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,
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_factorization.h>
18 #include <isl_union_map_private.h>
19 #include <isl_constraint_private.h>
20 #include <isl_polynomial_private.h>
21 #include <isl_point_private.h>
22 #include <isl_space_private.h>
23 #include <isl_div_private.h>
24 #include <isl_mat_private.h>
25 #include <isl_range.h>
26 #include <isl_local_space_private.h>
27 #include <isl_aff_private.h>
28 #include <isl_config.h>
30 static unsigned pos(__isl_keep isl_space *dim, enum isl_dim_type type)
33 case isl_dim_param: return 0;
34 case isl_dim_in: return dim->nparam;
35 case isl_dim_out: return dim->nparam + dim->n_in;
40 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
48 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
53 isl_assert(up->ctx, up->var < 0, return NULL);
55 return (struct isl_upoly_cst *)up;
58 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
63 isl_assert(up->ctx, up->var >= 0, return NULL);
65 return (struct isl_upoly_rec *)up;
68 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
69 __isl_keep struct isl_upoly *up2)
72 struct isl_upoly_rec *rec1, *rec2;
78 if (up1->var != up2->var)
80 if (isl_upoly_is_cst(up1)) {
81 struct isl_upoly_cst *cst1, *cst2;
82 cst1 = isl_upoly_as_cst(up1);
83 cst2 = isl_upoly_as_cst(up2);
86 return isl_int_eq(cst1->n, cst2->n) &&
87 isl_int_eq(cst1->d, cst2->d);
90 rec1 = isl_upoly_as_rec(up1);
91 rec2 = isl_upoly_as_rec(up2);
95 if (rec1->n != rec2->n)
98 for (i = 0; i < rec1->n; ++i) {
99 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
107 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
109 struct isl_upoly_cst *cst;
113 if (!isl_upoly_is_cst(up))
116 cst = isl_upoly_as_cst(up);
120 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
123 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
125 struct isl_upoly_cst *cst;
129 if (!isl_upoly_is_cst(up))
132 cst = isl_upoly_as_cst(up);
136 return isl_int_sgn(cst->n);
139 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
141 struct isl_upoly_cst *cst;
145 if (!isl_upoly_is_cst(up))
148 cst = isl_upoly_as_cst(up);
152 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
155 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
157 struct isl_upoly_cst *cst;
161 if (!isl_upoly_is_cst(up))
164 cst = isl_upoly_as_cst(up);
168 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
171 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
173 struct isl_upoly_cst *cst;
177 if (!isl_upoly_is_cst(up))
180 cst = isl_upoly_as_cst(up);
184 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
187 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
189 struct isl_upoly_cst *cst;
193 if (!isl_upoly_is_cst(up))
196 cst = isl_upoly_as_cst(up);
200 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
203 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
205 struct isl_upoly_cst *cst;
209 if (!isl_upoly_is_cst(up))
212 cst = isl_upoly_as_cst(up);
216 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
219 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
221 struct isl_upoly_cst *cst;
223 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
232 isl_int_init(cst->n);
233 isl_int_init(cst->d);
238 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
240 struct isl_upoly_cst *cst;
242 cst = isl_upoly_cst_alloc(ctx);
246 isl_int_set_si(cst->n, 0);
247 isl_int_set_si(cst->d, 1);
252 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
254 struct isl_upoly_cst *cst;
256 cst = isl_upoly_cst_alloc(ctx);
260 isl_int_set_si(cst->n, 1);
261 isl_int_set_si(cst->d, 1);
266 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
268 struct isl_upoly_cst *cst;
270 cst = isl_upoly_cst_alloc(ctx);
274 isl_int_set_si(cst->n, 1);
275 isl_int_set_si(cst->d, 0);
280 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
282 struct isl_upoly_cst *cst;
284 cst = isl_upoly_cst_alloc(ctx);
288 isl_int_set_si(cst->n, -1);
289 isl_int_set_si(cst->d, 0);
294 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
296 struct isl_upoly_cst *cst;
298 cst = isl_upoly_cst_alloc(ctx);
302 isl_int_set_si(cst->n, 0);
303 isl_int_set_si(cst->d, 0);
308 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
309 isl_int n, isl_int d)
311 struct isl_upoly_cst *cst;
313 cst = isl_upoly_cst_alloc(ctx);
317 isl_int_set(cst->n, n);
318 isl_int_set(cst->d, d);
323 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
326 struct isl_upoly_rec *rec;
328 isl_assert(ctx, var >= 0, return NULL);
329 isl_assert(ctx, size >= 0, return NULL);
330 rec = isl_calloc(ctx, struct isl_upoly_rec,
331 sizeof(struct isl_upoly_rec) +
332 size * sizeof(struct isl_upoly *));
347 __isl_give isl_qpolynomial *isl_qpolynomial_reset_space(
348 __isl_take isl_qpolynomial *qp, __isl_take isl_space *dim)
350 qp = isl_qpolynomial_cow(qp);
354 isl_space_free(qp->dim);
359 isl_qpolynomial_free(qp);
364 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
366 return qp ? qp->dim->ctx : NULL;
369 __isl_give isl_space *isl_qpolynomial_get_space(__isl_keep isl_qpolynomial *qp)
371 return qp ? isl_space_copy(qp->dim) : NULL;
374 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
375 enum isl_dim_type type)
377 return qp ? isl_space_dim(qp->dim, type) : 0;
380 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
382 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
385 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
387 return qp ? isl_upoly_is_one(qp->upoly) : -1;
390 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
392 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
395 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
397 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
400 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
402 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
405 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
407 return qp ? isl_upoly_sgn(qp->upoly) : 0;
410 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
412 isl_int_clear(cst->n);
413 isl_int_clear(cst->d);
416 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
420 for (i = 0; i < rec->n; ++i)
421 isl_upoly_free(rec->p[i]);
424 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
433 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
435 struct isl_upoly_cst *cst;
436 struct isl_upoly_cst *dup;
438 cst = isl_upoly_as_cst(up);
442 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
445 isl_int_set(dup->n, cst->n);
446 isl_int_set(dup->d, cst->d);
451 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
454 struct isl_upoly_rec *rec;
455 struct isl_upoly_rec *dup;
457 rec = isl_upoly_as_rec(up);
461 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
465 for (i = 0; i < rec->n; ++i) {
466 dup->p[i] = isl_upoly_copy(rec->p[i]);
474 isl_upoly_free(&dup->up);
478 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
483 if (isl_upoly_is_cst(up))
484 return isl_upoly_dup_cst(up);
486 return isl_upoly_dup_rec(up);
489 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
497 return isl_upoly_dup(up);
500 void isl_upoly_free(__isl_take struct isl_upoly *up)
509 upoly_free_cst((struct isl_upoly_cst *)up);
511 upoly_free_rec((struct isl_upoly_rec *)up);
513 isl_ctx_deref(up->ctx);
517 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
522 isl_int_gcd(gcd, cst->n, cst->d);
523 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
524 isl_int_divexact(cst->n, cst->n, gcd);
525 isl_int_divexact(cst->d, cst->d, gcd);
530 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
531 __isl_take struct isl_upoly *up2)
533 struct isl_upoly_cst *cst1;
534 struct isl_upoly_cst *cst2;
536 up1 = isl_upoly_cow(up1);
540 cst1 = isl_upoly_as_cst(up1);
541 cst2 = isl_upoly_as_cst(up2);
543 if (isl_int_eq(cst1->d, cst2->d))
544 isl_int_add(cst1->n, cst1->n, cst2->n);
546 isl_int_mul(cst1->n, cst1->n, cst2->d);
547 isl_int_addmul(cst1->n, cst2->n, cst1->d);
548 isl_int_mul(cst1->d, cst1->d, cst2->d);
551 isl_upoly_cst_reduce(cst1);
561 static __isl_give struct isl_upoly *replace_by_zero(
562 __isl_take struct isl_upoly *up)
570 return isl_upoly_zero(ctx);
573 static __isl_give struct isl_upoly *replace_by_constant_term(
574 __isl_take struct isl_upoly *up)
576 struct isl_upoly_rec *rec;
577 struct isl_upoly *cst;
582 rec = isl_upoly_as_rec(up);
585 cst = isl_upoly_copy(rec->p[0]);
593 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
594 __isl_take struct isl_upoly *up2)
597 struct isl_upoly_rec *rec1, *rec2;
602 if (isl_upoly_is_nan(up1)) {
607 if (isl_upoly_is_nan(up2)) {
612 if (isl_upoly_is_zero(up1)) {
617 if (isl_upoly_is_zero(up2)) {
622 if (up1->var < up2->var)
623 return isl_upoly_sum(up2, up1);
625 if (up2->var < up1->var) {
626 struct isl_upoly_rec *rec;
627 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
631 up1 = isl_upoly_cow(up1);
632 rec = isl_upoly_as_rec(up1);
635 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
637 up1 = replace_by_constant_term(up1);
641 if (isl_upoly_is_cst(up1))
642 return isl_upoly_sum_cst(up1, up2);
644 rec1 = isl_upoly_as_rec(up1);
645 rec2 = isl_upoly_as_rec(up2);
649 if (rec1->n < rec2->n)
650 return isl_upoly_sum(up2, up1);
652 up1 = isl_upoly_cow(up1);
653 rec1 = isl_upoly_as_rec(up1);
657 for (i = rec2->n - 1; i >= 0; --i) {
658 rec1->p[i] = isl_upoly_sum(rec1->p[i],
659 isl_upoly_copy(rec2->p[i]));
662 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
663 isl_upoly_free(rec1->p[i]);
669 up1 = replace_by_zero(up1);
670 else if (rec1->n == 1)
671 up1 = replace_by_constant_term(up1);
682 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
683 __isl_take struct isl_upoly *up, isl_int v)
685 struct isl_upoly_cst *cst;
687 up = isl_upoly_cow(up);
691 cst = isl_upoly_as_cst(up);
693 isl_int_addmul(cst->n, cst->d, v);
698 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
699 __isl_take struct isl_upoly *up, isl_int v)
701 struct isl_upoly_rec *rec;
706 if (isl_upoly_is_cst(up))
707 return isl_upoly_cst_add_isl_int(up, v);
709 up = isl_upoly_cow(up);
710 rec = isl_upoly_as_rec(up);
714 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
724 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
725 __isl_take struct isl_upoly *up, isl_int v)
727 struct isl_upoly_cst *cst;
729 if (isl_upoly_is_zero(up))
732 up = isl_upoly_cow(up);
736 cst = isl_upoly_as_cst(up);
738 isl_int_mul(cst->n, cst->n, v);
743 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
744 __isl_take struct isl_upoly *up, isl_int v)
747 struct isl_upoly_rec *rec;
752 if (isl_upoly_is_cst(up))
753 return isl_upoly_cst_mul_isl_int(up, v);
755 up = isl_upoly_cow(up);
756 rec = isl_upoly_as_rec(up);
760 for (i = 0; i < rec->n; ++i) {
761 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
772 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
773 __isl_take struct isl_upoly *up2)
775 struct isl_upoly_cst *cst1;
776 struct isl_upoly_cst *cst2;
778 up1 = isl_upoly_cow(up1);
782 cst1 = isl_upoly_as_cst(up1);
783 cst2 = isl_upoly_as_cst(up2);
785 isl_int_mul(cst1->n, cst1->n, cst2->n);
786 isl_int_mul(cst1->d, cst1->d, cst2->d);
788 isl_upoly_cst_reduce(cst1);
798 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
799 __isl_take struct isl_upoly *up2)
801 struct isl_upoly_rec *rec1;
802 struct isl_upoly_rec *rec2;
803 struct isl_upoly_rec *res = NULL;
807 rec1 = isl_upoly_as_rec(up1);
808 rec2 = isl_upoly_as_rec(up2);
811 size = rec1->n + rec2->n - 1;
812 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
816 for (i = 0; i < rec1->n; ++i) {
817 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
818 isl_upoly_copy(rec1->p[i]));
823 for (; i < size; ++i) {
824 res->p[i] = isl_upoly_zero(up1->ctx);
829 for (i = 0; i < rec1->n; ++i) {
830 for (j = 1; j < rec2->n; ++j) {
831 struct isl_upoly *up;
832 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
833 isl_upoly_copy(rec1->p[i]));
834 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
847 isl_upoly_free(&res->up);
851 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
852 __isl_take struct isl_upoly *up2)
857 if (isl_upoly_is_nan(up1)) {
862 if (isl_upoly_is_nan(up2)) {
867 if (isl_upoly_is_zero(up1)) {
872 if (isl_upoly_is_zero(up2)) {
877 if (isl_upoly_is_one(up1)) {
882 if (isl_upoly_is_one(up2)) {
887 if (up1->var < up2->var)
888 return isl_upoly_mul(up2, up1);
890 if (up2->var < up1->var) {
892 struct isl_upoly_rec *rec;
893 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
894 isl_ctx *ctx = up1->ctx;
897 return isl_upoly_nan(ctx);
899 up1 = isl_upoly_cow(up1);
900 rec = isl_upoly_as_rec(up1);
904 for (i = 0; i < rec->n; ++i) {
905 rec->p[i] = isl_upoly_mul(rec->p[i],
906 isl_upoly_copy(up2));
914 if (isl_upoly_is_cst(up1))
915 return isl_upoly_mul_cst(up1, up2);
917 return isl_upoly_mul_rec(up1, up2);
924 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
927 struct isl_upoly *res;
935 res = isl_upoly_copy(up);
937 res = isl_upoly_one(up->ctx);
939 while (power >>= 1) {
940 up = isl_upoly_mul(up, isl_upoly_copy(up));
942 res = isl_upoly_mul(res, isl_upoly_copy(up));
949 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_space *dim,
950 unsigned n_div, __isl_take struct isl_upoly *up)
952 struct isl_qpolynomial *qp = NULL;
958 total = isl_space_dim(dim, isl_dim_all);
960 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
965 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
976 isl_qpolynomial_free(qp);
980 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
989 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
991 struct isl_qpolynomial *dup;
996 dup = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row,
997 isl_upoly_copy(qp->upoly));
1000 isl_mat_free(dup->div);
1001 dup->div = isl_mat_copy(qp->div);
1007 isl_qpolynomial_free(dup);
1011 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1019 return isl_qpolynomial_dup(qp);
1022 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1030 isl_space_free(qp->dim);
1031 isl_mat_free(qp->div);
1032 isl_upoly_free(qp->upoly);
1038 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1041 struct isl_upoly_rec *rec;
1042 struct isl_upoly_cst *cst;
1044 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1047 for (i = 0; i < 1 + power; ++i) {
1048 rec->p[i] = isl_upoly_zero(ctx);
1053 cst = isl_upoly_as_cst(rec->p[power]);
1054 isl_int_set_si(cst->n, 1);
1058 isl_upoly_free(&rec->up);
1062 /* r array maps original positions to new positions.
1064 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1068 struct isl_upoly_rec *rec;
1069 struct isl_upoly *base;
1070 struct isl_upoly *res;
1072 if (isl_upoly_is_cst(up))
1075 rec = isl_upoly_as_rec(up);
1079 isl_assert(up->ctx, rec->n >= 1, goto error);
1081 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1082 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1084 for (i = rec->n - 2; i >= 0; --i) {
1085 res = isl_upoly_mul(res, isl_upoly_copy(base));
1086 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1089 isl_upoly_free(base);
1098 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1103 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1104 div1->n_col >= div2->n_col, return -1);
1106 if (div1->n_row == div2->n_row)
1107 return isl_mat_is_equal(div1, div2);
1109 n_row = div1->n_row;
1110 n_col = div1->n_col;
1111 div1->n_row = div2->n_row;
1112 div1->n_col = div2->n_col;
1114 equal = isl_mat_is_equal(div1, div2);
1116 div1->n_row = n_row;
1117 div1->n_col = n_col;
1122 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1126 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1127 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1132 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1135 struct isl_div_sort_info {
1140 static int div_sort_cmp(const void *p1, const void *p2)
1142 const struct isl_div_sort_info *i1, *i2;
1143 i1 = (const struct isl_div_sort_info *) p1;
1144 i2 = (const struct isl_div_sort_info *) p2;
1146 return cmp_row(i1->div, i1->row, i2->row);
1149 /* Sort divs and remove duplicates.
1151 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1156 struct isl_div_sort_info *array = NULL;
1157 int *pos = NULL, *at = NULL;
1158 int *reordering = NULL;
1163 if (qp->div->n_row <= 1)
1166 div_pos = isl_space_dim(qp->dim, isl_dim_all);
1168 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1170 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1171 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1172 len = qp->div->n_col - 2;
1173 reordering = isl_alloc_array(qp->div->ctx, int, len);
1174 if (!array || !pos || !at || !reordering)
1177 for (i = 0; i < qp->div->n_row; ++i) {
1178 array[i].div = qp->div;
1184 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1187 for (i = 0; i < div_pos; ++i)
1190 for (i = 0; i < qp->div->n_row; ++i) {
1191 if (pos[array[i].row] == i)
1193 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1194 pos[at[i]] = pos[array[i].row];
1195 at[pos[array[i].row]] = at[i];
1196 at[i] = array[i].row;
1197 pos[array[i].row] = i;
1201 for (i = 0; i < len - div_pos; ++i) {
1203 isl_seq_eq(qp->div->row[i - skip - 1],
1204 qp->div->row[i - skip], qp->div->n_col)) {
1205 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1206 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1207 2 + div_pos + i - skip);
1208 qp->div = isl_mat_drop_cols(qp->div,
1209 2 + div_pos + i - skip, 1);
1212 reordering[div_pos + array[i].row] = div_pos + i - skip;
1215 qp->upoly = reorder(qp->upoly, reordering);
1217 if (!qp->upoly || !qp->div)
1231 isl_qpolynomial_free(qp);
1235 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1236 int *exp, int first)
1239 struct isl_upoly_rec *rec;
1241 if (isl_upoly_is_cst(up))
1244 if (up->var < first)
1247 if (exp[up->var - first] == up->var - first)
1250 up = isl_upoly_cow(up);
1254 up->var = exp[up->var - first] + first;
1256 rec = isl_upoly_as_rec(up);
1260 for (i = 0; i < rec->n; ++i) {
1261 rec->p[i] = expand(rec->p[i], exp, first);
1272 static __isl_give isl_qpolynomial *with_merged_divs(
1273 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1274 __isl_take isl_qpolynomial *qp2),
1275 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1279 isl_mat *div = NULL;
1281 qp1 = isl_qpolynomial_cow(qp1);
1282 qp2 = isl_qpolynomial_cow(qp2);
1287 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1288 qp1->div->n_col >= qp2->div->n_col, goto error);
1290 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1291 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1295 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1299 isl_mat_free(qp1->div);
1300 qp1->div = isl_mat_copy(div);
1301 isl_mat_free(qp2->div);
1302 qp2->div = isl_mat_copy(div);
1304 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1305 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1307 if (!qp1->upoly || !qp2->upoly)
1314 return fn(qp1, qp2);
1319 isl_qpolynomial_free(qp1);
1320 isl_qpolynomial_free(qp2);
1324 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1325 __isl_take isl_qpolynomial *qp2)
1327 qp1 = isl_qpolynomial_cow(qp1);
1332 if (qp1->div->n_row < qp2->div->n_row)
1333 return isl_qpolynomial_add(qp2, qp1);
1335 isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1336 if (!compatible_divs(qp1->div, qp2->div))
1337 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1339 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1343 isl_qpolynomial_free(qp2);
1347 isl_qpolynomial_free(qp1);
1348 isl_qpolynomial_free(qp2);
1352 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1353 __isl_keep isl_set *dom,
1354 __isl_take isl_qpolynomial *qp1,
1355 __isl_take isl_qpolynomial *qp2)
1357 qp1 = isl_qpolynomial_add(qp1, qp2);
1358 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1362 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1363 __isl_take isl_qpolynomial *qp2)
1365 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1368 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1369 __isl_take isl_qpolynomial *qp, isl_int v)
1371 if (isl_int_is_zero(v))
1374 qp = isl_qpolynomial_cow(qp);
1378 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1384 isl_qpolynomial_free(qp);
1389 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1394 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1397 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1398 __isl_take isl_qpolynomial *qp, isl_int v)
1400 if (isl_int_is_one(v))
1403 if (qp && isl_int_is_zero(v)) {
1404 isl_qpolynomial *zero;
1405 zero = isl_qpolynomial_zero(isl_space_copy(qp->dim));
1406 isl_qpolynomial_free(qp);
1410 qp = isl_qpolynomial_cow(qp);
1414 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1420 isl_qpolynomial_free(qp);
1424 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
1425 __isl_take isl_qpolynomial *qp, isl_int v)
1427 return isl_qpolynomial_mul_isl_int(qp, v);
1430 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1431 __isl_take isl_qpolynomial *qp2)
1433 qp1 = isl_qpolynomial_cow(qp1);
1438 if (qp1->div->n_row < qp2->div->n_row)
1439 return isl_qpolynomial_mul(qp2, qp1);
1441 isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1442 if (!compatible_divs(qp1->div, qp2->div))
1443 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1445 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1449 isl_qpolynomial_free(qp2);
1453 isl_qpolynomial_free(qp1);
1454 isl_qpolynomial_free(qp2);
1458 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1461 qp = isl_qpolynomial_cow(qp);
1466 qp->upoly = isl_upoly_pow(qp->upoly, power);
1472 isl_qpolynomial_free(qp);
1476 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
1477 __isl_take isl_pw_qpolynomial *pwqp, unsigned power)
1484 pwqp = isl_pw_qpolynomial_cow(pwqp);
1488 for (i = 0; i < pwqp->n; ++i) {
1489 pwqp->p[i].qp = isl_qpolynomial_pow(pwqp->p[i].qp, power);
1491 return isl_pw_qpolynomial_free(pwqp);
1497 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_space *dim)
1501 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1504 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_space *dim)
1508 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1511 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_space *dim)
1515 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1518 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_space *dim)
1522 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1525 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_space *dim)
1529 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1532 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_space *dim,
1535 struct isl_qpolynomial *qp;
1536 struct isl_upoly_cst *cst;
1541 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1545 cst = isl_upoly_as_cst(qp->upoly);
1546 isl_int_set(cst->n, v);
1551 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1552 isl_int *n, isl_int *d)
1554 struct isl_upoly_cst *cst;
1559 if (!isl_upoly_is_cst(qp->upoly))
1562 cst = isl_upoly_as_cst(qp->upoly);
1567 isl_int_set(*n, cst->n);
1569 isl_int_set(*d, cst->d);
1574 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1577 struct isl_upoly_rec *rec;
1585 rec = isl_upoly_as_rec(up);
1592 isl_assert(up->ctx, rec->n > 1, return -1);
1594 is_cst = isl_upoly_is_cst(rec->p[1]);
1600 return isl_upoly_is_affine(rec->p[0]);
1603 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1608 if (qp->div->n_row > 0)
1611 return isl_upoly_is_affine(qp->upoly);
1614 static void update_coeff(__isl_keep isl_vec *aff,
1615 __isl_keep struct isl_upoly_cst *cst, int pos)
1620 if (isl_int_is_zero(cst->n))
1625 isl_int_gcd(gcd, cst->d, aff->el[0]);
1626 isl_int_divexact(f, cst->d, gcd);
1627 isl_int_divexact(gcd, aff->el[0], gcd);
1628 isl_seq_scale(aff->el, aff->el, f, aff->size);
1629 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1634 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1635 __isl_keep isl_vec *aff)
1637 struct isl_upoly_cst *cst;
1638 struct isl_upoly_rec *rec;
1644 struct isl_upoly_cst *cst;
1646 cst = isl_upoly_as_cst(up);
1649 update_coeff(aff, cst, 0);
1653 rec = isl_upoly_as_rec(up);
1656 isl_assert(up->ctx, rec->n == 2, return -1);
1658 cst = isl_upoly_as_cst(rec->p[1]);
1661 update_coeff(aff, cst, 1 + up->var);
1663 return isl_upoly_update_affine(rec->p[0], aff);
1666 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1667 __isl_keep isl_qpolynomial *qp)
1675 d = isl_space_dim(qp->dim, isl_dim_all);
1676 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1680 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1681 isl_int_set_si(aff->el[0], 1);
1683 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1692 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1693 __isl_keep isl_qpolynomial *qp2)
1700 equal = isl_space_is_equal(qp1->dim, qp2->dim);
1701 if (equal < 0 || !equal)
1704 equal = isl_mat_is_equal(qp1->div, qp2->div);
1705 if (equal < 0 || !equal)
1708 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1711 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1714 struct isl_upoly_rec *rec;
1716 if (isl_upoly_is_cst(up)) {
1717 struct isl_upoly_cst *cst;
1718 cst = isl_upoly_as_cst(up);
1721 isl_int_lcm(*d, *d, cst->d);
1725 rec = isl_upoly_as_rec(up);
1729 for (i = 0; i < rec->n; ++i)
1730 upoly_update_den(rec->p[i], d);
1733 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1735 isl_int_set_si(*d, 1);
1738 upoly_update_den(qp->upoly, d);
1741 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_space *dim,
1744 struct isl_ctx *ctx;
1751 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1754 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_space *dim,
1755 enum isl_dim_type type, unsigned pos)
1760 isl_assert(dim->ctx, isl_space_dim(dim, isl_dim_in) == 0, goto error);
1761 isl_assert(dim->ctx, pos < isl_space_dim(dim, type), goto error);
1763 if (type == isl_dim_set)
1764 pos += isl_space_dim(dim, isl_dim_param);
1766 return isl_qpolynomial_var_pow(dim, pos, 1);
1768 isl_space_free(dim);
1772 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1773 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1776 struct isl_upoly_rec *rec;
1777 struct isl_upoly *base, *res;
1782 if (isl_upoly_is_cst(up))
1785 if (up->var < first)
1788 rec = isl_upoly_as_rec(up);
1792 isl_assert(up->ctx, rec->n >= 1, goto error);
1794 if (up->var >= first + n)
1795 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1797 base = isl_upoly_copy(subs[up->var - first]);
1799 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1800 for (i = rec->n - 2; i >= 0; --i) {
1801 struct isl_upoly *t;
1802 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1803 res = isl_upoly_mul(res, isl_upoly_copy(base));
1804 res = isl_upoly_sum(res, t);
1807 isl_upoly_free(base);
1816 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1817 isl_int denom, unsigned len)
1820 struct isl_upoly *up;
1822 isl_assert(ctx, len >= 1, return NULL);
1824 up = isl_upoly_rat_cst(ctx, f[0], denom);
1825 for (i = 0; i < len - 1; ++i) {
1826 struct isl_upoly *t;
1827 struct isl_upoly *c;
1829 if (isl_int_is_zero(f[1 + i]))
1832 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1833 t = isl_upoly_var_pow(ctx, i, 1);
1834 t = isl_upoly_mul(c, t);
1835 up = isl_upoly_sum(up, t);
1841 /* Remove common factor of non-constant terms and denominator.
1843 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1845 isl_ctx *ctx = qp->div->ctx;
1846 unsigned total = qp->div->n_col - 2;
1848 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1849 isl_int_gcd(ctx->normalize_gcd,
1850 ctx->normalize_gcd, qp->div->row[div][0]);
1851 if (isl_int_is_one(ctx->normalize_gcd))
1854 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1855 ctx->normalize_gcd, total);
1856 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1857 ctx->normalize_gcd);
1858 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1859 ctx->normalize_gcd);
1862 /* Replace the integer division identified by "div" by the polynomial "s".
1863 * The integer division is assumed not to appear in the definition
1864 * of any other integer divisions.
1866 static __isl_give isl_qpolynomial *substitute_div(
1867 __isl_take isl_qpolynomial *qp,
1868 int div, __isl_take struct isl_upoly *s)
1877 qp = isl_qpolynomial_cow(qp);
1881 total = isl_space_dim(qp->dim, isl_dim_all);
1882 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1886 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1889 for (i = 0; i < total + div; ++i)
1891 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1892 reordering[i] = i - 1;
1893 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1894 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1895 qp->upoly = reorder(qp->upoly, reordering);
1898 if (!qp->upoly || !qp->div)
1904 isl_qpolynomial_free(qp);
1909 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1910 * divisions because d is equal to 1 by their definition, i.e., e.
1912 static __isl_give isl_qpolynomial *substitute_non_divs(
1913 __isl_take isl_qpolynomial *qp)
1917 struct isl_upoly *s;
1922 total = isl_space_dim(qp->dim, isl_dim_all);
1923 for (i = 0; qp && i < qp->div->n_row; ++i) {
1924 if (!isl_int_is_one(qp->div->row[i][0]))
1926 for (j = i + 1; j < qp->div->n_row; ++j) {
1927 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1929 isl_seq_combine(qp->div->row[j] + 1,
1930 qp->div->ctx->one, qp->div->row[j] + 1,
1931 qp->div->row[j][2 + total + i],
1932 qp->div->row[i] + 1, 1 + total + i);
1933 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1934 normalize_div(qp, j);
1936 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1937 qp->div->row[i][0], qp->div->n_col - 1);
1938 qp = substitute_div(qp, i, s);
1945 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1946 * with d the denominator. When replacing the coefficient e of x by
1947 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1948 * inside the division, so we need to add floor(e/d) * x outside.
1949 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1950 * to adjust the coefficient of x in each later div that depends on the
1951 * current div "div" and also in the affine expression "aff"
1952 * (if it too depends on "div").
1954 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1955 __isl_keep isl_vec *aff)
1959 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1962 for (i = 0; i < 1 + total + div; ++i) {
1963 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1964 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1966 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1967 isl_int_fdiv_r(qp->div->row[div][1 + i],
1968 qp->div->row[div][1 + i], qp->div->row[div][0]);
1969 if (!isl_int_is_zero(aff->el[1 + total + div]))
1970 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1971 for (j = div + 1; j < qp->div->n_row; ++j) {
1972 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1974 isl_int_addmul(qp->div->row[j][1 + i],
1975 v, qp->div->row[j][2 + total + div]);
1981 /* Check if the last non-zero coefficient is bigger that half of the
1982 * denominator. If so, we will invert the div to further reduce the number
1983 * of distinct divs that may appear.
1984 * If the last non-zero coefficient is exactly half the denominator,
1985 * then we continue looking for earlier coefficients that are bigger
1986 * than half the denominator.
1988 static int needs_invert(__isl_keep isl_mat *div, int row)
1993 for (i = div->n_col - 1; i >= 1; --i) {
1994 if (isl_int_is_zero(div->row[row][i]))
1996 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1997 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1998 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
2008 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2009 * We only invert the coefficients of e (and the coefficient of q in
2010 * later divs and in "aff"). After calling this function, the
2011 * coefficients of e should be reduced again.
2013 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
2014 __isl_keep isl_vec *aff)
2016 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2018 isl_seq_neg(qp->div->row[div] + 1,
2019 qp->div->row[div] + 1, qp->div->n_col - 1);
2020 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2021 isl_int_add(qp->div->row[div][1],
2022 qp->div->row[div][1], qp->div->row[div][0]);
2023 if (!isl_int_is_zero(aff->el[1 + total + div]))
2024 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2025 isl_mat_col_mul(qp->div, 2 + total + div,
2026 qp->div->ctx->negone, 2 + total + div);
2029 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2030 * in the interval [0, d-1], with d the denominator and such that the
2031 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2033 * After the reduction, some divs may have become redundant or identical,
2034 * so we call substitute_non_divs and sort_divs. If these functions
2035 * eliminate divs or merge two or more divs into one, the coefficients
2036 * of the enclosing divs may have to be reduced again, so we call
2037 * ourselves recursively if the number of divs decreases.
2039 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2042 isl_vec *aff = NULL;
2043 struct isl_upoly *s;
2049 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2050 aff = isl_vec_clr(aff);
2054 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2056 for (i = 0; i < qp->div->n_row; ++i) {
2057 normalize_div(qp, i);
2058 reduce_div(qp, i, aff);
2059 if (needs_invert(qp->div, i)) {
2060 invert_div(qp, i, aff);
2061 reduce_div(qp, i, aff);
2065 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2066 qp->div->ctx->one, aff->size);
2067 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2074 n_div = qp->div->n_row;
2075 qp = substitute_non_divs(qp);
2077 if (qp && qp->div->n_row < n_div)
2078 return reduce_divs(qp);
2082 isl_qpolynomial_free(qp);
2087 /* Assumes each div only depends on earlier divs.
2089 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2092 struct isl_qpolynomial *qp = NULL;
2093 struct isl_upoly_rec *rec;
2094 struct isl_upoly_cst *cst;
2101 d = div->line - div->bmap->div;
2103 pos = isl_space_dim(div->bmap->dim, isl_dim_all) + d;
2104 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2105 qp = isl_qpolynomial_alloc(isl_basic_map_get_space(div->bmap),
2106 div->bmap->n_div, &rec->up);
2110 for (i = 0; i < div->bmap->n_div; ++i)
2111 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2113 for (i = 0; i < 1 + power; ++i) {
2114 rec->p[i] = isl_upoly_zero(div->ctx);
2119 cst = isl_upoly_as_cst(rec->p[power]);
2120 isl_int_set_si(cst->n, 1);
2124 qp = reduce_divs(qp);
2128 isl_qpolynomial_free(qp);
2133 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2135 return isl_qpolynomial_div_pow(div, 1);
2138 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_space *dim,
2139 const isl_int n, const isl_int d)
2141 struct isl_qpolynomial *qp;
2142 struct isl_upoly_cst *cst;
2147 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2151 cst = isl_upoly_as_cst(qp->upoly);
2152 isl_int_set(cst->n, n);
2153 isl_int_set(cst->d, d);
2158 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2160 struct isl_upoly_rec *rec;
2166 if (isl_upoly_is_cst(up))
2170 active[up->var] = 1;
2172 rec = isl_upoly_as_rec(up);
2173 for (i = 0; i < rec->n; ++i)
2174 if (up_set_active(rec->p[i], active, d) < 0)
2180 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2183 int d = isl_space_dim(qp->dim, isl_dim_all);
2188 for (i = 0; i < d; ++i)
2189 for (j = 0; j < qp->div->n_row; ++j) {
2190 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2196 return up_set_active(qp->upoly, active, d);
2199 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2200 enum isl_dim_type type, unsigned first, unsigned n)
2211 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
2213 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2214 type == isl_dim_set, return -1);
2216 active = isl_calloc_array(qp->dim->ctx, int,
2217 isl_space_dim(qp->dim, isl_dim_all));
2218 if (set_active(qp, active) < 0)
2221 if (type == isl_dim_set)
2222 first += isl_space_dim(qp->dim, isl_dim_param);
2223 for (i = 0; i < n; ++i)
2224 if (active[first + i]) {
2237 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2238 * of the divs that do appear in the quasi-polynomial.
2240 static __isl_give isl_qpolynomial *remove_redundant_divs(
2241 __isl_take isl_qpolynomial *qp)
2248 int *reordering = NULL;
2255 if (qp->div->n_row == 0)
2258 d = isl_space_dim(qp->dim, isl_dim_all);
2259 len = qp->div->n_col - 2;
2260 ctx = isl_qpolynomial_get_ctx(qp);
2261 active = isl_calloc_array(ctx, int, len);
2265 if (up_set_active(qp->upoly, active, len) < 0)
2268 for (i = qp->div->n_row - 1; i >= 0; --i) {
2269 if (!active[d + i]) {
2273 for (j = 0; j < i; ++j) {
2274 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2286 reordering = isl_alloc_array(qp->div->ctx, int, len);
2290 for (i = 0; i < d; ++i)
2294 n_div = qp->div->n_row;
2295 for (i = 0; i < n_div; ++i) {
2296 if (!active[d + i]) {
2297 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2298 qp->div = isl_mat_drop_cols(qp->div,
2299 2 + d + i - skip, 1);
2302 reordering[d + i] = d + i - skip;
2305 qp->upoly = reorder(qp->upoly, reordering);
2307 if (!qp->upoly || !qp->div)
2317 isl_qpolynomial_free(qp);
2321 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2322 unsigned first, unsigned n)
2325 struct isl_upoly_rec *rec;
2329 if (n == 0 || up->var < 0 || up->var < first)
2331 if (up->var < first + n) {
2332 up = replace_by_constant_term(up);
2333 return isl_upoly_drop(up, first, n);
2335 up = isl_upoly_cow(up);
2339 rec = isl_upoly_as_rec(up);
2343 for (i = 0; i < rec->n; ++i) {
2344 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2355 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2356 __isl_take isl_qpolynomial *qp,
2357 enum isl_dim_type type, unsigned pos, const char *s)
2359 qp = isl_qpolynomial_cow(qp);
2362 qp->dim = isl_space_set_dim_name(qp->dim, type, pos, s);
2367 isl_qpolynomial_free(qp);
2371 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2372 __isl_take isl_qpolynomial *qp,
2373 enum isl_dim_type type, unsigned first, unsigned n)
2377 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2380 qp = isl_qpolynomial_cow(qp);
2384 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
2386 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2387 type == isl_dim_set, goto error);
2389 qp->dim = isl_space_drop_dims(qp->dim, type, first, n);
2393 if (type == isl_dim_set)
2394 first += isl_space_dim(qp->dim, isl_dim_param);
2396 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2400 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2406 isl_qpolynomial_free(qp);
2410 static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted(
2411 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2417 struct isl_upoly *up;
2421 if (eq->n_eq == 0) {
2422 isl_basic_set_free(eq);
2426 qp = isl_qpolynomial_cow(qp);
2429 qp->div = isl_mat_cow(qp->div);
2433 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
2435 isl_int_init(denom);
2436 for (i = 0; i < eq->n_eq; ++i) {
2437 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2438 if (j < 0 || j == 0 || j >= total)
2441 for (k = 0; k < qp->div->n_row; ++k) {
2442 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2444 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2445 &qp->div->row[k][0]);
2446 normalize_div(qp, k);
2449 if (isl_int_is_pos(eq->eq[i][j]))
2450 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2451 isl_int_abs(denom, eq->eq[i][j]);
2452 isl_int_set_si(eq->eq[i][j], 0);
2454 up = isl_upoly_from_affine(qp->dim->ctx,
2455 eq->eq[i], denom, total);
2456 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2459 isl_int_clear(denom);
2464 isl_basic_set_free(eq);
2466 qp = substitute_non_divs(qp);
2471 isl_basic_set_free(eq);
2472 isl_qpolynomial_free(qp);
2476 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2478 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2479 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2483 if (qp->div->n_row > 0)
2484 eq = isl_basic_set_add(eq, isl_dim_set, qp->div->n_row);
2485 return isl_qpolynomial_substitute_equalities_lifted(qp, eq);
2487 isl_basic_set_free(eq);
2488 isl_qpolynomial_free(qp);
2492 static __isl_give isl_basic_set *add_div_constraints(
2493 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2501 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2504 total = isl_basic_set_total_dim(bset);
2505 for (i = 0; i < div->n_row; ++i)
2506 if (isl_basic_set_add_div_constraints_var(bset,
2507 total - div->n_row + i, div->row[i]) < 0)
2514 isl_basic_set_free(bset);
2518 /* Look for equalities among the variables shared by context and qp
2519 * and the integer divisions of qp, if any.
2520 * The equalities are then used to eliminate variables and/or integer
2521 * divisions from qp.
2523 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2524 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2530 if (qp->div->n_row > 0) {
2531 isl_basic_set *bset;
2532 context = isl_set_add_dims(context, isl_dim_set,
2534 bset = isl_basic_set_universe(isl_set_get_space(context));
2535 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2536 context = isl_set_intersect(context,
2537 isl_set_from_basic_set(bset));
2540 aff = isl_set_affine_hull(context);
2541 return isl_qpolynomial_substitute_equalities_lifted(qp, aff);
2543 isl_qpolynomial_free(qp);
2544 isl_set_free(context);
2548 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2549 __isl_take isl_qpolynomial *qp)
2555 if (isl_qpolynomial_is_zero(qp)) {
2556 isl_space *dim = isl_qpolynomial_get_space(qp);
2557 isl_qpolynomial_free(qp);
2558 return isl_pw_qpolynomial_zero(dim);
2561 dom = isl_set_universe(isl_qpolynomial_get_space(qp));
2562 return isl_pw_qpolynomial_alloc(dom, qp);
2566 #define PW isl_pw_qpolynomial
2568 #define EL isl_qpolynomial
2570 #define EL_IS_ZERO is_zero
2574 #define IS_ZERO is_zero
2578 #include <isl_pw_templ.c>
2581 #define UNION isl_union_pw_qpolynomial
2583 #define PART isl_pw_qpolynomial
2585 #define PARTS pw_qpolynomial
2587 #include <isl_union_templ.c>
2589 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2597 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2600 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2603 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2604 __isl_take isl_pw_qpolynomial *pwqp1,
2605 __isl_take isl_pw_qpolynomial *pwqp2)
2608 struct isl_pw_qpolynomial *res;
2610 if (!pwqp1 || !pwqp2)
2613 isl_assert(pwqp1->dim->ctx, isl_space_is_equal(pwqp1->dim, pwqp2->dim),
2616 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2617 isl_pw_qpolynomial_free(pwqp2);
2621 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2622 isl_pw_qpolynomial_free(pwqp1);
2626 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2627 isl_pw_qpolynomial_free(pwqp1);
2631 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2632 isl_pw_qpolynomial_free(pwqp2);
2636 n = pwqp1->n * pwqp2->n;
2637 res = isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1->dim), n);
2639 for (i = 0; i < pwqp1->n; ++i) {
2640 for (j = 0; j < pwqp2->n; ++j) {
2641 struct isl_set *common;
2642 struct isl_qpolynomial *prod;
2643 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2644 isl_set_copy(pwqp2->p[j].set));
2645 if (isl_set_plain_is_empty(common)) {
2646 isl_set_free(common);
2650 prod = isl_qpolynomial_mul(
2651 isl_qpolynomial_copy(pwqp1->p[i].qp),
2652 isl_qpolynomial_copy(pwqp2->p[j].qp));
2654 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2658 isl_pw_qpolynomial_free(pwqp1);
2659 isl_pw_qpolynomial_free(pwqp2);
2663 isl_pw_qpolynomial_free(pwqp1);
2664 isl_pw_qpolynomial_free(pwqp2);
2668 __isl_give struct isl_upoly *isl_upoly_eval(
2669 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2672 struct isl_upoly_rec *rec;
2673 struct isl_upoly *res;
2674 struct isl_upoly *base;
2676 if (isl_upoly_is_cst(up)) {
2681 rec = isl_upoly_as_rec(up);
2685 isl_assert(up->ctx, rec->n >= 1, goto error);
2687 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2689 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2692 for (i = rec->n - 2; i >= 0; --i) {
2693 res = isl_upoly_mul(res, isl_upoly_copy(base));
2694 res = isl_upoly_sum(res,
2695 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2696 isl_vec_copy(vec)));
2699 isl_upoly_free(base);
2709 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2710 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2713 struct isl_upoly *up;
2718 isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, qp->dim), goto error);
2720 if (qp->div->n_row == 0)
2721 ext = isl_vec_copy(pnt->vec);
2724 unsigned dim = isl_space_dim(qp->dim, isl_dim_all);
2725 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2729 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2730 for (i = 0; i < qp->div->n_row; ++i) {
2731 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2732 1 + dim + i, &ext->el[1+dim+i]);
2733 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2734 qp->div->row[i][0]);
2738 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2742 dim = isl_space_copy(qp->dim);
2743 isl_qpolynomial_free(qp);
2744 isl_point_free(pnt);
2746 return isl_qpolynomial_alloc(dim, 0, up);
2748 isl_qpolynomial_free(qp);
2749 isl_point_free(pnt);
2753 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2754 __isl_keep struct isl_upoly_cst *cst2)
2759 isl_int_mul(t, cst1->n, cst2->d);
2760 isl_int_submul(t, cst2->n, cst1->d);
2761 cmp = isl_int_sgn(t);
2766 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2767 __isl_keep isl_qpolynomial *qp2)
2769 struct isl_upoly_cst *cst1, *cst2;
2773 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2774 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2775 if (isl_qpolynomial_is_nan(qp1))
2777 if (isl_qpolynomial_is_nan(qp2))
2779 cst1 = isl_upoly_as_cst(qp1->upoly);
2780 cst2 = isl_upoly_as_cst(qp2->upoly);
2782 return isl_upoly_cmp(cst1, cst2) <= 0;
2785 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2786 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2788 struct isl_upoly_cst *cst1, *cst2;
2793 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2794 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2795 cst1 = isl_upoly_as_cst(qp1->upoly);
2796 cst2 = isl_upoly_as_cst(qp2->upoly);
2797 cmp = isl_upoly_cmp(cst1, cst2);
2800 isl_qpolynomial_free(qp2);
2802 isl_qpolynomial_free(qp1);
2807 isl_qpolynomial_free(qp1);
2808 isl_qpolynomial_free(qp2);
2812 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2813 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2815 struct isl_upoly_cst *cst1, *cst2;
2820 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2821 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2822 cst1 = isl_upoly_as_cst(qp1->upoly);
2823 cst2 = isl_upoly_as_cst(qp2->upoly);
2824 cmp = isl_upoly_cmp(cst1, cst2);
2827 isl_qpolynomial_free(qp2);
2829 isl_qpolynomial_free(qp1);
2834 isl_qpolynomial_free(qp1);
2835 isl_qpolynomial_free(qp2);
2839 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2840 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2841 unsigned first, unsigned n)
2847 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2850 qp = isl_qpolynomial_cow(qp);
2854 isl_assert(qp->div->ctx, first <= isl_space_dim(qp->dim, type),
2857 g_pos = pos(qp->dim, type) + first;
2859 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2863 total = qp->div->n_col - 2;
2864 if (total > g_pos) {
2866 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2869 for (i = 0; i < total - g_pos; ++i)
2871 qp->upoly = expand(qp->upoly, exp, g_pos);
2877 qp->dim = isl_space_insert_dims(qp->dim, type, first, n);
2883 isl_qpolynomial_free(qp);
2887 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2888 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2892 pos = isl_qpolynomial_dim(qp, type);
2894 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2897 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2898 __isl_take isl_pw_qpolynomial *pwqp,
2899 enum isl_dim_type type, unsigned n)
2903 pos = isl_pw_qpolynomial_dim(pwqp, type);
2905 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2908 static int *reordering_move(isl_ctx *ctx,
2909 unsigned len, unsigned dst, unsigned src, unsigned n)
2914 reordering = isl_alloc_array(ctx, int, len);
2919 for (i = 0; i < dst; ++i)
2921 for (i = 0; i < n; ++i)
2922 reordering[src + i] = dst + i;
2923 for (i = 0; i < src - dst; ++i)
2924 reordering[dst + i] = dst + n + i;
2925 for (i = 0; i < len - src - n; ++i)
2926 reordering[src + n + i] = src + n + i;
2928 for (i = 0; i < src; ++i)
2930 for (i = 0; i < n; ++i)
2931 reordering[src + i] = dst + i;
2932 for (i = 0; i < dst - src; ++i)
2933 reordering[src + n + i] = src + i;
2934 for (i = 0; i < len - dst - n; ++i)
2935 reordering[dst + n + i] = dst + n + i;
2941 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2942 __isl_take isl_qpolynomial *qp,
2943 enum isl_dim_type dst_type, unsigned dst_pos,
2944 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2950 qp = isl_qpolynomial_cow(qp);
2954 isl_assert(qp->dim->ctx, src_pos + n <= isl_space_dim(qp->dim, src_type),
2957 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2958 g_src_pos = pos(qp->dim, src_type) + src_pos;
2959 if (dst_type > src_type)
2962 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2969 reordering = reordering_move(qp->dim->ctx,
2970 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2974 qp->upoly = reorder(qp->upoly, reordering);
2979 qp->dim = isl_space_move_dims(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2985 isl_qpolynomial_free(qp);
2989 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_space *dim,
2990 isl_int *f, isl_int denom)
2992 struct isl_upoly *up;
2997 up = isl_upoly_from_affine(dim->ctx, f, denom,
2998 1 + isl_space_dim(dim, isl_dim_all));
3000 return isl_qpolynomial_alloc(dim, 0, up);
3003 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
3006 struct isl_upoly *up;
3007 isl_qpolynomial *qp;
3012 ctx = isl_aff_get_ctx(aff);
3013 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
3016 qp = isl_qpolynomial_alloc(isl_aff_get_space(aff),
3017 aff->ls->div->n_row, up);
3021 isl_mat_free(qp->div);
3022 qp->div = isl_mat_copy(aff->ls->div);
3023 qp->div = isl_mat_cow(qp->div);
3028 qp = reduce_divs(qp);
3029 qp = remove_redundant_divs(qp);
3036 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3037 __isl_take isl_pw_aff *pwaff)
3040 isl_pw_qpolynomial *pwqp;
3045 pwqp = isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff),
3048 for (i = 0; i < pwaff->n; ++i) {
3050 isl_qpolynomial *qp;
3052 dom = isl_set_copy(pwaff->p[i].set);
3053 qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff));
3054 pwqp = isl_pw_qpolynomial_add_piece(pwqp, dom, qp);
3057 isl_pw_aff_free(pwaff);
3061 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3062 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3066 aff = isl_constraint_get_bound(c, type, pos);
3067 isl_constraint_free(c);
3068 return isl_qpolynomial_from_aff(aff);
3071 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3072 * in "qp" by subs[i].
3074 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3075 __isl_take isl_qpolynomial *qp,
3076 enum isl_dim_type type, unsigned first, unsigned n,
3077 __isl_keep isl_qpolynomial **subs)
3080 struct isl_upoly **ups;
3085 qp = isl_qpolynomial_cow(qp);
3088 for (i = 0; i < n; ++i)
3092 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
3095 for (i = 0; i < n; ++i)
3096 isl_assert(qp->dim->ctx, isl_space_is_equal(qp->dim, subs[i]->dim),
3099 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3100 for (i = 0; i < n; ++i)
3101 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3103 first += pos(qp->dim, type);
3105 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3108 for (i = 0; i < n; ++i)
3109 ups[i] = subs[i]->upoly;
3111 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3120 isl_qpolynomial_free(qp);
3124 /* Extend "bset" with extra set dimensions for each integer division
3125 * in "qp" and then call "fn" with the extended bset and the polynomial
3126 * that results from replacing each of the integer divisions by the
3127 * corresponding extra set dimension.
3129 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3130 __isl_keep isl_basic_set *bset,
3131 int (*fn)(__isl_take isl_basic_set *bset,
3132 __isl_take isl_qpolynomial *poly, void *user), void *user)
3136 isl_qpolynomial *poly;
3140 if (qp->div->n_row == 0)
3141 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3144 div = isl_mat_copy(qp->div);
3145 dim = isl_space_copy(qp->dim);
3146 dim = isl_space_add_dims(dim, isl_dim_set, qp->div->n_row);
3147 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3148 bset = isl_basic_set_copy(bset);
3149 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3150 bset = add_div_constraints(bset, div);
3152 return fn(bset, poly, user);
3157 /* Return total degree in variables first (inclusive) up to last (exclusive).
3159 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3163 struct isl_upoly_rec *rec;
3167 if (isl_upoly_is_zero(up))
3169 if (isl_upoly_is_cst(up) || up->var < first)
3172 rec = isl_upoly_as_rec(up);
3176 for (i = 0; i < rec->n; ++i) {
3179 if (isl_upoly_is_zero(rec->p[i]))
3181 d = isl_upoly_degree(rec->p[i], first, last);
3191 /* Return total degree in set variables.
3193 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3201 ovar = isl_space_offset(poly->dim, isl_dim_set);
3202 nvar = isl_space_dim(poly->dim, isl_dim_set);
3203 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3206 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3207 unsigned pos, int deg)
3210 struct isl_upoly_rec *rec;
3215 if (isl_upoly_is_cst(up) || up->var < pos) {
3217 return isl_upoly_copy(up);
3219 return isl_upoly_zero(up->ctx);
3222 rec = isl_upoly_as_rec(up);
3226 if (up->var == pos) {
3228 return isl_upoly_copy(rec->p[deg]);
3230 return isl_upoly_zero(up->ctx);
3233 up = isl_upoly_copy(up);
3234 up = isl_upoly_cow(up);
3235 rec = isl_upoly_as_rec(up);
3239 for (i = 0; i < rec->n; ++i) {
3240 struct isl_upoly *t;
3241 t = isl_upoly_coeff(rec->p[i], pos, deg);
3244 isl_upoly_free(rec->p[i]);
3254 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3256 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3257 __isl_keep isl_qpolynomial *qp,
3258 enum isl_dim_type type, unsigned t_pos, int deg)
3261 struct isl_upoly *up;
3267 isl_assert(qp->div->ctx, t_pos < isl_space_dim(qp->dim, type),
3270 g_pos = pos(qp->dim, type) + t_pos;
3271 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3273 c = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row, up);
3276 isl_mat_free(c->div);
3277 c->div = isl_mat_copy(qp->div);
3282 isl_qpolynomial_free(c);
3286 /* Homogenize the polynomial in the variables first (inclusive) up to
3287 * last (exclusive) by inserting powers of variable first.
3288 * Variable first is assumed not to appear in the input.
3290 __isl_give struct isl_upoly *isl_upoly_homogenize(
3291 __isl_take struct isl_upoly *up, int deg, int target,
3292 int first, int last)
3295 struct isl_upoly_rec *rec;
3299 if (isl_upoly_is_zero(up))
3303 if (isl_upoly_is_cst(up) || up->var < first) {
3304 struct isl_upoly *hom;
3306 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3309 rec = isl_upoly_as_rec(hom);
3310 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3315 up = isl_upoly_cow(up);
3316 rec = isl_upoly_as_rec(up);
3320 for (i = 0; i < rec->n; ++i) {
3321 if (isl_upoly_is_zero(rec->p[i]))
3323 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3324 up->var < last ? deg + i : i, target,
3336 /* Homogenize the polynomial in the set variables by introducing
3337 * powers of an extra set variable at position 0.
3339 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3340 __isl_take isl_qpolynomial *poly)
3344 int deg = isl_qpolynomial_degree(poly);
3349 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3350 poly = isl_qpolynomial_cow(poly);
3354 ovar = isl_space_offset(poly->dim, isl_dim_set);
3355 nvar = isl_space_dim(poly->dim, isl_dim_set);
3356 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3363 isl_qpolynomial_free(poly);
3367 __isl_give isl_term *isl_term_alloc(__isl_take isl_space *dim,
3368 __isl_take isl_mat *div)
3376 n = isl_space_dim(dim, isl_dim_all) + div->n_row;
3378 term = isl_calloc(dim->ctx, struct isl_term,
3379 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3386 isl_int_init(term->n);
3387 isl_int_init(term->d);
3391 isl_space_free(dim);
3396 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3405 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3414 total = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3416 dup = isl_term_alloc(isl_space_copy(term->dim), isl_mat_copy(term->div));
3420 isl_int_set(dup->n, term->n);
3421 isl_int_set(dup->d, term->d);
3423 for (i = 0; i < total; ++i)
3424 dup->pow[i] = term->pow[i];
3429 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3437 return isl_term_dup(term);
3440 void isl_term_free(__isl_take isl_term *term)
3445 if (--term->ref > 0)
3448 isl_space_free(term->dim);
3449 isl_mat_free(term->div);
3450 isl_int_clear(term->n);
3451 isl_int_clear(term->d);
3455 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3463 case isl_dim_out: return isl_space_dim(term->dim, type);
3464 case isl_dim_div: return term->div->n_row;
3465 case isl_dim_all: return isl_space_dim(term->dim, isl_dim_all) +
3471 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3473 return term ? term->dim->ctx : NULL;
3476 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3480 isl_int_set(*n, term->n);
3483 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3487 isl_int_set(*d, term->d);
3490 int isl_term_get_exp(__isl_keep isl_term *term,
3491 enum isl_dim_type type, unsigned pos)
3496 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3498 if (type >= isl_dim_set)
3499 pos += isl_space_dim(term->dim, isl_dim_param);
3500 if (type >= isl_dim_div)
3501 pos += isl_space_dim(term->dim, isl_dim_set);
3503 return term->pow[pos];
3506 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3508 isl_basic_map *bmap;
3515 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3518 total = term->div->n_col - term->div->n_row - 2;
3519 /* No nested divs for now */
3520 isl_assert(term->dim->ctx,
3521 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3522 term->div->n_row) == -1,
3525 bmap = isl_basic_map_alloc_space(isl_space_copy(term->dim), 1, 0, 0);
3526 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3529 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3531 return isl_basic_map_div(bmap, k);
3533 isl_basic_map_free(bmap);
3537 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3538 int (*fn)(__isl_take isl_term *term, void *user),
3539 __isl_take isl_term *term, void *user)
3542 struct isl_upoly_rec *rec;
3547 if (isl_upoly_is_zero(up))
3550 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3551 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3552 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3554 if (isl_upoly_is_cst(up)) {
3555 struct isl_upoly_cst *cst;
3556 cst = isl_upoly_as_cst(up);
3559 term = isl_term_cow(term);
3562 isl_int_set(term->n, cst->n);
3563 isl_int_set(term->d, cst->d);
3564 if (fn(isl_term_copy(term), user) < 0)
3569 rec = isl_upoly_as_rec(up);
3573 for (i = 0; i < rec->n; ++i) {
3574 term = isl_term_cow(term);
3577 term->pow[up->var] = i;
3578 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3582 term->pow[up->var] = 0;
3586 isl_term_free(term);
3590 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3591 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3598 term = isl_term_alloc(isl_space_copy(qp->dim), isl_mat_copy(qp->div));
3602 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3604 isl_term_free(term);
3606 return term ? 0 : -1;
3609 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3611 struct isl_upoly *up;
3612 isl_qpolynomial *qp;
3618 n = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3620 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3621 for (i = 0; i < n; ++i) {
3624 up = isl_upoly_mul(up,
3625 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3628 qp = isl_qpolynomial_alloc(isl_space_copy(term->dim), term->div->n_row, up);
3631 isl_mat_free(qp->div);
3632 qp->div = isl_mat_copy(term->div);
3636 isl_term_free(term);
3639 isl_qpolynomial_free(qp);
3640 isl_term_free(term);
3644 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3645 __isl_take isl_space *dim)
3654 if (isl_space_is_equal(qp->dim, dim)) {
3655 isl_space_free(dim);
3659 qp = isl_qpolynomial_cow(qp);
3663 extra = isl_space_dim(dim, isl_dim_set) -
3664 isl_space_dim(qp->dim, isl_dim_set);
3665 total = isl_space_dim(qp->dim, isl_dim_all);
3666 if (qp->div->n_row) {
3669 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3672 for (i = 0; i < qp->div->n_row; ++i)
3674 qp->upoly = expand(qp->upoly, exp, total);
3679 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3682 for (i = 0; i < qp->div->n_row; ++i)
3683 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3685 isl_space_free(qp->dim);
3690 isl_space_free(dim);
3691 isl_qpolynomial_free(qp);
3695 /* For each parameter or variable that does not appear in qp,
3696 * first eliminate the variable from all constraints and then set it to zero.
3698 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3699 __isl_keep isl_qpolynomial *qp)
3710 d = isl_space_dim(set->dim, isl_dim_all);
3711 active = isl_calloc_array(set->ctx, int, d);
3712 if (set_active(qp, active) < 0)
3715 for (i = 0; i < d; ++i)
3724 nparam = isl_space_dim(set->dim, isl_dim_param);
3725 nvar = isl_space_dim(set->dim, isl_dim_set);
3726 for (i = 0; i < nparam; ++i) {
3729 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3730 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3732 for (i = 0; i < nvar; ++i) {
3733 if (active[nparam + i])
3735 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3736 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3748 struct isl_opt_data {
3749 isl_qpolynomial *qp;
3751 isl_qpolynomial *opt;
3755 static int opt_fn(__isl_take isl_point *pnt, void *user)
3757 struct isl_opt_data *data = (struct isl_opt_data *)user;
3758 isl_qpolynomial *val;
3760 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3764 } else if (data->max) {
3765 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3767 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3773 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3774 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3776 struct isl_opt_data data = { NULL, 1, NULL, max };
3781 if (isl_upoly_is_cst(qp->upoly)) {
3786 set = fix_inactive(set, qp);
3789 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3793 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_space(qp));
3796 isl_qpolynomial_free(qp);
3800 isl_qpolynomial_free(qp);
3801 isl_qpolynomial_free(data.opt);
3805 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3806 __isl_take isl_morph *morph)
3811 struct isl_upoly **subs;
3814 qp = isl_qpolynomial_cow(qp);
3819 isl_assert(ctx, isl_space_is_equal(qp->dim, morph->dom->dim), goto error);
3821 n_sub = morph->inv->n_row - 1;
3822 if (morph->inv->n_row != morph->inv->n_col)
3823 n_sub += qp->div->n_row;
3824 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3828 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3829 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3830 morph->inv->row[0][0], morph->inv->n_col);
3831 if (morph->inv->n_row != morph->inv->n_col)
3832 for (i = 0; i < qp->div->n_row; ++i)
3833 subs[morph->inv->n_row - 1 + i] =
3834 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3836 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3838 for (i = 0; i < n_sub; ++i)
3839 isl_upoly_free(subs[i]);
3842 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3843 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3844 qp->div = isl_mat_product(qp->div, mat);
3845 isl_space_free(qp->dim);
3846 qp->dim = isl_space_copy(morph->ran->dim);
3848 if (!qp->upoly || !qp->div || !qp->dim)
3851 isl_morph_free(morph);
3855 isl_qpolynomial_free(qp);
3856 isl_morph_free(morph);
3860 static int neg_entry(void **entry, void *user)
3862 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3864 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3866 return *pwqp ? 0 : -1;
3869 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3870 __isl_take isl_union_pw_qpolynomial *upwqp)
3872 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3876 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3877 &neg_entry, NULL) < 0)
3882 isl_union_pw_qpolynomial_free(upwqp);
3886 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3887 __isl_take isl_union_pw_qpolynomial *upwqp1,
3888 __isl_take isl_union_pw_qpolynomial *upwqp2)
3890 return isl_union_pw_qpolynomial_add(upwqp1,
3891 isl_union_pw_qpolynomial_neg(upwqp2));
3894 static int mul_entry(void **entry, void *user)
3896 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3898 struct isl_hash_table_entry *entry2;
3899 isl_pw_qpolynomial *pwpq = *entry;
3902 hash = isl_space_get_hash(pwpq->dim);
3903 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3904 hash, &has_dim, pwpq->dim, 0);
3908 pwpq = isl_pw_qpolynomial_copy(pwpq);
3909 pwpq = isl_pw_qpolynomial_mul(pwpq,
3910 isl_pw_qpolynomial_copy(entry2->data));
3912 empty = isl_pw_qpolynomial_is_zero(pwpq);
3914 isl_pw_qpolynomial_free(pwpq);
3918 isl_pw_qpolynomial_free(pwpq);
3922 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3927 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3928 __isl_take isl_union_pw_qpolynomial *upwqp1,
3929 __isl_take isl_union_pw_qpolynomial *upwqp2)
3931 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3934 /* Reorder the columns of the given div definitions according to the
3937 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3938 __isl_take isl_reordering *r)
3947 extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
3948 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3952 for (i = 0; i < div->n_row; ++i) {
3953 isl_seq_cpy(mat->row[i], div->row[i], 2);
3954 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3955 for (j = 0; j < r->len; ++j)
3956 isl_int_set(mat->row[i][2 + r->pos[j]],
3957 div->row[i][2 + j]);
3960 isl_reordering_free(r);
3964 isl_reordering_free(r);
3969 /* Reorder the dimension of "qp" according to the given reordering.
3971 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3972 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3974 qp = isl_qpolynomial_cow(qp);
3978 r = isl_reordering_extend(r, qp->div->n_row);
3982 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3986 qp->upoly = reorder(qp->upoly, r->pos);
3990 qp = isl_qpolynomial_reset_space(qp, isl_space_copy(r->dim));
3992 isl_reordering_free(r);
3995 isl_qpolynomial_free(qp);
3996 isl_reordering_free(r);
4000 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4001 __isl_take isl_qpolynomial *qp, __isl_take isl_space *model)
4006 if (!isl_space_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
4007 isl_reordering *exp;
4009 model = isl_space_drop_dims(model, isl_dim_in,
4010 0, isl_space_dim(model, isl_dim_in));
4011 model = isl_space_drop_dims(model, isl_dim_out,
4012 0, isl_space_dim(model, isl_dim_out));
4013 exp = isl_parameter_alignment_reordering(qp->dim, model);
4014 exp = isl_reordering_extend_space(exp,
4015 isl_qpolynomial_get_space(qp));
4016 qp = isl_qpolynomial_realign(qp, exp);
4019 isl_space_free(model);
4022 isl_space_free(model);
4023 isl_qpolynomial_free(qp);
4027 struct isl_split_periods_data {
4029 isl_pw_qpolynomial *res;
4032 /* Create a slice where the integer division "div" has the fixed value "v".
4033 * In particular, if "div" refers to floor(f/m), then create a slice
4035 * m v <= f <= m v + (m - 1)
4040 * -f + m v + (m - 1) >= 0
4042 static __isl_give isl_set *set_div_slice(__isl_take isl_space *dim,
4043 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4046 isl_basic_set *bset = NULL;
4052 total = isl_space_dim(dim, isl_dim_all);
4053 bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0, 0, 2);
4055 k = isl_basic_set_alloc_inequality(bset);
4058 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4059 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4061 k = isl_basic_set_alloc_inequality(bset);
4064 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4065 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4066 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4067 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4069 isl_space_free(dim);
4070 return isl_set_from_basic_set(bset);
4072 isl_basic_set_free(bset);
4073 isl_space_free(dim);
4077 static int split_periods(__isl_take isl_set *set,
4078 __isl_take isl_qpolynomial *qp, void *user);
4080 /* Create a slice of the domain "set" such that integer division "div"
4081 * has the fixed value "v" and add the results to data->res,
4082 * replacing the integer division by "v" in "qp".
4084 static int set_div(__isl_take isl_set *set,
4085 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4086 struct isl_split_periods_data *data)
4091 struct isl_upoly *cst;
4093 slice = set_div_slice(isl_set_get_space(set), qp, div, v);
4094 set = isl_set_intersect(set, slice);
4099 total = isl_space_dim(qp->dim, isl_dim_all);
4101 for (i = div + 1; i < qp->div->n_row; ++i) {
4102 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4104 isl_int_addmul(qp->div->row[i][1],
4105 qp->div->row[i][2 + total + div], v);
4106 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4109 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4110 qp = substitute_div(qp, div, cst);
4112 return split_periods(set, qp, data);
4115 isl_qpolynomial_free(qp);
4119 /* Split the domain "set" such that integer division "div"
4120 * has a fixed value (ranging from "min" to "max") on each slice
4121 * and add the results to data->res.
4123 static int split_div(__isl_take isl_set *set,
4124 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4125 struct isl_split_periods_data *data)
4127 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4128 isl_set *set_i = isl_set_copy(set);
4129 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4131 if (set_div(set_i, qp_i, div, min, data) < 0)
4135 isl_qpolynomial_free(qp);
4139 isl_qpolynomial_free(qp);
4143 /* If "qp" refers to any integer division
4144 * that can only attain "max_periods" distinct values on "set"
4145 * then split the domain along those distinct values.
4146 * Add the results (or the original if no splitting occurs)
4149 static int split_periods(__isl_take isl_set *set,
4150 __isl_take isl_qpolynomial *qp, void *user)
4153 isl_pw_qpolynomial *pwqp;
4154 struct isl_split_periods_data *data;
4159 data = (struct isl_split_periods_data *)user;
4164 if (qp->div->n_row == 0) {
4165 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4166 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4172 total = isl_space_dim(qp->dim, isl_dim_all);
4173 for (i = 0; i < qp->div->n_row; ++i) {
4174 enum isl_lp_result lp_res;
4176 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4177 qp->div->n_row) != -1)
4180 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4181 set->ctx->one, &min, NULL, NULL);
4182 if (lp_res == isl_lp_error)
4184 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4186 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4188 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4189 set->ctx->one, &max, NULL, NULL);
4190 if (lp_res == isl_lp_error)
4192 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4194 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4196 isl_int_sub(max, max, min);
4197 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4198 isl_int_add(max, max, min);
4203 if (i < qp->div->n_row) {
4204 r = split_div(set, qp, i, min, max, data);
4206 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4207 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4219 isl_qpolynomial_free(qp);
4223 /* If any quasi-polynomial in pwqp refers to any integer division
4224 * that can only attain "max_periods" distinct values on its domain
4225 * then split the domain along those distinct values.
4227 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4228 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4230 struct isl_split_periods_data data;
4232 data.max_periods = max_periods;
4233 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4235 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4238 isl_pw_qpolynomial_free(pwqp);
4242 isl_pw_qpolynomial_free(data.res);
4243 isl_pw_qpolynomial_free(pwqp);
4247 /* Construct a piecewise quasipolynomial that is constant on the given
4248 * domain. In particular, it is
4251 * infinity if cst == -1
4253 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4254 __isl_take isl_basic_set *bset, int cst)
4257 isl_qpolynomial *qp;
4262 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4263 dim = isl_basic_set_get_space(bset);
4265 qp = isl_qpolynomial_infty(dim);
4267 qp = isl_qpolynomial_zero(dim);
4269 qp = isl_qpolynomial_one(dim);
4270 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4273 /* Factor bset, call fn on each of the factors and return the product.
4275 * If no factors can be found, simply call fn on the input.
4276 * Otherwise, construct the factors based on the factorizer,
4277 * call fn on each factor and compute the product.
4279 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4280 __isl_take isl_basic_set *bset,
4281 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4287 isl_qpolynomial *qp;
4288 isl_pw_qpolynomial *pwqp;
4292 f = isl_basic_set_factorizer(bset);
4295 if (f->n_group == 0) {
4296 isl_factorizer_free(f);
4300 nparam = isl_basic_set_dim(bset, isl_dim_param);
4301 nvar = isl_basic_set_dim(bset, isl_dim_set);
4303 dim = isl_basic_set_get_space(bset);
4304 dim = isl_space_domain(dim);
4305 set = isl_set_universe(isl_space_copy(dim));
4306 qp = isl_qpolynomial_one(dim);
4307 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4309 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4311 for (i = 0, n = 0; i < f->n_group; ++i) {
4312 isl_basic_set *bset_i;
4313 isl_pw_qpolynomial *pwqp_i;
4315 bset_i = isl_basic_set_copy(bset);
4316 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4317 nparam + n + f->len[i], nvar - n - f->len[i]);
4318 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4320 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4321 n + f->len[i], nvar - n - f->len[i]);
4322 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4324 pwqp_i = fn(bset_i);
4325 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4330 isl_basic_set_free(bset);
4331 isl_factorizer_free(f);
4335 isl_basic_set_free(bset);
4339 /* Factor bset, call fn on each of the factors and return the product.
4340 * The function is assumed to evaluate to zero on empty domains,
4341 * to one on zero-dimensional domains and to infinity on unbounded domains
4342 * and will not be called explicitly on zero-dimensional or unbounded domains.
4344 * We first check for some special cases and remove all equalities.
4345 * Then we hand over control to compressed_multiplicative_call.
4347 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4348 __isl_take isl_basic_set *bset,
4349 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4353 isl_pw_qpolynomial *pwqp;
4354 unsigned orig_nvar, final_nvar;
4359 if (isl_basic_set_plain_is_empty(bset))
4360 return constant_on_domain(bset, 0);
4362 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4365 return constant_on_domain(bset, 1);
4367 bounded = isl_basic_set_is_bounded(bset);
4371 return constant_on_domain(bset, -1);
4373 if (bset->n_eq == 0)
4374 return compressed_multiplicative_call(bset, fn);
4376 morph = isl_basic_set_full_compression(bset);
4377 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4379 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4381 pwqp = compressed_multiplicative_call(bset, fn);
4383 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4384 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4385 morph = isl_morph_inverse(morph);
4387 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4391 isl_basic_set_free(bset);
4395 /* Drop all floors in "qp", turning each integer division [a/m] into
4396 * a rational division a/m. If "down" is set, then the integer division
4397 * is replaces by (a-(m-1))/m instead.
4399 static __isl_give isl_qpolynomial *qp_drop_floors(
4400 __isl_take isl_qpolynomial *qp, int down)
4403 struct isl_upoly *s;
4407 if (qp->div->n_row == 0)
4410 qp = isl_qpolynomial_cow(qp);
4414 for (i = qp->div->n_row - 1; i >= 0; --i) {
4416 isl_int_sub(qp->div->row[i][1],
4417 qp->div->row[i][1], qp->div->row[i][0]);
4418 isl_int_add_ui(qp->div->row[i][1],
4419 qp->div->row[i][1], 1);
4421 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4422 qp->div->row[i][0], qp->div->n_col - 1);
4423 qp = substitute_div(qp, i, s);
4431 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4432 * a rational division a/m.
4434 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4435 __isl_take isl_pw_qpolynomial *pwqp)
4442 if (isl_pw_qpolynomial_is_zero(pwqp))
4445 pwqp = isl_pw_qpolynomial_cow(pwqp);
4449 for (i = 0; i < pwqp->n; ++i) {
4450 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4457 isl_pw_qpolynomial_free(pwqp);
4461 /* Adjust all the integer divisions in "qp" such that they are at least
4462 * one over the given orthant (identified by "signs"). This ensures
4463 * that they will still be non-negative even after subtracting (m-1)/m.
4465 * In particular, f is replaced by f' + v, changing f = [a/m]
4466 * to f' = [(a - m v)/m].
4467 * If the constant term k in a is smaller than m,
4468 * the constant term of v is set to floor(k/m) - 1.
4469 * For any other term, if the coefficient c and the variable x have
4470 * the same sign, then no changes are needed.
4471 * Otherwise, if the variable is positive (and c is negative),
4472 * then the coefficient of x in v is set to floor(c/m).
4473 * If the variable is negative (and c is positive),
4474 * then the coefficient of x in v is set to ceil(c/m).
4476 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4482 struct isl_upoly *s;
4484 qp = isl_qpolynomial_cow(qp);
4487 qp->div = isl_mat_cow(qp->div);
4491 total = isl_space_dim(qp->dim, isl_dim_all);
4492 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4494 for (i = 0; i < qp->div->n_row; ++i) {
4495 isl_int *row = qp->div->row[i];
4499 if (isl_int_lt(row[1], row[0])) {
4500 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4501 isl_int_sub_ui(v->el[0], v->el[0], 1);
4502 isl_int_submul(row[1], row[0], v->el[0]);
4504 for (j = 0; j < total; ++j) {
4505 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4508 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4510 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4511 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4513 for (j = 0; j < i; ++j) {
4514 if (isl_int_sgn(row[2 + total + j]) >= 0)
4516 isl_int_fdiv_q(v->el[1 + total + j],
4517 row[2 + total + j], row[0]);
4518 isl_int_submul(row[2 + total + j],
4519 row[0], v->el[1 + total + j]);
4521 for (j = i + 1; j < qp->div->n_row; ++j) {
4522 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4524 isl_seq_combine(qp->div->row[j] + 1,
4525 qp->div->ctx->one, qp->div->row[j] + 1,
4526 qp->div->row[j][2 + total + i], v->el, v->size);
4528 isl_int_set_si(v->el[1 + total + i], 1);
4529 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4530 qp->div->ctx->one, v->size);
4531 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4541 isl_qpolynomial_free(qp);
4545 struct isl_to_poly_data {
4547 isl_pw_qpolynomial *res;
4548 isl_qpolynomial *qp;
4551 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4552 * We first make all integer divisions positive and then split the
4553 * quasipolynomials into terms with sign data->sign (the direction
4554 * of the requested approximation) and terms with the opposite sign.
4555 * In the first set of terms, each integer division [a/m] is
4556 * overapproximated by a/m, while in the second it is underapproximated
4559 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4562 struct isl_to_poly_data *data = user;
4563 isl_pw_qpolynomial *t;
4564 isl_qpolynomial *qp, *up, *down;
4566 qp = isl_qpolynomial_copy(data->qp);
4567 qp = make_divs_pos(qp, signs);
4569 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4570 up = qp_drop_floors(up, 0);
4571 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4572 down = qp_drop_floors(down, 1);
4574 isl_qpolynomial_free(qp);
4575 qp = isl_qpolynomial_add(up, down);
4577 t = isl_pw_qpolynomial_alloc(orthant, qp);
4578 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4583 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4584 * the polynomial will be an overapproximation. If "sign" is negative,
4585 * it will be an underapproximation. If "sign" is zero, the approximation
4586 * will lie somewhere in between.
4588 * In particular, is sign == 0, we simply drop the floors, turning
4589 * the integer divisions into rational divisions.
4590 * Otherwise, we split the domains into orthants, make all integer divisions
4591 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4592 * depending on the requested sign and the sign of the term in which
4593 * the integer division appears.
4595 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4596 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4599 struct isl_to_poly_data data;
4602 return pwqp_drop_floors(pwqp);
4608 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4610 for (i = 0; i < pwqp->n; ++i) {
4611 if (pwqp->p[i].qp->div->n_row == 0) {
4612 isl_pw_qpolynomial *t;
4613 t = isl_pw_qpolynomial_alloc(
4614 isl_set_copy(pwqp->p[i].set),
4615 isl_qpolynomial_copy(pwqp->p[i].qp));
4616 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4619 data.qp = pwqp->p[i].qp;
4620 if (isl_set_foreach_orthant(pwqp->p[i].set,
4621 &to_polynomial_on_orthant, &data) < 0)
4625 isl_pw_qpolynomial_free(pwqp);
4629 isl_pw_qpolynomial_free(pwqp);
4630 isl_pw_qpolynomial_free(data.res);
4634 static int poly_entry(void **entry, void *user)
4637 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4639 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4641 return *pwqp ? 0 : -1;
4644 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4645 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4647 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4651 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4652 &poly_entry, &sign) < 0)
4657 isl_union_pw_qpolynomial_free(upwqp);
4661 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4662 __isl_take isl_qpolynomial *qp)
4666 isl_vec *aff = NULL;
4667 isl_basic_map *bmap = NULL;
4673 if (!isl_upoly_is_affine(qp->upoly))
4674 isl_die(qp->dim->ctx, isl_error_invalid,
4675 "input quasi-polynomial not affine", goto error);
4676 aff = isl_qpolynomial_extract_affine(qp);
4679 dim = isl_qpolynomial_get_space(qp);
4680 dim = isl_space_from_domain(dim);
4681 pos = 1 + isl_space_offset(dim, isl_dim_out);
4682 dim = isl_space_add_dims(dim, isl_dim_out, 1);
4683 n_div = qp->div->n_row;
4684 bmap = isl_basic_map_alloc_space(dim, n_div, 1, 2 * n_div);
4686 for (i = 0; i < n_div; ++i) {
4687 k = isl_basic_map_alloc_div(bmap);
4690 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4691 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4692 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4695 k = isl_basic_map_alloc_equality(bmap);
4698 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4699 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4700 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4703 isl_qpolynomial_free(qp);
4704 bmap = isl_basic_map_finalize(bmap);
4708 isl_qpolynomial_free(qp);
4709 isl_basic_map_free(bmap);