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_get_tuple_name(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 IS_ZERO is_zero
2513 #include <isl_pw_templ.c>
2516 #define UNION isl_union_pw_qpolynomial
2518 #define PART isl_pw_qpolynomial
2520 #define PARTS pw_qpolynomial
2522 #include <isl_union_templ.c>
2524 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2532 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2535 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2538 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2539 __isl_take isl_pw_qpolynomial *pwqp1,
2540 __isl_take isl_pw_qpolynomial *pwqp2)
2543 struct isl_pw_qpolynomial *res;
2545 if (!pwqp1 || !pwqp2)
2548 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2551 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2552 isl_pw_qpolynomial_free(pwqp2);
2556 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2557 isl_pw_qpolynomial_free(pwqp1);
2561 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2562 isl_pw_qpolynomial_free(pwqp1);
2566 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2567 isl_pw_qpolynomial_free(pwqp2);
2571 n = pwqp1->n * pwqp2->n;
2572 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2574 for (i = 0; i < pwqp1->n; ++i) {
2575 for (j = 0; j < pwqp2->n; ++j) {
2576 struct isl_set *common;
2577 struct isl_qpolynomial *prod;
2578 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2579 isl_set_copy(pwqp2->p[j].set));
2580 if (isl_set_plain_is_empty(common)) {
2581 isl_set_free(common);
2585 prod = isl_qpolynomial_mul(
2586 isl_qpolynomial_copy(pwqp1->p[i].qp),
2587 isl_qpolynomial_copy(pwqp2->p[j].qp));
2589 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2593 isl_pw_qpolynomial_free(pwqp1);
2594 isl_pw_qpolynomial_free(pwqp2);
2598 isl_pw_qpolynomial_free(pwqp1);
2599 isl_pw_qpolynomial_free(pwqp2);
2603 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2604 __isl_take isl_pw_qpolynomial *pwqp)
2611 if (isl_pw_qpolynomial_is_zero(pwqp))
2614 pwqp = isl_pw_qpolynomial_cow(pwqp);
2618 for (i = 0; i < pwqp->n; ++i) {
2619 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2626 isl_pw_qpolynomial_free(pwqp);
2630 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2631 __isl_take isl_pw_qpolynomial *pwqp1,
2632 __isl_take isl_pw_qpolynomial *pwqp2)
2634 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2637 __isl_give struct isl_upoly *isl_upoly_eval(
2638 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2641 struct isl_upoly_rec *rec;
2642 struct isl_upoly *res;
2643 struct isl_upoly *base;
2645 if (isl_upoly_is_cst(up)) {
2650 rec = isl_upoly_as_rec(up);
2654 isl_assert(up->ctx, rec->n >= 1, goto error);
2656 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2658 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2661 for (i = rec->n - 2; i >= 0; --i) {
2662 res = isl_upoly_mul(res, isl_upoly_copy(base));
2663 res = isl_upoly_sum(res,
2664 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2665 isl_vec_copy(vec)));
2668 isl_upoly_free(base);
2678 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2679 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2682 struct isl_upoly *up;
2687 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2689 if (qp->div->n_row == 0)
2690 ext = isl_vec_copy(pnt->vec);
2693 unsigned dim = isl_dim_total(qp->dim);
2694 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2698 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2699 for (i = 0; i < qp->div->n_row; ++i) {
2700 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2701 1 + dim + i, &ext->el[1+dim+i]);
2702 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2703 qp->div->row[i][0]);
2707 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2711 dim = isl_dim_copy(qp->dim);
2712 isl_qpolynomial_free(qp);
2713 isl_point_free(pnt);
2715 return isl_qpolynomial_alloc(dim, 0, up);
2717 isl_qpolynomial_free(qp);
2718 isl_point_free(pnt);
2722 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2723 __isl_keep struct isl_upoly_cst *cst2)
2728 isl_int_mul(t, cst1->n, cst2->d);
2729 isl_int_submul(t, cst2->n, cst1->d);
2730 cmp = isl_int_sgn(t);
2735 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2736 __isl_keep isl_qpolynomial *qp2)
2738 struct isl_upoly_cst *cst1, *cst2;
2742 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2743 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2744 if (isl_qpolynomial_is_nan(qp1))
2746 if (isl_qpolynomial_is_nan(qp2))
2748 cst1 = isl_upoly_as_cst(qp1->upoly);
2749 cst2 = isl_upoly_as_cst(qp2->upoly);
2751 return isl_upoly_cmp(cst1, cst2) <= 0;
2754 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2755 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2757 struct isl_upoly_cst *cst1, *cst2;
2762 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2763 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2764 cst1 = isl_upoly_as_cst(qp1->upoly);
2765 cst2 = isl_upoly_as_cst(qp2->upoly);
2766 cmp = isl_upoly_cmp(cst1, cst2);
2769 isl_qpolynomial_free(qp2);
2771 isl_qpolynomial_free(qp1);
2776 isl_qpolynomial_free(qp1);
2777 isl_qpolynomial_free(qp2);
2781 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2782 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2784 struct isl_upoly_cst *cst1, *cst2;
2789 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2790 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2791 cst1 = isl_upoly_as_cst(qp1->upoly);
2792 cst2 = isl_upoly_as_cst(qp2->upoly);
2793 cmp = isl_upoly_cmp(cst1, cst2);
2796 isl_qpolynomial_free(qp2);
2798 isl_qpolynomial_free(qp1);
2803 isl_qpolynomial_free(qp1);
2804 isl_qpolynomial_free(qp2);
2808 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2809 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2810 unsigned first, unsigned n)
2819 qp = isl_qpolynomial_cow(qp);
2823 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2826 g_pos = pos(qp->dim, type) + first;
2828 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2832 total = qp->div->n_col - 2;
2833 if (total > g_pos) {
2835 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2838 for (i = 0; i < total - g_pos; ++i)
2840 qp->upoly = expand(qp->upoly, exp, g_pos);
2846 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2852 isl_qpolynomial_free(qp);
2856 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2857 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2861 pos = isl_qpolynomial_dim(qp, type);
2863 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2866 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2867 __isl_take isl_pw_qpolynomial *pwqp,
2868 enum isl_dim_type type, unsigned n)
2872 pos = isl_pw_qpolynomial_dim(pwqp, type);
2874 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2877 static int *reordering_move(isl_ctx *ctx,
2878 unsigned len, unsigned dst, unsigned src, unsigned n)
2883 reordering = isl_alloc_array(ctx, int, len);
2888 for (i = 0; i < dst; ++i)
2890 for (i = 0; i < n; ++i)
2891 reordering[src + i] = dst + i;
2892 for (i = 0; i < src - dst; ++i)
2893 reordering[dst + i] = dst + n + i;
2894 for (i = 0; i < len - src - n; ++i)
2895 reordering[src + n + i] = src + n + i;
2897 for (i = 0; i < src; ++i)
2899 for (i = 0; i < n; ++i)
2900 reordering[src + i] = dst + i;
2901 for (i = 0; i < dst - src; ++i)
2902 reordering[src + n + i] = src + i;
2903 for (i = 0; i < len - dst - n; ++i)
2904 reordering[dst + n + i] = dst + n + i;
2910 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2911 __isl_take isl_qpolynomial *qp,
2912 enum isl_dim_type dst_type, unsigned dst_pos,
2913 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2919 qp = isl_qpolynomial_cow(qp);
2923 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2926 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2927 g_src_pos = pos(qp->dim, src_type) + src_pos;
2928 if (dst_type > src_type)
2931 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2938 reordering = reordering_move(qp->dim->ctx,
2939 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2943 qp->upoly = reorder(qp->upoly, reordering);
2948 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2954 isl_qpolynomial_free(qp);
2958 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2959 isl_int *f, isl_int denom)
2961 struct isl_upoly *up;
2966 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2968 return isl_qpolynomial_alloc(dim, 0, up);
2971 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
2974 struct isl_upoly *up;
2975 isl_qpolynomial *qp;
2980 ctx = isl_aff_get_ctx(aff);
2981 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
2984 qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff),
2985 aff->ls->div->n_row, up);
2989 isl_mat_free(qp->div);
2990 qp->div = isl_mat_copy(aff->ls->div);
2991 qp->div = isl_mat_cow(qp->div);
2996 qp = reduce_divs(qp);
2997 qp = remove_redundant_divs(qp);
3004 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3005 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3009 struct isl_upoly *up;
3010 isl_qpolynomial *qp;
3016 isl_int_init(denom);
3018 isl_constraint_get_coefficient(c, type, pos, &denom);
3019 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
3020 sgn = isl_int_sgn(denom);
3021 isl_int_abs(denom, denom);
3022 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
3023 1 + isl_constraint_dim(c, isl_dim_all));
3025 isl_int_neg(denom, denom);
3026 isl_constraint_set_coefficient(c, type, pos, denom);
3028 dim = isl_dim_copy(c->bmap->dim);
3030 isl_int_clear(denom);
3031 isl_constraint_free(c);
3033 qp = isl_qpolynomial_alloc(dim, 0, up);
3035 qp = isl_qpolynomial_neg(qp);
3039 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3040 * in "qp" by subs[i].
3042 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3043 __isl_take isl_qpolynomial *qp,
3044 enum isl_dim_type type, unsigned first, unsigned n,
3045 __isl_keep isl_qpolynomial **subs)
3048 struct isl_upoly **ups;
3053 qp = isl_qpolynomial_cow(qp);
3056 for (i = 0; i < n; ++i)
3060 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
3063 for (i = 0; i < n; ++i)
3064 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3067 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3068 for (i = 0; i < n; ++i)
3069 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3071 first += pos(qp->dim, type);
3073 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3076 for (i = 0; i < n; ++i)
3077 ups[i] = subs[i]->upoly;
3079 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3088 isl_qpolynomial_free(qp);
3092 /* Extend "bset" with extra set dimensions for each integer division
3093 * in "qp" and then call "fn" with the extended bset and the polynomial
3094 * that results from replacing each of the integer divisions by the
3095 * corresponding extra set dimension.
3097 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3098 __isl_keep isl_basic_set *bset,
3099 int (*fn)(__isl_take isl_basic_set *bset,
3100 __isl_take isl_qpolynomial *poly, void *user), void *user)
3104 isl_qpolynomial *poly;
3108 if (qp->div->n_row == 0)
3109 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3112 div = isl_mat_copy(qp->div);
3113 dim = isl_dim_copy(qp->dim);
3114 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3115 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3116 bset = isl_basic_set_copy(bset);
3117 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3118 bset = add_div_constraints(bset, div);
3120 return fn(bset, poly, user);
3125 /* Return total degree in variables first (inclusive) up to last (exclusive).
3127 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3131 struct isl_upoly_rec *rec;
3135 if (isl_upoly_is_zero(up))
3137 if (isl_upoly_is_cst(up) || up->var < first)
3140 rec = isl_upoly_as_rec(up);
3144 for (i = 0; i < rec->n; ++i) {
3147 if (isl_upoly_is_zero(rec->p[i]))
3149 d = isl_upoly_degree(rec->p[i], first, last);
3159 /* Return total degree in set variables.
3161 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3169 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3170 nvar = isl_dim_size(poly->dim, isl_dim_set);
3171 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3174 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3175 unsigned pos, int deg)
3178 struct isl_upoly_rec *rec;
3183 if (isl_upoly_is_cst(up) || up->var < pos) {
3185 return isl_upoly_copy(up);
3187 return isl_upoly_zero(up->ctx);
3190 rec = isl_upoly_as_rec(up);
3194 if (up->var == pos) {
3196 return isl_upoly_copy(rec->p[deg]);
3198 return isl_upoly_zero(up->ctx);
3201 up = isl_upoly_copy(up);
3202 up = isl_upoly_cow(up);
3203 rec = isl_upoly_as_rec(up);
3207 for (i = 0; i < rec->n; ++i) {
3208 struct isl_upoly *t;
3209 t = isl_upoly_coeff(rec->p[i], pos, deg);
3212 isl_upoly_free(rec->p[i]);
3222 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3224 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3225 __isl_keep isl_qpolynomial *qp,
3226 enum isl_dim_type type, unsigned t_pos, int deg)
3229 struct isl_upoly *up;
3235 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3238 g_pos = pos(qp->dim, type) + t_pos;
3239 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3241 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3244 isl_mat_free(c->div);
3245 c->div = isl_mat_copy(qp->div);
3250 isl_qpolynomial_free(c);
3254 /* Homogenize the polynomial in the variables first (inclusive) up to
3255 * last (exclusive) by inserting powers of variable first.
3256 * Variable first is assumed not to appear in the input.
3258 __isl_give struct isl_upoly *isl_upoly_homogenize(
3259 __isl_take struct isl_upoly *up, int deg, int target,
3260 int first, int last)
3263 struct isl_upoly_rec *rec;
3267 if (isl_upoly_is_zero(up))
3271 if (isl_upoly_is_cst(up) || up->var < first) {
3272 struct isl_upoly *hom;
3274 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3277 rec = isl_upoly_as_rec(hom);
3278 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3283 up = isl_upoly_cow(up);
3284 rec = isl_upoly_as_rec(up);
3288 for (i = 0; i < rec->n; ++i) {
3289 if (isl_upoly_is_zero(rec->p[i]))
3291 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3292 up->var < last ? deg + i : i, target,
3304 /* Homogenize the polynomial in the set variables by introducing
3305 * powers of an extra set variable at position 0.
3307 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3308 __isl_take isl_qpolynomial *poly)
3312 int deg = isl_qpolynomial_degree(poly);
3317 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3318 poly = isl_qpolynomial_cow(poly);
3322 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3323 nvar = isl_dim_size(poly->dim, isl_dim_set);
3324 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3331 isl_qpolynomial_free(poly);
3335 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3336 __isl_take isl_mat *div)
3344 n = isl_dim_total(dim) + div->n_row;
3346 term = isl_calloc(dim->ctx, struct isl_term,
3347 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3354 isl_int_init(term->n);
3355 isl_int_init(term->d);
3364 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3373 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3382 total = isl_dim_total(term->dim) + term->div->n_row;
3384 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3388 isl_int_set(dup->n, term->n);
3389 isl_int_set(dup->d, term->d);
3391 for (i = 0; i < total; ++i)
3392 dup->pow[i] = term->pow[i];
3397 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3405 return isl_term_dup(term);
3408 void isl_term_free(__isl_take isl_term *term)
3413 if (--term->ref > 0)
3416 isl_dim_free(term->dim);
3417 isl_mat_free(term->div);
3418 isl_int_clear(term->n);
3419 isl_int_clear(term->d);
3423 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3431 case isl_dim_out: return isl_dim_size(term->dim, type);
3432 case isl_dim_div: return term->div->n_row;
3433 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3438 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3440 return term ? term->dim->ctx : NULL;
3443 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3447 isl_int_set(*n, term->n);
3450 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3454 isl_int_set(*d, term->d);
3457 int isl_term_get_exp(__isl_keep isl_term *term,
3458 enum isl_dim_type type, unsigned pos)
3463 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3465 if (type >= isl_dim_set)
3466 pos += isl_dim_size(term->dim, isl_dim_param);
3467 if (type >= isl_dim_div)
3468 pos += isl_dim_size(term->dim, isl_dim_set);
3470 return term->pow[pos];
3473 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3475 isl_basic_map *bmap;
3482 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3485 total = term->div->n_col - term->div->n_row - 2;
3486 /* No nested divs for now */
3487 isl_assert(term->dim->ctx,
3488 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3489 term->div->n_row) == -1,
3492 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3493 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3496 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3498 return isl_basic_map_div(bmap, k);
3500 isl_basic_map_free(bmap);
3504 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3505 int (*fn)(__isl_take isl_term *term, void *user),
3506 __isl_take isl_term *term, void *user)
3509 struct isl_upoly_rec *rec;
3514 if (isl_upoly_is_zero(up))
3517 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3518 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3519 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3521 if (isl_upoly_is_cst(up)) {
3522 struct isl_upoly_cst *cst;
3523 cst = isl_upoly_as_cst(up);
3526 term = isl_term_cow(term);
3529 isl_int_set(term->n, cst->n);
3530 isl_int_set(term->d, cst->d);
3531 if (fn(isl_term_copy(term), user) < 0)
3536 rec = isl_upoly_as_rec(up);
3540 for (i = 0; i < rec->n; ++i) {
3541 term = isl_term_cow(term);
3544 term->pow[up->var] = i;
3545 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3549 term->pow[up->var] = 0;
3553 isl_term_free(term);
3557 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3558 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3565 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3569 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3571 isl_term_free(term);
3573 return term ? 0 : -1;
3576 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3578 struct isl_upoly *up;
3579 isl_qpolynomial *qp;
3585 n = isl_dim_total(term->dim) + term->div->n_row;
3587 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3588 for (i = 0; i < n; ++i) {
3591 up = isl_upoly_mul(up,
3592 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3595 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3598 isl_mat_free(qp->div);
3599 qp->div = isl_mat_copy(term->div);
3603 isl_term_free(term);
3606 isl_qpolynomial_free(qp);
3607 isl_term_free(term);
3611 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3612 __isl_take isl_dim *dim)
3621 if (isl_dim_equal(qp->dim, dim)) {
3626 qp = isl_qpolynomial_cow(qp);
3630 extra = isl_dim_size(dim, isl_dim_set) -
3631 isl_dim_size(qp->dim, isl_dim_set);
3632 total = isl_dim_total(qp->dim);
3633 if (qp->div->n_row) {
3636 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3639 for (i = 0; i < qp->div->n_row; ++i)
3641 qp->upoly = expand(qp->upoly, exp, total);
3646 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3649 for (i = 0; i < qp->div->n_row; ++i)
3650 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3652 isl_dim_free(qp->dim);
3658 isl_qpolynomial_free(qp);
3662 /* For each parameter or variable that does not appear in qp,
3663 * first eliminate the variable from all constraints and then set it to zero.
3665 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3666 __isl_keep isl_qpolynomial *qp)
3677 d = isl_dim_total(set->dim);
3678 active = isl_calloc_array(set->ctx, int, d);
3679 if (set_active(qp, active) < 0)
3682 for (i = 0; i < d; ++i)
3691 nparam = isl_dim_size(set->dim, isl_dim_param);
3692 nvar = isl_dim_size(set->dim, isl_dim_set);
3693 for (i = 0; i < nparam; ++i) {
3696 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3697 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3699 for (i = 0; i < nvar; ++i) {
3700 if (active[nparam + i])
3702 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3703 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3715 struct isl_opt_data {
3716 isl_qpolynomial *qp;
3718 isl_qpolynomial *opt;
3722 static int opt_fn(__isl_take isl_point *pnt, void *user)
3724 struct isl_opt_data *data = (struct isl_opt_data *)user;
3725 isl_qpolynomial *val;
3727 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3731 } else if (data->max) {
3732 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3734 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3740 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3741 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3743 struct isl_opt_data data = { NULL, 1, NULL, max };
3748 if (isl_upoly_is_cst(qp->upoly)) {
3753 set = fix_inactive(set, qp);
3756 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3760 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3763 isl_qpolynomial_free(qp);
3767 isl_qpolynomial_free(qp);
3768 isl_qpolynomial_free(data.opt);
3772 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3773 __isl_take isl_morph *morph)
3778 struct isl_upoly **subs;
3781 qp = isl_qpolynomial_cow(qp);
3786 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3788 n_sub = morph->inv->n_row - 1;
3789 if (morph->inv->n_row != morph->inv->n_col)
3790 n_sub += qp->div->n_row;
3791 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3795 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3796 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3797 morph->inv->row[0][0], morph->inv->n_col);
3798 if (morph->inv->n_row != morph->inv->n_col)
3799 for (i = 0; i < qp->div->n_row; ++i)
3800 subs[morph->inv->n_row - 1 + i] =
3801 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3803 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3805 for (i = 0; i < n_sub; ++i)
3806 isl_upoly_free(subs[i]);
3809 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3810 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3811 qp->div = isl_mat_product(qp->div, mat);
3812 isl_dim_free(qp->dim);
3813 qp->dim = isl_dim_copy(morph->ran->dim);
3815 if (!qp->upoly || !qp->div || !qp->dim)
3818 isl_morph_free(morph);
3822 isl_qpolynomial_free(qp);
3823 isl_morph_free(morph);
3827 static int neg_entry(void **entry, void *user)
3829 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3831 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3833 return *pwqp ? 0 : -1;
3836 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3837 __isl_take isl_union_pw_qpolynomial *upwqp)
3839 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3843 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3844 &neg_entry, NULL) < 0)
3849 isl_union_pw_qpolynomial_free(upwqp);
3853 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3854 __isl_take isl_union_pw_qpolynomial *upwqp1,
3855 __isl_take isl_union_pw_qpolynomial *upwqp2)
3857 return isl_union_pw_qpolynomial_add(upwqp1,
3858 isl_union_pw_qpolynomial_neg(upwqp2));
3861 static int mul_entry(void **entry, void *user)
3863 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3865 struct isl_hash_table_entry *entry2;
3866 isl_pw_qpolynomial *pwpq = *entry;
3869 hash = isl_dim_get_hash(pwpq->dim);
3870 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3871 hash, &has_dim, pwpq->dim, 0);
3875 pwpq = isl_pw_qpolynomial_copy(pwpq);
3876 pwpq = isl_pw_qpolynomial_mul(pwpq,
3877 isl_pw_qpolynomial_copy(entry2->data));
3879 empty = isl_pw_qpolynomial_is_zero(pwpq);
3881 isl_pw_qpolynomial_free(pwpq);
3885 isl_pw_qpolynomial_free(pwpq);
3889 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3894 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3895 __isl_take isl_union_pw_qpolynomial *upwqp1,
3896 __isl_take isl_union_pw_qpolynomial *upwqp2)
3898 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3901 /* Reorder the columns of the given div definitions according to the
3904 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3905 __isl_take isl_reordering *r)
3914 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3915 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3919 for (i = 0; i < div->n_row; ++i) {
3920 isl_seq_cpy(mat->row[i], div->row[i], 2);
3921 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3922 for (j = 0; j < r->len; ++j)
3923 isl_int_set(mat->row[i][2 + r->pos[j]],
3924 div->row[i][2 + j]);
3927 isl_reordering_free(r);
3931 isl_reordering_free(r);
3936 /* Reorder the dimension of "qp" according to the given reordering.
3938 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3939 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3941 qp = isl_qpolynomial_cow(qp);
3945 r = isl_reordering_extend(r, qp->div->n_row);
3949 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3953 qp->upoly = reorder(qp->upoly, r->pos);
3957 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3959 isl_reordering_free(r);
3962 isl_qpolynomial_free(qp);
3963 isl_reordering_free(r);
3967 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3968 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3973 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3974 isl_reordering *exp;
3976 model = isl_dim_drop(model, isl_dim_in,
3977 0, isl_dim_size(model, isl_dim_in));
3978 model = isl_dim_drop(model, isl_dim_out,
3979 0, isl_dim_size(model, isl_dim_out));
3980 exp = isl_parameter_alignment_reordering(qp->dim, model);
3981 exp = isl_reordering_extend_dim(exp,
3982 isl_qpolynomial_get_dim(qp));
3983 qp = isl_qpolynomial_realign(qp, exp);
3986 isl_dim_free(model);
3989 isl_dim_free(model);
3990 isl_qpolynomial_free(qp);
3994 struct isl_split_periods_data {
3996 isl_pw_qpolynomial *res;
3999 /* Create a slice where the integer division "div" has the fixed value "v".
4000 * In particular, if "div" refers to floor(f/m), then create a slice
4002 * m v <= f <= m v + (m - 1)
4007 * -f + m v + (m - 1) >= 0
4009 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
4010 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4013 isl_basic_set *bset = NULL;
4019 total = isl_dim_total(dim);
4020 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
4022 k = isl_basic_set_alloc_inequality(bset);
4025 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4026 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4028 k = isl_basic_set_alloc_inequality(bset);
4031 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4032 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4033 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4034 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4037 return isl_set_from_basic_set(bset);
4039 isl_basic_set_free(bset);
4044 static int split_periods(__isl_take isl_set *set,
4045 __isl_take isl_qpolynomial *qp, void *user);
4047 /* Create a slice of the domain "set" such that integer division "div"
4048 * has the fixed value "v" and add the results to data->res,
4049 * replacing the integer division by "v" in "qp".
4051 static int set_div(__isl_take isl_set *set,
4052 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4053 struct isl_split_periods_data *data)
4058 struct isl_upoly *cst;
4060 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
4061 set = isl_set_intersect(set, slice);
4066 total = isl_dim_total(qp->dim);
4068 for (i = div + 1; i < qp->div->n_row; ++i) {
4069 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4071 isl_int_addmul(qp->div->row[i][1],
4072 qp->div->row[i][2 + total + div], v);
4073 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4076 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4077 qp = substitute_div(qp, div, cst);
4079 return split_periods(set, qp, data);
4082 isl_qpolynomial_free(qp);
4086 /* Split the domain "set" such that integer division "div"
4087 * has a fixed value (ranging from "min" to "max") on each slice
4088 * and add the results to data->res.
4090 static int split_div(__isl_take isl_set *set,
4091 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4092 struct isl_split_periods_data *data)
4094 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4095 isl_set *set_i = isl_set_copy(set);
4096 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4098 if (set_div(set_i, qp_i, div, min, data) < 0)
4102 isl_qpolynomial_free(qp);
4106 isl_qpolynomial_free(qp);
4110 /* If "qp" refers to any integer division
4111 * that can only attain "max_periods" distinct values on "set"
4112 * then split the domain along those distinct values.
4113 * Add the results (or the original if no splitting occurs)
4116 static int split_periods(__isl_take isl_set *set,
4117 __isl_take isl_qpolynomial *qp, void *user)
4120 isl_pw_qpolynomial *pwqp;
4121 struct isl_split_periods_data *data;
4126 data = (struct isl_split_periods_data *)user;
4131 if (qp->div->n_row == 0) {
4132 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4133 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4139 total = isl_dim_total(qp->dim);
4140 for (i = 0; i < qp->div->n_row; ++i) {
4141 enum isl_lp_result lp_res;
4143 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4144 qp->div->n_row) != -1)
4147 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4148 set->ctx->one, &min, NULL, NULL);
4149 if (lp_res == isl_lp_error)
4151 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4153 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4155 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4156 set->ctx->one, &max, NULL, NULL);
4157 if (lp_res == isl_lp_error)
4159 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4161 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4163 isl_int_sub(max, max, min);
4164 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4165 isl_int_add(max, max, min);
4170 if (i < qp->div->n_row) {
4171 r = split_div(set, qp, i, min, max, data);
4173 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4174 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4186 isl_qpolynomial_free(qp);
4190 /* If any quasi-polynomial in pwqp refers to any integer division
4191 * that can only attain "max_periods" distinct values on its domain
4192 * then split the domain along those distinct values.
4194 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4195 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4197 struct isl_split_periods_data data;
4199 data.max_periods = max_periods;
4200 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4202 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4205 isl_pw_qpolynomial_free(pwqp);
4209 isl_pw_qpolynomial_free(data.res);
4210 isl_pw_qpolynomial_free(pwqp);
4214 /* Construct a piecewise quasipolynomial that is constant on the given
4215 * domain. In particular, it is
4218 * infinity if cst == -1
4220 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4221 __isl_take isl_basic_set *bset, int cst)
4224 isl_qpolynomial *qp;
4229 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4230 dim = isl_basic_set_get_dim(bset);
4232 qp = isl_qpolynomial_infty(dim);
4234 qp = isl_qpolynomial_zero(dim);
4236 qp = isl_qpolynomial_one(dim);
4237 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4240 /* Factor bset, call fn on each of the factors and return the product.
4242 * If no factors can be found, simply call fn on the input.
4243 * Otherwise, construct the factors based on the factorizer,
4244 * call fn on each factor and compute the product.
4246 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4247 __isl_take isl_basic_set *bset,
4248 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4254 isl_qpolynomial *qp;
4255 isl_pw_qpolynomial *pwqp;
4259 f = isl_basic_set_factorizer(bset);
4262 if (f->n_group == 0) {
4263 isl_factorizer_free(f);
4267 nparam = isl_basic_set_dim(bset, isl_dim_param);
4268 nvar = isl_basic_set_dim(bset, isl_dim_set);
4270 dim = isl_basic_set_get_dim(bset);
4271 dim = isl_dim_domain(dim);
4272 set = isl_set_universe(isl_dim_copy(dim));
4273 qp = isl_qpolynomial_one(dim);
4274 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4276 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4278 for (i = 0, n = 0; i < f->n_group; ++i) {
4279 isl_basic_set *bset_i;
4280 isl_pw_qpolynomial *pwqp_i;
4282 bset_i = isl_basic_set_copy(bset);
4283 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4284 nparam + n + f->len[i], nvar - n - f->len[i]);
4285 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4287 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4288 n + f->len[i], nvar - n - f->len[i]);
4289 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4291 pwqp_i = fn(bset_i);
4292 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4297 isl_basic_set_free(bset);
4298 isl_factorizer_free(f);
4302 isl_basic_set_free(bset);
4306 /* Factor bset, call fn on each of the factors and return the product.
4307 * The function is assumed to evaluate to zero on empty domains,
4308 * to one on zero-dimensional domains and to infinity on unbounded domains
4309 * and will not be called explicitly on zero-dimensional or unbounded domains.
4311 * We first check for some special cases and remove all equalities.
4312 * Then we hand over control to compressed_multiplicative_call.
4314 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4315 __isl_take isl_basic_set *bset,
4316 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4320 isl_pw_qpolynomial *pwqp;
4321 unsigned orig_nvar, final_nvar;
4326 if (isl_basic_set_plain_is_empty(bset))
4327 return constant_on_domain(bset, 0);
4329 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4332 return constant_on_domain(bset, 1);
4334 bounded = isl_basic_set_is_bounded(bset);
4338 return constant_on_domain(bset, -1);
4340 if (bset->n_eq == 0)
4341 return compressed_multiplicative_call(bset, fn);
4343 morph = isl_basic_set_full_compression(bset);
4344 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4346 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4348 pwqp = compressed_multiplicative_call(bset, fn);
4350 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4351 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4352 morph = isl_morph_inverse(morph);
4354 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4358 isl_basic_set_free(bset);
4362 /* Drop all floors in "qp", turning each integer division [a/m] into
4363 * a rational division a/m. If "down" is set, then the integer division
4364 * is replaces by (a-(m-1))/m instead.
4366 static __isl_give isl_qpolynomial *qp_drop_floors(
4367 __isl_take isl_qpolynomial *qp, int down)
4370 struct isl_upoly *s;
4374 if (qp->div->n_row == 0)
4377 qp = isl_qpolynomial_cow(qp);
4381 for (i = qp->div->n_row - 1; i >= 0; --i) {
4383 isl_int_sub(qp->div->row[i][1],
4384 qp->div->row[i][1], qp->div->row[i][0]);
4385 isl_int_add_ui(qp->div->row[i][1],
4386 qp->div->row[i][1], 1);
4388 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4389 qp->div->row[i][0], qp->div->n_col - 1);
4390 qp = substitute_div(qp, i, s);
4398 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4399 * a rational division a/m.
4401 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4402 __isl_take isl_pw_qpolynomial *pwqp)
4409 if (isl_pw_qpolynomial_is_zero(pwqp))
4412 pwqp = isl_pw_qpolynomial_cow(pwqp);
4416 for (i = 0; i < pwqp->n; ++i) {
4417 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4424 isl_pw_qpolynomial_free(pwqp);
4428 /* Adjust all the integer divisions in "qp" such that they are at least
4429 * one over the given orthant (identified by "signs"). This ensures
4430 * that they will still be non-negative even after subtracting (m-1)/m.
4432 * In particular, f is replaced by f' + v, changing f = [a/m]
4433 * to f' = [(a - m v)/m].
4434 * If the constant term k in a is smaller than m,
4435 * the constant term of v is set to floor(k/m) - 1.
4436 * For any other term, if the coefficient c and the variable x have
4437 * the same sign, then no changes are needed.
4438 * Otherwise, if the variable is positive (and c is negative),
4439 * then the coefficient of x in v is set to floor(c/m).
4440 * If the variable is negative (and c is positive),
4441 * then the coefficient of x in v is set to ceil(c/m).
4443 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4449 struct isl_upoly *s;
4451 qp = isl_qpolynomial_cow(qp);
4454 qp->div = isl_mat_cow(qp->div);
4458 total = isl_dim_total(qp->dim);
4459 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4461 for (i = 0; i < qp->div->n_row; ++i) {
4462 isl_int *row = qp->div->row[i];
4466 if (isl_int_lt(row[1], row[0])) {
4467 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4468 isl_int_sub_ui(v->el[0], v->el[0], 1);
4469 isl_int_submul(row[1], row[0], v->el[0]);
4471 for (j = 0; j < total; ++j) {
4472 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4475 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4477 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4478 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4480 for (j = 0; j < i; ++j) {
4481 if (isl_int_sgn(row[2 + total + j]) >= 0)
4483 isl_int_fdiv_q(v->el[1 + total + j],
4484 row[2 + total + j], row[0]);
4485 isl_int_submul(row[2 + total + j],
4486 row[0], v->el[1 + total + j]);
4488 for (j = i + 1; j < qp->div->n_row; ++j) {
4489 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4491 isl_seq_combine(qp->div->row[j] + 1,
4492 qp->div->ctx->one, qp->div->row[j] + 1,
4493 qp->div->row[j][2 + total + i], v->el, v->size);
4495 isl_int_set_si(v->el[1 + total + i], 1);
4496 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4497 qp->div->ctx->one, v->size);
4498 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4508 isl_qpolynomial_free(qp);
4512 struct isl_to_poly_data {
4514 isl_pw_qpolynomial *res;
4515 isl_qpolynomial *qp;
4518 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4519 * We first make all integer divisions positive and then split the
4520 * quasipolynomials into terms with sign data->sign (the direction
4521 * of the requested approximation) and terms with the opposite sign.
4522 * In the first set of terms, each integer division [a/m] is
4523 * overapproximated by a/m, while in the second it is underapproximated
4526 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4529 struct isl_to_poly_data *data = user;
4530 isl_pw_qpolynomial *t;
4531 isl_qpolynomial *qp, *up, *down;
4533 qp = isl_qpolynomial_copy(data->qp);
4534 qp = make_divs_pos(qp, signs);
4536 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4537 up = qp_drop_floors(up, 0);
4538 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4539 down = qp_drop_floors(down, 1);
4541 isl_qpolynomial_free(qp);
4542 qp = isl_qpolynomial_add(up, down);
4544 t = isl_pw_qpolynomial_alloc(orthant, qp);
4545 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4550 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4551 * the polynomial will be an overapproximation. If "sign" is negative,
4552 * it will be an underapproximation. If "sign" is zero, the approximation
4553 * will lie somewhere in between.
4555 * In particular, is sign == 0, we simply drop the floors, turning
4556 * the integer divisions into rational divisions.
4557 * Otherwise, we split the domains into orthants, make all integer divisions
4558 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4559 * depending on the requested sign and the sign of the term in which
4560 * the integer division appears.
4562 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4563 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4566 struct isl_to_poly_data data;
4569 return pwqp_drop_floors(pwqp);
4575 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4577 for (i = 0; i < pwqp->n; ++i) {
4578 if (pwqp->p[i].qp->div->n_row == 0) {
4579 isl_pw_qpolynomial *t;
4580 t = isl_pw_qpolynomial_alloc(
4581 isl_set_copy(pwqp->p[i].set),
4582 isl_qpolynomial_copy(pwqp->p[i].qp));
4583 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4586 data.qp = pwqp->p[i].qp;
4587 if (isl_set_foreach_orthant(pwqp->p[i].set,
4588 &to_polynomial_on_orthant, &data) < 0)
4592 isl_pw_qpolynomial_free(pwqp);
4596 isl_pw_qpolynomial_free(pwqp);
4597 isl_pw_qpolynomial_free(data.res);
4601 static int poly_entry(void **entry, void *user)
4604 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4606 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4608 return *pwqp ? 0 : -1;
4611 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4612 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4614 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4618 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4619 &poly_entry, &sign) < 0)
4624 isl_union_pw_qpolynomial_free(upwqp);
4628 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4629 __isl_take isl_qpolynomial *qp)
4633 isl_vec *aff = NULL;
4634 isl_basic_map *bmap = NULL;
4640 if (!isl_upoly_is_affine(qp->upoly))
4641 isl_die(qp->dim->ctx, isl_error_invalid,
4642 "input quasi-polynomial not affine", goto error);
4643 aff = isl_qpolynomial_extract_affine(qp);
4646 dim = isl_qpolynomial_get_dim(qp);
4647 dim = isl_dim_from_domain(dim);
4648 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4649 dim = isl_dim_add(dim, isl_dim_out, 1);
4650 n_div = qp->div->n_row;
4651 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4653 for (i = 0; i < n_div; ++i) {
4654 k = isl_basic_map_alloc_div(bmap);
4657 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4658 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4659 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4662 k = isl_basic_map_alloc_equality(bmap);
4665 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4666 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4667 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4670 isl_qpolynomial_free(qp);
4671 bmap = isl_basic_map_finalize(bmap);
4675 isl_qpolynomial_free(qp);
4676 isl_basic_map_free(bmap);