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_constraint_private.h>
19 #include <isl_polynomial_private.h>
20 #include <isl_point_private.h>
21 #include <isl_dim_private.h>
22 #include <isl_div_private.h>
23 #include <isl_mat_private.h>
24 #include <isl_range.h>
25 #include <isl_local_space_private.h>
26 #include <isl_aff_private.h>
27 #include <isl_config.h>
29 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
32 case isl_dim_param: return 0;
33 case isl_dim_in: return dim->nparam;
34 case isl_dim_out: return dim->nparam + dim->n_in;
39 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
47 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
52 isl_assert(up->ctx, up->var < 0, return NULL);
54 return (struct isl_upoly_cst *)up;
57 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
62 isl_assert(up->ctx, up->var >= 0, return NULL);
64 return (struct isl_upoly_rec *)up;
67 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
68 __isl_keep struct isl_upoly *up2)
71 struct isl_upoly_rec *rec1, *rec2;
77 if (up1->var != up2->var)
79 if (isl_upoly_is_cst(up1)) {
80 struct isl_upoly_cst *cst1, *cst2;
81 cst1 = isl_upoly_as_cst(up1);
82 cst2 = isl_upoly_as_cst(up2);
85 return isl_int_eq(cst1->n, cst2->n) &&
86 isl_int_eq(cst1->d, cst2->d);
89 rec1 = isl_upoly_as_rec(up1);
90 rec2 = isl_upoly_as_rec(up2);
94 if (rec1->n != rec2->n)
97 for (i = 0; i < rec1->n; ++i) {
98 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
106 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
108 struct isl_upoly_cst *cst;
112 if (!isl_upoly_is_cst(up))
115 cst = isl_upoly_as_cst(up);
119 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
122 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
124 struct isl_upoly_cst *cst;
128 if (!isl_upoly_is_cst(up))
131 cst = isl_upoly_as_cst(up);
135 return isl_int_sgn(cst->n);
138 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
140 struct isl_upoly_cst *cst;
144 if (!isl_upoly_is_cst(up))
147 cst = isl_upoly_as_cst(up);
151 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
154 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
156 struct isl_upoly_cst *cst;
160 if (!isl_upoly_is_cst(up))
163 cst = isl_upoly_as_cst(up);
167 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
170 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
172 struct isl_upoly_cst *cst;
176 if (!isl_upoly_is_cst(up))
179 cst = isl_upoly_as_cst(up);
183 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
186 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
188 struct isl_upoly_cst *cst;
192 if (!isl_upoly_is_cst(up))
195 cst = isl_upoly_as_cst(up);
199 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
202 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
204 struct isl_upoly_cst *cst;
208 if (!isl_upoly_is_cst(up))
211 cst = isl_upoly_as_cst(up);
215 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
218 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
220 struct isl_upoly_cst *cst;
222 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
231 isl_int_init(cst->n);
232 isl_int_init(cst->d);
237 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
239 struct isl_upoly_cst *cst;
241 cst = isl_upoly_cst_alloc(ctx);
245 isl_int_set_si(cst->n, 0);
246 isl_int_set_si(cst->d, 1);
251 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
253 struct isl_upoly_cst *cst;
255 cst = isl_upoly_cst_alloc(ctx);
259 isl_int_set_si(cst->n, 1);
260 isl_int_set_si(cst->d, 1);
265 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
267 struct isl_upoly_cst *cst;
269 cst = isl_upoly_cst_alloc(ctx);
273 isl_int_set_si(cst->n, 1);
274 isl_int_set_si(cst->d, 0);
279 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
281 struct isl_upoly_cst *cst;
283 cst = isl_upoly_cst_alloc(ctx);
287 isl_int_set_si(cst->n, -1);
288 isl_int_set_si(cst->d, 0);
293 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
295 struct isl_upoly_cst *cst;
297 cst = isl_upoly_cst_alloc(ctx);
301 isl_int_set_si(cst->n, 0);
302 isl_int_set_si(cst->d, 0);
307 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
308 isl_int n, isl_int d)
310 struct isl_upoly_cst *cst;
312 cst = isl_upoly_cst_alloc(ctx);
316 isl_int_set(cst->n, n);
317 isl_int_set(cst->d, d);
322 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
325 struct isl_upoly_rec *rec;
327 isl_assert(ctx, var >= 0, return NULL);
328 isl_assert(ctx, size >= 0, return NULL);
329 rec = isl_calloc(ctx, struct isl_upoly_rec,
330 sizeof(struct isl_upoly_rec) +
331 size * sizeof(struct isl_upoly *));
346 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
347 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
349 qp = isl_qpolynomial_cow(qp);
353 isl_dim_free(qp->dim);
358 isl_qpolynomial_free(qp);
363 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
365 return qp ? qp->dim->ctx : NULL;
368 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
370 return qp ? isl_dim_copy(qp->dim) : NULL;
373 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
374 enum isl_dim_type type)
376 return qp ? isl_dim_size(qp->dim, type) : 0;
379 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
381 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
384 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
386 return qp ? isl_upoly_is_one(qp->upoly) : -1;
389 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
391 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
394 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
396 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
399 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
401 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
404 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
406 return qp ? isl_upoly_sgn(qp->upoly) : 0;
409 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
411 isl_int_clear(cst->n);
412 isl_int_clear(cst->d);
415 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
419 for (i = 0; i < rec->n; ++i)
420 isl_upoly_free(rec->p[i]);
423 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
432 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
434 struct isl_upoly_cst *cst;
435 struct isl_upoly_cst *dup;
437 cst = isl_upoly_as_cst(up);
441 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
444 isl_int_set(dup->n, cst->n);
445 isl_int_set(dup->d, cst->d);
450 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
453 struct isl_upoly_rec *rec;
454 struct isl_upoly_rec *dup;
456 rec = isl_upoly_as_rec(up);
460 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
464 for (i = 0; i < rec->n; ++i) {
465 dup->p[i] = isl_upoly_copy(rec->p[i]);
473 isl_upoly_free(&dup->up);
477 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
482 if (isl_upoly_is_cst(up))
483 return isl_upoly_dup_cst(up);
485 return isl_upoly_dup_rec(up);
488 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
496 return isl_upoly_dup(up);
499 void isl_upoly_free(__isl_take struct isl_upoly *up)
508 upoly_free_cst((struct isl_upoly_cst *)up);
510 upoly_free_rec((struct isl_upoly_rec *)up);
512 isl_ctx_deref(up->ctx);
516 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
521 isl_int_gcd(gcd, cst->n, cst->d);
522 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
523 isl_int_divexact(cst->n, cst->n, gcd);
524 isl_int_divexact(cst->d, cst->d, gcd);
529 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
530 __isl_take struct isl_upoly *up2)
532 struct isl_upoly_cst *cst1;
533 struct isl_upoly_cst *cst2;
535 up1 = isl_upoly_cow(up1);
539 cst1 = isl_upoly_as_cst(up1);
540 cst2 = isl_upoly_as_cst(up2);
542 if (isl_int_eq(cst1->d, cst2->d))
543 isl_int_add(cst1->n, cst1->n, cst2->n);
545 isl_int_mul(cst1->n, cst1->n, cst2->d);
546 isl_int_addmul(cst1->n, cst2->n, cst1->d);
547 isl_int_mul(cst1->d, cst1->d, cst2->d);
550 isl_upoly_cst_reduce(cst1);
560 static __isl_give struct isl_upoly *replace_by_zero(
561 __isl_take struct isl_upoly *up)
569 return isl_upoly_zero(ctx);
572 static __isl_give struct isl_upoly *replace_by_constant_term(
573 __isl_take struct isl_upoly *up)
575 struct isl_upoly_rec *rec;
576 struct isl_upoly *cst;
581 rec = isl_upoly_as_rec(up);
584 cst = isl_upoly_copy(rec->p[0]);
592 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
593 __isl_take struct isl_upoly *up2)
596 struct isl_upoly_rec *rec1, *rec2;
601 if (isl_upoly_is_nan(up1)) {
606 if (isl_upoly_is_nan(up2)) {
611 if (isl_upoly_is_zero(up1)) {
616 if (isl_upoly_is_zero(up2)) {
621 if (up1->var < up2->var)
622 return isl_upoly_sum(up2, up1);
624 if (up2->var < up1->var) {
625 struct isl_upoly_rec *rec;
626 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
630 up1 = isl_upoly_cow(up1);
631 rec = isl_upoly_as_rec(up1);
634 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
636 up1 = replace_by_constant_term(up1);
640 if (isl_upoly_is_cst(up1))
641 return isl_upoly_sum_cst(up1, up2);
643 rec1 = isl_upoly_as_rec(up1);
644 rec2 = isl_upoly_as_rec(up2);
648 if (rec1->n < rec2->n)
649 return isl_upoly_sum(up2, up1);
651 up1 = isl_upoly_cow(up1);
652 rec1 = isl_upoly_as_rec(up1);
656 for (i = rec2->n - 1; i >= 0; --i) {
657 rec1->p[i] = isl_upoly_sum(rec1->p[i],
658 isl_upoly_copy(rec2->p[i]));
661 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
662 isl_upoly_free(rec1->p[i]);
668 up1 = replace_by_zero(up1);
669 else if (rec1->n == 1)
670 up1 = replace_by_constant_term(up1);
681 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
682 __isl_take struct isl_upoly *up, isl_int v)
684 struct isl_upoly_cst *cst;
686 up = isl_upoly_cow(up);
690 cst = isl_upoly_as_cst(up);
692 isl_int_addmul(cst->n, cst->d, v);
697 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
698 __isl_take struct isl_upoly *up, isl_int v)
700 struct isl_upoly_rec *rec;
705 if (isl_upoly_is_cst(up))
706 return isl_upoly_cst_add_isl_int(up, v);
708 up = isl_upoly_cow(up);
709 rec = isl_upoly_as_rec(up);
713 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
723 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
724 __isl_take struct isl_upoly *up, isl_int v)
726 struct isl_upoly_cst *cst;
728 if (isl_upoly_is_zero(up))
731 up = isl_upoly_cow(up);
735 cst = isl_upoly_as_cst(up);
737 isl_int_mul(cst->n, cst->n, v);
742 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
743 __isl_take struct isl_upoly *up, isl_int v)
746 struct isl_upoly_rec *rec;
751 if (isl_upoly_is_cst(up))
752 return isl_upoly_cst_mul_isl_int(up, v);
754 up = isl_upoly_cow(up);
755 rec = isl_upoly_as_rec(up);
759 for (i = 0; i < rec->n; ++i) {
760 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
771 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
772 __isl_take struct isl_upoly *up2)
774 struct isl_upoly_cst *cst1;
775 struct isl_upoly_cst *cst2;
777 up1 = isl_upoly_cow(up1);
781 cst1 = isl_upoly_as_cst(up1);
782 cst2 = isl_upoly_as_cst(up2);
784 isl_int_mul(cst1->n, cst1->n, cst2->n);
785 isl_int_mul(cst1->d, cst1->d, cst2->d);
787 isl_upoly_cst_reduce(cst1);
797 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
798 __isl_take struct isl_upoly *up2)
800 struct isl_upoly_rec *rec1;
801 struct isl_upoly_rec *rec2;
802 struct isl_upoly_rec *res = NULL;
806 rec1 = isl_upoly_as_rec(up1);
807 rec2 = isl_upoly_as_rec(up2);
810 size = rec1->n + rec2->n - 1;
811 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
815 for (i = 0; i < rec1->n; ++i) {
816 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
817 isl_upoly_copy(rec1->p[i]));
822 for (; i < size; ++i) {
823 res->p[i] = isl_upoly_zero(up1->ctx);
828 for (i = 0; i < rec1->n; ++i) {
829 for (j = 1; j < rec2->n; ++j) {
830 struct isl_upoly *up;
831 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
832 isl_upoly_copy(rec1->p[i]));
833 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
846 isl_upoly_free(&res->up);
850 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
851 __isl_take struct isl_upoly *up2)
856 if (isl_upoly_is_nan(up1)) {
861 if (isl_upoly_is_nan(up2)) {
866 if (isl_upoly_is_zero(up1)) {
871 if (isl_upoly_is_zero(up2)) {
876 if (isl_upoly_is_one(up1)) {
881 if (isl_upoly_is_one(up2)) {
886 if (up1->var < up2->var)
887 return isl_upoly_mul(up2, up1);
889 if (up2->var < up1->var) {
891 struct isl_upoly_rec *rec;
892 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
893 isl_ctx *ctx = up1->ctx;
896 return isl_upoly_nan(ctx);
898 up1 = isl_upoly_cow(up1);
899 rec = isl_upoly_as_rec(up1);
903 for (i = 0; i < rec->n; ++i) {
904 rec->p[i] = isl_upoly_mul(rec->p[i],
905 isl_upoly_copy(up2));
913 if (isl_upoly_is_cst(up1))
914 return isl_upoly_mul_cst(up1, up2);
916 return isl_upoly_mul_rec(up1, up2);
923 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
926 struct isl_upoly *res;
934 res = isl_upoly_copy(up);
936 res = isl_upoly_one(up->ctx);
938 while (power >>= 1) {
939 up = isl_upoly_mul(up, isl_upoly_copy(up));
941 res = isl_upoly_mul(res, isl_upoly_copy(up));
948 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
949 unsigned n_div, __isl_take struct isl_upoly *up)
951 struct isl_qpolynomial *qp = NULL;
957 total = isl_dim_total(dim);
959 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
964 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
975 isl_qpolynomial_free(qp);
979 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
988 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
990 struct isl_qpolynomial *dup;
995 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
996 isl_upoly_copy(qp->upoly));
999 isl_mat_free(dup->div);
1000 dup->div = isl_mat_copy(qp->div);
1006 isl_qpolynomial_free(dup);
1010 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1018 return isl_qpolynomial_dup(qp);
1021 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1029 isl_dim_free(qp->dim);
1030 isl_mat_free(qp->div);
1031 isl_upoly_free(qp->upoly);
1036 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
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_scale(
1423 __isl_take isl_qpolynomial *qp, isl_int v)
1425 return isl_qpolynomial_mul_isl_int(qp, v);
1428 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1429 __isl_take isl_qpolynomial *qp2)
1431 qp1 = isl_qpolynomial_cow(qp1);
1436 if (qp1->div->n_row < qp2->div->n_row)
1437 return isl_qpolynomial_mul(qp2, qp1);
1439 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1440 if (!compatible_divs(qp1->div, qp2->div))
1441 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1443 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1447 isl_qpolynomial_free(qp2);
1451 isl_qpolynomial_free(qp1);
1452 isl_qpolynomial_free(qp2);
1456 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1459 qp = isl_qpolynomial_cow(qp);
1464 qp->upoly = isl_upoly_pow(qp->upoly, power);
1470 isl_qpolynomial_free(qp);
1474 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
1475 __isl_take isl_pw_qpolynomial *pwqp, unsigned power)
1482 pwqp = isl_pw_qpolynomial_cow(pwqp);
1486 for (i = 0; i < pwqp->n; ++i) {
1487 pwqp->p[i].qp = isl_qpolynomial_pow(pwqp->p[i].qp, power);
1489 return isl_pw_qpolynomial_free(pwqp);
1495 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1499 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1502 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1506 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1509 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1513 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1516 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1520 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1523 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1527 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1530 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1533 struct isl_qpolynomial *qp;
1534 struct isl_upoly_cst *cst;
1539 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1543 cst = isl_upoly_as_cst(qp->upoly);
1544 isl_int_set(cst->n, v);
1549 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1550 isl_int *n, isl_int *d)
1552 struct isl_upoly_cst *cst;
1557 if (!isl_upoly_is_cst(qp->upoly))
1560 cst = isl_upoly_as_cst(qp->upoly);
1565 isl_int_set(*n, cst->n);
1567 isl_int_set(*d, cst->d);
1572 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1575 struct isl_upoly_rec *rec;
1583 rec = isl_upoly_as_rec(up);
1590 isl_assert(up->ctx, rec->n > 1, return -1);
1592 is_cst = isl_upoly_is_cst(rec->p[1]);
1598 return isl_upoly_is_affine(rec->p[0]);
1601 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1606 if (qp->div->n_row > 0)
1609 return isl_upoly_is_affine(qp->upoly);
1612 static void update_coeff(__isl_keep isl_vec *aff,
1613 __isl_keep struct isl_upoly_cst *cst, int pos)
1618 if (isl_int_is_zero(cst->n))
1623 isl_int_gcd(gcd, cst->d, aff->el[0]);
1624 isl_int_divexact(f, cst->d, gcd);
1625 isl_int_divexact(gcd, aff->el[0], gcd);
1626 isl_seq_scale(aff->el, aff->el, f, aff->size);
1627 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1632 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1633 __isl_keep isl_vec *aff)
1635 struct isl_upoly_cst *cst;
1636 struct isl_upoly_rec *rec;
1642 struct isl_upoly_cst *cst;
1644 cst = isl_upoly_as_cst(up);
1647 update_coeff(aff, cst, 0);
1651 rec = isl_upoly_as_rec(up);
1654 isl_assert(up->ctx, rec->n == 2, return -1);
1656 cst = isl_upoly_as_cst(rec->p[1]);
1659 update_coeff(aff, cst, 1 + up->var);
1661 return isl_upoly_update_affine(rec->p[0], aff);
1664 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1665 __isl_keep isl_qpolynomial *qp)
1673 d = isl_dim_total(qp->dim);
1674 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1678 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1679 isl_int_set_si(aff->el[0], 1);
1681 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1690 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1691 __isl_keep isl_qpolynomial *qp2)
1698 equal = isl_dim_equal(qp1->dim, qp2->dim);
1699 if (equal < 0 || !equal)
1702 equal = isl_mat_is_equal(qp1->div, qp2->div);
1703 if (equal < 0 || !equal)
1706 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1709 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1712 struct isl_upoly_rec *rec;
1714 if (isl_upoly_is_cst(up)) {
1715 struct isl_upoly_cst *cst;
1716 cst = isl_upoly_as_cst(up);
1719 isl_int_lcm(*d, *d, cst->d);
1723 rec = isl_upoly_as_rec(up);
1727 for (i = 0; i < rec->n; ++i)
1728 upoly_update_den(rec->p[i], d);
1731 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1733 isl_int_set_si(*d, 1);
1736 upoly_update_den(qp->upoly, d);
1739 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1742 struct isl_ctx *ctx;
1749 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1752 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1753 enum isl_dim_type type, unsigned pos)
1758 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1759 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1761 if (type == isl_dim_set)
1762 pos += isl_dim_size(dim, isl_dim_param);
1764 return isl_qpolynomial_var_pow(dim, pos, 1);
1770 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1771 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1774 struct isl_upoly_rec *rec;
1775 struct isl_upoly *base, *res;
1780 if (isl_upoly_is_cst(up))
1783 if (up->var < first)
1786 rec = isl_upoly_as_rec(up);
1790 isl_assert(up->ctx, rec->n >= 1, goto error);
1792 if (up->var >= first + n)
1793 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1795 base = isl_upoly_copy(subs[up->var - first]);
1797 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1798 for (i = rec->n - 2; i >= 0; --i) {
1799 struct isl_upoly *t;
1800 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1801 res = isl_upoly_mul(res, isl_upoly_copy(base));
1802 res = isl_upoly_sum(res, t);
1805 isl_upoly_free(base);
1814 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1815 isl_int denom, unsigned len)
1818 struct isl_upoly *up;
1820 isl_assert(ctx, len >= 1, return NULL);
1822 up = isl_upoly_rat_cst(ctx, f[0], denom);
1823 for (i = 0; i < len - 1; ++i) {
1824 struct isl_upoly *t;
1825 struct isl_upoly *c;
1827 if (isl_int_is_zero(f[1 + i]))
1830 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1831 t = isl_upoly_var_pow(ctx, i, 1);
1832 t = isl_upoly_mul(c, t);
1833 up = isl_upoly_sum(up, t);
1839 /* Remove common factor of non-constant terms and denominator.
1841 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1843 isl_ctx *ctx = qp->div->ctx;
1844 unsigned total = qp->div->n_col - 2;
1846 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1847 isl_int_gcd(ctx->normalize_gcd,
1848 ctx->normalize_gcd, qp->div->row[div][0]);
1849 if (isl_int_is_one(ctx->normalize_gcd))
1852 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1853 ctx->normalize_gcd, total);
1854 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1855 ctx->normalize_gcd);
1856 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1857 ctx->normalize_gcd);
1860 /* Replace the integer division identified by "div" by the polynomial "s".
1861 * The integer division is assumed not to appear in the definition
1862 * of any other integer divisions.
1864 static __isl_give isl_qpolynomial *substitute_div(
1865 __isl_take isl_qpolynomial *qp,
1866 int div, __isl_take struct isl_upoly *s)
1875 qp = isl_qpolynomial_cow(qp);
1879 total = isl_dim_total(qp->dim);
1880 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1884 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1887 for (i = 0; i < total + div; ++i)
1889 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1890 reordering[i] = i - 1;
1891 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1892 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1893 qp->upoly = reorder(qp->upoly, reordering);
1896 if (!qp->upoly || !qp->div)
1902 isl_qpolynomial_free(qp);
1907 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1908 * divisions because d is equal to 1 by their definition, i.e., e.
1910 static __isl_give isl_qpolynomial *substitute_non_divs(
1911 __isl_take isl_qpolynomial *qp)
1915 struct isl_upoly *s;
1920 total = isl_dim_total(qp->dim);
1921 for (i = 0; qp && i < qp->div->n_row; ++i) {
1922 if (!isl_int_is_one(qp->div->row[i][0]))
1924 for (j = i + 1; j < qp->div->n_row; ++j) {
1925 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1927 isl_seq_combine(qp->div->row[j] + 1,
1928 qp->div->ctx->one, qp->div->row[j] + 1,
1929 qp->div->row[j][2 + total + i],
1930 qp->div->row[i] + 1, 1 + total + i);
1931 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1932 normalize_div(qp, j);
1934 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1935 qp->div->row[i][0], qp->div->n_col - 1);
1936 qp = substitute_div(qp, i, s);
1943 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1944 * with d the denominator. When replacing the coefficient e of x by
1945 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1946 * inside the division, so we need to add floor(e/d) * x outside.
1947 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1948 * to adjust the coefficient of x in each later div that depends on the
1949 * current div "div" and also in the affine expression "aff"
1950 * (if it too depends on "div").
1952 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1953 __isl_keep isl_vec *aff)
1957 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1960 for (i = 0; i < 1 + total + div; ++i) {
1961 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1962 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1964 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1965 isl_int_fdiv_r(qp->div->row[div][1 + i],
1966 qp->div->row[div][1 + i], qp->div->row[div][0]);
1967 if (!isl_int_is_zero(aff->el[1 + total + div]))
1968 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1969 for (j = div + 1; j < qp->div->n_row; ++j) {
1970 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1972 isl_int_addmul(qp->div->row[j][1 + i],
1973 v, qp->div->row[j][2 + total + div]);
1979 /* Check if the last non-zero coefficient is bigger that half of the
1980 * denominator. If so, we will invert the div to further reduce the number
1981 * of distinct divs that may appear.
1982 * If the last non-zero coefficient is exactly half the denominator,
1983 * then we continue looking for earlier coefficients that are bigger
1984 * than half the denominator.
1986 static int needs_invert(__isl_keep isl_mat *div, int row)
1991 for (i = div->n_col - 1; i >= 1; --i) {
1992 if (isl_int_is_zero(div->row[row][i]))
1994 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1995 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1996 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
2006 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2007 * We only invert the coefficients of e (and the coefficient of q in
2008 * later divs and in "aff"). After calling this function, the
2009 * coefficients of e should be reduced again.
2011 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
2012 __isl_keep isl_vec *aff)
2014 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2016 isl_seq_neg(qp->div->row[div] + 1,
2017 qp->div->row[div] + 1, qp->div->n_col - 1);
2018 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2019 isl_int_add(qp->div->row[div][1],
2020 qp->div->row[div][1], qp->div->row[div][0]);
2021 if (!isl_int_is_zero(aff->el[1 + total + div]))
2022 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2023 isl_mat_col_mul(qp->div, 2 + total + div,
2024 qp->div->ctx->negone, 2 + total + div);
2027 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2028 * in the interval [0, d-1], with d the denominator and such that the
2029 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2031 * After the reduction, some divs may have become redundant or identical,
2032 * so we call substitute_non_divs and sort_divs. If these functions
2033 * eliminate divs or merge two or more divs into one, the coefficients
2034 * of the enclosing divs may have to be reduced again, so we call
2035 * ourselves recursively if the number of divs decreases.
2037 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2040 isl_vec *aff = NULL;
2041 struct isl_upoly *s;
2047 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2048 aff = isl_vec_clr(aff);
2052 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2054 for (i = 0; i < qp->div->n_row; ++i) {
2055 normalize_div(qp, i);
2056 reduce_div(qp, i, aff);
2057 if (needs_invert(qp->div, i)) {
2058 invert_div(qp, i, aff);
2059 reduce_div(qp, i, aff);
2063 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2064 qp->div->ctx->one, aff->size);
2065 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2072 n_div = qp->div->n_row;
2073 qp = substitute_non_divs(qp);
2075 if (qp && qp->div->n_row < n_div)
2076 return reduce_divs(qp);
2080 isl_qpolynomial_free(qp);
2085 /* Assumes each div only depends on earlier divs.
2087 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2090 struct isl_qpolynomial *qp = NULL;
2091 struct isl_upoly_rec *rec;
2092 struct isl_upoly_cst *cst;
2099 d = div->line - div->bmap->div;
2101 pos = isl_dim_total(div->bmap->dim) + d;
2102 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2103 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2104 div->bmap->n_div, &rec->up);
2108 for (i = 0; i < div->bmap->n_div; ++i)
2109 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2111 for (i = 0; i < 1 + power; ++i) {
2112 rec->p[i] = isl_upoly_zero(div->ctx);
2117 cst = isl_upoly_as_cst(rec->p[power]);
2118 isl_int_set_si(cst->n, 1);
2122 qp = reduce_divs(qp);
2126 isl_qpolynomial_free(qp);
2131 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2133 return isl_qpolynomial_div_pow(div, 1);
2136 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2137 const isl_int n, const isl_int d)
2139 struct isl_qpolynomial *qp;
2140 struct isl_upoly_cst *cst;
2142 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2146 cst = isl_upoly_as_cst(qp->upoly);
2147 isl_int_set(cst->n, n);
2148 isl_int_set(cst->d, d);
2153 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2155 struct isl_upoly_rec *rec;
2161 if (isl_upoly_is_cst(up))
2165 active[up->var] = 1;
2167 rec = isl_upoly_as_rec(up);
2168 for (i = 0; i < rec->n; ++i)
2169 if (up_set_active(rec->p[i], active, d) < 0)
2175 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2178 int d = isl_dim_total(qp->dim);
2183 for (i = 0; i < d; ++i)
2184 for (j = 0; j < qp->div->n_row; ++j) {
2185 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2191 return up_set_active(qp->upoly, active, d);
2194 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2195 enum isl_dim_type type, unsigned first, unsigned n)
2206 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2208 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2209 type == isl_dim_set, return -1);
2211 active = isl_calloc_array(qp->dim->ctx, int, isl_dim_total(qp->dim));
2212 if (set_active(qp, active) < 0)
2215 if (type == isl_dim_set)
2216 first += isl_dim_size(qp->dim, isl_dim_param);
2217 for (i = 0; i < n; ++i)
2218 if (active[first + i]) {
2231 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2232 * of the divs that do appear in the quasi-polynomial.
2234 static __isl_give isl_qpolynomial *remove_redundant_divs(
2235 __isl_take isl_qpolynomial *qp)
2242 int *reordering = NULL;
2249 if (qp->div->n_row == 0)
2252 d = isl_dim_total(qp->dim);
2253 len = qp->div->n_col - 2;
2254 ctx = isl_qpolynomial_get_ctx(qp);
2255 active = isl_calloc_array(ctx, int, len);
2259 if (up_set_active(qp->upoly, active, len) < 0)
2262 for (i = qp->div->n_row - 1; i >= 0; --i) {
2263 if (!active[d + i]) {
2267 for (j = 0; j < i; ++j) {
2268 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2280 reordering = isl_alloc_array(qp->div->ctx, int, len);
2284 for (i = 0; i < d; ++i)
2288 n_div = qp->div->n_row;
2289 for (i = 0; i < n_div; ++i) {
2290 if (!active[d + i]) {
2291 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2292 qp->div = isl_mat_drop_cols(qp->div,
2293 2 + d + i - skip, 1);
2296 reordering[d + i] = d + i - skip;
2299 qp->upoly = reorder(qp->upoly, reordering);
2301 if (!qp->upoly || !qp->div)
2311 isl_qpolynomial_free(qp);
2315 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2316 unsigned first, unsigned n)
2319 struct isl_upoly_rec *rec;
2323 if (n == 0 || up->var < 0 || up->var < first)
2325 if (up->var < first + n) {
2326 up = replace_by_constant_term(up);
2327 return isl_upoly_drop(up, first, n);
2329 up = isl_upoly_cow(up);
2333 rec = isl_upoly_as_rec(up);
2337 for (i = 0; i < rec->n; ++i) {
2338 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2349 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2350 __isl_take isl_qpolynomial *qp,
2351 enum isl_dim_type type, unsigned pos, const char *s)
2353 qp = isl_qpolynomial_cow(qp);
2356 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2361 isl_qpolynomial_free(qp);
2365 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2366 __isl_take isl_qpolynomial *qp,
2367 enum isl_dim_type type, unsigned first, unsigned n)
2371 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2374 qp = isl_qpolynomial_cow(qp);
2378 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2380 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2381 type == isl_dim_set, goto error);
2383 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2387 if (type == isl_dim_set)
2388 first += isl_dim_size(qp->dim, isl_dim_param);
2390 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2394 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2400 isl_qpolynomial_free(qp);
2404 static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted(
2405 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2411 struct isl_upoly *up;
2415 if (eq->n_eq == 0) {
2416 isl_basic_set_free(eq);
2420 qp = isl_qpolynomial_cow(qp);
2423 qp->div = isl_mat_cow(qp->div);
2427 total = 1 + isl_dim_total(eq->dim);
2429 isl_int_init(denom);
2430 for (i = 0; i < eq->n_eq; ++i) {
2431 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2432 if (j < 0 || j == 0 || j >= total)
2435 for (k = 0; k < qp->div->n_row; ++k) {
2436 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2438 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2439 &qp->div->row[k][0]);
2440 normalize_div(qp, k);
2443 if (isl_int_is_pos(eq->eq[i][j]))
2444 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2445 isl_int_abs(denom, eq->eq[i][j]);
2446 isl_int_set_si(eq->eq[i][j], 0);
2448 up = isl_upoly_from_affine(qp->dim->ctx,
2449 eq->eq[i], denom, total);
2450 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2453 isl_int_clear(denom);
2458 isl_basic_set_free(eq);
2460 qp = substitute_non_divs(qp);
2465 isl_basic_set_free(eq);
2466 isl_qpolynomial_free(qp);
2470 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2472 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2473 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2477 if (qp->div->n_row > 0)
2478 eq = isl_basic_set_add(eq, isl_dim_set, qp->div->n_row);
2479 return isl_qpolynomial_substitute_equalities_lifted(qp, eq);
2481 isl_basic_set_free(eq);
2482 isl_qpolynomial_free(qp);
2486 static __isl_give isl_basic_set *add_div_constraints(
2487 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2495 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2498 total = isl_basic_set_total_dim(bset);
2499 for (i = 0; i < div->n_row; ++i)
2500 if (isl_basic_set_add_div_constraints_var(bset,
2501 total - div->n_row + i, div->row[i]) < 0)
2508 isl_basic_set_free(bset);
2512 /* Look for equalities among the variables shared by context and qp
2513 * and the integer divisions of qp, if any.
2514 * The equalities are then used to eliminate variables and/or integer
2515 * divisions from qp.
2517 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2518 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2524 if (qp->div->n_row > 0) {
2525 isl_basic_set *bset;
2526 context = isl_set_add_dims(context, isl_dim_set,
2528 bset = isl_basic_set_universe(isl_set_get_dim(context));
2529 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2530 context = isl_set_intersect(context,
2531 isl_set_from_basic_set(bset));
2534 aff = isl_set_affine_hull(context);
2535 return isl_qpolynomial_substitute_equalities_lifted(qp, aff);
2537 isl_qpolynomial_free(qp);
2538 isl_set_free(context);
2542 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2543 __isl_take isl_qpolynomial *qp)
2549 if (isl_qpolynomial_is_zero(qp)) {
2550 isl_dim *dim = isl_qpolynomial_get_dim(qp);
2551 isl_qpolynomial_free(qp);
2552 return isl_pw_qpolynomial_zero(dim);
2555 dom = isl_set_universe(isl_qpolynomial_get_dim(qp));
2556 return isl_pw_qpolynomial_alloc(dom, qp);
2560 #define PW isl_pw_qpolynomial
2562 #define EL isl_qpolynomial
2564 #define EL_IS_ZERO is_zero
2568 #define IS_ZERO is_zero
2572 #include <isl_pw_templ.c>
2575 #define UNION isl_union_pw_qpolynomial
2577 #define PART isl_pw_qpolynomial
2579 #define PARTS pw_qpolynomial
2581 #include <isl_union_templ.c>
2583 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2591 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2594 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2597 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2598 __isl_take isl_pw_qpolynomial *pwqp1,
2599 __isl_take isl_pw_qpolynomial *pwqp2)
2602 struct isl_pw_qpolynomial *res;
2604 if (!pwqp1 || !pwqp2)
2607 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2610 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2611 isl_pw_qpolynomial_free(pwqp2);
2615 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2616 isl_pw_qpolynomial_free(pwqp1);
2620 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2621 isl_pw_qpolynomial_free(pwqp1);
2625 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2626 isl_pw_qpolynomial_free(pwqp2);
2630 n = pwqp1->n * pwqp2->n;
2631 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2633 for (i = 0; i < pwqp1->n; ++i) {
2634 for (j = 0; j < pwqp2->n; ++j) {
2635 struct isl_set *common;
2636 struct isl_qpolynomial *prod;
2637 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2638 isl_set_copy(pwqp2->p[j].set));
2639 if (isl_set_plain_is_empty(common)) {
2640 isl_set_free(common);
2644 prod = isl_qpolynomial_mul(
2645 isl_qpolynomial_copy(pwqp1->p[i].qp),
2646 isl_qpolynomial_copy(pwqp2->p[j].qp));
2648 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2652 isl_pw_qpolynomial_free(pwqp1);
2653 isl_pw_qpolynomial_free(pwqp2);
2657 isl_pw_qpolynomial_free(pwqp1);
2658 isl_pw_qpolynomial_free(pwqp2);
2662 __isl_give struct isl_upoly *isl_upoly_eval(
2663 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2666 struct isl_upoly_rec *rec;
2667 struct isl_upoly *res;
2668 struct isl_upoly *base;
2670 if (isl_upoly_is_cst(up)) {
2675 rec = isl_upoly_as_rec(up);
2679 isl_assert(up->ctx, rec->n >= 1, goto error);
2681 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2683 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2686 for (i = rec->n - 2; i >= 0; --i) {
2687 res = isl_upoly_mul(res, isl_upoly_copy(base));
2688 res = isl_upoly_sum(res,
2689 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2690 isl_vec_copy(vec)));
2693 isl_upoly_free(base);
2703 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2704 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2707 struct isl_upoly *up;
2712 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2714 if (qp->div->n_row == 0)
2715 ext = isl_vec_copy(pnt->vec);
2718 unsigned dim = isl_dim_total(qp->dim);
2719 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2723 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2724 for (i = 0; i < qp->div->n_row; ++i) {
2725 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2726 1 + dim + i, &ext->el[1+dim+i]);
2727 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2728 qp->div->row[i][0]);
2732 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2736 dim = isl_dim_copy(qp->dim);
2737 isl_qpolynomial_free(qp);
2738 isl_point_free(pnt);
2740 return isl_qpolynomial_alloc(dim, 0, up);
2742 isl_qpolynomial_free(qp);
2743 isl_point_free(pnt);
2747 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2748 __isl_keep struct isl_upoly_cst *cst2)
2753 isl_int_mul(t, cst1->n, cst2->d);
2754 isl_int_submul(t, cst2->n, cst1->d);
2755 cmp = isl_int_sgn(t);
2760 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2761 __isl_keep isl_qpolynomial *qp2)
2763 struct isl_upoly_cst *cst1, *cst2;
2767 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2768 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2769 if (isl_qpolynomial_is_nan(qp1))
2771 if (isl_qpolynomial_is_nan(qp2))
2773 cst1 = isl_upoly_as_cst(qp1->upoly);
2774 cst2 = isl_upoly_as_cst(qp2->upoly);
2776 return isl_upoly_cmp(cst1, cst2) <= 0;
2779 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2780 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2782 struct isl_upoly_cst *cst1, *cst2;
2787 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2788 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2789 cst1 = isl_upoly_as_cst(qp1->upoly);
2790 cst2 = isl_upoly_as_cst(qp2->upoly);
2791 cmp = isl_upoly_cmp(cst1, cst2);
2794 isl_qpolynomial_free(qp2);
2796 isl_qpolynomial_free(qp1);
2801 isl_qpolynomial_free(qp1);
2802 isl_qpolynomial_free(qp2);
2806 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2807 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2809 struct isl_upoly_cst *cst1, *cst2;
2814 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2815 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2816 cst1 = isl_upoly_as_cst(qp1->upoly);
2817 cst2 = isl_upoly_as_cst(qp2->upoly);
2818 cmp = isl_upoly_cmp(cst1, cst2);
2821 isl_qpolynomial_free(qp2);
2823 isl_qpolynomial_free(qp1);
2828 isl_qpolynomial_free(qp1);
2829 isl_qpolynomial_free(qp2);
2833 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2834 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2835 unsigned first, unsigned n)
2841 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2844 qp = isl_qpolynomial_cow(qp);
2848 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2851 g_pos = pos(qp->dim, type) + first;
2853 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2857 total = qp->div->n_col - 2;
2858 if (total > g_pos) {
2860 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2863 for (i = 0; i < total - g_pos; ++i)
2865 qp->upoly = expand(qp->upoly, exp, g_pos);
2871 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2877 isl_qpolynomial_free(qp);
2881 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2882 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2886 pos = isl_qpolynomial_dim(qp, type);
2888 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2891 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2892 __isl_take isl_pw_qpolynomial *pwqp,
2893 enum isl_dim_type type, unsigned n)
2897 pos = isl_pw_qpolynomial_dim(pwqp, type);
2899 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2902 static int *reordering_move(isl_ctx *ctx,
2903 unsigned len, unsigned dst, unsigned src, unsigned n)
2908 reordering = isl_alloc_array(ctx, int, len);
2913 for (i = 0; i < dst; ++i)
2915 for (i = 0; i < n; ++i)
2916 reordering[src + i] = dst + i;
2917 for (i = 0; i < src - dst; ++i)
2918 reordering[dst + i] = dst + n + i;
2919 for (i = 0; i < len - src - n; ++i)
2920 reordering[src + n + i] = src + n + i;
2922 for (i = 0; i < src; ++i)
2924 for (i = 0; i < n; ++i)
2925 reordering[src + i] = dst + i;
2926 for (i = 0; i < dst - src; ++i)
2927 reordering[src + n + i] = src + i;
2928 for (i = 0; i < len - dst - n; ++i)
2929 reordering[dst + n + i] = dst + n + i;
2935 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2936 __isl_take isl_qpolynomial *qp,
2937 enum isl_dim_type dst_type, unsigned dst_pos,
2938 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2944 qp = isl_qpolynomial_cow(qp);
2948 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2951 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2952 g_src_pos = pos(qp->dim, src_type) + src_pos;
2953 if (dst_type > src_type)
2956 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2963 reordering = reordering_move(qp->dim->ctx,
2964 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2968 qp->upoly = reorder(qp->upoly, reordering);
2973 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2979 isl_qpolynomial_free(qp);
2983 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2984 isl_int *f, isl_int denom)
2986 struct isl_upoly *up;
2991 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2993 return isl_qpolynomial_alloc(dim, 0, up);
2996 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
2999 struct isl_upoly *up;
3000 isl_qpolynomial *qp;
3005 ctx = isl_aff_get_ctx(aff);
3006 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
3009 qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff),
3010 aff->ls->div->n_row, up);
3014 isl_mat_free(qp->div);
3015 qp->div = isl_mat_copy(aff->ls->div);
3016 qp->div = isl_mat_cow(qp->div);
3021 qp = reduce_divs(qp);
3022 qp = remove_redundant_divs(qp);
3029 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3030 __isl_take isl_pw_aff *pwaff)
3033 isl_pw_qpolynomial *pwqp;
3038 pwqp = isl_pw_qpolynomial_alloc_(isl_pw_aff_get_dim(pwaff), pwaff->n);
3040 for (i = 0; i < pwaff->n; ++i) {
3042 isl_qpolynomial *qp;
3044 dom = isl_set_copy(pwaff->p[i].set);
3045 qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff));
3046 pwqp = isl_pw_qpolynomial_add_piece(pwqp, dom, qp);
3049 isl_pw_aff_free(pwaff);
3053 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3054 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3058 aff = isl_constraint_get_bound(c, type, pos);
3059 isl_constraint_free(c);
3060 return isl_qpolynomial_from_aff(aff);
3063 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3064 * in "qp" by subs[i].
3066 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3067 __isl_take isl_qpolynomial *qp,
3068 enum isl_dim_type type, unsigned first, unsigned n,
3069 __isl_keep isl_qpolynomial **subs)
3072 struct isl_upoly **ups;
3077 qp = isl_qpolynomial_cow(qp);
3080 for (i = 0; i < n; ++i)
3084 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
3087 for (i = 0; i < n; ++i)
3088 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3091 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3092 for (i = 0; i < n; ++i)
3093 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3095 first += pos(qp->dim, type);
3097 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3100 for (i = 0; i < n; ++i)
3101 ups[i] = subs[i]->upoly;
3103 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3112 isl_qpolynomial_free(qp);
3116 /* Extend "bset" with extra set dimensions for each integer division
3117 * in "qp" and then call "fn" with the extended bset and the polynomial
3118 * that results from replacing each of the integer divisions by the
3119 * corresponding extra set dimension.
3121 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3122 __isl_keep isl_basic_set *bset,
3123 int (*fn)(__isl_take isl_basic_set *bset,
3124 __isl_take isl_qpolynomial *poly, void *user), void *user)
3128 isl_qpolynomial *poly;
3132 if (qp->div->n_row == 0)
3133 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3136 div = isl_mat_copy(qp->div);
3137 dim = isl_dim_copy(qp->dim);
3138 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3139 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3140 bset = isl_basic_set_copy(bset);
3141 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3142 bset = add_div_constraints(bset, div);
3144 return fn(bset, poly, user);
3149 /* Return total degree in variables first (inclusive) up to last (exclusive).
3151 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3155 struct isl_upoly_rec *rec;
3159 if (isl_upoly_is_zero(up))
3161 if (isl_upoly_is_cst(up) || up->var < first)
3164 rec = isl_upoly_as_rec(up);
3168 for (i = 0; i < rec->n; ++i) {
3171 if (isl_upoly_is_zero(rec->p[i]))
3173 d = isl_upoly_degree(rec->p[i], first, last);
3183 /* Return total degree in set variables.
3185 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3193 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3194 nvar = isl_dim_size(poly->dim, isl_dim_set);
3195 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3198 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3199 unsigned pos, int deg)
3202 struct isl_upoly_rec *rec;
3207 if (isl_upoly_is_cst(up) || up->var < pos) {
3209 return isl_upoly_copy(up);
3211 return isl_upoly_zero(up->ctx);
3214 rec = isl_upoly_as_rec(up);
3218 if (up->var == pos) {
3220 return isl_upoly_copy(rec->p[deg]);
3222 return isl_upoly_zero(up->ctx);
3225 up = isl_upoly_copy(up);
3226 up = isl_upoly_cow(up);
3227 rec = isl_upoly_as_rec(up);
3231 for (i = 0; i < rec->n; ++i) {
3232 struct isl_upoly *t;
3233 t = isl_upoly_coeff(rec->p[i], pos, deg);
3236 isl_upoly_free(rec->p[i]);
3246 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3248 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3249 __isl_keep isl_qpolynomial *qp,
3250 enum isl_dim_type type, unsigned t_pos, int deg)
3253 struct isl_upoly *up;
3259 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3262 g_pos = pos(qp->dim, type) + t_pos;
3263 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3265 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3268 isl_mat_free(c->div);
3269 c->div = isl_mat_copy(qp->div);
3274 isl_qpolynomial_free(c);
3278 /* Homogenize the polynomial in the variables first (inclusive) up to
3279 * last (exclusive) by inserting powers of variable first.
3280 * Variable first is assumed not to appear in the input.
3282 __isl_give struct isl_upoly *isl_upoly_homogenize(
3283 __isl_take struct isl_upoly *up, int deg, int target,
3284 int first, int last)
3287 struct isl_upoly_rec *rec;
3291 if (isl_upoly_is_zero(up))
3295 if (isl_upoly_is_cst(up) || up->var < first) {
3296 struct isl_upoly *hom;
3298 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3301 rec = isl_upoly_as_rec(hom);
3302 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3307 up = isl_upoly_cow(up);
3308 rec = isl_upoly_as_rec(up);
3312 for (i = 0; i < rec->n; ++i) {
3313 if (isl_upoly_is_zero(rec->p[i]))
3315 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3316 up->var < last ? deg + i : i, target,
3328 /* Homogenize the polynomial in the set variables by introducing
3329 * powers of an extra set variable at position 0.
3331 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3332 __isl_take isl_qpolynomial *poly)
3336 int deg = isl_qpolynomial_degree(poly);
3341 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3342 poly = isl_qpolynomial_cow(poly);
3346 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3347 nvar = isl_dim_size(poly->dim, isl_dim_set);
3348 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3355 isl_qpolynomial_free(poly);
3359 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3360 __isl_take isl_mat *div)
3368 n = isl_dim_total(dim) + div->n_row;
3370 term = isl_calloc(dim->ctx, struct isl_term,
3371 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3378 isl_int_init(term->n);
3379 isl_int_init(term->d);
3388 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3397 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3406 total = isl_dim_total(term->dim) + term->div->n_row;
3408 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3412 isl_int_set(dup->n, term->n);
3413 isl_int_set(dup->d, term->d);
3415 for (i = 0; i < total; ++i)
3416 dup->pow[i] = term->pow[i];
3421 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3429 return isl_term_dup(term);
3432 void isl_term_free(__isl_take isl_term *term)
3437 if (--term->ref > 0)
3440 isl_dim_free(term->dim);
3441 isl_mat_free(term->div);
3442 isl_int_clear(term->n);
3443 isl_int_clear(term->d);
3447 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3455 case isl_dim_out: return isl_dim_size(term->dim, type);
3456 case isl_dim_div: return term->div->n_row;
3457 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3462 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3464 return term ? term->dim->ctx : NULL;
3467 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3471 isl_int_set(*n, term->n);
3474 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3478 isl_int_set(*d, term->d);
3481 int isl_term_get_exp(__isl_keep isl_term *term,
3482 enum isl_dim_type type, unsigned pos)
3487 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3489 if (type >= isl_dim_set)
3490 pos += isl_dim_size(term->dim, isl_dim_param);
3491 if (type >= isl_dim_div)
3492 pos += isl_dim_size(term->dim, isl_dim_set);
3494 return term->pow[pos];
3497 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3499 isl_basic_map *bmap;
3506 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3509 total = term->div->n_col - term->div->n_row - 2;
3510 /* No nested divs for now */
3511 isl_assert(term->dim->ctx,
3512 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3513 term->div->n_row) == -1,
3516 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3517 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3520 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3522 return isl_basic_map_div(bmap, k);
3524 isl_basic_map_free(bmap);
3528 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3529 int (*fn)(__isl_take isl_term *term, void *user),
3530 __isl_take isl_term *term, void *user)
3533 struct isl_upoly_rec *rec;
3538 if (isl_upoly_is_zero(up))
3541 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3542 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3543 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3545 if (isl_upoly_is_cst(up)) {
3546 struct isl_upoly_cst *cst;
3547 cst = isl_upoly_as_cst(up);
3550 term = isl_term_cow(term);
3553 isl_int_set(term->n, cst->n);
3554 isl_int_set(term->d, cst->d);
3555 if (fn(isl_term_copy(term), user) < 0)
3560 rec = isl_upoly_as_rec(up);
3564 for (i = 0; i < rec->n; ++i) {
3565 term = isl_term_cow(term);
3568 term->pow[up->var] = i;
3569 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3573 term->pow[up->var] = 0;
3577 isl_term_free(term);
3581 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3582 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3589 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3593 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3595 isl_term_free(term);
3597 return term ? 0 : -1;
3600 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3602 struct isl_upoly *up;
3603 isl_qpolynomial *qp;
3609 n = isl_dim_total(term->dim) + term->div->n_row;
3611 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3612 for (i = 0; i < n; ++i) {
3615 up = isl_upoly_mul(up,
3616 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3619 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3622 isl_mat_free(qp->div);
3623 qp->div = isl_mat_copy(term->div);
3627 isl_term_free(term);
3630 isl_qpolynomial_free(qp);
3631 isl_term_free(term);
3635 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3636 __isl_take isl_dim *dim)
3645 if (isl_dim_equal(qp->dim, dim)) {
3650 qp = isl_qpolynomial_cow(qp);
3654 extra = isl_dim_size(dim, isl_dim_set) -
3655 isl_dim_size(qp->dim, isl_dim_set);
3656 total = isl_dim_total(qp->dim);
3657 if (qp->div->n_row) {
3660 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3663 for (i = 0; i < qp->div->n_row; ++i)
3665 qp->upoly = expand(qp->upoly, exp, total);
3670 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3673 for (i = 0; i < qp->div->n_row; ++i)
3674 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3676 isl_dim_free(qp->dim);
3682 isl_qpolynomial_free(qp);
3686 /* For each parameter or variable that does not appear in qp,
3687 * first eliminate the variable from all constraints and then set it to zero.
3689 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3690 __isl_keep isl_qpolynomial *qp)
3701 d = isl_dim_total(set->dim);
3702 active = isl_calloc_array(set->ctx, int, d);
3703 if (set_active(qp, active) < 0)
3706 for (i = 0; i < d; ++i)
3715 nparam = isl_dim_size(set->dim, isl_dim_param);
3716 nvar = isl_dim_size(set->dim, isl_dim_set);
3717 for (i = 0; i < nparam; ++i) {
3720 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3721 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3723 for (i = 0; i < nvar; ++i) {
3724 if (active[nparam + i])
3726 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3727 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3739 struct isl_opt_data {
3740 isl_qpolynomial *qp;
3742 isl_qpolynomial *opt;
3746 static int opt_fn(__isl_take isl_point *pnt, void *user)
3748 struct isl_opt_data *data = (struct isl_opt_data *)user;
3749 isl_qpolynomial *val;
3751 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3755 } else if (data->max) {
3756 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3758 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3764 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3765 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3767 struct isl_opt_data data = { NULL, 1, NULL, max };
3772 if (isl_upoly_is_cst(qp->upoly)) {
3777 set = fix_inactive(set, qp);
3780 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3784 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3787 isl_qpolynomial_free(qp);
3791 isl_qpolynomial_free(qp);
3792 isl_qpolynomial_free(data.opt);
3796 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3797 __isl_take isl_morph *morph)
3802 struct isl_upoly **subs;
3805 qp = isl_qpolynomial_cow(qp);
3810 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3812 n_sub = morph->inv->n_row - 1;
3813 if (morph->inv->n_row != morph->inv->n_col)
3814 n_sub += qp->div->n_row;
3815 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3819 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3820 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3821 morph->inv->row[0][0], morph->inv->n_col);
3822 if (morph->inv->n_row != morph->inv->n_col)
3823 for (i = 0; i < qp->div->n_row; ++i)
3824 subs[morph->inv->n_row - 1 + i] =
3825 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3827 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3829 for (i = 0; i < n_sub; ++i)
3830 isl_upoly_free(subs[i]);
3833 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3834 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3835 qp->div = isl_mat_product(qp->div, mat);
3836 isl_dim_free(qp->dim);
3837 qp->dim = isl_dim_copy(morph->ran->dim);
3839 if (!qp->upoly || !qp->div || !qp->dim)
3842 isl_morph_free(morph);
3846 isl_qpolynomial_free(qp);
3847 isl_morph_free(morph);
3851 static int neg_entry(void **entry, void *user)
3853 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3855 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3857 return *pwqp ? 0 : -1;
3860 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3861 __isl_take isl_union_pw_qpolynomial *upwqp)
3863 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3867 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3868 &neg_entry, NULL) < 0)
3873 isl_union_pw_qpolynomial_free(upwqp);
3877 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3878 __isl_take isl_union_pw_qpolynomial *upwqp1,
3879 __isl_take isl_union_pw_qpolynomial *upwqp2)
3881 return isl_union_pw_qpolynomial_add(upwqp1,
3882 isl_union_pw_qpolynomial_neg(upwqp2));
3885 static int mul_entry(void **entry, void *user)
3887 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3889 struct isl_hash_table_entry *entry2;
3890 isl_pw_qpolynomial *pwpq = *entry;
3893 hash = isl_dim_get_hash(pwpq->dim);
3894 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3895 hash, &has_dim, pwpq->dim, 0);
3899 pwpq = isl_pw_qpolynomial_copy(pwpq);
3900 pwpq = isl_pw_qpolynomial_mul(pwpq,
3901 isl_pw_qpolynomial_copy(entry2->data));
3903 empty = isl_pw_qpolynomial_is_zero(pwpq);
3905 isl_pw_qpolynomial_free(pwpq);
3909 isl_pw_qpolynomial_free(pwpq);
3913 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3918 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3919 __isl_take isl_union_pw_qpolynomial *upwqp1,
3920 __isl_take isl_union_pw_qpolynomial *upwqp2)
3922 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3925 /* Reorder the columns of the given div definitions according to the
3928 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3929 __isl_take isl_reordering *r)
3938 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3939 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3943 for (i = 0; i < div->n_row; ++i) {
3944 isl_seq_cpy(mat->row[i], div->row[i], 2);
3945 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3946 for (j = 0; j < r->len; ++j)
3947 isl_int_set(mat->row[i][2 + r->pos[j]],
3948 div->row[i][2 + j]);
3951 isl_reordering_free(r);
3955 isl_reordering_free(r);
3960 /* Reorder the dimension of "qp" according to the given reordering.
3962 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3963 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3965 qp = isl_qpolynomial_cow(qp);
3969 r = isl_reordering_extend(r, qp->div->n_row);
3973 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3977 qp->upoly = reorder(qp->upoly, r->pos);
3981 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3983 isl_reordering_free(r);
3986 isl_qpolynomial_free(qp);
3987 isl_reordering_free(r);
3991 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3992 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3997 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3998 isl_reordering *exp;
4000 model = isl_dim_drop(model, isl_dim_in,
4001 0, isl_dim_size(model, isl_dim_in));
4002 model = isl_dim_drop(model, isl_dim_out,
4003 0, isl_dim_size(model, isl_dim_out));
4004 exp = isl_parameter_alignment_reordering(qp->dim, model);
4005 exp = isl_reordering_extend_dim(exp,
4006 isl_qpolynomial_get_dim(qp));
4007 qp = isl_qpolynomial_realign(qp, exp);
4010 isl_dim_free(model);
4013 isl_dim_free(model);
4014 isl_qpolynomial_free(qp);
4018 struct isl_split_periods_data {
4020 isl_pw_qpolynomial *res;
4023 /* Create a slice where the integer division "div" has the fixed value "v".
4024 * In particular, if "div" refers to floor(f/m), then create a slice
4026 * m v <= f <= m v + (m - 1)
4031 * -f + m v + (m - 1) >= 0
4033 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
4034 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4037 isl_basic_set *bset = NULL;
4043 total = isl_dim_total(dim);
4044 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
4046 k = isl_basic_set_alloc_inequality(bset);
4049 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4050 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4052 k = isl_basic_set_alloc_inequality(bset);
4055 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4056 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4057 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4058 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4061 return isl_set_from_basic_set(bset);
4063 isl_basic_set_free(bset);
4068 static int split_periods(__isl_take isl_set *set,
4069 __isl_take isl_qpolynomial *qp, void *user);
4071 /* Create a slice of the domain "set" such that integer division "div"
4072 * has the fixed value "v" and add the results to data->res,
4073 * replacing the integer division by "v" in "qp".
4075 static int set_div(__isl_take isl_set *set,
4076 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4077 struct isl_split_periods_data *data)
4082 struct isl_upoly *cst;
4084 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
4085 set = isl_set_intersect(set, slice);
4090 total = isl_dim_total(qp->dim);
4092 for (i = div + 1; i < qp->div->n_row; ++i) {
4093 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4095 isl_int_addmul(qp->div->row[i][1],
4096 qp->div->row[i][2 + total + div], v);
4097 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4100 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4101 qp = substitute_div(qp, div, cst);
4103 return split_periods(set, qp, data);
4106 isl_qpolynomial_free(qp);
4110 /* Split the domain "set" such that integer division "div"
4111 * has a fixed value (ranging from "min" to "max") on each slice
4112 * and add the results to data->res.
4114 static int split_div(__isl_take isl_set *set,
4115 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4116 struct isl_split_periods_data *data)
4118 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4119 isl_set *set_i = isl_set_copy(set);
4120 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4122 if (set_div(set_i, qp_i, div, min, data) < 0)
4126 isl_qpolynomial_free(qp);
4130 isl_qpolynomial_free(qp);
4134 /* If "qp" refers to any integer division
4135 * that can only attain "max_periods" distinct values on "set"
4136 * then split the domain along those distinct values.
4137 * Add the results (or the original if no splitting occurs)
4140 static int split_periods(__isl_take isl_set *set,
4141 __isl_take isl_qpolynomial *qp, void *user)
4144 isl_pw_qpolynomial *pwqp;
4145 struct isl_split_periods_data *data;
4150 data = (struct isl_split_periods_data *)user;
4155 if (qp->div->n_row == 0) {
4156 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4157 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4163 total = isl_dim_total(qp->dim);
4164 for (i = 0; i < qp->div->n_row; ++i) {
4165 enum isl_lp_result lp_res;
4167 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4168 qp->div->n_row) != -1)
4171 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4172 set->ctx->one, &min, NULL, NULL);
4173 if (lp_res == isl_lp_error)
4175 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4177 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4179 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4180 set->ctx->one, &max, NULL, NULL);
4181 if (lp_res == isl_lp_error)
4183 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4185 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4187 isl_int_sub(max, max, min);
4188 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4189 isl_int_add(max, max, min);
4194 if (i < qp->div->n_row) {
4195 r = split_div(set, qp, i, min, max, data);
4197 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4198 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4210 isl_qpolynomial_free(qp);
4214 /* If any quasi-polynomial in pwqp refers to any integer division
4215 * that can only attain "max_periods" distinct values on its domain
4216 * then split the domain along those distinct values.
4218 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4219 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4221 struct isl_split_periods_data data;
4223 data.max_periods = max_periods;
4224 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4226 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4229 isl_pw_qpolynomial_free(pwqp);
4233 isl_pw_qpolynomial_free(data.res);
4234 isl_pw_qpolynomial_free(pwqp);
4238 /* Construct a piecewise quasipolynomial that is constant on the given
4239 * domain. In particular, it is
4242 * infinity if cst == -1
4244 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4245 __isl_take isl_basic_set *bset, int cst)
4248 isl_qpolynomial *qp;
4253 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4254 dim = isl_basic_set_get_dim(bset);
4256 qp = isl_qpolynomial_infty(dim);
4258 qp = isl_qpolynomial_zero(dim);
4260 qp = isl_qpolynomial_one(dim);
4261 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4264 /* Factor bset, call fn on each of the factors and return the product.
4266 * If no factors can be found, simply call fn on the input.
4267 * Otherwise, construct the factors based on the factorizer,
4268 * call fn on each factor and compute the product.
4270 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4271 __isl_take isl_basic_set *bset,
4272 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4278 isl_qpolynomial *qp;
4279 isl_pw_qpolynomial *pwqp;
4283 f = isl_basic_set_factorizer(bset);
4286 if (f->n_group == 0) {
4287 isl_factorizer_free(f);
4291 nparam = isl_basic_set_dim(bset, isl_dim_param);
4292 nvar = isl_basic_set_dim(bset, isl_dim_set);
4294 dim = isl_basic_set_get_dim(bset);
4295 dim = isl_dim_domain(dim);
4296 set = isl_set_universe(isl_dim_copy(dim));
4297 qp = isl_qpolynomial_one(dim);
4298 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4300 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4302 for (i = 0, n = 0; i < f->n_group; ++i) {
4303 isl_basic_set *bset_i;
4304 isl_pw_qpolynomial *pwqp_i;
4306 bset_i = isl_basic_set_copy(bset);
4307 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4308 nparam + n + f->len[i], nvar - n - f->len[i]);
4309 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4311 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4312 n + f->len[i], nvar - n - f->len[i]);
4313 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4315 pwqp_i = fn(bset_i);
4316 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4321 isl_basic_set_free(bset);
4322 isl_factorizer_free(f);
4326 isl_basic_set_free(bset);
4330 /* Factor bset, call fn on each of the factors and return the product.
4331 * The function is assumed to evaluate to zero on empty domains,
4332 * to one on zero-dimensional domains and to infinity on unbounded domains
4333 * and will not be called explicitly on zero-dimensional or unbounded domains.
4335 * We first check for some special cases and remove all equalities.
4336 * Then we hand over control to compressed_multiplicative_call.
4338 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4339 __isl_take isl_basic_set *bset,
4340 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4344 isl_pw_qpolynomial *pwqp;
4345 unsigned orig_nvar, final_nvar;
4350 if (isl_basic_set_plain_is_empty(bset))
4351 return constant_on_domain(bset, 0);
4353 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4356 return constant_on_domain(bset, 1);
4358 bounded = isl_basic_set_is_bounded(bset);
4362 return constant_on_domain(bset, -1);
4364 if (bset->n_eq == 0)
4365 return compressed_multiplicative_call(bset, fn);
4367 morph = isl_basic_set_full_compression(bset);
4368 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4370 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4372 pwqp = compressed_multiplicative_call(bset, fn);
4374 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4375 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4376 morph = isl_morph_inverse(morph);
4378 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4382 isl_basic_set_free(bset);
4386 /* Drop all floors in "qp", turning each integer division [a/m] into
4387 * a rational division a/m. If "down" is set, then the integer division
4388 * is replaces by (a-(m-1))/m instead.
4390 static __isl_give isl_qpolynomial *qp_drop_floors(
4391 __isl_take isl_qpolynomial *qp, int down)
4394 struct isl_upoly *s;
4398 if (qp->div->n_row == 0)
4401 qp = isl_qpolynomial_cow(qp);
4405 for (i = qp->div->n_row - 1; i >= 0; --i) {
4407 isl_int_sub(qp->div->row[i][1],
4408 qp->div->row[i][1], qp->div->row[i][0]);
4409 isl_int_add_ui(qp->div->row[i][1],
4410 qp->div->row[i][1], 1);
4412 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4413 qp->div->row[i][0], qp->div->n_col - 1);
4414 qp = substitute_div(qp, i, s);
4422 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4423 * a rational division a/m.
4425 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4426 __isl_take isl_pw_qpolynomial *pwqp)
4433 if (isl_pw_qpolynomial_is_zero(pwqp))
4436 pwqp = isl_pw_qpolynomial_cow(pwqp);
4440 for (i = 0; i < pwqp->n; ++i) {
4441 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4448 isl_pw_qpolynomial_free(pwqp);
4452 /* Adjust all the integer divisions in "qp" such that they are at least
4453 * one over the given orthant (identified by "signs"). This ensures
4454 * that they will still be non-negative even after subtracting (m-1)/m.
4456 * In particular, f is replaced by f' + v, changing f = [a/m]
4457 * to f' = [(a - m v)/m].
4458 * If the constant term k in a is smaller than m,
4459 * the constant term of v is set to floor(k/m) - 1.
4460 * For any other term, if the coefficient c and the variable x have
4461 * the same sign, then no changes are needed.
4462 * Otherwise, if the variable is positive (and c is negative),
4463 * then the coefficient of x in v is set to floor(c/m).
4464 * If the variable is negative (and c is positive),
4465 * then the coefficient of x in v is set to ceil(c/m).
4467 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4473 struct isl_upoly *s;
4475 qp = isl_qpolynomial_cow(qp);
4478 qp->div = isl_mat_cow(qp->div);
4482 total = isl_dim_total(qp->dim);
4483 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4485 for (i = 0; i < qp->div->n_row; ++i) {
4486 isl_int *row = qp->div->row[i];
4490 if (isl_int_lt(row[1], row[0])) {
4491 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4492 isl_int_sub_ui(v->el[0], v->el[0], 1);
4493 isl_int_submul(row[1], row[0], v->el[0]);
4495 for (j = 0; j < total; ++j) {
4496 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4499 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4501 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4502 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4504 for (j = 0; j < i; ++j) {
4505 if (isl_int_sgn(row[2 + total + j]) >= 0)
4507 isl_int_fdiv_q(v->el[1 + total + j],
4508 row[2 + total + j], row[0]);
4509 isl_int_submul(row[2 + total + j],
4510 row[0], v->el[1 + total + j]);
4512 for (j = i + 1; j < qp->div->n_row; ++j) {
4513 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4515 isl_seq_combine(qp->div->row[j] + 1,
4516 qp->div->ctx->one, qp->div->row[j] + 1,
4517 qp->div->row[j][2 + total + i], v->el, v->size);
4519 isl_int_set_si(v->el[1 + total + i], 1);
4520 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4521 qp->div->ctx->one, v->size);
4522 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4532 isl_qpolynomial_free(qp);
4536 struct isl_to_poly_data {
4538 isl_pw_qpolynomial *res;
4539 isl_qpolynomial *qp;
4542 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4543 * We first make all integer divisions positive and then split the
4544 * quasipolynomials into terms with sign data->sign (the direction
4545 * of the requested approximation) and terms with the opposite sign.
4546 * In the first set of terms, each integer division [a/m] is
4547 * overapproximated by a/m, while in the second it is underapproximated
4550 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4553 struct isl_to_poly_data *data = user;
4554 isl_pw_qpolynomial *t;
4555 isl_qpolynomial *qp, *up, *down;
4557 qp = isl_qpolynomial_copy(data->qp);
4558 qp = make_divs_pos(qp, signs);
4560 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4561 up = qp_drop_floors(up, 0);
4562 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4563 down = qp_drop_floors(down, 1);
4565 isl_qpolynomial_free(qp);
4566 qp = isl_qpolynomial_add(up, down);
4568 t = isl_pw_qpolynomial_alloc(orthant, qp);
4569 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4574 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4575 * the polynomial will be an overapproximation. If "sign" is negative,
4576 * it will be an underapproximation. If "sign" is zero, the approximation
4577 * will lie somewhere in between.
4579 * In particular, is sign == 0, we simply drop the floors, turning
4580 * the integer divisions into rational divisions.
4581 * Otherwise, we split the domains into orthants, make all integer divisions
4582 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4583 * depending on the requested sign and the sign of the term in which
4584 * the integer division appears.
4586 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4587 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4590 struct isl_to_poly_data data;
4593 return pwqp_drop_floors(pwqp);
4599 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4601 for (i = 0; i < pwqp->n; ++i) {
4602 if (pwqp->p[i].qp->div->n_row == 0) {
4603 isl_pw_qpolynomial *t;
4604 t = isl_pw_qpolynomial_alloc(
4605 isl_set_copy(pwqp->p[i].set),
4606 isl_qpolynomial_copy(pwqp->p[i].qp));
4607 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4610 data.qp = pwqp->p[i].qp;
4611 if (isl_set_foreach_orthant(pwqp->p[i].set,
4612 &to_polynomial_on_orthant, &data) < 0)
4616 isl_pw_qpolynomial_free(pwqp);
4620 isl_pw_qpolynomial_free(pwqp);
4621 isl_pw_qpolynomial_free(data.res);
4625 static int poly_entry(void **entry, void *user)
4628 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4630 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4632 return *pwqp ? 0 : -1;
4635 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4636 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4638 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4642 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4643 &poly_entry, &sign) < 0)
4648 isl_union_pw_qpolynomial_free(upwqp);
4652 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4653 __isl_take isl_qpolynomial *qp)
4657 isl_vec *aff = NULL;
4658 isl_basic_map *bmap = NULL;
4664 if (!isl_upoly_is_affine(qp->upoly))
4665 isl_die(qp->dim->ctx, isl_error_invalid,
4666 "input quasi-polynomial not affine", goto error);
4667 aff = isl_qpolynomial_extract_affine(qp);
4670 dim = isl_qpolynomial_get_dim(qp);
4671 dim = isl_dim_from_domain(dim);
4672 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4673 dim = isl_dim_add(dim, isl_dim_out, 1);
4674 n_div = qp->div->n_row;
4675 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4677 for (i = 0; i < n_div; ++i) {
4678 k = isl_basic_map_alloc_div(bmap);
4681 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4682 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4683 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4686 k = isl_basic_map_alloc_equality(bmap);
4689 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4690 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4691 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4694 isl_qpolynomial_free(qp);
4695 bmap = isl_basic_map_finalize(bmap);
4699 isl_qpolynomial_free(qp);
4700 isl_basic_map_free(bmap);