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_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_factorization.h>
17 #include <isl_union_map_private.h>
18 #include <isl_polynomial_private.h>
19 #include <isl_point_private.h>
20 #include <isl_dim_private.h>
21 #include <isl_div_private.h>
22 #include <isl_mat_private.h>
23 #include <isl_range.h>
24 #include <isl_local_space_private.h>
25 #include <isl_aff_private.h>
26 #include <isl_config.h>
28 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
31 case isl_dim_param: return 0;
32 case isl_dim_in: return dim->nparam;
33 case isl_dim_out: return dim->nparam + dim->n_in;
38 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
46 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
51 isl_assert(up->ctx, up->var < 0, return NULL);
53 return (struct isl_upoly_cst *)up;
56 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
61 isl_assert(up->ctx, up->var >= 0, return NULL);
63 return (struct isl_upoly_rec *)up;
66 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
67 __isl_keep struct isl_upoly *up2)
70 struct isl_upoly_rec *rec1, *rec2;
76 if (up1->var != up2->var)
78 if (isl_upoly_is_cst(up1)) {
79 struct isl_upoly_cst *cst1, *cst2;
80 cst1 = isl_upoly_as_cst(up1);
81 cst2 = isl_upoly_as_cst(up2);
84 return isl_int_eq(cst1->n, cst2->n) &&
85 isl_int_eq(cst1->d, cst2->d);
88 rec1 = isl_upoly_as_rec(up1);
89 rec2 = isl_upoly_as_rec(up2);
93 if (rec1->n != rec2->n)
96 for (i = 0; i < rec1->n; ++i) {
97 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
105 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
107 struct isl_upoly_cst *cst;
111 if (!isl_upoly_is_cst(up))
114 cst = isl_upoly_as_cst(up);
118 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
121 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
123 struct isl_upoly_cst *cst;
127 if (!isl_upoly_is_cst(up))
130 cst = isl_upoly_as_cst(up);
134 return isl_int_sgn(cst->n);
137 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
139 struct isl_upoly_cst *cst;
143 if (!isl_upoly_is_cst(up))
146 cst = isl_upoly_as_cst(up);
150 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
153 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
155 struct isl_upoly_cst *cst;
159 if (!isl_upoly_is_cst(up))
162 cst = isl_upoly_as_cst(up);
166 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
169 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
171 struct isl_upoly_cst *cst;
175 if (!isl_upoly_is_cst(up))
178 cst = isl_upoly_as_cst(up);
182 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
185 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
187 struct isl_upoly_cst *cst;
191 if (!isl_upoly_is_cst(up))
194 cst = isl_upoly_as_cst(up);
198 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
201 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
203 struct isl_upoly_cst *cst;
207 if (!isl_upoly_is_cst(up))
210 cst = isl_upoly_as_cst(up);
214 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
217 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
219 struct isl_upoly_cst *cst;
221 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
230 isl_int_init(cst->n);
231 isl_int_init(cst->d);
236 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
238 struct isl_upoly_cst *cst;
240 cst = isl_upoly_cst_alloc(ctx);
244 isl_int_set_si(cst->n, 0);
245 isl_int_set_si(cst->d, 1);
250 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
252 struct isl_upoly_cst *cst;
254 cst = isl_upoly_cst_alloc(ctx);
258 isl_int_set_si(cst->n, 1);
259 isl_int_set_si(cst->d, 1);
264 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
266 struct isl_upoly_cst *cst;
268 cst = isl_upoly_cst_alloc(ctx);
272 isl_int_set_si(cst->n, 1);
273 isl_int_set_si(cst->d, 0);
278 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
280 struct isl_upoly_cst *cst;
282 cst = isl_upoly_cst_alloc(ctx);
286 isl_int_set_si(cst->n, -1);
287 isl_int_set_si(cst->d, 0);
292 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
294 struct isl_upoly_cst *cst;
296 cst = isl_upoly_cst_alloc(ctx);
300 isl_int_set_si(cst->n, 0);
301 isl_int_set_si(cst->d, 0);
306 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
307 isl_int n, isl_int d)
309 struct isl_upoly_cst *cst;
311 cst = isl_upoly_cst_alloc(ctx);
315 isl_int_set(cst->n, n);
316 isl_int_set(cst->d, d);
321 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
324 struct isl_upoly_rec *rec;
326 isl_assert(ctx, var >= 0, return NULL);
327 isl_assert(ctx, size >= 0, return NULL);
328 rec = isl_calloc(ctx, struct isl_upoly_rec,
329 sizeof(struct isl_upoly_rec) +
330 size * sizeof(struct isl_upoly *));
345 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
346 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
348 qp = isl_qpolynomial_cow(qp);
352 isl_dim_free(qp->dim);
357 isl_qpolynomial_free(qp);
362 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
364 return qp ? qp->dim->ctx : NULL;
367 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
369 return qp ? isl_dim_copy(qp->dim) : NULL;
372 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
373 enum isl_dim_type type)
375 return qp ? isl_dim_size(qp->dim, type) : 0;
378 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
380 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
383 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
385 return qp ? isl_upoly_is_one(qp->upoly) : -1;
388 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
390 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
393 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
395 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
398 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
400 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
403 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
405 return qp ? isl_upoly_sgn(qp->upoly) : 0;
408 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
410 isl_int_clear(cst->n);
411 isl_int_clear(cst->d);
414 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
418 for (i = 0; i < rec->n; ++i)
419 isl_upoly_free(rec->p[i]);
422 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
431 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
433 struct isl_upoly_cst *cst;
434 struct isl_upoly_cst *dup;
436 cst = isl_upoly_as_cst(up);
440 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
443 isl_int_set(dup->n, cst->n);
444 isl_int_set(dup->d, cst->d);
449 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
452 struct isl_upoly_rec *rec;
453 struct isl_upoly_rec *dup;
455 rec = isl_upoly_as_rec(up);
459 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
463 for (i = 0; i < rec->n; ++i) {
464 dup->p[i] = isl_upoly_copy(rec->p[i]);
472 isl_upoly_free(&dup->up);
476 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
481 if (isl_upoly_is_cst(up))
482 return isl_upoly_dup_cst(up);
484 return isl_upoly_dup_rec(up);
487 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
495 return isl_upoly_dup(up);
498 void isl_upoly_free(__isl_take struct isl_upoly *up)
507 upoly_free_cst((struct isl_upoly_cst *)up);
509 upoly_free_rec((struct isl_upoly_rec *)up);
511 isl_ctx_deref(up->ctx);
515 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
520 isl_int_gcd(gcd, cst->n, cst->d);
521 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
522 isl_int_divexact(cst->n, cst->n, gcd);
523 isl_int_divexact(cst->d, cst->d, gcd);
528 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
529 __isl_take struct isl_upoly *up2)
531 struct isl_upoly_cst *cst1;
532 struct isl_upoly_cst *cst2;
534 up1 = isl_upoly_cow(up1);
538 cst1 = isl_upoly_as_cst(up1);
539 cst2 = isl_upoly_as_cst(up2);
541 if (isl_int_eq(cst1->d, cst2->d))
542 isl_int_add(cst1->n, cst1->n, cst2->n);
544 isl_int_mul(cst1->n, cst1->n, cst2->d);
545 isl_int_addmul(cst1->n, cst2->n, cst1->d);
546 isl_int_mul(cst1->d, cst1->d, cst2->d);
549 isl_upoly_cst_reduce(cst1);
559 static __isl_give struct isl_upoly *replace_by_zero(
560 __isl_take struct isl_upoly *up)
568 return isl_upoly_zero(ctx);
571 static __isl_give struct isl_upoly *replace_by_constant_term(
572 __isl_take struct isl_upoly *up)
574 struct isl_upoly_rec *rec;
575 struct isl_upoly *cst;
580 rec = isl_upoly_as_rec(up);
583 cst = isl_upoly_copy(rec->p[0]);
591 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
592 __isl_take struct isl_upoly *up2)
595 struct isl_upoly_rec *rec1, *rec2;
600 if (isl_upoly_is_nan(up1)) {
605 if (isl_upoly_is_nan(up2)) {
610 if (isl_upoly_is_zero(up1)) {
615 if (isl_upoly_is_zero(up2)) {
620 if (up1->var < up2->var)
621 return isl_upoly_sum(up2, up1);
623 if (up2->var < up1->var) {
624 struct isl_upoly_rec *rec;
625 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
629 up1 = isl_upoly_cow(up1);
630 rec = isl_upoly_as_rec(up1);
633 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
635 up1 = replace_by_constant_term(up1);
639 if (isl_upoly_is_cst(up1))
640 return isl_upoly_sum_cst(up1, up2);
642 rec1 = isl_upoly_as_rec(up1);
643 rec2 = isl_upoly_as_rec(up2);
647 if (rec1->n < rec2->n)
648 return isl_upoly_sum(up2, up1);
650 up1 = isl_upoly_cow(up1);
651 rec1 = isl_upoly_as_rec(up1);
655 for (i = rec2->n - 1; i >= 0; --i) {
656 rec1->p[i] = isl_upoly_sum(rec1->p[i],
657 isl_upoly_copy(rec2->p[i]));
660 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
661 isl_upoly_free(rec1->p[i]);
667 up1 = replace_by_zero(up1);
668 else if (rec1->n == 1)
669 up1 = replace_by_constant_term(up1);
680 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
681 __isl_take struct isl_upoly *up, isl_int v)
683 struct isl_upoly_cst *cst;
685 up = isl_upoly_cow(up);
689 cst = isl_upoly_as_cst(up);
691 isl_int_addmul(cst->n, cst->d, v);
696 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
697 __isl_take struct isl_upoly *up, isl_int v)
699 struct isl_upoly_rec *rec;
704 if (isl_upoly_is_cst(up))
705 return isl_upoly_cst_add_isl_int(up, v);
707 up = isl_upoly_cow(up);
708 rec = isl_upoly_as_rec(up);
712 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
722 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
723 __isl_take struct isl_upoly *up, isl_int v)
725 struct isl_upoly_cst *cst;
727 if (isl_upoly_is_zero(up))
730 up = isl_upoly_cow(up);
734 cst = isl_upoly_as_cst(up);
736 isl_int_mul(cst->n, cst->n, v);
741 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
742 __isl_take struct isl_upoly *up, isl_int v)
745 struct isl_upoly_rec *rec;
750 if (isl_upoly_is_cst(up))
751 return isl_upoly_cst_mul_isl_int(up, v);
753 up = isl_upoly_cow(up);
754 rec = isl_upoly_as_rec(up);
758 for (i = 0; i < rec->n; ++i) {
759 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
770 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
771 __isl_take struct isl_upoly *up2)
773 struct isl_upoly_cst *cst1;
774 struct isl_upoly_cst *cst2;
776 up1 = isl_upoly_cow(up1);
780 cst1 = isl_upoly_as_cst(up1);
781 cst2 = isl_upoly_as_cst(up2);
783 isl_int_mul(cst1->n, cst1->n, cst2->n);
784 isl_int_mul(cst1->d, cst1->d, cst2->d);
786 isl_upoly_cst_reduce(cst1);
796 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
797 __isl_take struct isl_upoly *up2)
799 struct isl_upoly_rec *rec1;
800 struct isl_upoly_rec *rec2;
801 struct isl_upoly_rec *res = NULL;
805 rec1 = isl_upoly_as_rec(up1);
806 rec2 = isl_upoly_as_rec(up2);
809 size = rec1->n + rec2->n - 1;
810 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
814 for (i = 0; i < rec1->n; ++i) {
815 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
816 isl_upoly_copy(rec1->p[i]));
821 for (; i < size; ++i) {
822 res->p[i] = isl_upoly_zero(up1->ctx);
827 for (i = 0; i < rec1->n; ++i) {
828 for (j = 1; j < rec2->n; ++j) {
829 struct isl_upoly *up;
830 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
831 isl_upoly_copy(rec1->p[i]));
832 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
845 isl_upoly_free(&res->up);
849 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
850 __isl_take struct isl_upoly *up2)
855 if (isl_upoly_is_nan(up1)) {
860 if (isl_upoly_is_nan(up2)) {
865 if (isl_upoly_is_zero(up1)) {
870 if (isl_upoly_is_zero(up2)) {
875 if (isl_upoly_is_one(up1)) {
880 if (isl_upoly_is_one(up2)) {
885 if (up1->var < up2->var)
886 return isl_upoly_mul(up2, up1);
888 if (up2->var < up1->var) {
890 struct isl_upoly_rec *rec;
891 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
892 isl_ctx *ctx = up1->ctx;
895 return isl_upoly_nan(ctx);
897 up1 = isl_upoly_cow(up1);
898 rec = isl_upoly_as_rec(up1);
902 for (i = 0; i < rec->n; ++i) {
903 rec->p[i] = isl_upoly_mul(rec->p[i],
904 isl_upoly_copy(up2));
912 if (isl_upoly_is_cst(up1))
913 return isl_upoly_mul_cst(up1, up2);
915 return isl_upoly_mul_rec(up1, up2);
922 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
925 struct isl_upoly *res;
933 res = isl_upoly_copy(up);
935 res = isl_upoly_one(up->ctx);
937 while (power >>= 1) {
938 up = isl_upoly_mul(up, isl_upoly_copy(up));
940 res = isl_upoly_mul(res, isl_upoly_copy(up));
947 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
948 unsigned n_div, __isl_take struct isl_upoly *up)
950 struct isl_qpolynomial *qp = NULL;
956 total = isl_dim_total(dim);
958 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
963 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
974 isl_qpolynomial_free(qp);
978 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
987 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
989 struct isl_qpolynomial *dup;
994 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
995 isl_upoly_copy(qp->upoly));
998 isl_mat_free(dup->div);
999 dup->div = isl_mat_copy(qp->div);
1005 isl_qpolynomial_free(dup);
1009 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1017 return isl_qpolynomial_dup(qp);
1020 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1028 isl_dim_free(qp->dim);
1029 isl_mat_free(qp->div);
1030 isl_upoly_free(qp->upoly);
1035 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1038 struct isl_upoly_rec *rec;
1039 struct isl_upoly_cst *cst;
1041 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1044 for (i = 0; i < 1 + power; ++i) {
1045 rec->p[i] = isl_upoly_zero(ctx);
1050 cst = isl_upoly_as_cst(rec->p[power]);
1051 isl_int_set_si(cst->n, 1);
1055 isl_upoly_free(&rec->up);
1059 /* r array maps original positions to new positions.
1061 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1065 struct isl_upoly_rec *rec;
1066 struct isl_upoly *base;
1067 struct isl_upoly *res;
1069 if (isl_upoly_is_cst(up))
1072 rec = isl_upoly_as_rec(up);
1076 isl_assert(up->ctx, rec->n >= 1, goto error);
1078 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1079 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1081 for (i = rec->n - 2; i >= 0; --i) {
1082 res = isl_upoly_mul(res, isl_upoly_copy(base));
1083 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1086 isl_upoly_free(base);
1095 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1100 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1101 div1->n_col >= div2->n_col, return -1);
1103 if (div1->n_row == div2->n_row)
1104 return isl_mat_is_equal(div1, div2);
1106 n_row = div1->n_row;
1107 n_col = div1->n_col;
1108 div1->n_row = div2->n_row;
1109 div1->n_col = div2->n_col;
1111 equal = isl_mat_is_equal(div1, div2);
1113 div1->n_row = n_row;
1114 div1->n_col = n_col;
1119 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1123 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1124 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1129 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1132 struct isl_div_sort_info {
1137 static int div_sort_cmp(const void *p1, const void *p2)
1139 const struct isl_div_sort_info *i1, *i2;
1140 i1 = (const struct isl_div_sort_info *) p1;
1141 i2 = (const struct isl_div_sort_info *) p2;
1143 return cmp_row(i1->div, i1->row, i2->row);
1146 /* Sort divs and remove duplicates.
1148 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1153 struct isl_div_sort_info *array = NULL;
1154 int *pos = NULL, *at = NULL;
1155 int *reordering = NULL;
1160 if (qp->div->n_row <= 1)
1163 div_pos = isl_dim_total(qp->dim);
1165 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1167 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1168 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1169 len = qp->div->n_col - 2;
1170 reordering = isl_alloc_array(qp->div->ctx, int, len);
1171 if (!array || !pos || !at || !reordering)
1174 for (i = 0; i < qp->div->n_row; ++i) {
1175 array[i].div = qp->div;
1181 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1184 for (i = 0; i < div_pos; ++i)
1187 for (i = 0; i < qp->div->n_row; ++i) {
1188 if (pos[array[i].row] == i)
1190 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1191 pos[at[i]] = pos[array[i].row];
1192 at[pos[array[i].row]] = at[i];
1193 at[i] = array[i].row;
1194 pos[array[i].row] = i;
1198 for (i = 0; i < len - div_pos; ++i) {
1200 isl_seq_eq(qp->div->row[i - skip - 1],
1201 qp->div->row[i - skip], qp->div->n_col)) {
1202 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1203 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1204 2 + div_pos + i - skip);
1205 qp->div = isl_mat_drop_cols(qp->div,
1206 2 + div_pos + i - skip, 1);
1209 reordering[div_pos + array[i].row] = div_pos + i - skip;
1212 qp->upoly = reorder(qp->upoly, reordering);
1214 if (!qp->upoly || !qp->div)
1228 isl_qpolynomial_free(qp);
1232 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1233 int *exp, int first)
1236 struct isl_upoly_rec *rec;
1238 if (isl_upoly_is_cst(up))
1241 if (up->var < first)
1244 if (exp[up->var - first] == up->var - first)
1247 up = isl_upoly_cow(up);
1251 up->var = exp[up->var - first] + first;
1253 rec = isl_upoly_as_rec(up);
1257 for (i = 0; i < rec->n; ++i) {
1258 rec->p[i] = expand(rec->p[i], exp, first);
1269 static __isl_give isl_qpolynomial *with_merged_divs(
1270 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1271 __isl_take isl_qpolynomial *qp2),
1272 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1276 isl_mat *div = NULL;
1278 qp1 = isl_qpolynomial_cow(qp1);
1279 qp2 = isl_qpolynomial_cow(qp2);
1284 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1285 qp1->div->n_col >= qp2->div->n_col, goto error);
1287 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1288 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1292 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1296 isl_mat_free(qp1->div);
1297 qp1->div = isl_mat_copy(div);
1298 isl_mat_free(qp2->div);
1299 qp2->div = isl_mat_copy(div);
1301 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1302 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1304 if (!qp1->upoly || !qp2->upoly)
1311 return fn(qp1, qp2);
1316 isl_qpolynomial_free(qp1);
1317 isl_qpolynomial_free(qp2);
1321 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1322 __isl_take isl_qpolynomial *qp2)
1324 qp1 = isl_qpolynomial_cow(qp1);
1329 if (qp1->div->n_row < qp2->div->n_row)
1330 return isl_qpolynomial_add(qp2, qp1);
1332 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1333 if (!compatible_divs(qp1->div, qp2->div))
1334 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1336 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1340 isl_qpolynomial_free(qp2);
1344 isl_qpolynomial_free(qp1);
1345 isl_qpolynomial_free(qp2);
1349 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1350 __isl_keep isl_set *dom,
1351 __isl_take isl_qpolynomial *qp1,
1352 __isl_take isl_qpolynomial *qp2)
1354 qp1 = isl_qpolynomial_add(qp1, qp2);
1355 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1359 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1360 __isl_take isl_qpolynomial *qp2)
1362 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1365 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1366 __isl_take isl_qpolynomial *qp, isl_int v)
1368 if (isl_int_is_zero(v))
1371 qp = isl_qpolynomial_cow(qp);
1375 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1381 isl_qpolynomial_free(qp);
1386 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1391 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1394 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1395 __isl_take isl_qpolynomial *qp, isl_int v)
1397 if (isl_int_is_one(v))
1400 if (qp && isl_int_is_zero(v)) {
1401 isl_qpolynomial *zero;
1402 zero = isl_qpolynomial_zero(isl_dim_copy(qp->dim));
1403 isl_qpolynomial_free(qp);
1407 qp = isl_qpolynomial_cow(qp);
1411 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1417 isl_qpolynomial_free(qp);
1421 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
1422 __isl_take isl_qpolynomial *qp, isl_int v)
1424 return isl_qpolynomial_mul_isl_int(qp, v);
1427 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1428 __isl_take isl_qpolynomial *qp2)
1430 qp1 = isl_qpolynomial_cow(qp1);
1435 if (qp1->div->n_row < qp2->div->n_row)
1436 return isl_qpolynomial_mul(qp2, qp1);
1438 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1439 if (!compatible_divs(qp1->div, qp2->div))
1440 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1442 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1446 isl_qpolynomial_free(qp2);
1450 isl_qpolynomial_free(qp1);
1451 isl_qpolynomial_free(qp2);
1455 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1458 qp = isl_qpolynomial_cow(qp);
1463 qp->upoly = isl_upoly_pow(qp->upoly, power);
1469 isl_qpolynomial_free(qp);
1473 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1477 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1480 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1484 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1487 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1491 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1494 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1498 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1501 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1505 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1508 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1511 struct isl_qpolynomial *qp;
1512 struct isl_upoly_cst *cst;
1517 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1521 cst = isl_upoly_as_cst(qp->upoly);
1522 isl_int_set(cst->n, v);
1527 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1528 isl_int *n, isl_int *d)
1530 struct isl_upoly_cst *cst;
1535 if (!isl_upoly_is_cst(qp->upoly))
1538 cst = isl_upoly_as_cst(qp->upoly);
1543 isl_int_set(*n, cst->n);
1545 isl_int_set(*d, cst->d);
1550 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1553 struct isl_upoly_rec *rec;
1561 rec = isl_upoly_as_rec(up);
1568 isl_assert(up->ctx, rec->n > 1, return -1);
1570 is_cst = isl_upoly_is_cst(rec->p[1]);
1576 return isl_upoly_is_affine(rec->p[0]);
1579 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1584 if (qp->div->n_row > 0)
1587 return isl_upoly_is_affine(qp->upoly);
1590 static void update_coeff(__isl_keep isl_vec *aff,
1591 __isl_keep struct isl_upoly_cst *cst, int pos)
1596 if (isl_int_is_zero(cst->n))
1601 isl_int_gcd(gcd, cst->d, aff->el[0]);
1602 isl_int_divexact(f, cst->d, gcd);
1603 isl_int_divexact(gcd, aff->el[0], gcd);
1604 isl_seq_scale(aff->el, aff->el, f, aff->size);
1605 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1610 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1611 __isl_keep isl_vec *aff)
1613 struct isl_upoly_cst *cst;
1614 struct isl_upoly_rec *rec;
1620 struct isl_upoly_cst *cst;
1622 cst = isl_upoly_as_cst(up);
1625 update_coeff(aff, cst, 0);
1629 rec = isl_upoly_as_rec(up);
1632 isl_assert(up->ctx, rec->n == 2, return -1);
1634 cst = isl_upoly_as_cst(rec->p[1]);
1637 update_coeff(aff, cst, 1 + up->var);
1639 return isl_upoly_update_affine(rec->p[0], aff);
1642 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1643 __isl_keep isl_qpolynomial *qp)
1651 d = isl_dim_total(qp->dim);
1652 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1656 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1657 isl_int_set_si(aff->el[0], 1);
1659 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1668 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1669 __isl_keep isl_qpolynomial *qp2)
1676 equal = isl_dim_equal(qp1->dim, qp2->dim);
1677 if (equal < 0 || !equal)
1680 equal = isl_mat_is_equal(qp1->div, qp2->div);
1681 if (equal < 0 || !equal)
1684 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1687 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1690 struct isl_upoly_rec *rec;
1692 if (isl_upoly_is_cst(up)) {
1693 struct isl_upoly_cst *cst;
1694 cst = isl_upoly_as_cst(up);
1697 isl_int_lcm(*d, *d, cst->d);
1701 rec = isl_upoly_as_rec(up);
1705 for (i = 0; i < rec->n; ++i)
1706 upoly_update_den(rec->p[i], d);
1709 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1711 isl_int_set_si(*d, 1);
1714 upoly_update_den(qp->upoly, d);
1717 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1720 struct isl_ctx *ctx;
1727 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1730 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1731 enum isl_dim_type type, unsigned pos)
1736 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1737 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1739 if (type == isl_dim_set)
1740 pos += isl_dim_size(dim, isl_dim_param);
1742 return isl_qpolynomial_var_pow(dim, pos, 1);
1748 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1749 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1752 struct isl_upoly_rec *rec;
1753 struct isl_upoly *base, *res;
1758 if (isl_upoly_is_cst(up))
1761 if (up->var < first)
1764 rec = isl_upoly_as_rec(up);
1768 isl_assert(up->ctx, rec->n >= 1, goto error);
1770 if (up->var >= first + n)
1771 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1773 base = isl_upoly_copy(subs[up->var - first]);
1775 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1776 for (i = rec->n - 2; i >= 0; --i) {
1777 struct isl_upoly *t;
1778 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1779 res = isl_upoly_mul(res, isl_upoly_copy(base));
1780 res = isl_upoly_sum(res, t);
1783 isl_upoly_free(base);
1792 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1793 isl_int denom, unsigned len)
1796 struct isl_upoly *up;
1798 isl_assert(ctx, len >= 1, return NULL);
1800 up = isl_upoly_rat_cst(ctx, f[0], denom);
1801 for (i = 0; i < len - 1; ++i) {
1802 struct isl_upoly *t;
1803 struct isl_upoly *c;
1805 if (isl_int_is_zero(f[1 + i]))
1808 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1809 t = isl_upoly_var_pow(ctx, i, 1);
1810 t = isl_upoly_mul(c, t);
1811 up = isl_upoly_sum(up, t);
1817 /* Remove common factor of non-constant terms and denominator.
1819 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1821 isl_ctx *ctx = qp->div->ctx;
1822 unsigned total = qp->div->n_col - 2;
1824 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1825 isl_int_gcd(ctx->normalize_gcd,
1826 ctx->normalize_gcd, qp->div->row[div][0]);
1827 if (isl_int_is_one(ctx->normalize_gcd))
1830 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1831 ctx->normalize_gcd, total);
1832 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1833 ctx->normalize_gcd);
1834 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1835 ctx->normalize_gcd);
1838 /* Replace the integer division identified by "div" by the polynomial "s".
1839 * The integer division is assumed not to appear in the definition
1840 * of any other integer divisions.
1842 static __isl_give isl_qpolynomial *substitute_div(
1843 __isl_take isl_qpolynomial *qp,
1844 int div, __isl_take struct isl_upoly *s)
1853 qp = isl_qpolynomial_cow(qp);
1857 total = isl_dim_total(qp->dim);
1858 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1862 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1865 for (i = 0; i < total + div; ++i)
1867 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1868 reordering[i] = i - 1;
1869 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1870 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1871 qp->upoly = reorder(qp->upoly, reordering);
1874 if (!qp->upoly || !qp->div)
1880 isl_qpolynomial_free(qp);
1885 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1886 * divisions because d is equal to 1 by their definition, i.e., e.
1888 static __isl_give isl_qpolynomial *substitute_non_divs(
1889 __isl_take isl_qpolynomial *qp)
1893 struct isl_upoly *s;
1898 total = isl_dim_total(qp->dim);
1899 for (i = 0; qp && i < qp->div->n_row; ++i) {
1900 if (!isl_int_is_one(qp->div->row[i][0]))
1902 for (j = i + 1; j < qp->div->n_row; ++j) {
1903 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1905 isl_seq_combine(qp->div->row[j] + 1,
1906 qp->div->ctx->one, qp->div->row[j] + 1,
1907 qp->div->row[j][2 + total + i],
1908 qp->div->row[i] + 1, 1 + total + i);
1909 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1910 normalize_div(qp, j);
1912 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1913 qp->div->row[i][0], qp->div->n_col - 1);
1914 qp = substitute_div(qp, i, s);
1921 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1922 * with d the denominator. When replacing the coefficient e of x by
1923 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1924 * inside the division, so we need to add floor(e/d) * x outside.
1925 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1926 * to adjust the coefficient of x in each later div that depends on the
1927 * current div "div" and also in the affine expression "aff"
1928 * (if it too depends on "div").
1930 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1931 __isl_keep isl_vec *aff)
1935 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1938 for (i = 0; i < 1 + total + div; ++i) {
1939 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1940 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1942 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1943 isl_int_fdiv_r(qp->div->row[div][1 + i],
1944 qp->div->row[div][1 + i], qp->div->row[div][0]);
1945 if (!isl_int_is_zero(aff->el[1 + total + div]))
1946 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1947 for (j = div + 1; j < qp->div->n_row; ++j) {
1948 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1950 isl_int_addmul(qp->div->row[j][1 + i],
1951 v, qp->div->row[j][2 + total + div]);
1957 /* Check if the last non-zero coefficient is bigger that half of the
1958 * denominator. If so, we will invert the div to further reduce the number
1959 * of distinct divs that may appear.
1960 * If the last non-zero coefficient is exactly half the denominator,
1961 * then we continue looking for earlier coefficients that are bigger
1962 * than half the denominator.
1964 static int needs_invert(__isl_keep isl_mat *div, int row)
1969 for (i = div->n_col - 1; i >= 1; --i) {
1970 if (isl_int_is_zero(div->row[row][i]))
1972 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1973 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1974 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1984 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1985 * We only invert the coefficients of e (and the coefficient of q in
1986 * later divs and in "aff"). After calling this function, the
1987 * coefficients of e should be reduced again.
1989 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1990 __isl_keep isl_vec *aff)
1992 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1994 isl_seq_neg(qp->div->row[div] + 1,
1995 qp->div->row[div] + 1, qp->div->n_col - 1);
1996 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
1997 isl_int_add(qp->div->row[div][1],
1998 qp->div->row[div][1], qp->div->row[div][0]);
1999 if (!isl_int_is_zero(aff->el[1 + total + div]))
2000 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2001 isl_mat_col_mul(qp->div, 2 + total + div,
2002 qp->div->ctx->negone, 2 + total + div);
2005 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2006 * in the interval [0, d-1], with d the denominator and such that the
2007 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2009 * After the reduction, some divs may have become redundant or identical,
2010 * so we call substitute_non_divs and sort_divs. If these functions
2011 * eliminate divs or merge two or more divs into one, the coefficients
2012 * of the enclosing divs may have to be reduced again, so we call
2013 * ourselves recursively if the number of divs decreases.
2015 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2018 isl_vec *aff = NULL;
2019 struct isl_upoly *s;
2025 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2026 aff = isl_vec_clr(aff);
2030 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2032 for (i = 0; i < qp->div->n_row; ++i) {
2033 normalize_div(qp, i);
2034 reduce_div(qp, i, aff);
2035 if (needs_invert(qp->div, i)) {
2036 invert_div(qp, i, aff);
2037 reduce_div(qp, i, aff);
2041 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2042 qp->div->ctx->one, aff->size);
2043 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2050 n_div = qp->div->n_row;
2051 qp = substitute_non_divs(qp);
2053 if (qp && qp->div->n_row < n_div)
2054 return reduce_divs(qp);
2058 isl_qpolynomial_free(qp);
2063 /* Assumes each div only depends on earlier divs.
2065 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2068 struct isl_qpolynomial *qp = NULL;
2069 struct isl_upoly_rec *rec;
2070 struct isl_upoly_cst *cst;
2077 d = div->line - div->bmap->div;
2079 pos = isl_dim_total(div->bmap->dim) + d;
2080 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2081 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2082 div->bmap->n_div, &rec->up);
2086 for (i = 0; i < div->bmap->n_div; ++i)
2087 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2089 for (i = 0; i < 1 + power; ++i) {
2090 rec->p[i] = isl_upoly_zero(div->ctx);
2095 cst = isl_upoly_as_cst(rec->p[power]);
2096 isl_int_set_si(cst->n, 1);
2100 qp = reduce_divs(qp);
2104 isl_qpolynomial_free(qp);
2109 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2111 return isl_qpolynomial_div_pow(div, 1);
2114 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2115 const isl_int n, const isl_int d)
2117 struct isl_qpolynomial *qp;
2118 struct isl_upoly_cst *cst;
2120 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2124 cst = isl_upoly_as_cst(qp->upoly);
2125 isl_int_set(cst->n, n);
2126 isl_int_set(cst->d, d);
2131 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2133 struct isl_upoly_rec *rec;
2139 if (isl_upoly_is_cst(up))
2143 active[up->var] = 1;
2145 rec = isl_upoly_as_rec(up);
2146 for (i = 0; i < rec->n; ++i)
2147 if (up_set_active(rec->p[i], active, d) < 0)
2153 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2156 int d = isl_dim_total(qp->dim);
2161 for (i = 0; i < d; ++i)
2162 for (j = 0; j < qp->div->n_row; ++j) {
2163 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2169 return up_set_active(qp->upoly, active, d);
2172 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2173 enum isl_dim_type type, unsigned first, unsigned n)
2184 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2186 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2187 type == isl_dim_set, return -1);
2189 active = isl_calloc_array(qp->dim->ctx, int, isl_dim_total(qp->dim));
2190 if (set_active(qp, active) < 0)
2193 if (type == isl_dim_set)
2194 first += isl_dim_size(qp->dim, isl_dim_param);
2195 for (i = 0; i < n; ++i)
2196 if (active[first + i]) {
2209 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2210 * of the divs that do appear in the quasi-polynomial.
2212 static __isl_give isl_qpolynomial *remove_redundant_divs(
2213 __isl_take isl_qpolynomial *qp)
2220 int *reordering = NULL;
2227 if (qp->div->n_row == 0)
2230 d = isl_dim_total(qp->dim);
2231 len = qp->div->n_col - 2;
2232 ctx = isl_qpolynomial_get_ctx(qp);
2233 active = isl_calloc_array(ctx, int, len);
2237 if (up_set_active(qp->upoly, active, len) < 0)
2240 for (i = qp->div->n_row - 1; i >= 0; --i) {
2241 if (!active[d + i]) {
2245 for (j = 0; j < i; ++j) {
2246 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2258 reordering = isl_alloc_array(qp->div->ctx, int, len);
2262 for (i = 0; i < d; ++i)
2266 n_div = qp->div->n_row;
2267 for (i = 0; i < n_div; ++i) {
2268 if (!active[d + i]) {
2269 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2270 qp->div = isl_mat_drop_cols(qp->div,
2271 2 + d + i - skip, 1);
2274 reordering[d + i] = d + i - skip;
2277 qp->upoly = reorder(qp->upoly, reordering);
2279 if (!qp->upoly || !qp->div)
2289 isl_qpolynomial_free(qp);
2293 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2294 unsigned first, unsigned n)
2297 struct isl_upoly_rec *rec;
2301 if (n == 0 || up->var < 0 || up->var < first)
2303 if (up->var < first + n) {
2304 up = replace_by_constant_term(up);
2305 return isl_upoly_drop(up, first, n);
2307 up = isl_upoly_cow(up);
2311 rec = isl_upoly_as_rec(up);
2315 for (i = 0; i < rec->n; ++i) {
2316 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2327 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2328 __isl_take isl_qpolynomial *qp,
2329 enum isl_dim_type type, unsigned pos, const char *s)
2331 qp = isl_qpolynomial_cow(qp);
2334 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2339 isl_qpolynomial_free(qp);
2343 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2344 __isl_take isl_qpolynomial *qp,
2345 enum isl_dim_type type, unsigned first, unsigned n)
2349 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2352 qp = isl_qpolynomial_cow(qp);
2356 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2358 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2359 type == isl_dim_set, goto error);
2361 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2365 if (type == isl_dim_set)
2366 first += isl_dim_size(qp->dim, isl_dim_param);
2368 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2372 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2378 isl_qpolynomial_free(qp);
2382 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2383 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2389 struct isl_upoly *up;
2393 if (eq->n_eq == 0) {
2394 isl_basic_set_free(eq);
2398 qp = isl_qpolynomial_cow(qp);
2401 qp->div = isl_mat_cow(qp->div);
2405 total = 1 + isl_dim_total(eq->dim);
2407 isl_int_init(denom);
2408 for (i = 0; i < eq->n_eq; ++i) {
2409 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2410 if (j < 0 || j == 0 || j >= total)
2413 for (k = 0; k < qp->div->n_row; ++k) {
2414 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2416 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2417 &qp->div->row[k][0]);
2418 normalize_div(qp, k);
2421 if (isl_int_is_pos(eq->eq[i][j]))
2422 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2423 isl_int_abs(denom, eq->eq[i][j]);
2424 isl_int_set_si(eq->eq[i][j], 0);
2426 up = isl_upoly_from_affine(qp->dim->ctx,
2427 eq->eq[i], denom, total);
2428 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2431 isl_int_clear(denom);
2436 isl_basic_set_free(eq);
2438 qp = substitute_non_divs(qp);
2443 isl_basic_set_free(eq);
2444 isl_qpolynomial_free(qp);
2448 static __isl_give isl_basic_set *add_div_constraints(
2449 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2457 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2460 total = isl_basic_set_total_dim(bset);
2461 for (i = 0; i < div->n_row; ++i)
2462 if (isl_basic_set_add_div_constraints_var(bset,
2463 total - div->n_row + i, div->row[i]) < 0)
2470 isl_basic_set_free(bset);
2474 /* Look for equalities among the variables shared by context and qp
2475 * and the integer divisions of qp, if any.
2476 * The equalities are then used to eliminate variables and/or integer
2477 * divisions from qp.
2479 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2480 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2486 if (qp->div->n_row > 0) {
2487 isl_basic_set *bset;
2488 context = isl_set_add_dims(context, isl_dim_set,
2490 bset = isl_basic_set_universe(isl_set_get_dim(context));
2491 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2492 context = isl_set_intersect(context,
2493 isl_set_from_basic_set(bset));
2496 aff = isl_set_affine_hull(context);
2497 return isl_qpolynomial_substitute_equalities(qp, aff);
2499 isl_qpolynomial_free(qp);
2500 isl_set_free(context);
2505 #define PW isl_pw_qpolynomial
2507 #define EL isl_qpolynomial
2509 #define EL_IS_ZERO is_zero
2513 #define IS_ZERO is_zero
2517 #include <isl_pw_templ.c>
2520 #define UNION isl_union_pw_qpolynomial
2522 #define PART isl_pw_qpolynomial
2524 #define PARTS pw_qpolynomial
2526 #include <isl_union_templ.c>
2528 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2536 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2539 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2542 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2543 __isl_take isl_pw_qpolynomial *pwqp1,
2544 __isl_take isl_pw_qpolynomial *pwqp2)
2547 struct isl_pw_qpolynomial *res;
2549 if (!pwqp1 || !pwqp2)
2552 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2555 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2556 isl_pw_qpolynomial_free(pwqp2);
2560 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2561 isl_pw_qpolynomial_free(pwqp1);
2565 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2566 isl_pw_qpolynomial_free(pwqp1);
2570 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2571 isl_pw_qpolynomial_free(pwqp2);
2575 n = pwqp1->n * pwqp2->n;
2576 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2578 for (i = 0; i < pwqp1->n; ++i) {
2579 for (j = 0; j < pwqp2->n; ++j) {
2580 struct isl_set *common;
2581 struct isl_qpolynomial *prod;
2582 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2583 isl_set_copy(pwqp2->p[j].set));
2584 if (isl_set_plain_is_empty(common)) {
2585 isl_set_free(common);
2589 prod = isl_qpolynomial_mul(
2590 isl_qpolynomial_copy(pwqp1->p[i].qp),
2591 isl_qpolynomial_copy(pwqp2->p[j].qp));
2593 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2597 isl_pw_qpolynomial_free(pwqp1);
2598 isl_pw_qpolynomial_free(pwqp2);
2602 isl_pw_qpolynomial_free(pwqp1);
2603 isl_pw_qpolynomial_free(pwqp2);
2607 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2608 __isl_take isl_pw_qpolynomial *pwqp1,
2609 __isl_take isl_pw_qpolynomial *pwqp2)
2611 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2614 __isl_give struct isl_upoly *isl_upoly_eval(
2615 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2618 struct isl_upoly_rec *rec;
2619 struct isl_upoly *res;
2620 struct isl_upoly *base;
2622 if (isl_upoly_is_cst(up)) {
2627 rec = isl_upoly_as_rec(up);
2631 isl_assert(up->ctx, rec->n >= 1, goto error);
2633 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2635 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2638 for (i = rec->n - 2; i >= 0; --i) {
2639 res = isl_upoly_mul(res, isl_upoly_copy(base));
2640 res = isl_upoly_sum(res,
2641 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2642 isl_vec_copy(vec)));
2645 isl_upoly_free(base);
2655 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2656 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2659 struct isl_upoly *up;
2664 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2666 if (qp->div->n_row == 0)
2667 ext = isl_vec_copy(pnt->vec);
2670 unsigned dim = isl_dim_total(qp->dim);
2671 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2675 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2676 for (i = 0; i < qp->div->n_row; ++i) {
2677 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2678 1 + dim + i, &ext->el[1+dim+i]);
2679 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2680 qp->div->row[i][0]);
2684 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2688 dim = isl_dim_copy(qp->dim);
2689 isl_qpolynomial_free(qp);
2690 isl_point_free(pnt);
2692 return isl_qpolynomial_alloc(dim, 0, up);
2694 isl_qpolynomial_free(qp);
2695 isl_point_free(pnt);
2699 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2700 __isl_keep struct isl_upoly_cst *cst2)
2705 isl_int_mul(t, cst1->n, cst2->d);
2706 isl_int_submul(t, cst2->n, cst1->d);
2707 cmp = isl_int_sgn(t);
2712 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2713 __isl_keep isl_qpolynomial *qp2)
2715 struct isl_upoly_cst *cst1, *cst2;
2719 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2720 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2721 if (isl_qpolynomial_is_nan(qp1))
2723 if (isl_qpolynomial_is_nan(qp2))
2725 cst1 = isl_upoly_as_cst(qp1->upoly);
2726 cst2 = isl_upoly_as_cst(qp2->upoly);
2728 return isl_upoly_cmp(cst1, cst2) <= 0;
2731 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2732 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2734 struct isl_upoly_cst *cst1, *cst2;
2739 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2740 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2741 cst1 = isl_upoly_as_cst(qp1->upoly);
2742 cst2 = isl_upoly_as_cst(qp2->upoly);
2743 cmp = isl_upoly_cmp(cst1, cst2);
2746 isl_qpolynomial_free(qp2);
2748 isl_qpolynomial_free(qp1);
2753 isl_qpolynomial_free(qp1);
2754 isl_qpolynomial_free(qp2);
2758 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2759 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2761 struct isl_upoly_cst *cst1, *cst2;
2766 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2767 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2768 cst1 = isl_upoly_as_cst(qp1->upoly);
2769 cst2 = isl_upoly_as_cst(qp2->upoly);
2770 cmp = isl_upoly_cmp(cst1, cst2);
2773 isl_qpolynomial_free(qp2);
2775 isl_qpolynomial_free(qp1);
2780 isl_qpolynomial_free(qp1);
2781 isl_qpolynomial_free(qp2);
2785 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2786 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2787 unsigned first, unsigned n)
2793 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2796 qp = isl_qpolynomial_cow(qp);
2800 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2803 g_pos = pos(qp->dim, type) + first;
2805 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2809 total = qp->div->n_col - 2;
2810 if (total > g_pos) {
2812 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2815 for (i = 0; i < total - g_pos; ++i)
2817 qp->upoly = expand(qp->upoly, exp, g_pos);
2823 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2829 isl_qpolynomial_free(qp);
2833 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2834 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2838 pos = isl_qpolynomial_dim(qp, type);
2840 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2843 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2844 __isl_take isl_pw_qpolynomial *pwqp,
2845 enum isl_dim_type type, unsigned n)
2849 pos = isl_pw_qpolynomial_dim(pwqp, type);
2851 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2854 static int *reordering_move(isl_ctx *ctx,
2855 unsigned len, unsigned dst, unsigned src, unsigned n)
2860 reordering = isl_alloc_array(ctx, int, len);
2865 for (i = 0; i < dst; ++i)
2867 for (i = 0; i < n; ++i)
2868 reordering[src + i] = dst + i;
2869 for (i = 0; i < src - dst; ++i)
2870 reordering[dst + i] = dst + n + i;
2871 for (i = 0; i < len - src - n; ++i)
2872 reordering[src + n + i] = src + n + i;
2874 for (i = 0; i < src; ++i)
2876 for (i = 0; i < n; ++i)
2877 reordering[src + i] = dst + i;
2878 for (i = 0; i < dst - src; ++i)
2879 reordering[src + n + i] = src + i;
2880 for (i = 0; i < len - dst - n; ++i)
2881 reordering[dst + n + i] = dst + n + i;
2887 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2888 __isl_take isl_qpolynomial *qp,
2889 enum isl_dim_type dst_type, unsigned dst_pos,
2890 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2896 qp = isl_qpolynomial_cow(qp);
2900 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2903 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2904 g_src_pos = pos(qp->dim, src_type) + src_pos;
2905 if (dst_type > src_type)
2908 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2915 reordering = reordering_move(qp->dim->ctx,
2916 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2920 qp->upoly = reorder(qp->upoly, reordering);
2925 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2931 isl_qpolynomial_free(qp);
2935 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2936 isl_int *f, isl_int denom)
2938 struct isl_upoly *up;
2943 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2945 return isl_qpolynomial_alloc(dim, 0, up);
2948 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
2951 struct isl_upoly *up;
2952 isl_qpolynomial *qp;
2957 ctx = isl_aff_get_ctx(aff);
2958 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
2961 qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff),
2962 aff->ls->div->n_row, up);
2966 isl_mat_free(qp->div);
2967 qp->div = isl_mat_copy(aff->ls->div);
2968 qp->div = isl_mat_cow(qp->div);
2973 qp = reduce_divs(qp);
2974 qp = remove_redundant_divs(qp);
2981 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2982 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2986 aff = isl_constraint_get_bound(c, type, pos);
2987 isl_constraint_free(c);
2988 return isl_qpolynomial_from_aff(aff);
2991 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2992 * in "qp" by subs[i].
2994 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2995 __isl_take isl_qpolynomial *qp,
2996 enum isl_dim_type type, unsigned first, unsigned n,
2997 __isl_keep isl_qpolynomial **subs)
3000 struct isl_upoly **ups;
3005 qp = isl_qpolynomial_cow(qp);
3008 for (i = 0; i < n; ++i)
3012 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
3015 for (i = 0; i < n; ++i)
3016 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3019 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3020 for (i = 0; i < n; ++i)
3021 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3023 first += pos(qp->dim, type);
3025 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3028 for (i = 0; i < n; ++i)
3029 ups[i] = subs[i]->upoly;
3031 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3040 isl_qpolynomial_free(qp);
3044 /* Extend "bset" with extra set dimensions for each integer division
3045 * in "qp" and then call "fn" with the extended bset and the polynomial
3046 * that results from replacing each of the integer divisions by the
3047 * corresponding extra set dimension.
3049 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3050 __isl_keep isl_basic_set *bset,
3051 int (*fn)(__isl_take isl_basic_set *bset,
3052 __isl_take isl_qpolynomial *poly, void *user), void *user)
3056 isl_qpolynomial *poly;
3060 if (qp->div->n_row == 0)
3061 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3064 div = isl_mat_copy(qp->div);
3065 dim = isl_dim_copy(qp->dim);
3066 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3067 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3068 bset = isl_basic_set_copy(bset);
3069 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3070 bset = add_div_constraints(bset, div);
3072 return fn(bset, poly, user);
3077 /* Return total degree in variables first (inclusive) up to last (exclusive).
3079 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3083 struct isl_upoly_rec *rec;
3087 if (isl_upoly_is_zero(up))
3089 if (isl_upoly_is_cst(up) || up->var < first)
3092 rec = isl_upoly_as_rec(up);
3096 for (i = 0; i < rec->n; ++i) {
3099 if (isl_upoly_is_zero(rec->p[i]))
3101 d = isl_upoly_degree(rec->p[i], first, last);
3111 /* Return total degree in set variables.
3113 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3121 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3122 nvar = isl_dim_size(poly->dim, isl_dim_set);
3123 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3126 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3127 unsigned pos, int deg)
3130 struct isl_upoly_rec *rec;
3135 if (isl_upoly_is_cst(up) || up->var < pos) {
3137 return isl_upoly_copy(up);
3139 return isl_upoly_zero(up->ctx);
3142 rec = isl_upoly_as_rec(up);
3146 if (up->var == pos) {
3148 return isl_upoly_copy(rec->p[deg]);
3150 return isl_upoly_zero(up->ctx);
3153 up = isl_upoly_copy(up);
3154 up = isl_upoly_cow(up);
3155 rec = isl_upoly_as_rec(up);
3159 for (i = 0; i < rec->n; ++i) {
3160 struct isl_upoly *t;
3161 t = isl_upoly_coeff(rec->p[i], pos, deg);
3164 isl_upoly_free(rec->p[i]);
3174 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3176 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3177 __isl_keep isl_qpolynomial *qp,
3178 enum isl_dim_type type, unsigned t_pos, int deg)
3181 struct isl_upoly *up;
3187 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3190 g_pos = pos(qp->dim, type) + t_pos;
3191 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3193 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3196 isl_mat_free(c->div);
3197 c->div = isl_mat_copy(qp->div);
3202 isl_qpolynomial_free(c);
3206 /* Homogenize the polynomial in the variables first (inclusive) up to
3207 * last (exclusive) by inserting powers of variable first.
3208 * Variable first is assumed not to appear in the input.
3210 __isl_give struct isl_upoly *isl_upoly_homogenize(
3211 __isl_take struct isl_upoly *up, int deg, int target,
3212 int first, int last)
3215 struct isl_upoly_rec *rec;
3219 if (isl_upoly_is_zero(up))
3223 if (isl_upoly_is_cst(up) || up->var < first) {
3224 struct isl_upoly *hom;
3226 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3229 rec = isl_upoly_as_rec(hom);
3230 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3235 up = isl_upoly_cow(up);
3236 rec = isl_upoly_as_rec(up);
3240 for (i = 0; i < rec->n; ++i) {
3241 if (isl_upoly_is_zero(rec->p[i]))
3243 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3244 up->var < last ? deg + i : i, target,
3256 /* Homogenize the polynomial in the set variables by introducing
3257 * powers of an extra set variable at position 0.
3259 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3260 __isl_take isl_qpolynomial *poly)
3264 int deg = isl_qpolynomial_degree(poly);
3269 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3270 poly = isl_qpolynomial_cow(poly);
3274 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3275 nvar = isl_dim_size(poly->dim, isl_dim_set);
3276 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3283 isl_qpolynomial_free(poly);
3287 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3288 __isl_take isl_mat *div)
3296 n = isl_dim_total(dim) + div->n_row;
3298 term = isl_calloc(dim->ctx, struct isl_term,
3299 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3306 isl_int_init(term->n);
3307 isl_int_init(term->d);
3316 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3325 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3334 total = isl_dim_total(term->dim) + term->div->n_row;
3336 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3340 isl_int_set(dup->n, term->n);
3341 isl_int_set(dup->d, term->d);
3343 for (i = 0; i < total; ++i)
3344 dup->pow[i] = term->pow[i];
3349 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3357 return isl_term_dup(term);
3360 void isl_term_free(__isl_take isl_term *term)
3365 if (--term->ref > 0)
3368 isl_dim_free(term->dim);
3369 isl_mat_free(term->div);
3370 isl_int_clear(term->n);
3371 isl_int_clear(term->d);
3375 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3383 case isl_dim_out: return isl_dim_size(term->dim, type);
3384 case isl_dim_div: return term->div->n_row;
3385 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3390 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3392 return term ? term->dim->ctx : NULL;
3395 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3399 isl_int_set(*n, term->n);
3402 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3406 isl_int_set(*d, term->d);
3409 int isl_term_get_exp(__isl_keep isl_term *term,
3410 enum isl_dim_type type, unsigned pos)
3415 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3417 if (type >= isl_dim_set)
3418 pos += isl_dim_size(term->dim, isl_dim_param);
3419 if (type >= isl_dim_div)
3420 pos += isl_dim_size(term->dim, isl_dim_set);
3422 return term->pow[pos];
3425 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3427 isl_basic_map *bmap;
3434 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3437 total = term->div->n_col - term->div->n_row - 2;
3438 /* No nested divs for now */
3439 isl_assert(term->dim->ctx,
3440 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3441 term->div->n_row) == -1,
3444 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3445 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3448 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3450 return isl_basic_map_div(bmap, k);
3452 isl_basic_map_free(bmap);
3456 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3457 int (*fn)(__isl_take isl_term *term, void *user),
3458 __isl_take isl_term *term, void *user)
3461 struct isl_upoly_rec *rec;
3466 if (isl_upoly_is_zero(up))
3469 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3470 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3471 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3473 if (isl_upoly_is_cst(up)) {
3474 struct isl_upoly_cst *cst;
3475 cst = isl_upoly_as_cst(up);
3478 term = isl_term_cow(term);
3481 isl_int_set(term->n, cst->n);
3482 isl_int_set(term->d, cst->d);
3483 if (fn(isl_term_copy(term), user) < 0)
3488 rec = isl_upoly_as_rec(up);
3492 for (i = 0; i < rec->n; ++i) {
3493 term = isl_term_cow(term);
3496 term->pow[up->var] = i;
3497 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3501 term->pow[up->var] = 0;
3505 isl_term_free(term);
3509 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3510 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3517 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3521 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3523 isl_term_free(term);
3525 return term ? 0 : -1;
3528 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3530 struct isl_upoly *up;
3531 isl_qpolynomial *qp;
3537 n = isl_dim_total(term->dim) + term->div->n_row;
3539 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3540 for (i = 0; i < n; ++i) {
3543 up = isl_upoly_mul(up,
3544 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3547 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3550 isl_mat_free(qp->div);
3551 qp->div = isl_mat_copy(term->div);
3555 isl_term_free(term);
3558 isl_qpolynomial_free(qp);
3559 isl_term_free(term);
3563 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3564 __isl_take isl_dim *dim)
3573 if (isl_dim_equal(qp->dim, dim)) {
3578 qp = isl_qpolynomial_cow(qp);
3582 extra = isl_dim_size(dim, isl_dim_set) -
3583 isl_dim_size(qp->dim, isl_dim_set);
3584 total = isl_dim_total(qp->dim);
3585 if (qp->div->n_row) {
3588 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3591 for (i = 0; i < qp->div->n_row; ++i)
3593 qp->upoly = expand(qp->upoly, exp, total);
3598 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3601 for (i = 0; i < qp->div->n_row; ++i)
3602 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3604 isl_dim_free(qp->dim);
3610 isl_qpolynomial_free(qp);
3614 /* For each parameter or variable that does not appear in qp,
3615 * first eliminate the variable from all constraints and then set it to zero.
3617 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3618 __isl_keep isl_qpolynomial *qp)
3629 d = isl_dim_total(set->dim);
3630 active = isl_calloc_array(set->ctx, int, d);
3631 if (set_active(qp, active) < 0)
3634 for (i = 0; i < d; ++i)
3643 nparam = isl_dim_size(set->dim, isl_dim_param);
3644 nvar = isl_dim_size(set->dim, isl_dim_set);
3645 for (i = 0; i < nparam; ++i) {
3648 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3649 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3651 for (i = 0; i < nvar; ++i) {
3652 if (active[nparam + i])
3654 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3655 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3667 struct isl_opt_data {
3668 isl_qpolynomial *qp;
3670 isl_qpolynomial *opt;
3674 static int opt_fn(__isl_take isl_point *pnt, void *user)
3676 struct isl_opt_data *data = (struct isl_opt_data *)user;
3677 isl_qpolynomial *val;
3679 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3683 } else if (data->max) {
3684 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3686 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3692 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3693 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3695 struct isl_opt_data data = { NULL, 1, NULL, max };
3700 if (isl_upoly_is_cst(qp->upoly)) {
3705 set = fix_inactive(set, qp);
3708 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3712 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3715 isl_qpolynomial_free(qp);
3719 isl_qpolynomial_free(qp);
3720 isl_qpolynomial_free(data.opt);
3724 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3725 __isl_take isl_morph *morph)
3730 struct isl_upoly **subs;
3733 qp = isl_qpolynomial_cow(qp);
3738 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3740 n_sub = morph->inv->n_row - 1;
3741 if (morph->inv->n_row != morph->inv->n_col)
3742 n_sub += qp->div->n_row;
3743 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3747 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3748 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3749 morph->inv->row[0][0], morph->inv->n_col);
3750 if (morph->inv->n_row != morph->inv->n_col)
3751 for (i = 0; i < qp->div->n_row; ++i)
3752 subs[morph->inv->n_row - 1 + i] =
3753 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3755 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3757 for (i = 0; i < n_sub; ++i)
3758 isl_upoly_free(subs[i]);
3761 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3762 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3763 qp->div = isl_mat_product(qp->div, mat);
3764 isl_dim_free(qp->dim);
3765 qp->dim = isl_dim_copy(morph->ran->dim);
3767 if (!qp->upoly || !qp->div || !qp->dim)
3770 isl_morph_free(morph);
3774 isl_qpolynomial_free(qp);
3775 isl_morph_free(morph);
3779 static int neg_entry(void **entry, void *user)
3781 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3783 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3785 return *pwqp ? 0 : -1;
3788 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3789 __isl_take isl_union_pw_qpolynomial *upwqp)
3791 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3795 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3796 &neg_entry, NULL) < 0)
3801 isl_union_pw_qpolynomial_free(upwqp);
3805 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3806 __isl_take isl_union_pw_qpolynomial *upwqp1,
3807 __isl_take isl_union_pw_qpolynomial *upwqp2)
3809 return isl_union_pw_qpolynomial_add(upwqp1,
3810 isl_union_pw_qpolynomial_neg(upwqp2));
3813 static int mul_entry(void **entry, void *user)
3815 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3817 struct isl_hash_table_entry *entry2;
3818 isl_pw_qpolynomial *pwpq = *entry;
3821 hash = isl_dim_get_hash(pwpq->dim);
3822 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3823 hash, &has_dim, pwpq->dim, 0);
3827 pwpq = isl_pw_qpolynomial_copy(pwpq);
3828 pwpq = isl_pw_qpolynomial_mul(pwpq,
3829 isl_pw_qpolynomial_copy(entry2->data));
3831 empty = isl_pw_qpolynomial_is_zero(pwpq);
3833 isl_pw_qpolynomial_free(pwpq);
3837 isl_pw_qpolynomial_free(pwpq);
3841 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3846 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3847 __isl_take isl_union_pw_qpolynomial *upwqp1,
3848 __isl_take isl_union_pw_qpolynomial *upwqp2)
3850 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3853 /* Reorder the columns of the given div definitions according to the
3856 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3857 __isl_take isl_reordering *r)
3866 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3867 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3871 for (i = 0; i < div->n_row; ++i) {
3872 isl_seq_cpy(mat->row[i], div->row[i], 2);
3873 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3874 for (j = 0; j < r->len; ++j)
3875 isl_int_set(mat->row[i][2 + r->pos[j]],
3876 div->row[i][2 + j]);
3879 isl_reordering_free(r);
3883 isl_reordering_free(r);
3888 /* Reorder the dimension of "qp" according to the given reordering.
3890 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3891 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3893 qp = isl_qpolynomial_cow(qp);
3897 r = isl_reordering_extend(r, qp->div->n_row);
3901 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3905 qp->upoly = reorder(qp->upoly, r->pos);
3909 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3911 isl_reordering_free(r);
3914 isl_qpolynomial_free(qp);
3915 isl_reordering_free(r);
3919 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3920 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3925 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3926 isl_reordering *exp;
3928 model = isl_dim_drop(model, isl_dim_in,
3929 0, isl_dim_size(model, isl_dim_in));
3930 model = isl_dim_drop(model, isl_dim_out,
3931 0, isl_dim_size(model, isl_dim_out));
3932 exp = isl_parameter_alignment_reordering(qp->dim, model);
3933 exp = isl_reordering_extend_dim(exp,
3934 isl_qpolynomial_get_dim(qp));
3935 qp = isl_qpolynomial_realign(qp, exp);
3938 isl_dim_free(model);
3941 isl_dim_free(model);
3942 isl_qpolynomial_free(qp);
3946 struct isl_split_periods_data {
3948 isl_pw_qpolynomial *res;
3951 /* Create a slice where the integer division "div" has the fixed value "v".
3952 * In particular, if "div" refers to floor(f/m), then create a slice
3954 * m v <= f <= m v + (m - 1)
3959 * -f + m v + (m - 1) >= 0
3961 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3962 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3965 isl_basic_set *bset = NULL;
3971 total = isl_dim_total(dim);
3972 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3974 k = isl_basic_set_alloc_inequality(bset);
3977 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3978 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3980 k = isl_basic_set_alloc_inequality(bset);
3983 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3984 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3985 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3986 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3989 return isl_set_from_basic_set(bset);
3991 isl_basic_set_free(bset);
3996 static int split_periods(__isl_take isl_set *set,
3997 __isl_take isl_qpolynomial *qp, void *user);
3999 /* Create a slice of the domain "set" such that integer division "div"
4000 * has the fixed value "v" and add the results to data->res,
4001 * replacing the integer division by "v" in "qp".
4003 static int set_div(__isl_take isl_set *set,
4004 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4005 struct isl_split_periods_data *data)
4010 struct isl_upoly *cst;
4012 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
4013 set = isl_set_intersect(set, slice);
4018 total = isl_dim_total(qp->dim);
4020 for (i = div + 1; i < qp->div->n_row; ++i) {
4021 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4023 isl_int_addmul(qp->div->row[i][1],
4024 qp->div->row[i][2 + total + div], v);
4025 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4028 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4029 qp = substitute_div(qp, div, cst);
4031 return split_periods(set, qp, data);
4034 isl_qpolynomial_free(qp);
4038 /* Split the domain "set" such that integer division "div"
4039 * has a fixed value (ranging from "min" to "max") on each slice
4040 * and add the results to data->res.
4042 static int split_div(__isl_take isl_set *set,
4043 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4044 struct isl_split_periods_data *data)
4046 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4047 isl_set *set_i = isl_set_copy(set);
4048 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4050 if (set_div(set_i, qp_i, div, min, data) < 0)
4054 isl_qpolynomial_free(qp);
4058 isl_qpolynomial_free(qp);
4062 /* If "qp" refers to any integer division
4063 * that can only attain "max_periods" distinct values on "set"
4064 * then split the domain along those distinct values.
4065 * Add the results (or the original if no splitting occurs)
4068 static int split_periods(__isl_take isl_set *set,
4069 __isl_take isl_qpolynomial *qp, void *user)
4072 isl_pw_qpolynomial *pwqp;
4073 struct isl_split_periods_data *data;
4078 data = (struct isl_split_periods_data *)user;
4083 if (qp->div->n_row == 0) {
4084 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4085 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4091 total = isl_dim_total(qp->dim);
4092 for (i = 0; i < qp->div->n_row; ++i) {
4093 enum isl_lp_result lp_res;
4095 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4096 qp->div->n_row) != -1)
4099 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4100 set->ctx->one, &min, NULL, NULL);
4101 if (lp_res == isl_lp_error)
4103 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4105 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4107 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4108 set->ctx->one, &max, NULL, NULL);
4109 if (lp_res == isl_lp_error)
4111 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4113 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4115 isl_int_sub(max, max, min);
4116 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4117 isl_int_add(max, max, min);
4122 if (i < qp->div->n_row) {
4123 r = split_div(set, qp, i, min, max, data);
4125 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4126 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4138 isl_qpolynomial_free(qp);
4142 /* If any quasi-polynomial in pwqp refers to any integer division
4143 * that can only attain "max_periods" distinct values on its domain
4144 * then split the domain along those distinct values.
4146 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4147 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4149 struct isl_split_periods_data data;
4151 data.max_periods = max_periods;
4152 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4154 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4157 isl_pw_qpolynomial_free(pwqp);
4161 isl_pw_qpolynomial_free(data.res);
4162 isl_pw_qpolynomial_free(pwqp);
4166 /* Construct a piecewise quasipolynomial that is constant on the given
4167 * domain. In particular, it is
4170 * infinity if cst == -1
4172 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4173 __isl_take isl_basic_set *bset, int cst)
4176 isl_qpolynomial *qp;
4181 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4182 dim = isl_basic_set_get_dim(bset);
4184 qp = isl_qpolynomial_infty(dim);
4186 qp = isl_qpolynomial_zero(dim);
4188 qp = isl_qpolynomial_one(dim);
4189 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4192 /* Factor bset, call fn on each of the factors and return the product.
4194 * If no factors can be found, simply call fn on the input.
4195 * Otherwise, construct the factors based on the factorizer,
4196 * call fn on each factor and compute the product.
4198 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4199 __isl_take isl_basic_set *bset,
4200 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4206 isl_qpolynomial *qp;
4207 isl_pw_qpolynomial *pwqp;
4211 f = isl_basic_set_factorizer(bset);
4214 if (f->n_group == 0) {
4215 isl_factorizer_free(f);
4219 nparam = isl_basic_set_dim(bset, isl_dim_param);
4220 nvar = isl_basic_set_dim(bset, isl_dim_set);
4222 dim = isl_basic_set_get_dim(bset);
4223 dim = isl_dim_domain(dim);
4224 set = isl_set_universe(isl_dim_copy(dim));
4225 qp = isl_qpolynomial_one(dim);
4226 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4228 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4230 for (i = 0, n = 0; i < f->n_group; ++i) {
4231 isl_basic_set *bset_i;
4232 isl_pw_qpolynomial *pwqp_i;
4234 bset_i = isl_basic_set_copy(bset);
4235 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4236 nparam + n + f->len[i], nvar - n - f->len[i]);
4237 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4239 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4240 n + f->len[i], nvar - n - f->len[i]);
4241 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4243 pwqp_i = fn(bset_i);
4244 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4249 isl_basic_set_free(bset);
4250 isl_factorizer_free(f);
4254 isl_basic_set_free(bset);
4258 /* Factor bset, call fn on each of the factors and return the product.
4259 * The function is assumed to evaluate to zero on empty domains,
4260 * to one on zero-dimensional domains and to infinity on unbounded domains
4261 * and will not be called explicitly on zero-dimensional or unbounded domains.
4263 * We first check for some special cases and remove all equalities.
4264 * Then we hand over control to compressed_multiplicative_call.
4266 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4267 __isl_take isl_basic_set *bset,
4268 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4272 isl_pw_qpolynomial *pwqp;
4273 unsigned orig_nvar, final_nvar;
4278 if (isl_basic_set_plain_is_empty(bset))
4279 return constant_on_domain(bset, 0);
4281 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4284 return constant_on_domain(bset, 1);
4286 bounded = isl_basic_set_is_bounded(bset);
4290 return constant_on_domain(bset, -1);
4292 if (bset->n_eq == 0)
4293 return compressed_multiplicative_call(bset, fn);
4295 morph = isl_basic_set_full_compression(bset);
4296 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4298 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4300 pwqp = compressed_multiplicative_call(bset, fn);
4302 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4303 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4304 morph = isl_morph_inverse(morph);
4306 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4310 isl_basic_set_free(bset);
4314 /* Drop all floors in "qp", turning each integer division [a/m] into
4315 * a rational division a/m. If "down" is set, then the integer division
4316 * is replaces by (a-(m-1))/m instead.
4318 static __isl_give isl_qpolynomial *qp_drop_floors(
4319 __isl_take isl_qpolynomial *qp, int down)
4322 struct isl_upoly *s;
4326 if (qp->div->n_row == 0)
4329 qp = isl_qpolynomial_cow(qp);
4333 for (i = qp->div->n_row - 1; i >= 0; --i) {
4335 isl_int_sub(qp->div->row[i][1],
4336 qp->div->row[i][1], qp->div->row[i][0]);
4337 isl_int_add_ui(qp->div->row[i][1],
4338 qp->div->row[i][1], 1);
4340 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4341 qp->div->row[i][0], qp->div->n_col - 1);
4342 qp = substitute_div(qp, i, s);
4350 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4351 * a rational division a/m.
4353 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4354 __isl_take isl_pw_qpolynomial *pwqp)
4361 if (isl_pw_qpolynomial_is_zero(pwqp))
4364 pwqp = isl_pw_qpolynomial_cow(pwqp);
4368 for (i = 0; i < pwqp->n; ++i) {
4369 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4376 isl_pw_qpolynomial_free(pwqp);
4380 /* Adjust all the integer divisions in "qp" such that they are at least
4381 * one over the given orthant (identified by "signs"). This ensures
4382 * that they will still be non-negative even after subtracting (m-1)/m.
4384 * In particular, f is replaced by f' + v, changing f = [a/m]
4385 * to f' = [(a - m v)/m].
4386 * If the constant term k in a is smaller than m,
4387 * the constant term of v is set to floor(k/m) - 1.
4388 * For any other term, if the coefficient c and the variable x have
4389 * the same sign, then no changes are needed.
4390 * Otherwise, if the variable is positive (and c is negative),
4391 * then the coefficient of x in v is set to floor(c/m).
4392 * If the variable is negative (and c is positive),
4393 * then the coefficient of x in v is set to ceil(c/m).
4395 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4401 struct isl_upoly *s;
4403 qp = isl_qpolynomial_cow(qp);
4406 qp->div = isl_mat_cow(qp->div);
4410 total = isl_dim_total(qp->dim);
4411 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4413 for (i = 0; i < qp->div->n_row; ++i) {
4414 isl_int *row = qp->div->row[i];
4418 if (isl_int_lt(row[1], row[0])) {
4419 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4420 isl_int_sub_ui(v->el[0], v->el[0], 1);
4421 isl_int_submul(row[1], row[0], v->el[0]);
4423 for (j = 0; j < total; ++j) {
4424 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4427 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4429 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4430 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4432 for (j = 0; j < i; ++j) {
4433 if (isl_int_sgn(row[2 + total + j]) >= 0)
4435 isl_int_fdiv_q(v->el[1 + total + j],
4436 row[2 + total + j], row[0]);
4437 isl_int_submul(row[2 + total + j],
4438 row[0], v->el[1 + total + j]);
4440 for (j = i + 1; j < qp->div->n_row; ++j) {
4441 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4443 isl_seq_combine(qp->div->row[j] + 1,
4444 qp->div->ctx->one, qp->div->row[j] + 1,
4445 qp->div->row[j][2 + total + i], v->el, v->size);
4447 isl_int_set_si(v->el[1 + total + i], 1);
4448 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4449 qp->div->ctx->one, v->size);
4450 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4460 isl_qpolynomial_free(qp);
4464 struct isl_to_poly_data {
4466 isl_pw_qpolynomial *res;
4467 isl_qpolynomial *qp;
4470 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4471 * We first make all integer divisions positive and then split the
4472 * quasipolynomials into terms with sign data->sign (the direction
4473 * of the requested approximation) and terms with the opposite sign.
4474 * In the first set of terms, each integer division [a/m] is
4475 * overapproximated by a/m, while in the second it is underapproximated
4478 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4481 struct isl_to_poly_data *data = user;
4482 isl_pw_qpolynomial *t;
4483 isl_qpolynomial *qp, *up, *down;
4485 qp = isl_qpolynomial_copy(data->qp);
4486 qp = make_divs_pos(qp, signs);
4488 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4489 up = qp_drop_floors(up, 0);
4490 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4491 down = qp_drop_floors(down, 1);
4493 isl_qpolynomial_free(qp);
4494 qp = isl_qpolynomial_add(up, down);
4496 t = isl_pw_qpolynomial_alloc(orthant, qp);
4497 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4502 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4503 * the polynomial will be an overapproximation. If "sign" is negative,
4504 * it will be an underapproximation. If "sign" is zero, the approximation
4505 * will lie somewhere in between.
4507 * In particular, is sign == 0, we simply drop the floors, turning
4508 * the integer divisions into rational divisions.
4509 * Otherwise, we split the domains into orthants, make all integer divisions
4510 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4511 * depending on the requested sign and the sign of the term in which
4512 * the integer division appears.
4514 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4515 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4518 struct isl_to_poly_data data;
4521 return pwqp_drop_floors(pwqp);
4527 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4529 for (i = 0; i < pwqp->n; ++i) {
4530 if (pwqp->p[i].qp->div->n_row == 0) {
4531 isl_pw_qpolynomial *t;
4532 t = isl_pw_qpolynomial_alloc(
4533 isl_set_copy(pwqp->p[i].set),
4534 isl_qpolynomial_copy(pwqp->p[i].qp));
4535 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4538 data.qp = pwqp->p[i].qp;
4539 if (isl_set_foreach_orthant(pwqp->p[i].set,
4540 &to_polynomial_on_orthant, &data) < 0)
4544 isl_pw_qpolynomial_free(pwqp);
4548 isl_pw_qpolynomial_free(pwqp);
4549 isl_pw_qpolynomial_free(data.res);
4553 static int poly_entry(void **entry, void *user)
4556 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4558 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4560 return *pwqp ? 0 : -1;
4563 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4564 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4566 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4570 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4571 &poly_entry, &sign) < 0)
4576 isl_union_pw_qpolynomial_free(upwqp);
4580 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4581 __isl_take isl_qpolynomial *qp)
4585 isl_vec *aff = NULL;
4586 isl_basic_map *bmap = NULL;
4592 if (!isl_upoly_is_affine(qp->upoly))
4593 isl_die(qp->dim->ctx, isl_error_invalid,
4594 "input quasi-polynomial not affine", goto error);
4595 aff = isl_qpolynomial_extract_affine(qp);
4598 dim = isl_qpolynomial_get_dim(qp);
4599 dim = isl_dim_from_domain(dim);
4600 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4601 dim = isl_dim_add(dim, isl_dim_out, 1);
4602 n_div = qp->div->n_row;
4603 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4605 for (i = 0; i < n_div; ++i) {
4606 k = isl_basic_map_alloc_div(bmap);
4609 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4610 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4611 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4614 k = isl_basic_map_alloc_equality(bmap);
4617 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4618 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4619 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4622 isl_qpolynomial_free(qp);
4623 bmap = isl_basic_map_finalize(bmap);
4627 isl_qpolynomial_free(qp);
4628 isl_basic_map_free(bmap);