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_mul(__isl_take isl_qpolynomial *qp1,
1422 __isl_take isl_qpolynomial *qp2)
1424 qp1 = isl_qpolynomial_cow(qp1);
1429 if (qp1->div->n_row < qp2->div->n_row)
1430 return isl_qpolynomial_mul(qp2, qp1);
1432 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1433 if (!compatible_divs(qp1->div, qp2->div))
1434 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1436 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1440 isl_qpolynomial_free(qp2);
1444 isl_qpolynomial_free(qp1);
1445 isl_qpolynomial_free(qp2);
1449 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1452 qp = isl_qpolynomial_cow(qp);
1457 qp->upoly = isl_upoly_pow(qp->upoly, power);
1463 isl_qpolynomial_free(qp);
1467 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1471 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1474 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1478 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1481 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1485 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1488 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1492 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1495 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1499 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1502 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1505 struct isl_qpolynomial *qp;
1506 struct isl_upoly_cst *cst;
1511 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1515 cst = isl_upoly_as_cst(qp->upoly);
1516 isl_int_set(cst->n, v);
1521 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1522 isl_int *n, isl_int *d)
1524 struct isl_upoly_cst *cst;
1529 if (!isl_upoly_is_cst(qp->upoly))
1532 cst = isl_upoly_as_cst(qp->upoly);
1537 isl_int_set(*n, cst->n);
1539 isl_int_set(*d, cst->d);
1544 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1547 struct isl_upoly_rec *rec;
1555 rec = isl_upoly_as_rec(up);
1562 isl_assert(up->ctx, rec->n > 1, return -1);
1564 is_cst = isl_upoly_is_cst(rec->p[1]);
1570 return isl_upoly_is_affine(rec->p[0]);
1573 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1578 if (qp->div->n_row > 0)
1581 return isl_upoly_is_affine(qp->upoly);
1584 static void update_coeff(__isl_keep isl_vec *aff,
1585 __isl_keep struct isl_upoly_cst *cst, int pos)
1590 if (isl_int_is_zero(cst->n))
1595 isl_int_gcd(gcd, cst->d, aff->el[0]);
1596 isl_int_divexact(f, cst->d, gcd);
1597 isl_int_divexact(gcd, aff->el[0], gcd);
1598 isl_seq_scale(aff->el, aff->el, f, aff->size);
1599 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1604 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1605 __isl_keep isl_vec *aff)
1607 struct isl_upoly_cst *cst;
1608 struct isl_upoly_rec *rec;
1614 struct isl_upoly_cst *cst;
1616 cst = isl_upoly_as_cst(up);
1619 update_coeff(aff, cst, 0);
1623 rec = isl_upoly_as_rec(up);
1626 isl_assert(up->ctx, rec->n == 2, return -1);
1628 cst = isl_upoly_as_cst(rec->p[1]);
1631 update_coeff(aff, cst, 1 + up->var);
1633 return isl_upoly_update_affine(rec->p[0], aff);
1636 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1637 __isl_keep isl_qpolynomial *qp)
1645 d = isl_dim_total(qp->dim);
1646 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1650 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1651 isl_int_set_si(aff->el[0], 1);
1653 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1662 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1663 __isl_keep isl_qpolynomial *qp2)
1668 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1671 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1674 struct isl_upoly_rec *rec;
1676 if (isl_upoly_is_cst(up)) {
1677 struct isl_upoly_cst *cst;
1678 cst = isl_upoly_as_cst(up);
1681 isl_int_lcm(*d, *d, cst->d);
1685 rec = isl_upoly_as_rec(up);
1689 for (i = 0; i < rec->n; ++i)
1690 upoly_update_den(rec->p[i], d);
1693 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1695 isl_int_set_si(*d, 1);
1698 upoly_update_den(qp->upoly, d);
1701 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1704 struct isl_ctx *ctx;
1711 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1714 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1715 enum isl_dim_type type, unsigned pos)
1720 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1721 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1723 if (type == isl_dim_set)
1724 pos += isl_dim_size(dim, isl_dim_param);
1726 return isl_qpolynomial_var_pow(dim, pos, 1);
1732 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1733 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1736 struct isl_upoly_rec *rec;
1737 struct isl_upoly *base, *res;
1742 if (isl_upoly_is_cst(up))
1745 if (up->var < first)
1748 rec = isl_upoly_as_rec(up);
1752 isl_assert(up->ctx, rec->n >= 1, goto error);
1754 if (up->var >= first + n)
1755 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1757 base = isl_upoly_copy(subs[up->var - first]);
1759 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1760 for (i = rec->n - 2; i >= 0; --i) {
1761 struct isl_upoly *t;
1762 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1763 res = isl_upoly_mul(res, isl_upoly_copy(base));
1764 res = isl_upoly_sum(res, t);
1767 isl_upoly_free(base);
1776 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1777 isl_int denom, unsigned len)
1780 struct isl_upoly *up;
1782 isl_assert(ctx, len >= 1, return NULL);
1784 up = isl_upoly_rat_cst(ctx, f[0], denom);
1785 for (i = 0; i < len - 1; ++i) {
1786 struct isl_upoly *t;
1787 struct isl_upoly *c;
1789 if (isl_int_is_zero(f[1 + i]))
1792 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1793 t = isl_upoly_var_pow(ctx, i, 1);
1794 t = isl_upoly_mul(c, t);
1795 up = isl_upoly_sum(up, t);
1801 /* Remove common factor of non-constant terms and denominator.
1803 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1805 isl_ctx *ctx = qp->div->ctx;
1806 unsigned total = qp->div->n_col - 2;
1808 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1809 isl_int_gcd(ctx->normalize_gcd,
1810 ctx->normalize_gcd, qp->div->row[div][0]);
1811 if (isl_int_is_one(ctx->normalize_gcd))
1814 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1815 ctx->normalize_gcd, total);
1816 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1817 ctx->normalize_gcd);
1818 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1819 ctx->normalize_gcd);
1822 /* Replace the integer division identified by "div" by the polynomial "s".
1823 * The integer division is assumed not to appear in the definition
1824 * of any other integer divisions.
1826 static __isl_give isl_qpolynomial *substitute_div(
1827 __isl_take isl_qpolynomial *qp,
1828 int div, __isl_take struct isl_upoly *s)
1837 qp = isl_qpolynomial_cow(qp);
1841 total = isl_dim_total(qp->dim);
1842 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1846 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1849 for (i = 0; i < total + div; ++i)
1851 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1852 reordering[i] = i - 1;
1853 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1854 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1855 qp->upoly = reorder(qp->upoly, reordering);
1858 if (!qp->upoly || !qp->div)
1864 isl_qpolynomial_free(qp);
1869 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1870 * divisions because d is equal to 1 by their definition, i.e., e.
1872 static __isl_give isl_qpolynomial *substitute_non_divs(
1873 __isl_take isl_qpolynomial *qp)
1877 struct isl_upoly *s;
1882 total = isl_dim_total(qp->dim);
1883 for (i = 0; qp && i < qp->div->n_row; ++i) {
1884 if (!isl_int_is_one(qp->div->row[i][0]))
1886 for (j = i + 1; j < qp->div->n_row; ++j) {
1887 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1889 isl_seq_combine(qp->div->row[j] + 1,
1890 qp->div->ctx->one, qp->div->row[j] + 1,
1891 qp->div->row[j][2 + total + i],
1892 qp->div->row[i] + 1, 1 + total + i);
1893 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1894 normalize_div(qp, j);
1896 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1897 qp->div->row[i][0], qp->div->n_col - 1);
1898 qp = substitute_div(qp, i, s);
1905 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1906 * with d the denominator. When replacing the coefficient e of x by
1907 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1908 * inside the division, so we need to add floor(e/d) * x outside.
1909 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1910 * to adjust the coefficient of x in each later div that depends on the
1911 * current div "div" and also in the affine expression "aff"
1912 * (if it too depends on "div").
1914 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1915 __isl_keep isl_vec *aff)
1919 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1922 for (i = 0; i < 1 + total + div; ++i) {
1923 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1924 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1926 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1927 isl_int_fdiv_r(qp->div->row[div][1 + i],
1928 qp->div->row[div][1 + i], qp->div->row[div][0]);
1929 if (!isl_int_is_zero(aff->el[1 + total + div]))
1930 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1931 for (j = div + 1; j < qp->div->n_row; ++j) {
1932 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1934 isl_int_addmul(qp->div->row[j][1 + i],
1935 v, qp->div->row[j][2 + total + div]);
1941 /* Check if the last non-zero coefficient is bigger that half of the
1942 * denominator. If so, we will invert the div to further reduce the number
1943 * of distinct divs that may appear.
1944 * If the last non-zero coefficient is exactly half the denominator,
1945 * then we continue looking for earlier coefficients that are bigger
1946 * than half the denominator.
1948 static int needs_invert(__isl_keep isl_mat *div, int row)
1953 for (i = div->n_col - 1; i >= 1; --i) {
1954 if (isl_int_is_zero(div->row[row][i]))
1956 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1957 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1958 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1968 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1969 * We only invert the coefficients of e (and the coefficient of q in
1970 * later divs and in "aff"). After calling this function, the
1971 * coefficients of e should be reduced again.
1973 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1974 __isl_keep isl_vec *aff)
1976 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1978 isl_seq_neg(qp->div->row[div] + 1,
1979 qp->div->row[div] + 1, qp->div->n_col - 1);
1980 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
1981 isl_int_add(qp->div->row[div][1],
1982 qp->div->row[div][1], qp->div->row[div][0]);
1983 if (!isl_int_is_zero(aff->el[1 + total + div]))
1984 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
1985 isl_mat_col_mul(qp->div, 2 + total + div,
1986 qp->div->ctx->negone, 2 + total + div);
1989 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
1990 * in the interval [0, d-1], with d the denominator and such that the
1991 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
1993 * After the reduction, some divs may have become redundant or identical,
1994 * so we call substitute_non_divs and sort_divs. If these functions
1995 * eliminate divs or merge two or more divs into one, the coefficients
1996 * of the enclosing divs may have to be reduced again, so we call
1997 * ourselves recursively if the number of divs decreases.
1999 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2002 isl_vec *aff = NULL;
2003 struct isl_upoly *s;
2009 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2010 aff = isl_vec_clr(aff);
2014 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2016 for (i = 0; i < qp->div->n_row; ++i) {
2017 normalize_div(qp, i);
2018 reduce_div(qp, i, aff);
2019 if (needs_invert(qp->div, i)) {
2020 invert_div(qp, i, aff);
2021 reduce_div(qp, i, aff);
2025 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2026 qp->div->ctx->one, aff->size);
2027 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2034 n_div = qp->div->n_row;
2035 qp = substitute_non_divs(qp);
2037 if (qp && qp->div->n_row < n_div)
2038 return reduce_divs(qp);
2042 isl_qpolynomial_free(qp);
2047 /* Assumes each div only depends on earlier divs.
2049 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2052 struct isl_qpolynomial *qp = NULL;
2053 struct isl_upoly_rec *rec;
2054 struct isl_upoly_cst *cst;
2061 d = div->line - div->bmap->div;
2063 pos = isl_dim_total(div->bmap->dim) + d;
2064 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2065 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2066 div->bmap->n_div, &rec->up);
2070 for (i = 0; i < div->bmap->n_div; ++i)
2071 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2073 for (i = 0; i < 1 + power; ++i) {
2074 rec->p[i] = isl_upoly_zero(div->ctx);
2079 cst = isl_upoly_as_cst(rec->p[power]);
2080 isl_int_set_si(cst->n, 1);
2084 qp = reduce_divs(qp);
2088 isl_qpolynomial_free(qp);
2093 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2095 return isl_qpolynomial_div_pow(div, 1);
2098 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2099 const isl_int n, const isl_int d)
2101 struct isl_qpolynomial *qp;
2102 struct isl_upoly_cst *cst;
2104 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2108 cst = isl_upoly_as_cst(qp->upoly);
2109 isl_int_set(cst->n, n);
2110 isl_int_set(cst->d, d);
2115 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2117 struct isl_upoly_rec *rec;
2123 if (isl_upoly_is_cst(up))
2127 active[up->var] = 1;
2129 rec = isl_upoly_as_rec(up);
2130 for (i = 0; i < rec->n; ++i)
2131 if (up_set_active(rec->p[i], active, d) < 0)
2137 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2140 int d = isl_dim_total(qp->dim);
2145 for (i = 0; i < d; ++i)
2146 for (j = 0; j < qp->div->n_row; ++j) {
2147 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2153 return up_set_active(qp->upoly, active, d);
2156 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2157 enum isl_dim_type type, unsigned first, unsigned n)
2168 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2170 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2171 type == isl_dim_set, return -1);
2173 active = isl_calloc_array(qp->dim->ctx, int, isl_dim_total(qp->dim));
2174 if (set_active(qp, active) < 0)
2177 if (type == isl_dim_set)
2178 first += isl_dim_size(qp->dim, isl_dim_param);
2179 for (i = 0; i < n; ++i)
2180 if (active[first + i]) {
2193 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2194 * of the divs that do appear in the quasi-polynomial.
2196 static __isl_give isl_qpolynomial *remove_redundant_divs(
2197 __isl_take isl_qpolynomial *qp)
2204 int *reordering = NULL;
2211 if (qp->div->n_row == 0)
2214 d = isl_dim_total(qp->dim);
2215 len = qp->div->n_col - 2;
2216 ctx = isl_qpolynomial_get_ctx(qp);
2217 active = isl_calloc_array(ctx, int, len);
2221 if (up_set_active(qp->upoly, active, len) < 0)
2224 for (i = qp->div->n_row - 1; i >= 0; --i) {
2225 if (!active[d + i]) {
2229 for (j = 0; j < i; ++j) {
2230 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2242 reordering = isl_alloc_array(qp->div->ctx, int, len);
2246 for (i = 0; i < d; ++i)
2250 n_div = qp->div->n_row;
2251 for (i = 0; i < n_div; ++i) {
2252 if (!active[d + i]) {
2253 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2254 qp->div = isl_mat_drop_cols(qp->div,
2255 2 + d + i - skip, 1);
2258 reordering[d + i] = d + i - skip;
2261 qp->upoly = reorder(qp->upoly, reordering);
2263 if (!qp->upoly || !qp->div)
2273 isl_qpolynomial_free(qp);
2277 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2278 unsigned first, unsigned n)
2281 struct isl_upoly_rec *rec;
2285 if (n == 0 || up->var < 0 || up->var < first)
2287 if (up->var < first + n) {
2288 up = replace_by_constant_term(up);
2289 return isl_upoly_drop(up, first, n);
2291 up = isl_upoly_cow(up);
2295 rec = isl_upoly_as_rec(up);
2299 for (i = 0; i < rec->n; ++i) {
2300 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2311 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2312 __isl_take isl_qpolynomial *qp,
2313 enum isl_dim_type type, unsigned pos, const char *s)
2315 qp = isl_qpolynomial_cow(qp);
2318 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2323 isl_qpolynomial_free(qp);
2327 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2328 __isl_take isl_qpolynomial *qp,
2329 enum isl_dim_type type, unsigned first, unsigned n)
2333 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
2336 qp = isl_qpolynomial_cow(qp);
2340 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2342 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2343 type == isl_dim_set, goto error);
2345 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2349 if (type == isl_dim_set)
2350 first += isl_dim_size(qp->dim, isl_dim_param);
2352 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2356 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2362 isl_qpolynomial_free(qp);
2366 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2367 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2373 struct isl_upoly *up;
2377 if (eq->n_eq == 0) {
2378 isl_basic_set_free(eq);
2382 qp = isl_qpolynomial_cow(qp);
2385 qp->div = isl_mat_cow(qp->div);
2389 total = 1 + isl_dim_total(eq->dim);
2391 isl_int_init(denom);
2392 for (i = 0; i < eq->n_eq; ++i) {
2393 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2394 if (j < 0 || j == 0 || j >= total)
2397 for (k = 0; k < qp->div->n_row; ++k) {
2398 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2400 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2401 &qp->div->row[k][0]);
2402 normalize_div(qp, k);
2405 if (isl_int_is_pos(eq->eq[i][j]))
2406 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2407 isl_int_abs(denom, eq->eq[i][j]);
2408 isl_int_set_si(eq->eq[i][j], 0);
2410 up = isl_upoly_from_affine(qp->dim->ctx,
2411 eq->eq[i], denom, total);
2412 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2415 isl_int_clear(denom);
2420 isl_basic_set_free(eq);
2422 qp = substitute_non_divs(qp);
2427 isl_basic_set_free(eq);
2428 isl_qpolynomial_free(qp);
2432 static __isl_give isl_basic_set *add_div_constraints(
2433 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2441 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2444 total = isl_basic_set_total_dim(bset);
2445 for (i = 0; i < div->n_row; ++i)
2446 if (isl_basic_set_add_div_constraints_var(bset,
2447 total - div->n_row + i, div->row[i]) < 0)
2454 isl_basic_set_free(bset);
2458 /* Look for equalities among the variables shared by context and qp
2459 * and the integer divisions of qp, if any.
2460 * The equalities are then used to eliminate variables and/or integer
2461 * divisions from qp.
2463 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2464 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2470 if (qp->div->n_row > 0) {
2471 isl_basic_set *bset;
2472 context = isl_set_add_dims(context, isl_dim_set,
2474 bset = isl_basic_set_universe(isl_set_get_dim(context));
2475 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2476 context = isl_set_intersect(context,
2477 isl_set_from_basic_set(bset));
2480 aff = isl_set_affine_hull(context);
2481 return isl_qpolynomial_substitute_equalities(qp, aff);
2483 isl_qpolynomial_free(qp);
2484 isl_set_free(context);
2489 #define PW isl_pw_qpolynomial
2491 #define EL isl_qpolynomial
2493 #define IS_ZERO is_zero
2497 #include <isl_pw_templ.c>
2500 #define UNION isl_union_pw_qpolynomial
2502 #define PART isl_pw_qpolynomial
2504 #define PARTS pw_qpolynomial
2506 #include <isl_union_templ.c>
2508 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2516 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2519 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2522 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2523 __isl_take isl_pw_qpolynomial *pwqp1,
2524 __isl_take isl_pw_qpolynomial *pwqp2)
2527 struct isl_pw_qpolynomial *res;
2529 if (!pwqp1 || !pwqp2)
2532 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2535 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2536 isl_pw_qpolynomial_free(pwqp2);
2540 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2541 isl_pw_qpolynomial_free(pwqp1);
2545 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2546 isl_pw_qpolynomial_free(pwqp1);
2550 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2551 isl_pw_qpolynomial_free(pwqp2);
2555 n = pwqp1->n * pwqp2->n;
2556 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2558 for (i = 0; i < pwqp1->n; ++i) {
2559 for (j = 0; j < pwqp2->n; ++j) {
2560 struct isl_set *common;
2561 struct isl_qpolynomial *prod;
2562 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2563 isl_set_copy(pwqp2->p[j].set));
2564 if (isl_set_plain_is_empty(common)) {
2565 isl_set_free(common);
2569 prod = isl_qpolynomial_mul(
2570 isl_qpolynomial_copy(pwqp1->p[i].qp),
2571 isl_qpolynomial_copy(pwqp2->p[j].qp));
2573 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2577 isl_pw_qpolynomial_free(pwqp1);
2578 isl_pw_qpolynomial_free(pwqp2);
2582 isl_pw_qpolynomial_free(pwqp1);
2583 isl_pw_qpolynomial_free(pwqp2);
2587 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2588 __isl_take isl_pw_qpolynomial *pwqp)
2595 if (isl_pw_qpolynomial_is_zero(pwqp))
2598 pwqp = isl_pw_qpolynomial_cow(pwqp);
2602 for (i = 0; i < pwqp->n; ++i) {
2603 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2610 isl_pw_qpolynomial_free(pwqp);
2614 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2615 __isl_take isl_pw_qpolynomial *pwqp1,
2616 __isl_take isl_pw_qpolynomial *pwqp2)
2618 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2621 __isl_give struct isl_upoly *isl_upoly_eval(
2622 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2625 struct isl_upoly_rec *rec;
2626 struct isl_upoly *res;
2627 struct isl_upoly *base;
2629 if (isl_upoly_is_cst(up)) {
2634 rec = isl_upoly_as_rec(up);
2638 isl_assert(up->ctx, rec->n >= 1, goto error);
2640 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2642 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2645 for (i = rec->n - 2; i >= 0; --i) {
2646 res = isl_upoly_mul(res, isl_upoly_copy(base));
2647 res = isl_upoly_sum(res,
2648 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2649 isl_vec_copy(vec)));
2652 isl_upoly_free(base);
2662 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2663 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2666 struct isl_upoly *up;
2671 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2673 if (qp->div->n_row == 0)
2674 ext = isl_vec_copy(pnt->vec);
2677 unsigned dim = isl_dim_total(qp->dim);
2678 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2682 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2683 for (i = 0; i < qp->div->n_row; ++i) {
2684 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2685 1 + dim + i, &ext->el[1+dim+i]);
2686 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2687 qp->div->row[i][0]);
2691 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2695 dim = isl_dim_copy(qp->dim);
2696 isl_qpolynomial_free(qp);
2697 isl_point_free(pnt);
2699 return isl_qpolynomial_alloc(dim, 0, up);
2701 isl_qpolynomial_free(qp);
2702 isl_point_free(pnt);
2706 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2707 __isl_keep struct isl_upoly_cst *cst2)
2712 isl_int_mul(t, cst1->n, cst2->d);
2713 isl_int_submul(t, cst2->n, cst1->d);
2714 cmp = isl_int_sgn(t);
2719 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2720 __isl_keep isl_qpolynomial *qp2)
2722 struct isl_upoly_cst *cst1, *cst2;
2726 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2727 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2728 if (isl_qpolynomial_is_nan(qp1))
2730 if (isl_qpolynomial_is_nan(qp2))
2732 cst1 = isl_upoly_as_cst(qp1->upoly);
2733 cst2 = isl_upoly_as_cst(qp2->upoly);
2735 return isl_upoly_cmp(cst1, cst2) <= 0;
2738 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2739 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2741 struct isl_upoly_cst *cst1, *cst2;
2746 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2747 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2748 cst1 = isl_upoly_as_cst(qp1->upoly);
2749 cst2 = isl_upoly_as_cst(qp2->upoly);
2750 cmp = isl_upoly_cmp(cst1, cst2);
2753 isl_qpolynomial_free(qp2);
2755 isl_qpolynomial_free(qp1);
2760 isl_qpolynomial_free(qp1);
2761 isl_qpolynomial_free(qp2);
2765 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2766 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2768 struct isl_upoly_cst *cst1, *cst2;
2773 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2774 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2775 cst1 = isl_upoly_as_cst(qp1->upoly);
2776 cst2 = isl_upoly_as_cst(qp2->upoly);
2777 cmp = isl_upoly_cmp(cst1, cst2);
2780 isl_qpolynomial_free(qp2);
2782 isl_qpolynomial_free(qp1);
2787 isl_qpolynomial_free(qp1);
2788 isl_qpolynomial_free(qp2);
2792 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2793 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2794 unsigned first, unsigned n)
2803 qp = isl_qpolynomial_cow(qp);
2807 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2810 g_pos = pos(qp->dim, type) + first;
2812 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2816 total = qp->div->n_col - 2;
2817 if (total > g_pos) {
2819 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2822 for (i = 0; i < total - g_pos; ++i)
2824 qp->upoly = expand(qp->upoly, exp, g_pos);
2830 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2836 isl_qpolynomial_free(qp);
2840 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2841 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2845 pos = isl_qpolynomial_dim(qp, type);
2847 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2850 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2851 __isl_take isl_pw_qpolynomial *pwqp,
2852 enum isl_dim_type type, unsigned n)
2856 pos = isl_pw_qpolynomial_dim(pwqp, type);
2858 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2861 static int *reordering_move(isl_ctx *ctx,
2862 unsigned len, unsigned dst, unsigned src, unsigned n)
2867 reordering = isl_alloc_array(ctx, int, len);
2872 for (i = 0; i < dst; ++i)
2874 for (i = 0; i < n; ++i)
2875 reordering[src + i] = dst + i;
2876 for (i = 0; i < src - dst; ++i)
2877 reordering[dst + i] = dst + n + i;
2878 for (i = 0; i < len - src - n; ++i)
2879 reordering[src + n + i] = src + n + i;
2881 for (i = 0; i < src; ++i)
2883 for (i = 0; i < n; ++i)
2884 reordering[src + i] = dst + i;
2885 for (i = 0; i < dst - src; ++i)
2886 reordering[src + n + i] = src + i;
2887 for (i = 0; i < len - dst - n; ++i)
2888 reordering[dst + n + i] = dst + n + i;
2894 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2895 __isl_take isl_qpolynomial *qp,
2896 enum isl_dim_type dst_type, unsigned dst_pos,
2897 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2903 qp = isl_qpolynomial_cow(qp);
2907 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2910 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2911 g_src_pos = pos(qp->dim, src_type) + src_pos;
2912 if (dst_type > src_type)
2915 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2922 reordering = reordering_move(qp->dim->ctx,
2923 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2927 qp->upoly = reorder(qp->upoly, reordering);
2932 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2938 isl_qpolynomial_free(qp);
2942 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2943 isl_int *f, isl_int denom)
2945 struct isl_upoly *up;
2950 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2952 return isl_qpolynomial_alloc(dim, 0, up);
2955 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
2958 struct isl_upoly *up;
2959 isl_qpolynomial *qp;
2964 ctx = isl_aff_get_ctx(aff);
2965 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
2968 qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff),
2969 aff->ls->div->n_row, up);
2973 isl_mat_free(qp->div);
2974 qp->div = isl_mat_copy(aff->ls->div);
2975 qp->div = isl_mat_cow(qp->div);
2980 qp = reduce_divs(qp);
2981 qp = remove_redundant_divs(qp);
2988 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2989 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2993 struct isl_upoly *up;
2994 isl_qpolynomial *qp;
3000 isl_int_init(denom);
3002 isl_constraint_get_coefficient(c, type, pos, &denom);
3003 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
3004 sgn = isl_int_sgn(denom);
3005 isl_int_abs(denom, denom);
3006 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
3007 1 + isl_constraint_dim(c, isl_dim_all));
3009 isl_int_neg(denom, denom);
3010 isl_constraint_set_coefficient(c, type, pos, denom);
3012 dim = isl_dim_copy(c->bmap->dim);
3014 isl_int_clear(denom);
3015 isl_constraint_free(c);
3017 qp = isl_qpolynomial_alloc(dim, 0, up);
3019 qp = isl_qpolynomial_neg(qp);
3023 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3024 * in "qp" by subs[i].
3026 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3027 __isl_take isl_qpolynomial *qp,
3028 enum isl_dim_type type, unsigned first, unsigned n,
3029 __isl_keep isl_qpolynomial **subs)
3032 struct isl_upoly **ups;
3037 qp = isl_qpolynomial_cow(qp);
3040 for (i = 0; i < n; ++i)
3044 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
3047 for (i = 0; i < n; ++i)
3048 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3051 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3052 for (i = 0; i < n; ++i)
3053 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3055 first += pos(qp->dim, type);
3057 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3060 for (i = 0; i < n; ++i)
3061 ups[i] = subs[i]->upoly;
3063 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3072 isl_qpolynomial_free(qp);
3076 /* Extend "bset" with extra set dimensions for each integer division
3077 * in "qp" and then call "fn" with the extended bset and the polynomial
3078 * that results from replacing each of the integer divisions by the
3079 * corresponding extra set dimension.
3081 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3082 __isl_keep isl_basic_set *bset,
3083 int (*fn)(__isl_take isl_basic_set *bset,
3084 __isl_take isl_qpolynomial *poly, void *user), void *user)
3088 isl_qpolynomial *poly;
3092 if (qp->div->n_row == 0)
3093 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3096 div = isl_mat_copy(qp->div);
3097 dim = isl_dim_copy(qp->dim);
3098 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3099 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3100 bset = isl_basic_set_copy(bset);
3101 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3102 bset = add_div_constraints(bset, div);
3104 return fn(bset, poly, user);
3109 /* Return total degree in variables first (inclusive) up to last (exclusive).
3111 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3115 struct isl_upoly_rec *rec;
3119 if (isl_upoly_is_zero(up))
3121 if (isl_upoly_is_cst(up) || up->var < first)
3124 rec = isl_upoly_as_rec(up);
3128 for (i = 0; i < rec->n; ++i) {
3131 if (isl_upoly_is_zero(rec->p[i]))
3133 d = isl_upoly_degree(rec->p[i], first, last);
3143 /* Return total degree in set variables.
3145 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3153 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3154 nvar = isl_dim_size(poly->dim, isl_dim_set);
3155 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3158 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3159 unsigned pos, int deg)
3162 struct isl_upoly_rec *rec;
3167 if (isl_upoly_is_cst(up) || up->var < pos) {
3169 return isl_upoly_copy(up);
3171 return isl_upoly_zero(up->ctx);
3174 rec = isl_upoly_as_rec(up);
3178 if (up->var == pos) {
3180 return isl_upoly_copy(rec->p[deg]);
3182 return isl_upoly_zero(up->ctx);
3185 up = isl_upoly_copy(up);
3186 up = isl_upoly_cow(up);
3187 rec = isl_upoly_as_rec(up);
3191 for (i = 0; i < rec->n; ++i) {
3192 struct isl_upoly *t;
3193 t = isl_upoly_coeff(rec->p[i], pos, deg);
3196 isl_upoly_free(rec->p[i]);
3206 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3208 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3209 __isl_keep isl_qpolynomial *qp,
3210 enum isl_dim_type type, unsigned t_pos, int deg)
3213 struct isl_upoly *up;
3219 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3222 g_pos = pos(qp->dim, type) + t_pos;
3223 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3225 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3228 isl_mat_free(c->div);
3229 c->div = isl_mat_copy(qp->div);
3234 isl_qpolynomial_free(c);
3238 /* Homogenize the polynomial in the variables first (inclusive) up to
3239 * last (exclusive) by inserting powers of variable first.
3240 * Variable first is assumed not to appear in the input.
3242 __isl_give struct isl_upoly *isl_upoly_homogenize(
3243 __isl_take struct isl_upoly *up, int deg, int target,
3244 int first, int last)
3247 struct isl_upoly_rec *rec;
3251 if (isl_upoly_is_zero(up))
3255 if (isl_upoly_is_cst(up) || up->var < first) {
3256 struct isl_upoly *hom;
3258 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3261 rec = isl_upoly_as_rec(hom);
3262 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3267 up = isl_upoly_cow(up);
3268 rec = isl_upoly_as_rec(up);
3272 for (i = 0; i < rec->n; ++i) {
3273 if (isl_upoly_is_zero(rec->p[i]))
3275 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3276 up->var < last ? deg + i : i, target,
3288 /* Homogenize the polynomial in the set variables by introducing
3289 * powers of an extra set variable at position 0.
3291 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3292 __isl_take isl_qpolynomial *poly)
3296 int deg = isl_qpolynomial_degree(poly);
3301 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3302 poly = isl_qpolynomial_cow(poly);
3306 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3307 nvar = isl_dim_size(poly->dim, isl_dim_set);
3308 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3315 isl_qpolynomial_free(poly);
3319 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3320 __isl_take isl_mat *div)
3328 n = isl_dim_total(dim) + div->n_row;
3330 term = isl_calloc(dim->ctx, struct isl_term,
3331 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3338 isl_int_init(term->n);
3339 isl_int_init(term->d);
3348 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3357 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3366 total = isl_dim_total(term->dim) + term->div->n_row;
3368 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3372 isl_int_set(dup->n, term->n);
3373 isl_int_set(dup->d, term->d);
3375 for (i = 0; i < total; ++i)
3376 dup->pow[i] = term->pow[i];
3381 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3389 return isl_term_dup(term);
3392 void isl_term_free(__isl_take isl_term *term)
3397 if (--term->ref > 0)
3400 isl_dim_free(term->dim);
3401 isl_mat_free(term->div);
3402 isl_int_clear(term->n);
3403 isl_int_clear(term->d);
3407 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3415 case isl_dim_out: return isl_dim_size(term->dim, type);
3416 case isl_dim_div: return term->div->n_row;
3417 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3422 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3424 return term ? term->dim->ctx : NULL;
3427 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3431 isl_int_set(*n, term->n);
3434 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3438 isl_int_set(*d, term->d);
3441 int isl_term_get_exp(__isl_keep isl_term *term,
3442 enum isl_dim_type type, unsigned pos)
3447 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3449 if (type >= isl_dim_set)
3450 pos += isl_dim_size(term->dim, isl_dim_param);
3451 if (type >= isl_dim_div)
3452 pos += isl_dim_size(term->dim, isl_dim_set);
3454 return term->pow[pos];
3457 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3459 isl_basic_map *bmap;
3466 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3469 total = term->div->n_col - term->div->n_row - 2;
3470 /* No nested divs for now */
3471 isl_assert(term->dim->ctx,
3472 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3473 term->div->n_row) == -1,
3476 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3477 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3480 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3482 return isl_basic_map_div(bmap, k);
3484 isl_basic_map_free(bmap);
3488 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3489 int (*fn)(__isl_take isl_term *term, void *user),
3490 __isl_take isl_term *term, void *user)
3493 struct isl_upoly_rec *rec;
3498 if (isl_upoly_is_zero(up))
3501 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3502 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3503 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3505 if (isl_upoly_is_cst(up)) {
3506 struct isl_upoly_cst *cst;
3507 cst = isl_upoly_as_cst(up);
3510 term = isl_term_cow(term);
3513 isl_int_set(term->n, cst->n);
3514 isl_int_set(term->d, cst->d);
3515 if (fn(isl_term_copy(term), user) < 0)
3520 rec = isl_upoly_as_rec(up);
3524 for (i = 0; i < rec->n; ++i) {
3525 term = isl_term_cow(term);
3528 term->pow[up->var] = i;
3529 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3533 term->pow[up->var] = 0;
3537 isl_term_free(term);
3541 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3542 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3549 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3553 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3555 isl_term_free(term);
3557 return term ? 0 : -1;
3560 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3562 struct isl_upoly *up;
3563 isl_qpolynomial *qp;
3569 n = isl_dim_total(term->dim) + term->div->n_row;
3571 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3572 for (i = 0; i < n; ++i) {
3575 up = isl_upoly_mul(up,
3576 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3579 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3582 isl_mat_free(qp->div);
3583 qp->div = isl_mat_copy(term->div);
3587 isl_term_free(term);
3590 isl_qpolynomial_free(qp);
3591 isl_term_free(term);
3595 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3596 __isl_take isl_dim *dim)
3605 if (isl_dim_equal(qp->dim, dim)) {
3610 qp = isl_qpolynomial_cow(qp);
3614 extra = isl_dim_size(dim, isl_dim_set) -
3615 isl_dim_size(qp->dim, isl_dim_set);
3616 total = isl_dim_total(qp->dim);
3617 if (qp->div->n_row) {
3620 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3623 for (i = 0; i < qp->div->n_row; ++i)
3625 qp->upoly = expand(qp->upoly, exp, total);
3630 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3633 for (i = 0; i < qp->div->n_row; ++i)
3634 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3636 isl_dim_free(qp->dim);
3642 isl_qpolynomial_free(qp);
3646 /* For each parameter or variable that does not appear in qp,
3647 * first eliminate the variable from all constraints and then set it to zero.
3649 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3650 __isl_keep isl_qpolynomial *qp)
3661 d = isl_dim_total(set->dim);
3662 active = isl_calloc_array(set->ctx, int, d);
3663 if (set_active(qp, active) < 0)
3666 for (i = 0; i < d; ++i)
3675 nparam = isl_dim_size(set->dim, isl_dim_param);
3676 nvar = isl_dim_size(set->dim, isl_dim_set);
3677 for (i = 0; i < nparam; ++i) {
3680 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3681 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3683 for (i = 0; i < nvar; ++i) {
3684 if (active[nparam + i])
3686 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3687 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3699 struct isl_opt_data {
3700 isl_qpolynomial *qp;
3702 isl_qpolynomial *opt;
3706 static int opt_fn(__isl_take isl_point *pnt, void *user)
3708 struct isl_opt_data *data = (struct isl_opt_data *)user;
3709 isl_qpolynomial *val;
3711 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3715 } else if (data->max) {
3716 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3718 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3724 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3725 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3727 struct isl_opt_data data = { NULL, 1, NULL, max };
3732 if (isl_upoly_is_cst(qp->upoly)) {
3737 set = fix_inactive(set, qp);
3740 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3744 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3747 isl_qpolynomial_free(qp);
3751 isl_qpolynomial_free(qp);
3752 isl_qpolynomial_free(data.opt);
3756 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3757 __isl_take isl_morph *morph)
3762 struct isl_upoly **subs;
3765 qp = isl_qpolynomial_cow(qp);
3770 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3772 n_sub = morph->inv->n_row - 1;
3773 if (morph->inv->n_row != morph->inv->n_col)
3774 n_sub += qp->div->n_row;
3775 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3779 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3780 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3781 morph->inv->row[0][0], morph->inv->n_col);
3782 if (morph->inv->n_row != morph->inv->n_col)
3783 for (i = 0; i < qp->div->n_row; ++i)
3784 subs[morph->inv->n_row - 1 + i] =
3785 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3787 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3789 for (i = 0; i < n_sub; ++i)
3790 isl_upoly_free(subs[i]);
3793 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3794 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3795 qp->div = isl_mat_product(qp->div, mat);
3796 isl_dim_free(qp->dim);
3797 qp->dim = isl_dim_copy(morph->ran->dim);
3799 if (!qp->upoly || !qp->div || !qp->dim)
3802 isl_morph_free(morph);
3806 isl_qpolynomial_free(qp);
3807 isl_morph_free(morph);
3811 static int neg_entry(void **entry, void *user)
3813 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3815 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3817 return *pwqp ? 0 : -1;
3820 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3821 __isl_take isl_union_pw_qpolynomial *upwqp)
3823 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3827 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3828 &neg_entry, NULL) < 0)
3833 isl_union_pw_qpolynomial_free(upwqp);
3837 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3838 __isl_take isl_union_pw_qpolynomial *upwqp1,
3839 __isl_take isl_union_pw_qpolynomial *upwqp2)
3841 return isl_union_pw_qpolynomial_add(upwqp1,
3842 isl_union_pw_qpolynomial_neg(upwqp2));
3845 static int mul_entry(void **entry, void *user)
3847 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3849 struct isl_hash_table_entry *entry2;
3850 isl_pw_qpolynomial *pwpq = *entry;
3853 hash = isl_dim_get_hash(pwpq->dim);
3854 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3855 hash, &has_dim, pwpq->dim, 0);
3859 pwpq = isl_pw_qpolynomial_copy(pwpq);
3860 pwpq = isl_pw_qpolynomial_mul(pwpq,
3861 isl_pw_qpolynomial_copy(entry2->data));
3863 empty = isl_pw_qpolynomial_is_zero(pwpq);
3865 isl_pw_qpolynomial_free(pwpq);
3869 isl_pw_qpolynomial_free(pwpq);
3873 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3878 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3879 __isl_take isl_union_pw_qpolynomial *upwqp1,
3880 __isl_take isl_union_pw_qpolynomial *upwqp2)
3882 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3885 /* Reorder the columns of the given div definitions according to the
3888 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3889 __isl_take isl_reordering *r)
3898 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3899 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3903 for (i = 0; i < div->n_row; ++i) {
3904 isl_seq_cpy(mat->row[i], div->row[i], 2);
3905 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3906 for (j = 0; j < r->len; ++j)
3907 isl_int_set(mat->row[i][2 + r->pos[j]],
3908 div->row[i][2 + j]);
3911 isl_reordering_free(r);
3915 isl_reordering_free(r);
3920 /* Reorder the dimension of "qp" according to the given reordering.
3922 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3923 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3925 qp = isl_qpolynomial_cow(qp);
3929 r = isl_reordering_extend(r, qp->div->n_row);
3933 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3937 qp->upoly = reorder(qp->upoly, r->pos);
3941 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3943 isl_reordering_free(r);
3946 isl_qpolynomial_free(qp);
3947 isl_reordering_free(r);
3951 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3952 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3957 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3958 isl_reordering *exp;
3960 model = isl_dim_drop(model, isl_dim_in,
3961 0, isl_dim_size(model, isl_dim_in));
3962 model = isl_dim_drop(model, isl_dim_out,
3963 0, isl_dim_size(model, isl_dim_out));
3964 exp = isl_parameter_alignment_reordering(qp->dim, model);
3965 exp = isl_reordering_extend_dim(exp,
3966 isl_qpolynomial_get_dim(qp));
3967 qp = isl_qpolynomial_realign(qp, exp);
3970 isl_dim_free(model);
3973 isl_dim_free(model);
3974 isl_qpolynomial_free(qp);
3978 struct isl_split_periods_data {
3980 isl_pw_qpolynomial *res;
3983 /* Create a slice where the integer division "div" has the fixed value "v".
3984 * In particular, if "div" refers to floor(f/m), then create a slice
3986 * m v <= f <= m v + (m - 1)
3991 * -f + m v + (m - 1) >= 0
3993 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3994 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3997 isl_basic_set *bset = NULL;
4003 total = isl_dim_total(dim);
4004 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
4006 k = isl_basic_set_alloc_inequality(bset);
4009 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4010 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4012 k = isl_basic_set_alloc_inequality(bset);
4015 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4016 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4017 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4018 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4021 return isl_set_from_basic_set(bset);
4023 isl_basic_set_free(bset);
4028 static int split_periods(__isl_take isl_set *set,
4029 __isl_take isl_qpolynomial *qp, void *user);
4031 /* Create a slice of the domain "set" such that integer division "div"
4032 * has the fixed value "v" and add the results to data->res,
4033 * replacing the integer division by "v" in "qp".
4035 static int set_div(__isl_take isl_set *set,
4036 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4037 struct isl_split_periods_data *data)
4042 struct isl_upoly *cst;
4044 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
4045 set = isl_set_intersect(set, slice);
4050 total = isl_dim_total(qp->dim);
4052 for (i = div + 1; i < qp->div->n_row; ++i) {
4053 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4055 isl_int_addmul(qp->div->row[i][1],
4056 qp->div->row[i][2 + total + div], v);
4057 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4060 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4061 qp = substitute_div(qp, div, cst);
4063 return split_periods(set, qp, data);
4066 isl_qpolynomial_free(qp);
4070 /* Split the domain "set" such that integer division "div"
4071 * has a fixed value (ranging from "min" to "max") on each slice
4072 * and add the results to data->res.
4074 static int split_div(__isl_take isl_set *set,
4075 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4076 struct isl_split_periods_data *data)
4078 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4079 isl_set *set_i = isl_set_copy(set);
4080 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4082 if (set_div(set_i, qp_i, div, min, data) < 0)
4086 isl_qpolynomial_free(qp);
4090 isl_qpolynomial_free(qp);
4094 /* If "qp" refers to any integer division
4095 * that can only attain "max_periods" distinct values on "set"
4096 * then split the domain along those distinct values.
4097 * Add the results (or the original if no splitting occurs)
4100 static int split_periods(__isl_take isl_set *set,
4101 __isl_take isl_qpolynomial *qp, void *user)
4104 isl_pw_qpolynomial *pwqp;
4105 struct isl_split_periods_data *data;
4110 data = (struct isl_split_periods_data *)user;
4115 if (qp->div->n_row == 0) {
4116 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4117 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4123 total = isl_dim_total(qp->dim);
4124 for (i = 0; i < qp->div->n_row; ++i) {
4125 enum isl_lp_result lp_res;
4127 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4128 qp->div->n_row) != -1)
4131 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4132 set->ctx->one, &min, NULL, NULL);
4133 if (lp_res == isl_lp_error)
4135 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4137 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4139 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4140 set->ctx->one, &max, NULL, NULL);
4141 if (lp_res == isl_lp_error)
4143 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4145 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4147 isl_int_sub(max, max, min);
4148 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4149 isl_int_add(max, max, min);
4154 if (i < qp->div->n_row) {
4155 r = split_div(set, qp, i, min, max, data);
4157 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4158 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4170 isl_qpolynomial_free(qp);
4174 /* If any quasi-polynomial in pwqp refers to any integer division
4175 * that can only attain "max_periods" distinct values on its domain
4176 * then split the domain along those distinct values.
4178 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4179 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4181 struct isl_split_periods_data data;
4183 data.max_periods = max_periods;
4184 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4186 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4189 isl_pw_qpolynomial_free(pwqp);
4193 isl_pw_qpolynomial_free(data.res);
4194 isl_pw_qpolynomial_free(pwqp);
4198 /* Construct a piecewise quasipolynomial that is constant on the given
4199 * domain. In particular, it is
4202 * infinity if cst == -1
4204 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4205 __isl_take isl_basic_set *bset, int cst)
4208 isl_qpolynomial *qp;
4213 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4214 dim = isl_basic_set_get_dim(bset);
4216 qp = isl_qpolynomial_infty(dim);
4218 qp = isl_qpolynomial_zero(dim);
4220 qp = isl_qpolynomial_one(dim);
4221 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4224 /* Factor bset, call fn on each of the factors and return the product.
4226 * If no factors can be found, simply call fn on the input.
4227 * Otherwise, construct the factors based on the factorizer,
4228 * call fn on each factor and compute the product.
4230 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4231 __isl_take isl_basic_set *bset,
4232 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4238 isl_qpolynomial *qp;
4239 isl_pw_qpolynomial *pwqp;
4243 f = isl_basic_set_factorizer(bset);
4246 if (f->n_group == 0) {
4247 isl_factorizer_free(f);
4251 nparam = isl_basic_set_dim(bset, isl_dim_param);
4252 nvar = isl_basic_set_dim(bset, isl_dim_set);
4254 dim = isl_basic_set_get_dim(bset);
4255 dim = isl_dim_domain(dim);
4256 set = isl_set_universe(isl_dim_copy(dim));
4257 qp = isl_qpolynomial_one(dim);
4258 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4260 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4262 for (i = 0, n = 0; i < f->n_group; ++i) {
4263 isl_basic_set *bset_i;
4264 isl_pw_qpolynomial *pwqp_i;
4266 bset_i = isl_basic_set_copy(bset);
4267 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4268 nparam + n + f->len[i], nvar - n - f->len[i]);
4269 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4271 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4272 n + f->len[i], nvar - n - f->len[i]);
4273 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4275 pwqp_i = fn(bset_i);
4276 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4281 isl_basic_set_free(bset);
4282 isl_factorizer_free(f);
4286 isl_basic_set_free(bset);
4290 /* Factor bset, call fn on each of the factors and return the product.
4291 * The function is assumed to evaluate to zero on empty domains,
4292 * to one on zero-dimensional domains and to infinity on unbounded domains
4293 * and will not be called explicitly on zero-dimensional or unbounded domains.
4295 * We first check for some special cases and remove all equalities.
4296 * Then we hand over control to compressed_multiplicative_call.
4298 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4299 __isl_take isl_basic_set *bset,
4300 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4304 isl_pw_qpolynomial *pwqp;
4305 unsigned orig_nvar, final_nvar;
4310 if (isl_basic_set_plain_is_empty(bset))
4311 return constant_on_domain(bset, 0);
4313 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4316 return constant_on_domain(bset, 1);
4318 bounded = isl_basic_set_is_bounded(bset);
4322 return constant_on_domain(bset, -1);
4324 if (bset->n_eq == 0)
4325 return compressed_multiplicative_call(bset, fn);
4327 morph = isl_basic_set_full_compression(bset);
4328 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4330 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4332 pwqp = compressed_multiplicative_call(bset, fn);
4334 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4335 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4336 morph = isl_morph_inverse(morph);
4338 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4342 isl_basic_set_free(bset);
4346 /* Drop all floors in "qp", turning each integer division [a/m] into
4347 * a rational division a/m. If "down" is set, then the integer division
4348 * is replaces by (a-(m-1))/m instead.
4350 static __isl_give isl_qpolynomial *qp_drop_floors(
4351 __isl_take isl_qpolynomial *qp, int down)
4354 struct isl_upoly *s;
4358 if (qp->div->n_row == 0)
4361 qp = isl_qpolynomial_cow(qp);
4365 for (i = qp->div->n_row - 1; i >= 0; --i) {
4367 isl_int_sub(qp->div->row[i][1],
4368 qp->div->row[i][1], qp->div->row[i][0]);
4369 isl_int_add_ui(qp->div->row[i][1],
4370 qp->div->row[i][1], 1);
4372 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4373 qp->div->row[i][0], qp->div->n_col - 1);
4374 qp = substitute_div(qp, i, s);
4382 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4383 * a rational division a/m.
4385 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4386 __isl_take isl_pw_qpolynomial *pwqp)
4393 if (isl_pw_qpolynomial_is_zero(pwqp))
4396 pwqp = isl_pw_qpolynomial_cow(pwqp);
4400 for (i = 0; i < pwqp->n; ++i) {
4401 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4408 isl_pw_qpolynomial_free(pwqp);
4412 /* Adjust all the integer divisions in "qp" such that they are at least
4413 * one over the given orthant (identified by "signs"). This ensures
4414 * that they will still be non-negative even after subtracting (m-1)/m.
4416 * In particular, f is replaced by f' + v, changing f = [a/m]
4417 * to f' = [(a - m v)/m].
4418 * If the constant term k in a is smaller than m,
4419 * the constant term of v is set to floor(k/m) - 1.
4420 * For any other term, if the coefficient c and the variable x have
4421 * the same sign, then no changes are needed.
4422 * Otherwise, if the variable is positive (and c is negative),
4423 * then the coefficient of x in v is set to floor(c/m).
4424 * If the variable is negative (and c is positive),
4425 * then the coefficient of x in v is set to ceil(c/m).
4427 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4433 struct isl_upoly *s;
4435 qp = isl_qpolynomial_cow(qp);
4438 qp->div = isl_mat_cow(qp->div);
4442 total = isl_dim_total(qp->dim);
4443 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4445 for (i = 0; i < qp->div->n_row; ++i) {
4446 isl_int *row = qp->div->row[i];
4450 if (isl_int_lt(row[1], row[0])) {
4451 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4452 isl_int_sub_ui(v->el[0], v->el[0], 1);
4453 isl_int_submul(row[1], row[0], v->el[0]);
4455 for (j = 0; j < total; ++j) {
4456 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4459 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4461 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4462 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4464 for (j = 0; j < i; ++j) {
4465 if (isl_int_sgn(row[2 + total + j]) >= 0)
4467 isl_int_fdiv_q(v->el[1 + total + j],
4468 row[2 + total + j], row[0]);
4469 isl_int_submul(row[2 + total + j],
4470 row[0], v->el[1 + total + j]);
4472 for (j = i + 1; j < qp->div->n_row; ++j) {
4473 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4475 isl_seq_combine(qp->div->row[j] + 1,
4476 qp->div->ctx->one, qp->div->row[j] + 1,
4477 qp->div->row[j][2 + total + i], v->el, v->size);
4479 isl_int_set_si(v->el[1 + total + i], 1);
4480 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4481 qp->div->ctx->one, v->size);
4482 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4492 isl_qpolynomial_free(qp);
4496 struct isl_to_poly_data {
4498 isl_pw_qpolynomial *res;
4499 isl_qpolynomial *qp;
4502 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4503 * We first make all integer divisions positive and then split the
4504 * quasipolynomials into terms with sign data->sign (the direction
4505 * of the requested approximation) and terms with the opposite sign.
4506 * In the first set of terms, each integer division [a/m] is
4507 * overapproximated by a/m, while in the second it is underapproximated
4510 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4513 struct isl_to_poly_data *data = user;
4514 isl_pw_qpolynomial *t;
4515 isl_qpolynomial *qp, *up, *down;
4517 qp = isl_qpolynomial_copy(data->qp);
4518 qp = make_divs_pos(qp, signs);
4520 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4521 up = qp_drop_floors(up, 0);
4522 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4523 down = qp_drop_floors(down, 1);
4525 isl_qpolynomial_free(qp);
4526 qp = isl_qpolynomial_add(up, down);
4528 t = isl_pw_qpolynomial_alloc(orthant, qp);
4529 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4534 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4535 * the polynomial will be an overapproximation. If "sign" is negative,
4536 * it will be an underapproximation. If "sign" is zero, the approximation
4537 * will lie somewhere in between.
4539 * In particular, is sign == 0, we simply drop the floors, turning
4540 * the integer divisions into rational divisions.
4541 * Otherwise, we split the domains into orthants, make all integer divisions
4542 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4543 * depending on the requested sign and the sign of the term in which
4544 * the integer division appears.
4546 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4547 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4550 struct isl_to_poly_data data;
4553 return pwqp_drop_floors(pwqp);
4559 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4561 for (i = 0; i < pwqp->n; ++i) {
4562 if (pwqp->p[i].qp->div->n_row == 0) {
4563 isl_pw_qpolynomial *t;
4564 t = isl_pw_qpolynomial_alloc(
4565 isl_set_copy(pwqp->p[i].set),
4566 isl_qpolynomial_copy(pwqp->p[i].qp));
4567 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4570 data.qp = pwqp->p[i].qp;
4571 if (isl_set_foreach_orthant(pwqp->p[i].set,
4572 &to_polynomial_on_orthant, &data) < 0)
4576 isl_pw_qpolynomial_free(pwqp);
4580 isl_pw_qpolynomial_free(pwqp);
4581 isl_pw_qpolynomial_free(data.res);
4585 static int poly_entry(void **entry, void *user)
4588 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4590 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4592 return *pwqp ? 0 : -1;
4595 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4596 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4598 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4602 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4603 &poly_entry, &sign) < 0)
4608 isl_union_pw_qpolynomial_free(upwqp);
4612 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4613 __isl_take isl_qpolynomial *qp)
4617 isl_vec *aff = NULL;
4618 isl_basic_map *bmap = NULL;
4624 if (!isl_upoly_is_affine(qp->upoly))
4625 isl_die(qp->dim->ctx, isl_error_invalid,
4626 "input quasi-polynomial not affine", goto error);
4627 aff = isl_qpolynomial_extract_affine(qp);
4630 dim = isl_qpolynomial_get_dim(qp);
4631 dim = isl_dim_from_domain(dim);
4632 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4633 dim = isl_dim_add(dim, isl_dim_out, 1);
4634 n_div = qp->div->n_row;
4635 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4637 for (i = 0; i < n_div; ++i) {
4638 k = isl_basic_map_alloc_div(bmap);
4641 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4642 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4643 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4646 k = isl_basic_map_alloc_equality(bmap);
4649 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4650 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4651 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4654 isl_qpolynomial_free(qp);
4655 bmap = isl_basic_map_finalize(bmap);
4659 isl_qpolynomial_free(qp);
4660 isl_basic_map_free(bmap);