2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
12 #include <isl_factorization.h>
15 #include <isl_union_map_private.h>
16 #include <isl_polynomial_private.h>
17 #include <isl_point_private.h>
18 #include <isl_dim_private.h>
19 #include <isl_map_private.h>
20 #include <isl_mat_private.h>
21 #include <isl_range.h>
23 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
26 case isl_dim_param: return 0;
27 case isl_dim_in: return dim->nparam;
28 case isl_dim_out: return dim->nparam + dim->n_in;
33 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
41 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
46 isl_assert(up->ctx, up->var < 0, return NULL);
48 return (struct isl_upoly_cst *)up;
51 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
56 isl_assert(up->ctx, up->var >= 0, return NULL);
58 return (struct isl_upoly_rec *)up;
61 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
62 __isl_keep struct isl_upoly *up2)
65 struct isl_upoly_rec *rec1, *rec2;
71 if (up1->var != up2->var)
73 if (isl_upoly_is_cst(up1)) {
74 struct isl_upoly_cst *cst1, *cst2;
75 cst1 = isl_upoly_as_cst(up1);
76 cst2 = isl_upoly_as_cst(up2);
79 return isl_int_eq(cst1->n, cst2->n) &&
80 isl_int_eq(cst1->d, cst2->d);
83 rec1 = isl_upoly_as_rec(up1);
84 rec2 = isl_upoly_as_rec(up2);
88 if (rec1->n != rec2->n)
91 for (i = 0; i < rec1->n; ++i) {
92 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
100 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
102 struct isl_upoly_cst *cst;
106 if (!isl_upoly_is_cst(up))
109 cst = isl_upoly_as_cst(up);
113 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
116 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
118 struct isl_upoly_cst *cst;
122 if (!isl_upoly_is_cst(up))
125 cst = isl_upoly_as_cst(up);
129 return isl_int_sgn(cst->n);
132 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
134 struct isl_upoly_cst *cst;
138 if (!isl_upoly_is_cst(up))
141 cst = isl_upoly_as_cst(up);
145 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
148 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
150 struct isl_upoly_cst *cst;
154 if (!isl_upoly_is_cst(up))
157 cst = isl_upoly_as_cst(up);
161 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
164 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
166 struct isl_upoly_cst *cst;
170 if (!isl_upoly_is_cst(up))
173 cst = isl_upoly_as_cst(up);
177 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
180 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
182 struct isl_upoly_cst *cst;
186 if (!isl_upoly_is_cst(up))
189 cst = isl_upoly_as_cst(up);
193 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
196 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
198 struct isl_upoly_cst *cst;
202 if (!isl_upoly_is_cst(up))
205 cst = isl_upoly_as_cst(up);
209 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
212 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
214 struct isl_upoly_cst *cst;
216 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
225 isl_int_init(cst->n);
226 isl_int_init(cst->d);
231 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
233 struct isl_upoly_cst *cst;
235 cst = isl_upoly_cst_alloc(ctx);
239 isl_int_set_si(cst->n, 0);
240 isl_int_set_si(cst->d, 1);
245 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
247 struct isl_upoly_cst *cst;
249 cst = isl_upoly_cst_alloc(ctx);
253 isl_int_set_si(cst->n, 1);
254 isl_int_set_si(cst->d, 1);
259 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
261 struct isl_upoly_cst *cst;
263 cst = isl_upoly_cst_alloc(ctx);
267 isl_int_set_si(cst->n, 1);
268 isl_int_set_si(cst->d, 0);
273 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
275 struct isl_upoly_cst *cst;
277 cst = isl_upoly_cst_alloc(ctx);
281 isl_int_set_si(cst->n, -1);
282 isl_int_set_si(cst->d, 0);
287 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
289 struct isl_upoly_cst *cst;
291 cst = isl_upoly_cst_alloc(ctx);
295 isl_int_set_si(cst->n, 0);
296 isl_int_set_si(cst->d, 0);
301 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
302 isl_int n, isl_int d)
304 struct isl_upoly_cst *cst;
306 cst = isl_upoly_cst_alloc(ctx);
310 isl_int_set(cst->n, n);
311 isl_int_set(cst->d, d);
316 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
319 struct isl_upoly_rec *rec;
321 isl_assert(ctx, var >= 0, return NULL);
322 isl_assert(ctx, size >= 0, return NULL);
323 rec = isl_calloc(ctx, struct isl_upoly_rec,
324 sizeof(struct isl_upoly_rec) +
325 (size - 1) * sizeof(struct isl_upoly *));
340 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
341 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
343 qp = isl_qpolynomial_cow(qp);
347 isl_dim_free(qp->dim);
352 isl_qpolynomial_free(qp);
357 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
359 return qp ? qp->dim->ctx : NULL;
362 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
364 return qp ? isl_dim_copy(qp->dim) : NULL;
367 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
368 enum isl_dim_type type)
370 return qp ? isl_dim_size(qp->dim, type) : 0;
373 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
375 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
378 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
380 return qp ? isl_upoly_is_one(qp->upoly) : -1;
383 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
385 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
388 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
390 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
393 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
395 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
398 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
400 return qp ? isl_upoly_sgn(qp->upoly) : 0;
403 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
405 isl_int_clear(cst->n);
406 isl_int_clear(cst->d);
409 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
413 for (i = 0; i < rec->n; ++i)
414 isl_upoly_free(rec->p[i]);
417 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
426 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
428 struct isl_upoly_cst *cst;
429 struct isl_upoly_cst *dup;
431 cst = isl_upoly_as_cst(up);
435 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
438 isl_int_set(dup->n, cst->n);
439 isl_int_set(dup->d, cst->d);
444 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
447 struct isl_upoly_rec *rec;
448 struct isl_upoly_rec *dup;
450 rec = isl_upoly_as_rec(up);
454 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
458 for (i = 0; i < rec->n; ++i) {
459 dup->p[i] = isl_upoly_copy(rec->p[i]);
467 isl_upoly_free(&dup->up);
471 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
473 struct isl_upoly *dup;
478 if (isl_upoly_is_cst(up))
479 return isl_upoly_dup_cst(up);
481 return isl_upoly_dup_rec(up);
484 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
492 return isl_upoly_dup(up);
495 void isl_upoly_free(__isl_take struct isl_upoly *up)
504 upoly_free_cst((struct isl_upoly_cst *)up);
506 upoly_free_rec((struct isl_upoly_rec *)up);
508 isl_ctx_deref(up->ctx);
512 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
517 isl_int_gcd(gcd, cst->n, cst->d);
518 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
519 isl_int_divexact(cst->n, cst->n, gcd);
520 isl_int_divexact(cst->d, cst->d, gcd);
525 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
526 __isl_take struct isl_upoly *up2)
528 struct isl_upoly_cst *cst1;
529 struct isl_upoly_cst *cst2;
531 up1 = isl_upoly_cow(up1);
535 cst1 = isl_upoly_as_cst(up1);
536 cst2 = isl_upoly_as_cst(up2);
538 if (isl_int_eq(cst1->d, cst2->d))
539 isl_int_add(cst1->n, cst1->n, cst2->n);
541 isl_int_mul(cst1->n, cst1->n, cst2->d);
542 isl_int_addmul(cst1->n, cst2->n, cst1->d);
543 isl_int_mul(cst1->d, cst1->d, cst2->d);
546 isl_upoly_cst_reduce(cst1);
556 static __isl_give struct isl_upoly *replace_by_zero(
557 __isl_take struct isl_upoly *up)
565 return isl_upoly_zero(ctx);
568 static __isl_give struct isl_upoly *replace_by_constant_term(
569 __isl_take struct isl_upoly *up)
571 struct isl_upoly_rec *rec;
572 struct isl_upoly *cst;
577 rec = isl_upoly_as_rec(up);
580 cst = isl_upoly_copy(rec->p[0]);
588 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
589 __isl_take struct isl_upoly *up2)
592 struct isl_upoly_rec *rec1, *rec2;
597 if (isl_upoly_is_nan(up1)) {
602 if (isl_upoly_is_nan(up2)) {
607 if (isl_upoly_is_zero(up1)) {
612 if (isl_upoly_is_zero(up2)) {
617 if (up1->var < up2->var)
618 return isl_upoly_sum(up2, up1);
620 if (up2->var < up1->var) {
621 struct isl_upoly_rec *rec;
622 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
626 up1 = isl_upoly_cow(up1);
627 rec = isl_upoly_as_rec(up1);
630 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
632 up1 = replace_by_constant_term(up1);
636 if (isl_upoly_is_cst(up1))
637 return isl_upoly_sum_cst(up1, up2);
639 rec1 = isl_upoly_as_rec(up1);
640 rec2 = isl_upoly_as_rec(up2);
644 if (rec1->n < rec2->n)
645 return isl_upoly_sum(up2, up1);
647 up1 = isl_upoly_cow(up1);
648 rec1 = isl_upoly_as_rec(up1);
652 for (i = rec2->n - 1; i >= 0; --i) {
653 rec1->p[i] = isl_upoly_sum(rec1->p[i],
654 isl_upoly_copy(rec2->p[i]));
657 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
658 isl_upoly_free(rec1->p[i]);
664 up1 = replace_by_zero(up1);
665 else if (rec1->n == 1)
666 up1 = replace_by_constant_term(up1);
677 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
678 __isl_take struct isl_upoly *up, isl_int v)
680 struct isl_upoly_cst *cst;
682 up = isl_upoly_cow(up);
686 cst = isl_upoly_as_cst(up);
688 isl_int_addmul(cst->n, cst->d, v);
693 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
694 __isl_take struct isl_upoly *up, isl_int v)
696 struct isl_upoly_rec *rec;
701 if (isl_upoly_is_cst(up))
702 return isl_upoly_cst_add_isl_int(up, v);
704 up = isl_upoly_cow(up);
705 rec = isl_upoly_as_rec(up);
709 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
719 __isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up)
721 struct isl_upoly_cst *cst;
723 if (isl_upoly_is_zero(up))
726 up = isl_upoly_cow(up);
730 cst = isl_upoly_as_cst(up);
732 isl_int_neg(cst->n, cst->n);
737 __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up)
740 struct isl_upoly_rec *rec;
745 if (isl_upoly_is_cst(up))
746 return isl_upoly_neg_cst(up);
748 up = isl_upoly_cow(up);
749 rec = isl_upoly_as_rec(up);
753 for (i = 0; i < rec->n; ++i) {
754 rec->p[i] = isl_upoly_neg(rec->p[i]);
765 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
766 __isl_take struct isl_upoly *up2)
768 struct isl_upoly_cst *cst1;
769 struct isl_upoly_cst *cst2;
771 up1 = isl_upoly_cow(up1);
775 cst1 = isl_upoly_as_cst(up1);
776 cst2 = isl_upoly_as_cst(up2);
778 isl_int_mul(cst1->n, cst1->n, cst2->n);
779 isl_int_mul(cst1->d, cst1->d, cst2->d);
781 isl_upoly_cst_reduce(cst1);
791 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
792 __isl_take struct isl_upoly *up2)
794 struct isl_upoly_rec *rec1;
795 struct isl_upoly_rec *rec2;
796 struct isl_upoly_rec *res;
800 rec1 = isl_upoly_as_rec(up1);
801 rec2 = isl_upoly_as_rec(up2);
804 size = rec1->n + rec2->n - 1;
805 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
809 for (i = 0; i < rec1->n; ++i) {
810 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
811 isl_upoly_copy(rec1->p[i]));
816 for (; i < size; ++i) {
817 res->p[i] = isl_upoly_zero(up1->ctx);
822 for (i = 0; i < rec1->n; ++i) {
823 for (j = 1; j < rec2->n; ++j) {
824 struct isl_upoly *up;
825 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
826 isl_upoly_copy(rec1->p[i]));
827 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
840 isl_upoly_free(&res->up);
844 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
845 __isl_take struct isl_upoly *up2)
850 if (isl_upoly_is_nan(up1)) {
855 if (isl_upoly_is_nan(up2)) {
860 if (isl_upoly_is_zero(up1)) {
865 if (isl_upoly_is_zero(up2)) {
870 if (isl_upoly_is_one(up1)) {
875 if (isl_upoly_is_one(up2)) {
880 if (up1->var < up2->var)
881 return isl_upoly_mul(up2, up1);
883 if (up2->var < up1->var) {
885 struct isl_upoly_rec *rec;
886 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
887 isl_ctx *ctx = up1->ctx;
890 return isl_upoly_nan(ctx);
892 up1 = isl_upoly_cow(up1);
893 rec = isl_upoly_as_rec(up1);
897 for (i = 0; i < rec->n; ++i) {
898 rec->p[i] = isl_upoly_mul(rec->p[i],
899 isl_upoly_copy(up2));
907 if (isl_upoly_is_cst(up1))
908 return isl_upoly_mul_cst(up1, up2);
910 return isl_upoly_mul_rec(up1, up2);
917 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
920 struct isl_upoly *res;
928 res = isl_upoly_copy(up);
930 res = isl_upoly_one(up->ctx);
932 while (power >>= 1) {
933 up = isl_upoly_mul(up, isl_upoly_copy(up));
935 res = isl_upoly_mul(res, isl_upoly_copy(up));
942 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
943 unsigned n_div, __isl_take struct isl_upoly *up)
945 struct isl_qpolynomial *qp = NULL;
951 total = isl_dim_total(dim);
953 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
958 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
969 isl_qpolynomial_free(qp);
973 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
982 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
984 struct isl_qpolynomial *dup;
989 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
990 isl_upoly_copy(qp->upoly));
993 isl_mat_free(dup->div);
994 dup->div = isl_mat_copy(qp->div);
1000 isl_qpolynomial_free(dup);
1004 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1012 return isl_qpolynomial_dup(qp);
1015 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1023 isl_dim_free(qp->dim);
1024 isl_mat_free(qp->div);
1025 isl_upoly_free(qp->upoly);
1030 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1033 struct isl_upoly *up;
1034 struct isl_upoly_rec *rec;
1035 struct isl_upoly_cst *cst;
1037 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1040 for (i = 0; i < 1 + power; ++i) {
1041 rec->p[i] = isl_upoly_zero(ctx);
1046 cst = isl_upoly_as_cst(rec->p[power]);
1047 isl_int_set_si(cst->n, 1);
1051 isl_upoly_free(&rec->up);
1055 /* r array maps original positions to new positions.
1057 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1061 struct isl_upoly_rec *rec;
1062 struct isl_upoly *base;
1063 struct isl_upoly *res;
1065 if (isl_upoly_is_cst(up))
1068 rec = isl_upoly_as_rec(up);
1072 isl_assert(up->ctx, rec->n >= 1, goto error);
1074 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1075 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1077 for (i = rec->n - 2; i >= 0; --i) {
1078 res = isl_upoly_mul(res, isl_upoly_copy(base));
1079 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1082 isl_upoly_free(base);
1091 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1096 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1097 div1->n_col >= div2->n_col, return -1);
1099 if (div1->n_row == div2->n_row)
1100 return isl_mat_is_equal(div1, div2);
1102 n_row = div1->n_row;
1103 n_col = div1->n_col;
1104 div1->n_row = div2->n_row;
1105 div1->n_col = div2->n_col;
1107 equal = isl_mat_is_equal(div1, div2);
1109 div1->n_row = n_row;
1110 div1->n_col = n_col;
1115 static void expand_row(__isl_keep isl_mat *dst, int d,
1116 __isl_keep isl_mat *src, int s, int *exp)
1119 unsigned c = src->n_col - src->n_row;
1121 isl_seq_cpy(dst->row[d], src->row[s], c);
1122 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
1124 for (i = 0; i < s; ++i)
1125 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
1128 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1132 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1133 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1138 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1141 struct isl_div_sort_info {
1146 static int div_sort_cmp(const void *p1, const void *p2)
1148 const struct isl_div_sort_info *i1, *i2;
1149 i1 = (const struct isl_div_sort_info *) p1;
1150 i2 = (const struct isl_div_sort_info *) p2;
1152 return cmp_row(i1->div, i1->row, i2->row);
1155 /* Sort divs and remove duplicates.
1157 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1162 struct isl_div_sort_info *array = NULL;
1163 int *pos = NULL, *at = NULL;
1164 int *reordering = NULL;
1169 if (qp->div->n_row <= 1)
1172 div_pos = isl_dim_total(qp->dim);
1174 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1176 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1177 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1178 len = qp->div->n_col - 2;
1179 reordering = isl_alloc_array(qp->div->ctx, int, len);
1180 if (!array || !pos || !at || !reordering)
1183 for (i = 0; i < qp->div->n_row; ++i) {
1184 array[i].div = qp->div;
1190 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1193 for (i = 0; i < div_pos; ++i)
1196 for (i = 0; i < qp->div->n_row; ++i) {
1197 if (pos[array[i].row] == i)
1199 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1200 pos[at[i]] = pos[array[i].row];
1201 at[pos[array[i].row]] = at[i];
1202 at[i] = array[i].row;
1203 pos[array[i].row] = i;
1207 for (i = 0; i < len - div_pos; ++i) {
1209 isl_seq_eq(qp->div->row[i - skip - 1],
1210 qp->div->row[i - skip], qp->div->n_col)) {
1211 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1212 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1213 2 + div_pos + i - skip);
1214 qp->div = isl_mat_drop_cols(qp->div,
1215 2 + div_pos + i - skip, 1);
1218 reordering[div_pos + array[i].row] = div_pos + i - skip;
1221 qp->upoly = reorder(qp->upoly, reordering);
1223 if (!qp->upoly || !qp->div)
1237 isl_qpolynomial_free(qp);
1241 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1242 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1245 isl_mat *div = NULL;
1246 unsigned d = div1->n_col - div1->n_row;
1248 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1249 d + div1->n_row + div2->n_row);
1253 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1256 expand_row(div, k, div1, i, exp1);
1257 expand_row(div, k + 1, div2, j, exp2);
1259 cmp = cmp_row(div, k, k + 1);
1263 } else if (cmp < 0) {
1267 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1270 for (; i < div1->n_row; ++i, ++k) {
1271 expand_row(div, k, div1, i, exp1);
1274 for (; j < div2->n_row; ++j, ++k) {
1275 expand_row(div, k, div2, j, exp2);
1285 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1286 int *exp, int first)
1289 struct isl_upoly_rec *rec;
1291 if (isl_upoly_is_cst(up))
1294 if (up->var < first)
1297 if (exp[up->var - first] == up->var - first)
1300 up = isl_upoly_cow(up);
1304 up->var = exp[up->var - first] + first;
1306 rec = isl_upoly_as_rec(up);
1310 for (i = 0; i < rec->n; ++i) {
1311 rec->p[i] = expand(rec->p[i], exp, first);
1322 static __isl_give isl_qpolynomial *with_merged_divs(
1323 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1324 __isl_take isl_qpolynomial *qp2),
1325 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1329 isl_mat *div = NULL;
1331 qp1 = isl_qpolynomial_cow(qp1);
1332 qp2 = isl_qpolynomial_cow(qp2);
1337 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1338 qp1->div->n_col >= qp2->div->n_col, goto error);
1340 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1341 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1345 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1349 isl_mat_free(qp1->div);
1350 qp1->div = isl_mat_copy(div);
1351 isl_mat_free(qp2->div);
1352 qp2->div = isl_mat_copy(div);
1354 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1355 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1357 if (!qp1->upoly || !qp2->upoly)
1364 return fn(qp1, qp2);
1369 isl_qpolynomial_free(qp1);
1370 isl_qpolynomial_free(qp2);
1374 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1375 __isl_take isl_qpolynomial *qp2)
1377 qp1 = isl_qpolynomial_cow(qp1);
1382 if (qp1->div->n_row < qp2->div->n_row)
1383 return isl_qpolynomial_add(qp2, qp1);
1385 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1386 if (!compatible_divs(qp1->div, qp2->div))
1387 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1389 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1393 isl_qpolynomial_free(qp2);
1397 isl_qpolynomial_free(qp1);
1398 isl_qpolynomial_free(qp2);
1402 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1403 __isl_keep isl_set *dom,
1404 __isl_take isl_qpolynomial *qp1,
1405 __isl_take isl_qpolynomial *qp2)
1407 qp1 = isl_qpolynomial_add(qp1, qp2);
1408 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1412 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1413 __isl_take isl_qpolynomial *qp2)
1415 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1418 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1419 __isl_take isl_qpolynomial *qp, isl_int v)
1421 if (isl_int_is_zero(v))
1424 qp = isl_qpolynomial_cow(qp);
1428 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1434 isl_qpolynomial_free(qp);
1439 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1441 qp = isl_qpolynomial_cow(qp);
1446 qp->upoly = isl_upoly_neg(qp->upoly);
1452 isl_qpolynomial_free(qp);
1456 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1457 __isl_take isl_qpolynomial *qp2)
1459 qp1 = isl_qpolynomial_cow(qp1);
1464 if (qp1->div->n_row < qp2->div->n_row)
1465 return isl_qpolynomial_mul(qp2, qp1);
1467 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1468 if (!compatible_divs(qp1->div, qp2->div))
1469 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1471 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1475 isl_qpolynomial_free(qp2);
1479 isl_qpolynomial_free(qp1);
1480 isl_qpolynomial_free(qp2);
1484 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1487 qp = isl_qpolynomial_cow(qp);
1492 qp->upoly = isl_upoly_pow(qp->upoly, power);
1498 isl_qpolynomial_free(qp);
1502 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1504 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1507 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1509 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1512 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1514 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1517 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1519 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1522 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1524 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1527 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1530 struct isl_qpolynomial *qp;
1531 struct isl_upoly_cst *cst;
1533 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1537 cst = isl_upoly_as_cst(qp->upoly);
1538 isl_int_set(cst->n, v);
1543 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1544 isl_int *n, isl_int *d)
1546 struct isl_upoly_cst *cst;
1551 if (!isl_upoly_is_cst(qp->upoly))
1554 cst = isl_upoly_as_cst(qp->upoly);
1559 isl_int_set(*n, cst->n);
1561 isl_int_set(*d, cst->d);
1566 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1569 struct isl_upoly_rec *rec;
1577 rec = isl_upoly_as_rec(up);
1584 isl_assert(up->ctx, rec->n > 1, return -1);
1586 is_cst = isl_upoly_is_cst(rec->p[1]);
1592 return isl_upoly_is_affine(rec->p[0]);
1595 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1600 if (qp->div->n_row > 0)
1603 return isl_upoly_is_affine(qp->upoly);
1606 static void update_coeff(__isl_keep isl_vec *aff,
1607 __isl_keep struct isl_upoly_cst *cst, int pos)
1612 if (isl_int_is_zero(cst->n))
1617 isl_int_gcd(gcd, cst->d, aff->el[0]);
1618 isl_int_divexact(f, cst->d, gcd);
1619 isl_int_divexact(gcd, aff->el[0], gcd);
1620 isl_seq_scale(aff->el, aff->el, f, aff->size);
1621 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1626 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1627 __isl_keep isl_vec *aff)
1629 struct isl_upoly_cst *cst;
1630 struct isl_upoly_rec *rec;
1636 struct isl_upoly_cst *cst;
1638 cst = isl_upoly_as_cst(up);
1641 update_coeff(aff, cst, 0);
1645 rec = isl_upoly_as_rec(up);
1648 isl_assert(up->ctx, rec->n == 2, return -1);
1650 cst = isl_upoly_as_cst(rec->p[1]);
1653 update_coeff(aff, cst, 1 + up->var);
1655 return isl_upoly_update_affine(rec->p[0], aff);
1658 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1659 __isl_keep isl_qpolynomial *qp)
1667 isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1668 d = isl_dim_total(qp->dim);
1669 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1673 isl_seq_clr(aff->el + 1, 1 + d);
1674 isl_int_set_si(aff->el[0], 1);
1676 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1685 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1686 __isl_keep isl_qpolynomial *qp2)
1691 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1694 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1697 struct isl_upoly_rec *rec;
1699 if (isl_upoly_is_cst(up)) {
1700 struct isl_upoly_cst *cst;
1701 cst = isl_upoly_as_cst(up);
1704 isl_int_lcm(*d, *d, cst->d);
1708 rec = isl_upoly_as_rec(up);
1712 for (i = 0; i < rec->n; ++i)
1713 upoly_update_den(rec->p[i], d);
1716 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1718 isl_int_set_si(*d, 1);
1721 upoly_update_den(qp->upoly, d);
1724 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1727 struct isl_ctx *ctx;
1734 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1737 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1738 enum isl_dim_type type, unsigned pos)
1743 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1744 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1746 if (type == isl_dim_set)
1747 pos += isl_dim_size(dim, isl_dim_param);
1749 return isl_qpolynomial_var_pow(dim, pos, 1);
1755 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1756 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1759 struct isl_upoly_rec *rec;
1760 struct isl_upoly *base, *res;
1765 if (isl_upoly_is_cst(up))
1768 if (up->var < first)
1771 rec = isl_upoly_as_rec(up);
1775 isl_assert(up->ctx, rec->n >= 1, goto error);
1777 if (up->var >= first + n)
1778 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1780 base = isl_upoly_copy(subs[up->var - first]);
1782 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1783 for (i = rec->n - 2; i >= 0; --i) {
1784 struct isl_upoly *t;
1785 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1786 res = isl_upoly_mul(res, isl_upoly_copy(base));
1787 res = isl_upoly_sum(res, t);
1790 isl_upoly_free(base);
1799 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1800 isl_int denom, unsigned len)
1803 struct isl_upoly *up;
1805 isl_assert(ctx, len >= 1, return NULL);
1807 up = isl_upoly_rat_cst(ctx, f[0], denom);
1808 for (i = 0; i < len - 1; ++i) {
1809 struct isl_upoly *t;
1810 struct isl_upoly *c;
1812 if (isl_int_is_zero(f[1 + i]))
1815 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1816 t = isl_upoly_var_pow(ctx, i, 1);
1817 t = isl_upoly_mul(c, t);
1818 up = isl_upoly_sum(up, t);
1824 /* Remove common factor of non-constant terms and denominator.
1826 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1828 isl_ctx *ctx = qp->div->ctx;
1829 unsigned total = qp->div->n_col - 2;
1831 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1832 isl_int_gcd(ctx->normalize_gcd,
1833 ctx->normalize_gcd, qp->div->row[div][0]);
1834 if (isl_int_is_one(ctx->normalize_gcd))
1837 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1838 ctx->normalize_gcd, total);
1839 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1840 ctx->normalize_gcd);
1841 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1842 ctx->normalize_gcd);
1845 /* Replace the integer division identified by "div" by the polynomial "s".
1846 * The integer division is assumed not to appear in the definition
1847 * of any other integer divisions.
1849 static __isl_give isl_qpolynomial *substitute_div(
1850 __isl_take isl_qpolynomial *qp,
1851 int div, __isl_take struct isl_upoly *s)
1860 qp = isl_qpolynomial_cow(qp);
1864 total = isl_dim_total(qp->dim);
1865 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1869 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1872 for (i = 0; i < total + div; ++i)
1874 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1875 reordering[i] = i - 1;
1876 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1877 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1878 qp->upoly = reorder(qp->upoly, reordering);
1881 if (!qp->upoly || !qp->div)
1887 isl_qpolynomial_free(qp);
1892 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1893 * divisions because d is equal to 1 by their definition, i.e., e.
1895 static __isl_give isl_qpolynomial *substitute_non_divs(
1896 __isl_take isl_qpolynomial *qp)
1900 struct isl_upoly *s;
1905 total = isl_dim_total(qp->dim);
1906 for (i = 0; qp && i < qp->div->n_row; ++i) {
1907 if (!isl_int_is_one(qp->div->row[i][0]))
1909 for (j = i + 1; j < qp->div->n_row; ++j) {
1910 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1912 isl_seq_combine(qp->div->row[j] + 1,
1913 qp->div->ctx->one, qp->div->row[j] + 1,
1914 qp->div->row[j][2 + total + i],
1915 qp->div->row[i] + 1, 1 + total + i);
1916 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1917 normalize_div(qp, j);
1919 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1920 qp->div->row[i][0], qp->div->n_col - 1);
1921 qp = substitute_div(qp, i, s);
1928 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1929 * with d the denominator. When replacing the coefficient e of x by
1930 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1931 * inside the division, so we need to add floor(e/d) * x outside.
1932 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1933 * to adjust the coefficient of x in each later div that depends on the
1934 * current div "div" and also in the affine expression "aff"
1935 * (if it too depends on "div").
1937 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1938 __isl_keep isl_vec *aff)
1942 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1945 for (i = 0; i < 1 + total + div; ++i) {
1946 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1947 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1949 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1950 isl_int_fdiv_r(qp->div->row[div][1 + i],
1951 qp->div->row[div][1 + i], qp->div->row[div][0]);
1952 if (!isl_int_is_zero(aff->el[1 + total + div]))
1953 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1954 for (j = div + 1; j < qp->div->n_row; ++j) {
1955 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1957 isl_int_addmul(qp->div->row[j][1 + i],
1958 v, qp->div->row[j][2 + total + div]);
1964 /* Check if the last non-zero coefficient is bigger that half of the
1965 * denominator. If so, we will invert the div to further reduce the number
1966 * of distinct divs that may appear.
1967 * If the last non-zero coefficient is exactly half the denominator,
1968 * then we continue looking for earlier coefficients that are bigger
1969 * than half the denominator.
1971 static int needs_invert(__isl_keep isl_mat *div, int row)
1976 for (i = div->n_col - 1; i >= 1; --i) {
1977 if (isl_int_is_zero(div->row[row][i]))
1979 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1980 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1981 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1991 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1992 * We only invert the coefficients of e (and the coefficient of q in
1993 * later divs and in "aff"). After calling this function, the
1994 * coefficients of e should be reduced again.
1996 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1997 __isl_keep isl_vec *aff)
1999 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2001 isl_seq_neg(qp->div->row[div] + 1,
2002 qp->div->row[div] + 1, qp->div->n_col - 1);
2003 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2004 isl_int_add(qp->div->row[div][1],
2005 qp->div->row[div][1], qp->div->row[div][0]);
2006 if (!isl_int_is_zero(aff->el[1 + total + div]))
2007 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2008 isl_mat_col_mul(qp->div, 2 + total + div,
2009 qp->div->ctx->negone, 2 + total + div);
2012 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2013 * in the interval [0, d-1], with d the denominator and such that the
2014 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2016 * After the reduction, some divs may have become redundant or identical,
2017 * so we call substitute_non_divs and sort_divs. If these functions
2018 * eliminate divs of merge * two or more divs into one, the coefficients
2019 * of the enclosing divs may have to be reduced again, so we call
2020 * ourselves recursively if the number of divs decreases.
2022 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2025 isl_vec *aff = NULL;
2026 struct isl_upoly *s;
2032 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2033 aff = isl_vec_clr(aff);
2037 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2039 for (i = 0; i < qp->div->n_row; ++i) {
2040 normalize_div(qp, i);
2041 reduce_div(qp, i, aff);
2042 if (needs_invert(qp->div, i)) {
2043 invert_div(qp, i, aff);
2044 reduce_div(qp, i, aff);
2048 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2049 qp->div->ctx->one, aff->size);
2050 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2057 n_div = qp->div->n_row;
2058 qp = substitute_non_divs(qp);
2060 if (qp && qp->div->n_row < n_div)
2061 return reduce_divs(qp);
2065 isl_qpolynomial_free(qp);
2070 /* Assumes each div only depends on earlier divs.
2072 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2075 struct isl_qpolynomial *qp = NULL;
2076 struct isl_upoly_rec *rec;
2077 struct isl_upoly_cst *cst;
2084 d = div->line - div->bmap->div;
2086 pos = isl_dim_total(div->bmap->dim) + d;
2087 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2088 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2089 div->bmap->n_div, &rec->up);
2093 for (i = 0; i < div->bmap->n_div; ++i)
2094 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2096 for (i = 0; i < 1 + power; ++i) {
2097 rec->p[i] = isl_upoly_zero(div->ctx);
2102 cst = isl_upoly_as_cst(rec->p[power]);
2103 isl_int_set_si(cst->n, 1);
2107 qp = reduce_divs(qp);
2111 isl_qpolynomial_free(qp);
2116 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2118 return isl_qpolynomial_div_pow(div, 1);
2121 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2122 const isl_int n, const isl_int d)
2124 struct isl_qpolynomial *qp;
2125 struct isl_upoly_cst *cst;
2127 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2131 cst = isl_upoly_as_cst(qp->upoly);
2132 isl_int_set(cst->n, n);
2133 isl_int_set(cst->d, d);
2138 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2140 struct isl_upoly_rec *rec;
2146 if (isl_upoly_is_cst(up))
2150 active[up->var] = 1;
2152 rec = isl_upoly_as_rec(up);
2153 for (i = 0; i < rec->n; ++i)
2154 if (up_set_active(rec->p[i], active, d) < 0)
2160 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2163 int d = isl_dim_total(qp->dim);
2168 for (i = 0; i < d; ++i)
2169 for (j = 0; j < qp->div->n_row; ++j) {
2170 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2176 return up_set_active(qp->upoly, active, d);
2179 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2180 enum isl_dim_type type, unsigned first, unsigned n)
2191 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2193 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2194 type == isl_dim_set, return -1);
2196 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
2197 if (set_active(qp, active) < 0)
2200 if (type == isl_dim_set)
2201 first += isl_dim_size(qp->dim, isl_dim_param);
2202 for (i = 0; i < n; ++i)
2203 if (active[first + i]) {
2216 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2217 unsigned first, unsigned n)
2220 struct isl_upoly_rec *rec;
2224 if (n == 0 || up->var < 0 || up->var < first)
2226 if (up->var < first + n) {
2227 up = replace_by_constant_term(up);
2228 return isl_upoly_drop(up, first, n);
2230 up = isl_upoly_cow(up);
2234 rec = isl_upoly_as_rec(up);
2238 for (i = 0; i < rec->n; ++i) {
2239 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2250 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2251 __isl_take isl_qpolynomial *qp,
2252 enum isl_dim_type type, unsigned pos, const char *s)
2254 qp = isl_qpolynomial_cow(qp);
2257 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2262 isl_qpolynomial_free(qp);
2266 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2267 __isl_take isl_qpolynomial *qp,
2268 enum isl_dim_type type, unsigned first, unsigned n)
2272 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
2275 qp = isl_qpolynomial_cow(qp);
2279 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2281 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2282 type == isl_dim_set, goto error);
2284 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2288 if (type == isl_dim_set)
2289 first += isl_dim_size(qp->dim, isl_dim_param);
2291 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2295 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2301 isl_qpolynomial_free(qp);
2305 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2306 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2312 struct isl_upoly *up;
2316 if (eq->n_eq == 0) {
2317 isl_basic_set_free(eq);
2321 qp = isl_qpolynomial_cow(qp);
2324 qp->div = isl_mat_cow(qp->div);
2328 total = 1 + isl_dim_total(eq->dim);
2330 isl_int_init(denom);
2331 for (i = 0; i < eq->n_eq; ++i) {
2332 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2333 if (j < 0 || j == 0 || j >= total)
2336 for (k = 0; k < qp->div->n_row; ++k) {
2337 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2339 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2340 &qp->div->row[k][0]);
2341 normalize_div(qp, k);
2344 if (isl_int_is_pos(eq->eq[i][j]))
2345 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2346 isl_int_abs(denom, eq->eq[i][j]);
2347 isl_int_set_si(eq->eq[i][j], 0);
2349 up = isl_upoly_from_affine(qp->dim->ctx,
2350 eq->eq[i], denom, total);
2351 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2354 isl_int_clear(denom);
2359 isl_basic_set_free(eq);
2361 qp = substitute_non_divs(qp);
2366 isl_basic_set_free(eq);
2367 isl_qpolynomial_free(qp);
2371 static __isl_give isl_basic_set *add_div_constraints(
2372 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2380 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2383 total = isl_basic_set_total_dim(bset);
2384 for (i = 0; i < div->n_row; ++i)
2385 if (isl_basic_set_add_div_constraints_var(bset,
2386 total - div->n_row + i, div->row[i]) < 0)
2393 isl_basic_set_free(bset);
2397 /* Look for equalities among the variables shared by context and qp
2398 * and the integer divisions of qp, if any.
2399 * The equalities are then used to eliminate variables and/or integer
2400 * divisions from qp.
2402 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2403 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2409 if (qp->div->n_row > 0) {
2410 isl_basic_set *bset;
2411 context = isl_set_add_dims(context, isl_dim_set,
2413 bset = isl_basic_set_universe(isl_set_get_dim(context));
2414 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2415 context = isl_set_intersect(context,
2416 isl_set_from_basic_set(bset));
2419 aff = isl_set_affine_hull(context);
2420 return isl_qpolynomial_substitute_equalities(qp, aff);
2422 isl_qpolynomial_free(qp);
2423 isl_set_free(context);
2428 #define PW isl_pw_qpolynomial
2430 #define EL isl_qpolynomial
2432 #define IS_ZERO is_zero
2436 #include <isl_pw_templ.c>
2439 #define UNION isl_union_pw_qpolynomial
2441 #define PART isl_pw_qpolynomial
2443 #define PARTS pw_qpolynomial
2445 #include <isl_union_templ.c>
2447 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2455 if (!isl_set_fast_is_universe(pwqp->p[0].set))
2458 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2461 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2462 __isl_take isl_pw_qpolynomial *pwqp1,
2463 __isl_take isl_pw_qpolynomial *pwqp2)
2466 struct isl_pw_qpolynomial *res;
2469 if (!pwqp1 || !pwqp2)
2472 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2475 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2476 isl_pw_qpolynomial_free(pwqp2);
2480 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2481 isl_pw_qpolynomial_free(pwqp1);
2485 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2486 isl_pw_qpolynomial_free(pwqp1);
2490 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2491 isl_pw_qpolynomial_free(pwqp2);
2495 n = pwqp1->n * pwqp2->n;
2496 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2498 for (i = 0; i < pwqp1->n; ++i) {
2499 for (j = 0; j < pwqp2->n; ++j) {
2500 struct isl_set *common;
2501 struct isl_qpolynomial *prod;
2502 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2503 isl_set_copy(pwqp2->p[j].set));
2504 if (isl_set_fast_is_empty(common)) {
2505 isl_set_free(common);
2509 prod = isl_qpolynomial_mul(
2510 isl_qpolynomial_copy(pwqp1->p[i].qp),
2511 isl_qpolynomial_copy(pwqp2->p[j].qp));
2513 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2517 isl_pw_qpolynomial_free(pwqp1);
2518 isl_pw_qpolynomial_free(pwqp2);
2522 isl_pw_qpolynomial_free(pwqp1);
2523 isl_pw_qpolynomial_free(pwqp2);
2527 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2528 __isl_take isl_pw_qpolynomial *pwqp)
2535 if (isl_pw_qpolynomial_is_zero(pwqp))
2538 pwqp = isl_pw_qpolynomial_cow(pwqp);
2542 for (i = 0; i < pwqp->n; ++i) {
2543 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2550 isl_pw_qpolynomial_free(pwqp);
2554 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2555 __isl_take isl_pw_qpolynomial *pwqp1,
2556 __isl_take isl_pw_qpolynomial *pwqp2)
2558 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2561 __isl_give struct isl_upoly *isl_upoly_eval(
2562 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2565 struct isl_upoly_rec *rec;
2566 struct isl_upoly *res;
2567 struct isl_upoly *base;
2569 if (isl_upoly_is_cst(up)) {
2574 rec = isl_upoly_as_rec(up);
2578 isl_assert(up->ctx, rec->n >= 1, goto error);
2580 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2582 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2585 for (i = rec->n - 2; i >= 0; --i) {
2586 res = isl_upoly_mul(res, isl_upoly_copy(base));
2587 res = isl_upoly_sum(res,
2588 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2589 isl_vec_copy(vec)));
2592 isl_upoly_free(base);
2602 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2603 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2606 struct isl_upoly *up;
2611 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2613 if (qp->div->n_row == 0)
2614 ext = isl_vec_copy(pnt->vec);
2617 unsigned dim = isl_dim_total(qp->dim);
2618 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2622 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2623 for (i = 0; i < qp->div->n_row; ++i) {
2624 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2625 1 + dim + i, &ext->el[1+dim+i]);
2626 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2627 qp->div->row[i][0]);
2631 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2635 dim = isl_dim_copy(qp->dim);
2636 isl_qpolynomial_free(qp);
2637 isl_point_free(pnt);
2639 return isl_qpolynomial_alloc(dim, 0, up);
2641 isl_qpolynomial_free(qp);
2642 isl_point_free(pnt);
2646 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2647 __isl_keep struct isl_upoly_cst *cst2)
2652 isl_int_mul(t, cst1->n, cst2->d);
2653 isl_int_submul(t, cst2->n, cst1->d);
2654 cmp = isl_int_sgn(t);
2659 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2660 __isl_keep isl_qpolynomial *qp2)
2662 struct isl_upoly_cst *cst1, *cst2;
2666 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2667 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2668 if (isl_qpolynomial_is_nan(qp1))
2670 if (isl_qpolynomial_is_nan(qp2))
2672 cst1 = isl_upoly_as_cst(qp1->upoly);
2673 cst2 = isl_upoly_as_cst(qp2->upoly);
2675 return isl_upoly_cmp(cst1, cst2) <= 0;
2678 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2679 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2681 struct isl_upoly_cst *cst1, *cst2;
2686 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2687 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2688 cst1 = isl_upoly_as_cst(qp1->upoly);
2689 cst2 = isl_upoly_as_cst(qp2->upoly);
2690 cmp = isl_upoly_cmp(cst1, cst2);
2693 isl_qpolynomial_free(qp2);
2695 isl_qpolynomial_free(qp1);
2700 isl_qpolynomial_free(qp1);
2701 isl_qpolynomial_free(qp2);
2705 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2706 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2708 struct isl_upoly_cst *cst1, *cst2;
2713 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2714 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2715 cst1 = isl_upoly_as_cst(qp1->upoly);
2716 cst2 = isl_upoly_as_cst(qp2->upoly);
2717 cmp = isl_upoly_cmp(cst1, cst2);
2720 isl_qpolynomial_free(qp2);
2722 isl_qpolynomial_free(qp1);
2727 isl_qpolynomial_free(qp1);
2728 isl_qpolynomial_free(qp2);
2732 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2733 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2734 unsigned first, unsigned n)
2743 qp = isl_qpolynomial_cow(qp);
2747 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2750 g_pos = pos(qp->dim, type) + first;
2752 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2756 total = qp->div->n_col - 2;
2757 if (total > g_pos) {
2759 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2762 for (i = 0; i < total - g_pos; ++i)
2764 qp->upoly = expand(qp->upoly, exp, g_pos);
2770 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2776 isl_qpolynomial_free(qp);
2780 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2781 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2785 pos = isl_qpolynomial_dim(qp, type);
2787 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2790 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2791 __isl_take isl_pw_qpolynomial *pwqp,
2792 enum isl_dim_type type, unsigned n)
2796 pos = isl_pw_qpolynomial_dim(pwqp, type);
2798 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2801 static int *reordering_move(isl_ctx *ctx,
2802 unsigned len, unsigned dst, unsigned src, unsigned n)
2807 reordering = isl_alloc_array(ctx, int, len);
2812 for (i = 0; i < dst; ++i)
2814 for (i = 0; i < n; ++i)
2815 reordering[src + i] = dst + i;
2816 for (i = 0; i < src - dst; ++i)
2817 reordering[dst + i] = dst + n + i;
2818 for (i = 0; i < len - src - n; ++i)
2819 reordering[src + n + i] = src + n + i;
2821 for (i = 0; i < src; ++i)
2823 for (i = 0; i < n; ++i)
2824 reordering[src + i] = dst + i;
2825 for (i = 0; i < dst - src; ++i)
2826 reordering[src + n + i] = src + i;
2827 for (i = 0; i < len - dst - n; ++i)
2828 reordering[dst + n + i] = dst + n + i;
2834 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2835 __isl_take isl_qpolynomial *qp,
2836 enum isl_dim_type dst_type, unsigned dst_pos,
2837 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2843 qp = isl_qpolynomial_cow(qp);
2847 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2850 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2851 g_src_pos = pos(qp->dim, src_type) + src_pos;
2852 if (dst_type > src_type)
2855 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2862 reordering = reordering_move(qp->dim->ctx,
2863 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2867 qp->upoly = reorder(qp->upoly, reordering);
2872 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2878 isl_qpolynomial_free(qp);
2882 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2883 isl_int *f, isl_int denom)
2885 struct isl_upoly *up;
2890 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2892 return isl_qpolynomial_alloc(dim, 0, up);
2895 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2896 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2900 struct isl_upoly *up;
2901 isl_qpolynomial *qp;
2907 isl_int_init(denom);
2909 isl_constraint_get_coefficient(c, type, pos, &denom);
2910 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2911 sgn = isl_int_sgn(denom);
2912 isl_int_abs(denom, denom);
2913 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2914 1 + isl_constraint_dim(c, isl_dim_all));
2916 isl_int_neg(denom, denom);
2917 isl_constraint_set_coefficient(c, type, pos, denom);
2919 dim = isl_dim_copy(c->bmap->dim);
2921 isl_int_clear(denom);
2922 isl_constraint_free(c);
2924 qp = isl_qpolynomial_alloc(dim, 0, up);
2926 qp = isl_qpolynomial_neg(qp);
2930 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2931 * in "qp" by subs[i].
2933 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2934 __isl_take isl_qpolynomial *qp,
2935 enum isl_dim_type type, unsigned first, unsigned n,
2936 __isl_keep isl_qpolynomial **subs)
2939 struct isl_upoly **ups;
2944 qp = isl_qpolynomial_cow(qp);
2947 for (i = 0; i < n; ++i)
2951 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2954 for (i = 0; i < n; ++i)
2955 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2958 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2959 for (i = 0; i < n; ++i)
2960 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2962 first += pos(qp->dim, type);
2964 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2967 for (i = 0; i < n; ++i)
2968 ups[i] = subs[i]->upoly;
2970 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2979 isl_qpolynomial_free(qp);
2983 /* Extend "bset" with extra set dimensions for each integer division
2984 * in "qp" and then call "fn" with the extended bset and the polynomial
2985 * that results from replacing each of the integer divisions by the
2986 * corresponding extra set dimension.
2988 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2989 __isl_keep isl_basic_set *bset,
2990 int (*fn)(__isl_take isl_basic_set *bset,
2991 __isl_take isl_qpolynomial *poly, void *user), void *user)
2995 isl_qpolynomial *poly;
2999 if (qp->div->n_row == 0)
3000 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3003 div = isl_mat_copy(qp->div);
3004 dim = isl_dim_copy(qp->dim);
3005 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3006 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3007 bset = isl_basic_set_copy(bset);
3008 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3009 bset = add_div_constraints(bset, div);
3011 return fn(bset, poly, user);
3016 /* Return total degree in variables first (inclusive) up to last (exclusive).
3018 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3022 struct isl_upoly_rec *rec;
3026 if (isl_upoly_is_zero(up))
3028 if (isl_upoly_is_cst(up) || up->var < first)
3031 rec = isl_upoly_as_rec(up);
3035 for (i = 0; i < rec->n; ++i) {
3038 if (isl_upoly_is_zero(rec->p[i]))
3040 d = isl_upoly_degree(rec->p[i], first, last);
3050 /* Return total degree in set variables.
3052 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3060 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3061 nvar = isl_dim_size(poly->dim, isl_dim_set);
3062 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3065 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3066 unsigned pos, int deg)
3069 struct isl_upoly_rec *rec;
3074 if (isl_upoly_is_cst(up) || up->var < pos) {
3076 return isl_upoly_copy(up);
3078 return isl_upoly_zero(up->ctx);
3081 rec = isl_upoly_as_rec(up);
3085 if (up->var == pos) {
3087 return isl_upoly_copy(rec->p[deg]);
3089 return isl_upoly_zero(up->ctx);
3092 up = isl_upoly_copy(up);
3093 up = isl_upoly_cow(up);
3094 rec = isl_upoly_as_rec(up);
3098 for (i = 0; i < rec->n; ++i) {
3099 struct isl_upoly *t;
3100 t = isl_upoly_coeff(rec->p[i], pos, deg);
3103 isl_upoly_free(rec->p[i]);
3113 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3115 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3116 __isl_keep isl_qpolynomial *qp,
3117 enum isl_dim_type type, unsigned t_pos, int deg)
3120 struct isl_upoly *up;
3126 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3129 g_pos = pos(qp->dim, type) + t_pos;
3130 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3132 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3135 isl_mat_free(c->div);
3136 c->div = isl_mat_copy(qp->div);
3141 isl_qpolynomial_free(c);
3145 /* Homogenize the polynomial in the variables first (inclusive) up to
3146 * last (exclusive) by inserting powers of variable first.
3147 * Variable first is assumed not to appear in the input.
3149 __isl_give struct isl_upoly *isl_upoly_homogenize(
3150 __isl_take struct isl_upoly *up, int deg, int target,
3151 int first, int last)
3154 struct isl_upoly_rec *rec;
3158 if (isl_upoly_is_zero(up))
3162 if (isl_upoly_is_cst(up) || up->var < first) {
3163 struct isl_upoly *hom;
3165 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3168 rec = isl_upoly_as_rec(hom);
3169 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3174 up = isl_upoly_cow(up);
3175 rec = isl_upoly_as_rec(up);
3179 for (i = 0; i < rec->n; ++i) {
3180 if (isl_upoly_is_zero(rec->p[i]))
3182 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3183 up->var < last ? deg + i : i, target,
3195 /* Homogenize the polynomial in the set variables by introducing
3196 * powers of an extra set variable at position 0.
3198 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3199 __isl_take isl_qpolynomial *poly)
3203 int deg = isl_qpolynomial_degree(poly);
3208 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3209 poly = isl_qpolynomial_cow(poly);
3213 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3214 nvar = isl_dim_size(poly->dim, isl_dim_set);
3215 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3222 isl_qpolynomial_free(poly);
3226 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3227 __isl_take isl_mat *div)
3235 n = isl_dim_total(dim) + div->n_row;
3237 term = isl_calloc(dim->ctx, struct isl_term,
3238 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3245 isl_int_init(term->n);
3246 isl_int_init(term->d);
3255 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3264 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3273 total = isl_dim_total(term->dim) + term->div->n_row;
3275 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3279 isl_int_set(dup->n, term->n);
3280 isl_int_set(dup->d, term->d);
3282 for (i = 0; i < total; ++i)
3283 dup->pow[i] = term->pow[i];
3288 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3296 return isl_term_dup(term);
3299 void isl_term_free(__isl_take isl_term *term)
3304 if (--term->ref > 0)
3307 isl_dim_free(term->dim);
3308 isl_mat_free(term->div);
3309 isl_int_clear(term->n);
3310 isl_int_clear(term->d);
3314 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3322 case isl_dim_out: return isl_dim_size(term->dim, type);
3323 case isl_dim_div: return term->div->n_row;
3324 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3329 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3331 return term ? term->dim->ctx : NULL;
3334 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3338 isl_int_set(*n, term->n);
3341 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3345 isl_int_set(*d, term->d);
3348 int isl_term_get_exp(__isl_keep isl_term *term,
3349 enum isl_dim_type type, unsigned pos)
3354 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3356 if (type >= isl_dim_set)
3357 pos += isl_dim_size(term->dim, isl_dim_param);
3358 if (type >= isl_dim_div)
3359 pos += isl_dim_size(term->dim, isl_dim_set);
3361 return term->pow[pos];
3364 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3366 isl_basic_map *bmap;
3373 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3376 total = term->div->n_col - term->div->n_row - 2;
3377 /* No nested divs for now */
3378 isl_assert(term->dim->ctx,
3379 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3380 term->div->n_row) == -1,
3383 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3384 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3387 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3389 return isl_basic_map_div(bmap, k);
3391 isl_basic_map_free(bmap);
3395 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3396 int (*fn)(__isl_take isl_term *term, void *user),
3397 __isl_take isl_term *term, void *user)
3400 struct isl_upoly_rec *rec;
3405 if (isl_upoly_is_zero(up))
3408 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3409 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3410 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3412 if (isl_upoly_is_cst(up)) {
3413 struct isl_upoly_cst *cst;
3414 cst = isl_upoly_as_cst(up);
3417 term = isl_term_cow(term);
3420 isl_int_set(term->n, cst->n);
3421 isl_int_set(term->d, cst->d);
3422 if (fn(isl_term_copy(term), user) < 0)
3427 rec = isl_upoly_as_rec(up);
3431 for (i = 0; i < rec->n; ++i) {
3432 term = isl_term_cow(term);
3435 term->pow[up->var] = i;
3436 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3440 term->pow[up->var] = 0;
3444 isl_term_free(term);
3448 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3449 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3456 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3460 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3462 isl_term_free(term);
3464 return term ? 0 : -1;
3467 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3469 struct isl_upoly *up;
3470 isl_qpolynomial *qp;
3476 n = isl_dim_total(term->dim) + term->div->n_row;
3478 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3479 for (i = 0; i < n; ++i) {
3482 up = isl_upoly_mul(up,
3483 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3486 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3489 isl_mat_free(qp->div);
3490 qp->div = isl_mat_copy(term->div);
3494 isl_term_free(term);
3497 isl_qpolynomial_free(qp);
3498 isl_term_free(term);
3502 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3503 __isl_take isl_dim *dim)
3512 if (isl_dim_equal(qp->dim, dim)) {
3517 qp = isl_qpolynomial_cow(qp);
3521 extra = isl_dim_size(dim, isl_dim_set) -
3522 isl_dim_size(qp->dim, isl_dim_set);
3523 total = isl_dim_total(qp->dim);
3524 if (qp->div->n_row) {
3527 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3530 for (i = 0; i < qp->div->n_row; ++i)
3532 qp->upoly = expand(qp->upoly, exp, total);
3537 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3540 for (i = 0; i < qp->div->n_row; ++i)
3541 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3543 isl_dim_free(qp->dim);
3549 isl_qpolynomial_free(qp);
3553 /* For each parameter or variable that does not appear in qp,
3554 * first eliminate the variable from all constraints and then set it to zero.
3556 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3557 __isl_keep isl_qpolynomial *qp)
3568 d = isl_dim_total(set->dim);
3569 active = isl_calloc_array(set->ctx, int, d);
3570 if (set_active(qp, active) < 0)
3573 for (i = 0; i < d; ++i)
3582 nparam = isl_dim_size(set->dim, isl_dim_param);
3583 nvar = isl_dim_size(set->dim, isl_dim_set);
3584 for (i = 0; i < nparam; ++i) {
3587 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3588 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3590 for (i = 0; i < nvar; ++i) {
3591 if (active[nparam + i])
3593 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3594 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3606 struct isl_opt_data {
3607 isl_qpolynomial *qp;
3609 isl_qpolynomial *opt;
3613 static int opt_fn(__isl_take isl_point *pnt, void *user)
3615 struct isl_opt_data *data = (struct isl_opt_data *)user;
3616 isl_qpolynomial *val;
3618 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3622 } else if (data->max) {
3623 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3625 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3631 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3632 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3634 struct isl_opt_data data = { NULL, 1, NULL, max };
3639 if (isl_upoly_is_cst(qp->upoly)) {
3644 set = fix_inactive(set, qp);
3647 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3651 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3654 isl_qpolynomial_free(qp);
3658 isl_qpolynomial_free(qp);
3659 isl_qpolynomial_free(data.opt);
3663 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3664 __isl_take isl_morph *morph)
3669 struct isl_upoly *up;
3671 struct isl_upoly **subs;
3674 qp = isl_qpolynomial_cow(qp);
3679 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3681 n_sub = morph->inv->n_row - 1;
3682 if (morph->inv->n_row != morph->inv->n_col)
3683 n_sub += qp->div->n_row;
3684 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3688 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3689 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3690 morph->inv->row[0][0], morph->inv->n_col);
3691 if (morph->inv->n_row != morph->inv->n_col)
3692 for (i = 0; i < qp->div->n_row; ++i)
3693 subs[morph->inv->n_row - 1 + i] =
3694 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3696 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3698 for (i = 0; i < n_sub; ++i)
3699 isl_upoly_free(subs[i]);
3702 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3703 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3704 qp->div = isl_mat_product(qp->div, mat);
3705 isl_dim_free(qp->dim);
3706 qp->dim = isl_dim_copy(morph->ran->dim);
3708 if (!qp->upoly || !qp->div || !qp->dim)
3711 isl_morph_free(morph);
3715 isl_qpolynomial_free(qp);
3716 isl_morph_free(morph);
3720 static int neg_entry(void **entry, void *user)
3722 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3724 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3726 return *pwqp ? 0 : -1;
3729 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3730 __isl_take isl_union_pw_qpolynomial *upwqp)
3732 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3736 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3737 &neg_entry, NULL) < 0)
3742 isl_union_pw_qpolynomial_free(upwqp);
3746 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3747 __isl_take isl_union_pw_qpolynomial *upwqp1,
3748 __isl_take isl_union_pw_qpolynomial *upwqp2)
3750 return isl_union_pw_qpolynomial_add(upwqp1,
3751 isl_union_pw_qpolynomial_neg(upwqp2));
3754 static int mul_entry(void **entry, void *user)
3756 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3758 struct isl_hash_table_entry *entry2;
3759 isl_pw_qpolynomial *pwpq = *entry;
3762 hash = isl_dim_get_hash(pwpq->dim);
3763 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3764 hash, &has_dim, pwpq->dim, 0);
3768 pwpq = isl_pw_qpolynomial_copy(pwpq);
3769 pwpq = isl_pw_qpolynomial_mul(pwpq,
3770 isl_pw_qpolynomial_copy(entry2->data));
3772 empty = isl_pw_qpolynomial_is_zero(pwpq);
3774 isl_pw_qpolynomial_free(pwpq);
3778 isl_pw_qpolynomial_free(pwpq);
3782 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3787 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3788 __isl_take isl_union_pw_qpolynomial *upwqp1,
3789 __isl_take isl_union_pw_qpolynomial *upwqp2)
3791 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3794 /* Reorder the columns of the given div definitions according to the
3797 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3798 __isl_take isl_reordering *r)
3807 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3808 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3812 for (i = 0; i < div->n_row; ++i) {
3813 isl_seq_cpy(mat->row[i], div->row[i], 2);
3814 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3815 for (j = 0; j < r->len; ++j)
3816 isl_int_set(mat->row[i][2 + r->pos[j]],
3817 div->row[i][2 + j]);
3820 isl_reordering_free(r);
3824 isl_reordering_free(r);
3829 /* Reorder the dimension of "qp" according to the given reordering.
3831 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3832 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3834 qp = isl_qpolynomial_cow(qp);
3838 r = isl_reordering_extend(r, qp->div->n_row);
3842 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3846 qp->upoly = reorder(qp->upoly, r->pos);
3850 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3852 isl_reordering_free(r);
3855 isl_qpolynomial_free(qp);
3856 isl_reordering_free(r);
3860 struct isl_split_periods_data {
3862 isl_pw_qpolynomial *res;
3865 /* Create a slice where the integer division "div" has the fixed value "v".
3866 * In particular, if "div" refers to floor(f/m), then create a slice
3868 * m v <= f <= m v + (m - 1)
3873 * -f + m v + (m - 1) >= 0
3875 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3876 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3879 isl_basic_set *bset = NULL;
3885 total = isl_dim_total(dim);
3886 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3888 k = isl_basic_set_alloc_inequality(bset);
3891 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3892 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3894 k = isl_basic_set_alloc_inequality(bset);
3897 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3898 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3899 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3900 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3903 return isl_set_from_basic_set(bset);
3905 isl_basic_set_free(bset);
3910 static int split_periods(__isl_take isl_set *set,
3911 __isl_take isl_qpolynomial *qp, void *user);
3913 /* Create a slice of the domain "set" such that integer division "div"
3914 * has the fixed value "v" and add the results to data->res,
3915 * replacing the integer division by "v" in "qp".
3917 static int set_div(__isl_take isl_set *set,
3918 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3919 struct isl_split_periods_data *data)
3924 struct isl_upoly *cst;
3926 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3927 set = isl_set_intersect(set, slice);
3932 total = isl_dim_total(qp->dim);
3934 for (i = div + 1; i < qp->div->n_row; ++i) {
3935 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3937 isl_int_addmul(qp->div->row[i][1],
3938 qp->div->row[i][2 + total + div], v);
3939 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3942 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3943 qp = substitute_div(qp, div, cst);
3945 return split_periods(set, qp, data);
3948 isl_qpolynomial_free(qp);
3952 /* Split the domain "set" such that integer division "div"
3953 * has a fixed value (ranging from "min" to "max") on each slice
3954 * and add the results to data->res.
3956 static int split_div(__isl_take isl_set *set,
3957 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
3958 struct isl_split_periods_data *data)
3960 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
3961 isl_set *set_i = isl_set_copy(set);
3962 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
3964 if (set_div(set_i, qp_i, div, min, data) < 0)
3968 isl_qpolynomial_free(qp);
3972 isl_qpolynomial_free(qp);
3976 /* If "qp" refers to any integer division
3977 * that can only attain "max_periods" distinct values on "set"
3978 * then split the domain along those distinct values.
3979 * Add the results (or the original if no splitting occurs)
3982 static int split_periods(__isl_take isl_set *set,
3983 __isl_take isl_qpolynomial *qp, void *user)
3986 isl_pw_qpolynomial *pwqp;
3987 struct isl_split_periods_data *data;
3992 data = (struct isl_split_periods_data *)user;
3997 if (qp->div->n_row == 0) {
3998 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3999 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4005 total = isl_dim_total(qp->dim);
4006 for (i = 0; i < qp->div->n_row; ++i) {
4007 enum isl_lp_result lp_res;
4009 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4010 qp->div->n_row) != -1)
4013 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4014 set->ctx->one, &min, NULL, NULL);
4015 if (lp_res == isl_lp_error)
4017 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4019 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4021 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4022 set->ctx->one, &max, NULL, NULL);
4023 if (lp_res == isl_lp_error)
4025 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4027 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4029 isl_int_sub(max, max, min);
4030 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4031 isl_int_add(max, max, min);
4036 if (i < qp->div->n_row) {
4037 r = split_div(set, qp, i, min, max, data);
4039 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4040 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4052 isl_qpolynomial_free(qp);
4056 /* If any quasi-polynomial in pwqp refers to any integer division
4057 * that can only attain "max_periods" distinct values on its domain
4058 * then split the domain along those distinct values.
4060 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4061 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4063 struct isl_split_periods_data data;
4065 data.max_periods = max_periods;
4066 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4068 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4071 isl_pw_qpolynomial_free(pwqp);
4075 isl_pw_qpolynomial_free(data.res);
4076 isl_pw_qpolynomial_free(pwqp);
4080 /* Construct a piecewise quasipolynomial that is constant on the given
4081 * domain. In particular, it is
4084 * infinity if cst == -1
4086 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4087 __isl_take isl_basic_set *bset, int cst)
4090 isl_qpolynomial *qp;
4095 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4096 dim = isl_basic_set_get_dim(bset);
4098 qp = isl_qpolynomial_infty(dim);
4100 qp = isl_qpolynomial_zero(dim);
4102 qp = isl_qpolynomial_one(dim);
4103 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4106 /* Factor bset, call fn on each of the factors and return the product.
4108 * If no factors can be found, simply call fn on the input.
4109 * Otherwise, construct the factors based on the factorizer,
4110 * call fn on each factor and compute the product.
4112 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4113 __isl_take isl_basic_set *bset,
4114 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4120 isl_qpolynomial *qp;
4121 isl_pw_qpolynomial *pwqp;
4125 f = isl_basic_set_factorizer(bset);
4128 if (f->n_group == 0) {
4129 isl_factorizer_free(f);
4133 nparam = isl_basic_set_dim(bset, isl_dim_param);
4134 nvar = isl_basic_set_dim(bset, isl_dim_set);
4136 dim = isl_basic_set_get_dim(bset);
4137 dim = isl_dim_domain(dim);
4138 set = isl_set_universe(isl_dim_copy(dim));
4139 qp = isl_qpolynomial_one(dim);
4140 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4142 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4144 for (i = 0, n = 0; i < f->n_group; ++i) {
4145 isl_basic_set *bset_i;
4146 isl_pw_qpolynomial *pwqp_i;
4148 bset_i = isl_basic_set_copy(bset);
4149 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4150 nparam + n + f->len[i], nvar - n - f->len[i]);
4151 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4153 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4154 n + f->len[i], nvar - n - f->len[i]);
4155 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4157 pwqp_i = fn(bset_i);
4158 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4163 isl_basic_set_free(bset);
4164 isl_factorizer_free(f);
4168 isl_basic_set_free(bset);
4172 /* Factor bset, call fn on each of the factors and return the product.
4173 * The function is assumed to evaluate to zero on empty domains,
4174 * to one on zero-dimensional domains and to infinity on unbounded domains
4175 * and will not be called explicitly on zero-dimensional or unbounded domains.
4177 * We first check for some special cases and remove all equalities.
4178 * Then we hand over control to compressed_multiplicative_call.
4180 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4181 __isl_take isl_basic_set *bset,
4182 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4186 isl_pw_qpolynomial *pwqp;
4187 unsigned orig_nvar, final_nvar;
4192 if (isl_basic_set_fast_is_empty(bset))
4193 return constant_on_domain(bset, 0);
4195 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4198 return constant_on_domain(bset, 1);
4200 bounded = isl_basic_set_is_bounded(bset);
4204 return constant_on_domain(bset, -1);
4206 if (bset->n_eq == 0)
4207 return compressed_multiplicative_call(bset, fn);
4209 morph = isl_basic_set_full_compression(bset);
4210 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4212 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4214 pwqp = compressed_multiplicative_call(bset, fn);
4216 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4217 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4218 morph = isl_morph_inverse(morph);
4220 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4224 isl_basic_set_free(bset);
4228 /* Drop all floors in "qp", turning each integer division [a/m] into
4229 * a rational division a/m. If "down" is set, then the integer division
4230 * is replaces by (a-(m-1))/m instead.
4232 static __isl_give isl_qpolynomial *qp_drop_floors(
4233 __isl_take isl_qpolynomial *qp, int down)
4236 struct isl_upoly *s;
4240 if (qp->div->n_row == 0)
4243 qp = isl_qpolynomial_cow(qp);
4247 for (i = qp->div->n_row - 1; i >= 0; --i) {
4249 isl_int_sub(qp->div->row[i][1],
4250 qp->div->row[i][1], qp->div->row[i][0]);
4251 isl_int_add_ui(qp->div->row[i][1],
4252 qp->div->row[i][1], 1);
4254 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4255 qp->div->row[i][0], qp->div->n_col - 1);
4256 qp = substitute_div(qp, i, s);
4264 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4265 * a rational division a/m.
4267 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4268 __isl_take isl_pw_qpolynomial *pwqp)
4275 if (isl_pw_qpolynomial_is_zero(pwqp))
4278 pwqp = isl_pw_qpolynomial_cow(pwqp);
4282 for (i = 0; i < pwqp->n; ++i) {
4283 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4290 isl_pw_qpolynomial_free(pwqp);
4294 /* Adjust all the integer divisions in "qp" such that they are at least
4295 * one over the given orthant (identified by "signs"). This ensures
4296 * that they will still be non-negative even after subtracting (m-1)/m.
4298 * In particular, f is replaced by f' + v, changing f = [a/m]
4299 * to f' = [(a - m v)/m].
4300 * If the constant term k in a is smaller than m,
4301 * the constant term of v is set to floor(k/m) - 1.
4302 * For any other term, if the coefficient c and the variable x have
4303 * the same sign, then no changes are needed.
4304 * Otherwise, if the variable is positive (and c is negative),
4305 * then the coefficient of x in v is set to floor(c/m).
4306 * If the variable is negative (and c is positive),
4307 * then the coefficient of x in v is set to ceil(c/m).
4309 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4315 struct isl_upoly *s;
4317 qp = isl_qpolynomial_cow(qp);
4320 qp->div = isl_mat_cow(qp->div);
4324 total = isl_dim_total(qp->dim);
4325 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4327 for (i = 0; i < qp->div->n_row; ++i) {
4328 isl_int *row = qp->div->row[i];
4332 if (isl_int_lt(row[1], row[0])) {
4333 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4334 isl_int_sub_ui(v->el[0], v->el[0], 1);
4335 isl_int_submul(row[1], row[0], v->el[0]);
4337 for (j = 0; j < total; ++j) {
4338 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4341 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4343 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4344 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4346 for (j = 0; j < i; ++j) {
4347 if (isl_int_sgn(row[2 + total + j]) >= 0)
4349 isl_int_fdiv_q(v->el[1 + total + j],
4350 row[2 + total + j], row[0]);
4351 isl_int_submul(row[2 + total + j],
4352 row[0], v->el[1 + total + j]);
4354 for (j = i + 1; j < qp->div->n_row; ++j) {
4355 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4357 isl_seq_combine(qp->div->row[j] + 1,
4358 qp->div->ctx->one, qp->div->row[j] + 1,
4359 qp->div->row[j][2 + total + i], v->el, v->size);
4361 isl_int_set_si(v->el[1 + total + i], 1);
4362 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4363 qp->div->ctx->one, v->size);
4364 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4374 isl_qpolynomial_free(qp);
4378 struct isl_to_poly_data {
4380 isl_pw_qpolynomial *res;
4381 isl_qpolynomial *qp;
4384 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4385 * We first make all integer divisions positive and then split the
4386 * quasipolynomials into terms with sign data->sign (the direction
4387 * of the requested approximation) and terms with the opposite sign.
4388 * In the first set of terms, each integer division [a/m] is
4389 * overapproximated by a/m, while in the second it is underapproximated
4392 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4395 struct isl_to_poly_data *data = user;
4396 isl_pw_qpolynomial *t;
4397 isl_qpolynomial *qp, *up, *down;
4399 qp = isl_qpolynomial_copy(data->qp);
4400 qp = make_divs_pos(qp, signs);
4402 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4403 up = qp_drop_floors(up, 0);
4404 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4405 down = qp_drop_floors(down, 1);
4407 isl_qpolynomial_free(qp);
4408 qp = isl_qpolynomial_add(up, down);
4410 t = isl_pw_qpolynomial_alloc(orthant, qp);
4411 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4416 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4417 * the polynomial will be an overapproximation. If "sign" is negative,
4418 * it will be an underapproximation. If "sign" is zero, the approximation
4419 * will lie somewhere in between.
4421 * In particular, is sign == 0, we simply drop the floors, turning
4422 * the integer divisions into rational divisions.
4423 * Otherwise, we split the domains into orthants, make all integer divisions
4424 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4425 * depending on the requested sign and the sign of the term in which
4426 * the integer division appears.
4428 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4429 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4432 struct isl_to_poly_data data;
4435 return pwqp_drop_floors(pwqp);
4441 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4443 for (i = 0; i < pwqp->n; ++i) {
4444 if (pwqp->p[i].qp->div->n_row == 0) {
4445 isl_pw_qpolynomial *t;
4446 t = isl_pw_qpolynomial_alloc(
4447 isl_set_copy(pwqp->p[i].set),
4448 isl_qpolynomial_copy(pwqp->p[i].qp));
4449 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4452 data.qp = pwqp->p[i].qp;
4453 if (isl_set_foreach_orthant(pwqp->p[i].set,
4454 &to_polynomial_on_orthant, &data) < 0)
4458 isl_pw_qpolynomial_free(pwqp);
4462 isl_pw_qpolynomial_free(pwqp);
4463 isl_pw_qpolynomial_free(data.res);
4467 static int poly_entry(void **entry, void *user)
4470 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4472 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4474 return *pwqp ? 0 : -1;
4477 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4478 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4480 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4484 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4485 &poly_entry, &sign) < 0)
4490 isl_union_pw_qpolynomial_free(upwqp);