qpolynomial *qp = NULL;
1525 struct isl_upoly_rec *rec;
1526 struct isl_upoly_cst *cst;
1532 isl_assert(div->ctx, div->bmap->n_div == 1, goto error);
1534 pos = isl_dim_total(div->bmap->dim);
1535 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
1536 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap), 1,
1541 isl_seq_cpy(qp->div->row[0], div->line[0], qp->div->n_col - 1);
1542 isl_int_set_si(qp->div->row[0][qp->div->n_col - 1], 0);
1544 for (i = 0; i < 1 + power; ++i) {
1545 rec->p[i] = isl_upoly_zero(div->ctx);
1550 cst = isl_upoly_as_cst(rec->p[power]);
1551 isl_int_set_si(cst->n, 1);
1557 isl_qpolynomial_free(qp);
1562 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
1564 return isl_qpolynomial_div_pow(div, 1);
1567 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
1568 const isl_int n, const isl_int d)
1570 struct isl_qpolynomial *qp;
1571 struct isl_upoly_cst *cst;
1573 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1577 cst = isl_upoly_as_cst(qp->upoly);
1578 isl_int_set(cst->n, n);
1579 isl_int_set(cst->d, d);
1583 isl_qpolynomial_free(qp);
1587 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
1589 struct isl_upoly_rec *rec;
1595 if (isl_upoly_is_cst(up))
1599 active[up->var] = 1;
1601 rec = isl_upoly_as_rec(up);
1602 for (i = 0; i < rec->n; ++i)
1603 if (up_set_active(rec->p[i], active, d) < 0)
1609 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
1612 int d = isl_dim_total(qp->dim);
1617 for (i = 0; i < d; ++i)
1618 for (j = 0; j < qp->div->n_row; ++j) {
1619 if (isl_int_is_zero(qp->div->row[j][2 + i]))
1625 return up_set_active(qp->upoly, active, d);
1628 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
1629 enum isl_dim_type type, unsigned first, unsigned n)
1640 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1642 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1643 type == isl_dim_set, return -1);
1645 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
1646 if (set_active(qp, active) < 0)
1649 if (type == isl_dim_set)
1650 first += isl_dim_size(qp->dim, isl_dim_param);
1651 for (i = 0; i < n; ++i)
1652 if (active[first + i]) {
1665 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
1666 unsigned first, unsigned n)
1669 struct isl_upoly_rec *rec;
1673 if (n == 0 || up->var < 0 || up->var < first)
1675 if (up->var < first + n) {
1676 up = replace_by_constant_term(up);
1677 return isl_upoly_drop(up, first, n);
1679 up = isl_upoly_cow(up);
1683 rec = isl_upoly_as_rec(up);
1687 for (i = 0; i < rec->n; ++i) {
1688 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
1699 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
1700 __isl_take isl_qpolynomial *qp,
1701 enum isl_dim_type type, unsigned first, unsigned n)
1708 qp = isl_qpolynomial_cow(qp);
1712 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1714 isl_assert(qp->dim->ctx, type == isl_dim_param ||
1715 type == isl_dim_set, goto error);
1717 qp->dim = isl_dim_drop(qp->dim, type, first, n);
1721 if (type == isl_dim_set)
1722 first += isl_dim_size(qp->dim, isl_dim_param);
1724 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
1728 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
1734 isl_qpolynomial_free(qp);
1739 #define PW isl_pw_qpolynomial
1741 #define EL isl_qpolynomial
1743 #define IS_ZERO is_zero
1747 #define ADD(d,e1,e2) isl_qpolynomial_add(e1,e2)
1749 #include <isl_pw_templ.c>
1751 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
1759 if (!isl_set_fast_is_universe(pwqp->p[0].set))
1762 return isl_qpolynomial_is_one(pwqp->p[0].qp);
1765 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1766 __isl_take isl_pw_qpolynomial *pwqp1,
1767 __isl_take isl_pw_qpolynomial *pwqp2)
1770 struct isl_pw_qpolynomial *res;
1773 if (!pwqp1 || !pwqp2)
1776 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
1779 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
1780 isl_pw_qpolynomial_free(pwqp2);
1784 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
1785 isl_pw_qpolynomial_free(pwqp1);
1789 if (isl_pw_qpolynomial_is_one(pwqp1)) {
1790 isl_pw_qpolynomial_free(pwqp1);
1794 if (isl_pw_qpolynomial_is_one(pwqp2)) {
1795 isl_pw_qpolynomial_free(pwqp2);
1799 n = pwqp1->n * pwqp2->n;
1800 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
1802 for (i = 0; i < pwqp1->n; ++i) {
1803 for (j = 0; j < pwqp2->n; ++j) {
1804 struct isl_set *common;
1805 struct isl_qpolynomial *prod;
1806 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
1807 isl_set_copy(pwqp2->p[j].set));
1808 if (isl_set_fast_is_empty(common)) {
1809 isl_set_free(common);
1813 prod = isl_qpolynomial_mul(
1814 isl_qpolynomial_copy(pwqp1->p[i].qp),
1815 isl_qpolynomial_copy(pwqp2->p[j].qp));
1817 res = isl_pw_qpolynomial_add_piece(res, common, prod);
1821 isl_pw_qpolynomial_free(pwqp1);
1822 isl_pw_qpolynomial_free(pwqp2);
1826 isl_pw_qpolynomial_free(pwqp1);
1827 isl_pw_qpolynomial_free(pwqp2);
1831 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1832 __isl_take isl_pw_qpolynomial *pwqp)
1835 struct isl_pw_qpolynomial *res;
1841 if (isl_pw_qpolynomial_is_zero(pwqp))
1844 pwqp = isl_pw_qpolynomial_cow(pwqp);
1846 for (i = 0; i < pwqp->n; ++i) {
1847 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
1854 isl_pw_qpolynomial_free(pwqp);
1858 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1859 __isl_take isl_pw_qpolynomial *pwqp1,
1860 __isl_take isl_pw_qpolynomial *pwqp2)
1862 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
1865 __isl_give struct isl_upoly *isl_upoly_eval(
1866 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
1869 struct isl_upoly_rec *rec;
1870 struct isl_upoly *res;
1871 struct isl_upoly *base;
1873 if (isl_upoly_is_cst(up)) {
1878 rec = isl_upoly_as_rec(up);
1882 isl_assert(up->ctx, rec->n >= 1, goto error);
1884 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
1886 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
1889 for (i = rec->n - 2; i >= 0; --i) {
1890 res = isl_upoly_mul(res, isl_upoly_copy(base));
1891 res = isl_upoly_sum(res,
1892 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
1893 isl_vec_copy(vec)));
1896 isl_upoly_free(base);
1906 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
1907 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
1910 struct isl_upoly *up;
1915 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
1917 if (qp->div->n_row == 0)
1918 ext = isl_vec_copy(pnt->vec);
1921 unsigned dim = isl_dim_total(qp->dim);
1922 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
1926 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
1927 for (i = 0; i < qp->div->n_row; ++i) {
1928 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
1929 1 + dim + i, &ext->el[1+dim+i]);
1930 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
1931 qp->div->row[i][0]);
1935 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
1939 dim = isl_dim_copy(qp->dim);
1940 isl_qpolynomial_free(qp);
1941 isl_point_free(pnt);
1943 return isl_qpolynomial_alloc(dim, 0, up);
1945 isl_qpolynomial_free(qp);
1946 isl_point_free(pnt);
1950 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
1951 __isl_keep struct isl_upoly_cst *cst2)
1956 isl_int_mul(t, cst1->n, cst2->d);
1957 isl_int_submul(t, cst2->n, cst1->d);
1958 cmp = isl_int_sgn(t);
1963 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
1964 __isl_keep isl_qpolynomial *qp2)
1966 struct isl_upoly_cst *cst1, *cst2;
1970 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
1971 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
1972 if (isl_qpolynomial_is_nan(qp1))
1974 if (isl_qpolynomial_is_nan(qp2))
1976 cst1 = isl_upoly_as_cst(qp1->upoly);
1977 cst2 = isl_upoly_as_cst(qp2->upoly);
1979 return isl_upoly_cmp(cst1, cst2) <= 0;
1982 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
1983 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1985 struct isl_upoly_cst *cst1, *cst2;
1990 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
1991 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
1992 cst1 = isl_upoly_as_cst(qp1->upoly);
1993 cst2 = isl_upoly_as_cst(qp2->upoly);
1994 cmp = isl_upoly_cmp(cst1, cst2);
1997 isl_qpolynomial_free(qp2);
1999 isl_qpolynomial_free(qp1);
2004 isl_qpolynomial_free(qp1);
2005 isl_qpolynomial_free(qp2);
2009 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2010 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2012 struct isl_upoly_cst *cst1, *cst2;
2017 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2018 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2019 cst1 = isl_upoly_as_cst(qp1->upoly);
2020 cst2 = isl_upoly_as_cst(qp2->upoly);
2021 cmp = isl_upoly_cmp(cst1, cst2);
2024 isl_qpolynomial_free(qp2);
2026 isl_qpolynomial_free(qp1);
2031 isl_qpolynomial_free(qp1);
2032 isl_qpolynomial_free(qp2);
2036 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2037 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2046 qp = isl_qpolynomial_cow(qp);
2050 g_pos = pos(qp->dim, type) + isl_dim_size(qp->dim, type);
2052 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2056 total = qp->div->n_col - 2;
2057 if (total > g_pos) {
2059 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2062 for (i = 0; i < total - g_pos; ++i)
2064 qp->upoly = expand(qp->upoly, exp, g_pos);
2070 qp->dim = isl_dim_add(qp->dim, type, n);
2076 isl_qpolynomial_free(qp);
2080 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2081 __isl_take isl_pw_qpolynomial *pwqp,
2082 enum isl_dim_type type, unsigned n)
2089 pwqp = isl_pw_qpolynomial_cow(pwqp);
2093 pwqp->dim = isl_dim_add(pwqp->dim, type, n);
2097 for (i = 0; i < pwqp->n; ++i) {
2098 pwqp->p[i].set = isl_set_add(pwqp->p[i].set, type, n);
2099 if (!pwqp->p[i].set)
2101 pwqp->p[i].qp = isl_qpolynomial_add_dims(pwqp->p[i].qp, type, n);
2108 isl_pw_qpolynomial_free(pwqp);
2112 static int *reordering_move(isl_ctx *ctx,
2113 unsigned len, unsigned dst, unsigned src, unsigned n)
2118 reordering = isl_alloc_array(ctx, int, len);
2123 for (i = 0; i < dst; ++i)
2125 for (i = 0; i < n; ++i)
2126 reordering[src + i] = dst + i;
2127 for (i = 0; i < src - dst; ++i)
2128 reordering[dst + i] = dst + n + i;
2129 for (i = 0; i < len - src - n; ++i)
2130 reordering[src + n + i] = src + n + i;
2132 for (i = 0; i < src; ++i)
2134 for (i = 0; i < n; ++i)
2135 reordering[src + i] = dst + i;
2136 for (i = 0; i < dst - src; ++i)
2137 reordering[src + n + i] = src + i;
2138 for (i = 0; i < len - dst - n; ++i)
2139 reordering[dst + n + i] = dst + n + i;
2145 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
2149 struct isl_upoly_rec *rec;
2150 struct isl_upoly *base;
2151 struct isl_upoly *res;
2153 if (isl_upoly_is_cst(up))
2156 rec = isl_upoly_as_rec(up);
2160 isl_assert(up->ctx, rec->n >= 1, goto error);
2162 base = isl_upoly_pow(up->ctx, r[up->var], 1);
2163 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
2165 for (i = rec->n - 2; i >= 0; --i) {
2166 res = isl_upoly_mul(res, isl_upoly_copy(base));
2167 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
2170 isl_upoly_free(base);
2179 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2180 __isl_take isl_qpolynomial *qp,
2181 enum isl_dim_type dst_type, unsigned dst_pos,
2182 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2188 qp = isl_qpolynomial_cow(qp);
2192 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2195 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2196 g_src_pos = pos(qp->dim, src_type) + src_pos;
2197 if (dst_type > src_type)
2200 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2201 qp->div = sort_divs(qp->div);
2205 reordering = reordering_move(qp->dim->ctx,
2206 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2210 qp->upoly = reorder(qp->upoly, reordering);
2215 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2221 isl_qpolynomial_free(qp);
2225 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_move(
2226 __isl_take isl_pw_qpolynomial *pwqp,
2227 enum isl_dim_type dst_type, unsigned dst_pos,
2228 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2232 pwqp = isl_pw_qpolynomial_cow(pwqp);
2236 pwqp->dim = isl_dim_move(pwqp->dim,
2237 dst_type, dst_pos, src_type, src_pos, n);
2241 for (i = 0; i < pwqp->n; ++i) {
2242 pwqp->p[i].set = isl_set_move_dims(pwqp->p[i].set,
2244 src_type, src_pos, n);
2245 if (!pwqp->p[i].set)
2247 pwqp->p[i].qp = isl_qpolynomial_move_dims(pwqp->p[i].qp,
2248 dst_type, dst_pos, src_type, src_pos, n);
2255 isl_pw_qpolynomial_free(pwqp);
2260 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
2261 isl_int denom, unsigned len)
2264 struct isl_upoly *up;
2266 isl_assert(ctx, len >= 1, return NULL);
2268 up = isl_upoly_rat_cst(ctx, f[0], denom);
2269 for (i = 0; i < len - 1; ++i) {
2270 struct isl_upoly *t;
2271 struct isl_upoly *c;
2273 if (isl_int_is_zero(f[1 + i]))
2276 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
2277 t = isl_upoly_pow(ctx, i, 1);
2278 t = isl_upoly_mul(c, t);
2279 up = isl_upoly_sum(up, t);
2285 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2286 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2290 struct isl_upoly *up;
2291 isl_qpolynomial *qp;
2297 isl_int_init(denom);
2299 isl_constraint_get_coefficient(c, type, pos, &denom);
2300 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2301 sgn = isl_int_sgn(denom);
2302 isl_int_abs(denom, denom);
2303 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2304 1 + isl_constraint_dim(c, isl_dim_all));
2306 isl_int_neg(denom, denom);
2307 isl_constraint_set_coefficient(c, type, pos, denom);
2309 dim = isl_dim_copy(c->bmap->dim);
2311 isl_int_clear(denom);
2312 isl_constraint_free(c);
2314 qp = isl_qpolynomial_alloc(dim, 0, up);
2316 qp = isl_qpolynomial_neg(qp);
2320 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
2321 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
2324 struct isl_upoly_rec *rec;
2325 struct isl_upoly *base, *res;
2330 if (isl_upoly_is_cst(up))
2333 if (up->var < first)
2336 rec = isl_upoly_as_rec(up);
2340 isl_assert(up->ctx, rec->n >= 1, goto error);
2342 if (up->var >= first + n)
2343 base = isl_upoly_pow(up->ctx, up->var, 1);
2345 base = isl_upoly_copy(subs[up->var - first]);
2347 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
2348 for (i = rec->n - 2; i >= 0; --i) {
2349 struct isl_upoly *t;
2350 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
2351 res = isl_upoly_mul(res, isl_upoly_copy(base));
2352 res = isl_upoly_sum(res, t);
2355 isl_upoly_free(base);
2364 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2365 * in "qp" by subs[i].
2367 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2368 __isl_take isl_qpolynomial *qp,
2369 enum isl_dim_type type, unsigned first, unsigned n,
2370 __isl_keep isl_qpolynomial **subs)
2373 struct isl_upoly **ups;
2378 qp = isl_qpolynomial_cow(qp);
2381 for (i = 0; i < n; ++i)
2385 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2388 for (i = 0; i < n; ++i)
2389 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2392 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2393 for (i = 0; i < n; ++i)
2394 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2396 first += pos(qp->dim, type);
2398 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2401 for (i = 0; i < n; ++i)
2402 ups[i] = subs[i]->upoly;
2404 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2413 isl_qpolynomial_free(qp);
2417 __isl_give isl_basic_set *add_div_constraints(__isl_take isl_basic_set *bset,
2418 __isl_take isl_mat *div)
2426 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2429 total = isl_basic_set_total_dim(bset);
2430 for (i = 0; i < div->n_row; ++i)
2431 if (isl_basic_set_add_div_constraints_var(bset,
2432 total - div->n_row + i, div->row[i]) < 0)
2439 isl_basic_set_free(bset);
2443 /* Extend "bset" with extra set dimensions for each integer division
2444 * in "qp" and then call "fn" with the extended bset and the polynomial
2445 * that results from replacing each of the integer divisions by the
2446 * corresponding extra set dimension.
2448 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2449 __isl_keep isl_basic_set *bset,
2450 int (*fn)(__isl_take isl_basic_set *bset,
2451 __isl_take isl_qpolynomial *poly, void *user), void *user)
2455 isl_qpolynomial *poly;
2459 if (qp->div->n_row == 0)
2460 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
2463 div = isl_mat_copy(qp->div);
2464 dim = isl_dim_copy(qp->dim);
2465 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
2466 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
2467 bset = isl_basic_set_copy(bset);
2468 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
2469 bset = add_div_constraints(bset, div);
2471 return fn(bset, poly, user);
2476 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
2477 __isl_take isl_mat *div)
2485 n = isl_dim_total(dim) + div->n_row;
2487 term = isl_calloc(dim->ctx, struct isl_term,
2488 sizeof(struct isl_term) + (n - 1) * sizeof(int));
2495 isl_int_init(term->n);
2496 isl_int_init(term->d);
2505 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
2514 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
2523 total = isl_dim_total(term->dim) + term->div->n_row;
2525 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
2529 isl_int_set(dup->n, term->n);
2530 isl_int_set(dup->d, term->d);
2532 for (i = 0; i < total; ++i)
2533 dup->pow[i] = term->pow[i];
2538 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
2546 return isl_term_dup(term);
2549 void isl_term_free(__isl_take isl_term *term)
2554 if (--term->ref > 0)
2557 isl_dim_free(term->dim);
2558 isl_mat_free(term->div);
2559 isl_int_clear(term->n);
2560 isl_int_clear(term->d);
2564 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
2572 case isl_dim_out: return isl_dim_size(term->dim, type);
2573 case isl_dim_div: return term->div->n_row;
2574 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
2578 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
2580 return term ? term->dim->ctx : NULL;
2583 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
2587 isl_int_set(*n, term->n);
2590 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
2594 isl_int_set(*d, term->d);
2597 int isl_term_get_exp(__isl_keep isl_term *term,
2598 enum isl_dim_type type, unsigned pos)
2603 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
2605 if (type >= isl_dim_set)
2606 pos += isl_dim_size(term->dim, isl_dim_param);
2607 if (type >= isl_dim_div)
2608 pos += isl_dim_size(term->dim, isl_dim_set);
2610 return term->pow[pos];
2613 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
2615 isl_basic_map *bmap;
2622 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
2625 total = term->div->n_col - term->div->n_row - 2;
2626 /* No nested divs for now */
2627 isl_assert(term->dim->ctx,
2628 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
2629 term->div->n_row) == -1,
2632 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
2633 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
2636 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
2638 return isl_basic_map_div(bmap, k);
2640 isl_basic_map_free(bmap);
2644 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
2645 int (*fn)(__isl_take isl_term *term, void *user),
2646 __isl_take isl_term *term, void *user)
2649 struct isl_upoly_rec *rec;
2654 if (isl_upoly_is_zero(up))
2657 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
2658 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
2659 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
2661 if (isl_upoly_is_cst(up)) {
2662 struct isl_upoly_cst *cst;
2663 cst = isl_upoly_as_cst(up);
2666 term = isl_term_cow(term);
2669 isl_int_set(term->n, cst->n);
2670 isl_int_set(term->d, cst->d);
2671 if (fn(isl_term_copy(term), user) < 0)
2676 rec = isl_upoly_as_rec(up);
2680 for (i = 0; i < rec->n; ++i) {
2681 term = isl_term_cow(term);
2684 term->pow[up->var] = i;
2685 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
2689 term->pow[up->var] = 0;
2693 isl_term_free(term);
2697 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
2698 int (*fn)(__isl_take isl_term *term, void *user), void *user)
2705 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
2709 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
2711 isl_term_free(term);
2713 return term ? 0 : -1;
2716 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
2718 struct isl_upoly *up;
2719 isl_qpolynomial *qp;
2725 n = isl_dim_total(term->dim) + term->div->n_row;
2727 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
2728 for (i = 0; i < n; ++i) {
2731 up = isl_upoly_mul(up,
2732 isl_upoly_pow(term->dim->ctx, i, term->pow[i]));
2735 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
2738 isl_mat_free(qp->div);
2739 qp->div = isl_mat_copy(term->div);
2743 isl_term_free(term);
2746 isl_qpolynomial_free(qp);
2747 isl_term_free(term);
2751 int isl_pw_qpolynomial_foreach_piece(__isl_keep isl_pw_qpolynomial *pwqp,
2752 int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp,
2753 void *user), void *user)
2760 for (i = 0; i < pwqp->n; ++i)
2761 if (fn(isl_set_copy(pwqp->p[i].set),
2762 isl_qpolynomial_copy(pwqp->p[i].qp), user) < 0)
2768 static int any_divs(__isl_keep isl_set *set)
2775 for (i = 0; i < set->n; ++i)
2776 if (set->p[i]->n_div > 0)
2782 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
2783 __isl_take isl_dim *dim)
2788 if (isl_dim_equal(qp->dim, dim)) {
2793 qp = isl_qpolynomial_cow(qp);
2797 if (qp->div->n_row) {
2803 extra = isl_dim_size(dim, isl_dim_set) -
2804 isl_dim_size(qp->dim, isl_dim_set);
2805 total = isl_dim_total(qp->dim);
2806 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
2809 for (i = 0; i < qp->div->n_row; ++i)
2811 qp->upoly = expand(qp->upoly, exp, total);
2815 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
2818 for (i = 0; i < qp->div->n_row; ++i)
2819 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
2822 isl_dim_free(qp->dim);
2828 isl_qpolynomial_free(qp);
2832 static int foreach_lifted_subset(__isl_take isl_set *set,
2833 __isl_take isl_qpolynomial *qp,
2834 int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp,
2835 void *user), void *user)
2842 for (i = 0; i < set->n; ++i) {
2844 isl_qpolynomial *copy;
2846 lift = isl_set_from_basic_set(isl_basic_set_copy(set->p[i]));
2847 lift = isl_set_lift(lift);
2849 copy = isl_qpolynomial_copy(qp);
2850 copy = isl_qpolynomial_lift(copy, isl_set_get_dim(lift));
2852 if (fn(lift, copy, user) < 0)
2857 isl_qpolynomial_free(qp);
2862 isl_qpolynomial_free(qp);
2866 int isl_pw_qpolynomial_foreach_lifted_piece(__isl_keep isl_pw_qpolynomial *pwqp,
2867 int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp,
2868 void *user), void *user)
2875 for (i = 0; i < pwqp->n; ++i) {
2877 isl_qpolynomial *qp;
2879 set = isl_set_copy(pwqp->p[i].set);
2880 qp = isl_qpolynomial_copy(pwqp->p[i].qp);
2881 if (!any_divs(set)) {
2882 if (fn(set, qp, user) < 0)
2886 if (foreach_lifted_subset(set, qp, fn, user) < 0)
2893 /* For each parameter or variable that does not appear in qp,
2894 * first eliminate the variable from all constraints and then set it to zero.
2896 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
2897 __isl_keep isl_qpolynomial *qp)
2908 d = isl_dim_total(set->dim);
2909 active = isl_calloc_array(set->ctx, int, d);
2910 if (set_active(qp, active) < 0)
2913 for (i = 0; i < d; ++i)
2922 nparam = isl_dim_size(set->dim, isl_dim_param);
2923 nvar = isl_dim_size(set->dim, isl_dim_set);
2924 for (i = 0; i < nparam; ++i) {
2927 set = isl_set_eliminate(set, isl_dim_param, i, 1);
2928 set = isl_set_fix_si(set, isl_dim_param, i, 0);
2930 for (i = 0; i < nvar; ++i) {
2931 if (active[nparam + i])
2933 set = isl_set_eliminate(set, isl_dim_set, i, 1);
2934 set = isl_set_fix_si(set, isl_dim_set, i, 0);
2946 struct isl_opt_data {
2947 isl_qpolynomial *qp;
2949 isl_qpolynomial *opt;
2953 static int opt_fn(__isl_take isl_point *pnt, void *user)
2955 struct isl_opt_data *data = (struct isl_opt_data *)user;
2956 isl_qpolynomial *val;
2958 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
2962 } else if (data->max) {
2963 data->opt = isl_qpolynomial_max_cst(data->opt, val);
2965 data->opt = isl_qpolynomial_min_cst(data->opt, val);
2971 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
2972 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
2974 struct isl_opt_data data = { NULL, 1, NULL, max };
2979 if (isl_upoly_is_cst(qp->upoly)) {
2984 set = fix_inactive(set, qp);
2987 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
2991 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
2994 isl_qpolynomial_free(qp);
2998 isl_qpolynomial_free(qp);
2999 isl_qpolynomial_free(data.opt);