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>
26 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
29 case isl_dim_param: return 0;
30 case isl_dim_in: return dim->nparam;
31 case isl_dim_out: return dim->nparam + dim->n_in;
36 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
44 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
49 isl_assert(up->ctx, up->var < 0, return NULL);
51 return (struct isl_upoly_cst *)up;
54 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
59 isl_assert(up->ctx, up->var >= 0, return NULL);
61 return (struct isl_upoly_rec *)up;
64 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
65 __isl_keep struct isl_upoly *up2)
68 struct isl_upoly_rec *rec1, *rec2;
74 if (up1->var != up2->var)
76 if (isl_upoly_is_cst(up1)) {
77 struct isl_upoly_cst *cst1, *cst2;
78 cst1 = isl_upoly_as_cst(up1);
79 cst2 = isl_upoly_as_cst(up2);
82 return isl_int_eq(cst1->n, cst2->n) &&
83 isl_int_eq(cst1->d, cst2->d);
86 rec1 = isl_upoly_as_rec(up1);
87 rec2 = isl_upoly_as_rec(up2);
91 if (rec1->n != rec2->n)
94 for (i = 0; i < rec1->n; ++i) {
95 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
103 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
105 struct isl_upoly_cst *cst;
109 if (!isl_upoly_is_cst(up))
112 cst = isl_upoly_as_cst(up);
116 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
119 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
121 struct isl_upoly_cst *cst;
125 if (!isl_upoly_is_cst(up))
128 cst = isl_upoly_as_cst(up);
132 return isl_int_sgn(cst->n);
135 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
137 struct isl_upoly_cst *cst;
141 if (!isl_upoly_is_cst(up))
144 cst = isl_upoly_as_cst(up);
148 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
151 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
153 struct isl_upoly_cst *cst;
157 if (!isl_upoly_is_cst(up))
160 cst = isl_upoly_as_cst(up);
164 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
167 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
169 struct isl_upoly_cst *cst;
173 if (!isl_upoly_is_cst(up))
176 cst = isl_upoly_as_cst(up);
180 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
183 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
185 struct isl_upoly_cst *cst;
189 if (!isl_upoly_is_cst(up))
192 cst = isl_upoly_as_cst(up);
196 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
199 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
201 struct isl_upoly_cst *cst;
205 if (!isl_upoly_is_cst(up))
208 cst = isl_upoly_as_cst(up);
212 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
215 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
217 struct isl_upoly_cst *cst;
219 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
228 isl_int_init(cst->n);
229 isl_int_init(cst->d);
234 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
236 struct isl_upoly_cst *cst;
238 cst = isl_upoly_cst_alloc(ctx);
242 isl_int_set_si(cst->n, 0);
243 isl_int_set_si(cst->d, 1);
248 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
250 struct isl_upoly_cst *cst;
252 cst = isl_upoly_cst_alloc(ctx);
256 isl_int_set_si(cst->n, 1);
257 isl_int_set_si(cst->d, 1);
262 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
264 struct isl_upoly_cst *cst;
266 cst = isl_upoly_cst_alloc(ctx);
270 isl_int_set_si(cst->n, 1);
271 isl_int_set_si(cst->d, 0);
276 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
278 struct isl_upoly_cst *cst;
280 cst = isl_upoly_cst_alloc(ctx);
284 isl_int_set_si(cst->n, -1);
285 isl_int_set_si(cst->d, 0);
290 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
292 struct isl_upoly_cst *cst;
294 cst = isl_upoly_cst_alloc(ctx);
298 isl_int_set_si(cst->n, 0);
299 isl_int_set_si(cst->d, 0);
304 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
305 isl_int n, isl_int d)
307 struct isl_upoly_cst *cst;
309 cst = isl_upoly_cst_alloc(ctx);
313 isl_int_set(cst->n, n);
314 isl_int_set(cst->d, d);
319 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
322 struct isl_upoly_rec *rec;
324 isl_assert(ctx, var >= 0, return NULL);
325 isl_assert(ctx, size >= 0, return NULL);
326 rec = isl_calloc(ctx, struct isl_upoly_rec,
327 sizeof(struct isl_upoly_rec) +
328 (size - 1) * sizeof(struct isl_upoly *));
343 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
344 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
346 qp = isl_qpolynomial_cow(qp);
350 isl_dim_free(qp->dim);
355 isl_qpolynomial_free(qp);
360 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
362 return qp ? qp->dim->ctx : NULL;
365 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
367 return qp ? isl_dim_copy(qp->dim) : NULL;
370 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
371 enum isl_dim_type type)
373 return qp ? isl_dim_size(qp->dim, type) : 0;
376 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
378 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
381 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
383 return qp ? isl_upoly_is_one(qp->upoly) : -1;
386 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
388 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
391 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
393 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
396 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
398 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
401 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
403 return qp ? isl_upoly_sgn(qp->upoly) : 0;
406 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
408 isl_int_clear(cst->n);
409 isl_int_clear(cst->d);
412 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
416 for (i = 0; i < rec->n; ++i)
417 isl_upoly_free(rec->p[i]);
420 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
429 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
431 struct isl_upoly_cst *cst;
432 struct isl_upoly_cst *dup;
434 cst = isl_upoly_as_cst(up);
438 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
441 isl_int_set(dup->n, cst->n);
442 isl_int_set(dup->d, cst->d);
447 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
450 struct isl_upoly_rec *rec;
451 struct isl_upoly_rec *dup;
453 rec = isl_upoly_as_rec(up);
457 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
461 for (i = 0; i < rec->n; ++i) {
462 dup->p[i] = isl_upoly_copy(rec->p[i]);
470 isl_upoly_free(&dup->up);
474 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
476 struct isl_upoly *dup;
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;
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 *up;
1039 struct isl_upoly_rec *rec;
1040 struct isl_upoly_cst *cst;
1042 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1045 for (i = 0; i < 1 + power; ++i) {
1046 rec->p[i] = isl_upoly_zero(ctx);
1051 cst = isl_upoly_as_cst(rec->p[power]);
1052 isl_int_set_si(cst->n, 1);
1056 isl_upoly_free(&rec->up);
1060 /* r array maps original positions to new positions.
1062 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1066 struct isl_upoly_rec *rec;
1067 struct isl_upoly *base;
1068 struct isl_upoly *res;
1070 if (isl_upoly_is_cst(up))
1073 rec = isl_upoly_as_rec(up);
1077 isl_assert(up->ctx, rec->n >= 1, goto error);
1079 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1080 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1082 for (i = rec->n - 2; i >= 0; --i) {
1083 res = isl_upoly_mul(res, isl_upoly_copy(base));
1084 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1087 isl_upoly_free(base);
1096 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1101 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1102 div1->n_col >= div2->n_col, return -1);
1104 if (div1->n_row == div2->n_row)
1105 return isl_mat_is_equal(div1, div2);
1107 n_row = div1->n_row;
1108 n_col = div1->n_col;
1109 div1->n_row = div2->n_row;
1110 div1->n_col = div2->n_col;
1112 equal = isl_mat_is_equal(div1, div2);
1114 div1->n_row = n_row;
1115 div1->n_col = n_col;
1120 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1124 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1125 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1130 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1133 struct isl_div_sort_info {
1138 static int div_sort_cmp(const void *p1, const void *p2)
1140 const struct isl_div_sort_info *i1, *i2;
1141 i1 = (const struct isl_div_sort_info *) p1;
1142 i2 = (const struct isl_div_sort_info *) p2;
1144 return cmp_row(i1->div, i1->row, i2->row);
1147 /* Sort divs and remove duplicates.
1149 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1154 struct isl_div_sort_info *array = NULL;
1155 int *pos = NULL, *at = NULL;
1156 int *reordering = NULL;
1161 if (qp->div->n_row <= 1)
1164 div_pos = isl_dim_total(qp->dim);
1166 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1168 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1169 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1170 len = qp->div->n_col - 2;
1171 reordering = isl_alloc_array(qp->div->ctx, int, len);
1172 if (!array || !pos || !at || !reordering)
1175 for (i = 0; i < qp->div->n_row; ++i) {
1176 array[i].div = qp->div;
1182 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1185 for (i = 0; i < div_pos; ++i)
1188 for (i = 0; i < qp->div->n_row; ++i) {
1189 if (pos[array[i].row] == i)
1191 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1192 pos[at[i]] = pos[array[i].row];
1193 at[pos[array[i].row]] = at[i];
1194 at[i] = array[i].row;
1195 pos[array[i].row] = i;
1199 for (i = 0; i < len - div_pos; ++i) {
1201 isl_seq_eq(qp->div->row[i - skip - 1],
1202 qp->div->row[i - skip], qp->div->n_col)) {
1203 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1204 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1205 2 + div_pos + i - skip);
1206 qp->div = isl_mat_drop_cols(qp->div,
1207 2 + div_pos + i - skip, 1);
1210 reordering[div_pos + array[i].row] = div_pos + i - skip;
1213 qp->upoly = reorder(qp->upoly, reordering);
1215 if (!qp->upoly || !qp->div)
1229 isl_qpolynomial_free(qp);
1233 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1234 int *exp, int first)
1237 struct isl_upoly_rec *rec;
1239 if (isl_upoly_is_cst(up))
1242 if (up->var < first)
1245 if (exp[up->var - first] == up->var - first)
1248 up = isl_upoly_cow(up);
1252 up->var = exp[up->var - first] + first;
1254 rec = isl_upoly_as_rec(up);
1258 for (i = 0; i < rec->n; ++i) {
1259 rec->p[i] = expand(rec->p[i], exp, first);
1270 static __isl_give isl_qpolynomial *with_merged_divs(
1271 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1272 __isl_take isl_qpolynomial *qp2),
1273 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1277 isl_mat *div = NULL;
1279 qp1 = isl_qpolynomial_cow(qp1);
1280 qp2 = isl_qpolynomial_cow(qp2);
1285 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1286 qp1->div->n_col >= qp2->div->n_col, goto error);
1288 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1289 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1293 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1297 isl_mat_free(qp1->div);
1298 qp1->div = isl_mat_copy(div);
1299 isl_mat_free(qp2->div);
1300 qp2->div = isl_mat_copy(div);
1302 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1303 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1305 if (!qp1->upoly || !qp2->upoly)
1312 return fn(qp1, qp2);
1317 isl_qpolynomial_free(qp1);
1318 isl_qpolynomial_free(qp2);
1322 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1323 __isl_take isl_qpolynomial *qp2)
1325 qp1 = isl_qpolynomial_cow(qp1);
1330 if (qp1->div->n_row < qp2->div->n_row)
1331 return isl_qpolynomial_add(qp2, qp1);
1333 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1334 if (!compatible_divs(qp1->div, qp2->div))
1335 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1337 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1341 isl_qpolynomial_free(qp2);
1345 isl_qpolynomial_free(qp1);
1346 isl_qpolynomial_free(qp2);
1350 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1351 __isl_keep isl_set *dom,
1352 __isl_take isl_qpolynomial *qp1,
1353 __isl_take isl_qpolynomial *qp2)
1355 qp1 = isl_qpolynomial_add(qp1, qp2);
1356 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1360 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1361 __isl_take isl_qpolynomial *qp2)
1363 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1366 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1367 __isl_take isl_qpolynomial *qp, isl_int v)
1369 if (isl_int_is_zero(v))
1372 qp = isl_qpolynomial_cow(qp);
1376 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1382 isl_qpolynomial_free(qp);
1387 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1392 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1395 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1396 __isl_take isl_qpolynomial *qp, isl_int v)
1398 if (isl_int_is_one(v))
1401 if (qp && isl_int_is_zero(v)) {
1402 isl_qpolynomial *zero;
1403 zero = isl_qpolynomial_zero(isl_dim_copy(qp->dim));
1404 isl_qpolynomial_free(qp);
1408 qp = isl_qpolynomial_cow(qp);
1412 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1418 isl_qpolynomial_free(qp);
1422 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1423 __isl_take isl_qpolynomial *qp2)
1425 qp1 = isl_qpolynomial_cow(qp1);
1430 if (qp1->div->n_row < qp2->div->n_row)
1431 return isl_qpolynomial_mul(qp2, qp1);
1433 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1434 if (!compatible_divs(qp1->div, qp2->div))
1435 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1437 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1441 isl_qpolynomial_free(qp2);
1445 isl_qpolynomial_free(qp1);
1446 isl_qpolynomial_free(qp2);
1450 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1453 qp = isl_qpolynomial_cow(qp);
1458 qp->upoly = isl_upoly_pow(qp->upoly, power);
1464 isl_qpolynomial_free(qp);
1468 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1470 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1473 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1475 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1478 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1480 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1483 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1485 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1488 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1490 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1493 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1496 struct isl_qpolynomial *qp;
1497 struct isl_upoly_cst *cst;
1499 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1503 cst = isl_upoly_as_cst(qp->upoly);
1504 isl_int_set(cst->n, v);
1509 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1510 isl_int *n, isl_int *d)
1512 struct isl_upoly_cst *cst;
1517 if (!isl_upoly_is_cst(qp->upoly))
1520 cst = isl_upoly_as_cst(qp->upoly);
1525 isl_int_set(*n, cst->n);
1527 isl_int_set(*d, cst->d);
1532 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1535 struct isl_upoly_rec *rec;
1543 rec = isl_upoly_as_rec(up);
1550 isl_assert(up->ctx, rec->n > 1, return -1);
1552 is_cst = isl_upoly_is_cst(rec->p[1]);
1558 return isl_upoly_is_affine(rec->p[0]);
1561 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1566 if (qp->div->n_row > 0)
1569 return isl_upoly_is_affine(qp->upoly);
1572 static void update_coeff(__isl_keep isl_vec *aff,
1573 __isl_keep struct isl_upoly_cst *cst, int pos)
1578 if (isl_int_is_zero(cst->n))
1583 isl_int_gcd(gcd, cst->d, aff->el[0]);
1584 isl_int_divexact(f, cst->d, gcd);
1585 isl_int_divexact(gcd, aff->el[0], gcd);
1586 isl_seq_scale(aff->el, aff->el, f, aff->size);
1587 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1592 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1593 __isl_keep isl_vec *aff)
1595 struct isl_upoly_cst *cst;
1596 struct isl_upoly_rec *rec;
1602 struct isl_upoly_cst *cst;
1604 cst = isl_upoly_as_cst(up);
1607 update_coeff(aff, cst, 0);
1611 rec = isl_upoly_as_rec(up);
1614 isl_assert(up->ctx, rec->n == 2, return -1);
1616 cst = isl_upoly_as_cst(rec->p[1]);
1619 update_coeff(aff, cst, 1 + up->var);
1621 return isl_upoly_update_affine(rec->p[0], aff);
1624 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1625 __isl_keep isl_qpolynomial *qp)
1633 d = isl_dim_total(qp->dim);
1634 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1638 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1639 isl_int_set_si(aff->el[0], 1);
1641 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1650 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1651 __isl_keep isl_qpolynomial *qp2)
1656 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1659 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1662 struct isl_upoly_rec *rec;
1664 if (isl_upoly_is_cst(up)) {
1665 struct isl_upoly_cst *cst;
1666 cst = isl_upoly_as_cst(up);
1669 isl_int_lcm(*d, *d, cst->d);
1673 rec = isl_upoly_as_rec(up);
1677 for (i = 0; i < rec->n; ++i)
1678 upoly_update_den(rec->p[i], d);
1681 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1683 isl_int_set_si(*d, 1);
1686 upoly_update_den(qp->upoly, d);
1689 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1692 struct isl_ctx *ctx;
1699 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1702 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1703 enum isl_dim_type type, unsigned pos)
1708 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1709 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1711 if (type == isl_dim_set)
1712 pos += isl_dim_size(dim, isl_dim_param);
1714 return isl_qpolynomial_var_pow(dim, pos, 1);
1720 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1721 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1724 struct isl_upoly_rec *rec;
1725 struct isl_upoly *base, *res;
1730 if (isl_upoly_is_cst(up))
1733 if (up->var < first)
1736 rec = isl_upoly_as_rec(up);
1740 isl_assert(up->ctx, rec->n >= 1, goto error);
1742 if (up->var >= first + n)
1743 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1745 base = isl_upoly_copy(subs[up->var - first]);
1747 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1748 for (i = rec->n - 2; i >= 0; --i) {
1749 struct isl_upoly *t;
1750 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1751 res = isl_upoly_mul(res, isl_upoly_copy(base));
1752 res = isl_upoly_sum(res, t);
1755 isl_upoly_free(base);
1764 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1765 isl_int denom, unsigned len)
1768 struct isl_upoly *up;
1770 isl_assert(ctx, len >= 1, return NULL);
1772 up = isl_upoly_rat_cst(ctx, f[0], denom);
1773 for (i = 0; i < len - 1; ++i) {
1774 struct isl_upoly *t;
1775 struct isl_upoly *c;
1777 if (isl_int_is_zero(f[1 + i]))
1780 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1781 t = isl_upoly_var_pow(ctx, i, 1);
1782 t = isl_upoly_mul(c, t);
1783 up = isl_upoly_sum(up, t);
1789 /* Remove common factor of non-constant terms and denominator.
1791 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1793 isl_ctx *ctx = qp->div->ctx;
1794 unsigned total = qp->div->n_col - 2;
1796 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1797 isl_int_gcd(ctx->normalize_gcd,
1798 ctx->normalize_gcd, qp->div->row[div][0]);
1799 if (isl_int_is_one(ctx->normalize_gcd))
1802 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1803 ctx->normalize_gcd, total);
1804 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1805 ctx->normalize_gcd);
1806 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1807 ctx->normalize_gcd);
1810 /* Replace the integer division identified by "div" by the polynomial "s".
1811 * The integer division is assumed not to appear in the definition
1812 * of any other integer divisions.
1814 static __isl_give isl_qpolynomial *substitute_div(
1815 __isl_take isl_qpolynomial *qp,
1816 int div, __isl_take struct isl_upoly *s)
1825 qp = isl_qpolynomial_cow(qp);
1829 total = isl_dim_total(qp->dim);
1830 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1834 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1837 for (i = 0; i < total + div; ++i)
1839 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1840 reordering[i] = i - 1;
1841 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1842 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1843 qp->upoly = reorder(qp->upoly, reordering);
1846 if (!qp->upoly || !qp->div)
1852 isl_qpolynomial_free(qp);
1857 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1858 * divisions because d is equal to 1 by their definition, i.e., e.
1860 static __isl_give isl_qpolynomial *substitute_non_divs(
1861 __isl_take isl_qpolynomial *qp)
1865 struct isl_upoly *s;
1870 total = isl_dim_total(qp->dim);
1871 for (i = 0; qp && i < qp->div->n_row; ++i) {
1872 if (!isl_int_is_one(qp->div->row[i][0]))
1874 for (j = i + 1; j < qp->div->n_row; ++j) {
1875 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1877 isl_seq_combine(qp->div->row[j] + 1,
1878 qp->div->ctx->one, qp->div->row[j] + 1,
1879 qp->div->row[j][2 + total + i],
1880 qp->div->row[i] + 1, 1 + total + i);
1881 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1882 normalize_div(qp, j);
1884 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1885 qp->div->row[i][0], qp->div->n_col - 1);
1886 qp = substitute_div(qp, i, s);
1893 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1894 * with d the denominator. When replacing the coefficient e of x by
1895 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1896 * inside the division, so we need to add floor(e/d) * x outside.
1897 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1898 * to adjust the coefficient of x in each later div that depends on the
1899 * current div "div" and also in the affine expression "aff"
1900 * (if it too depends on "div").
1902 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1903 __isl_keep isl_vec *aff)
1907 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1910 for (i = 0; i < 1 + total + div; ++i) {
1911 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1912 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1914 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1915 isl_int_fdiv_r(qp->div->row[div][1 + i],
1916 qp->div->row[div][1 + i], qp->div->row[div][0]);
1917 if (!isl_int_is_zero(aff->el[1 + total + div]))
1918 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1919 for (j = div + 1; j < qp->div->n_row; ++j) {
1920 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1922 isl_int_addmul(qp->div->row[j][1 + i],
1923 v, qp->div->row[j][2 + total + div]);
1929 /* Check if the last non-zero coefficient is bigger that half of the
1930 * denominator. If so, we will invert the div to further reduce the number
1931 * of distinct divs that may appear.
1932 * If the last non-zero coefficient is exactly half the denominator,
1933 * then we continue looking for earlier coefficients that are bigger
1934 * than half the denominator.
1936 static int needs_invert(__isl_keep isl_mat *div, int row)
1941 for (i = div->n_col - 1; i >= 1; --i) {
1942 if (isl_int_is_zero(div->row[row][i]))
1944 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1945 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1946 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1956 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1957 * We only invert the coefficients of e (and the coefficient of q in
1958 * later divs and in "aff"). After calling this function, the
1959 * coefficients of e should be reduced again.
1961 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1962 __isl_keep isl_vec *aff)
1964 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1966 isl_seq_neg(qp->div->row[div] + 1,
1967 qp->div->row[div] + 1, qp->div->n_col - 1);
1968 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
1969 isl_int_add(qp->div->row[div][1],
1970 qp->div->row[div][1], qp->div->row[div][0]);
1971 if (!isl_int_is_zero(aff->el[1 + total + div]))
1972 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
1973 isl_mat_col_mul(qp->div, 2 + total + div,
1974 qp->div->ctx->negone, 2 + total + div);
1977 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
1978 * in the interval [0, d-1], with d the denominator and such that the
1979 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
1981 * After the reduction, some divs may have become redundant or identical,
1982 * so we call substitute_non_divs and sort_divs. If these functions
1983 * eliminate divs or merge two or more divs into one, the coefficients
1984 * of the enclosing divs may have to be reduced again, so we call
1985 * ourselves recursively if the number of divs decreases.
1987 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
1990 isl_vec *aff = NULL;
1991 struct isl_upoly *s;
1997 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
1998 aff = isl_vec_clr(aff);
2002 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2004 for (i = 0; i < qp->div->n_row; ++i) {
2005 normalize_div(qp, i);
2006 reduce_div(qp, i, aff);
2007 if (needs_invert(qp->div, i)) {
2008 invert_div(qp, i, aff);
2009 reduce_div(qp, i, aff);
2013 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2014 qp->div->ctx->one, aff->size);
2015 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2022 n_div = qp->div->n_row;
2023 qp = substitute_non_divs(qp);
2025 if (qp && qp->div->n_row < n_div)
2026 return reduce_divs(qp);
2030 isl_qpolynomial_free(qp);
2035 /* Assumes each div only depends on earlier divs.
2037 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2040 struct isl_qpolynomial *qp = NULL;
2041 struct isl_upoly_rec *rec;
2042 struct isl_upoly_cst *cst;
2049 d = div->line - div->bmap->div;
2051 pos = isl_dim_total(div->bmap->dim) + d;
2052 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2053 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2054 div->bmap->n_div, &rec->up);
2058 for (i = 0; i < div->bmap->n_div; ++i)
2059 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2061 for (i = 0; i < 1 + power; ++i) {
2062 rec->p[i] = isl_upoly_zero(div->ctx);
2067 cst = isl_upoly_as_cst(rec->p[power]);
2068 isl_int_set_si(cst->n, 1);
2072 qp = reduce_divs(qp);
2076 isl_qpolynomial_free(qp);
2081 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2083 return isl_qpolynomial_div_pow(div, 1);
2086 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2087 const isl_int n, const isl_int d)
2089 struct isl_qpolynomial *qp;
2090 struct isl_upoly_cst *cst;
2092 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2096 cst = isl_upoly_as_cst(qp->upoly);
2097 isl_int_set(cst->n, n);
2098 isl_int_set(cst->d, d);
2103 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2105 struct isl_upoly_rec *rec;
2111 if (isl_upoly_is_cst(up))
2115 active[up->var] = 1;
2117 rec = isl_upoly_as_rec(up);
2118 for (i = 0; i < rec->n; ++i)
2119 if (up_set_active(rec->p[i], active, d) < 0)
2125 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2128 int d = isl_dim_total(qp->dim);
2133 for (i = 0; i < d; ++i)
2134 for (j = 0; j < qp->div->n_row; ++j) {
2135 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2141 return up_set_active(qp->upoly, active, d);
2144 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2145 enum isl_dim_type type, unsigned first, unsigned n)
2156 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2158 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2159 type == isl_dim_set, return -1);
2161 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
2162 if (set_active(qp, active) < 0)
2165 if (type == isl_dim_set)
2166 first += isl_dim_size(qp->dim, isl_dim_param);
2167 for (i = 0; i < n; ++i)
2168 if (active[first + i]) {
2181 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2182 unsigned first, unsigned n)
2185 struct isl_upoly_rec *rec;
2189 if (n == 0 || up->var < 0 || up->var < first)
2191 if (up->var < first + n) {
2192 up = replace_by_constant_term(up);
2193 return isl_upoly_drop(up, first, n);
2195 up = isl_upoly_cow(up);
2199 rec = isl_upoly_as_rec(up);
2203 for (i = 0; i < rec->n; ++i) {
2204 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2215 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2216 __isl_take isl_qpolynomial *qp,
2217 enum isl_dim_type type, unsigned pos, const char *s)
2219 qp = isl_qpolynomial_cow(qp);
2222 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2227 isl_qpolynomial_free(qp);
2231 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2232 __isl_take isl_qpolynomial *qp,
2233 enum isl_dim_type type, unsigned first, unsigned n)
2237 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
2240 qp = isl_qpolynomial_cow(qp);
2244 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2246 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2247 type == isl_dim_set, goto error);
2249 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2253 if (type == isl_dim_set)
2254 first += isl_dim_size(qp->dim, isl_dim_param);
2256 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2260 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2266 isl_qpolynomial_free(qp);
2270 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2271 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2277 struct isl_upoly *up;
2281 if (eq->n_eq == 0) {
2282 isl_basic_set_free(eq);
2286 qp = isl_qpolynomial_cow(qp);
2289 qp->div = isl_mat_cow(qp->div);
2293 total = 1 + isl_dim_total(eq->dim);
2295 isl_int_init(denom);
2296 for (i = 0; i < eq->n_eq; ++i) {
2297 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2298 if (j < 0 || j == 0 || j >= total)
2301 for (k = 0; k < qp->div->n_row; ++k) {
2302 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2304 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2305 &qp->div->row[k][0]);
2306 normalize_div(qp, k);
2309 if (isl_int_is_pos(eq->eq[i][j]))
2310 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2311 isl_int_abs(denom, eq->eq[i][j]);
2312 isl_int_set_si(eq->eq[i][j], 0);
2314 up = isl_upoly_from_affine(qp->dim->ctx,
2315 eq->eq[i], denom, total);
2316 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2319 isl_int_clear(denom);
2324 isl_basic_set_free(eq);
2326 qp = substitute_non_divs(qp);
2331 isl_basic_set_free(eq);
2332 isl_qpolynomial_free(qp);
2336 static __isl_give isl_basic_set *add_div_constraints(
2337 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2345 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2348 total = isl_basic_set_total_dim(bset);
2349 for (i = 0; i < div->n_row; ++i)
2350 if (isl_basic_set_add_div_constraints_var(bset,
2351 total - div->n_row + i, div->row[i]) < 0)
2358 isl_basic_set_free(bset);
2362 /* Look for equalities among the variables shared by context and qp
2363 * and the integer divisions of qp, if any.
2364 * The equalities are then used to eliminate variables and/or integer
2365 * divisions from qp.
2367 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2368 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2374 if (qp->div->n_row > 0) {
2375 isl_basic_set *bset;
2376 context = isl_set_add_dims(context, isl_dim_set,
2378 bset = isl_basic_set_universe(isl_set_get_dim(context));
2379 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2380 context = isl_set_intersect(context,
2381 isl_set_from_basic_set(bset));
2384 aff = isl_set_affine_hull(context);
2385 return isl_qpolynomial_substitute_equalities(qp, aff);
2387 isl_qpolynomial_free(qp);
2388 isl_set_free(context);
2393 #define PW isl_pw_qpolynomial
2395 #define EL isl_qpolynomial
2397 #define IS_ZERO is_zero
2401 #include <isl_pw_templ.c>
2404 #define UNION isl_union_pw_qpolynomial
2406 #define PART isl_pw_qpolynomial
2408 #define PARTS pw_qpolynomial
2410 #include <isl_union_templ.c>
2412 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2420 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2423 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2426 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2427 __isl_take isl_pw_qpolynomial *pwqp1,
2428 __isl_take isl_pw_qpolynomial *pwqp2)
2431 struct isl_pw_qpolynomial *res;
2434 if (!pwqp1 || !pwqp2)
2437 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2440 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2441 isl_pw_qpolynomial_free(pwqp2);
2445 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2446 isl_pw_qpolynomial_free(pwqp1);
2450 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2451 isl_pw_qpolynomial_free(pwqp1);
2455 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2456 isl_pw_qpolynomial_free(pwqp2);
2460 n = pwqp1->n * pwqp2->n;
2461 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2463 for (i = 0; i < pwqp1->n; ++i) {
2464 for (j = 0; j < pwqp2->n; ++j) {
2465 struct isl_set *common;
2466 struct isl_qpolynomial *prod;
2467 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2468 isl_set_copy(pwqp2->p[j].set));
2469 if (isl_set_plain_is_empty(common)) {
2470 isl_set_free(common);
2474 prod = isl_qpolynomial_mul(
2475 isl_qpolynomial_copy(pwqp1->p[i].qp),
2476 isl_qpolynomial_copy(pwqp2->p[j].qp));
2478 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2482 isl_pw_qpolynomial_free(pwqp1);
2483 isl_pw_qpolynomial_free(pwqp2);
2487 isl_pw_qpolynomial_free(pwqp1);
2488 isl_pw_qpolynomial_free(pwqp2);
2492 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2493 __isl_take isl_pw_qpolynomial *pwqp)
2500 if (isl_pw_qpolynomial_is_zero(pwqp))
2503 pwqp = isl_pw_qpolynomial_cow(pwqp);
2507 for (i = 0; i < pwqp->n; ++i) {
2508 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2515 isl_pw_qpolynomial_free(pwqp);
2519 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2520 __isl_take isl_pw_qpolynomial *pwqp1,
2521 __isl_take isl_pw_qpolynomial *pwqp2)
2523 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2526 __isl_give struct isl_upoly *isl_upoly_eval(
2527 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2530 struct isl_upoly_rec *rec;
2531 struct isl_upoly *res;
2532 struct isl_upoly *base;
2534 if (isl_upoly_is_cst(up)) {
2539 rec = isl_upoly_as_rec(up);
2543 isl_assert(up->ctx, rec->n >= 1, goto error);
2545 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2547 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2550 for (i = rec->n - 2; i >= 0; --i) {
2551 res = isl_upoly_mul(res, isl_upoly_copy(base));
2552 res = isl_upoly_sum(res,
2553 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2554 isl_vec_copy(vec)));
2557 isl_upoly_free(base);
2567 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2568 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2571 struct isl_upoly *up;
2576 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2578 if (qp->div->n_row == 0)
2579 ext = isl_vec_copy(pnt->vec);
2582 unsigned dim = isl_dim_total(qp->dim);
2583 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2587 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2588 for (i = 0; i < qp->div->n_row; ++i) {
2589 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2590 1 + dim + i, &ext->el[1+dim+i]);
2591 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2592 qp->div->row[i][0]);
2596 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2600 dim = isl_dim_copy(qp->dim);
2601 isl_qpolynomial_free(qp);
2602 isl_point_free(pnt);
2604 return isl_qpolynomial_alloc(dim, 0, up);
2606 isl_qpolynomial_free(qp);
2607 isl_point_free(pnt);
2611 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2612 __isl_keep struct isl_upoly_cst *cst2)
2617 isl_int_mul(t, cst1->n, cst2->d);
2618 isl_int_submul(t, cst2->n, cst1->d);
2619 cmp = isl_int_sgn(t);
2624 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2625 __isl_keep isl_qpolynomial *qp2)
2627 struct isl_upoly_cst *cst1, *cst2;
2631 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2632 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2633 if (isl_qpolynomial_is_nan(qp1))
2635 if (isl_qpolynomial_is_nan(qp2))
2637 cst1 = isl_upoly_as_cst(qp1->upoly);
2638 cst2 = isl_upoly_as_cst(qp2->upoly);
2640 return isl_upoly_cmp(cst1, cst2) <= 0;
2643 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2644 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2646 struct isl_upoly_cst *cst1, *cst2;
2651 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2652 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2653 cst1 = isl_upoly_as_cst(qp1->upoly);
2654 cst2 = isl_upoly_as_cst(qp2->upoly);
2655 cmp = isl_upoly_cmp(cst1, cst2);
2658 isl_qpolynomial_free(qp2);
2660 isl_qpolynomial_free(qp1);
2665 isl_qpolynomial_free(qp1);
2666 isl_qpolynomial_free(qp2);
2670 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2671 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2673 struct isl_upoly_cst *cst1, *cst2;
2678 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2679 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2680 cst1 = isl_upoly_as_cst(qp1->upoly);
2681 cst2 = isl_upoly_as_cst(qp2->upoly);
2682 cmp = isl_upoly_cmp(cst1, cst2);
2685 isl_qpolynomial_free(qp2);
2687 isl_qpolynomial_free(qp1);
2692 isl_qpolynomial_free(qp1);
2693 isl_qpolynomial_free(qp2);
2697 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2698 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2699 unsigned first, unsigned n)
2708 qp = isl_qpolynomial_cow(qp);
2712 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2715 g_pos = pos(qp->dim, type) + first;
2717 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2721 total = qp->div->n_col - 2;
2722 if (total > g_pos) {
2724 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2727 for (i = 0; i < total - g_pos; ++i)
2729 qp->upoly = expand(qp->upoly, exp, g_pos);
2735 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2741 isl_qpolynomial_free(qp);
2745 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2746 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2750 pos = isl_qpolynomial_dim(qp, type);
2752 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2755 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2756 __isl_take isl_pw_qpolynomial *pwqp,
2757 enum isl_dim_type type, unsigned n)
2761 pos = isl_pw_qpolynomial_dim(pwqp, type);
2763 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2766 static int *reordering_move(isl_ctx *ctx,
2767 unsigned len, unsigned dst, unsigned src, unsigned n)
2772 reordering = isl_alloc_array(ctx, int, len);
2777 for (i = 0; i < dst; ++i)
2779 for (i = 0; i < n; ++i)
2780 reordering[src + i] = dst + i;
2781 for (i = 0; i < src - dst; ++i)
2782 reordering[dst + i] = dst + n + i;
2783 for (i = 0; i < len - src - n; ++i)
2784 reordering[src + n + i] = src + n + i;
2786 for (i = 0; i < src; ++i)
2788 for (i = 0; i < n; ++i)
2789 reordering[src + i] = dst + i;
2790 for (i = 0; i < dst - src; ++i)
2791 reordering[src + n + i] = src + i;
2792 for (i = 0; i < len - dst - n; ++i)
2793 reordering[dst + n + i] = dst + n + i;
2799 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2800 __isl_take isl_qpolynomial *qp,
2801 enum isl_dim_type dst_type, unsigned dst_pos,
2802 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2808 qp = isl_qpolynomial_cow(qp);
2812 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2815 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2816 g_src_pos = pos(qp->dim, src_type) + src_pos;
2817 if (dst_type > src_type)
2820 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2827 reordering = reordering_move(qp->dim->ctx,
2828 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2832 qp->upoly = reorder(qp->upoly, reordering);
2837 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2843 isl_qpolynomial_free(qp);
2847 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2848 isl_int *f, isl_int denom)
2850 struct isl_upoly *up;
2855 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2857 return isl_qpolynomial_alloc(dim, 0, up);
2860 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2861 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2865 struct isl_upoly *up;
2866 isl_qpolynomial *qp;
2872 isl_int_init(denom);
2874 isl_constraint_get_coefficient(c, type, pos, &denom);
2875 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2876 sgn = isl_int_sgn(denom);
2877 isl_int_abs(denom, denom);
2878 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2879 1 + isl_constraint_dim(c, isl_dim_all));
2881 isl_int_neg(denom, denom);
2882 isl_constraint_set_coefficient(c, type, pos, denom);
2884 dim = isl_dim_copy(c->bmap->dim);
2886 isl_int_clear(denom);
2887 isl_constraint_free(c);
2889 qp = isl_qpolynomial_alloc(dim, 0, up);
2891 qp = isl_qpolynomial_neg(qp);
2895 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2896 * in "qp" by subs[i].
2898 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2899 __isl_take isl_qpolynomial *qp,
2900 enum isl_dim_type type, unsigned first, unsigned n,
2901 __isl_keep isl_qpolynomial **subs)
2904 struct isl_upoly **ups;
2909 qp = isl_qpolynomial_cow(qp);
2912 for (i = 0; i < n; ++i)
2916 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2919 for (i = 0; i < n; ++i)
2920 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2923 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2924 for (i = 0; i < n; ++i)
2925 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2927 first += pos(qp->dim, type);
2929 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2932 for (i = 0; i < n; ++i)
2933 ups[i] = subs[i]->upoly;
2935 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2944 isl_qpolynomial_free(qp);
2948 /* Extend "bset" with extra set dimensions for each integer division
2949 * in "qp" and then call "fn" with the extended bset and the polynomial
2950 * that results from replacing each of the integer divisions by the
2951 * corresponding extra set dimension.
2953 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2954 __isl_keep isl_basic_set *bset,
2955 int (*fn)(__isl_take isl_basic_set *bset,
2956 __isl_take isl_qpolynomial *poly, void *user), void *user)
2960 isl_qpolynomial *poly;
2964 if (qp->div->n_row == 0)
2965 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
2968 div = isl_mat_copy(qp->div);
2969 dim = isl_dim_copy(qp->dim);
2970 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
2971 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
2972 bset = isl_basic_set_copy(bset);
2973 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
2974 bset = add_div_constraints(bset, div);
2976 return fn(bset, poly, user);
2981 /* Return total degree in variables first (inclusive) up to last (exclusive).
2983 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
2987 struct isl_upoly_rec *rec;
2991 if (isl_upoly_is_zero(up))
2993 if (isl_upoly_is_cst(up) || up->var < first)
2996 rec = isl_upoly_as_rec(up);
3000 for (i = 0; i < rec->n; ++i) {
3003 if (isl_upoly_is_zero(rec->p[i]))
3005 d = isl_upoly_degree(rec->p[i], first, last);
3015 /* Return total degree in set variables.
3017 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3025 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3026 nvar = isl_dim_size(poly->dim, isl_dim_set);
3027 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3030 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3031 unsigned pos, int deg)
3034 struct isl_upoly_rec *rec;
3039 if (isl_upoly_is_cst(up) || up->var < pos) {
3041 return isl_upoly_copy(up);
3043 return isl_upoly_zero(up->ctx);
3046 rec = isl_upoly_as_rec(up);
3050 if (up->var == pos) {
3052 return isl_upoly_copy(rec->p[deg]);
3054 return isl_upoly_zero(up->ctx);
3057 up = isl_upoly_copy(up);
3058 up = isl_upoly_cow(up);
3059 rec = isl_upoly_as_rec(up);
3063 for (i = 0; i < rec->n; ++i) {
3064 struct isl_upoly *t;
3065 t = isl_upoly_coeff(rec->p[i], pos, deg);
3068 isl_upoly_free(rec->p[i]);
3078 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3080 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3081 __isl_keep isl_qpolynomial *qp,
3082 enum isl_dim_type type, unsigned t_pos, int deg)
3085 struct isl_upoly *up;
3091 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3094 g_pos = pos(qp->dim, type) + t_pos;
3095 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3097 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3100 isl_mat_free(c->div);
3101 c->div = isl_mat_copy(qp->div);
3106 isl_qpolynomial_free(c);
3110 /* Homogenize the polynomial in the variables first (inclusive) up to
3111 * last (exclusive) by inserting powers of variable first.
3112 * Variable first is assumed not to appear in the input.
3114 __isl_give struct isl_upoly *isl_upoly_homogenize(
3115 __isl_take struct isl_upoly *up, int deg, int target,
3116 int first, int last)
3119 struct isl_upoly_rec *rec;
3123 if (isl_upoly_is_zero(up))
3127 if (isl_upoly_is_cst(up) || up->var < first) {
3128 struct isl_upoly *hom;
3130 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3133 rec = isl_upoly_as_rec(hom);
3134 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3139 up = isl_upoly_cow(up);
3140 rec = isl_upoly_as_rec(up);
3144 for (i = 0; i < rec->n; ++i) {
3145 if (isl_upoly_is_zero(rec->p[i]))
3147 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3148 up->var < last ? deg + i : i, target,
3160 /* Homogenize the polynomial in the set variables by introducing
3161 * powers of an extra set variable at position 0.
3163 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3164 __isl_take isl_qpolynomial *poly)
3168 int deg = isl_qpolynomial_degree(poly);
3173 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3174 poly = isl_qpolynomial_cow(poly);
3178 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3179 nvar = isl_dim_size(poly->dim, isl_dim_set);
3180 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3187 isl_qpolynomial_free(poly);
3191 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3192 __isl_take isl_mat *div)
3200 n = isl_dim_total(dim) + div->n_row;
3202 term = isl_calloc(dim->ctx, struct isl_term,
3203 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3210 isl_int_init(term->n);
3211 isl_int_init(term->d);
3220 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3229 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3238 total = isl_dim_total(term->dim) + term->div->n_row;
3240 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3244 isl_int_set(dup->n, term->n);
3245 isl_int_set(dup->d, term->d);
3247 for (i = 0; i < total; ++i)
3248 dup->pow[i] = term->pow[i];
3253 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3261 return isl_term_dup(term);
3264 void isl_term_free(__isl_take isl_term *term)
3269 if (--term->ref > 0)
3272 isl_dim_free(term->dim);
3273 isl_mat_free(term->div);
3274 isl_int_clear(term->n);
3275 isl_int_clear(term->d);
3279 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3287 case isl_dim_out: return isl_dim_size(term->dim, type);
3288 case isl_dim_div: return term->div->n_row;
3289 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3294 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3296 return term ? term->dim->ctx : NULL;
3299 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3303 isl_int_set(*n, term->n);
3306 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3310 isl_int_set(*d, term->d);
3313 int isl_term_get_exp(__isl_keep isl_term *term,
3314 enum isl_dim_type type, unsigned pos)
3319 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3321 if (type >= isl_dim_set)
3322 pos += isl_dim_size(term->dim, isl_dim_param);
3323 if (type >= isl_dim_div)
3324 pos += isl_dim_size(term->dim, isl_dim_set);
3326 return term->pow[pos];
3329 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3331 isl_basic_map *bmap;
3338 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3341 total = term->div->n_col - term->div->n_row - 2;
3342 /* No nested divs for now */
3343 isl_assert(term->dim->ctx,
3344 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3345 term->div->n_row) == -1,
3348 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3349 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3352 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3354 return isl_basic_map_div(bmap, k);
3356 isl_basic_map_free(bmap);
3360 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3361 int (*fn)(__isl_take isl_term *term, void *user),
3362 __isl_take isl_term *term, void *user)
3365 struct isl_upoly_rec *rec;
3370 if (isl_upoly_is_zero(up))
3373 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3374 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3375 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3377 if (isl_upoly_is_cst(up)) {
3378 struct isl_upoly_cst *cst;
3379 cst = isl_upoly_as_cst(up);
3382 term = isl_term_cow(term);
3385 isl_int_set(term->n, cst->n);
3386 isl_int_set(term->d, cst->d);
3387 if (fn(isl_term_copy(term), user) < 0)
3392 rec = isl_upoly_as_rec(up);
3396 for (i = 0; i < rec->n; ++i) {
3397 term = isl_term_cow(term);
3400 term->pow[up->var] = i;
3401 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3405 term->pow[up->var] = 0;
3409 isl_term_free(term);
3413 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3414 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3421 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3425 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3427 isl_term_free(term);
3429 return term ? 0 : -1;
3432 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3434 struct isl_upoly *up;
3435 isl_qpolynomial *qp;
3441 n = isl_dim_total(term->dim) + term->div->n_row;
3443 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3444 for (i = 0; i < n; ++i) {
3447 up = isl_upoly_mul(up,
3448 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3451 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3454 isl_mat_free(qp->div);
3455 qp->div = isl_mat_copy(term->div);
3459 isl_term_free(term);
3462 isl_qpolynomial_free(qp);
3463 isl_term_free(term);
3467 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3468 __isl_take isl_dim *dim)
3477 if (isl_dim_equal(qp->dim, dim)) {
3482 qp = isl_qpolynomial_cow(qp);
3486 extra = isl_dim_size(dim, isl_dim_set) -
3487 isl_dim_size(qp->dim, isl_dim_set);
3488 total = isl_dim_total(qp->dim);
3489 if (qp->div->n_row) {
3492 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3495 for (i = 0; i < qp->div->n_row; ++i)
3497 qp->upoly = expand(qp->upoly, exp, total);
3502 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3505 for (i = 0; i < qp->div->n_row; ++i)
3506 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3508 isl_dim_free(qp->dim);
3514 isl_qpolynomial_free(qp);
3518 /* For each parameter or variable that does not appear in qp,
3519 * first eliminate the variable from all constraints and then set it to zero.
3521 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3522 __isl_keep isl_qpolynomial *qp)
3533 d = isl_dim_total(set->dim);
3534 active = isl_calloc_array(set->ctx, int, d);
3535 if (set_active(qp, active) < 0)
3538 for (i = 0; i < d; ++i)
3547 nparam = isl_dim_size(set->dim, isl_dim_param);
3548 nvar = isl_dim_size(set->dim, isl_dim_set);
3549 for (i = 0; i < nparam; ++i) {
3552 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3553 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3555 for (i = 0; i < nvar; ++i) {
3556 if (active[nparam + i])
3558 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3559 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3571 struct isl_opt_data {
3572 isl_qpolynomial *qp;
3574 isl_qpolynomial *opt;
3578 static int opt_fn(__isl_take isl_point *pnt, void *user)
3580 struct isl_opt_data *data = (struct isl_opt_data *)user;
3581 isl_qpolynomial *val;
3583 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3587 } else if (data->max) {
3588 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3590 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3596 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3597 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3599 struct isl_opt_data data = { NULL, 1, NULL, max };
3604 if (isl_upoly_is_cst(qp->upoly)) {
3609 set = fix_inactive(set, qp);
3612 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3616 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3619 isl_qpolynomial_free(qp);
3623 isl_qpolynomial_free(qp);
3624 isl_qpolynomial_free(data.opt);
3628 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3629 __isl_take isl_morph *morph)
3634 struct isl_upoly *up;
3636 struct isl_upoly **subs;
3639 qp = isl_qpolynomial_cow(qp);
3644 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3646 n_sub = morph->inv->n_row - 1;
3647 if (morph->inv->n_row != morph->inv->n_col)
3648 n_sub += qp->div->n_row;
3649 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3653 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3654 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3655 morph->inv->row[0][0], morph->inv->n_col);
3656 if (morph->inv->n_row != morph->inv->n_col)
3657 for (i = 0; i < qp->div->n_row; ++i)
3658 subs[morph->inv->n_row - 1 + i] =
3659 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3661 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3663 for (i = 0; i < n_sub; ++i)
3664 isl_upoly_free(subs[i]);
3667 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3668 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3669 qp->div = isl_mat_product(qp->div, mat);
3670 isl_dim_free(qp->dim);
3671 qp->dim = isl_dim_copy(morph->ran->dim);
3673 if (!qp->upoly || !qp->div || !qp->dim)
3676 isl_morph_free(morph);
3680 isl_qpolynomial_free(qp);
3681 isl_morph_free(morph);
3685 static int neg_entry(void **entry, void *user)
3687 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3689 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3691 return *pwqp ? 0 : -1;
3694 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3695 __isl_take isl_union_pw_qpolynomial *upwqp)
3697 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3701 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3702 &neg_entry, NULL) < 0)
3707 isl_union_pw_qpolynomial_free(upwqp);
3711 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3712 __isl_take isl_union_pw_qpolynomial *upwqp1,
3713 __isl_take isl_union_pw_qpolynomial *upwqp2)
3715 return isl_union_pw_qpolynomial_add(upwqp1,
3716 isl_union_pw_qpolynomial_neg(upwqp2));
3719 static int mul_entry(void **entry, void *user)
3721 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3723 struct isl_hash_table_entry *entry2;
3724 isl_pw_qpolynomial *pwpq = *entry;
3727 hash = isl_dim_get_hash(pwpq->dim);
3728 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3729 hash, &has_dim, pwpq->dim, 0);
3733 pwpq = isl_pw_qpolynomial_copy(pwpq);
3734 pwpq = isl_pw_qpolynomial_mul(pwpq,
3735 isl_pw_qpolynomial_copy(entry2->data));
3737 empty = isl_pw_qpolynomial_is_zero(pwpq);
3739 isl_pw_qpolynomial_free(pwpq);
3743 isl_pw_qpolynomial_free(pwpq);
3747 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3752 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3753 __isl_take isl_union_pw_qpolynomial *upwqp1,
3754 __isl_take isl_union_pw_qpolynomial *upwqp2)
3756 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3759 /* Reorder the columns of the given div definitions according to the
3762 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3763 __isl_take isl_reordering *r)
3772 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3773 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3777 for (i = 0; i < div->n_row; ++i) {
3778 isl_seq_cpy(mat->row[i], div->row[i], 2);
3779 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3780 for (j = 0; j < r->len; ++j)
3781 isl_int_set(mat->row[i][2 + r->pos[j]],
3782 div->row[i][2 + j]);
3785 isl_reordering_free(r);
3789 isl_reordering_free(r);
3794 /* Reorder the dimension of "qp" according to the given reordering.
3796 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3797 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3799 qp = isl_qpolynomial_cow(qp);
3803 r = isl_reordering_extend(r, qp->div->n_row);
3807 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3811 qp->upoly = reorder(qp->upoly, r->pos);
3815 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3817 isl_reordering_free(r);
3820 isl_qpolynomial_free(qp);
3821 isl_reordering_free(r);
3825 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3826 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3831 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3832 isl_reordering *exp;
3834 model = isl_dim_drop(model, isl_dim_in,
3835 0, isl_dim_size(model, isl_dim_in));
3836 model = isl_dim_drop(model, isl_dim_out,
3837 0, isl_dim_size(model, isl_dim_out));
3838 exp = isl_parameter_alignment_reordering(qp->dim, model);
3839 exp = isl_reordering_extend_dim(exp,
3840 isl_qpolynomial_get_dim(qp));
3841 qp = isl_qpolynomial_realign(qp, exp);
3844 isl_dim_free(model);
3847 isl_dim_free(model);
3848 isl_qpolynomial_free(qp);
3852 struct isl_split_periods_data {
3854 isl_pw_qpolynomial *res;
3857 /* Create a slice where the integer division "div" has the fixed value "v".
3858 * In particular, if "div" refers to floor(f/m), then create a slice
3860 * m v <= f <= m v + (m - 1)
3865 * -f + m v + (m - 1) >= 0
3867 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3868 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3871 isl_basic_set *bset = NULL;
3877 total = isl_dim_total(dim);
3878 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3880 k = isl_basic_set_alloc_inequality(bset);
3883 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3884 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3886 k = isl_basic_set_alloc_inequality(bset);
3889 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3890 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3891 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3892 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3895 return isl_set_from_basic_set(bset);
3897 isl_basic_set_free(bset);
3902 static int split_periods(__isl_take isl_set *set,
3903 __isl_take isl_qpolynomial *qp, void *user);
3905 /* Create a slice of the domain "set" such that integer division "div"
3906 * has the fixed value "v" and add the results to data->res,
3907 * replacing the integer division by "v" in "qp".
3909 static int set_div(__isl_take isl_set *set,
3910 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3911 struct isl_split_periods_data *data)
3916 struct isl_upoly *cst;
3918 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3919 set = isl_set_intersect(set, slice);
3924 total = isl_dim_total(qp->dim);
3926 for (i = div + 1; i < qp->div->n_row; ++i) {
3927 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3929 isl_int_addmul(qp->div->row[i][1],
3930 qp->div->row[i][2 + total + div], v);
3931 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3934 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3935 qp = substitute_div(qp, div, cst);
3937 return split_periods(set, qp, data);
3940 isl_qpolynomial_free(qp);
3944 /* Split the domain "set" such that integer division "div"
3945 * has a fixed value (ranging from "min" to "max") on each slice
3946 * and add the results to data->res.
3948 static int split_div(__isl_take isl_set *set,
3949 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
3950 struct isl_split_periods_data *data)
3952 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
3953 isl_set *set_i = isl_set_copy(set);
3954 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
3956 if (set_div(set_i, qp_i, div, min, data) < 0)
3960 isl_qpolynomial_free(qp);
3964 isl_qpolynomial_free(qp);
3968 /* If "qp" refers to any integer division
3969 * that can only attain "max_periods" distinct values on "set"
3970 * then split the domain along those distinct values.
3971 * Add the results (or the original if no splitting occurs)
3974 static int split_periods(__isl_take isl_set *set,
3975 __isl_take isl_qpolynomial *qp, void *user)
3978 isl_pw_qpolynomial *pwqp;
3979 struct isl_split_periods_data *data;
3984 data = (struct isl_split_periods_data *)user;
3989 if (qp->div->n_row == 0) {
3990 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3991 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3997 total = isl_dim_total(qp->dim);
3998 for (i = 0; i < qp->div->n_row; ++i) {
3999 enum isl_lp_result lp_res;
4001 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4002 qp->div->n_row) != -1)
4005 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4006 set->ctx->one, &min, NULL, NULL);
4007 if (lp_res == isl_lp_error)
4009 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4011 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4013 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4014 set->ctx->one, &max, NULL, NULL);
4015 if (lp_res == isl_lp_error)
4017 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4019 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4021 isl_int_sub(max, max, min);
4022 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4023 isl_int_add(max, max, min);
4028 if (i < qp->div->n_row) {
4029 r = split_div(set, qp, i, min, max, data);
4031 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4032 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4044 isl_qpolynomial_free(qp);
4048 /* If any quasi-polynomial in pwqp refers to any integer division
4049 * that can only attain "max_periods" distinct values on its domain
4050 * then split the domain along those distinct values.
4052 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4053 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4055 struct isl_split_periods_data data;
4057 data.max_periods = max_periods;
4058 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4060 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4063 isl_pw_qpolynomial_free(pwqp);
4067 isl_pw_qpolynomial_free(data.res);
4068 isl_pw_qpolynomial_free(pwqp);
4072 /* Construct a piecewise quasipolynomial that is constant on the given
4073 * domain. In particular, it is
4076 * infinity if cst == -1
4078 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4079 __isl_take isl_basic_set *bset, int cst)
4082 isl_qpolynomial *qp;
4087 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4088 dim = isl_basic_set_get_dim(bset);
4090 qp = isl_qpolynomial_infty(dim);
4092 qp = isl_qpolynomial_zero(dim);
4094 qp = isl_qpolynomial_one(dim);
4095 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4098 /* Factor bset, call fn on each of the factors and return the product.
4100 * If no factors can be found, simply call fn on the input.
4101 * Otherwise, construct the factors based on the factorizer,
4102 * call fn on each factor and compute the product.
4104 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4105 __isl_take isl_basic_set *bset,
4106 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4112 isl_qpolynomial *qp;
4113 isl_pw_qpolynomial *pwqp;
4117 f = isl_basic_set_factorizer(bset);
4120 if (f->n_group == 0) {
4121 isl_factorizer_free(f);
4125 nparam = isl_basic_set_dim(bset, isl_dim_param);
4126 nvar = isl_basic_set_dim(bset, isl_dim_set);
4128 dim = isl_basic_set_get_dim(bset);
4129 dim = isl_dim_domain(dim);
4130 set = isl_set_universe(isl_dim_copy(dim));
4131 qp = isl_qpolynomial_one(dim);
4132 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4134 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4136 for (i = 0, n = 0; i < f->n_group; ++i) {
4137 isl_basic_set *bset_i;
4138 isl_pw_qpolynomial *pwqp_i;
4140 bset_i = isl_basic_set_copy(bset);
4141 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4142 nparam + n + f->len[i], nvar - n - f->len[i]);
4143 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4145 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4146 n + f->len[i], nvar - n - f->len[i]);
4147 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4149 pwqp_i = fn(bset_i);
4150 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4155 isl_basic_set_free(bset);
4156 isl_factorizer_free(f);
4160 isl_basic_set_free(bset);
4164 /* Factor bset, call fn on each of the factors and return the product.
4165 * The function is assumed to evaluate to zero on empty domains,
4166 * to one on zero-dimensional domains and to infinity on unbounded domains
4167 * and will not be called explicitly on zero-dimensional or unbounded domains.
4169 * We first check for some special cases and remove all equalities.
4170 * Then we hand over control to compressed_multiplicative_call.
4172 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4173 __isl_take isl_basic_set *bset,
4174 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4178 isl_pw_qpolynomial *pwqp;
4179 unsigned orig_nvar, final_nvar;
4184 if (isl_basic_set_plain_is_empty(bset))
4185 return constant_on_domain(bset, 0);
4187 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4190 return constant_on_domain(bset, 1);
4192 bounded = isl_basic_set_is_bounded(bset);
4196 return constant_on_domain(bset, -1);
4198 if (bset->n_eq == 0)
4199 return compressed_multiplicative_call(bset, fn);
4201 morph = isl_basic_set_full_compression(bset);
4202 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4204 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4206 pwqp = compressed_multiplicative_call(bset, fn);
4208 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4209 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4210 morph = isl_morph_inverse(morph);
4212 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4216 isl_basic_set_free(bset);
4220 /* Drop all floors in "qp", turning each integer division [a/m] into
4221 * a rational division a/m. If "down" is set, then the integer division
4222 * is replaces by (a-(m-1))/m instead.
4224 static __isl_give isl_qpolynomial *qp_drop_floors(
4225 __isl_take isl_qpolynomial *qp, int down)
4228 struct isl_upoly *s;
4232 if (qp->div->n_row == 0)
4235 qp = isl_qpolynomial_cow(qp);
4239 for (i = qp->div->n_row - 1; i >= 0; --i) {
4241 isl_int_sub(qp->div->row[i][1],
4242 qp->div->row[i][1], qp->div->row[i][0]);
4243 isl_int_add_ui(qp->div->row[i][1],
4244 qp->div->row[i][1], 1);
4246 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4247 qp->div->row[i][0], qp->div->n_col - 1);
4248 qp = substitute_div(qp, i, s);
4256 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4257 * a rational division a/m.
4259 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4260 __isl_take isl_pw_qpolynomial *pwqp)
4267 if (isl_pw_qpolynomial_is_zero(pwqp))
4270 pwqp = isl_pw_qpolynomial_cow(pwqp);
4274 for (i = 0; i < pwqp->n; ++i) {
4275 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4282 isl_pw_qpolynomial_free(pwqp);
4286 /* Adjust all the integer divisions in "qp" such that they are at least
4287 * one over the given orthant (identified by "signs"). This ensures
4288 * that they will still be non-negative even after subtracting (m-1)/m.
4290 * In particular, f is replaced by f' + v, changing f = [a/m]
4291 * to f' = [(a - m v)/m].
4292 * If the constant term k in a is smaller than m,
4293 * the constant term of v is set to floor(k/m) - 1.
4294 * For any other term, if the coefficient c and the variable x have
4295 * the same sign, then no changes are needed.
4296 * Otherwise, if the variable is positive (and c is negative),
4297 * then the coefficient of x in v is set to floor(c/m).
4298 * If the variable is negative (and c is positive),
4299 * then the coefficient of x in v is set to ceil(c/m).
4301 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4307 struct isl_upoly *s;
4309 qp = isl_qpolynomial_cow(qp);
4312 qp->div = isl_mat_cow(qp->div);
4316 total = isl_dim_total(qp->dim);
4317 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4319 for (i = 0; i < qp->div->n_row; ++i) {
4320 isl_int *row = qp->div->row[i];
4324 if (isl_int_lt(row[1], row[0])) {
4325 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4326 isl_int_sub_ui(v->el[0], v->el[0], 1);
4327 isl_int_submul(row[1], row[0], v->el[0]);
4329 for (j = 0; j < total; ++j) {
4330 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4333 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4335 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4336 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4338 for (j = 0; j < i; ++j) {
4339 if (isl_int_sgn(row[2 + total + j]) >= 0)
4341 isl_int_fdiv_q(v->el[1 + total + j],
4342 row[2 + total + j], row[0]);
4343 isl_int_submul(row[2 + total + j],
4344 row[0], v->el[1 + total + j]);
4346 for (j = i + 1; j < qp->div->n_row; ++j) {
4347 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4349 isl_seq_combine(qp->div->row[j] + 1,
4350 qp->div->ctx->one, qp->div->row[j] + 1,
4351 qp->div->row[j][2 + total + i], v->el, v->size);
4353 isl_int_set_si(v->el[1 + total + i], 1);
4354 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4355 qp->div->ctx->one, v->size);
4356 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4366 isl_qpolynomial_free(qp);
4370 struct isl_to_poly_data {
4372 isl_pw_qpolynomial *res;
4373 isl_qpolynomial *qp;
4376 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4377 * We first make all integer divisions positive and then split the
4378 * quasipolynomials into terms with sign data->sign (the direction
4379 * of the requested approximation) and terms with the opposite sign.
4380 * In the first set of terms, each integer division [a/m] is
4381 * overapproximated by a/m, while in the second it is underapproximated
4384 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4387 struct isl_to_poly_data *data = user;
4388 isl_pw_qpolynomial *t;
4389 isl_qpolynomial *qp, *up, *down;
4391 qp = isl_qpolynomial_copy(data->qp);
4392 qp = make_divs_pos(qp, signs);
4394 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4395 up = qp_drop_floors(up, 0);
4396 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4397 down = qp_drop_floors(down, 1);
4399 isl_qpolynomial_free(qp);
4400 qp = isl_qpolynomial_add(up, down);
4402 t = isl_pw_qpolynomial_alloc(orthant, qp);
4403 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4408 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4409 * the polynomial will be an overapproximation. If "sign" is negative,
4410 * it will be an underapproximation. If "sign" is zero, the approximation
4411 * will lie somewhere in between.
4413 * In particular, is sign == 0, we simply drop the floors, turning
4414 * the integer divisions into rational divisions.
4415 * Otherwise, we split the domains into orthants, make all integer divisions
4416 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4417 * depending on the requested sign and the sign of the term in which
4418 * the integer division appears.
4420 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4421 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4424 struct isl_to_poly_data data;
4427 return pwqp_drop_floors(pwqp);
4433 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4435 for (i = 0; i < pwqp->n; ++i) {
4436 if (pwqp->p[i].qp->div->n_row == 0) {
4437 isl_pw_qpolynomial *t;
4438 t = isl_pw_qpolynomial_alloc(
4439 isl_set_copy(pwqp->p[i].set),
4440 isl_qpolynomial_copy(pwqp->p[i].qp));
4441 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4444 data.qp = pwqp->p[i].qp;
4445 if (isl_set_foreach_orthant(pwqp->p[i].set,
4446 &to_polynomial_on_orthant, &data) < 0)
4450 isl_pw_qpolynomial_free(pwqp);
4454 isl_pw_qpolynomial_free(pwqp);
4455 isl_pw_qpolynomial_free(data.res);
4459 static int poly_entry(void **entry, void *user)
4462 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4464 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4466 return *pwqp ? 0 : -1;
4469 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4470 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4472 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4476 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4477 &poly_entry, &sign) < 0)
4482 isl_union_pw_qpolynomial_free(upwqp);
4486 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4487 __isl_take isl_qpolynomial *qp)
4491 isl_vec *aff = NULL;
4492 isl_basic_map *bmap = NULL;
4498 if (!isl_upoly_is_affine(qp->upoly))
4499 isl_die(qp->dim->ctx, isl_error_invalid,
4500 "input quasi-polynomial not affine", goto error);
4501 aff = isl_qpolynomial_extract_affine(qp);
4504 dim = isl_qpolynomial_get_dim(qp);
4505 dim = isl_dim_from_domain(dim);
4506 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4507 dim = isl_dim_add(dim, isl_dim_out, 1);
4508 n_div = qp->div->n_row;
4509 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4511 for (i = 0; i < n_div; ++i) {
4512 k = isl_basic_map_alloc_div(bmap);
4515 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4516 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4517 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4520 k = isl_basic_map_alloc_equality(bmap);
4523 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4524 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4525 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4528 isl_qpolynomial_free(qp);
4529 bmap = isl_basic_map_finalize(bmap);
4533 isl_qpolynomial_free(qp);
4534 isl_basic_map_free(bmap);