2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_factorization.h>
17 #include <isl_union_map_private.h>
18 #include <isl_polynomial_private.h>
19 #include <isl_point_private.h>
20 #include <isl_dim_private.h>
21 #include <isl_mat_private.h>
22 #include <isl_range.h>
24 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
27 case isl_dim_param: return 0;
28 case isl_dim_in: return dim->nparam;
29 case isl_dim_out: return dim->nparam + dim->n_in;
34 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
42 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
47 isl_assert(up->ctx, up->var < 0, return NULL);
49 return (struct isl_upoly_cst *)up;
52 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
57 isl_assert(up->ctx, up->var >= 0, return NULL);
59 return (struct isl_upoly_rec *)up;
62 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
63 __isl_keep struct isl_upoly *up2)
66 struct isl_upoly_rec *rec1, *rec2;
72 if (up1->var != up2->var)
74 if (isl_upoly_is_cst(up1)) {
75 struct isl_upoly_cst *cst1, *cst2;
76 cst1 = isl_upoly_as_cst(up1);
77 cst2 = isl_upoly_as_cst(up2);
80 return isl_int_eq(cst1->n, cst2->n) &&
81 isl_int_eq(cst1->d, cst2->d);
84 rec1 = isl_upoly_as_rec(up1);
85 rec2 = isl_upoly_as_rec(up2);
89 if (rec1->n != rec2->n)
92 for (i = 0; i < rec1->n; ++i) {
93 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
101 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
103 struct isl_upoly_cst *cst;
107 if (!isl_upoly_is_cst(up))
110 cst = isl_upoly_as_cst(up);
114 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
117 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
119 struct isl_upoly_cst *cst;
123 if (!isl_upoly_is_cst(up))
126 cst = isl_upoly_as_cst(up);
130 return isl_int_sgn(cst->n);
133 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
135 struct isl_upoly_cst *cst;
139 if (!isl_upoly_is_cst(up))
142 cst = isl_upoly_as_cst(up);
146 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
149 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
151 struct isl_upoly_cst *cst;
155 if (!isl_upoly_is_cst(up))
158 cst = isl_upoly_as_cst(up);
162 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
165 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
167 struct isl_upoly_cst *cst;
171 if (!isl_upoly_is_cst(up))
174 cst = isl_upoly_as_cst(up);
178 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
181 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
183 struct isl_upoly_cst *cst;
187 if (!isl_upoly_is_cst(up))
190 cst = isl_upoly_as_cst(up);
194 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
197 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
199 struct isl_upoly_cst *cst;
203 if (!isl_upoly_is_cst(up))
206 cst = isl_upoly_as_cst(up);
210 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
213 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
215 struct isl_upoly_cst *cst;
217 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
226 isl_int_init(cst->n);
227 isl_int_init(cst->d);
232 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
234 struct isl_upoly_cst *cst;
236 cst = isl_upoly_cst_alloc(ctx);
240 isl_int_set_si(cst->n, 0);
241 isl_int_set_si(cst->d, 1);
246 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
248 struct isl_upoly_cst *cst;
250 cst = isl_upoly_cst_alloc(ctx);
254 isl_int_set_si(cst->n, 1);
255 isl_int_set_si(cst->d, 1);
260 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
262 struct isl_upoly_cst *cst;
264 cst = isl_upoly_cst_alloc(ctx);
268 isl_int_set_si(cst->n, 1);
269 isl_int_set_si(cst->d, 0);
274 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
276 struct isl_upoly_cst *cst;
278 cst = isl_upoly_cst_alloc(ctx);
282 isl_int_set_si(cst->n, -1);
283 isl_int_set_si(cst->d, 0);
288 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
290 struct isl_upoly_cst *cst;
292 cst = isl_upoly_cst_alloc(ctx);
296 isl_int_set_si(cst->n, 0);
297 isl_int_set_si(cst->d, 0);
302 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
303 isl_int n, isl_int d)
305 struct isl_upoly_cst *cst;
307 cst = isl_upoly_cst_alloc(ctx);
311 isl_int_set(cst->n, n);
312 isl_int_set(cst->d, d);
317 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
320 struct isl_upoly_rec *rec;
322 isl_assert(ctx, var >= 0, return NULL);
323 isl_assert(ctx, size >= 0, return NULL);
324 rec = isl_calloc(ctx, struct isl_upoly_rec,
325 sizeof(struct isl_upoly_rec) +
326 (size - 1) * sizeof(struct isl_upoly *));
341 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
342 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
344 qp = isl_qpolynomial_cow(qp);
348 isl_dim_free(qp->dim);
353 isl_qpolynomial_free(qp);
358 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
360 return qp ? qp->dim->ctx : NULL;
363 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
365 return qp ? isl_dim_copy(qp->dim) : NULL;
368 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
369 enum isl_dim_type type)
371 return qp ? isl_dim_size(qp->dim, type) : 0;
374 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
376 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
379 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
381 return qp ? isl_upoly_is_one(qp->upoly) : -1;
384 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
386 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
389 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
391 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
394 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
396 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
399 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
401 return qp ? isl_upoly_sgn(qp->upoly) : 0;
404 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
406 isl_int_clear(cst->n);
407 isl_int_clear(cst->d);
410 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
414 for (i = 0; i < rec->n; ++i)
415 isl_upoly_free(rec->p[i]);
418 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
427 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
429 struct isl_upoly_cst *cst;
430 struct isl_upoly_cst *dup;
432 cst = isl_upoly_as_cst(up);
436 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
439 isl_int_set(dup->n, cst->n);
440 isl_int_set(dup->d, cst->d);
445 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
448 struct isl_upoly_rec *rec;
449 struct isl_upoly_rec *dup;
451 rec = isl_upoly_as_rec(up);
455 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
459 for (i = 0; i < rec->n; ++i) {
460 dup->p[i] = isl_upoly_copy(rec->p[i]);
468 isl_upoly_free(&dup->up);
472 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
474 struct isl_upoly *dup;
479 if (isl_upoly_is_cst(up))
480 return isl_upoly_dup_cst(up);
482 return isl_upoly_dup_rec(up);
485 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
493 return isl_upoly_dup(up);
496 void isl_upoly_free(__isl_take struct isl_upoly *up)
505 upoly_free_cst((struct isl_upoly_cst *)up);
507 upoly_free_rec((struct isl_upoly_rec *)up);
509 isl_ctx_deref(up->ctx);
513 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
518 isl_int_gcd(gcd, cst->n, cst->d);
519 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
520 isl_int_divexact(cst->n, cst->n, gcd);
521 isl_int_divexact(cst->d, cst->d, gcd);
526 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
527 __isl_take struct isl_upoly *up2)
529 struct isl_upoly_cst *cst1;
530 struct isl_upoly_cst *cst2;
532 up1 = isl_upoly_cow(up1);
536 cst1 = isl_upoly_as_cst(up1);
537 cst2 = isl_upoly_as_cst(up2);
539 if (isl_int_eq(cst1->d, cst2->d))
540 isl_int_add(cst1->n, cst1->n, cst2->n);
542 isl_int_mul(cst1->n, cst1->n, cst2->d);
543 isl_int_addmul(cst1->n, cst2->n, cst1->d);
544 isl_int_mul(cst1->d, cst1->d, cst2->d);
547 isl_upoly_cst_reduce(cst1);
557 static __isl_give struct isl_upoly *replace_by_zero(
558 __isl_take struct isl_upoly *up)
566 return isl_upoly_zero(ctx);
569 static __isl_give struct isl_upoly *replace_by_constant_term(
570 __isl_take struct isl_upoly *up)
572 struct isl_upoly_rec *rec;
573 struct isl_upoly *cst;
578 rec = isl_upoly_as_rec(up);
581 cst = isl_upoly_copy(rec->p[0]);
589 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
590 __isl_take struct isl_upoly *up2)
593 struct isl_upoly_rec *rec1, *rec2;
598 if (isl_upoly_is_nan(up1)) {
603 if (isl_upoly_is_nan(up2)) {
608 if (isl_upoly_is_zero(up1)) {
613 if (isl_upoly_is_zero(up2)) {
618 if (up1->var < up2->var)
619 return isl_upoly_sum(up2, up1);
621 if (up2->var < up1->var) {
622 struct isl_upoly_rec *rec;
623 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
627 up1 = isl_upoly_cow(up1);
628 rec = isl_upoly_as_rec(up1);
631 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
633 up1 = replace_by_constant_term(up1);
637 if (isl_upoly_is_cst(up1))
638 return isl_upoly_sum_cst(up1, up2);
640 rec1 = isl_upoly_as_rec(up1);
641 rec2 = isl_upoly_as_rec(up2);
645 if (rec1->n < rec2->n)
646 return isl_upoly_sum(up2, up1);
648 up1 = isl_upoly_cow(up1);
649 rec1 = isl_upoly_as_rec(up1);
653 for (i = rec2->n - 1; i >= 0; --i) {
654 rec1->p[i] = isl_upoly_sum(rec1->p[i],
655 isl_upoly_copy(rec2->p[i]));
658 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
659 isl_upoly_free(rec1->p[i]);
665 up1 = replace_by_zero(up1);
666 else if (rec1->n == 1)
667 up1 = replace_by_constant_term(up1);
678 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
679 __isl_take struct isl_upoly *up, isl_int v)
681 struct isl_upoly_cst *cst;
683 up = isl_upoly_cow(up);
687 cst = isl_upoly_as_cst(up);
689 isl_int_addmul(cst->n, cst->d, v);
694 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
695 __isl_take struct isl_upoly *up, isl_int v)
697 struct isl_upoly_rec *rec;
702 if (isl_upoly_is_cst(up))
703 return isl_upoly_cst_add_isl_int(up, v);
705 up = isl_upoly_cow(up);
706 rec = isl_upoly_as_rec(up);
710 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
720 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
721 __isl_take struct isl_upoly *up, isl_int v)
723 struct isl_upoly_cst *cst;
725 if (isl_upoly_is_zero(up))
728 up = isl_upoly_cow(up);
732 cst = isl_upoly_as_cst(up);
734 isl_int_mul(cst->n, cst->n, v);
739 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
740 __isl_take struct isl_upoly *up, isl_int v)
743 struct isl_upoly_rec *rec;
748 if (isl_upoly_is_cst(up))
749 return isl_upoly_cst_mul_isl_int(up, v);
751 up = isl_upoly_cow(up);
752 rec = isl_upoly_as_rec(up);
756 for (i = 0; i < rec->n; ++i) {
757 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
768 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
769 __isl_take struct isl_upoly *up2)
771 struct isl_upoly_cst *cst1;
772 struct isl_upoly_cst *cst2;
774 up1 = isl_upoly_cow(up1);
778 cst1 = isl_upoly_as_cst(up1);
779 cst2 = isl_upoly_as_cst(up2);
781 isl_int_mul(cst1->n, cst1->n, cst2->n);
782 isl_int_mul(cst1->d, cst1->d, cst2->d);
784 isl_upoly_cst_reduce(cst1);
794 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
795 __isl_take struct isl_upoly *up2)
797 struct isl_upoly_rec *rec1;
798 struct isl_upoly_rec *rec2;
799 struct isl_upoly_rec *res;
803 rec1 = isl_upoly_as_rec(up1);
804 rec2 = isl_upoly_as_rec(up2);
807 size = rec1->n + rec2->n - 1;
808 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
812 for (i = 0; i < rec1->n; ++i) {
813 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
814 isl_upoly_copy(rec1->p[i]));
819 for (; i < size; ++i) {
820 res->p[i] = isl_upoly_zero(up1->ctx);
825 for (i = 0; i < rec1->n; ++i) {
826 for (j = 1; j < rec2->n; ++j) {
827 struct isl_upoly *up;
828 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
829 isl_upoly_copy(rec1->p[i]));
830 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
843 isl_upoly_free(&res->up);
847 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
848 __isl_take struct isl_upoly *up2)
853 if (isl_upoly_is_nan(up1)) {
858 if (isl_upoly_is_nan(up2)) {
863 if (isl_upoly_is_zero(up1)) {
868 if (isl_upoly_is_zero(up2)) {
873 if (isl_upoly_is_one(up1)) {
878 if (isl_upoly_is_one(up2)) {
883 if (up1->var < up2->var)
884 return isl_upoly_mul(up2, up1);
886 if (up2->var < up1->var) {
888 struct isl_upoly_rec *rec;
889 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
890 isl_ctx *ctx = up1->ctx;
893 return isl_upoly_nan(ctx);
895 up1 = isl_upoly_cow(up1);
896 rec = isl_upoly_as_rec(up1);
900 for (i = 0; i < rec->n; ++i) {
901 rec->p[i] = isl_upoly_mul(rec->p[i],
902 isl_upoly_copy(up2));
910 if (isl_upoly_is_cst(up1))
911 return isl_upoly_mul_cst(up1, up2);
913 return isl_upoly_mul_rec(up1, up2);
920 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
923 struct isl_upoly *res;
931 res = isl_upoly_copy(up);
933 res = isl_upoly_one(up->ctx);
935 while (power >>= 1) {
936 up = isl_upoly_mul(up, isl_upoly_copy(up));
938 res = isl_upoly_mul(res, isl_upoly_copy(up));
945 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
946 unsigned n_div, __isl_take struct isl_upoly *up)
948 struct isl_qpolynomial *qp = NULL;
954 total = isl_dim_total(dim);
956 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
961 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
972 isl_qpolynomial_free(qp);
976 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
985 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
987 struct isl_qpolynomial *dup;
992 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
993 isl_upoly_copy(qp->upoly));
996 isl_mat_free(dup->div);
997 dup->div = isl_mat_copy(qp->div);
1003 isl_qpolynomial_free(dup);
1007 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1015 return isl_qpolynomial_dup(qp);
1018 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1026 isl_dim_free(qp->dim);
1027 isl_mat_free(qp->div);
1028 isl_upoly_free(qp->upoly);
1033 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1036 struct isl_upoly *up;
1037 struct isl_upoly_rec *rec;
1038 struct isl_upoly_cst *cst;
1040 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1043 for (i = 0; i < 1 + power; ++i) {
1044 rec->p[i] = isl_upoly_zero(ctx);
1049 cst = isl_upoly_as_cst(rec->p[power]);
1050 isl_int_set_si(cst->n, 1);
1054 isl_upoly_free(&rec->up);
1058 /* r array maps original positions to new positions.
1060 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1064 struct isl_upoly_rec *rec;
1065 struct isl_upoly *base;
1066 struct isl_upoly *res;
1068 if (isl_upoly_is_cst(up))
1071 rec = isl_upoly_as_rec(up);
1075 isl_assert(up->ctx, rec->n >= 1, goto error);
1077 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1078 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1080 for (i = rec->n - 2; i >= 0; --i) {
1081 res = isl_upoly_mul(res, isl_upoly_copy(base));
1082 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1085 isl_upoly_free(base);
1094 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1099 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1100 div1->n_col >= div2->n_col, return -1);
1102 if (div1->n_row == div2->n_row)
1103 return isl_mat_is_equal(div1, div2);
1105 n_row = div1->n_row;
1106 n_col = div1->n_col;
1107 div1->n_row = div2->n_row;
1108 div1->n_col = div2->n_col;
1110 equal = isl_mat_is_equal(div1, div2);
1112 div1->n_row = n_row;
1113 div1->n_col = n_col;
1118 static void expand_row(__isl_keep isl_mat *dst, int d,
1119 __isl_keep isl_mat *src, int s, int *exp)
1122 unsigned c = src->n_col - src->n_row;
1124 isl_seq_cpy(dst->row[d], src->row[s], c);
1125 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
1127 for (i = 0; i < s; ++i)
1128 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
1131 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1135 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1136 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1141 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1144 struct isl_div_sort_info {
1149 static int div_sort_cmp(const void *p1, const void *p2)
1151 const struct isl_div_sort_info *i1, *i2;
1152 i1 = (const struct isl_div_sort_info *) p1;
1153 i2 = (const struct isl_div_sort_info *) p2;
1155 return cmp_row(i1->div, i1->row, i2->row);
1158 /* Sort divs and remove duplicates.
1160 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1165 struct isl_div_sort_info *array = NULL;
1166 int *pos = NULL, *at = NULL;
1167 int *reordering = NULL;
1172 if (qp->div->n_row <= 1)
1175 div_pos = isl_dim_total(qp->dim);
1177 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1179 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1180 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1181 len = qp->div->n_col - 2;
1182 reordering = isl_alloc_array(qp->div->ctx, int, len);
1183 if (!array || !pos || !at || !reordering)
1186 for (i = 0; i < qp->div->n_row; ++i) {
1187 array[i].div = qp->div;
1193 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1196 for (i = 0; i < div_pos; ++i)
1199 for (i = 0; i < qp->div->n_row; ++i) {
1200 if (pos[array[i].row] == i)
1202 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1203 pos[at[i]] = pos[array[i].row];
1204 at[pos[array[i].row]] = at[i];
1205 at[i] = array[i].row;
1206 pos[array[i].row] = i;
1210 for (i = 0; i < len - div_pos; ++i) {
1212 isl_seq_eq(qp->div->row[i - skip - 1],
1213 qp->div->row[i - skip], qp->div->n_col)) {
1214 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1215 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1216 2 + div_pos + i - skip);
1217 qp->div = isl_mat_drop_cols(qp->div,
1218 2 + div_pos + i - skip, 1);
1221 reordering[div_pos + array[i].row] = div_pos + i - skip;
1224 qp->upoly = reorder(qp->upoly, reordering);
1226 if (!qp->upoly || !qp->div)
1240 isl_qpolynomial_free(qp);
1244 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1245 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1248 isl_mat *div = NULL;
1249 unsigned d = div1->n_col - div1->n_row;
1251 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1252 d + div1->n_row + div2->n_row);
1256 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1259 expand_row(div, k, div1, i, exp1);
1260 expand_row(div, k + 1, div2, j, exp2);
1262 cmp = cmp_row(div, k, k + 1);
1266 } else if (cmp < 0) {
1270 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1273 for (; i < div1->n_row; ++i, ++k) {
1274 expand_row(div, k, div1, i, exp1);
1277 for (; j < div2->n_row; ++j, ++k) {
1278 expand_row(div, k, div2, j, exp2);
1288 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1289 int *exp, int first)
1292 struct isl_upoly_rec *rec;
1294 if (isl_upoly_is_cst(up))
1297 if (up->var < first)
1300 if (exp[up->var - first] == up->var - first)
1303 up = isl_upoly_cow(up);
1307 up->var = exp[up->var - first] + first;
1309 rec = isl_upoly_as_rec(up);
1313 for (i = 0; i < rec->n; ++i) {
1314 rec->p[i] = expand(rec->p[i], exp, first);
1325 static __isl_give isl_qpolynomial *with_merged_divs(
1326 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1327 __isl_take isl_qpolynomial *qp2),
1328 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1332 isl_mat *div = NULL;
1334 qp1 = isl_qpolynomial_cow(qp1);
1335 qp2 = isl_qpolynomial_cow(qp2);
1340 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1341 qp1->div->n_col >= qp2->div->n_col, goto error);
1343 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1344 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1348 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1352 isl_mat_free(qp1->div);
1353 qp1->div = isl_mat_copy(div);
1354 isl_mat_free(qp2->div);
1355 qp2->div = isl_mat_copy(div);
1357 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1358 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1360 if (!qp1->upoly || !qp2->upoly)
1367 return fn(qp1, qp2);
1372 isl_qpolynomial_free(qp1);
1373 isl_qpolynomial_free(qp2);
1377 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1378 __isl_take isl_qpolynomial *qp2)
1380 qp1 = isl_qpolynomial_cow(qp1);
1385 if (qp1->div->n_row < qp2->div->n_row)
1386 return isl_qpolynomial_add(qp2, qp1);
1388 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1389 if (!compatible_divs(qp1->div, qp2->div))
1390 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1392 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1396 isl_qpolynomial_free(qp2);
1400 isl_qpolynomial_free(qp1);
1401 isl_qpolynomial_free(qp2);
1405 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1406 __isl_keep isl_set *dom,
1407 __isl_take isl_qpolynomial *qp1,
1408 __isl_take isl_qpolynomial *qp2)
1410 qp1 = isl_qpolynomial_add(qp1, qp2);
1411 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1415 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1416 __isl_take isl_qpolynomial *qp2)
1418 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1421 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1422 __isl_take isl_qpolynomial *qp, isl_int v)
1424 if (isl_int_is_zero(v))
1427 qp = isl_qpolynomial_cow(qp);
1431 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1437 isl_qpolynomial_free(qp);
1442 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1447 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1450 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1451 __isl_take isl_qpolynomial *qp, isl_int v)
1453 if (isl_int_is_one(v))
1456 if (qp && isl_int_is_zero(v)) {
1457 isl_qpolynomial *zero;
1458 zero = isl_qpolynomial_zero(isl_dim_copy(qp->dim));
1459 isl_qpolynomial_free(qp);
1463 qp = isl_qpolynomial_cow(qp);
1467 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1473 isl_qpolynomial_free(qp);
1477 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1478 __isl_take isl_qpolynomial *qp2)
1480 qp1 = isl_qpolynomial_cow(qp1);
1485 if (qp1->div->n_row < qp2->div->n_row)
1486 return isl_qpolynomial_mul(qp2, qp1);
1488 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1489 if (!compatible_divs(qp1->div, qp2->div))
1490 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1492 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1496 isl_qpolynomial_free(qp2);
1500 isl_qpolynomial_free(qp1);
1501 isl_qpolynomial_free(qp2);
1505 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1508 qp = isl_qpolynomial_cow(qp);
1513 qp->upoly = isl_upoly_pow(qp->upoly, power);
1519 isl_qpolynomial_free(qp);
1523 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1527 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1530 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1534 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1537 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1541 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1544 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1548 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1551 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1555 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1558 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1561 struct isl_qpolynomial *qp;
1562 struct isl_upoly_cst *cst;
1567 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1571 cst = isl_upoly_as_cst(qp->upoly);
1572 isl_int_set(cst->n, v);
1577 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1578 isl_int *n, isl_int *d)
1580 struct isl_upoly_cst *cst;
1585 if (!isl_upoly_is_cst(qp->upoly))
1588 cst = isl_upoly_as_cst(qp->upoly);
1593 isl_int_set(*n, cst->n);
1595 isl_int_set(*d, cst->d);
1600 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1603 struct isl_upoly_rec *rec;
1611 rec = isl_upoly_as_rec(up);
1618 isl_assert(up->ctx, rec->n > 1, return -1);
1620 is_cst = isl_upoly_is_cst(rec->p[1]);
1626 return isl_upoly_is_affine(rec->p[0]);
1629 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1634 if (qp->div->n_row > 0)
1637 return isl_upoly_is_affine(qp->upoly);
1640 static void update_coeff(__isl_keep isl_vec *aff,
1641 __isl_keep struct isl_upoly_cst *cst, int pos)
1646 if (isl_int_is_zero(cst->n))
1651 isl_int_gcd(gcd, cst->d, aff->el[0]);
1652 isl_int_divexact(f, cst->d, gcd);
1653 isl_int_divexact(gcd, aff->el[0], gcd);
1654 isl_seq_scale(aff->el, aff->el, f, aff->size);
1655 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1660 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1661 __isl_keep isl_vec *aff)
1663 struct isl_upoly_cst *cst;
1664 struct isl_upoly_rec *rec;
1670 struct isl_upoly_cst *cst;
1672 cst = isl_upoly_as_cst(up);
1675 update_coeff(aff, cst, 0);
1679 rec = isl_upoly_as_rec(up);
1682 isl_assert(up->ctx, rec->n == 2, return -1);
1684 cst = isl_upoly_as_cst(rec->p[1]);
1687 update_coeff(aff, cst, 1 + up->var);
1689 return isl_upoly_update_affine(rec->p[0], aff);
1692 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1693 __isl_keep isl_qpolynomial *qp)
1701 d = isl_dim_total(qp->dim);
1702 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1706 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1707 isl_int_set_si(aff->el[0], 1);
1709 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1718 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1719 __isl_keep isl_qpolynomial *qp2)
1726 equal = isl_dim_equal(qp1->dim, qp2->dim);
1727 if (equal < 0 || !equal)
1730 equal = isl_mat_is_equal(qp1->div, qp2->div);
1731 if (equal < 0 || !equal)
1734 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1737 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1740 struct isl_upoly_rec *rec;
1742 if (isl_upoly_is_cst(up)) {
1743 struct isl_upoly_cst *cst;
1744 cst = isl_upoly_as_cst(up);
1747 isl_int_lcm(*d, *d, cst->d);
1751 rec = isl_upoly_as_rec(up);
1755 for (i = 0; i < rec->n; ++i)
1756 upoly_update_den(rec->p[i], d);
1759 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1761 isl_int_set_si(*d, 1);
1764 upoly_update_den(qp->upoly, d);
1767 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1770 struct isl_ctx *ctx;
1777 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1780 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1781 enum isl_dim_type type, unsigned pos)
1786 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1787 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1789 if (type == isl_dim_set)
1790 pos += isl_dim_size(dim, isl_dim_param);
1792 return isl_qpolynomial_var_pow(dim, pos, 1);
1798 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1799 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1802 struct isl_upoly_rec *rec;
1803 struct isl_upoly *base, *res;
1808 if (isl_upoly_is_cst(up))
1811 if (up->var < first)
1814 rec = isl_upoly_as_rec(up);
1818 isl_assert(up->ctx, rec->n >= 1, goto error);
1820 if (up->var >= first + n)
1821 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1823 base = isl_upoly_copy(subs[up->var - first]);
1825 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1826 for (i = rec->n - 2; i >= 0; --i) {
1827 struct isl_upoly *t;
1828 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1829 res = isl_upoly_mul(res, isl_upoly_copy(base));
1830 res = isl_upoly_sum(res, t);
1833 isl_upoly_free(base);
1842 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1843 isl_int denom, unsigned len)
1846 struct isl_upoly *up;
1848 isl_assert(ctx, len >= 1, return NULL);
1850 up = isl_upoly_rat_cst(ctx, f[0], denom);
1851 for (i = 0; i < len - 1; ++i) {
1852 struct isl_upoly *t;
1853 struct isl_upoly *c;
1855 if (isl_int_is_zero(f[1 + i]))
1858 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1859 t = isl_upoly_var_pow(ctx, i, 1);
1860 t = isl_upoly_mul(c, t);
1861 up = isl_upoly_sum(up, t);
1867 /* Remove common factor of non-constant terms and denominator.
1869 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1871 isl_ctx *ctx = qp->div->ctx;
1872 unsigned total = qp->div->n_col - 2;
1874 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1875 isl_int_gcd(ctx->normalize_gcd,
1876 ctx->normalize_gcd, qp->div->row[div][0]);
1877 if (isl_int_is_one(ctx->normalize_gcd))
1880 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1881 ctx->normalize_gcd, total);
1882 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1883 ctx->normalize_gcd);
1884 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1885 ctx->normalize_gcd);
1888 /* Replace the integer division identified by "div" by the polynomial "s".
1889 * The integer division is assumed not to appear in the definition
1890 * of any other integer divisions.
1892 static __isl_give isl_qpolynomial *substitute_div(
1893 __isl_take isl_qpolynomial *qp,
1894 int div, __isl_take struct isl_upoly *s)
1903 qp = isl_qpolynomial_cow(qp);
1907 total = isl_dim_total(qp->dim);
1908 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1912 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1915 for (i = 0; i < total + div; ++i)
1917 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1918 reordering[i] = i - 1;
1919 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1920 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1921 qp->upoly = reorder(qp->upoly, reordering);
1924 if (!qp->upoly || !qp->div)
1930 isl_qpolynomial_free(qp);
1935 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1936 * divisions because d is equal to 1 by their definition, i.e., e.
1938 static __isl_give isl_qpolynomial *substitute_non_divs(
1939 __isl_take isl_qpolynomial *qp)
1943 struct isl_upoly *s;
1948 total = isl_dim_total(qp->dim);
1949 for (i = 0; qp && i < qp->div->n_row; ++i) {
1950 if (!isl_int_is_one(qp->div->row[i][0]))
1952 for (j = i + 1; j < qp->div->n_row; ++j) {
1953 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1955 isl_seq_combine(qp->div->row[j] + 1,
1956 qp->div->ctx->one, qp->div->row[j] + 1,
1957 qp->div->row[j][2 + total + i],
1958 qp->div->row[i] + 1, 1 + total + i);
1959 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1960 normalize_div(qp, j);
1962 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1963 qp->div->row[i][0], qp->div->n_col - 1);
1964 qp = substitute_div(qp, i, s);
1971 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1972 * with d the denominator. When replacing the coefficient e of x by
1973 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1974 * inside the division, so we need to add floor(e/d) * x outside.
1975 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1976 * to adjust the coefficient of x in each later div that depends on the
1977 * current div "div" and also in the affine expression "aff"
1978 * (if it too depends on "div").
1980 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1981 __isl_keep isl_vec *aff)
1985 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1988 for (i = 0; i < 1 + total + div; ++i) {
1989 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1990 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1992 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1993 isl_int_fdiv_r(qp->div->row[div][1 + i],
1994 qp->div->row[div][1 + i], qp->div->row[div][0]);
1995 if (!isl_int_is_zero(aff->el[1 + total + div]))
1996 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1997 for (j = div + 1; j < qp->div->n_row; ++j) {
1998 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
2000 isl_int_addmul(qp->div->row[j][1 + i],
2001 v, qp->div->row[j][2 + total + div]);
2007 /* Check if the last non-zero coefficient is bigger that half of the
2008 * denominator. If so, we will invert the div to further reduce the number
2009 * of distinct divs that may appear.
2010 * If the last non-zero coefficient is exactly half the denominator,
2011 * then we continue looking for earlier coefficients that are bigger
2012 * than half the denominator.
2014 static int needs_invert(__isl_keep isl_mat *div, int row)
2019 for (i = div->n_col - 1; i >= 1; --i) {
2020 if (isl_int_is_zero(div->row[row][i]))
2022 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
2023 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
2024 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
2034 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2035 * We only invert the coefficients of e (and the coefficient of q in
2036 * later divs and in "aff"). After calling this function, the
2037 * coefficients of e should be reduced again.
2039 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
2040 __isl_keep isl_vec *aff)
2042 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2044 isl_seq_neg(qp->div->row[div] + 1,
2045 qp->div->row[div] + 1, qp->div->n_col - 1);
2046 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2047 isl_int_add(qp->div->row[div][1],
2048 qp->div->row[div][1], qp->div->row[div][0]);
2049 if (!isl_int_is_zero(aff->el[1 + total + div]))
2050 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2051 isl_mat_col_mul(qp->div, 2 + total + div,
2052 qp->div->ctx->negone, 2 + total + div);
2055 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2056 * in the interval [0, d-1], with d the denominator and such that the
2057 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2059 * After the reduction, some divs may have become redundant or identical,
2060 * so we call substitute_non_divs and sort_divs. If these functions
2061 * eliminate divs of merge * two or more divs into one, the coefficients
2062 * of the enclosing divs may have to be reduced again, so we call
2063 * ourselves recursively if the number of divs decreases.
2065 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2068 isl_vec *aff = NULL;
2069 struct isl_upoly *s;
2075 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2076 aff = isl_vec_clr(aff);
2080 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2082 for (i = 0; i < qp->div->n_row; ++i) {
2083 normalize_div(qp, i);
2084 reduce_div(qp, i, aff);
2085 if (needs_invert(qp->div, i)) {
2086 invert_div(qp, i, aff);
2087 reduce_div(qp, i, aff);
2091 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2092 qp->div->ctx->one, aff->size);
2093 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2100 n_div = qp->div->n_row;
2101 qp = substitute_non_divs(qp);
2103 if (qp && qp->div->n_row < n_div)
2104 return reduce_divs(qp);
2108 isl_qpolynomial_free(qp);
2113 /* Assumes each div only depends on earlier divs.
2115 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2118 struct isl_qpolynomial *qp = NULL;
2119 struct isl_upoly_rec *rec;
2120 struct isl_upoly_cst *cst;
2127 d = div->line - div->bmap->div;
2129 pos = isl_dim_total(div->bmap->dim) + d;
2130 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2131 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2132 div->bmap->n_div, &rec->up);
2136 for (i = 0; i < div->bmap->n_div; ++i)
2137 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2139 for (i = 0; i < 1 + power; ++i) {
2140 rec->p[i] = isl_upoly_zero(div->ctx);
2145 cst = isl_upoly_as_cst(rec->p[power]);
2146 isl_int_set_si(cst->n, 1);
2150 qp = reduce_divs(qp);
2154 isl_qpolynomial_free(qp);
2159 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2161 return isl_qpolynomial_div_pow(div, 1);
2164 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2165 const isl_int n, const isl_int d)
2167 struct isl_qpolynomial *qp;
2168 struct isl_upoly_cst *cst;
2170 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2174 cst = isl_upoly_as_cst(qp->upoly);
2175 isl_int_set(cst->n, n);
2176 isl_int_set(cst->d, d);
2181 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2183 struct isl_upoly_rec *rec;
2189 if (isl_upoly_is_cst(up))
2193 active[up->var] = 1;
2195 rec = isl_upoly_as_rec(up);
2196 for (i = 0; i < rec->n; ++i)
2197 if (up_set_active(rec->p[i], active, d) < 0)
2203 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2206 int d = isl_dim_total(qp->dim);
2211 for (i = 0; i < d; ++i)
2212 for (j = 0; j < qp->div->n_row; ++j) {
2213 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2219 return up_set_active(qp->upoly, active, d);
2222 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2223 enum isl_dim_type type, unsigned first, unsigned n)
2234 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2236 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2237 type == isl_dim_set, return -1);
2239 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
2240 if (set_active(qp, active) < 0)
2243 if (type == isl_dim_set)
2244 first += isl_dim_size(qp->dim, isl_dim_param);
2245 for (i = 0; i < n; ++i)
2246 if (active[first + i]) {
2259 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2260 unsigned first, unsigned n)
2263 struct isl_upoly_rec *rec;
2267 if (n == 0 || up->var < 0 || up->var < first)
2269 if (up->var < first + n) {
2270 up = replace_by_constant_term(up);
2271 return isl_upoly_drop(up, first, n);
2273 up = isl_upoly_cow(up);
2277 rec = isl_upoly_as_rec(up);
2281 for (i = 0; i < rec->n; ++i) {
2282 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2293 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2294 __isl_take isl_qpolynomial *qp,
2295 enum isl_dim_type type, unsigned pos, const char *s)
2297 qp = isl_qpolynomial_cow(qp);
2300 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2305 isl_qpolynomial_free(qp);
2309 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2310 __isl_take isl_qpolynomial *qp,
2311 enum isl_dim_type type, unsigned first, unsigned n)
2315 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2318 qp = isl_qpolynomial_cow(qp);
2322 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2324 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2325 type == isl_dim_set, goto error);
2327 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2331 if (type == isl_dim_set)
2332 first += isl_dim_size(qp->dim, isl_dim_param);
2334 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2338 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2344 isl_qpolynomial_free(qp);
2348 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2349 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2355 struct isl_upoly *up;
2359 if (eq->n_eq == 0) {
2360 isl_basic_set_free(eq);
2364 qp = isl_qpolynomial_cow(qp);
2367 qp->div = isl_mat_cow(qp->div);
2371 total = 1 + isl_dim_total(eq->dim);
2373 isl_int_init(denom);
2374 for (i = 0; i < eq->n_eq; ++i) {
2375 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2376 if (j < 0 || j == 0 || j >= total)
2379 for (k = 0; k < qp->div->n_row; ++k) {
2380 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2382 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2383 &qp->div->row[k][0]);
2384 normalize_div(qp, k);
2387 if (isl_int_is_pos(eq->eq[i][j]))
2388 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2389 isl_int_abs(denom, eq->eq[i][j]);
2390 isl_int_set_si(eq->eq[i][j], 0);
2392 up = isl_upoly_from_affine(qp->dim->ctx,
2393 eq->eq[i], denom, total);
2394 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2397 isl_int_clear(denom);
2402 isl_basic_set_free(eq);
2404 qp = substitute_non_divs(qp);
2409 isl_basic_set_free(eq);
2410 isl_qpolynomial_free(qp);
2414 static __isl_give isl_basic_set *add_div_constraints(
2415 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2423 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2426 total = isl_basic_set_total_dim(bset);
2427 for (i = 0; i < div->n_row; ++i)
2428 if (isl_basic_set_add_div_constraints_var(bset,
2429 total - div->n_row + i, div->row[i]) < 0)
2436 isl_basic_set_free(bset);
2440 /* Look for equalities among the variables shared by context and qp
2441 * and the integer divisions of qp, if any.
2442 * The equalities are then used to eliminate variables and/or integer
2443 * divisions from qp.
2445 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2446 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2452 if (qp->div->n_row > 0) {
2453 isl_basic_set *bset;
2454 context = isl_set_add_dims(context, isl_dim_set,
2456 bset = isl_basic_set_universe(isl_set_get_dim(context));
2457 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2458 context = isl_set_intersect(context,
2459 isl_set_from_basic_set(bset));
2462 aff = isl_set_affine_hull(context);
2463 return isl_qpolynomial_substitute_equalities(qp, aff);
2465 isl_qpolynomial_free(qp);
2466 isl_set_free(context);
2471 #define PW isl_pw_qpolynomial
2473 #define EL isl_qpolynomial
2475 #define IS_ZERO is_zero
2479 #include <isl_pw_templ.c>
2482 #define UNION isl_union_pw_qpolynomial
2484 #define PART isl_pw_qpolynomial
2486 #define PARTS pw_qpolynomial
2488 #include <isl_union_templ.c>
2490 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2498 if (!isl_set_fast_is_universe(pwqp->p[0].set))
2501 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2504 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2505 __isl_take isl_pw_qpolynomial *pwqp1,
2506 __isl_take isl_pw_qpolynomial *pwqp2)
2509 struct isl_pw_qpolynomial *res;
2512 if (!pwqp1 || !pwqp2)
2515 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2518 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2519 isl_pw_qpolynomial_free(pwqp2);
2523 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2524 isl_pw_qpolynomial_free(pwqp1);
2528 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2529 isl_pw_qpolynomial_free(pwqp1);
2533 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2534 isl_pw_qpolynomial_free(pwqp2);
2538 n = pwqp1->n * pwqp2->n;
2539 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2541 for (i = 0; i < pwqp1->n; ++i) {
2542 for (j = 0; j < pwqp2->n; ++j) {
2543 struct isl_set *common;
2544 struct isl_qpolynomial *prod;
2545 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2546 isl_set_copy(pwqp2->p[j].set));
2547 if (isl_set_fast_is_empty(common)) {
2548 isl_set_free(common);
2552 prod = isl_qpolynomial_mul(
2553 isl_qpolynomial_copy(pwqp1->p[i].qp),
2554 isl_qpolynomial_copy(pwqp2->p[j].qp));
2556 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2560 isl_pw_qpolynomial_free(pwqp1);
2561 isl_pw_qpolynomial_free(pwqp2);
2565 isl_pw_qpolynomial_free(pwqp1);
2566 isl_pw_qpolynomial_free(pwqp2);
2570 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2571 __isl_take isl_pw_qpolynomial *pwqp)
2578 if (isl_pw_qpolynomial_is_zero(pwqp))
2581 pwqp = isl_pw_qpolynomial_cow(pwqp);
2585 for (i = 0; i < pwqp->n; ++i) {
2586 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2593 isl_pw_qpolynomial_free(pwqp);
2597 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2598 __isl_take isl_pw_qpolynomial *pwqp1,
2599 __isl_take isl_pw_qpolynomial *pwqp2)
2601 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2604 __isl_give struct isl_upoly *isl_upoly_eval(
2605 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2608 struct isl_upoly_rec *rec;
2609 struct isl_upoly *res;
2610 struct isl_upoly *base;
2612 if (isl_upoly_is_cst(up)) {
2617 rec = isl_upoly_as_rec(up);
2621 isl_assert(up->ctx, rec->n >= 1, goto error);
2623 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2625 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2628 for (i = rec->n - 2; i >= 0; --i) {
2629 res = isl_upoly_mul(res, isl_upoly_copy(base));
2630 res = isl_upoly_sum(res,
2631 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2632 isl_vec_copy(vec)));
2635 isl_upoly_free(base);
2645 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2646 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2649 struct isl_upoly *up;
2654 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2656 if (qp->div->n_row == 0)
2657 ext = isl_vec_copy(pnt->vec);
2660 unsigned dim = isl_dim_total(qp->dim);
2661 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2665 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2666 for (i = 0; i < qp->div->n_row; ++i) {
2667 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2668 1 + dim + i, &ext->el[1+dim+i]);
2669 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2670 qp->div->row[i][0]);
2674 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2678 dim = isl_dim_copy(qp->dim);
2679 isl_qpolynomial_free(qp);
2680 isl_point_free(pnt);
2682 return isl_qpolynomial_alloc(dim, 0, up);
2684 isl_qpolynomial_free(qp);
2685 isl_point_free(pnt);
2689 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2690 __isl_keep struct isl_upoly_cst *cst2)
2695 isl_int_mul(t, cst1->n, cst2->d);
2696 isl_int_submul(t, cst2->n, cst1->d);
2697 cmp = isl_int_sgn(t);
2702 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2703 __isl_keep isl_qpolynomial *qp2)
2705 struct isl_upoly_cst *cst1, *cst2;
2709 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2710 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2711 if (isl_qpolynomial_is_nan(qp1))
2713 if (isl_qpolynomial_is_nan(qp2))
2715 cst1 = isl_upoly_as_cst(qp1->upoly);
2716 cst2 = isl_upoly_as_cst(qp2->upoly);
2718 return isl_upoly_cmp(cst1, cst2) <= 0;
2721 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2722 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2724 struct isl_upoly_cst *cst1, *cst2;
2729 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2730 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2731 cst1 = isl_upoly_as_cst(qp1->upoly);
2732 cst2 = isl_upoly_as_cst(qp2->upoly);
2733 cmp = isl_upoly_cmp(cst1, cst2);
2736 isl_qpolynomial_free(qp2);
2738 isl_qpolynomial_free(qp1);
2743 isl_qpolynomial_free(qp1);
2744 isl_qpolynomial_free(qp2);
2748 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2749 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2751 struct isl_upoly_cst *cst1, *cst2;
2756 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2757 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2758 cst1 = isl_upoly_as_cst(qp1->upoly);
2759 cst2 = isl_upoly_as_cst(qp2->upoly);
2760 cmp = isl_upoly_cmp(cst1, cst2);
2763 isl_qpolynomial_free(qp2);
2765 isl_qpolynomial_free(qp1);
2770 isl_qpolynomial_free(qp1);
2771 isl_qpolynomial_free(qp2);
2775 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2776 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2777 unsigned first, unsigned n)
2783 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2786 qp = isl_qpolynomial_cow(qp);
2790 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2793 g_pos = pos(qp->dim, type) + first;
2795 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2799 total = qp->div->n_col - 2;
2800 if (total > g_pos) {
2802 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2805 for (i = 0; i < total - g_pos; ++i)
2807 qp->upoly = expand(qp->upoly, exp, g_pos);
2813 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2819 isl_qpolynomial_free(qp);
2823 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2824 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2828 pos = isl_qpolynomial_dim(qp, type);
2830 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2833 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2834 __isl_take isl_pw_qpolynomial *pwqp,
2835 enum isl_dim_type type, unsigned n)
2839 pos = isl_pw_qpolynomial_dim(pwqp, type);
2841 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2844 static int *reordering_move(isl_ctx *ctx,
2845 unsigned len, unsigned dst, unsigned src, unsigned n)
2850 reordering = isl_alloc_array(ctx, int, len);
2855 for (i = 0; i < dst; ++i)
2857 for (i = 0; i < n; ++i)
2858 reordering[src + i] = dst + i;
2859 for (i = 0; i < src - dst; ++i)
2860 reordering[dst + i] = dst + n + i;
2861 for (i = 0; i < len - src - n; ++i)
2862 reordering[src + n + i] = src + n + i;
2864 for (i = 0; i < src; ++i)
2866 for (i = 0; i < n; ++i)
2867 reordering[src + i] = dst + i;
2868 for (i = 0; i < dst - src; ++i)
2869 reordering[src + n + i] = src + i;
2870 for (i = 0; i < len - dst - n; ++i)
2871 reordering[dst + n + i] = dst + n + i;
2877 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2878 __isl_take isl_qpolynomial *qp,
2879 enum isl_dim_type dst_type, unsigned dst_pos,
2880 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2886 qp = isl_qpolynomial_cow(qp);
2890 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2893 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2894 g_src_pos = pos(qp->dim, src_type) + src_pos;
2895 if (dst_type > src_type)
2898 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2905 reordering = reordering_move(qp->dim->ctx,
2906 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2910 qp->upoly = reorder(qp->upoly, reordering);
2915 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2921 isl_qpolynomial_free(qp);
2925 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2926 isl_int *f, isl_int denom)
2928 struct isl_upoly *up;
2933 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2935 return isl_qpolynomial_alloc(dim, 0, up);
2938 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2939 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2943 struct isl_upoly *up;
2944 isl_qpolynomial *qp;
2950 isl_int_init(denom);
2952 isl_constraint_get_coefficient(c, type, pos, &denom);
2953 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2954 sgn = isl_int_sgn(denom);
2955 isl_int_abs(denom, denom);
2956 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2957 1 + isl_constraint_dim(c, isl_dim_all));
2959 isl_int_neg(denom, denom);
2960 isl_constraint_set_coefficient(c, type, pos, denom);
2962 dim = isl_dim_copy(c->bmap->dim);
2964 isl_int_clear(denom);
2965 isl_constraint_free(c);
2967 qp = isl_qpolynomial_alloc(dim, 0, up);
2969 qp = isl_qpolynomial_neg(qp);
2973 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2974 * in "qp" by subs[i].
2976 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2977 __isl_take isl_qpolynomial *qp,
2978 enum isl_dim_type type, unsigned first, unsigned n,
2979 __isl_keep isl_qpolynomial **subs)
2982 struct isl_upoly **ups;
2987 qp = isl_qpolynomial_cow(qp);
2990 for (i = 0; i < n; ++i)
2994 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2997 for (i = 0; i < n; ++i)
2998 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3001 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3002 for (i = 0; i < n; ++i)
3003 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3005 first += pos(qp->dim, type);
3007 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3010 for (i = 0; i < n; ++i)
3011 ups[i] = subs[i]->upoly;
3013 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3022 isl_qpolynomial_free(qp);
3026 /* Extend "bset" with extra set dimensions for each integer division
3027 * in "qp" and then call "fn" with the extended bset and the polynomial
3028 * that results from replacing each of the integer divisions by the
3029 * corresponding extra set dimension.
3031 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3032 __isl_keep isl_basic_set *bset,
3033 int (*fn)(__isl_take isl_basic_set *bset,
3034 __isl_take isl_qpolynomial *poly, void *user), void *user)
3038 isl_qpolynomial *poly;
3042 if (qp->div->n_row == 0)
3043 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3046 div = isl_mat_copy(qp->div);
3047 dim = isl_dim_copy(qp->dim);
3048 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3049 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3050 bset = isl_basic_set_copy(bset);
3051 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3052 bset = add_div_constraints(bset, div);
3054 return fn(bset, poly, user);
3059 /* Return total degree in variables first (inclusive) up to last (exclusive).
3061 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3065 struct isl_upoly_rec *rec;
3069 if (isl_upoly_is_zero(up))
3071 if (isl_upoly_is_cst(up) || up->var < first)
3074 rec = isl_upoly_as_rec(up);
3078 for (i = 0; i < rec->n; ++i) {
3081 if (isl_upoly_is_zero(rec->p[i]))
3083 d = isl_upoly_degree(rec->p[i], first, last);
3093 /* Return total degree in set variables.
3095 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3103 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3104 nvar = isl_dim_size(poly->dim, isl_dim_set);
3105 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3108 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3109 unsigned pos, int deg)
3112 struct isl_upoly_rec *rec;
3117 if (isl_upoly_is_cst(up) || up->var < pos) {
3119 return isl_upoly_copy(up);
3121 return isl_upoly_zero(up->ctx);
3124 rec = isl_upoly_as_rec(up);
3128 if (up->var == pos) {
3130 return isl_upoly_copy(rec->p[deg]);
3132 return isl_upoly_zero(up->ctx);
3135 up = isl_upoly_copy(up);
3136 up = isl_upoly_cow(up);
3137 rec = isl_upoly_as_rec(up);
3141 for (i = 0; i < rec->n; ++i) {
3142 struct isl_upoly *t;
3143 t = isl_upoly_coeff(rec->p[i], pos, deg);
3146 isl_upoly_free(rec->p[i]);
3156 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3158 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3159 __isl_keep isl_qpolynomial *qp,
3160 enum isl_dim_type type, unsigned t_pos, int deg)
3163 struct isl_upoly *up;
3169 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3172 g_pos = pos(qp->dim, type) + t_pos;
3173 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3175 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3178 isl_mat_free(c->div);
3179 c->div = isl_mat_copy(qp->div);
3184 isl_qpolynomial_free(c);
3188 /* Homogenize the polynomial in the variables first (inclusive) up to
3189 * last (exclusive) by inserting powers of variable first.
3190 * Variable first is assumed not to appear in the input.
3192 __isl_give struct isl_upoly *isl_upoly_homogenize(
3193 __isl_take struct isl_upoly *up, int deg, int target,
3194 int first, int last)
3197 struct isl_upoly_rec *rec;
3201 if (isl_upoly_is_zero(up))
3205 if (isl_upoly_is_cst(up) || up->var < first) {
3206 struct isl_upoly *hom;
3208 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3211 rec = isl_upoly_as_rec(hom);
3212 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3217 up = isl_upoly_cow(up);
3218 rec = isl_upoly_as_rec(up);
3222 for (i = 0; i < rec->n; ++i) {
3223 if (isl_upoly_is_zero(rec->p[i]))
3225 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3226 up->var < last ? deg + i : i, target,
3238 /* Homogenize the polynomial in the set variables by introducing
3239 * powers of an extra set variable at position 0.
3241 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3242 __isl_take isl_qpolynomial *poly)
3246 int deg = isl_qpolynomial_degree(poly);
3251 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3252 poly = isl_qpolynomial_cow(poly);
3256 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3257 nvar = isl_dim_size(poly->dim, isl_dim_set);
3258 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3265 isl_qpolynomial_free(poly);
3269 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3270 __isl_take isl_mat *div)
3278 n = isl_dim_total(dim) + div->n_row;
3280 term = isl_calloc(dim->ctx, struct isl_term,
3281 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3288 isl_int_init(term->n);
3289 isl_int_init(term->d);
3298 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3307 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3316 total = isl_dim_total(term->dim) + term->div->n_row;
3318 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3322 isl_int_set(dup->n, term->n);
3323 isl_int_set(dup->d, term->d);
3325 for (i = 0; i < total; ++i)
3326 dup->pow[i] = term->pow[i];
3331 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3339 return isl_term_dup(term);
3342 void isl_term_free(__isl_take isl_term *term)
3347 if (--term->ref > 0)
3350 isl_dim_free(term->dim);
3351 isl_mat_free(term->div);
3352 isl_int_clear(term->n);
3353 isl_int_clear(term->d);
3357 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3365 case isl_dim_out: return isl_dim_size(term->dim, type);
3366 case isl_dim_div: return term->div->n_row;
3367 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3372 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3374 return term ? term->dim->ctx : NULL;
3377 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3381 isl_int_set(*n, term->n);
3384 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3388 isl_int_set(*d, term->d);
3391 int isl_term_get_exp(__isl_keep isl_term *term,
3392 enum isl_dim_type type, unsigned pos)
3397 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3399 if (type >= isl_dim_set)
3400 pos += isl_dim_size(term->dim, isl_dim_param);
3401 if (type >= isl_dim_div)
3402 pos += isl_dim_size(term->dim, isl_dim_set);
3404 return term->pow[pos];
3407 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3409 isl_basic_map *bmap;
3416 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3419 total = term->div->n_col - term->div->n_row - 2;
3420 /* No nested divs for now */
3421 isl_assert(term->dim->ctx,
3422 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3423 term->div->n_row) == -1,
3426 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3427 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3430 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3432 return isl_basic_map_div(bmap, k);
3434 isl_basic_map_free(bmap);
3438 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3439 int (*fn)(__isl_take isl_term *term, void *user),
3440 __isl_take isl_term *term, void *user)
3443 struct isl_upoly_rec *rec;
3448 if (isl_upoly_is_zero(up))
3451 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3452 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3453 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3455 if (isl_upoly_is_cst(up)) {
3456 struct isl_upoly_cst *cst;
3457 cst = isl_upoly_as_cst(up);
3460 term = isl_term_cow(term);
3463 isl_int_set(term->n, cst->n);
3464 isl_int_set(term->d, cst->d);
3465 if (fn(isl_term_copy(term), user) < 0)
3470 rec = isl_upoly_as_rec(up);
3474 for (i = 0; i < rec->n; ++i) {
3475 term = isl_term_cow(term);
3478 term->pow[up->var] = i;
3479 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3483 term->pow[up->var] = 0;
3487 isl_term_free(term);
3491 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3492 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3499 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3503 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3505 isl_term_free(term);
3507 return term ? 0 : -1;
3510 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3512 struct isl_upoly *up;
3513 isl_qpolynomial *qp;
3519 n = isl_dim_total(term->dim) + term->div->n_row;
3521 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3522 for (i = 0; i < n; ++i) {
3525 up = isl_upoly_mul(up,
3526 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3529 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3532 isl_mat_free(qp->div);
3533 qp->div = isl_mat_copy(term->div);
3537 isl_term_free(term);
3540 isl_qpolynomial_free(qp);
3541 isl_term_free(term);
3545 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3546 __isl_take isl_dim *dim)
3555 if (isl_dim_equal(qp->dim, dim)) {
3560 qp = isl_qpolynomial_cow(qp);
3564 extra = isl_dim_size(dim, isl_dim_set) -
3565 isl_dim_size(qp->dim, isl_dim_set);
3566 total = isl_dim_total(qp->dim);
3567 if (qp->div->n_row) {
3570 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3573 for (i = 0; i < qp->div->n_row; ++i)
3575 qp->upoly = expand(qp->upoly, exp, total);
3580 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3583 for (i = 0; i < qp->div->n_row; ++i)
3584 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3586 isl_dim_free(qp->dim);
3592 isl_qpolynomial_free(qp);
3596 /* For each parameter or variable that does not appear in qp,
3597 * first eliminate the variable from all constraints and then set it to zero.
3599 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3600 __isl_keep isl_qpolynomial *qp)
3611 d = isl_dim_total(set->dim);
3612 active = isl_calloc_array(set->ctx, int, d);
3613 if (set_active(qp, active) < 0)
3616 for (i = 0; i < d; ++i)
3625 nparam = isl_dim_size(set->dim, isl_dim_param);
3626 nvar = isl_dim_size(set->dim, isl_dim_set);
3627 for (i = 0; i < nparam; ++i) {
3630 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3631 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3633 for (i = 0; i < nvar; ++i) {
3634 if (active[nparam + i])
3636 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3637 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3649 struct isl_opt_data {
3650 isl_qpolynomial *qp;
3652 isl_qpolynomial *opt;
3656 static int opt_fn(__isl_take isl_point *pnt, void *user)
3658 struct isl_opt_data *data = (struct isl_opt_data *)user;
3659 isl_qpolynomial *val;
3661 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3665 } else if (data->max) {
3666 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3668 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3674 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3675 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3677 struct isl_opt_data data = { NULL, 1, NULL, max };
3682 if (isl_upoly_is_cst(qp->upoly)) {
3687 set = fix_inactive(set, qp);
3690 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3694 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3697 isl_qpolynomial_free(qp);
3701 isl_qpolynomial_free(qp);
3702 isl_qpolynomial_free(data.opt);
3706 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3707 __isl_take isl_morph *morph)
3712 struct isl_upoly *up;
3714 struct isl_upoly **subs;
3717 qp = isl_qpolynomial_cow(qp);
3722 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3724 n_sub = morph->inv->n_row - 1;
3725 if (morph->inv->n_row != morph->inv->n_col)
3726 n_sub += qp->div->n_row;
3727 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3731 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3732 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3733 morph->inv->row[0][0], morph->inv->n_col);
3734 if (morph->inv->n_row != morph->inv->n_col)
3735 for (i = 0; i < qp->div->n_row; ++i)
3736 subs[morph->inv->n_row - 1 + i] =
3737 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3739 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3741 for (i = 0; i < n_sub; ++i)
3742 isl_upoly_free(subs[i]);
3745 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3746 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3747 qp->div = isl_mat_product(qp->div, mat);
3748 isl_dim_free(qp->dim);
3749 qp->dim = isl_dim_copy(morph->ran->dim);
3751 if (!qp->upoly || !qp->div || !qp->dim)
3754 isl_morph_free(morph);
3758 isl_qpolynomial_free(qp);
3759 isl_morph_free(morph);
3763 static int neg_entry(void **entry, void *user)
3765 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3767 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3769 return *pwqp ? 0 : -1;
3772 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3773 __isl_take isl_union_pw_qpolynomial *upwqp)
3775 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3779 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3780 &neg_entry, NULL) < 0)
3785 isl_union_pw_qpolynomial_free(upwqp);
3789 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3790 __isl_take isl_union_pw_qpolynomial *upwqp1,
3791 __isl_take isl_union_pw_qpolynomial *upwqp2)
3793 return isl_union_pw_qpolynomial_add(upwqp1,
3794 isl_union_pw_qpolynomial_neg(upwqp2));
3797 static int mul_entry(void **entry, void *user)
3799 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3801 struct isl_hash_table_entry *entry2;
3802 isl_pw_qpolynomial *pwpq = *entry;
3805 hash = isl_dim_get_hash(pwpq->dim);
3806 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3807 hash, &has_dim, pwpq->dim, 0);
3811 pwpq = isl_pw_qpolynomial_copy(pwpq);
3812 pwpq = isl_pw_qpolynomial_mul(pwpq,
3813 isl_pw_qpolynomial_copy(entry2->data));
3815 empty = isl_pw_qpolynomial_is_zero(pwpq);
3817 isl_pw_qpolynomial_free(pwpq);
3821 isl_pw_qpolynomial_free(pwpq);
3825 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3830 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3831 __isl_take isl_union_pw_qpolynomial *upwqp1,
3832 __isl_take isl_union_pw_qpolynomial *upwqp2)
3834 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3837 /* Reorder the columns of the given div definitions according to the
3840 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3841 __isl_take isl_reordering *r)
3850 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3851 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3855 for (i = 0; i < div->n_row; ++i) {
3856 isl_seq_cpy(mat->row[i], div->row[i], 2);
3857 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3858 for (j = 0; j < r->len; ++j)
3859 isl_int_set(mat->row[i][2 + r->pos[j]],
3860 div->row[i][2 + j]);
3863 isl_reordering_free(r);
3867 isl_reordering_free(r);
3872 /* Reorder the dimension of "qp" according to the given reordering.
3874 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3875 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3877 qp = isl_qpolynomial_cow(qp);
3881 r = isl_reordering_extend(r, qp->div->n_row);
3885 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3889 qp->upoly = reorder(qp->upoly, r->pos);
3893 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3895 isl_reordering_free(r);
3898 isl_qpolynomial_free(qp);
3899 isl_reordering_free(r);
3903 struct isl_split_periods_data {
3905 isl_pw_qpolynomial *res;
3908 /* Create a slice where the integer division "div" has the fixed value "v".
3909 * In particular, if "div" refers to floor(f/m), then create a slice
3911 * m v <= f <= m v + (m - 1)
3916 * -f + m v + (m - 1) >= 0
3918 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3919 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3922 isl_basic_set *bset = NULL;
3928 total = isl_dim_total(dim);
3929 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3931 k = isl_basic_set_alloc_inequality(bset);
3934 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3935 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3937 k = isl_basic_set_alloc_inequality(bset);
3940 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3941 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3942 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3943 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3946 return isl_set_from_basic_set(bset);
3948 isl_basic_set_free(bset);
3953 static int split_periods(__isl_take isl_set *set,
3954 __isl_take isl_qpolynomial *qp, void *user);
3956 /* Create a slice of the domain "set" such that integer division "div"
3957 * has the fixed value "v" and add the results to data->res,
3958 * replacing the integer division by "v" in "qp".
3960 static int set_div(__isl_take isl_set *set,
3961 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3962 struct isl_split_periods_data *data)
3967 struct isl_upoly *cst;
3969 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3970 set = isl_set_intersect(set, slice);
3975 total = isl_dim_total(qp->dim);
3977 for (i = div + 1; i < qp->div->n_row; ++i) {
3978 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3980 isl_int_addmul(qp->div->row[i][1],
3981 qp->div->row[i][2 + total + div], v);
3982 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3985 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3986 qp = substitute_div(qp, div, cst);
3988 return split_periods(set, qp, data);
3991 isl_qpolynomial_free(qp);
3995 /* Split the domain "set" such that integer division "div"
3996 * has a fixed value (ranging from "min" to "max") on each slice
3997 * and add the results to data->res.
3999 static int split_div(__isl_take isl_set *set,
4000 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4001 struct isl_split_periods_data *data)
4003 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4004 isl_set *set_i = isl_set_copy(set);
4005 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4007 if (set_div(set_i, qp_i, div, min, data) < 0)
4011 isl_qpolynomial_free(qp);
4015 isl_qpolynomial_free(qp);
4019 /* If "qp" refers to any integer division
4020 * that can only attain "max_periods" distinct values on "set"
4021 * then split the domain along those distinct values.
4022 * Add the results (or the original if no splitting occurs)
4025 static int split_periods(__isl_take isl_set *set,
4026 __isl_take isl_qpolynomial *qp, void *user)
4029 isl_pw_qpolynomial *pwqp;
4030 struct isl_split_periods_data *data;
4035 data = (struct isl_split_periods_data *)user;
4040 if (qp->div->n_row == 0) {
4041 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4042 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4048 total = isl_dim_total(qp->dim);
4049 for (i = 0; i < qp->div->n_row; ++i) {
4050 enum isl_lp_result lp_res;
4052 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4053 qp->div->n_row) != -1)
4056 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4057 set->ctx->one, &min, NULL, NULL);
4058 if (lp_res == isl_lp_error)
4060 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4062 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4064 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4065 set->ctx->one, &max, NULL, NULL);
4066 if (lp_res == isl_lp_error)
4068 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4070 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4072 isl_int_sub(max, max, min);
4073 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4074 isl_int_add(max, max, min);
4079 if (i < qp->div->n_row) {
4080 r = split_div(set, qp, i, min, max, data);
4082 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4083 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4095 isl_qpolynomial_free(qp);
4099 /* If any quasi-polynomial in pwqp refers to any integer division
4100 * that can only attain "max_periods" distinct values on its domain
4101 * then split the domain along those distinct values.
4103 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4104 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4106 struct isl_split_periods_data data;
4108 data.max_periods = max_periods;
4109 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4111 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4114 isl_pw_qpolynomial_free(pwqp);
4118 isl_pw_qpolynomial_free(data.res);
4119 isl_pw_qpolynomial_free(pwqp);
4123 /* Construct a piecewise quasipolynomial that is constant on the given
4124 * domain. In particular, it is
4127 * infinity if cst == -1
4129 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4130 __isl_take isl_basic_set *bset, int cst)
4133 isl_qpolynomial *qp;
4138 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4139 dim = isl_basic_set_get_dim(bset);
4141 qp = isl_qpolynomial_infty(dim);
4143 qp = isl_qpolynomial_zero(dim);
4145 qp = isl_qpolynomial_one(dim);
4146 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4149 /* Factor bset, call fn on each of the factors and return the product.
4151 * If no factors can be found, simply call fn on the input.
4152 * Otherwise, construct the factors based on the factorizer,
4153 * call fn on each factor and compute the product.
4155 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4156 __isl_take isl_basic_set *bset,
4157 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4163 isl_qpolynomial *qp;
4164 isl_pw_qpolynomial *pwqp;
4168 f = isl_basic_set_factorizer(bset);
4171 if (f->n_group == 0) {
4172 isl_factorizer_free(f);
4176 nparam = isl_basic_set_dim(bset, isl_dim_param);
4177 nvar = isl_basic_set_dim(bset, isl_dim_set);
4179 dim = isl_basic_set_get_dim(bset);
4180 dim = isl_dim_domain(dim);
4181 set = isl_set_universe(isl_dim_copy(dim));
4182 qp = isl_qpolynomial_one(dim);
4183 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4185 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4187 for (i = 0, n = 0; i < f->n_group; ++i) {
4188 isl_basic_set *bset_i;
4189 isl_pw_qpolynomial *pwqp_i;
4191 bset_i = isl_basic_set_copy(bset);
4192 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4193 nparam + n + f->len[i], nvar - n - f->len[i]);
4194 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4196 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4197 n + f->len[i], nvar - n - f->len[i]);
4198 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4200 pwqp_i = fn(bset_i);
4201 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4206 isl_basic_set_free(bset);
4207 isl_factorizer_free(f);
4211 isl_basic_set_free(bset);
4215 /* Factor bset, call fn on each of the factors and return the product.
4216 * The function is assumed to evaluate to zero on empty domains,
4217 * to one on zero-dimensional domains and to infinity on unbounded domains
4218 * and will not be called explicitly on zero-dimensional or unbounded domains.
4220 * We first check for some special cases and remove all equalities.
4221 * Then we hand over control to compressed_multiplicative_call.
4223 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4224 __isl_take isl_basic_set *bset,
4225 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4229 isl_pw_qpolynomial *pwqp;
4230 unsigned orig_nvar, final_nvar;
4235 if (isl_basic_set_fast_is_empty(bset))
4236 return constant_on_domain(bset, 0);
4238 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4241 return constant_on_domain(bset, 1);
4243 bounded = isl_basic_set_is_bounded(bset);
4247 return constant_on_domain(bset, -1);
4249 if (bset->n_eq == 0)
4250 return compressed_multiplicative_call(bset, fn);
4252 morph = isl_basic_set_full_compression(bset);
4253 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4255 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4257 pwqp = compressed_multiplicative_call(bset, fn);
4259 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4260 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4261 morph = isl_morph_inverse(morph);
4263 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4267 isl_basic_set_free(bset);
4271 /* Drop all floors in "qp", turning each integer division [a/m] into
4272 * a rational division a/m. If "down" is set, then the integer division
4273 * is replaces by (a-(m-1))/m instead.
4275 static __isl_give isl_qpolynomial *qp_drop_floors(
4276 __isl_take isl_qpolynomial *qp, int down)
4279 struct isl_upoly *s;
4283 if (qp->div->n_row == 0)
4286 qp = isl_qpolynomial_cow(qp);
4290 for (i = qp->div->n_row - 1; i >= 0; --i) {
4292 isl_int_sub(qp->div->row[i][1],
4293 qp->div->row[i][1], qp->div->row[i][0]);
4294 isl_int_add_ui(qp->div->row[i][1],
4295 qp->div->row[i][1], 1);
4297 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4298 qp->div->row[i][0], qp->div->n_col - 1);
4299 qp = substitute_div(qp, i, s);
4307 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4308 * a rational division a/m.
4310 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4311 __isl_take isl_pw_qpolynomial *pwqp)
4318 if (isl_pw_qpolynomial_is_zero(pwqp))
4321 pwqp = isl_pw_qpolynomial_cow(pwqp);
4325 for (i = 0; i < pwqp->n; ++i) {
4326 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4333 isl_pw_qpolynomial_free(pwqp);
4337 /* Adjust all the integer divisions in "qp" such that they are at least
4338 * one over the given orthant (identified by "signs"). This ensures
4339 * that they will still be non-negative even after subtracting (m-1)/m.
4341 * In particular, f is replaced by f' + v, changing f = [a/m]
4342 * to f' = [(a - m v)/m].
4343 * If the constant term k in a is smaller than m,
4344 * the constant term of v is set to floor(k/m) - 1.
4345 * For any other term, if the coefficient c and the variable x have
4346 * the same sign, then no changes are needed.
4347 * Otherwise, if the variable is positive (and c is negative),
4348 * then the coefficient of x in v is set to floor(c/m).
4349 * If the variable is negative (and c is positive),
4350 * then the coefficient of x in v is set to ceil(c/m).
4352 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4358 struct isl_upoly *s;
4360 qp = isl_qpolynomial_cow(qp);
4363 qp->div = isl_mat_cow(qp->div);
4367 total = isl_dim_total(qp->dim);
4368 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4370 for (i = 0; i < qp->div->n_row; ++i) {
4371 isl_int *row = qp->div->row[i];
4375 if (isl_int_lt(row[1], row[0])) {
4376 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4377 isl_int_sub_ui(v->el[0], v->el[0], 1);
4378 isl_int_submul(row[1], row[0], v->el[0]);
4380 for (j = 0; j < total; ++j) {
4381 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4384 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4386 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4387 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4389 for (j = 0; j < i; ++j) {
4390 if (isl_int_sgn(row[2 + total + j]) >= 0)
4392 isl_int_fdiv_q(v->el[1 + total + j],
4393 row[2 + total + j], row[0]);
4394 isl_int_submul(row[2 + total + j],
4395 row[0], v->el[1 + total + j]);
4397 for (j = i + 1; j < qp->div->n_row; ++j) {
4398 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4400 isl_seq_combine(qp->div->row[j] + 1,
4401 qp->div->ctx->one, qp->div->row[j] + 1,
4402 qp->div->row[j][2 + total + i], v->el, v->size);
4404 isl_int_set_si(v->el[1 + total + i], 1);
4405 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4406 qp->div->ctx->one, v->size);
4407 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4417 isl_qpolynomial_free(qp);
4421 struct isl_to_poly_data {
4423 isl_pw_qpolynomial *res;
4424 isl_qpolynomial *qp;
4427 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4428 * We first make all integer divisions positive and then split the
4429 * quasipolynomials into terms with sign data->sign (the direction
4430 * of the requested approximation) and terms with the opposite sign.
4431 * In the first set of terms, each integer division [a/m] is
4432 * overapproximated by a/m, while in the second it is underapproximated
4435 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4438 struct isl_to_poly_data *data = user;
4439 isl_pw_qpolynomial *t;
4440 isl_qpolynomial *qp, *up, *down;
4442 qp = isl_qpolynomial_copy(data->qp);
4443 qp = make_divs_pos(qp, signs);
4445 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4446 up = qp_drop_floors(up, 0);
4447 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4448 down = qp_drop_floors(down, 1);
4450 isl_qpolynomial_free(qp);
4451 qp = isl_qpolynomial_add(up, down);
4453 t = isl_pw_qpolynomial_alloc(orthant, qp);
4454 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4459 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4460 * the polynomial will be an overapproximation. If "sign" is negative,
4461 * it will be an underapproximation. If "sign" is zero, the approximation
4462 * will lie somewhere in between.
4464 * In particular, is sign == 0, we simply drop the floors, turning
4465 * the integer divisions into rational divisions.
4466 * Otherwise, we split the domains into orthants, make all integer divisions
4467 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4468 * depending on the requested sign and the sign of the term in which
4469 * the integer division appears.
4471 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4472 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4475 struct isl_to_poly_data data;
4478 return pwqp_drop_floors(pwqp);
4484 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4486 for (i = 0; i < pwqp->n; ++i) {
4487 if (pwqp->p[i].qp->div->n_row == 0) {
4488 isl_pw_qpolynomial *t;
4489 t = isl_pw_qpolynomial_alloc(
4490 isl_set_copy(pwqp->p[i].set),
4491 isl_qpolynomial_copy(pwqp->p[i].qp));
4492 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4495 data.qp = pwqp->p[i].qp;
4496 if (isl_set_foreach_orthant(pwqp->p[i].set,
4497 &to_polynomial_on_orthant, &data) < 0)
4501 isl_pw_qpolynomial_free(pwqp);
4505 isl_pw_qpolynomial_free(pwqp);
4506 isl_pw_qpolynomial_free(data.res);
4510 static int poly_entry(void **entry, void *user)
4513 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4515 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4517 return *pwqp ? 0 : -1;
4520 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4521 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4523 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4527 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4528 &poly_entry, &sign) < 0)
4533 isl_union_pw_qpolynomial_free(upwqp);
4537 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4538 __isl_take isl_qpolynomial *qp)
4542 isl_vec *aff = NULL;
4543 isl_basic_map *bmap = NULL;
4549 if (!isl_upoly_is_affine(qp->upoly))
4550 isl_die(qp->dim->ctx, isl_error_invalid,
4551 "input quasi-polynomial not affine", goto error);
4552 aff = isl_qpolynomial_extract_affine(qp);
4555 dim = isl_qpolynomial_get_dim(qp);
4556 dim = isl_dim_from_domain(dim);
4557 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4558 dim = isl_dim_add(dim, isl_dim_out, 1);
4559 n_div = qp->div->n_row;
4560 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4562 for (i = 0; i < n_div; ++i) {
4563 k = isl_basic_map_alloc_div(bmap);
4566 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4567 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4568 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4571 k = isl_basic_map_alloc_equality(bmap);
4574 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4575 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4576 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4579 isl_qpolynomial_free(qp);
4580 bmap = isl_basic_map_finalize(bmap);
4584 isl_qpolynomial_free(qp);
4585 isl_basic_map_free(bmap);