diff options
Diffstat (limited to 'polly/lib/External/isl/isl_polynomial.c')
| -rw-r--r-- | polly/lib/External/isl/isl_polynomial.c | 4866 |
1 files changed, 4866 insertions, 0 deletions
diff --git a/polly/lib/External/isl/isl_polynomial.c b/polly/lib/External/isl/isl_polynomial.c new file mode 100644 index 00000000000..6b73bb397d0 --- /dev/null +++ b/polly/lib/External/isl/isl_polynomial.c @@ -0,0 +1,4866 @@ +/* + * Copyright 2010 INRIA Saclay + * + * Use of this software is governed by the MIT license + * + * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France, + * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod, + * 91893 Orsay, France + */ + +#include <stdlib.h> +#define ISL_DIM_H +#include <isl_ctx_private.h> +#include <isl_map_private.h> +#include <isl_factorization.h> +#include <isl_lp_private.h> +#include <isl_seq.h> +#include <isl_union_map_private.h> +#include <isl_constraint_private.h> +#include <isl_polynomial_private.h> +#include <isl_point_private.h> +#include <isl_space_private.h> +#include <isl_mat_private.h> +#include <isl_vec_private.h> +#include <isl_range.h> +#include <isl_local_space_private.h> +#include <isl_aff_private.h> +#include <isl_val_private.h> +#include <isl_config.h> +#include <isl/deprecated/polynomial_int.h> + +static unsigned pos(__isl_keep isl_space *dim, enum isl_dim_type type) +{ + switch (type) { + case isl_dim_param: return 0; + case isl_dim_in: return dim->nparam; + case isl_dim_out: return dim->nparam + dim->n_in; + default: return 0; + } +} + +int isl_upoly_is_cst(__isl_keep struct isl_upoly *up) +{ + if (!up) + return -1; + + return up->var < 0; +} + +__isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up) +{ + if (!up) + return NULL; + + isl_assert(up->ctx, up->var < 0, return NULL); + + return (struct isl_upoly_cst *)up; +} + +__isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up) +{ + if (!up) + return NULL; + + isl_assert(up->ctx, up->var >= 0, return NULL); + + return (struct isl_upoly_rec *)up; +} + +int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1, + __isl_keep struct isl_upoly *up2) +{ + int i; + struct isl_upoly_rec *rec1, *rec2; + + if (!up1 || !up2) + return -1; + if (up1 == up2) + return 1; + if (up1->var != up2->var) + return 0; + if (isl_upoly_is_cst(up1)) { + struct isl_upoly_cst *cst1, *cst2; + cst1 = isl_upoly_as_cst(up1); + cst2 = isl_upoly_as_cst(up2); + if (!cst1 || !cst2) + return -1; + return isl_int_eq(cst1->n, cst2->n) && + isl_int_eq(cst1->d, cst2->d); + } + + rec1 = isl_upoly_as_rec(up1); + rec2 = isl_upoly_as_rec(up2); + if (!rec1 || !rec2) + return -1; + + if (rec1->n != rec2->n) + return 0; + + for (i = 0; i < rec1->n; ++i) { + int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]); + if (eq < 0 || !eq) + return eq; + } + + return 1; +} + +int isl_upoly_is_zero(__isl_keep struct isl_upoly *up) +{ + struct isl_upoly_cst *cst; + + if (!up) + return -1; + if (!isl_upoly_is_cst(up)) + return 0; + + cst = isl_upoly_as_cst(up); + if (!cst) + return -1; + + return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d); +} + +int isl_upoly_sgn(__isl_keep struct isl_upoly *up) +{ + struct isl_upoly_cst *cst; + + if (!up) + return 0; + if (!isl_upoly_is_cst(up)) + return 0; + + cst = isl_upoly_as_cst(up); + if (!cst) + return 0; + + return isl_int_sgn(cst->n); +} + +int isl_upoly_is_nan(__isl_keep struct isl_upoly *up) +{ + struct isl_upoly_cst *cst; + + if (!up) + return -1; + if (!isl_upoly_is_cst(up)) + return 0; + + cst = isl_upoly_as_cst(up); + if (!cst) + return -1; + + return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d); +} + +int isl_upoly_is_infty(__isl_keep struct isl_upoly *up) +{ + struct isl_upoly_cst *cst; + + if (!up) + return -1; + if (!isl_upoly_is_cst(up)) + return 0; + + cst = isl_upoly_as_cst(up); + if (!cst) + return -1; + + return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d); +} + +int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up) +{ + struct isl_upoly_cst *cst; + + if (!up) + return -1; + if (!isl_upoly_is_cst(up)) + return 0; + + cst = isl_upoly_as_cst(up); + if (!cst) + return -1; + + return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d); +} + +int isl_upoly_is_one(__isl_keep struct isl_upoly *up) +{ + struct isl_upoly_cst *cst; + + if (!up) + return -1; + if (!isl_upoly_is_cst(up)) + return 0; + + cst = isl_upoly_as_cst(up); + if (!cst) + return -1; + + return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d); +} + +int isl_upoly_is_negone(__isl_keep struct isl_upoly *up) +{ + struct isl_upoly_cst *cst; + + if (!up) + return -1; + if (!isl_upoly_is_cst(up)) + return 0; + + cst = isl_upoly_as_cst(up); + if (!cst) + return -1; + + return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d); +} + +__isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx) +{ + struct isl_upoly_cst *cst; + + cst = isl_alloc_type(ctx, struct isl_upoly_cst); + if (!cst) + return NULL; + + cst->up.ref = 1; + cst->up.ctx = ctx; + isl_ctx_ref(ctx); + cst->up.var = -1; + + isl_int_init(cst->n); + isl_int_init(cst->d); + + return cst; +} + +__isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx) +{ + struct isl_upoly_cst *cst; + + cst = isl_upoly_cst_alloc(ctx); + if (!cst) + return NULL; + + isl_int_set_si(cst->n, 0); + isl_int_set_si(cst->d, 1); + + return &cst->up; +} + +__isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx) +{ + struct isl_upoly_cst *cst; + + cst = isl_upoly_cst_alloc(ctx); + if (!cst) + return NULL; + + isl_int_set_si(cst->n, 1); + isl_int_set_si(cst->d, 1); + + return &cst->up; +} + +__isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx) +{ + struct isl_upoly_cst *cst; + + cst = isl_upoly_cst_alloc(ctx); + if (!cst) + return NULL; + + isl_int_set_si(cst->n, 1); + isl_int_set_si(cst->d, 0); + + return &cst->up; +} + +__isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx) +{ + struct isl_upoly_cst *cst; + + cst = isl_upoly_cst_alloc(ctx); + if (!cst) + return NULL; + + isl_int_set_si(cst->n, -1); + isl_int_set_si(cst->d, 0); + + return &cst->up; +} + +__isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx) +{ + struct isl_upoly_cst *cst; + + cst = isl_upoly_cst_alloc(ctx); + if (!cst) + return NULL; + + isl_int_set_si(cst->n, 0); + isl_int_set_si(cst->d, 0); + + return &cst->up; +} + +__isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx, + isl_int n, isl_int d) +{ + struct isl_upoly_cst *cst; + + cst = isl_upoly_cst_alloc(ctx); + if (!cst) + return NULL; + + isl_int_set(cst->n, n); + isl_int_set(cst->d, d); + + return &cst->up; +} + +__isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx, + int var, int size) +{ + struct isl_upoly_rec *rec; + + isl_assert(ctx, var >= 0, return NULL); + isl_assert(ctx, size >= 0, return NULL); + rec = isl_calloc(ctx, struct isl_upoly_rec, + sizeof(struct isl_upoly_rec) + + size * sizeof(struct isl_upoly *)); + if (!rec) + return NULL; + + rec->up.ref = 1; + rec->up.ctx = ctx; + isl_ctx_ref(ctx); + rec->up.var = var; + + rec->n = 0; + rec->size = size; + + return rec; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_reset_domain_space( + __isl_take isl_qpolynomial *qp, __isl_take isl_space *dim) +{ + qp = isl_qpolynomial_cow(qp); + if (!qp || !dim) + goto error; + + isl_space_free(qp->dim); + qp->dim = dim; + + return qp; +error: + isl_qpolynomial_free(qp); + isl_space_free(dim); + return NULL; +} + +/* Reset the space of "qp". This function is called from isl_pw_templ.c + * and doesn't know if the space of an element object is represented + * directly or through its domain. It therefore passes along both. + */ +__isl_give isl_qpolynomial *isl_qpolynomial_reset_space_and_domain( + __isl_take isl_qpolynomial *qp, __isl_take isl_space *space, + __isl_take isl_space *domain) +{ + isl_space_free(space); + return isl_qpolynomial_reset_domain_space(qp, domain); +} + +isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp) +{ + return qp ? qp->dim->ctx : NULL; +} + +__isl_give isl_space *isl_qpolynomial_get_domain_space( + __isl_keep isl_qpolynomial *qp) +{ + return qp ? isl_space_copy(qp->dim) : NULL; +} + +__isl_give isl_space *isl_qpolynomial_get_space(__isl_keep isl_qpolynomial *qp) +{ + isl_space *space; + if (!qp) + return NULL; + space = isl_space_copy(qp->dim); + space = isl_space_from_domain(space); + space = isl_space_add_dims(space, isl_dim_out, 1); + return space; +} + +/* Externally, an isl_qpolynomial has a map space, but internally, the + * ls field corresponds to the domain of that space. + */ +unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp, + enum isl_dim_type type) +{ + if (!qp) + return 0; + if (type == isl_dim_out) + return 1; + if (type == isl_dim_in) + type = isl_dim_set; + return isl_space_dim(qp->dim, type); +} + +int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp) +{ + return qp ? isl_upoly_is_zero(qp->upoly) : -1; +} + +int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp) +{ + return qp ? isl_upoly_is_one(qp->upoly) : -1; +} + +int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp) +{ + return qp ? isl_upoly_is_nan(qp->upoly) : -1; +} + +int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp) +{ + return qp ? isl_upoly_is_infty(qp->upoly) : -1; +} + +int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp) +{ + return qp ? isl_upoly_is_neginfty(qp->upoly) : -1; +} + +int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp) +{ + return qp ? isl_upoly_sgn(qp->upoly) : 0; +} + +static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst) +{ + isl_int_clear(cst->n); + isl_int_clear(cst->d); +} + +static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec) +{ + int i; + + for (i = 0; i < rec->n; ++i) + isl_upoly_free(rec->p[i]); +} + +__isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up) +{ + if (!up) + return NULL; + + up->ref++; + return up; +} + +__isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up) +{ + struct isl_upoly_cst *cst; + struct isl_upoly_cst *dup; + + cst = isl_upoly_as_cst(up); + if (!cst) + return NULL; + + dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx)); + if (!dup) + return NULL; + isl_int_set(dup->n, cst->n); + isl_int_set(dup->d, cst->d); + + return &dup->up; +} + +__isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up) +{ + int i; + struct isl_upoly_rec *rec; + struct isl_upoly_rec *dup; + + rec = isl_upoly_as_rec(up); + if (!rec) + return NULL; + + dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n); + if (!dup) + return NULL; + + for (i = 0; i < rec->n; ++i) { + dup->p[i] = isl_upoly_copy(rec->p[i]); + if (!dup->p[i]) + goto error; + dup->n++; + } + + return &dup->up; +error: + isl_upoly_free(&dup->up); + return NULL; +} + +__isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up) +{ + if (!up) + return NULL; + + if (isl_upoly_is_cst(up)) + return isl_upoly_dup_cst(up); + else + return isl_upoly_dup_rec(up); +} + +__isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up) +{ + if (!up) + return NULL; + + if (up->ref == 1) + return up; + up->ref--; + return isl_upoly_dup(up); +} + +void isl_upoly_free(__isl_take struct isl_upoly *up) +{ + if (!up) + return; + + if (--up->ref > 0) + return; + + if (up->var < 0) + upoly_free_cst((struct isl_upoly_cst *)up); + else + upoly_free_rec((struct isl_upoly_rec *)up); + + isl_ctx_deref(up->ctx); + free(up); +} + +static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst) +{ + isl_int gcd; + + isl_int_init(gcd); + isl_int_gcd(gcd, cst->n, cst->d); + if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) { + isl_int_divexact(cst->n, cst->n, gcd); + isl_int_divexact(cst->d, cst->d, gcd); + } + isl_int_clear(gcd); +} + +__isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1, + __isl_take struct isl_upoly *up2) +{ + struct isl_upoly_cst *cst1; + struct isl_upoly_cst *cst2; + + up1 = isl_upoly_cow(up1); + if (!up1 || !up2) + goto error; + + cst1 = isl_upoly_as_cst(up1); + cst2 = isl_upoly_as_cst(up2); + + if (isl_int_eq(cst1->d, cst2->d)) + isl_int_add(cst1->n, cst1->n, cst2->n); + else { + isl_int_mul(cst1->n, cst1->n, cst2->d); + isl_int_addmul(cst1->n, cst2->n, cst1->d); + isl_int_mul(cst1->d, cst1->d, cst2->d); + } + + isl_upoly_cst_reduce(cst1); + + isl_upoly_free(up2); + return up1; +error: + isl_upoly_free(up1); + isl_upoly_free(up2); + return NULL; +} + +static __isl_give struct isl_upoly *replace_by_zero( + __isl_take struct isl_upoly *up) +{ + struct isl_ctx *ctx; + + if (!up) + return NULL; + ctx = up->ctx; + isl_upoly_free(up); + return isl_upoly_zero(ctx); +} + +static __isl_give struct isl_upoly *replace_by_constant_term( + __isl_take struct isl_upoly *up) +{ + struct isl_upoly_rec *rec; + struct isl_upoly *cst; + + if (!up) + return NULL; + + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + cst = isl_upoly_copy(rec->p[0]); + isl_upoly_free(up); + return cst; +error: + isl_upoly_free(up); + return NULL; +} + +__isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1, + __isl_take struct isl_upoly *up2) +{ + int i; + struct isl_upoly_rec *rec1, *rec2; + + if (!up1 || !up2) + goto error; + + if (isl_upoly_is_nan(up1)) { + isl_upoly_free(up2); + return up1; + } + + if (isl_upoly_is_nan(up2)) { + isl_upoly_free(up1); + return up2; + } + + if (isl_upoly_is_zero(up1)) { + isl_upoly_free(up1); + return up2; + } + + if (isl_upoly_is_zero(up2)) { + isl_upoly_free(up2); + return up1; + } + + if (up1->var < up2->var) + return isl_upoly_sum(up2, up1); + + if (up2->var < up1->var) { + struct isl_upoly_rec *rec; + if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) { + isl_upoly_free(up1); + return up2; + } + up1 = isl_upoly_cow(up1); + rec = isl_upoly_as_rec(up1); + if (!rec) + goto error; + rec->p[0] = isl_upoly_sum(rec->p[0], up2); + if (rec->n == 1) + up1 = replace_by_constant_term(up1); + return up1; + } + + if (isl_upoly_is_cst(up1)) + return isl_upoly_sum_cst(up1, up2); + + rec1 = isl_upoly_as_rec(up1); + rec2 = isl_upoly_as_rec(up2); + if (!rec1 || !rec2) + goto error; + + if (rec1->n < rec2->n) + return isl_upoly_sum(up2, up1); + + up1 = isl_upoly_cow(up1); + rec1 = isl_upoly_as_rec(up1); + if (!rec1) + goto error; + + for (i = rec2->n - 1; i >= 0; --i) { + rec1->p[i] = isl_upoly_sum(rec1->p[i], + isl_upoly_copy(rec2->p[i])); + if (!rec1->p[i]) + goto error; + if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) { + isl_upoly_free(rec1->p[i]); + rec1->n--; + } + } + + if (rec1->n == 0) + up1 = replace_by_zero(up1); + else if (rec1->n == 1) + up1 = replace_by_constant_term(up1); + + isl_upoly_free(up2); + + return up1; +error: + isl_upoly_free(up1); + isl_upoly_free(up2); + return NULL; +} + +__isl_give struct isl_upoly *isl_upoly_cst_add_isl_int( + __isl_take struct isl_upoly *up, isl_int v) +{ + struct isl_upoly_cst *cst; + + up = isl_upoly_cow(up); + if (!up) + return NULL; + + cst = isl_upoly_as_cst(up); + + isl_int_addmul(cst->n, cst->d, v); + + return up; +} + +__isl_give struct isl_upoly *isl_upoly_add_isl_int( + __isl_take struct isl_upoly *up, isl_int v) +{ + struct isl_upoly_rec *rec; + + if (!up) + return NULL; + + if (isl_upoly_is_cst(up)) + return isl_upoly_cst_add_isl_int(up, v); + + up = isl_upoly_cow(up); + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v); + if (!rec->p[0]) + goto error; + + return up; +error: + isl_upoly_free(up); + return NULL; +} + +__isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int( + __isl_take struct isl_upoly *up, isl_int v) +{ + struct isl_upoly_cst *cst; + + if (isl_upoly_is_zero(up)) + return up; + + up = isl_upoly_cow(up); + if (!up) + return NULL; + + cst = isl_upoly_as_cst(up); + + isl_int_mul(cst->n, cst->n, v); + + return up; +} + +__isl_give struct isl_upoly *isl_upoly_mul_isl_int( + __isl_take struct isl_upoly *up, isl_int v) +{ + int i; + struct isl_upoly_rec *rec; + + if (!up) + return NULL; + + if (isl_upoly_is_cst(up)) + return isl_upoly_cst_mul_isl_int(up, v); + + up = isl_upoly_cow(up); + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + for (i = 0; i < rec->n; ++i) { + rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v); + if (!rec->p[i]) + goto error; + } + + return up; +error: + isl_upoly_free(up); + return NULL; +} + +/* Multiply the constant polynomial "up" by "v". + */ +static __isl_give struct isl_upoly *isl_upoly_cst_scale_val( + __isl_take struct isl_upoly *up, __isl_keep isl_val *v) +{ + struct isl_upoly_cst *cst; + + if (isl_upoly_is_zero(up)) + return up; + + up = isl_upoly_cow(up); + if (!up) + return NULL; + + cst = isl_upoly_as_cst(up); + + isl_int_mul(cst->n, cst->n, v->n); + isl_int_mul(cst->d, cst->d, v->d); + isl_upoly_cst_reduce(cst); + + return up; +} + +/* Multiply the polynomial "up" by "v". + */ +static __isl_give struct isl_upoly *isl_upoly_scale_val( + __isl_take struct isl_upoly *up, __isl_keep isl_val *v) +{ + int i; + struct isl_upoly_rec *rec; + + if (!up) + return NULL; + + if (isl_upoly_is_cst(up)) + return isl_upoly_cst_scale_val(up, v); + + up = isl_upoly_cow(up); + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + for (i = 0; i < rec->n; ++i) { + rec->p[i] = isl_upoly_scale_val(rec->p[i], v); + if (!rec->p[i]) + goto error; + } + + return up; +error: + isl_upoly_free(up); + return NULL; +} + +__isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1, + __isl_take struct isl_upoly *up2) +{ + struct isl_upoly_cst *cst1; + struct isl_upoly_cst *cst2; + + up1 = isl_upoly_cow(up1); + if (!up1 || !up2) + goto error; + + cst1 = isl_upoly_as_cst(up1); + cst2 = isl_upoly_as_cst(up2); + + isl_int_mul(cst1->n, cst1->n, cst2->n); + isl_int_mul(cst1->d, cst1->d, cst2->d); + + isl_upoly_cst_reduce(cst1); + + isl_upoly_free(up2); + return up1; +error: + isl_upoly_free(up1); + isl_upoly_free(up2); + return NULL; +} + +__isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1, + __isl_take struct isl_upoly *up2) +{ + struct isl_upoly_rec *rec1; + struct isl_upoly_rec *rec2; + struct isl_upoly_rec *res = NULL; + int i, j; + int size; + + rec1 = isl_upoly_as_rec(up1); + rec2 = isl_upoly_as_rec(up2); + if (!rec1 || !rec2) + goto error; + size = rec1->n + rec2->n - 1; + res = isl_upoly_alloc_rec(up1->ctx, up1->var, size); + if (!res) + goto error; + + for (i = 0; i < rec1->n; ++i) { + res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]), + isl_upoly_copy(rec1->p[i])); + if (!res->p[i]) + goto error; + res->n++; + } + for (; i < size; ++i) { + res->p[i] = isl_upoly_zero(up1->ctx); + if (!res->p[i]) + goto error; + res->n++; + } + for (i = 0; i < rec1->n; ++i) { + for (j = 1; j < rec2->n; ++j) { + struct isl_upoly *up; + up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]), + isl_upoly_copy(rec1->p[i])); + res->p[i + j] = isl_upoly_sum(res->p[i + j], up); + if (!res->p[i + j]) + goto error; + } + } + + isl_upoly_free(up1); + isl_upoly_free(up2); + + return &res->up; +error: + isl_upoly_free(up1); + isl_upoly_free(up2); + isl_upoly_free(&res->up); + return NULL; +} + +__isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1, + __isl_take struct isl_upoly *up2) +{ + if (!up1 || !up2) + goto error; + + if (isl_upoly_is_nan(up1)) { + isl_upoly_free(up2); + return up1; + } + + if (isl_upoly_is_nan(up2)) { + isl_upoly_free(up1); + return up2; + } + + if (isl_upoly_is_zero(up1)) { + isl_upoly_free(up2); + return up1; + } + + if (isl_upoly_is_zero(up2)) { + isl_upoly_free(up1); + return up2; + } + + if (isl_upoly_is_one(up1)) { + isl_upoly_free(up1); + return up2; + } + + if (isl_upoly_is_one(up2)) { + isl_upoly_free(up2); + return up1; + } + + if (up1->var < up2->var) + return isl_upoly_mul(up2, up1); + + if (up2->var < up1->var) { + int i; + struct isl_upoly_rec *rec; + if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) { + isl_ctx *ctx = up1->ctx; + isl_upoly_free(up1); + isl_upoly_free(up2); + return isl_upoly_nan(ctx); + } + up1 = isl_upoly_cow(up1); + rec = isl_upoly_as_rec(up1); + if (!rec) + goto error; + + for (i = 0; i < rec->n; ++i) { + rec->p[i] = isl_upoly_mul(rec->p[i], + isl_upoly_copy(up2)); + if (!rec->p[i]) + goto error; + } + isl_upoly_free(up2); + return up1; + } + + if (isl_upoly_is_cst(up1)) + return isl_upoly_mul_cst(up1, up2); + + return isl_upoly_mul_rec(up1, up2); +error: + isl_upoly_free(up1); + isl_upoly_free(up2); + return NULL; +} + +__isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up, + unsigned power) +{ + struct isl_upoly *res; + + if (!up) + return NULL; + if (power == 1) + return up; + + if (power % 2) + res = isl_upoly_copy(up); + else + res = isl_upoly_one(up->ctx); + + while (power >>= 1) { + up = isl_upoly_mul(up, isl_upoly_copy(up)); + if (power % 2) + res = isl_upoly_mul(res, isl_upoly_copy(up)); + } + + isl_upoly_free(up); + return res; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_space *dim, + unsigned n_div, __isl_take struct isl_upoly *up) +{ + struct isl_qpolynomial *qp = NULL; + unsigned total; + + if (!dim || !up) + goto error; + + if (!isl_space_is_set(dim)) + isl_die(isl_space_get_ctx(dim), isl_error_invalid, + "domain of polynomial should be a set", goto error); + + total = isl_space_dim(dim, isl_dim_all); + + qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial); + if (!qp) + goto error; + + qp->ref = 1; + qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div); + if (!qp->div) + goto error; + + qp->dim = dim; + qp->upoly = up; + + return qp; +error: + isl_space_free(dim); + isl_upoly_free(up); + isl_qpolynomial_free(qp); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp) +{ + if (!qp) + return NULL; + + qp->ref++; + return qp; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp) +{ + struct isl_qpolynomial *dup; + + if (!qp) + return NULL; + + dup = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row, + isl_upoly_copy(qp->upoly)); + if (!dup) + return NULL; + isl_mat_free(dup->div); + dup->div = isl_mat_copy(qp->div); + if (!dup->div) + goto error; + + return dup; +error: + isl_qpolynomial_free(dup); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp) +{ + if (!qp) + return NULL; + + if (qp->ref == 1) + return qp; + qp->ref--; + return isl_qpolynomial_dup(qp); +} + +__isl_null isl_qpolynomial *isl_qpolynomial_free( + __isl_take isl_qpolynomial *qp) +{ + if (!qp) + return NULL; + + if (--qp->ref > 0) + return NULL; + + isl_space_free(qp->dim); + isl_mat_free(qp->div); + isl_upoly_free(qp->upoly); + + free(qp); + return NULL; +} + +__isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power) +{ + int i; + struct isl_upoly_rec *rec; + struct isl_upoly_cst *cst; + + rec = isl_upoly_alloc_rec(ctx, pos, 1 + power); + if (!rec) + return NULL; + for (i = 0; i < 1 + power; ++i) { + rec->p[i] = isl_upoly_zero(ctx); + if (!rec->p[i]) + goto error; + rec->n++; + } + cst = isl_upoly_as_cst(rec->p[power]); + isl_int_set_si(cst->n, 1); + + return &rec->up; +error: + isl_upoly_free(&rec->up); + return NULL; +} + +/* r array maps original positions to new positions. + */ +static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up, + int *r) +{ + int i; + struct isl_upoly_rec *rec; + struct isl_upoly *base; + struct isl_upoly *res; + + if (isl_upoly_is_cst(up)) + return up; + + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + isl_assert(up->ctx, rec->n >= 1, goto error); + + base = isl_upoly_var_pow(up->ctx, r[up->var], 1); + res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r); + + for (i = rec->n - 2; i >= 0; --i) { + res = isl_upoly_mul(res, isl_upoly_copy(base)); + res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r)); + } + + isl_upoly_free(base); + isl_upoly_free(up); + + return res; +error: + isl_upoly_free(up); + return NULL; +} + +static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2) +{ + int n_row, n_col; + int equal; + + isl_assert(div1->ctx, div1->n_row >= div2->n_row && + div1->n_col >= div2->n_col, return -1); + + if (div1->n_row == div2->n_row) + return isl_mat_is_equal(div1, div2); + + n_row = div1->n_row; + n_col = div1->n_col; + div1->n_row = div2->n_row; + div1->n_col = div2->n_col; + + equal = isl_mat_is_equal(div1, div2); + + div1->n_row = n_row; + div1->n_col = n_col; + + return equal; +} + +static int cmp_row(__isl_keep isl_mat *div, int i, int j) +{ + int li, lj; + + li = isl_seq_last_non_zero(div->row[i], div->n_col); + lj = isl_seq_last_non_zero(div->row[j], div->n_col); + + if (li != lj) + return li - lj; + + return isl_seq_cmp(div->row[i], div->row[j], div->n_col); +} + +struct isl_div_sort_info { + isl_mat *div; + int row; +}; + +static int div_sort_cmp(const void *p1, const void *p2) +{ + const struct isl_div_sort_info *i1, *i2; + i1 = (const struct isl_div_sort_info *) p1; + i2 = (const struct isl_div_sort_info *) p2; + + return cmp_row(i1->div, i1->row, i2->row); +} + +/* Sort divs and remove duplicates. + */ +static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp) +{ + int i; + int skip; + int len; + struct isl_div_sort_info *array = NULL; + int *pos = NULL, *at = NULL; + int *reordering = NULL; + unsigned div_pos; + + if (!qp) + return NULL; + if (qp->div->n_row <= 1) + return qp; + + div_pos = isl_space_dim(qp->dim, isl_dim_all); + + array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info, + qp->div->n_row); + pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row); + at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row); + len = qp->div->n_col - 2; + reordering = isl_alloc_array(qp->div->ctx, int, len); + if (!array || !pos || !at || !reordering) + goto error; + + for (i = 0; i < qp->div->n_row; ++i) { + array[i].div = qp->div; + array[i].row = i; + pos[i] = i; + at[i] = i; + } + + qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info), + div_sort_cmp); + + for (i = 0; i < div_pos; ++i) + reordering[i] = i; + + for (i = 0; i < qp->div->n_row; ++i) { + if (pos[array[i].row] == i) + continue; + qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]); + pos[at[i]] = pos[array[i].row]; + at[pos[array[i].row]] = at[i]; + at[i] = array[i].row; + pos[array[i].row] = i; + } + + skip = 0; + for (i = 0; i < len - div_pos; ++i) { + if (i > 0 && + isl_seq_eq(qp->div->row[i - skip - 1], + qp->div->row[i - skip], qp->div->n_col)) { + qp->div = isl_mat_drop_rows(qp->div, i - skip, 1); + isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1, + 2 + div_pos + i - skip); + qp->div = isl_mat_drop_cols(qp->div, + 2 + div_pos + i - skip, 1); + skip++; + } + reordering[div_pos + array[i].row] = div_pos + i - skip; + } + + qp->upoly = reorder(qp->upoly, reordering); + + if (!qp->upoly || !qp->div) + goto error; + + free(at); + free(pos); + free(array); + free(reordering); + + return qp; +error: + free(at); + free(pos); + free(array); + free(reordering); + isl_qpolynomial_free(qp); + return NULL; +} + +static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up, + int *exp, int first) +{ + int i; + struct isl_upoly_rec *rec; + + if (isl_upoly_is_cst(up)) + return up; + + if (up->var < first) + return up; + + if (exp[up->var - first] == up->var - first) + return up; + + up = isl_upoly_cow(up); + if (!up) + goto error; + + up->var = exp[up->var - first] + first; + + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + for (i = 0; i < rec->n; ++i) { + rec->p[i] = expand(rec->p[i], exp, first); + if (!rec->p[i]) + goto error; + } + + return up; +error: + isl_upoly_free(up); + return NULL; +} + +static __isl_give isl_qpolynomial *with_merged_divs( + __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1, + __isl_take isl_qpolynomial *qp2), + __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2) +{ + int *exp1 = NULL; + int *exp2 = NULL; + isl_mat *div = NULL; + int n_div1, n_div2; + + qp1 = isl_qpolynomial_cow(qp1); + qp2 = isl_qpolynomial_cow(qp2); + + if (!qp1 || !qp2) + goto error; + + isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row && + qp1->div->n_col >= qp2->div->n_col, goto error); + + n_div1 = qp1->div->n_row; + n_div2 = qp2->div->n_row; + exp1 = isl_alloc_array(qp1->div->ctx, int, n_div1); + exp2 = isl_alloc_array(qp2->div->ctx, int, n_div2); + if ((n_div1 && !exp1) || (n_div2 && !exp2)) + goto error; + + div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2); + if (!div) + goto error; + + isl_mat_free(qp1->div); + qp1->div = isl_mat_copy(div); + isl_mat_free(qp2->div); + qp2->div = isl_mat_copy(div); + + qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2); + qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2); + + if (!qp1->upoly || !qp2->upoly) + goto error; + + isl_mat_free(div); + free(exp1); + free(exp2); + + return fn(qp1, qp2); +error: + isl_mat_free(div); + free(exp1); + free(exp2); + isl_qpolynomial_free(qp1); + isl_qpolynomial_free(qp2); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1, + __isl_take isl_qpolynomial *qp2) +{ + qp1 = isl_qpolynomial_cow(qp1); + + if (!qp1 || !qp2) + goto error; + + if (qp1->div->n_row < qp2->div->n_row) + return isl_qpolynomial_add(qp2, qp1); + + isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error); + if (!compatible_divs(qp1->div, qp2->div)) + return with_merged_divs(isl_qpolynomial_add, qp1, qp2); + + qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly)); + if (!qp1->upoly) + goto error; + + isl_qpolynomial_free(qp2); + + return qp1; +error: + isl_qpolynomial_free(qp1); + isl_qpolynomial_free(qp2); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain( + __isl_keep isl_set *dom, + __isl_take isl_qpolynomial *qp1, + __isl_take isl_qpolynomial *qp2) +{ + qp1 = isl_qpolynomial_add(qp1, qp2); + qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom)); + return qp1; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1, + __isl_take isl_qpolynomial *qp2) +{ + return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2)); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int( + __isl_take isl_qpolynomial *qp, isl_int v) +{ + if (isl_int_is_zero(v)) + return qp; + + qp = isl_qpolynomial_cow(qp); + if (!qp) + return NULL; + + qp->upoly = isl_upoly_add_isl_int(qp->upoly, v); + if (!qp->upoly) + goto error; + + return qp; +error: + isl_qpolynomial_free(qp); + return NULL; + +} + +__isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp) +{ + if (!qp) + return NULL; + + return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int( + __isl_take isl_qpolynomial *qp, isl_int v) +{ + if (isl_int_is_one(v)) + return qp; + + if (qp && isl_int_is_zero(v)) { + isl_qpolynomial *zero; + zero = isl_qpolynomial_zero_on_domain(isl_space_copy(qp->dim)); + isl_qpolynomial_free(qp); + return zero; + } + + qp = isl_qpolynomial_cow(qp); + if (!qp) + return NULL; + + qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v); + if (!qp->upoly) + goto error; + + return qp; +error: + isl_qpolynomial_free(qp); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_scale( + __isl_take isl_qpolynomial *qp, isl_int v) +{ + return isl_qpolynomial_mul_isl_int(qp, v); +} + +/* Multiply "qp" by "v". + */ +__isl_give isl_qpolynomial *isl_qpolynomial_scale_val( + __isl_take isl_qpolynomial *qp, __isl_take isl_val *v) +{ + if (!qp || !v) + goto error; + + if (!isl_val_is_rat(v)) + isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid, + "expecting rational factor", goto error); + + if (isl_val_is_one(v)) { + isl_val_free(v); + return qp; + } + + if (isl_val_is_zero(v)) { + isl_space *space; + + space = isl_qpolynomial_get_domain_space(qp); + isl_qpolynomial_free(qp); + isl_val_free(v); + return isl_qpolynomial_zero_on_domain(space); + } + + qp = isl_qpolynomial_cow(qp); + if (!qp) + goto error; + + qp->upoly = isl_upoly_scale_val(qp->upoly, v); + if (!qp->upoly) + qp = isl_qpolynomial_free(qp); + + isl_val_free(v); + return qp; +error: + isl_val_free(v); + isl_qpolynomial_free(qp); + return NULL; +} + +/* Divide "qp" by "v". + */ +__isl_give isl_qpolynomial *isl_qpolynomial_scale_down_val( + __isl_take isl_qpolynomial *qp, __isl_take isl_val *v) +{ + if (!qp || !v) + goto error; + + if (!isl_val_is_rat(v)) + isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid, + "expecting rational factor", goto error); + if (isl_val_is_zero(v)) + isl_die(isl_val_get_ctx(v), isl_error_invalid, + "cannot scale down by zero", goto error); + + return isl_qpolynomial_scale_val(qp, isl_val_inv(v)); +error: + isl_val_free(v); + isl_qpolynomial_free(qp); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1, + __isl_take isl_qpolynomial *qp2) +{ + qp1 = isl_qpolynomial_cow(qp1); + + if (!qp1 || !qp2) + goto error; + + if (qp1->div->n_row < qp2->div->n_row) + return isl_qpolynomial_mul(qp2, qp1); + + isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error); + if (!compatible_divs(qp1->div, qp2->div)) + return with_merged_divs(isl_qpolynomial_mul, qp1, qp2); + + qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly)); + if (!qp1->upoly) + goto error; + + isl_qpolynomial_free(qp2); + + return qp1; +error: + isl_qpolynomial_free(qp1); + isl_qpolynomial_free(qp2); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp, + unsigned power) +{ + qp = isl_qpolynomial_cow(qp); + + if (!qp) + return NULL; + + qp->upoly = isl_upoly_pow(qp->upoly, power); + if (!qp->upoly) + goto error; + + return qp; +error: + isl_qpolynomial_free(qp); + return NULL; +} + +__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow( + __isl_take isl_pw_qpolynomial *pwqp, unsigned power) +{ + int i; + + if (power == 1) + return pwqp; + + pwqp = isl_pw_qpolynomial_cow(pwqp); + if (!pwqp) + return NULL; + + for (i = 0; i < pwqp->n; ++i) { + pwqp->p[i].qp = isl_qpolynomial_pow(pwqp->p[i].qp, power); + if (!pwqp->p[i].qp) + return isl_pw_qpolynomial_free(pwqp); + } + + return pwqp; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain( + __isl_take isl_space *dim) +{ + if (!dim) + return NULL; + return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx)); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain( + __isl_take isl_space *dim) +{ + if (!dim) + return NULL; + return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx)); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain( + __isl_take isl_space *dim) +{ + if (!dim) + return NULL; + return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx)); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain( + __isl_take isl_space *dim) +{ + if (!dim) + return NULL; + return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx)); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain( + __isl_take isl_space *dim) +{ + if (!dim) + return NULL; + return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx)); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_cst_on_domain( + __isl_take isl_space *dim, + isl_int v) +{ + struct isl_qpolynomial *qp; + struct isl_upoly_cst *cst; + + if (!dim) + return NULL; + + qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx)); + if (!qp) + return NULL; + + cst = isl_upoly_as_cst(qp->upoly); + isl_int_set(cst->n, v); + + return qp; +} + +int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp, + isl_int *n, isl_int *d) +{ + struct isl_upoly_cst *cst; + + if (!qp) + return -1; + + if (!isl_upoly_is_cst(qp->upoly)) + return 0; + + cst = isl_upoly_as_cst(qp->upoly); + if (!cst) + return -1; + + if (n) + isl_int_set(*n, cst->n); + if (d) + isl_int_set(*d, cst->d); + + return 1; +} + +/* Return the constant term of "up". + */ +static __isl_give isl_val *isl_upoly_get_constant_val( + __isl_keep struct isl_upoly *up) +{ + struct isl_upoly_cst *cst; + + if (!up) + return NULL; + + while (!isl_upoly_is_cst(up)) { + struct isl_upoly_rec *rec; + + rec = isl_upoly_as_rec(up); + if (!rec) + return NULL; + up = rec->p[0]; + } + + cst = isl_upoly_as_cst(up); + if (!cst) + return NULL; + return isl_val_rat_from_isl_int(cst->up.ctx, cst->n, cst->d); +} + +/* Return the constant term of "qp". + */ +__isl_give isl_val *isl_qpolynomial_get_constant_val( + __isl_keep isl_qpolynomial *qp) +{ + if (!qp) + return NULL; + + return isl_upoly_get_constant_val(qp->upoly); +} + +int isl_upoly_is_affine(__isl_keep struct isl_upoly *up) +{ + int is_cst; + struct isl_upoly_rec *rec; + + if (!up) + return -1; + + if (up->var < 0) + return 1; + + rec = isl_upoly_as_rec(up); + if (!rec) + return -1; + + if (rec->n > 2) + return 0; + + isl_assert(up->ctx, rec->n > 1, return -1); + + is_cst = isl_upoly_is_cst(rec->p[1]); + if (is_cst < 0) + return -1; + if (!is_cst) + return 0; + + return isl_upoly_is_affine(rec->p[0]); +} + +int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp) +{ + if (!qp) + return -1; + + if (qp->div->n_row > 0) + return 0; + + return isl_upoly_is_affine(qp->upoly); +} + +static void update_coeff(__isl_keep isl_vec *aff, + __isl_keep struct isl_upoly_cst *cst, int pos) +{ + isl_int gcd; + isl_int f; + + if (isl_int_is_zero(cst->n)) + return; + + isl_int_init(gcd); + isl_int_init(f); + isl_int_gcd(gcd, cst->d, aff->el[0]); + isl_int_divexact(f, cst->d, gcd); + isl_int_divexact(gcd, aff->el[0], gcd); + isl_seq_scale(aff->el, aff->el, f, aff->size); + isl_int_mul(aff->el[1 + pos], gcd, cst->n); + isl_int_clear(gcd); + isl_int_clear(f); +} + +int isl_upoly_update_affine(__isl_keep struct isl_upoly *up, + __isl_keep isl_vec *aff) +{ + struct isl_upoly_cst *cst; + struct isl_upoly_rec *rec; + + if (!up || !aff) + return -1; + + if (up->var < 0) { + struct isl_upoly_cst *cst; + + cst = isl_upoly_as_cst(up); + if (!cst) + return -1; + update_coeff(aff, cst, 0); + return 0; + } + + rec = isl_upoly_as_rec(up); + if (!rec) + return -1; + isl_assert(up->ctx, rec->n == 2, return -1); + + cst = isl_upoly_as_cst(rec->p[1]); + if (!cst) + return -1; + update_coeff(aff, cst, 1 + up->var); + + return isl_upoly_update_affine(rec->p[0], aff); +} + +__isl_give isl_vec *isl_qpolynomial_extract_affine( + __isl_keep isl_qpolynomial *qp) +{ + isl_vec *aff; + unsigned d; + + if (!qp) + return NULL; + + d = isl_space_dim(qp->dim, isl_dim_all); + aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row); + if (!aff) + return NULL; + + isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row); + isl_int_set_si(aff->el[0], 1); + + if (isl_upoly_update_affine(qp->upoly, aff) < 0) + goto error; + + return aff; +error: + isl_vec_free(aff); + return NULL; +} + +int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1, + __isl_keep isl_qpolynomial *qp2) +{ + int equal; + + if (!qp1 || !qp2) + return -1; + + equal = isl_space_is_equal(qp1->dim, qp2->dim); + if (equal < 0 || !equal) + return equal; + + equal = isl_mat_is_equal(qp1->div, qp2->div); + if (equal < 0 || !equal) + return equal; + + return isl_upoly_is_equal(qp1->upoly, qp2->upoly); +} + +static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d) +{ + int i; + struct isl_upoly_rec *rec; + + if (isl_upoly_is_cst(up)) { + struct isl_upoly_cst *cst; + cst = isl_upoly_as_cst(up); + if (!cst) + return; + isl_int_lcm(*d, *d, cst->d); + return; + } + + rec = isl_upoly_as_rec(up); + if (!rec) + return; + + for (i = 0; i < rec->n; ++i) + upoly_update_den(rec->p[i], d); +} + +void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d) +{ + isl_int_set_si(*d, 1); + if (!qp) + return; + upoly_update_den(qp->upoly, d); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_var_pow_on_domain( + __isl_take isl_space *dim, int pos, int power) +{ + struct isl_ctx *ctx; + + if (!dim) + return NULL; + + ctx = dim->ctx; + + return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power)); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(__isl_take isl_space *dim, + enum isl_dim_type type, unsigned pos) +{ + if (!dim) + return NULL; + + isl_assert(dim->ctx, isl_space_dim(dim, isl_dim_in) == 0, goto error); + isl_assert(dim->ctx, pos < isl_space_dim(dim, type), goto error); + + if (type == isl_dim_set) + pos += isl_space_dim(dim, isl_dim_param); + + return isl_qpolynomial_var_pow_on_domain(dim, pos, 1); +error: + isl_space_free(dim); + return NULL; +} + +__isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up, + unsigned first, unsigned n, __isl_keep struct isl_upoly **subs) +{ + int i; + struct isl_upoly_rec *rec; + struct isl_upoly *base, *res; + + if (!up) + return NULL; + + if (isl_upoly_is_cst(up)) + return up; + + if (up->var < first) + return up; + + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + isl_assert(up->ctx, rec->n >= 1, goto error); + + if (up->var >= first + n) + base = isl_upoly_var_pow(up->ctx, up->var, 1); + else + base = isl_upoly_copy(subs[up->var - first]); + + res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs); + for (i = rec->n - 2; i >= 0; --i) { + struct isl_upoly *t; + t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs); + res = isl_upoly_mul(res, isl_upoly_copy(base)); + res = isl_upoly_sum(res, t); + } + + isl_upoly_free(base); + isl_upoly_free(up); + + return res; +error: + isl_upoly_free(up); + return NULL; +} + +__isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f, + isl_int denom, unsigned len) +{ + int i; + struct isl_upoly *up; + + isl_assert(ctx, len >= 1, return NULL); + + up = isl_upoly_rat_cst(ctx, f[0], denom); + for (i = 0; i < len - 1; ++i) { + struct isl_upoly *t; + struct isl_upoly *c; + + if (isl_int_is_zero(f[1 + i])) + continue; + + c = isl_upoly_rat_cst(ctx, f[1 + i], denom); + t = isl_upoly_var_pow(ctx, i, 1); + t = isl_upoly_mul(c, t); + up = isl_upoly_sum(up, t); + } + + return up; +} + +/* Remove common factor of non-constant terms and denominator. + */ +static void normalize_div(__isl_keep isl_qpolynomial *qp, int div) +{ + isl_ctx *ctx = qp->div->ctx; + unsigned total = qp->div->n_col - 2; + + isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd); + isl_int_gcd(ctx->normalize_gcd, + ctx->normalize_gcd, qp->div->row[div][0]); + if (isl_int_is_one(ctx->normalize_gcd)) + return; + + isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2, + ctx->normalize_gcd, total); + isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0], + ctx->normalize_gcd); + isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1], + ctx->normalize_gcd); +} + +/* Replace the integer division identified by "div" by the polynomial "s". + * The integer division is assumed not to appear in the definition + * of any other integer divisions. + */ +static __isl_give isl_qpolynomial *substitute_div( + __isl_take isl_qpolynomial *qp, + int div, __isl_take struct isl_upoly *s) +{ + int i; + int total; + int *reordering; + + if (!qp || !s) + goto error; + + qp = isl_qpolynomial_cow(qp); + if (!qp) + goto error; + + total = isl_space_dim(qp->dim, isl_dim_all); + qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s); + if (!qp->upoly) + goto error; + + reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row); + if (!reordering) + goto error; + for (i = 0; i < total + div; ++i) + reordering[i] = i; + for (i = total + div + 1; i < total + qp->div->n_row; ++i) + reordering[i] = i - 1; + qp->div = isl_mat_drop_rows(qp->div, div, 1); + qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1); + qp->upoly = reorder(qp->upoly, reordering); + free(reordering); + + if (!qp->upoly || !qp->div) + goto error; + + isl_upoly_free(s); + return qp; +error: + isl_qpolynomial_free(qp); + isl_upoly_free(s); + return NULL; +} + +/* Replace all integer divisions [e/d] that turn out to not actually be integer + * divisions because d is equal to 1 by their definition, i.e., e. + */ +static __isl_give isl_qpolynomial *substitute_non_divs( + __isl_take isl_qpolynomial *qp) +{ + int i, j; + int total; + struct isl_upoly *s; + + if (!qp) + return NULL; + + total = isl_space_dim(qp->dim, isl_dim_all); + for (i = 0; qp && i < qp->div->n_row; ++i) { + if (!isl_int_is_one(qp->div->row[i][0])) + continue; + for (j = i + 1; j < qp->div->n_row; ++j) { + if (isl_int_is_zero(qp->div->row[j][2 + total + i])) + continue; + isl_seq_combine(qp->div->row[j] + 1, + qp->div->ctx->one, qp->div->row[j] + 1, + qp->div->row[j][2 + total + i], + qp->div->row[i] + 1, 1 + total + i); + isl_int_set_si(qp->div->row[j][2 + total + i], 0); + normalize_div(qp, j); + } + s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1, + qp->div->row[i][0], qp->div->n_col - 1); + qp = substitute_div(qp, i, s); + --i; + } + + return qp; +} + +/* Reduce the coefficients of div "div" to lie in the interval [0, d-1], + * with d the denominator. When replacing the coefficient e of x by + * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x + * inside the division, so we need to add floor(e/d) * x outside. + * That is, we replace q by q' + floor(e/d) * x and we therefore need + * to adjust the coefficient of x in each later div that depends on the + * current div "div" and also in the affine expression "aff" + * (if it too depends on "div"). + */ +static void reduce_div(__isl_keep isl_qpolynomial *qp, int div, + __isl_keep isl_vec *aff) +{ + int i, j; + isl_int v; + unsigned total = qp->div->n_col - qp->div->n_row - 2; + + isl_int_init(v); + for (i = 0; i < 1 + total + div; ++i) { + if (isl_int_is_nonneg(qp->div->row[div][1 + i]) && + isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0])) + continue; + isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]); + isl_int_fdiv_r(qp->div->row[div][1 + i], + qp->div->row[div][1 + i], qp->div->row[div][0]); + if (!isl_int_is_zero(aff->el[1 + total + div])) + isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]); + for (j = div + 1; j < qp->div->n_row; ++j) { + if (isl_int_is_zero(qp->div->row[j][2 + total + div])) + continue; + isl_int_addmul(qp->div->row[j][1 + i], + v, qp->div->row[j][2 + total + div]); + } + } + isl_int_clear(v); +} + +/* Check if the last non-zero coefficient is bigger that half of the + * denominator. If so, we will invert the div to further reduce the number + * of distinct divs that may appear. + * If the last non-zero coefficient is exactly half the denominator, + * then we continue looking for earlier coefficients that are bigger + * than half the denominator. + */ +static int needs_invert(__isl_keep isl_mat *div, int row) +{ + int i; + int cmp; + + for (i = div->n_col - 1; i >= 1; --i) { + if (isl_int_is_zero(div->row[row][i])) + continue; + isl_int_mul_ui(div->row[row][i], div->row[row][i], 2); + cmp = isl_int_cmp(div->row[row][i], div->row[row][0]); + isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2); + if (cmp) + return cmp > 0; + if (i == 1) + return 1; + } + + return 0; +} + +/* Replace div "div" q = [e/d] by -[(-e+(d-1))/d]. + * We only invert the coefficients of e (and the coefficient of q in + * later divs and in "aff"). After calling this function, the + * coefficients of e should be reduced again. + */ +static void invert_div(__isl_keep isl_qpolynomial *qp, int div, + __isl_keep isl_vec *aff) +{ + unsigned total = qp->div->n_col - qp->div->n_row - 2; + + isl_seq_neg(qp->div->row[div] + 1, + qp->div->row[div] + 1, qp->div->n_col - 1); + isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1); + isl_int_add(qp->div->row[div][1], + qp->div->row[div][1], qp->div->row[div][0]); + if (!isl_int_is_zero(aff->el[1 + total + div])) + isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]); + isl_mat_col_mul(qp->div, 2 + total + div, + qp->div->ctx->negone, 2 + total + div); +} + +/* Assuming "qp" is a monomial, reduce all its divs to have coefficients + * in the interval [0, d-1], with d the denominator and such that the + * last non-zero coefficient that is not equal to d/2 is smaller than d/2. + * + * After the reduction, some divs may have become redundant or identical, + * so we call substitute_non_divs and sort_divs. If these functions + * eliminate divs or merge two or more divs into one, the coefficients + * of the enclosing divs may have to be reduced again, so we call + * ourselves recursively if the number of divs decreases. + */ +static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp) +{ + int i; + isl_vec *aff = NULL; + struct isl_upoly *s; + unsigned n_div; + + if (!qp) + return NULL; + + aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1); + aff = isl_vec_clr(aff); + if (!aff) + goto error; + + isl_int_set_si(aff->el[1 + qp->upoly->var], 1); + + for (i = 0; i < qp->div->n_row; ++i) { + normalize_div(qp, i); + reduce_div(qp, i, aff); + if (needs_invert(qp->div, i)) { + invert_div(qp, i, aff); + reduce_div(qp, i, aff); + } + } + + s = isl_upoly_from_affine(qp->div->ctx, aff->el, + qp->div->ctx->one, aff->size); + qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s); + isl_upoly_free(s); + if (!qp->upoly) + goto error; + + isl_vec_free(aff); + + n_div = qp->div->n_row; + qp = substitute_non_divs(qp); + qp = sort_divs(qp); + if (qp && qp->div->n_row < n_div) + return reduce_divs(qp); + + return qp; +error: + isl_qpolynomial_free(qp); + isl_vec_free(aff); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain( + __isl_take isl_space *dim, const isl_int n, const isl_int d) +{ + struct isl_qpolynomial *qp; + struct isl_upoly_cst *cst; + + if (!dim) + return NULL; + + qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx)); + if (!qp) + return NULL; + + cst = isl_upoly_as_cst(qp->upoly); + isl_int_set(cst->n, n); + isl_int_set(cst->d, d); + + return qp; +} + +/* Return an isl_qpolynomial that is equal to "val" on domain space "domain". + */ +__isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain( + __isl_take isl_space *domain, __isl_take isl_val *val) +{ + isl_qpolynomial *qp; + struct isl_upoly_cst *cst; + + if (!domain || !val) + goto error; + + qp = isl_qpolynomial_alloc(isl_space_copy(domain), 0, + isl_upoly_zero(domain->ctx)); + if (!qp) + goto error; + + cst = isl_upoly_as_cst(qp->upoly); + isl_int_set(cst->n, val->n); + isl_int_set(cst->d, val->d); + + isl_space_free(domain); + isl_val_free(val); + return qp; +error: + isl_space_free(domain); + isl_val_free(val); + return NULL; +} + +static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d) +{ + struct isl_upoly_rec *rec; + int i; + + if (!up) + return -1; + + if (isl_upoly_is_cst(up)) + return 0; + + if (up->var < d) + active[up->var] = 1; + + rec = isl_upoly_as_rec(up); + for (i = 0; i < rec->n; ++i) + if (up_set_active(rec->p[i], active, d) < 0) + return -1; + + return 0; +} + +static int set_active(__isl_keep isl_qpolynomial *qp, int *active) +{ + int i, j; + int d = isl_space_dim(qp->dim, isl_dim_all); + + if (!qp || !active) + return -1; + + for (i = 0; i < d; ++i) + for (j = 0; j < qp->div->n_row; ++j) { + if (isl_int_is_zero(qp->div->row[j][2 + i])) + continue; + active[i] = 1; + break; + } + + return up_set_active(qp->upoly, active, d); +} + +int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp, + enum isl_dim_type type, unsigned first, unsigned n) +{ + int i; + int *active = NULL; + int involves = 0; + + if (!qp) + return -1; + if (n == 0) + return 0; + + isl_assert(qp->dim->ctx, + first + n <= isl_qpolynomial_dim(qp, type), return -1); + isl_assert(qp->dim->ctx, type == isl_dim_param || + type == isl_dim_in, return -1); + + active = isl_calloc_array(qp->dim->ctx, int, + isl_space_dim(qp->dim, isl_dim_all)); + if (set_active(qp, active) < 0) + goto error; + + if (type == isl_dim_in) + first += isl_space_dim(qp->dim, isl_dim_param); + for (i = 0; i < n; ++i) + if (active[first + i]) { + involves = 1; + break; + } + + free(active); + + return involves; +error: + free(active); + return -1; +} + +/* Remove divs that do not appear in the quasi-polynomial, nor in any + * of the divs that do appear in the quasi-polynomial. + */ +static __isl_give isl_qpolynomial *remove_redundant_divs( + __isl_take isl_qpolynomial *qp) +{ + int i, j; + int d; + int len; + int skip; + int *active = NULL; + int *reordering = NULL; + int redundant = 0; + int n_div; + isl_ctx *ctx; + + if (!qp) + return NULL; + if (qp->div->n_row == 0) + return qp; + + d = isl_space_dim(qp->dim, isl_dim_all); + len = qp->div->n_col - 2; + ctx = isl_qpolynomial_get_ctx(qp); + active = isl_calloc_array(ctx, int, len); + if (!active) + goto error; + + if (up_set_active(qp->upoly, active, len) < 0) + goto error; + + for (i = qp->div->n_row - 1; i >= 0; --i) { + if (!active[d + i]) { + redundant = 1; + continue; + } + for (j = 0; j < i; ++j) { + if (isl_int_is_zero(qp->div->row[i][2 + d + j])) + continue; + active[d + j] = 1; + break; + } + } + + if (!redundant) { + free(active); + return qp; + } + + reordering = isl_alloc_array(qp->div->ctx, int, len); + if (!reordering) + goto error; + + for (i = 0; i < d; ++i) + reordering[i] = i; + + skip = 0; + n_div = qp->div->n_row; + for (i = 0; i < n_div; ++i) { + if (!active[d + i]) { + qp->div = isl_mat_drop_rows(qp->div, i - skip, 1); + qp->div = isl_mat_drop_cols(qp->div, + 2 + d + i - skip, 1); + skip++; + } + reordering[d + i] = d + i - skip; + } + + qp->upoly = reorder(qp->upoly, reordering); + + if (!qp->upoly || !qp->div) + goto error; + + free(active); + free(reordering); + + return qp; +error: + free(active); + free(reordering); + isl_qpolynomial_free(qp); + return NULL; +} + +__isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up, + unsigned first, unsigned n) +{ + int i; + struct isl_upoly_rec *rec; + + if (!up) + return NULL; + if (n == 0 || up->var < 0 || up->var < first) + return up; + if (up->var < first + n) { + up = replace_by_constant_term(up); + return isl_upoly_drop(up, first, n); + } + up = isl_upoly_cow(up); + if (!up) + return NULL; + up->var -= n; + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + for (i = 0; i < rec->n; ++i) { + rec->p[i] = isl_upoly_drop(rec->p[i], first, n); + if (!rec->p[i]) + goto error; + } + + return up; +error: + isl_upoly_free(up); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name( + __isl_take isl_qpolynomial *qp, + enum isl_dim_type type, unsigned pos, const char *s) +{ + qp = isl_qpolynomial_cow(qp); + if (!qp) + return NULL; + qp->dim = isl_space_set_dim_name(qp->dim, type, pos, s); + if (!qp->dim) + goto error; + return qp; +error: + isl_qpolynomial_free(qp); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_drop_dims( + __isl_take isl_qpolynomial *qp, + enum isl_dim_type type, unsigned first, unsigned n) +{ + if (!qp) + return NULL; + if (type == isl_dim_out) + isl_die(qp->dim->ctx, isl_error_invalid, + "cannot drop output/set dimension", + goto error); + if (type == isl_dim_in) + type = isl_dim_set; + if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type)) + return qp; + + qp = isl_qpolynomial_cow(qp); + if (!qp) + return NULL; + + isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type), + goto error); + isl_assert(qp->dim->ctx, type == isl_dim_param || + type == isl_dim_set, goto error); + + qp->dim = isl_space_drop_dims(qp->dim, type, first, n); + if (!qp->dim) + goto error; + + if (type == isl_dim_set) + first += isl_space_dim(qp->dim, isl_dim_param); + + qp->div = isl_mat_drop_cols(qp->div, 2 + first, n); + if (!qp->div) + goto error; + + qp->upoly = isl_upoly_drop(qp->upoly, first, n); + if (!qp->upoly) + goto error; + + return qp; +error: + isl_qpolynomial_free(qp); + return NULL; +} + +/* Project the domain of the quasi-polynomial onto its parameter space. + * The quasi-polynomial may not involve any of the domain dimensions. + */ +__isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params( + __isl_take isl_qpolynomial *qp) +{ + isl_space *space; + unsigned n; + int involves; + + n = isl_qpolynomial_dim(qp, isl_dim_in); + involves = isl_qpolynomial_involves_dims(qp, isl_dim_in, 0, n); + if (involves < 0) + return isl_qpolynomial_free(qp); + if (involves) + isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid, + "polynomial involves some of the domain dimensions", + return isl_qpolynomial_free(qp)); + qp = isl_qpolynomial_drop_dims(qp, isl_dim_in, 0, n); + space = isl_qpolynomial_get_domain_space(qp); + space = isl_space_params(space); + qp = isl_qpolynomial_reset_domain_space(qp, space); + return qp; +} + +static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted( + __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq) +{ + int i, j, k; + isl_int denom; + unsigned total; + unsigned n_div; + struct isl_upoly *up; + + if (!eq) + goto error; + if (eq->n_eq == 0) { + isl_basic_set_free(eq); + return qp; + } + + qp = isl_qpolynomial_cow(qp); + if (!qp) + goto error; + qp->div = isl_mat_cow(qp->div); + if (!qp->div) + goto error; + + total = 1 + isl_space_dim(eq->dim, isl_dim_all); + n_div = eq->n_div; + isl_int_init(denom); + for (i = 0; i < eq->n_eq; ++i) { + j = isl_seq_last_non_zero(eq->eq[i], total + n_div); + if (j < 0 || j == 0 || j >= total) + continue; + + for (k = 0; k < qp->div->n_row; ++k) { + if (isl_int_is_zero(qp->div->row[k][1 + j])) + continue; + isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total, + &qp->div->row[k][0]); + normalize_div(qp, k); + } + + if (isl_int_is_pos(eq->eq[i][j])) + isl_seq_neg(eq->eq[i], eq->eq[i], total); + isl_int_abs(denom, eq->eq[i][j]); + isl_int_set_si(eq->eq[i][j], 0); + + up = isl_upoly_from_affine(qp->dim->ctx, + eq->eq[i], denom, total); + qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up); + isl_upoly_free(up); + } + isl_int_clear(denom); + + if (!qp->upoly) + goto error; + + isl_basic_set_free(eq); + + qp = substitute_non_divs(qp); + qp = sort_divs(qp); + + return qp; +error: + isl_basic_set_free(eq); + isl_qpolynomial_free(qp); + return NULL; +} + +/* Exploit the equalities in "eq" to simplify the quasi-polynomial. + */ +__isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities( + __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq) +{ + if (!qp || !eq) + goto error; + if (qp->div->n_row > 0) + eq = isl_basic_set_add_dims(eq, isl_dim_set, qp->div->n_row); + return isl_qpolynomial_substitute_equalities_lifted(qp, eq); +error: + isl_basic_set_free(eq); + isl_qpolynomial_free(qp); + return NULL; +} + +static __isl_give isl_basic_set *add_div_constraints( + __isl_take isl_basic_set *bset, __isl_take isl_mat *div) +{ + int i; + unsigned total; + + if (!bset || !div) + goto error; + + bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row); + if (!bset) + goto error; + total = isl_basic_set_total_dim(bset); + for (i = 0; i < div->n_row; ++i) + if (isl_basic_set_add_div_constraints_var(bset, + total - div->n_row + i, div->row[i]) < 0) + goto error; + + isl_mat_free(div); + return bset; +error: + isl_mat_free(div); + isl_basic_set_free(bset); + return NULL; +} + +/* Look for equalities among the variables shared by context and qp + * and the integer divisions of qp, if any. + * The equalities are then used to eliminate variables and/or integer + * divisions from qp. + */ +__isl_give isl_qpolynomial *isl_qpolynomial_gist( + __isl_take isl_qpolynomial *qp, __isl_take isl_set *context) +{ + isl_basic_set *aff; + + if (!qp) + goto error; + if (qp->div->n_row > 0) { + isl_basic_set *bset; + context = isl_set_add_dims(context, isl_dim_set, + qp->div->n_row); + bset = isl_basic_set_universe(isl_set_get_space(context)); + bset = add_div_constraints(bset, isl_mat_copy(qp->div)); + context = isl_set_intersect(context, + isl_set_from_basic_set(bset)); + } + + aff = isl_set_affine_hull(context); + return isl_qpolynomial_substitute_equalities_lifted(qp, aff); +error: + isl_qpolynomial_free(qp); + isl_set_free(context); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_gist_params( + __isl_take isl_qpolynomial *qp, __isl_take isl_set *context) +{ + isl_space *space = isl_qpolynomial_get_domain_space(qp); + isl_set *dom_context = isl_set_universe(space); + dom_context = isl_set_intersect_params(dom_context, context); + return isl_qpolynomial_gist(qp, dom_context); +} + +__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial( + __isl_take isl_qpolynomial *qp) +{ + isl_set *dom; + + if (!qp) + return NULL; + if (isl_qpolynomial_is_zero(qp)) { + isl_space *dim = isl_qpolynomial_get_space(qp); + isl_qpolynomial_free(qp); + return isl_pw_qpolynomial_zero(dim); + } + + dom = isl_set_universe(isl_qpolynomial_get_domain_space(qp)); + return isl_pw_qpolynomial_alloc(dom, qp); +} + +#undef PW +#define PW isl_pw_qpolynomial +#undef EL +#define EL isl_qpolynomial +#undef EL_IS_ZERO +#define EL_IS_ZERO is_zero +#undef ZERO +#define ZERO zero +#undef IS_ZERO +#define IS_ZERO is_zero +#undef FIELD +#define FIELD qp +#undef DEFAULT_IS_ZERO +#define DEFAULT_IS_ZERO 1 + +#define NO_PULLBACK + +#include <isl_pw_templ.c> + +#undef UNION +#define UNION isl_union_pw_qpolynomial +#undef PART +#define PART isl_pw_qpolynomial +#undef PARTS +#define PARTS pw_qpolynomial +#define ALIGN_DOMAIN + +#include <isl_union_templ.c> + +int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp) +{ + if (!pwqp) + return -1; + + if (pwqp->n != -1) + return 0; + + if (!isl_set_plain_is_universe(pwqp->p[0].set)) + return 0; + + return isl_qpolynomial_is_one(pwqp->p[0].qp); +} + +__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add( + __isl_take isl_pw_qpolynomial *pwqp1, + __isl_take isl_pw_qpolynomial *pwqp2) +{ + return isl_pw_qpolynomial_union_add_(pwqp1, pwqp2); +} + +__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul( + __isl_take isl_pw_qpolynomial *pwqp1, + __isl_take isl_pw_qpolynomial *pwqp2) +{ + int i, j, n; + struct isl_pw_qpolynomial *res; + + if (!pwqp1 || !pwqp2) + goto error; + + isl_assert(pwqp1->dim->ctx, isl_space_is_equal(pwqp1->dim, pwqp2->dim), + goto error); + + if (isl_pw_qpolynomial_is_zero(pwqp1)) { + isl_pw_qpolynomial_free(pwqp2); + return pwqp1; + } + + if (isl_pw_qpolynomial_is_zero(pwqp2)) { + isl_pw_qpolynomial_free(pwqp1); + return pwqp2; + } + + if (isl_pw_qpolynomial_is_one(pwqp1)) { + isl_pw_qpolynomial_free(pwqp1); + return pwqp2; + } + + if (isl_pw_qpolynomial_is_one(pwqp2)) { + isl_pw_qpolynomial_free(pwqp2); + return pwqp1; + } + + n = pwqp1->n * pwqp2->n; + res = isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1->dim), n); + + for (i = 0; i < pwqp1->n; ++i) { + for (j = 0; j < pwqp2->n; ++j) { + struct isl_set *common; + struct isl_qpolynomial *prod; + common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set), + isl_set_copy(pwqp2->p[j].set)); + if (isl_set_plain_is_empty(common)) { + isl_set_free(common); + continue; + } + + prod = isl_qpolynomial_mul( + isl_qpolynomial_copy(pwqp1->p[i].qp), + isl_qpolynomial_copy(pwqp2->p[j].qp)); + + res = isl_pw_qpolynomial_add_piece(res, common, prod); + } + } + + isl_pw_qpolynomial_free(pwqp1); + isl_pw_qpolynomial_free(pwqp2); + + return res; +error: + isl_pw_qpolynomial_free(pwqp1); + isl_pw_qpolynomial_free(pwqp2); + return NULL; +} + +__isl_give isl_val *isl_upoly_eval(__isl_take struct isl_upoly *up, + __isl_take isl_vec *vec) +{ + int i; + struct isl_upoly_rec *rec; + isl_val *res; + isl_val *base; + + if (isl_upoly_is_cst(up)) { + isl_vec_free(vec); + res = isl_upoly_get_constant_val(up); + isl_upoly_free(up); + return res; + } + + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + isl_assert(up->ctx, rec->n >= 1, goto error); + + base = isl_val_rat_from_isl_int(up->ctx, + vec->el[1 + up->var], vec->el[0]); + + res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]), + isl_vec_copy(vec)); + + for (i = rec->n - 2; i >= 0; --i) { + res = isl_val_mul(res, isl_val_copy(base)); + res = isl_val_add(res, + isl_upoly_eval(isl_upoly_copy(rec->p[i]), + isl_vec_copy(vec))); + } + + isl_val_free(base); + isl_upoly_free(up); + isl_vec_free(vec); + return res; +error: + isl_upoly_free(up); + isl_vec_free(vec); + return NULL; +} + +__isl_give isl_val *isl_qpolynomial_eval(__isl_take isl_qpolynomial *qp, + __isl_take isl_point *pnt) +{ + isl_vec *ext; + isl_val *v; + + if (!qp || !pnt) + goto error; + isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, qp->dim), goto error); + + if (qp->div->n_row == 0) + ext = isl_vec_copy(pnt->vec); + else { + int i; + unsigned dim = isl_space_dim(qp->dim, isl_dim_all); + ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row); + if (!ext) + goto error; + + isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size); + for (i = 0; i < qp->div->n_row; ++i) { + isl_seq_inner_product(qp->div->row[i] + 1, ext->el, + 1 + dim + i, &ext->el[1+dim+i]); + isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i], + qp->div->row[i][0]); + } + } + + v = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext); + + isl_qpolynomial_free(qp); + isl_point_free(pnt); + + return v; +error: + isl_qpolynomial_free(qp); + isl_point_free(pnt); + return NULL; +} + +int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1, + __isl_keep struct isl_upoly_cst *cst2) +{ + int cmp; + isl_int t; + isl_int_init(t); + isl_int_mul(t, cst1->n, cst2->d); + isl_int_submul(t, cst2->n, cst1->d); + cmp = isl_int_sgn(t); + isl_int_clear(t); + return cmp; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_insert_dims( + __isl_take isl_qpolynomial *qp, enum isl_dim_type type, + unsigned first, unsigned n) +{ + unsigned total; + unsigned g_pos; + int *exp; + + if (!qp) + return NULL; + if (type == isl_dim_out) + isl_die(qp->div->ctx, isl_error_invalid, + "cannot insert output/set dimensions", + goto error); + if (type == isl_dim_in) + type = isl_dim_set; + if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type)) + return qp; + + qp = isl_qpolynomial_cow(qp); + if (!qp) + return NULL; + + isl_assert(qp->div->ctx, first <= isl_space_dim(qp->dim, type), + goto error); + + g_pos = pos(qp->dim, type) + first; + + qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n); + if (!qp->div) + goto error; + + total = qp->div->n_col - 2; + if (total > g_pos) { + int i; + exp = isl_alloc_array(qp->div->ctx, int, total - g_pos); + if (!exp) + goto error; + for (i = 0; i < total - g_pos; ++i) + exp[i] = i + n; + qp->upoly = expand(qp->upoly, exp, g_pos); + free(exp); + if (!qp->upoly) + goto error; + } + + qp->dim = isl_space_insert_dims(qp->dim, type, first, n); + if (!qp->dim) + goto error; + + return qp; +error: + isl_qpolynomial_free(qp); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_add_dims( + __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n) +{ + unsigned pos; + + pos = isl_qpolynomial_dim(qp, type); + + return isl_qpolynomial_insert_dims(qp, type, pos, n); +} + +__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims( + __isl_take isl_pw_qpolynomial *pwqp, + enum isl_dim_type type, unsigned n) +{ + unsigned pos; + + pos = isl_pw_qpolynomial_dim(pwqp, type); + + return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n); +} + +static int *reordering_move(isl_ctx *ctx, + unsigned len, unsigned dst, unsigned src, unsigned n) +{ + int i; + int *reordering; + + reordering = isl_alloc_array(ctx, int, len); + if (!reordering) + return NULL; + + if (dst <= src) { + for (i = 0; i < dst; ++i) + reordering[i] = i; + for (i = 0; i < n; ++i) + reordering[src + i] = dst + i; + for (i = 0; i < src - dst; ++i) + reordering[dst + i] = dst + n + i; + for (i = 0; i < len - src - n; ++i) + reordering[src + n + i] = src + n + i; + } else { + for (i = 0; i < src; ++i) + reordering[i] = i; + for (i = 0; i < n; ++i) + reordering[src + i] = dst + i; + for (i = 0; i < dst - src; ++i) + reordering[src + n + i] = src + i; + for (i = 0; i < len - dst - n; ++i) + reordering[dst + n + i] = dst + n + i; + } + + return reordering; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_move_dims( + __isl_take isl_qpolynomial *qp, + enum isl_dim_type dst_type, unsigned dst_pos, + enum isl_dim_type src_type, unsigned src_pos, unsigned n) +{ + unsigned g_dst_pos; + unsigned g_src_pos; + int *reordering; + + if (n == 0) + return qp; + + qp = isl_qpolynomial_cow(qp); + if (!qp) + return NULL; + + if (dst_type == isl_dim_out || src_type == isl_dim_out) + isl_die(qp->dim->ctx, isl_error_invalid, + "cannot move output/set dimension", + goto error); + if (dst_type == isl_dim_in) + dst_type = isl_dim_set; + if (src_type == isl_dim_in) + src_type = isl_dim_set; + + isl_assert(qp->dim->ctx, src_pos + n <= isl_space_dim(qp->dim, src_type), + goto error); + + g_dst_pos = pos(qp->dim, dst_type) + dst_pos; + g_src_pos = pos(qp->dim, src_type) + src_pos; + if (dst_type > src_type) + g_dst_pos -= n; + + qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n); + if (!qp->div) + goto error; + qp = sort_divs(qp); + if (!qp) + goto error; + + reordering = reordering_move(qp->dim->ctx, + qp->div->n_col - 2, g_dst_pos, g_src_pos, n); + if (!reordering) + goto error; + + qp->upoly = reorder(qp->upoly, reordering); + free(reordering); + if (!qp->upoly) + goto error; + + qp->dim = isl_space_move_dims(qp->dim, dst_type, dst_pos, src_type, src_pos, n); + if (!qp->dim) + goto error; + + return qp; +error: + isl_qpolynomial_free(qp); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_space *dim, + isl_int *f, isl_int denom) +{ + struct isl_upoly *up; + + dim = isl_space_domain(dim); + if (!dim) + return NULL; + + up = isl_upoly_from_affine(dim->ctx, f, denom, + 1 + isl_space_dim(dim, isl_dim_all)); + + return isl_qpolynomial_alloc(dim, 0, up); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff) +{ + isl_ctx *ctx; + struct isl_upoly *up; + isl_qpolynomial *qp; + + if (!aff) + return NULL; + + ctx = isl_aff_get_ctx(aff); + up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0], + aff->v->size - 1); + + qp = isl_qpolynomial_alloc(isl_aff_get_domain_space(aff), + aff->ls->div->n_row, up); + if (!qp) + goto error; + + isl_mat_free(qp->div); + qp->div = isl_mat_copy(aff->ls->div); + qp->div = isl_mat_cow(qp->div); + if (!qp->div) + goto error; + + isl_aff_free(aff); + qp = reduce_divs(qp); + qp = remove_redundant_divs(qp); + return qp; +error: + isl_aff_free(aff); + return isl_qpolynomial_free(qp); +} + +__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff( + __isl_take isl_pw_aff *pwaff) +{ + int i; + isl_pw_qpolynomial *pwqp; + + if (!pwaff) + return NULL; + + pwqp = isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff), + pwaff->n); + + for (i = 0; i < pwaff->n; ++i) { + isl_set *dom; + isl_qpolynomial *qp; + + dom = isl_set_copy(pwaff->p[i].set); + qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff)); + pwqp = isl_pw_qpolynomial_add_piece(pwqp, dom, qp); + } + + isl_pw_aff_free(pwaff); + return pwqp; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_from_constraint( + __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos) +{ + isl_aff *aff; + + aff = isl_constraint_get_bound(c, type, pos); + isl_constraint_free(c); + return isl_qpolynomial_from_aff(aff); +} + +/* For each 0 <= i < "n", replace variable "first" + i of type "type" + * in "qp" by subs[i]. + */ +__isl_give isl_qpolynomial *isl_qpolynomial_substitute( + __isl_take isl_qpolynomial *qp, + enum isl_dim_type type, unsigned first, unsigned n, + __isl_keep isl_qpolynomial **subs) +{ + int i; + struct isl_upoly **ups; + + if (n == 0) + return qp; + + qp = isl_qpolynomial_cow(qp); + if (!qp) + return NULL; + + if (type == isl_dim_out) + isl_die(qp->dim->ctx, isl_error_invalid, + "cannot substitute output/set dimension", + goto error); + if (type == isl_dim_in) + type = isl_dim_set; + + for (i = 0; i < n; ++i) + if (!subs[i]) + goto error; + + isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type), + goto error); + + for (i = 0; i < n; ++i) + isl_assert(qp->dim->ctx, isl_space_is_equal(qp->dim, subs[i]->dim), + goto error); + + isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error); + for (i = 0; i < n; ++i) + isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error); + + first += pos(qp->dim, type); + + ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n); + if (!ups) + goto error; + for (i = 0; i < n; ++i) + ups[i] = subs[i]->upoly; + + qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups); + + free(ups); + + if (!qp->upoly) + goto error; + + return qp; +error: + isl_qpolynomial_free(qp); + return NULL; +} + +/* Extend "bset" with extra set dimensions for each integer division + * in "qp" and then call "fn" with the extended bset and the polynomial + * that results from replacing each of the integer divisions by the + * corresponding extra set dimension. + */ +int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp, + __isl_keep isl_basic_set *bset, + int (*fn)(__isl_take isl_basic_set *bset, + __isl_take isl_qpolynomial *poly, void *user), void *user) +{ + isl_space *dim; + isl_mat *div; + isl_qpolynomial *poly; + + if (!qp || !bset) + goto error; + if (qp->div->n_row == 0) + return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp), + user); + + div = isl_mat_copy(qp->div); + dim = isl_space_copy(qp->dim); + dim = isl_space_add_dims(dim, isl_dim_set, qp->div->n_row); + poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly)); + bset = isl_basic_set_copy(bset); + bset = isl_basic_set_add_dims(bset, isl_dim_set, qp->div->n_row); + bset = add_div_constraints(bset, div); + + return fn(bset, poly, user); +error: + return -1; +} + +/* Return total degree in variables first (inclusive) up to last (exclusive). + */ +int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last) +{ + int deg = -1; + int i; + struct isl_upoly_rec *rec; + + if (!up) + return -2; + if (isl_upoly_is_zero(up)) + return -1; + if (isl_upoly_is_cst(up) || up->var < first) + return 0; + + rec = isl_upoly_as_rec(up); + if (!rec) + return -2; + + for (i = 0; i < rec->n; ++i) { + int d; + + if (isl_upoly_is_zero(rec->p[i])) + continue; + d = isl_upoly_degree(rec->p[i], first, last); + if (up->var < last) + d += i; + if (d > deg) + deg = d; + } + + return deg; +} + +/* Return total degree in set variables. + */ +int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly) +{ + unsigned ovar; + unsigned nvar; + + if (!poly) + return -2; + + ovar = isl_space_offset(poly->dim, isl_dim_set); + nvar = isl_space_dim(poly->dim, isl_dim_set); + return isl_upoly_degree(poly->upoly, ovar, ovar + nvar); +} + +__isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up, + unsigned pos, int deg) +{ + int i; + struct isl_upoly_rec *rec; + + if (!up) + return NULL; + + if (isl_upoly_is_cst(up) || up->var < pos) { + if (deg == 0) + return isl_upoly_copy(up); + else + return isl_upoly_zero(up->ctx); + } + + rec = isl_upoly_as_rec(up); + if (!rec) + return NULL; + + if (up->var == pos) { + if (deg < rec->n) + return isl_upoly_copy(rec->p[deg]); + else + return isl_upoly_zero(up->ctx); + } + + up = isl_upoly_copy(up); + up = isl_upoly_cow(up); + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + for (i = 0; i < rec->n; ++i) { + struct isl_upoly *t; + t = isl_upoly_coeff(rec->p[i], pos, deg); + if (!t) + goto error; + isl_upoly_free(rec->p[i]); + rec->p[i] = t; + } + + return up; +error: + isl_upoly_free(up); + return NULL; +} + +/* Return coefficient of power "deg" of variable "t_pos" of type "type". + */ +__isl_give isl_qpolynomial *isl_qpolynomial_coeff( + __isl_keep isl_qpolynomial *qp, + enum isl_dim_type type, unsigned t_pos, int deg) +{ + unsigned g_pos; + struct isl_upoly *up; + isl_qpolynomial *c; + + if (!qp) + return NULL; + + if (type == isl_dim_out) + isl_die(qp->div->ctx, isl_error_invalid, + "output/set dimension does not have a coefficient", + return NULL); + if (type == isl_dim_in) + type = isl_dim_set; + + isl_assert(qp->div->ctx, t_pos < isl_space_dim(qp->dim, type), + return NULL); + + g_pos = pos(qp->dim, type) + t_pos; + up = isl_upoly_coeff(qp->upoly, g_pos, deg); + + c = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row, up); + if (!c) + return NULL; + isl_mat_free(c->div); + c->div = isl_mat_copy(qp->div); + if (!c->div) + goto error; + return c; +error: + isl_qpolynomial_free(c); + return NULL; +} + +/* Homogenize the polynomial in the variables first (inclusive) up to + * last (exclusive) by inserting powers of variable first. + * Variable first is assumed not to appear in the input. + */ +__isl_give struct isl_upoly *isl_upoly_homogenize( + __isl_take struct isl_upoly *up, int deg, int target, + int first, int last) +{ + int i; + struct isl_upoly_rec *rec; + + if (!up) + return NULL; + if (isl_upoly_is_zero(up)) + return up; + if (deg == target) + return up; + if (isl_upoly_is_cst(up) || up->var < first) { + struct isl_upoly *hom; + + hom = isl_upoly_var_pow(up->ctx, first, target - deg); + if (!hom) + goto error; + rec = isl_upoly_as_rec(hom); + rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up); + + return hom; + } + + up = isl_upoly_cow(up); + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + for (i = 0; i < rec->n; ++i) { + if (isl_upoly_is_zero(rec->p[i])) + continue; + rec->p[i] = isl_upoly_homogenize(rec->p[i], + up->var < last ? deg + i : i, target, + first, last); + if (!rec->p[i]) + goto error; + } + + return up; +error: + isl_upoly_free(up); + return NULL; +} + +/* Homogenize the polynomial in the set variables by introducing + * powers of an extra set variable at position 0. + */ +__isl_give isl_qpolynomial *isl_qpolynomial_homogenize( + __isl_take isl_qpolynomial *poly) +{ + unsigned ovar; + unsigned nvar; + int deg = isl_qpolynomial_degree(poly); + + if (deg < -1) + goto error; + + poly = isl_qpolynomial_insert_dims(poly, isl_dim_in, 0, 1); + poly = isl_qpolynomial_cow(poly); + if (!poly) + goto error; + + ovar = isl_space_offset(poly->dim, isl_dim_set); + nvar = isl_space_dim(poly->dim, isl_dim_set); + poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg, + ovar, ovar + nvar); + if (!poly->upoly) + goto error; + + return poly; +error: + isl_qpolynomial_free(poly); + return NULL; +} + +__isl_give isl_term *isl_term_alloc(__isl_take isl_space *dim, + __isl_take isl_mat *div) +{ + isl_term *term; + int n; + + if (!dim || !div) + goto error; + + n = isl_space_dim(dim, isl_dim_all) + div->n_row; + + term = isl_calloc(dim->ctx, struct isl_term, + sizeof(struct isl_term) + (n - 1) * sizeof(int)); + if (!term) + goto error; + + term->ref = 1; + term->dim = dim; + term->div = div; + isl_int_init(term->n); + isl_int_init(term->d); + + return term; +error: + isl_space_free(dim); + isl_mat_free(div); + return NULL; +} + +__isl_give isl_term *isl_term_copy(__isl_keep isl_term *term) +{ + if (!term) + return NULL; + + term->ref++; + return term; +} + +__isl_give isl_term *isl_term_dup(__isl_keep isl_term *term) +{ + int i; + isl_term *dup; + unsigned total; + + if (!term) + return NULL; + + total = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row; + + dup = isl_term_alloc(isl_space_copy(term->dim), isl_mat_copy(term->div)); + if (!dup) + return NULL; + + isl_int_set(dup->n, term->n); + isl_int_set(dup->d, term->d); + + for (i = 0; i < total; ++i) + dup->pow[i] = term->pow[i]; + + return dup; +} + +__isl_give isl_term *isl_term_cow(__isl_take isl_term *term) +{ + if (!term) + return NULL; + + if (term->ref == 1) + return term; + term->ref--; + return isl_term_dup(term); +} + +void isl_term_free(__isl_take isl_term *term) +{ + if (!term) + return; + + if (--term->ref > 0) + return; + + isl_space_free(term->dim); + isl_mat_free(term->div); + isl_int_clear(term->n); + isl_int_clear(term->d); + free(term); +} + +unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type) +{ + if (!term) + return 0; + + switch (type) { + case isl_dim_param: + case isl_dim_in: + case isl_dim_out: return isl_space_dim(term->dim, type); + case isl_dim_div: return term->div->n_row; + case isl_dim_all: return isl_space_dim(term->dim, isl_dim_all) + + term->div->n_row; + default: return 0; + } +} + +isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term) +{ + return term ? term->dim->ctx : NULL; +} + +void isl_term_get_num(__isl_keep isl_term *term, isl_int *n) +{ + if (!term) + return; + isl_int_set(*n, term->n); +} + +void isl_term_get_den(__isl_keep isl_term *term, isl_int *d) +{ + if (!term) + return; + isl_int_set(*d, term->d); +} + +/* Return the coefficient of the term "term". + */ +__isl_give isl_val *isl_term_get_coefficient_val(__isl_keep isl_term *term) +{ + if (!term) + return NULL; + + return isl_val_rat_from_isl_int(isl_term_get_ctx(term), + term->n, term->d); +} + +int isl_term_get_exp(__isl_keep isl_term *term, + enum isl_dim_type type, unsigned pos) +{ + if (!term) + return -1; + + isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1); + + if (type >= isl_dim_set) + pos += isl_space_dim(term->dim, isl_dim_param); + if (type >= isl_dim_div) + pos += isl_space_dim(term->dim, isl_dim_set); + + return term->pow[pos]; +} + +__isl_give isl_aff *isl_term_get_div(__isl_keep isl_term *term, unsigned pos) +{ + isl_local_space *ls; + isl_aff *aff; + + if (!term) + return NULL; + + isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div), + return NULL); + + ls = isl_local_space_alloc_div(isl_space_copy(term->dim), + isl_mat_copy(term->div)); + aff = isl_aff_alloc(ls); + if (!aff) + return NULL; + + isl_seq_cpy(aff->v->el, term->div->row[pos], aff->v->size); + + aff = isl_aff_normalize(aff); + + return aff; +} + +__isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up, + int (*fn)(__isl_take isl_term *term, void *user), + __isl_take isl_term *term, void *user) +{ + int i; + struct isl_upoly_rec *rec; + + if (!up || !term) + goto error; + + if (isl_upoly_is_zero(up)) + return term; + + isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error); + isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error); + isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error); + + if (isl_upoly_is_cst(up)) { + struct isl_upoly_cst *cst; + cst = isl_upoly_as_cst(up); + if (!cst) + goto error; + term = isl_term_cow(term); + if (!term) + goto error; + isl_int_set(term->n, cst->n); + isl_int_set(term->d, cst->d); + if (fn(isl_term_copy(term), user) < 0) + goto error; + return term; + } + + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + for (i = 0; i < rec->n; ++i) { + term = isl_term_cow(term); + if (!term) + goto error; + term->pow[up->var] = i; + term = isl_upoly_foreach_term(rec->p[i], fn, term, user); + if (!term) + goto error; + } + term->pow[up->var] = 0; + + return term; +error: + isl_term_free(term); + return NULL; +} + +int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp, + int (*fn)(__isl_take isl_term *term, void *user), void *user) +{ + isl_term *term; + + if (!qp) + return -1; + + term = isl_term_alloc(isl_space_copy(qp->dim), isl_mat_copy(qp->div)); + if (!term) + return -1; + + term = isl_upoly_foreach_term(qp->upoly, fn, term, user); + + isl_term_free(term); + + return term ? 0 : -1; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term) +{ + struct isl_upoly *up; + isl_qpolynomial *qp; + int i, n; + + if (!term) + return NULL; + + n = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row; + + up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d); + for (i = 0; i < n; ++i) { + if (!term->pow[i]) + continue; + up = isl_upoly_mul(up, + isl_upoly_var_pow(term->dim->ctx, i, term->pow[i])); + } + + qp = isl_qpolynomial_alloc(isl_space_copy(term->dim), term->div->n_row, up); + if (!qp) + goto error; + isl_mat_free(qp->div); + qp->div = isl_mat_copy(term->div); + if (!qp->div) + goto error; + + isl_term_free(term); + return qp; +error: + isl_qpolynomial_free(qp); + isl_term_free(term); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp, + __isl_take isl_space *dim) +{ + int i; + int extra; + unsigned total; + + if (!qp || !dim) + goto error; + + if (isl_space_is_equal(qp->dim, dim)) { + isl_space_free(dim); + return qp; + } + + qp = isl_qpolynomial_cow(qp); + if (!qp) + goto error; + + extra = isl_space_dim(dim, isl_dim_set) - + isl_space_dim(qp->dim, isl_dim_set); + total = isl_space_dim(qp->dim, isl_dim_all); + if (qp->div->n_row) { + int *exp; + + exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row); + if (!exp) + goto error; + for (i = 0; i < qp->div->n_row; ++i) + exp[i] = extra + i; + qp->upoly = expand(qp->upoly, exp, total); + free(exp); + if (!qp->upoly) + goto error; + } + qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra); + if (!qp->div) + goto error; + for (i = 0; i < qp->div->n_row; ++i) + isl_seq_clr(qp->div->row[i] + 2 + total, extra); + + isl_space_free(qp->dim); + qp->dim = dim; + + return qp; +error: + isl_space_free(dim); + isl_qpolynomial_free(qp); + return NULL; +} + +/* For each parameter or variable that does not appear in qp, + * first eliminate the variable from all constraints and then set it to zero. + */ +static __isl_give isl_set *fix_inactive(__isl_take isl_set *set, + __isl_keep isl_qpolynomial *qp) +{ + int *active = NULL; + int i; + int d; + unsigned nparam; + unsigned nvar; + + if (!set || !qp) + goto error; + + d = isl_space_dim(set->dim, isl_dim_all); + active = isl_calloc_array(set->ctx, int, d); + if (set_active(qp, active) < 0) + goto error; + + for (i = 0; i < d; ++i) + if (!active[i]) + break; + + if (i == d) { + free(active); + return set; + } + + nparam = isl_space_dim(set->dim, isl_dim_param); + nvar = isl_space_dim(set->dim, isl_dim_set); + for (i = 0; i < nparam; ++i) { + if (active[i]) + continue; + set = isl_set_eliminate(set, isl_dim_param, i, 1); + set = isl_set_fix_si(set, isl_dim_param, i, 0); + } + for (i = 0; i < nvar; ++i) { + if (active[nparam + i]) + continue; + set = isl_set_eliminate(set, isl_dim_set, i, 1); + set = isl_set_fix_si(set, isl_dim_set, i, 0); + } + + free(active); + + return set; +error: + free(active); + isl_set_free(set); + return NULL; +} + +struct isl_opt_data { + isl_qpolynomial *qp; + int first; + isl_val *opt; + int max; +}; + +static int opt_fn(__isl_take isl_point *pnt, void *user) +{ + struct isl_opt_data *data = (struct isl_opt_data *)user; + isl_val *val; + + val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt); + if (data->first) { + data->first = 0; + data->opt = val; + } else if (data->max) { + data->opt = isl_val_max(data->opt, val); + } else { + data->opt = isl_val_min(data->opt, val); + } + + return 0; +} + +__isl_give isl_val *isl_qpolynomial_opt_on_domain( + __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max) +{ + struct isl_opt_data data = { NULL, 1, NULL, max }; + + if (!set || !qp) + goto error; + + if (isl_upoly_is_cst(qp->upoly)) { + isl_set_free(set); + data.opt = isl_qpolynomial_get_constant_val(qp); + isl_qpolynomial_free(qp); + return data.opt; + } + + set = fix_inactive(set, qp); + + data.qp = qp; + if (isl_set_foreach_point(set, opt_fn, &data) < 0) + goto error; + + if (data.first) + data.opt = isl_val_zero(isl_set_get_ctx(set)); + + isl_set_free(set); + isl_qpolynomial_free(qp); + return data.opt; +error: + isl_set_free(set); + isl_qpolynomial_free(qp); + isl_val_free(data.opt); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_morph_domain( + __isl_take isl_qpolynomial *qp, __isl_take isl_morph *morph) +{ + int i; + int n_sub; + isl_ctx *ctx; + struct isl_upoly **subs; + isl_mat *mat, *diag; + + qp = isl_qpolynomial_cow(qp); + if (!qp || !morph) + goto error; + + ctx = qp->dim->ctx; + isl_assert(ctx, isl_space_is_equal(qp->dim, morph->dom->dim), goto error); + + n_sub = morph->inv->n_row - 1; + if (morph->inv->n_row != morph->inv->n_col) + n_sub += qp->div->n_row; + subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub); + if (n_sub && !subs) + goto error; + + for (i = 0; 1 + i < morph->inv->n_row; ++i) + subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i], + morph->inv->row[0][0], morph->inv->n_col); + if (morph->inv->n_row != morph->inv->n_col) + for (i = 0; i < qp->div->n_row; ++i) + subs[morph->inv->n_row - 1 + i] = + isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1); + + qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs); + + for (i = 0; i < n_sub; ++i) + isl_upoly_free(subs[i]); + free(subs); + + diag = isl_mat_diag(ctx, 1, morph->inv->row[0][0]); + mat = isl_mat_diagonal(diag, isl_mat_copy(morph->inv)); + diag = isl_mat_diag(ctx, qp->div->n_row, morph->inv->row[0][0]); + mat = isl_mat_diagonal(mat, diag); + qp->div = isl_mat_product(qp->div, mat); + isl_space_free(qp->dim); + qp->dim = isl_space_copy(morph->ran->dim); + + if (!qp->upoly || !qp->div || !qp->dim) + goto error; + + isl_morph_free(morph); + + return qp; +error: + isl_qpolynomial_free(qp); + isl_morph_free(morph); + return NULL; +} + +static int neg_entry(void **entry, void *user) +{ + isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry; + + *pwqp = isl_pw_qpolynomial_neg(*pwqp); + + return *pwqp ? 0 : -1; +} + +__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg( + __isl_take isl_union_pw_qpolynomial *upwqp) +{ + upwqp = isl_union_pw_qpolynomial_cow(upwqp); + if (!upwqp) + return NULL; + + if (isl_hash_table_foreach(upwqp->space->ctx, &upwqp->table, + &neg_entry, NULL) < 0) + goto error; + + return upwqp; +error: + isl_union_pw_qpolynomial_free(upwqp); + return NULL; +} + +__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul( + __isl_take isl_union_pw_qpolynomial *upwqp1, + __isl_take isl_union_pw_qpolynomial *upwqp2) +{ + return match_bin_op(upwqp1, upwqp2, &isl_pw_qpolynomial_mul); +} + +/* Reorder the columns of the given div definitions according to the + * given reordering. + */ +static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div, + __isl_take isl_reordering *r) +{ + int i, j; + isl_mat *mat; + int extra; + + if (!div || !r) + goto error; + + extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len; + mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra); + if (!mat) + goto error; + + for (i = 0; i < div->n_row; ++i) { + isl_seq_cpy(mat->row[i], div->row[i], 2); + isl_seq_clr(mat->row[i] + 2, mat->n_col - 2); + for (j = 0; j < r->len; ++j) + isl_int_set(mat->row[i][2 + r->pos[j]], + div->row[i][2 + j]); + } + + isl_reordering_free(r); + isl_mat_free(div); + return mat; +error: + isl_reordering_free(r); + isl_mat_free(div); + return NULL; +} + +/* Reorder the dimension of "qp" according to the given reordering. + */ +__isl_give isl_qpolynomial *isl_qpolynomial_realign_domain( + __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r) +{ + qp = isl_qpolynomial_cow(qp); + if (!qp) + goto error; + + r = isl_reordering_extend(r, qp->div->n_row); + if (!r) + goto error; + + qp->div = reorder_divs(qp->div, isl_reordering_copy(r)); + if (!qp->div) + goto error; + + qp->upoly = reorder(qp->upoly, r->pos); + if (!qp->upoly) + goto error; + + qp = isl_qpolynomial_reset_domain_space(qp, isl_space_copy(r->dim)); + + isl_reordering_free(r); + return qp; +error: + isl_qpolynomial_free(qp); + isl_reordering_free(r); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_align_params( + __isl_take isl_qpolynomial *qp, __isl_take isl_space *model) +{ + if (!qp || !model) + goto error; + + if (!isl_space_match(qp->dim, isl_dim_param, model, isl_dim_param)) { + isl_reordering *exp; + + model = isl_space_drop_dims(model, isl_dim_in, + 0, isl_space_dim(model, isl_dim_in)); + model = isl_space_drop_dims(model, isl_dim_out, + 0, isl_space_dim(model, isl_dim_out)); + exp = isl_parameter_alignment_reordering(qp->dim, model); + exp = isl_reordering_extend_space(exp, + isl_qpolynomial_get_domain_space(qp)); + qp = isl_qpolynomial_realign_domain(qp, exp); + } + + isl_space_free(model); + return qp; +error: + isl_space_free(model); + isl_qpolynomial_free(qp); + return NULL; +} + +struct isl_split_periods_data { + int max_periods; + isl_pw_qpolynomial *res; +}; + +/* Create a slice where the integer division "div" has the fixed value "v". + * In particular, if "div" refers to floor(f/m), then create a slice + * + * m v <= f <= m v + (m - 1) + * + * or + * + * f - m v >= 0 + * -f + m v + (m - 1) >= 0 + */ +static __isl_give isl_set *set_div_slice(__isl_take isl_space *dim, + __isl_keep isl_qpolynomial *qp, int div, isl_int v) +{ + int total; + isl_basic_set *bset = NULL; + int k; + + if (!dim || !qp) + goto error; + + total = isl_space_dim(dim, isl_dim_all); + bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0, 0, 2); + + k = isl_basic_set_alloc_inequality(bset); + if (k < 0) + goto error; + isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total); + isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]); + + k = isl_basic_set_alloc_inequality(bset); + if (k < 0) + goto error; + isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total); + isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]); + isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]); + isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1); + + isl_space_free(dim); + return isl_set_from_basic_set(bset); +error: + isl_basic_set_free(bset); + isl_space_free(dim); + return NULL; +} + +static int split_periods(__isl_take isl_set *set, + __isl_take isl_qpolynomial *qp, void *user); + +/* Create a slice of the domain "set" such that integer division "div" + * has the fixed value "v" and add the results to data->res, + * replacing the integer division by "v" in "qp". + */ +static int set_div(__isl_take isl_set *set, + __isl_take isl_qpolynomial *qp, int div, isl_int v, + struct isl_split_periods_data *data) +{ + int i; + int total; + isl_set *slice; + struct isl_upoly *cst; + + slice = set_div_slice(isl_set_get_space(set), qp, div, v); + set = isl_set_intersect(set, slice); + + if (!qp) + goto error; + + total = isl_space_dim(qp->dim, isl_dim_all); + + for (i = div + 1; i < qp->div->n_row; ++i) { + if (isl_int_is_zero(qp->div->row[i][2 + total + div])) + continue; + isl_int_addmul(qp->div->row[i][1], + qp->div->row[i][2 + total + div], v); + isl_int_set_si(qp->div->row[i][2 + total + div], 0); + } + + cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one); + qp = substitute_div(qp, div, cst); + + return split_periods(set, qp, data); +error: + isl_set_free(set); + isl_qpolynomial_free(qp); + return -1; +} + +/* Split the domain "set" such that integer division "div" + * has a fixed value (ranging from "min" to "max") on each slice + * and add the results to data->res. + */ +static int split_div(__isl_take isl_set *set, + __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max, + struct isl_split_periods_data *data) +{ + for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) { + isl_set *set_i = isl_set_copy(set); + isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp); + + if (set_div(set_i, qp_i, div, min, data) < 0) + goto error; + } + isl_set_free(set); + isl_qpolynomial_free(qp); + return 0; +error: + isl_set_free(set); + isl_qpolynomial_free(qp); + return -1; +} + +/* If "qp" refers to any integer division + * that can only attain "max_periods" distinct values on "set" + * then split the domain along those distinct values. + * Add the results (or the original if no splitting occurs) + * to data->res. + */ +static int split_periods(__isl_take isl_set *set, + __isl_take isl_qpolynomial *qp, void *user) +{ + int i; + isl_pw_qpolynomial *pwqp; + struct isl_split_periods_data *data; + isl_int min, max; + int total; + int r = 0; + + data = (struct isl_split_periods_data *)user; + + if (!set || !qp) + goto error; + + if (qp->div->n_row == 0) { + pwqp = isl_pw_qpolynomial_alloc(set, qp); + data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp); + return 0; + } + + isl_int_init(min); + isl_int_init(max); + total = isl_space_dim(qp->dim, isl_dim_all); + for (i = 0; i < qp->div->n_row; ++i) { + enum isl_lp_result lp_res; + + if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total, + qp->div->n_row) != -1) + continue; + + lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1, + set->ctx->one, &min, NULL, NULL); + if (lp_res == isl_lp_error) + goto error2; + if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty) + continue; + isl_int_fdiv_q(min, min, qp->div->row[i][0]); + + lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1, + set->ctx->one, &max, NULL, NULL); + if (lp_res == isl_lp_error) + goto error2; + if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty) + continue; + isl_int_fdiv_q(max, max, qp->div->row[i][0]); + + isl_int_sub(max, max, min); + if (isl_int_cmp_si(max, data->max_periods) < 0) { + isl_int_add(max, max, min); + break; + } + } + + if (i < qp->div->n_row) { + r = split_div(set, qp, i, min, max, data); + } else { + pwqp = isl_pw_qpolynomial_alloc(set, qp); + data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp); + } + + isl_int_clear(max); + isl_int_clear(min); + + return r; +error2: + isl_int_clear(max); + isl_int_clear(min); +error: + isl_set_free(set); + isl_qpolynomial_free(qp); + return -1; +} + +/* If any quasi-polynomial in pwqp refers to any integer division + * that can only attain "max_periods" distinct values on its domain + * then split the domain along those distinct values. + */ +__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods( + __isl_take isl_pw_qpolynomial *pwqp, int max_periods) +{ + struct isl_split_periods_data data; + + data.max_periods = max_periods; + data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp)); + + if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0) + goto error; + + isl_pw_qpolynomial_free(pwqp); + + return data.res; +error: + isl_pw_qpolynomial_free(data.res); + isl_pw_qpolynomial_free(pwqp); + return NULL; +} + +/* Construct a piecewise quasipolynomial that is constant on the given + * domain. In particular, it is + * 0 if cst == 0 + * 1 if cst == 1 + * infinity if cst == -1 + */ +static __isl_give isl_pw_qpolynomial *constant_on_domain( + __isl_take isl_basic_set *bset, int cst) +{ + isl_space *dim; + isl_qpolynomial *qp; + + if (!bset) + return NULL; + + bset = isl_basic_set_params(bset); + dim = isl_basic_set_get_space(bset); + if (cst < 0) + qp = isl_qpolynomial_infty_on_domain(dim); + else if (cst == 0) + qp = isl_qpolynomial_zero_on_domain(dim); + else + qp = isl_qpolynomial_one_on_domain(dim); + return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp); +} + +/* Factor bset, call fn on each of the factors and return the product. + * + * If no factors can be found, simply call fn on the input. + * Otherwise, construct the factors based on the factorizer, + * call fn on each factor and compute the product. + */ +static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call( + __isl_take isl_basic_set *bset, + __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset)) +{ + int i, n; + isl_space *dim; + isl_set *set; + isl_factorizer *f; + isl_qpolynomial *qp; + isl_pw_qpolynomial *pwqp; + unsigned nparam; + unsigned nvar; + + f = isl_basic_set_factorizer(bset); + if (!f) + goto error; + if (f->n_group == 0) { + isl_factorizer_free(f); + return fn(bset); + } + + nparam = isl_basic_set_dim(bset, isl_dim_param); + nvar = isl_basic_set_dim(bset, isl_dim_set); + + dim = isl_basic_set_get_space(bset); + dim = isl_space_domain(dim); + set = isl_set_universe(isl_space_copy(dim)); + qp = isl_qpolynomial_one_on_domain(dim); + pwqp = isl_pw_qpolynomial_alloc(set, qp); + + bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset); + + for (i = 0, n = 0; i < f->n_group; ++i) { + isl_basic_set *bset_i; + isl_pw_qpolynomial *pwqp_i; + + bset_i = isl_basic_set_copy(bset); + bset_i = isl_basic_set_drop_constraints_involving(bset_i, + nparam + n + f->len[i], nvar - n - f->len[i]); + bset_i = isl_basic_set_drop_constraints_involving(bset_i, + nparam, n); + bset_i = isl_basic_set_drop(bset_i, isl_dim_set, + n + f->len[i], nvar - n - f->len[i]); + bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n); + + pwqp_i = fn(bset_i); + pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i); + + n += f->len[i]; + } + + isl_basic_set_free(bset); + isl_factorizer_free(f); + + return pwqp; +error: + isl_basic_set_free(bset); + return NULL; +} + +/* Factor bset, call fn on each of the factors and return the product. + * The function is assumed to evaluate to zero on empty domains, + * to one on zero-dimensional domains and to infinity on unbounded domains + * and will not be called explicitly on zero-dimensional or unbounded domains. + * + * We first check for some special cases and remove all equalities. + * Then we hand over control to compressed_multiplicative_call. + */ +__isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call( + __isl_take isl_basic_set *bset, + __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset)) +{ + int bounded; + isl_morph *morph; + isl_pw_qpolynomial *pwqp; + + if (!bset) + return NULL; + + if (isl_basic_set_plain_is_empty(bset)) + return constant_on_domain(bset, 0); + + if (isl_basic_set_dim(bset, isl_dim_set) == 0) + return constant_on_domain(bset, 1); + + bounded = isl_basic_set_is_bounded(bset); + if (bounded < 0) + goto error; + if (!bounded) + return constant_on_domain(bset, -1); + + if (bset->n_eq == 0) + return compressed_multiplicative_call(bset, fn); + + morph = isl_basic_set_full_compression(bset); + bset = isl_morph_basic_set(isl_morph_copy(morph), bset); + + pwqp = compressed_multiplicative_call(bset, fn); + + morph = isl_morph_dom_params(morph); + morph = isl_morph_ran_params(morph); + morph = isl_morph_inverse(morph); + + pwqp = isl_pw_qpolynomial_morph_domain(pwqp, morph); + + return pwqp; +error: + isl_basic_set_free(bset); + return NULL; +} + +/* Drop all floors in "qp", turning each integer division [a/m] into + * a rational division a/m. If "down" is set, then the integer division + * is replaced by (a-(m-1))/m instead. + */ +static __isl_give isl_qpolynomial *qp_drop_floors( + __isl_take isl_qpolynomial *qp, int down) +{ + int i; + struct isl_upoly *s; + + if (!qp) + return NULL; + if (qp->div->n_row == 0) + return qp; + + qp = isl_qpolynomial_cow(qp); + if (!qp) + return NULL; + + for (i = qp->div->n_row - 1; i >= 0; --i) { + if (down) { + isl_int_sub(qp->div->row[i][1], + qp->div->row[i][1], qp->div->row[i][0]); + isl_int_add_ui(qp->div->row[i][1], + qp->div->row[i][1], 1); + } + s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1, + qp->div->row[i][0], qp->div->n_col - 1); + qp = substitute_div(qp, i, s); + if (!qp) + return NULL; + } + + return qp; +} + +/* Drop all floors in "pwqp", turning each integer division [a/m] into + * a rational division a/m. + */ +static __isl_give isl_pw_qpolynomial *pwqp_drop_floors( + __isl_take isl_pw_qpolynomial *pwqp) +{ + int i; + + if (!pwqp) + return NULL; + + if (isl_pw_qpolynomial_is_zero(pwqp)) + return pwqp; + + pwqp = isl_pw_qpolynomial_cow(pwqp); + if (!pwqp) + return NULL; + + for (i = 0; i < pwqp->n; ++i) { + pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0); + if (!pwqp->p[i].qp) + goto error; + } + + return pwqp; +error: + isl_pw_qpolynomial_free(pwqp); + return NULL; +} + +/* Adjust all the integer divisions in "qp" such that they are at least + * one over the given orthant (identified by "signs"). This ensures + * that they will still be non-negative even after subtracting (m-1)/m. + * + * In particular, f is replaced by f' + v, changing f = [a/m] + * to f' = [(a - m v)/m]. + * If the constant term k in a is smaller than m, + * the constant term of v is set to floor(k/m) - 1. + * For any other term, if the coefficient c and the variable x have + * the same sign, then no changes are needed. + * Otherwise, if the variable is positive (and c is negative), + * then the coefficient of x in v is set to floor(c/m). + * If the variable is negative (and c is positive), + * then the coefficient of x in v is set to ceil(c/m). + */ +static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp, + int *signs) +{ + int i, j; + int total; + isl_vec *v = NULL; + struct isl_upoly *s; + + qp = isl_qpolynomial_cow(qp); + if (!qp) + return NULL; + qp->div = isl_mat_cow(qp->div); + if (!qp->div) + goto error; + + total = isl_space_dim(qp->dim, isl_dim_all); + v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1); + + for (i = 0; i < qp->div->n_row; ++i) { + isl_int *row = qp->div->row[i]; + v = isl_vec_clr(v); + if (!v) + goto error; + if (isl_int_lt(row[1], row[0])) { + isl_int_fdiv_q(v->el[0], row[1], row[0]); + isl_int_sub_ui(v->el[0], v->el[0], 1); + isl_int_submul(row[1], row[0], v->el[0]); + } + for (j = 0; j < total; ++j) { + if (isl_int_sgn(row[2 + j]) * signs[j] >= 0) + continue; + if (signs[j] < 0) + isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]); + else + isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]); + isl_int_submul(row[2 + j], row[0], v->el[1 + j]); + } + for (j = 0; j < i; ++j) { + if (isl_int_sgn(row[2 + total + j]) >= 0) + continue; + isl_int_fdiv_q(v->el[1 + total + j], + row[2 + total + j], row[0]); + isl_int_submul(row[2 + total + j], + row[0], v->el[1 + total + j]); + } + for (j = i + 1; j < qp->div->n_row; ++j) { + if (isl_int_is_zero(qp->div->row[j][2 + total + i])) + continue; + isl_seq_combine(qp->div->row[j] + 1, + qp->div->ctx->one, qp->div->row[j] + 1, + qp->div->row[j][2 + total + i], v->el, v->size); + } + isl_int_set_si(v->el[1 + total + i], 1); + s = isl_upoly_from_affine(qp->dim->ctx, v->el, + qp->div->ctx->one, v->size); + qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s); + isl_upoly_free(s); + if (!qp->upoly) + goto error; + } + + isl_vec_free(v); + return qp; +error: + isl_vec_free(v); + isl_qpolynomial_free(qp); + return NULL; +} + +struct isl_to_poly_data { + int sign; + isl_pw_qpolynomial *res; + isl_qpolynomial *qp; +}; + +/* Appoximate data->qp by a polynomial on the orthant identified by "signs". + * We first make all integer divisions positive and then split the + * quasipolynomials into terms with sign data->sign (the direction + * of the requested approximation) and terms with the opposite sign. + * In the first set of terms, each integer division [a/m] is + * overapproximated by a/m, while in the second it is underapproximated + * by (a-(m-1))/m. + */ +static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs, + void *user) +{ + struct isl_to_poly_data *data = user; + isl_pw_qpolynomial *t; + isl_qpolynomial *qp, *up, *down; + + qp = isl_qpolynomial_copy(data->qp); + qp = make_divs_pos(qp, signs); + + up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign); + up = qp_drop_floors(up, 0); + down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign); + down = qp_drop_floors(down, 1); + + isl_qpolynomial_free(qp); + qp = isl_qpolynomial_add(up, down); + + t = isl_pw_qpolynomial_alloc(orthant, qp); + data->res = isl_pw_qpolynomial_add_disjoint(data->res, t); + + return 0; +} + +/* Approximate each quasipolynomial by a polynomial. If "sign" is positive, + * the polynomial will be an overapproximation. If "sign" is negative, + * it will be an underapproximation. If "sign" is zero, the approximation + * will lie somewhere in between. + * + * In particular, is sign == 0, we simply drop the floors, turning + * the integer divisions into rational divisions. + * Otherwise, we split the domains into orthants, make all integer divisions + * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m, + * depending on the requested sign and the sign of the term in which + * the integer division appears. + */ +__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial( + __isl_take isl_pw_qpolynomial *pwqp, int sign) +{ + int i; + struct isl_to_poly_data data; + + if (sign == 0) + return pwqp_drop_floors(pwqp); + + if (!pwqp) + return NULL; + + data.sign = sign; + data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp)); + + for (i = 0; i < pwqp->n; ++i) { + if (pwqp->p[i].qp->div->n_row == 0) { + isl_pw_qpolynomial *t; + t = isl_pw_qpolynomial_alloc( + isl_set_copy(pwqp->p[i].set), + isl_qpolynomial_copy(pwqp->p[i].qp)); + data.res = isl_pw_qpolynomial_add_disjoint(data.res, t); + continue; + } + data.qp = pwqp->p[i].qp; + if (isl_set_foreach_orthant(pwqp->p[i].set, + &to_polynomial_on_orthant, &data) < 0) + goto error; + } + + isl_pw_qpolynomial_free(pwqp); + + return data.res; +error: + isl_pw_qpolynomial_free(pwqp); + isl_pw_qpolynomial_free(data.res); + return NULL; +} + +static int poly_entry(void **entry, void *user) +{ + int *sign = user; + isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry; + + *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign); + + return *pwqp ? 0 : -1; +} + +__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial( + __isl_take isl_union_pw_qpolynomial *upwqp, int sign) +{ + upwqp = isl_union_pw_qpolynomial_cow(upwqp); + if (!upwqp) + return NULL; + + if (isl_hash_table_foreach(upwqp->space->ctx, &upwqp->table, + &poly_entry, &sign) < 0) + goto error; + + return upwqp; +error: + isl_union_pw_qpolynomial_free(upwqp); + return NULL; +} + +__isl_give isl_basic_map *isl_basic_map_from_qpolynomial( + __isl_take isl_qpolynomial *qp) +{ + int i, k; + isl_space *dim; + isl_vec *aff = NULL; + isl_basic_map *bmap = NULL; + unsigned pos; + unsigned n_div; + + if (!qp) + return NULL; + if (!isl_upoly_is_affine(qp->upoly)) + isl_die(qp->dim->ctx, isl_error_invalid, + "input quasi-polynomial not affine", goto error); + aff = isl_qpolynomial_extract_affine(qp); + if (!aff) + goto error; + dim = isl_qpolynomial_get_space(qp); + pos = 1 + isl_space_offset(dim, isl_dim_out); + n_div = qp->div->n_row; + bmap = isl_basic_map_alloc_space(dim, n_div, 1, 2 * n_div); + + for (i = 0; i < n_div; ++i) { + k = isl_basic_map_alloc_div(bmap); + if (k < 0) + goto error; + isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col); + isl_int_set_si(bmap->div[k][qp->div->n_col], 0); + if (isl_basic_map_add_div_constraints(bmap, k) < 0) + goto error; + } + k = isl_basic_map_alloc_equality(bmap); + if (k < 0) + goto error; + isl_int_neg(bmap->eq[k][pos], aff->el[0]); + isl_seq_cpy(bmap->eq[k], aff->el + 1, pos); + isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div); + + isl_vec_free(aff); + isl_qpolynomial_free(qp); + bmap = isl_basic_map_finalize(bmap); + return bmap; +error: + isl_vec_free(aff); + isl_qpolynomial_free(qp); + isl_basic_map_free(bmap); + return NULL; +} |
