/* * Copyright 2011 INRIA Saclay * Copyright 2011 Sven Verdoolaege * Copyright 2012-2014 Ecole Normale Superieure * Copyright 2014 INRIA Rocquencourt * Copyright 2016 Sven Verdoolaege * Copyright 2018,2020 Cerebras Systems * Copyright 2021 Sven Verdoolaege * * 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 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt, * B.P. 105 - 78153 Le Chesnay, France * and Cerebras Systems, 175 S San Antonio Rd, Los Altos, CA, USA */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #undef EL_BASE #define EL_BASE aff #include #include #undef EL_BASE #define EL_BASE pw_aff #include #include #undef EL_BASE #define EL_BASE pw_multi_aff #include #include #undef EL_BASE #define EL_BASE union_pw_aff #include #include #undef EL_BASE #define EL_BASE union_pw_multi_aff #include __isl_give isl_aff *isl_aff_alloc_vec(__isl_take isl_local_space *ls, __isl_take isl_vec *v) { isl_aff *aff; if (!ls || !v) goto error; aff = isl_calloc_type(v->ctx, struct isl_aff); if (!aff) goto error; aff->ref = 1; aff->ls = ls; aff->v = v; return aff; error: isl_local_space_free(ls); isl_vec_free(v); return NULL; } __isl_give isl_aff *isl_aff_alloc(__isl_take isl_local_space *ls) { isl_ctx *ctx; isl_vec *v; isl_size total; if (!ls) return NULL; ctx = isl_local_space_get_ctx(ls); if (!isl_local_space_divs_known(ls)) isl_die(ctx, isl_error_invalid, "local space has unknown divs", goto error); if (!isl_local_space_is_set(ls)) isl_die(ctx, isl_error_invalid, "domain of affine expression should be a set", goto error); total = isl_local_space_dim(ls, isl_dim_all); if (total < 0) goto error; v = isl_vec_alloc(ctx, 1 + 1 + total); return isl_aff_alloc_vec(ls, v); error: isl_local_space_free(ls); return NULL; } __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff) { if (!aff) return NULL; aff->ref++; return aff; } __isl_give isl_aff *isl_aff_dup(__isl_keep isl_aff *aff) { if (!aff) return NULL; return isl_aff_alloc_vec(isl_local_space_copy(aff->ls), isl_vec_copy(aff->v)); } __isl_give isl_aff *isl_aff_cow(__isl_take isl_aff *aff) { if (!aff) return NULL; if (aff->ref == 1) return aff; aff->ref--; return isl_aff_dup(aff); } __isl_give isl_aff *isl_aff_zero_on_domain(__isl_take isl_local_space *ls) { isl_aff *aff; aff = isl_aff_alloc(ls); if (!aff) return NULL; isl_int_set_si(aff->v->el[0], 1); isl_seq_clr(aff->v->el + 1, aff->v->size - 1); return aff; } /* Return an affine expression that is equal to zero on domain space "space". */ __isl_give isl_aff *isl_aff_zero_on_domain_space(__isl_take isl_space *space) { return isl_aff_zero_on_domain(isl_local_space_from_space(space)); } /* This function performs the same operation as isl_aff_zero_on_domain_space, * but is considered as a function on an isl_space when exported. */ __isl_give isl_aff *isl_space_zero_aff_on_domain(__isl_take isl_space *space) { return isl_aff_zero_on_domain_space(space); } /* Return a piecewise affine expression defined on the specified domain * that is equal to zero. */ __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(__isl_take isl_local_space *ls) { return isl_pw_aff_from_aff(isl_aff_zero_on_domain(ls)); } /* Change "aff" into a NaN. * * Note that this function gets called from isl_aff_nan_on_domain, * so "aff" may not have been initialized yet. */ static __isl_give isl_aff *isl_aff_set_nan(__isl_take isl_aff *aff) { aff = isl_aff_cow(aff); if (!aff) return NULL; aff->v = isl_vec_clr(aff->v); if (!aff->v) return isl_aff_free(aff); return aff; } /* Return an affine expression defined on the specified domain * that represents NaN. */ __isl_give isl_aff *isl_aff_nan_on_domain(__isl_take isl_local_space *ls) { isl_aff *aff; aff = isl_aff_alloc(ls); return isl_aff_set_nan(aff); } /* Return an affine expression defined on the specified domain space * that represents NaN. */ __isl_give isl_aff *isl_aff_nan_on_domain_space(__isl_take isl_space *space) { return isl_aff_nan_on_domain(isl_local_space_from_space(space)); } /* Return a piecewise affine expression defined on the specified domain space * that represents NaN. */ __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain_space( __isl_take isl_space *space) { return isl_pw_aff_from_aff(isl_aff_nan_on_domain_space(space)); } /* Return a piecewise affine expression defined on the specified domain * that represents NaN. */ __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(__isl_take isl_local_space *ls) { return isl_pw_aff_from_aff(isl_aff_nan_on_domain(ls)); } /* Return an affine expression that is equal to "val" on * domain local space "ls". */ __isl_give isl_aff *isl_aff_val_on_domain(__isl_take isl_local_space *ls, __isl_take isl_val *val) { isl_aff *aff; if (!ls || !val) goto error; if (!isl_val_is_rat(val)) isl_die(isl_val_get_ctx(val), isl_error_invalid, "expecting rational value", goto error); aff = isl_aff_alloc(isl_local_space_copy(ls)); if (!aff) goto error; isl_seq_clr(aff->v->el + 2, aff->v->size - 2); isl_int_set(aff->v->el[1], val->n); isl_int_set(aff->v->el[0], val->d); isl_local_space_free(ls); isl_val_free(val); return aff; error: isl_local_space_free(ls); isl_val_free(val); return NULL; } /* Return an affine expression that is equal to "val" on domain space "space". */ __isl_give isl_aff *isl_aff_val_on_domain_space(__isl_take isl_space *space, __isl_take isl_val *val) { return isl_aff_val_on_domain(isl_local_space_from_space(space), val); } /* Return an affine expression that is equal to the specified dimension * in "ls". */ __isl_give isl_aff *isl_aff_var_on_domain(__isl_take isl_local_space *ls, enum isl_dim_type type, unsigned pos) { isl_space *space; isl_aff *aff; if (!ls) return NULL; space = isl_local_space_get_space(ls); if (!space) goto error; if (isl_space_is_map(space)) isl_die(isl_space_get_ctx(space), isl_error_invalid, "expecting (parameter) set space", goto error); if (isl_local_space_check_range(ls, type, pos, 1) < 0) goto error; isl_space_free(space); aff = isl_aff_alloc(ls); if (!aff) return NULL; pos += isl_local_space_offset(aff->ls, type); isl_int_set_si(aff->v->el[0], 1); isl_seq_clr(aff->v->el + 1, aff->v->size - 1); isl_int_set_si(aff->v->el[1 + pos], 1); return aff; error: isl_local_space_free(ls); isl_space_free(space); return NULL; } /* Return a piecewise affine expression that is equal to * the specified dimension in "ls". */ __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(__isl_take isl_local_space *ls, enum isl_dim_type type, unsigned pos) { return isl_pw_aff_from_aff(isl_aff_var_on_domain(ls, type, pos)); } /* Return an affine expression that is equal to the parameter * in the domain space "space" with identifier "id". */ __isl_give isl_aff *isl_aff_param_on_domain_space_id( __isl_take isl_space *space, __isl_take isl_id *id) { int pos; isl_local_space *ls; if (!space || !id) goto error; pos = isl_space_find_dim_by_id(space, isl_dim_param, id); if (pos < 0) isl_die(isl_space_get_ctx(space), isl_error_invalid, "parameter not found in space", goto error); isl_id_free(id); ls = isl_local_space_from_space(space); return isl_aff_var_on_domain(ls, isl_dim_param, pos); error: isl_space_free(space); isl_id_free(id); return NULL; } /* This function performs the same operation as * isl_aff_param_on_domain_space_id, * but is considered as a function on an isl_space when exported. */ __isl_give isl_aff *isl_space_param_aff_on_domain_id( __isl_take isl_space *space, __isl_take isl_id *id) { return isl_aff_param_on_domain_space_id(space, id); } __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff) { if (!aff) return NULL; if (--aff->ref > 0) return NULL; isl_local_space_free(aff->ls); isl_vec_free(aff->v); free(aff); return NULL; } isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff) { return aff ? isl_local_space_get_ctx(aff->ls) : NULL; } /* Return a hash value that digests "aff". */ uint32_t isl_aff_get_hash(__isl_keep isl_aff *aff) { uint32_t hash, ls_hash, v_hash; if (!aff) return 0; hash = isl_hash_init(); ls_hash = isl_local_space_get_hash(aff->ls); isl_hash_hash(hash, ls_hash); v_hash = isl_vec_get_hash(aff->v); isl_hash_hash(hash, v_hash); return hash; } /* Return the domain local space of "aff". */ static __isl_keep isl_local_space *isl_aff_peek_domain_local_space( __isl_keep isl_aff *aff) { return aff ? aff->ls : NULL; } /* Return the number of variables of the given type in the domain of "aff". */ isl_size isl_aff_domain_dim(__isl_keep isl_aff *aff, enum isl_dim_type type) { isl_local_space *ls; ls = isl_aff_peek_domain_local_space(aff); return isl_local_space_dim(ls, type); } /* Externally, an isl_aff has a map space, but internally, the * ls field corresponds to the domain of that space. */ isl_size isl_aff_dim(__isl_keep isl_aff *aff, enum isl_dim_type type) { if (!aff) return isl_size_error; if (type == isl_dim_out) return 1; if (type == isl_dim_in) type = isl_dim_set; return isl_aff_domain_dim(aff, type); } /* Return the offset of the first coefficient of type "type" in * the domain of "aff". */ isl_size isl_aff_domain_offset(__isl_keep isl_aff *aff, enum isl_dim_type type) { isl_local_space *ls; ls = isl_aff_peek_domain_local_space(aff); return isl_local_space_offset(ls, type); } /* Return the position of the dimension of the given type and name * in "aff". * Return -1 if no such dimension can be found. */ int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff, enum isl_dim_type type, const char *name) { if (!aff) return -1; if (type == isl_dim_out) return -1; if (type == isl_dim_in) type = isl_dim_set; return isl_local_space_find_dim_by_name(aff->ls, type, name); } /* Return the domain space of "aff". */ static __isl_keep isl_space *isl_aff_peek_domain_space(__isl_keep isl_aff *aff) { return aff ? isl_local_space_peek_space(aff->ls) : NULL; } __isl_give isl_space *isl_aff_get_domain_space(__isl_keep isl_aff *aff) { return isl_space_copy(isl_aff_peek_domain_space(aff)); } __isl_give isl_space *isl_aff_get_space(__isl_keep isl_aff *aff) { isl_space *space; if (!aff) return NULL; space = isl_local_space_get_space(aff->ls); space = isl_space_from_domain(space); space = isl_space_add_dims(space, isl_dim_out, 1); return space; } /* Return a copy of the domain space of "aff". */ __isl_give isl_local_space *isl_aff_get_domain_local_space( __isl_keep isl_aff *aff) { return isl_local_space_copy(isl_aff_peek_domain_local_space(aff)); } __isl_give isl_local_space *isl_aff_get_local_space(__isl_keep isl_aff *aff) { isl_local_space *ls; if (!aff) return NULL; ls = isl_local_space_copy(aff->ls); ls = isl_local_space_from_domain(ls); ls = isl_local_space_add_dims(ls, isl_dim_out, 1); return ls; } /* Return the local space of the domain of "aff". * This may be either a copy or the local space itself * if there is only one reference to "aff". * This allows the local space to be modified inplace * if both the expression and its local space have only a single reference. * The caller is not allowed to modify "aff" between this call and * a subsequent call to isl_aff_restore_domain_local_space. * The only exception is that isl_aff_free can be called instead. */ __isl_give isl_local_space *isl_aff_take_domain_local_space( __isl_keep isl_aff *aff) { isl_local_space *ls; if (!aff) return NULL; if (aff->ref != 1) return isl_aff_get_domain_local_space(aff); ls = aff->ls; aff->ls = NULL; return ls; } /* Set the local space of the domain of "aff" to "ls", * where the local space of "aff" may be missing * due to a preceding call to isl_aff_take_domain_local_space. * However, in this case, "aff" only has a single reference and * then the call to isl_aff_cow has no effect. */ __isl_give isl_aff *isl_aff_restore_domain_local_space( __isl_keep isl_aff *aff, __isl_take isl_local_space *ls) { if (!aff || !ls) goto error; if (aff->ls == ls) { isl_local_space_free(ls); return aff; } aff = isl_aff_cow(aff); if (!aff) goto error; isl_local_space_free(aff->ls); aff->ls = ls; return aff; error: isl_aff_free(aff); isl_local_space_free(ls); return NULL; } /* Externally, an isl_aff has a map space, but internally, the * ls field corresponds to the domain of that space. */ const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff, enum isl_dim_type type, unsigned pos) { if (!aff) return NULL; if (type == isl_dim_out) return NULL; if (type == isl_dim_in) type = isl_dim_set; return isl_local_space_get_dim_name(aff->ls, type, pos); } __isl_give isl_aff *isl_aff_reset_domain_space(__isl_take isl_aff *aff, __isl_take isl_space *space) { aff = isl_aff_cow(aff); if (!aff || !space) goto error; aff->ls = isl_local_space_reset_space(aff->ls, space); if (!aff->ls) return isl_aff_free(aff); return aff; error: isl_aff_free(aff); isl_space_free(space); return NULL; } /* Reset the space of "aff". 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_aff *isl_aff_reset_space_and_domain(__isl_take isl_aff *aff, __isl_take isl_space *space, __isl_take isl_space *domain) { isl_space_free(space); return isl_aff_reset_domain_space(aff, domain); } /* Reorder the coefficients of the affine expression based * on the given reordering. * The reordering r is assumed to have been extended with the local * variables. */ static __isl_give isl_vec *vec_reorder(__isl_take isl_vec *vec, __isl_take isl_reordering *r, int n_div) { isl_space *space; isl_vec *res; isl_size dim; int i; if (!vec || !r) goto error; space = isl_reordering_peek_space(r); dim = isl_space_dim(space, isl_dim_all); if (dim < 0) goto error; res = isl_vec_alloc(vec->ctx, 2 + dim + n_div); if (!res) goto error; isl_seq_cpy(res->el, vec->el, 2); isl_seq_clr(res->el + 2, res->size - 2); for (i = 0; i < r->len; ++i) isl_int_set(res->el[2 + r->pos[i]], vec->el[2 + i]); isl_reordering_free(r); isl_vec_free(vec); return res; error: isl_vec_free(vec); isl_reordering_free(r); return NULL; } /* Reorder the dimensions of the domain of "aff" according * to the given reordering. */ __isl_give isl_aff *isl_aff_realign_domain(__isl_take isl_aff *aff, __isl_take isl_reordering *r) { aff = isl_aff_cow(aff); if (!aff) goto error; r = isl_reordering_extend(r, aff->ls->div->n_row); aff->v = vec_reorder(aff->v, isl_reordering_copy(r), aff->ls->div->n_row); aff->ls = isl_local_space_realign(aff->ls, r); if (!aff->v || !aff->ls) return isl_aff_free(aff); return aff; error: isl_aff_free(aff); isl_reordering_free(r); return NULL; } __isl_give isl_aff *isl_aff_align_params(__isl_take isl_aff *aff, __isl_take isl_space *model) { isl_bool equal_params; if (!aff || !model) goto error; equal_params = isl_space_has_equal_params(aff->ls->dim, model); if (equal_params < 0) goto error; if (!equal_params) { isl_reordering *exp; exp = isl_parameter_alignment_reordering(aff->ls->dim, model); exp = isl_reordering_extend_space(exp, isl_aff_get_domain_space(aff)); aff = isl_aff_realign_domain(aff, exp); } isl_space_free(model); return aff; error: isl_space_free(model); isl_aff_free(aff); return NULL; } #undef TYPE #define TYPE isl_aff #include "isl_unbind_params_templ.c" /* Is "aff" obviously equal to zero? * * If the denominator is zero, then "aff" is not equal to zero. */ isl_bool isl_aff_plain_is_zero(__isl_keep isl_aff *aff) { int pos; if (!aff) return isl_bool_error; if (isl_int_is_zero(aff->v->el[0])) return isl_bool_false; pos = isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1); return isl_bool_ok(pos < 0); } /* Does "aff" represent NaN? */ isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff) { if (!aff) return isl_bool_error; return isl_bool_ok(isl_seq_first_non_zero(aff->v->el, 2) < 0); } /* Are "aff1" and "aff2" obviously equal? * * NaN is not equal to anything, not even to another NaN. */ isl_bool isl_aff_plain_is_equal(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2) { isl_bool equal; if (!aff1 || !aff2) return isl_bool_error; if (isl_aff_is_nan(aff1) || isl_aff_is_nan(aff2)) return isl_bool_false; equal = isl_local_space_is_equal(aff1->ls, aff2->ls); if (equal < 0 || !equal) return equal; return isl_vec_is_equal(aff1->v, aff2->v); } /* Return the common denominator of "aff" in "v". * * We cannot return anything meaningful in case of a NaN. */ isl_stat isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v) { if (!aff) return isl_stat_error; if (isl_aff_is_nan(aff)) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "cannot get denominator of NaN", return isl_stat_error); isl_int_set(*v, aff->v->el[0]); return isl_stat_ok; } /* Return the common denominator of "aff". */ __isl_give isl_val *isl_aff_get_denominator_val(__isl_keep isl_aff *aff) { isl_ctx *ctx; if (!aff) return NULL; ctx = isl_aff_get_ctx(aff); if (isl_aff_is_nan(aff)) return isl_val_nan(ctx); return isl_val_int_from_isl_int(ctx, aff->v->el[0]); } /* Return the constant term of "aff". */ __isl_give isl_val *isl_aff_get_constant_val(__isl_keep isl_aff *aff) { isl_ctx *ctx; isl_val *v; if (!aff) return NULL; ctx = isl_aff_get_ctx(aff); if (isl_aff_is_nan(aff)) return isl_val_nan(ctx); v = isl_val_rat_from_isl_int(ctx, aff->v->el[1], aff->v->el[0]); return isl_val_normalize(v); } /* Return the coefficient of the variable of type "type" at position "pos" * of "aff". */ __isl_give isl_val *isl_aff_get_coefficient_val(__isl_keep isl_aff *aff, enum isl_dim_type type, int pos) { isl_ctx *ctx; isl_val *v; if (!aff) return NULL; ctx = isl_aff_get_ctx(aff); if (type == isl_dim_out) isl_die(ctx, isl_error_invalid, "output/set dimension does not have a coefficient", return NULL); if (type == isl_dim_in) type = isl_dim_set; if (isl_local_space_check_range(aff->ls, type, pos, 1) < 0) return NULL; if (isl_aff_is_nan(aff)) return isl_val_nan(ctx); pos += isl_local_space_offset(aff->ls, type); v = isl_val_rat_from_isl_int(ctx, aff->v->el[1 + pos], aff->v->el[0]); return isl_val_normalize(v); } /* Return the sign of the coefficient of the variable of type "type" * at position "pos" of "aff". */ int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff, enum isl_dim_type type, int pos) { isl_ctx *ctx; if (!aff) return 0; ctx = isl_aff_get_ctx(aff); if (type == isl_dim_out) isl_die(ctx, isl_error_invalid, "output/set dimension does not have a coefficient", return 0); if (type == isl_dim_in) type = isl_dim_set; if (isl_local_space_check_range(aff->ls, type, pos, 1) < 0) return 0; pos += isl_local_space_offset(aff->ls, type); return isl_int_sgn(aff->v->el[1 + pos]); } /* Replace the numerator of the constant term of "aff" by "v". * * A NaN is unaffected by this operation. */ __isl_give isl_aff *isl_aff_set_constant(__isl_take isl_aff *aff, isl_int v) { if (!aff) return NULL; if (isl_aff_is_nan(aff)) return aff; aff = isl_aff_cow(aff); if (!aff) return NULL; aff->v = isl_vec_cow(aff->v); if (!aff->v) return isl_aff_free(aff); isl_int_set(aff->v->el[1], v); return aff; } /* Replace the constant term of "aff" by "v". * * A NaN is unaffected by this operation. */ __isl_give isl_aff *isl_aff_set_constant_val(__isl_take isl_aff *aff, __isl_take isl_val *v) { if (!aff || !v) goto error; if (isl_aff_is_nan(aff)) { isl_val_free(v); return aff; } if (!isl_val_is_rat(v)) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "expecting rational value", goto error); if (isl_int_eq(aff->v->el[1], v->n) && isl_int_eq(aff->v->el[0], v->d)) { isl_val_free(v); return aff; } aff = isl_aff_cow(aff); if (!aff) goto error; aff->v = isl_vec_cow(aff->v); if (!aff->v) goto error; if (isl_int_eq(aff->v->el[0], v->d)) { isl_int_set(aff->v->el[1], v->n); } else if (isl_int_is_one(v->d)) { isl_int_mul(aff->v->el[1], aff->v->el[0], v->n); } else { isl_seq_scale(aff->v->el + 1, aff->v->el + 1, v->d, aff->v->size - 1); isl_int_mul(aff->v->el[1], aff->v->el[0], v->n); isl_int_mul(aff->v->el[0], aff->v->el[0], v->d); aff->v = isl_vec_normalize(aff->v); if (!aff->v) goto error; } isl_val_free(v); return aff; error: isl_aff_free(aff); isl_val_free(v); return NULL; } /* Add "v" to the constant term of "aff". * * A NaN is unaffected by this operation. */ __isl_give isl_aff *isl_aff_add_constant(__isl_take isl_aff *aff, isl_int v) { if (isl_int_is_zero(v)) return aff; if (!aff) return NULL; if (isl_aff_is_nan(aff)) return aff; aff = isl_aff_cow(aff); if (!aff) return NULL; aff->v = isl_vec_cow(aff->v); if (!aff->v) return isl_aff_free(aff); isl_int_addmul(aff->v->el[1], aff->v->el[0], v); return aff; } /* Add "v" to the constant term of "aff", * in case "aff" is a rational expression. */ static __isl_give isl_aff *isl_aff_add_rat_constant_val(__isl_take isl_aff *aff, __isl_take isl_val *v) { aff = isl_aff_cow(aff); if (!aff) goto error; aff->v = isl_vec_cow(aff->v); if (!aff->v) goto error; if (isl_int_is_one(v->d)) { isl_int_addmul(aff->v->el[1], aff->v->el[0], v->n); } else if (isl_int_eq(aff->v->el[0], v->d)) { isl_int_add(aff->v->el[1], aff->v->el[1], v->n); aff->v = isl_vec_normalize(aff->v); if (!aff->v) goto error; } else { isl_seq_scale(aff->v->el + 1, aff->v->el + 1, v->d, aff->v->size - 1); isl_int_addmul(aff->v->el[1], aff->v->el[0], v->n); isl_int_mul(aff->v->el[0], aff->v->el[0], v->d); aff->v = isl_vec_normalize(aff->v); if (!aff->v) goto error; } isl_val_free(v); return aff; error: isl_aff_free(aff); isl_val_free(v); return NULL; } /* Return the first argument and free the second. */ static __isl_give isl_aff *pick_free(__isl_take isl_aff *aff, __isl_take isl_val *v) { isl_val_free(v); return aff; } /* Replace the first argument by NaN and free the second argument. */ static __isl_give isl_aff *set_nan_free_val(__isl_take isl_aff *aff, __isl_take isl_val *v) { isl_val_free(v); return isl_aff_set_nan(aff); } /* Add "v" to the constant term of "aff". * * A NaN is unaffected by this operation. * Conversely, adding a NaN turns "aff" into a NaN. */ __isl_give isl_aff *isl_aff_add_constant_val(__isl_take isl_aff *aff, __isl_take isl_val *v) { isl_bool is_nan, is_zero, is_rat; is_nan = isl_aff_is_nan(aff); is_zero = isl_val_is_zero(v); if (is_nan < 0 || is_zero < 0) goto error; if (is_nan || is_zero) return pick_free(aff, v); is_nan = isl_val_is_nan(v); is_rat = isl_val_is_rat(v); if (is_nan < 0 || is_rat < 0) goto error; if (is_nan) return set_nan_free_val(aff, v); if (!is_rat) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "expecting rational value or NaN", goto error); return isl_aff_add_rat_constant_val(aff, v); error: isl_aff_free(aff); isl_val_free(v); return NULL; } __isl_give isl_aff *isl_aff_add_constant_si(__isl_take isl_aff *aff, int v) { isl_int t; isl_int_init(t); isl_int_set_si(t, v); aff = isl_aff_add_constant(aff, t); isl_int_clear(t); return aff; } /* Add "v" to the numerator of the constant term of "aff". * * A NaN is unaffected by this operation. */ __isl_give isl_aff *isl_aff_add_constant_num(__isl_take isl_aff *aff, isl_int v) { if (isl_int_is_zero(v)) return aff; if (!aff) return NULL; if (isl_aff_is_nan(aff)) return aff; aff = isl_aff_cow(aff); if (!aff) return NULL; aff->v = isl_vec_cow(aff->v); if (!aff->v) return isl_aff_free(aff); isl_int_add(aff->v->el[1], aff->v->el[1], v); return aff; } /* Add "v" to the numerator of the constant term of "aff". * * A NaN is unaffected by this operation. */ __isl_give isl_aff *isl_aff_add_constant_num_si(__isl_take isl_aff *aff, int v) { isl_int t; if (v == 0) return aff; isl_int_init(t); isl_int_set_si(t, v); aff = isl_aff_add_constant_num(aff, t); isl_int_clear(t); return aff; } /* Replace the numerator of the constant term of "aff" by "v". * * A NaN is unaffected by this operation. */ __isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v) { if (!aff) return NULL; if (isl_aff_is_nan(aff)) return aff; aff = isl_aff_cow(aff); if (!aff) return NULL; aff->v = isl_vec_cow(aff->v); if (!aff->v) return isl_aff_free(aff); isl_int_set_si(aff->v->el[1], v); return aff; } /* Replace the numerator of the coefficient of the variable of type "type" * at position "pos" of "aff" by "v". * * A NaN is unaffected by this operation. */ __isl_give isl_aff *isl_aff_set_coefficient(__isl_take isl_aff *aff, enum isl_dim_type type, int pos, isl_int v) { if (!aff) return NULL; if (type == isl_dim_out) isl_die(aff->v->ctx, isl_error_invalid, "output/set dimension does not have a coefficient", return isl_aff_free(aff)); if (type == isl_dim_in) type = isl_dim_set; if (isl_local_space_check_range(aff->ls, type, pos, 1) < 0) return isl_aff_free(aff); if (isl_aff_is_nan(aff)) return aff; aff = isl_aff_cow(aff); if (!aff) return NULL; aff->v = isl_vec_cow(aff->v); if (!aff->v) return isl_aff_free(aff); pos += isl_local_space_offset(aff->ls, type); isl_int_set(aff->v->el[1 + pos], v); return aff; } /* Replace the numerator of the coefficient of the variable of type "type" * at position "pos" of "aff" by "v". * * A NaN is unaffected by this operation. */ __isl_give isl_aff *isl_aff_set_coefficient_si(__isl_take isl_aff *aff, enum isl_dim_type type, int pos, int v) { if (!aff) return NULL; if (type == isl_dim_out) isl_die(aff->v->ctx, isl_error_invalid, "output/set dimension does not have a coefficient", return isl_aff_free(aff)); if (type == isl_dim_in) type = isl_dim_set; if (isl_local_space_check_range(aff->ls, type, pos, 1) < 0) return isl_aff_free(aff); if (isl_aff_is_nan(aff)) return aff; pos += isl_local_space_offset(aff->ls, type); if (isl_int_cmp_si(aff->v->el[1 + pos], v) == 0) return aff; aff = isl_aff_cow(aff); if (!aff) return NULL; aff->v = isl_vec_cow(aff->v); if (!aff->v) return isl_aff_free(aff); isl_int_set_si(aff->v->el[1 + pos], v); return aff; } /* Replace the coefficient of the variable of type "type" at position "pos" * of "aff" by "v". * * A NaN is unaffected by this operation. */ __isl_give isl_aff *isl_aff_set_coefficient_val(__isl_take isl_aff *aff, enum isl_dim_type type, int pos, __isl_take isl_val *v) { if (!aff || !v) goto error; if (type == isl_dim_out) isl_die(aff->v->ctx, isl_error_invalid, "output/set dimension does not have a coefficient", goto error); if (type == isl_dim_in) type = isl_dim_set; if (isl_local_space_check_range(aff->ls, type, pos, 1) < 0) return isl_aff_free(aff); if (isl_aff_is_nan(aff)) { isl_val_free(v); return aff; } if (!isl_val_is_rat(v)) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "expecting rational value", goto error); pos += isl_local_space_offset(aff->ls, type); if (isl_int_eq(aff->v->el[1 + pos], v->n) && isl_int_eq(aff->v->el[0], v->d)) { isl_val_free(v); return aff; } aff = isl_aff_cow(aff); if (!aff) goto error; aff->v = isl_vec_cow(aff->v); if (!aff->v) goto error; if (isl_int_eq(aff->v->el[0], v->d)) { isl_int_set(aff->v->el[1 + pos], v->n); } else if (isl_int_is_one(v->d)) { isl_int_mul(aff->v->el[1 + pos], aff->v->el[0], v->n); } else { isl_seq_scale(aff->v->el + 1, aff->v->el + 1, v->d, aff->v->size - 1); isl_int_mul(aff->v->el[1 + pos], aff->v->el[0], v->n); isl_int_mul(aff->v->el[0], aff->v->el[0], v->d); aff->v = isl_vec_normalize(aff->v); if (!aff->v) goto error; } isl_val_free(v); return aff; error: isl_aff_free(aff); isl_val_free(v); return NULL; } /* Add "v" to the coefficient of the variable of type "type" * at position "pos" of "aff". * * A NaN is unaffected by this operation. */ __isl_give isl_aff *isl_aff_add_coefficient(__isl_take isl_aff *aff, enum isl_dim_type type, int pos, isl_int v) { if (!aff) return NULL; if (type == isl_dim_out) isl_die(aff->v->ctx, isl_error_invalid, "output/set dimension does not have a coefficient", return isl_aff_free(aff)); if (type == isl_dim_in) type = isl_dim_set; if (isl_local_space_check_range(aff->ls, type, pos, 1) < 0) return isl_aff_free(aff); if (isl_aff_is_nan(aff)) return aff; aff = isl_aff_cow(aff); if (!aff) return NULL; aff->v = isl_vec_cow(aff->v); if (!aff->v) return isl_aff_free(aff); pos += isl_local_space_offset(aff->ls, type); isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v); return aff; } /* Add "v" to the coefficient of the variable of type "type" * at position "pos" of "aff". * * A NaN is unaffected by this operation. */ __isl_give isl_aff *isl_aff_add_coefficient_val(__isl_take isl_aff *aff, enum isl_dim_type type, int pos, __isl_take isl_val *v) { if (!aff || !v) goto error; if (isl_val_is_zero(v)) { isl_val_free(v); return aff; } if (type == isl_dim_out) isl_die(aff->v->ctx, isl_error_invalid, "output/set dimension does not have a coefficient", goto error); if (type == isl_dim_in) type = isl_dim_set; if (isl_local_space_check_range(aff->ls, type, pos, 1) < 0) goto error; if (isl_aff_is_nan(aff)) { isl_val_free(v); return aff; } if (!isl_val_is_rat(v)) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "expecting rational value", goto error); aff = isl_aff_cow(aff); if (!aff) goto error; aff->v = isl_vec_cow(aff->v); if (!aff->v) goto error; pos += isl_local_space_offset(aff->ls, type); if (isl_int_is_one(v->d)) { isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v->n); } else if (isl_int_eq(aff->v->el[0], v->d)) { isl_int_add(aff->v->el[1 + pos], aff->v->el[1 + pos], v->n); aff->v = isl_vec_normalize(aff->v); if (!aff->v) goto error; } else { isl_seq_scale(aff->v->el + 1, aff->v->el + 1, v->d, aff->v->size - 1); isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v->n); isl_int_mul(aff->v->el[0], aff->v->el[0], v->d); aff->v = isl_vec_normalize(aff->v); if (!aff->v) goto error; } isl_val_free(v); return aff; error: isl_aff_free(aff); isl_val_free(v); return NULL; } __isl_give isl_aff *isl_aff_add_coefficient_si(__isl_take isl_aff *aff, enum isl_dim_type type, int pos, int v) { isl_int t; isl_int_init(t); isl_int_set_si(t, v); aff = isl_aff_add_coefficient(aff, type, pos, t); isl_int_clear(t); return aff; } __isl_give isl_aff *isl_aff_get_div(__isl_keep isl_aff *aff, int pos) { if (!aff) return NULL; return isl_local_space_get_div(aff->ls, pos); } /* Return the negation of "aff". * * As a special case, -NaN = NaN. */ __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff) { if (!aff) return NULL; if (isl_aff_is_nan(aff)) return aff; aff = isl_aff_cow(aff); if (!aff) return NULL; aff->v = isl_vec_cow(aff->v); if (!aff->v) return isl_aff_free(aff); isl_seq_neg(aff->v->el + 1, aff->v->el + 1, aff->v->size - 1); return aff; } /* Remove divs from the local space that do not appear in the affine * expression. * We currently only remove divs at the end. * Some intermediate divs may also not appear directly in the affine * expression, but we would also need to check that no other divs are * defined in terms of them. */ __isl_give isl_aff *isl_aff_remove_unused_divs(__isl_take isl_aff *aff) { int pos; isl_size off; isl_size n; n = isl_aff_domain_dim(aff, isl_dim_div); off = isl_aff_domain_offset(aff, isl_dim_div); if (n < 0 || off < 0) return isl_aff_free(aff); pos = isl_seq_last_non_zero(aff->v->el + 1 + off, n) + 1; if (pos == n) return aff; aff = isl_aff_cow(aff); if (!aff) return NULL; aff->ls = isl_local_space_drop_dims(aff->ls, isl_dim_div, pos, n - pos); aff->v = isl_vec_drop_els(aff->v, 1 + off + pos, n - pos); if (!aff->ls || !aff->v) return isl_aff_free(aff); return aff; } /* Look for any divs in the aff->ls with a denominator equal to one * and plug them into the affine expression and any subsequent divs * that may reference the div. */ static __isl_give isl_aff *plug_in_integral_divs(__isl_take isl_aff *aff) { int i; isl_size n; int len; isl_int v; isl_vec *vec; isl_local_space *ls; isl_size off; n = isl_aff_domain_dim(aff, isl_dim_div); off = isl_aff_domain_offset(aff, isl_dim_div); if (n < 0 || off < 0) return isl_aff_free(aff); len = aff->v->size; for (i = 0; i < n; ++i) { if (!isl_int_is_one(aff->ls->div->row[i][0])) continue; ls = isl_local_space_copy(aff->ls); ls = isl_local_space_substitute_seq(ls, isl_dim_div, i, aff->ls->div->row[i], len, i + 1, n - (i + 1)); vec = isl_vec_copy(aff->v); vec = isl_vec_cow(vec); if (!ls || !vec) goto error; isl_int_init(v); isl_seq_substitute(vec->el, off + i, aff->ls->div->row[i], len, len, v); isl_int_clear(v); isl_vec_free(aff->v); aff->v = vec; isl_local_space_free(aff->ls); aff->ls = ls; } return aff; error: isl_vec_free(vec); isl_local_space_free(ls); return isl_aff_free(aff); } /* Look for any divs j that appear with a unit coefficient inside * the definitions of other divs i and plug them into the definitions * of the divs i. * * In particular, an expression of the form * * floor((f(..) + floor(g(..)/n))/m) * * is simplified to * * floor((n * f(..) + g(..))/(n * m)) * * This simplification is correct because we can move the expression * f(..) into the inner floor in the original expression to obtain * * floor(floor((n * f(..) + g(..))/n)/m) * * from which we can derive the simplified expression. */ static __isl_give isl_aff *plug_in_unit_divs(__isl_take isl_aff *aff) { int i, j; isl_size n; isl_size off; n = isl_aff_domain_dim(aff, isl_dim_div); off = isl_aff_domain_offset(aff, isl_dim_div); if (n < 0 || off < 0) return isl_aff_free(aff); for (i = 1; i < n; ++i) { for (j = 0; j < i; ++j) { if (!isl_int_is_one(aff->ls->div->row[i][1 + off + j])) continue; aff->ls = isl_local_space_substitute_seq(aff->ls, isl_dim_div, j, aff->ls->div->row[j], aff->v->size, i, 1); if (!aff->ls) return isl_aff_free(aff); } } return aff; } /* Swap divs "a" and "b" in "aff", which is assumed to be non-NULL. * * Even though this function is only called on isl_affs with a single * reference, we are careful to only change aff->v and aff->ls together. */ static __isl_give isl_aff *swap_div(__isl_take isl_aff *aff, int a, int b) { isl_size off = isl_aff_domain_offset(aff, isl_dim_div); isl_local_space *ls; isl_vec *v; if (off < 0) return isl_aff_free(aff); ls = isl_local_space_copy(aff->ls); ls = isl_local_space_swap_div(ls, a, b); v = isl_vec_copy(aff->v); v = isl_vec_cow(v); if (!ls || !v) goto error; isl_int_swap(v->el[1 + off + a], v->el[1 + off + b]); isl_vec_free(aff->v); aff->v = v; isl_local_space_free(aff->ls); aff->ls = ls; return aff; error: isl_vec_free(v); isl_local_space_free(ls); return isl_aff_free(aff); } /* Merge divs "a" and "b" in "aff", which is assumed to be non-NULL. * * We currently do not actually remove div "b", but simply add its * coefficient to that of "a" and then zero it out. */ static __isl_give isl_aff *merge_divs(__isl_take isl_aff *aff, int a, int b) { isl_size off = isl_aff_domain_offset(aff, isl_dim_div); if (off < 0) return isl_aff_free(aff); if (isl_int_is_zero(aff->v->el[1 + off + b])) return aff; aff->v = isl_vec_cow(aff->v); if (!aff->v) return isl_aff_free(aff); isl_int_add(aff->v->el[1 + off + a], aff->v->el[1 + off + a], aff->v->el[1 + off + b]); isl_int_set_si(aff->v->el[1 + off + b], 0); return aff; } /* Sort the divs in the local space of "aff" according to * the comparison function "cmp_row" in isl_local_space.c, * combining the coefficients of identical divs. * * Reordering divs does not change the semantics of "aff", * so there is no need to call isl_aff_cow. * Moreover, this function is currently only called on isl_affs * with a single reference. */ static __isl_give isl_aff *sort_divs(__isl_take isl_aff *aff) { isl_size n; int i, j; n = isl_aff_dim(aff, isl_dim_div); if (n < 0) return isl_aff_free(aff); for (i = 1; i < n; ++i) { for (j = i - 1; j >= 0; --j) { int cmp = isl_mat_cmp_div(aff->ls->div, j, j + 1); if (cmp < 0) break; if (cmp == 0) aff = merge_divs(aff, j, j + 1); else aff = swap_div(aff, j, j + 1); if (!aff) return NULL; } } return aff; } /* Normalize the representation of "aff". * * This function should only be called on "new" isl_affs, i.e., * with only a single reference. We therefore do not need to * worry about affecting other instances. */ __isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff) { if (!aff) return NULL; aff->v = isl_vec_normalize(aff->v); if (!aff->v) return isl_aff_free(aff); aff = plug_in_integral_divs(aff); aff = plug_in_unit_divs(aff); aff = sort_divs(aff); aff = isl_aff_remove_unused_divs(aff); return aff; } /* Given f, return floor(f). * If f is an integer expression, then just return f. * If f is a constant, then return the constant floor(f). * Otherwise, if f = g/m, write g = q m + r, * create a new div d = [r/m] and return the expression q + d. * The coefficients in r are taken to lie between -m/2 and m/2. * * reduce_div_coefficients performs the same normalization. * * As a special case, floor(NaN) = NaN. */ __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff) { int i; int size; isl_ctx *ctx; isl_vec *div; if (!aff) return NULL; if (isl_aff_is_nan(aff)) return aff; if (isl_int_is_one(aff->v->el[0])) return aff; aff = isl_aff_cow(aff); if (!aff) return NULL; aff->v = isl_vec_cow(aff->v); if (!aff->v) return isl_aff_free(aff); if (isl_aff_is_cst(aff)) { isl_int_fdiv_q(aff->v->el[1], aff->v->el[1], aff->v->el[0]); isl_int_set_si(aff->v->el[0], 1); return aff; } div = isl_vec_copy(aff->v); div = isl_vec_cow(div); if (!div) return isl_aff_free(aff); ctx = isl_aff_get_ctx(aff); isl_int_fdiv_q(aff->v->el[0], aff->v->el[0], ctx->two); for (i = 1; i < aff->v->size; ++i) { isl_int_fdiv_r(div->el[i], div->el[i], div->el[0]); isl_int_fdiv_q(aff->v->el[i], aff->v->el[i], div->el[0]); if (isl_int_gt(div->el[i], aff->v->el[0])) { isl_int_sub(div->el[i], div->el[i], div->el[0]); isl_int_add_ui(aff->v->el[i], aff->v->el[i], 1); } } aff->ls = isl_local_space_add_div(aff->ls, div); if (!aff->ls) return isl_aff_free(aff); size = aff->v->size; aff->v = isl_vec_extend(aff->v, size + 1); if (!aff->v) return isl_aff_free(aff); isl_int_set_si(aff->v->el[0], 1); isl_int_set_si(aff->v->el[size], 1); aff = isl_aff_normalize(aff); return aff; } /* Compute * * aff mod m = aff - m * floor(aff/m) * * with m an integer value. */ __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff, __isl_take isl_val *m) { isl_aff *res; if (!aff || !m) goto error; if (!isl_val_is_int(m)) isl_die(isl_val_get_ctx(m), isl_error_invalid, "expecting integer modulo", goto error); res = isl_aff_copy(aff); aff = isl_aff_scale_down_val(aff, isl_val_copy(m)); aff = isl_aff_floor(aff); aff = isl_aff_scale_val(aff, m); res = isl_aff_sub(res, aff); return res; error: isl_aff_free(aff); isl_val_free(m); return NULL; } /* Compute * * pwaff mod m = pwaff - m * floor(pwaff/m) */ __isl_give isl_pw_aff *isl_pw_aff_mod(__isl_take isl_pw_aff *pwaff, isl_int m) { isl_pw_aff *res; res = isl_pw_aff_copy(pwaff); pwaff = isl_pw_aff_scale_down(pwaff, m); pwaff = isl_pw_aff_floor(pwaff); pwaff = isl_pw_aff_scale(pwaff, m); res = isl_pw_aff_sub(res, pwaff); return res; } /* Compute * * pa mod m = pa - m * floor(pa/m) * * with m an integer value. */ __isl_give isl_pw_aff *isl_pw_aff_mod_val(__isl_take isl_pw_aff *pa, __isl_take isl_val *m) { if (!pa || !m) goto error; if (!isl_val_is_int(m)) isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid, "expecting integer modulo", goto error); pa = isl_pw_aff_mod(pa, m->n); isl_val_free(m); return pa; error: isl_pw_aff_free(pa); isl_val_free(m); return NULL; } /* Given f, return ceil(f). * If f is an integer expression, then just return f. * Otherwise, let f be the expression * * e/m * * then return * * floor((e + m - 1)/m) * * As a special case, ceil(NaN) = NaN. */ __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff) { if (!aff) return NULL; if (isl_aff_is_nan(aff)) return aff; if (isl_int_is_one(aff->v->el[0])) return aff; aff = isl_aff_cow(aff); if (!aff) return NULL; aff->v = isl_vec_cow(aff->v); if (!aff->v) return isl_aff_free(aff); isl_int_add(aff->v->el[1], aff->v->el[1], aff->v->el[0]); isl_int_sub_ui(aff->v->el[1], aff->v->el[1], 1); aff = isl_aff_floor(aff); return aff; } /* Apply the expansion computed by isl_merge_divs. * The expansion itself is given by "exp" while the resulting * list of divs is given by "div". */ __isl_give isl_aff *isl_aff_expand_divs(__isl_take isl_aff *aff, __isl_take isl_mat *div, int *exp) { isl_size old_n_div; isl_size new_n_div; isl_size offset; aff = isl_aff_cow(aff); offset = isl_aff_domain_offset(aff, isl_dim_div); old_n_div = isl_aff_domain_dim(aff, isl_dim_div); new_n_div = isl_mat_rows(div); if (offset < 0 || old_n_div < 0 || new_n_div < 0) goto error; aff->v = isl_vec_expand(aff->v, 1 + offset, old_n_div, exp, new_n_div); aff->ls = isl_local_space_replace_divs(aff->ls, div); if (!aff->v || !aff->ls) return isl_aff_free(aff); return aff; error: isl_aff_free(aff); isl_mat_free(div); return NULL; } /* Add two affine expressions that live in the same local space. */ static __isl_give isl_aff *add_expanded(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { isl_int gcd, f; aff1 = isl_aff_cow(aff1); if (!aff1 || !aff2) goto error; aff1->v = isl_vec_cow(aff1->v); if (!aff1->v) goto error; isl_int_init(gcd); isl_int_init(f); isl_int_gcd(gcd, aff1->v->el[0], aff2->v->el[0]); isl_int_divexact(f, aff2->v->el[0], gcd); isl_seq_scale(aff1->v->el + 1, aff1->v->el + 1, f, aff1->v->size - 1); isl_int_divexact(f, aff1->v->el[0], gcd); isl_seq_addmul(aff1->v->el + 1, f, aff2->v->el + 1, aff1->v->size - 1); isl_int_divexact(f, aff2->v->el[0], gcd); isl_int_mul(aff1->v->el[0], aff1->v->el[0], f); isl_int_clear(f); isl_int_clear(gcd); isl_aff_free(aff2); aff1 = isl_aff_normalize(aff1); return aff1; error: isl_aff_free(aff1); isl_aff_free(aff2); return NULL; } /* Replace one of the arguments by a NaN and free the other one. */ static __isl_give isl_aff *set_nan_free(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { isl_aff_free(aff2); return isl_aff_set_nan(aff1); } /* Return the sum of "aff1" and "aff2". * * If either of the two is NaN, then the result is NaN. */ __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { isl_ctx *ctx; int *exp1 = NULL; int *exp2 = NULL; isl_mat *div; isl_size n_div1, n_div2; if (!aff1 || !aff2) goto error; ctx = isl_aff_get_ctx(aff1); if (!isl_space_is_equal(aff1->ls->dim, aff2->ls->dim)) isl_die(ctx, isl_error_invalid, "spaces don't match", goto error); if (isl_aff_is_nan(aff1)) { isl_aff_free(aff2); return aff1; } if (isl_aff_is_nan(aff2)) { isl_aff_free(aff1); return aff2; } n_div1 = isl_aff_dim(aff1, isl_dim_div); n_div2 = isl_aff_dim(aff2, isl_dim_div); if (n_div1 < 0 || n_div2 < 0) goto error; if (n_div1 == 0 && n_div2 == 0) return add_expanded(aff1, aff2); exp1 = isl_alloc_array(ctx, int, n_div1); exp2 = isl_alloc_array(ctx, int, n_div2); if ((n_div1 && !exp1) || (n_div2 && !exp2)) goto error; div = isl_merge_divs(aff1->ls->div, aff2->ls->div, exp1, exp2); aff1 = isl_aff_expand_divs(aff1, isl_mat_copy(div), exp1); aff2 = isl_aff_expand_divs(aff2, div, exp2); free(exp1); free(exp2); return add_expanded(aff1, aff2); error: free(exp1); free(exp2); isl_aff_free(aff1); isl_aff_free(aff2); return NULL; } __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { return isl_aff_add(aff1, isl_aff_neg(aff2)); } /* Return the result of scaling "aff" by a factor of "f". * * As a special case, f * NaN = NaN. */ __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff, isl_int f) { isl_int gcd; if (!aff) return NULL; if (isl_aff_is_nan(aff)) return aff; if (isl_int_is_one(f)) return aff; aff = isl_aff_cow(aff); if (!aff) return NULL; aff->v = isl_vec_cow(aff->v); if (!aff->v) return isl_aff_free(aff); if (isl_int_is_pos(f) && isl_int_is_divisible_by(aff->v->el[0], f)) { isl_int_divexact(aff->v->el[0], aff->v->el[0], f); return aff; } isl_int_init(gcd); isl_int_gcd(gcd, aff->v->el[0], f); isl_int_divexact(aff->v->el[0], aff->v->el[0], gcd); isl_int_divexact(gcd, f, gcd); isl_seq_scale(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1); isl_int_clear(gcd); return aff; } /* Multiple "aff" by "v". */ __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff, __isl_take isl_val *v) { if (!aff || !v) goto error; if (isl_val_is_one(v)) { isl_val_free(v); return aff; } if (!isl_val_is_rat(v)) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "expecting rational factor", goto error); aff = isl_aff_scale(aff, v->n); aff = isl_aff_scale_down(aff, v->d); isl_val_free(v); return aff; error: isl_aff_free(aff); isl_val_free(v); return NULL; } /* Return the result of scaling "aff" down by a factor of "f". * * As a special case, NaN/f = NaN. */ __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f) { isl_int gcd; if (!aff) return NULL; if (isl_aff_is_nan(aff)) return aff; if (isl_int_is_one(f)) return aff; aff = isl_aff_cow(aff); if (!aff) return NULL; if (isl_int_is_zero(f)) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "cannot scale down by zero", return isl_aff_free(aff)); aff->v = isl_vec_cow(aff->v); if (!aff->v) return isl_aff_free(aff); isl_int_init(gcd); isl_seq_gcd(aff->v->el + 1, aff->v->size - 1, &gcd); isl_int_gcd(gcd, gcd, f); isl_seq_scale_down(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1); isl_int_divexact(gcd, f, gcd); isl_int_mul(aff->v->el[0], aff->v->el[0], gcd); isl_int_clear(gcd); return aff; } /* Divide "aff" by "v". */ __isl_give isl_aff *isl_aff_scale_down_val(__isl_take isl_aff *aff, __isl_take isl_val *v) { if (!aff || !v) goto error; if (isl_val_is_one(v)) { isl_val_free(v); return aff; } if (!isl_val_is_rat(v)) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "expecting rational factor", goto error); if (!isl_val_is_pos(v)) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "factor needs to be positive", goto error); aff = isl_aff_scale(aff, v->d); aff = isl_aff_scale_down(aff, v->n); isl_val_free(v); return aff; error: isl_aff_free(aff); isl_val_free(v); return NULL; } __isl_give isl_aff *isl_aff_scale_down_ui(__isl_take isl_aff *aff, unsigned f) { isl_int v; if (f == 1) return aff; isl_int_init(v); isl_int_set_ui(v, f); aff = isl_aff_scale_down(aff, v); isl_int_clear(v); return aff; } __isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff, enum isl_dim_type type, unsigned pos, const char *s) { aff = isl_aff_cow(aff); if (!aff) return NULL; if (type == isl_dim_out) isl_die(aff->v->ctx, isl_error_invalid, "cannot set name of output/set dimension", return isl_aff_free(aff)); if (type == isl_dim_in) type = isl_dim_set; aff->ls = isl_local_space_set_dim_name(aff->ls, type, pos, s); if (!aff->ls) return isl_aff_free(aff); return aff; } __isl_give isl_aff *isl_aff_set_dim_id(__isl_take isl_aff *aff, enum isl_dim_type type, unsigned pos, __isl_take isl_id *id) { aff = isl_aff_cow(aff); if (!aff) goto error; if (type == isl_dim_out) isl_die(aff->v->ctx, isl_error_invalid, "cannot set name of output/set dimension", goto error); if (type == isl_dim_in) type = isl_dim_set; aff->ls = isl_local_space_set_dim_id(aff->ls, type, pos, id); if (!aff->ls) return isl_aff_free(aff); return aff; error: isl_id_free(id); isl_aff_free(aff); return NULL; } /* Replace the identifier of the input tuple of "aff" by "id". * type is currently required to be equal to isl_dim_in */ __isl_give isl_aff *isl_aff_set_tuple_id(__isl_take isl_aff *aff, enum isl_dim_type type, __isl_take isl_id *id) { aff = isl_aff_cow(aff); if (!aff) goto error; if (type != isl_dim_in) isl_die(aff->v->ctx, isl_error_invalid, "cannot only set id of input tuple", goto error); aff->ls = isl_local_space_set_tuple_id(aff->ls, isl_dim_set, id); if (!aff->ls) return isl_aff_free(aff); return aff; error: isl_id_free(id); isl_aff_free(aff); return NULL; } /* Exploit the equalities in "eq" to simplify the affine expression * and the expressions of the integer divisions in the local space. * The integer divisions in this local space are assumed to appear * as regular dimensions in "eq". */ static __isl_give isl_aff *isl_aff_substitute_equalities_lifted( __isl_take isl_aff *aff, __isl_take isl_basic_set *eq) { int i, j; unsigned o_div; unsigned n_div; if (!eq) goto error; if (eq->n_eq == 0) { isl_basic_set_free(eq); return aff; } aff = isl_aff_cow(aff); if (!aff) goto error; aff->ls = isl_local_space_substitute_equalities(aff->ls, isl_basic_set_copy(eq)); aff->v = isl_vec_cow(aff->v); if (!aff->ls || !aff->v) goto error; o_div = isl_basic_set_offset(eq, isl_dim_div); n_div = eq->n_div; for (i = 0; i < eq->n_eq; ++i) { j = isl_seq_last_non_zero(eq->eq[i], o_div + n_div); if (j < 0 || j == 0 || j >= o_div) continue; isl_seq_elim(aff->v->el + 1, eq->eq[i], j, o_div, &aff->v->el[0]); } isl_basic_set_free(eq); aff = isl_aff_normalize(aff); return aff; error: isl_basic_set_free(eq); isl_aff_free(aff); return NULL; } /* Exploit the equalities in "eq" to simplify the affine expression * and the expressions of the integer divisions in the local space. */ __isl_give isl_aff *isl_aff_substitute_equalities(__isl_take isl_aff *aff, __isl_take isl_basic_set *eq) { isl_size n_div; n_div = isl_aff_domain_dim(aff, isl_dim_div); if (n_div < 0) goto error; if (n_div > 0) eq = isl_basic_set_add_dims(eq, isl_dim_set, n_div); return isl_aff_substitute_equalities_lifted(aff, eq); error: isl_basic_set_free(eq); isl_aff_free(aff); return NULL; } /* Look for equalities among the variables shared by context and aff * and the integer divisions of aff, if any. * The equalities are then used to eliminate coefficients and/or integer * divisions from aff. */ __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff, __isl_take isl_set *context) { isl_local_space *ls; isl_basic_set *hull; ls = isl_aff_get_domain_local_space(aff); context = isl_local_space_lift_set(ls, context); hull = isl_set_affine_hull(context); return isl_aff_substitute_equalities_lifted(aff, hull); } __isl_give isl_aff *isl_aff_gist_params(__isl_take isl_aff *aff, __isl_take isl_set *context) { isl_set *dom_context = isl_set_universe(isl_aff_get_domain_space(aff)); dom_context = isl_set_intersect_params(dom_context, context); return isl_aff_gist(aff, dom_context); } /* Return a basic set containing those elements in the space * of aff where it is positive. "rational" should not be set. * * If "aff" is NaN, then it is not positive. */ static __isl_give isl_basic_set *aff_pos_basic_set(__isl_take isl_aff *aff, int rational, void *user) { isl_constraint *ineq; isl_basic_set *bset; isl_val *c; if (!aff) return NULL; if (isl_aff_is_nan(aff)) { isl_space *space = isl_aff_get_domain_space(aff); isl_aff_free(aff); return isl_basic_set_empty(space); } if (rational) isl_die(isl_aff_get_ctx(aff), isl_error_unsupported, "rational sets not supported", goto error); ineq = isl_inequality_from_aff(aff); c = isl_constraint_get_constant_val(ineq); c = isl_val_sub_ui(c, 1); ineq = isl_constraint_set_constant_val(ineq, c); bset = isl_basic_set_from_constraint(ineq); bset = isl_basic_set_simplify(bset); return bset; error: isl_aff_free(aff); return NULL; } /* Return a basic set containing those elements in the space * of aff where it is non-negative. * If "rational" is set, then return a rational basic set. * * If "aff" is NaN, then it is not non-negative (it's not negative either). */ static __isl_give isl_basic_set *aff_nonneg_basic_set( __isl_take isl_aff *aff, int rational, void *user) { isl_constraint *ineq; isl_basic_set *bset; if (!aff) return NULL; if (isl_aff_is_nan(aff)) { isl_space *space = isl_aff_get_domain_space(aff); isl_aff_free(aff); return isl_basic_set_empty(space); } ineq = isl_inequality_from_aff(aff); bset = isl_basic_set_from_constraint(ineq); if (rational) bset = isl_basic_set_set_rational(bset); bset = isl_basic_set_simplify(bset); return bset; } /* Return a basic set containing those elements in the space * of aff where it is non-negative. */ __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff) { return aff_nonneg_basic_set(aff, 0, NULL); } /* Return a basic set containing those elements in the domain space * of "aff" where it is positive. */ __isl_give isl_basic_set *isl_aff_pos_basic_set(__isl_take isl_aff *aff) { aff = isl_aff_add_constant_num_si(aff, -1); return isl_aff_nonneg_basic_set(aff); } /* Return a basic set containing those elements in the domain space * of aff where it is negative. */ __isl_give isl_basic_set *isl_aff_neg_basic_set(__isl_take isl_aff *aff) { aff = isl_aff_neg(aff); return isl_aff_pos_basic_set(aff); } /* Return a basic set containing those elements in the space * of aff where it is zero. * If "rational" is set, then return a rational basic set. * * If "aff" is NaN, then it is not zero. */ static __isl_give isl_basic_set *aff_zero_basic_set(__isl_take isl_aff *aff, int rational, void *user) { isl_constraint *ineq; isl_basic_set *bset; if (!aff) return NULL; if (isl_aff_is_nan(aff)) { isl_space *space = isl_aff_get_domain_space(aff); isl_aff_free(aff); return isl_basic_set_empty(space); } ineq = isl_equality_from_aff(aff); bset = isl_basic_set_from_constraint(ineq); if (rational) bset = isl_basic_set_set_rational(bset); bset = isl_basic_set_simplify(bset); return bset; } /* Return a basic set containing those elements in the space * of aff where it is zero. */ __isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff) { return aff_zero_basic_set(aff, 0, NULL); } /* Return a basic set containing those elements in the shared space * of aff1 and aff2 where aff1 is greater than or equal to aff2. */ __isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { aff1 = isl_aff_sub(aff1, aff2); return isl_aff_nonneg_basic_set(aff1); } /* Return a basic set containing those elements in the shared domain space * of "aff1" and "aff2" where "aff1" is greater than "aff2". */ __isl_give isl_basic_set *isl_aff_gt_basic_set(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { aff1 = isl_aff_sub(aff1, aff2); return isl_aff_pos_basic_set(aff1); } /* Return a set containing those elements in the shared space * of aff1 and aff2 where aff1 is greater than or equal to aff2. */ __isl_give isl_set *isl_aff_ge_set(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { return isl_set_from_basic_set(isl_aff_ge_basic_set(aff1, aff2)); } /* Return a set containing those elements in the shared domain space * of aff1 and aff2 where aff1 is greater than aff2. * * If either of the two inputs is NaN, then the result is empty, * as comparisons with NaN always return false. */ __isl_give isl_set *isl_aff_gt_set(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { return isl_set_from_basic_set(isl_aff_gt_basic_set(aff1, aff2)); } /* Return a basic set containing those elements in the shared space * of aff1 and aff2 where aff1 is smaller than or equal to aff2. */ __isl_give isl_basic_set *isl_aff_le_basic_set(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { return isl_aff_ge_basic_set(aff2, aff1); } /* Return a basic set containing those elements in the shared domain space * of "aff1" and "aff2" where "aff1" is smaller than "aff2". */ __isl_give isl_basic_set *isl_aff_lt_basic_set(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { return isl_aff_gt_basic_set(aff2, aff1); } /* Return a set containing those elements in the shared space * of aff1 and aff2 where aff1 is smaller than or equal to aff2. */ __isl_give isl_set *isl_aff_le_set(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { return isl_aff_ge_set(aff2, aff1); } /* Return a set containing those elements in the shared domain space * of "aff1" and "aff2" where "aff1" is smaller than "aff2". */ __isl_give isl_set *isl_aff_lt_set(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { return isl_set_from_basic_set(isl_aff_lt_basic_set(aff1, aff2)); } /* Return a basic set containing those elements in the shared space * of aff1 and aff2 where aff1 and aff2 are equal. */ __isl_give isl_basic_set *isl_aff_eq_basic_set(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { aff1 = isl_aff_sub(aff1, aff2); return isl_aff_zero_basic_set(aff1); } /* Return a set containing those elements in the shared space * of aff1 and aff2 where aff1 and aff2 are equal. */ __isl_give isl_set *isl_aff_eq_set(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { return isl_set_from_basic_set(isl_aff_eq_basic_set(aff1, aff2)); } /* Return a set containing those elements in the shared domain space * of aff1 and aff2 where aff1 and aff2 are not equal. * * If either of the two inputs is NaN, then the result is empty, * as comparisons with NaN always return false. */ __isl_give isl_set *isl_aff_ne_set(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { isl_set *set_lt, *set_gt; set_lt = isl_aff_lt_set(isl_aff_copy(aff1), isl_aff_copy(aff2)); set_gt = isl_aff_gt_set(aff1, aff2); return isl_set_union_disjoint(set_lt, set_gt); } __isl_give isl_aff *isl_aff_add_on_domain(__isl_keep isl_set *dom, __isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { aff1 = isl_aff_add(aff1, aff2); aff1 = isl_aff_gist(aff1, isl_set_copy(dom)); return aff1; } isl_bool isl_aff_is_empty(__isl_keep isl_aff *aff) { if (!aff) return isl_bool_error; return isl_bool_false; } #undef TYPE #define TYPE isl_aff static #include "check_type_range_templ.c" /* Check whether the given affine expression has non-zero coefficient * for any dimension in the given range or if any of these dimensions * appear with non-zero coefficients in any of the integer divisions * involved in the affine expression. */ isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff, enum isl_dim_type type, unsigned first, unsigned n) { int i; int *active = NULL; isl_bool involves = isl_bool_false; if (!aff) return isl_bool_error; if (n == 0) return isl_bool_false; if (isl_aff_check_range(aff, type, first, n) < 0) return isl_bool_error; active = isl_local_space_get_active(aff->ls, aff->v->el + 2); if (!active) goto error; first += isl_local_space_offset(aff->ls, type) - 1; for (i = 0; i < n; ++i) if (active[first + i]) { involves = isl_bool_true; break; } free(active); return involves; error: free(active); return isl_bool_error; } /* Does "aff" involve any local variables, i.e., integer divisions? */ isl_bool isl_aff_involves_locals(__isl_keep isl_aff *aff) { isl_size n; n = isl_aff_dim(aff, isl_dim_div); if (n < 0) return isl_bool_error; return isl_bool_ok(n > 0); } __isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff, enum isl_dim_type type, unsigned first, unsigned n) { isl_ctx *ctx; if (!aff) return NULL; if (type == isl_dim_out) isl_die(aff->v->ctx, isl_error_invalid, "cannot drop output/set dimension", return isl_aff_free(aff)); if (type == isl_dim_in) type = isl_dim_set; if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type)) return aff; ctx = isl_aff_get_ctx(aff); if (isl_local_space_check_range(aff->ls, type, first, n) < 0) return isl_aff_free(aff); aff = isl_aff_cow(aff); if (!aff) return NULL; aff->ls = isl_local_space_drop_dims(aff->ls, type, first, n); if (!aff->ls) return isl_aff_free(aff); first += 1 + isl_local_space_offset(aff->ls, type); aff->v = isl_vec_drop_els(aff->v, first, n); if (!aff->v) return isl_aff_free(aff); return aff; } /* Is the domain of "aff" a product? */ static isl_bool isl_aff_domain_is_product(__isl_keep isl_aff *aff) { return isl_space_is_product(isl_aff_peek_domain_space(aff)); } #undef TYPE #define TYPE isl_aff #include /* Project the domain of the affine expression onto its parameter space. * The affine expression may not involve any of the domain dimensions. */ __isl_give isl_aff *isl_aff_project_domain_on_params(__isl_take isl_aff *aff) { isl_space *space; isl_size n; n = isl_aff_dim(aff, isl_dim_in); if (n < 0) return isl_aff_free(aff); aff = isl_aff_drop_domain(aff, 0, n); space = isl_aff_get_domain_space(aff); space = isl_space_params(space); aff = isl_aff_reset_domain_space(aff, space); return aff; } /* Convert an affine expression defined over a parameter domain * into one that is defined over a zero-dimensional set. */ __isl_give isl_aff *isl_aff_from_range(__isl_take isl_aff *aff) { isl_local_space *ls; ls = isl_aff_take_domain_local_space(aff); ls = isl_local_space_set_from_params(ls); aff = isl_aff_restore_domain_local_space(aff, ls); return aff; } __isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff, enum isl_dim_type type, unsigned first, unsigned n) { isl_ctx *ctx; if (!aff) return NULL; if (type == isl_dim_out) isl_die(aff->v->ctx, isl_error_invalid, "cannot insert output/set dimensions", return isl_aff_free(aff)); if (type == isl_dim_in) type = isl_dim_set; if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type)) return aff; ctx = isl_aff_get_ctx(aff); if (isl_local_space_check_range(aff->ls, type, first, 0) < 0) return isl_aff_free(aff); aff = isl_aff_cow(aff); if (!aff) return NULL; aff->ls = isl_local_space_insert_dims(aff->ls, type, first, n); if (!aff->ls) return isl_aff_free(aff); first += 1 + isl_local_space_offset(aff->ls, type); aff->v = isl_vec_insert_zero_els(aff->v, first, n); if (!aff->v) return isl_aff_free(aff); return aff; } __isl_give isl_aff *isl_aff_add_dims(__isl_take isl_aff *aff, enum isl_dim_type type, unsigned n) { isl_size pos; pos = isl_aff_dim(aff, type); if (pos < 0) return isl_aff_free(aff); return isl_aff_insert_dims(aff, type, pos, n); } /* Move the "n" dimensions of "src_type" starting at "src_pos" of "aff" * to dimensions of "dst_type" at "dst_pos". * * We only support moving input dimensions to parameters and vice versa. */ __isl_give isl_aff *isl_aff_move_dims(__isl_take isl_aff *aff, 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; isl_size src_off, dst_off; if (!aff) return NULL; if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, src_type) && !isl_local_space_is_named_or_nested(aff->ls, dst_type)) return aff; if (dst_type == isl_dim_out || src_type == isl_dim_out) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "cannot move output/set dimension", return isl_aff_free(aff)); if (dst_type == isl_dim_div || src_type == isl_dim_div) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "cannot move divs", return isl_aff_free(aff)); if (dst_type == isl_dim_in) dst_type = isl_dim_set; if (src_type == isl_dim_in) src_type = isl_dim_set; if (isl_local_space_check_range(aff->ls, src_type, src_pos, n) < 0) return isl_aff_free(aff); if (dst_type == src_type) isl_die(isl_aff_get_ctx(aff), isl_error_unsupported, "moving dims within the same type not supported", return isl_aff_free(aff)); aff = isl_aff_cow(aff); src_off = isl_aff_domain_offset(aff, src_type); dst_off = isl_aff_domain_offset(aff, dst_type); if (src_off < 0 || dst_off < 0) return isl_aff_free(aff); g_src_pos = 1 + src_off + src_pos; g_dst_pos = 1 + dst_off + dst_pos; if (dst_type > src_type) g_dst_pos -= n; aff->v = isl_vec_move_els(aff->v, g_dst_pos, g_src_pos, n); aff->ls = isl_local_space_move_dims(aff->ls, dst_type, dst_pos, src_type, src_pos, n); if (!aff->v || !aff->ls) return isl_aff_free(aff); aff = sort_divs(aff); return aff; } /* Return a zero isl_aff in the given space. * * This is a helper function for isl_pw_*_as_* that ensures a uniform * interface over all piecewise types. */ static __isl_give isl_aff *isl_aff_zero_in_space(__isl_take isl_space *space) { isl_local_space *ls; ls = isl_local_space_from_space(isl_space_domain(space)); return isl_aff_zero_on_domain(ls); } #define isl_aff_involves_nan isl_aff_is_nan #undef PW #define PW isl_pw_aff #undef BASE #define BASE aff #undef EL_IS_ZERO #define EL_IS_ZERO is_empty #undef ZERO #define ZERO empty #undef IS_ZERO #define IS_ZERO is_empty #undef FIELD #define FIELD aff #undef DEFAULT_IS_ZERO #define DEFAULT_IS_ZERO 0 #include #include #include #include #include #include #include #include #include #include #include #include #undef BASE #define BASE pw_aff #include #include #undef BASE #define BASE aff #include /* Compute a piecewise quasi-affine expression with a domain that * is the union of those of pwaff1 and pwaff2 and such that on each * cell, the quasi-affine expression is the maximum of those of pwaff1 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given * cell, then the associated expression is the defined one. */ __isl_give isl_pw_aff *isl_pw_aff_union_max(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { isl_pw_aff_align_params_bin(&pwaff1, &pwaff2); return isl_pw_aff_union_opt_cmp(pwaff1, pwaff2, &isl_aff_ge_set); } /* Compute a piecewise quasi-affine expression with a domain that * is the union of those of pwaff1 and pwaff2 and such that on each * cell, the quasi-affine expression is the minimum of those of pwaff1 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given * cell, then the associated expression is the defined one. */ __isl_give isl_pw_aff *isl_pw_aff_union_min(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { isl_pw_aff_align_params_bin(&pwaff1, &pwaff2); return isl_pw_aff_union_opt_cmp(pwaff1, pwaff2, &isl_aff_le_set); } __isl_give isl_pw_aff *isl_pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2, int max) { if (max) return isl_pw_aff_union_max(pwaff1, pwaff2); else return isl_pw_aff_union_min(pwaff1, pwaff2); } /* Is the domain of "pa" a product? */ static isl_bool isl_pw_aff_domain_is_product(__isl_keep isl_pw_aff *pa) { return isl_space_domain_is_wrapping(isl_pw_aff_peek_space(pa)); } #undef TYPE #define TYPE isl_pw_aff #include /* Return a set containing those elements in the domain * of "pwaff" where it satisfies "fn" (if complement is 0) or * does not satisfy "fn" (if complement is 1). * * The pieces with a NaN never belong to the result since * NaN does not satisfy any property. */ static __isl_give isl_set *pw_aff_locus(__isl_take isl_pw_aff *pwaff, __isl_give isl_basic_set *(*fn)(__isl_take isl_aff *aff, int rational, void *user), int complement, void *user) { int i; isl_set *set; if (!pwaff) return NULL; set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff)); for (i = 0; i < pwaff->n; ++i) { isl_basic_set *bset; isl_set *set_i, *locus; isl_bool rational; if (isl_aff_is_nan(pwaff->p[i].aff)) continue; rational = isl_set_has_rational(pwaff->p[i].set); bset = fn(isl_aff_copy(pwaff->p[i].aff), rational, user); locus = isl_set_from_basic_set(bset); set_i = isl_set_copy(pwaff->p[i].set); if (complement) set_i = isl_set_subtract(set_i, locus); else set_i = isl_set_intersect(set_i, locus); set = isl_set_union_disjoint(set, set_i); } isl_pw_aff_free(pwaff); return set; } /* Return a set containing those elements in the domain * of "pa" where it is positive. */ __isl_give isl_set *isl_pw_aff_pos_set(__isl_take isl_pw_aff *pa) { return pw_aff_locus(pa, &aff_pos_basic_set, 0, NULL); } /* Return a set containing those elements in the domain * of pwaff where it is non-negative. */ __isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff) { return pw_aff_locus(pwaff, &aff_nonneg_basic_set, 0, NULL); } /* Return a set containing those elements in the domain * of pwaff where it is zero. */ __isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff) { return pw_aff_locus(pwaff, &aff_zero_basic_set, 0, NULL); } /* Return a set containing those elements in the domain * of pwaff where it is not zero. */ __isl_give isl_set *isl_pw_aff_non_zero_set(__isl_take isl_pw_aff *pwaff) { return pw_aff_locus(pwaff, &aff_zero_basic_set, 1, NULL); } /* Bind the affine function "aff" to the parameter "id", * returning the elements in the domain where the affine expression * is equal to the parameter. */ __isl_give isl_basic_set *isl_aff_bind_id(__isl_take isl_aff *aff, __isl_take isl_id *id) { isl_space *space; isl_aff *aff_id; space = isl_aff_get_domain_space(aff); space = isl_space_add_param_id(space, isl_id_copy(id)); aff = isl_aff_align_params(aff, isl_space_copy(space)); aff_id = isl_aff_param_on_domain_space_id(space, id); return isl_aff_eq_basic_set(aff, aff_id); } /* Wrapper around isl_aff_bind_id for use as pw_aff_locus callback. * "rational" should not be set. */ static __isl_give isl_basic_set *aff_bind_id(__isl_take isl_aff *aff, int rational, void *user) { isl_id *id = user; if (!aff) return NULL; if (rational) isl_die(isl_aff_get_ctx(aff), isl_error_unsupported, "rational binding not supported", goto error); return isl_aff_bind_id(aff, isl_id_copy(id)); error: isl_aff_free(aff); return NULL; } /* Bind the piecewise affine function "pa" to the parameter "id", * returning the elements in the domain where the expression * is equal to the parameter. */ __isl_give isl_set *isl_pw_aff_bind_id(__isl_take isl_pw_aff *pa, __isl_take isl_id *id) { isl_set *bound; bound = pw_aff_locus(pa, &aff_bind_id, 0, id); isl_id_free(id); return bound; } /* Return a set containing those elements in the shared domain * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2. * * We compute the difference on the shared domain and then construct * the set of values where this difference is non-negative. * If strict is set, we first subtract 1 from the difference. * If equal is set, we only return the elements where pwaff1 and pwaff2 * are equal. */ static __isl_give isl_set *pw_aff_gte_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2, int strict, int equal) { isl_set *set1, *set2; set1 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)); set2 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)); set1 = isl_set_intersect(set1, set2); pwaff1 = isl_pw_aff_intersect_domain(pwaff1, isl_set_copy(set1)); pwaff2 = isl_pw_aff_intersect_domain(pwaff2, isl_set_copy(set1)); pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_neg(pwaff2)); if (strict) { isl_space *space = isl_set_get_space(set1); isl_aff *aff; aff = isl_aff_zero_on_domain(isl_local_space_from_space(space)); aff = isl_aff_add_constant_si(aff, -1); pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_alloc(set1, aff)); } else isl_set_free(set1); if (equal) return isl_pw_aff_zero_set(pwaff1); return isl_pw_aff_nonneg_set(pwaff1); } /* Return a set containing those elements in the shared domain * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2. */ __isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { isl_pw_aff_align_params_bin(&pwaff1, &pwaff2); return pw_aff_gte_set(pwaff1, pwaff2, 0, 1); } /* Return a set containing those elements in the shared domain * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2. */ __isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { isl_pw_aff_align_params_bin(&pwaff1, &pwaff2); return pw_aff_gte_set(pwaff1, pwaff2, 0, 0); } /* Return a set containing those elements in the shared domain * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2. */ __isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { isl_pw_aff_align_params_bin(&pwaff1, &pwaff2); return pw_aff_gte_set(pwaff1, pwaff2, 1, 0); } __isl_give isl_set *isl_pw_aff_le_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return isl_pw_aff_ge_set(pwaff2, pwaff1); } __isl_give isl_set *isl_pw_aff_lt_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return isl_pw_aff_gt_set(pwaff2, pwaff1); } /* Return a map containing pairs of elements in the domains of "pa1" and "pa2" * where the function values are ordered in the same way as "order", * which returns a set in the shared domain of its two arguments. * * Let "pa1" and "pa2" be defined on domains A and B respectively. * We first pull back the two functions such that they are defined on * the domain [A -> B]. Then we apply "order", resulting in a set * in the space [A -> B]. Finally, we unwrap this set to obtain * a map in the space A -> B. */ static __isl_give isl_map *isl_pw_aff_order_map( __isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2, __isl_give isl_set *(*order)(__isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2)) { isl_space *space1, *space2; isl_multi_aff *ma; isl_set *set; isl_pw_aff_align_params_bin(&pa1, &pa2); space1 = isl_space_domain(isl_pw_aff_get_space(pa1)); space2 = isl_space_domain(isl_pw_aff_get_space(pa2)); space1 = isl_space_map_from_domain_and_range(space1, space2); ma = isl_multi_aff_domain_map(isl_space_copy(space1)); pa1 = isl_pw_aff_pullback_multi_aff(pa1, ma); ma = isl_multi_aff_range_map(space1); pa2 = isl_pw_aff_pullback_multi_aff(pa2, ma); set = order(pa1, pa2); return isl_set_unwrap(set); } /* Return a map containing pairs of elements in the domains of "pa1" and "pa2" * where the function values are equal. */ __isl_give isl_map *isl_pw_aff_eq_map(__isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2) { return isl_pw_aff_order_map(pa1, pa2, &isl_pw_aff_eq_set); } /* Return a map containing pairs of elements in the domains of "pa1" and "pa2" * where the function value of "pa1" is less than or equal to * the function value of "pa2". */ __isl_give isl_map *isl_pw_aff_le_map(__isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2) { return isl_pw_aff_order_map(pa1, pa2, &isl_pw_aff_le_set); } /* Return a map containing pairs of elements in the domains of "pa1" and "pa2" * where the function value of "pa1" is less than the function value of "pa2". */ __isl_give isl_map *isl_pw_aff_lt_map(__isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2) { return isl_pw_aff_order_map(pa1, pa2, &isl_pw_aff_lt_set); } /* Return a map containing pairs of elements in the domains of "pa1" and "pa2" * where the function value of "pa1" is greater than or equal to * the function value of "pa2". */ __isl_give isl_map *isl_pw_aff_ge_map(__isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2) { return isl_pw_aff_order_map(pa1, pa2, &isl_pw_aff_ge_set); } /* Return a map containing pairs of elements in the domains of "pa1" and "pa2" * where the function value of "pa1" is greater than the function value * of "pa2". */ __isl_give isl_map *isl_pw_aff_gt_map(__isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2) { return isl_pw_aff_order_map(pa1, pa2, &isl_pw_aff_gt_set); } /* Return a set containing those elements in the shared domain * of the elements of list1 and list2 where each element in list1 * has the relation specified by "fn" with each element in list2. */ static __isl_give isl_set *pw_aff_list_set(__isl_take isl_pw_aff_list *list1, __isl_take isl_pw_aff_list *list2, __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2)) { int i, j; isl_ctx *ctx; isl_set *set; if (!list1 || !list2) goto error; ctx = isl_pw_aff_list_get_ctx(list1); if (list1->n < 1 || list2->n < 1) isl_die(ctx, isl_error_invalid, "list should contain at least one element", goto error); set = isl_set_universe(isl_pw_aff_get_domain_space(list1->p[0])); for (i = 0; i < list1->n; ++i) for (j = 0; j < list2->n; ++j) { isl_set *set_ij; set_ij = fn(isl_pw_aff_copy(list1->p[i]), isl_pw_aff_copy(list2->p[j])); set = isl_set_intersect(set, set_ij); } isl_pw_aff_list_free(list1); isl_pw_aff_list_free(list2); return set; error: isl_pw_aff_list_free(list1); isl_pw_aff_list_free(list2); return NULL; } /* Return a set containing those elements in the shared domain * of the elements of list1 and list2 where each element in list1 * is equal to each element in list2. */ __isl_give isl_set *isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list *list1, __isl_take isl_pw_aff_list *list2) { return pw_aff_list_set(list1, list2, &isl_pw_aff_eq_set); } __isl_give isl_set *isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list *list1, __isl_take isl_pw_aff_list *list2) { return pw_aff_list_set(list1, list2, &isl_pw_aff_ne_set); } /* Return a set containing those elements in the shared domain * of the elements of list1 and list2 where each element in list1 * is less than or equal to each element in list2. */ __isl_give isl_set *isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list *list1, __isl_take isl_pw_aff_list *list2) { return pw_aff_list_set(list1, list2, &isl_pw_aff_le_set); } __isl_give isl_set *isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list *list1, __isl_take isl_pw_aff_list *list2) { return pw_aff_list_set(list1, list2, &isl_pw_aff_lt_set); } __isl_give isl_set *isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list *list1, __isl_take isl_pw_aff_list *list2) { return pw_aff_list_set(list1, list2, &isl_pw_aff_ge_set); } __isl_give isl_set *isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list *list1, __isl_take isl_pw_aff_list *list2) { return pw_aff_list_set(list1, list2, &isl_pw_aff_gt_set); } /* Return a set containing those elements in the shared domain * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2. */ __isl_give isl_set *isl_pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { isl_set *set_lt, *set_gt; isl_pw_aff_align_params_bin(&pwaff1, &pwaff2); set_lt = isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1), isl_pw_aff_copy(pwaff2)); set_gt = isl_pw_aff_gt_set(pwaff1, pwaff2); return isl_set_union_disjoint(set_lt, set_gt); } __isl_give isl_pw_aff *isl_pw_aff_scale_down(__isl_take isl_pw_aff *pwaff, isl_int v) { int i; if (isl_int_is_one(v)) return pwaff; if (!isl_int_is_pos(v)) isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid, "factor needs to be positive", return isl_pw_aff_free(pwaff)); pwaff = isl_pw_aff_cow(pwaff); if (!pwaff) return NULL; if (pwaff->n == 0) return pwaff; for (i = 0; i < pwaff->n; ++i) { pwaff->p[i].aff = isl_aff_scale_down(pwaff->p[i].aff, v); if (!pwaff->p[i].aff) return isl_pw_aff_free(pwaff); } return pwaff; } __isl_give isl_pw_aff *isl_pw_aff_floor(__isl_take isl_pw_aff *pwaff) { int i; pwaff = isl_pw_aff_cow(pwaff); if (!pwaff) return NULL; if (pwaff->n == 0) return pwaff; for (i = 0; i < pwaff->n; ++i) { pwaff->p[i].aff = isl_aff_floor(pwaff->p[i].aff); if (!pwaff->p[i].aff) return isl_pw_aff_free(pwaff); } return pwaff; } __isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff) { int i; pwaff = isl_pw_aff_cow(pwaff); if (!pwaff) return NULL; if (pwaff->n == 0) return pwaff; for (i = 0; i < pwaff->n; ++i) { pwaff->p[i].aff = isl_aff_ceil(pwaff->p[i].aff); if (!pwaff->p[i].aff) return isl_pw_aff_free(pwaff); } return pwaff; } /* Assuming that "cond1" and "cond2" are disjoint, * return an affine expression that is equal to pwaff1 on cond1 * and to pwaff2 on cond2. */ static __isl_give isl_pw_aff *isl_pw_aff_select( __isl_take isl_set *cond1, __isl_take isl_pw_aff *pwaff1, __isl_take isl_set *cond2, __isl_take isl_pw_aff *pwaff2) { pwaff1 = isl_pw_aff_intersect_domain(pwaff1, cond1); pwaff2 = isl_pw_aff_intersect_domain(pwaff2, cond2); return isl_pw_aff_add_disjoint(pwaff1, pwaff2); } /* Return an affine expression that is equal to pwaff_true for elements * where "cond" is non-zero and to pwaff_false for elements where "cond" * is zero. * That is, return cond ? pwaff_true : pwaff_false; * * If "cond" involves and NaN, then we conservatively return a NaN * on its entire domain. In principle, we could consider the pieces * where it is NaN separately from those where it is not. * * If "pwaff_true" and "pwaff_false" are obviously equal to each other, * then only use the domain of "cond" to restrict the domain. */ __isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_pw_aff *cond, __isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false) { isl_set *cond_true, *cond_false; isl_bool equal; if (!cond) goto error; if (isl_pw_aff_involves_nan(cond)) { isl_space *space = isl_pw_aff_get_domain_space(cond); isl_local_space *ls = isl_local_space_from_space(space); isl_pw_aff_free(cond); isl_pw_aff_free(pwaff_true); isl_pw_aff_free(pwaff_false); return isl_pw_aff_nan_on_domain(ls); } pwaff_true = isl_pw_aff_align_params(pwaff_true, isl_pw_aff_get_space(pwaff_false)); pwaff_false = isl_pw_aff_align_params(pwaff_false, isl_pw_aff_get_space(pwaff_true)); equal = isl_pw_aff_plain_is_equal(pwaff_true, pwaff_false); if (equal < 0) goto error; if (equal) { isl_set *dom; dom = isl_set_coalesce(isl_pw_aff_domain(cond)); isl_pw_aff_free(pwaff_false); return isl_pw_aff_intersect_domain(pwaff_true, dom); } cond_true = isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond)); cond_false = isl_pw_aff_zero_set(cond); return isl_pw_aff_select(cond_true, pwaff_true, cond_false, pwaff_false); error: isl_pw_aff_free(cond); isl_pw_aff_free(pwaff_true); isl_pw_aff_free(pwaff_false); return NULL; } isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff) { int pos; if (!aff) return isl_bool_error; pos = isl_seq_first_non_zero(aff->v->el + 2, aff->v->size - 2); return isl_bool_ok(pos == -1); } /* Check whether pwaff is a piecewise constant. */ isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff) { int i; if (!pwaff) return isl_bool_error; for (i = 0; i < pwaff->n; ++i) { isl_bool is_cst = isl_aff_is_cst(pwaff->p[i].aff); if (is_cst < 0 || !is_cst) return is_cst; } return isl_bool_true; } /* Return the product of "aff1" and "aff2". * * If either of the two is NaN, then the result is NaN. * * Otherwise, at least one of "aff1" or "aff2" needs to be a constant. */ __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { if (!aff1 || !aff2) goto error; if (isl_aff_is_nan(aff1)) { isl_aff_free(aff2); return aff1; } if (isl_aff_is_nan(aff2)) { isl_aff_free(aff1); return aff2; } if (!isl_aff_is_cst(aff2) && isl_aff_is_cst(aff1)) return isl_aff_mul(aff2, aff1); if (!isl_aff_is_cst(aff2)) isl_die(isl_aff_get_ctx(aff1), isl_error_invalid, "at least one affine expression should be constant", goto error); aff1 = isl_aff_cow(aff1); if (!aff1 || !aff2) goto error; aff1 = isl_aff_scale(aff1, aff2->v->el[1]); aff1 = isl_aff_scale_down(aff1, aff2->v->el[0]); isl_aff_free(aff2); return aff1; error: isl_aff_free(aff1); isl_aff_free(aff2); return NULL; } /* Divide "aff1" by "aff2", assuming "aff2" is a constant. * * If either of the two is NaN, then the result is NaN. * A division by zero also results in NaN. */ __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { isl_bool is_cst, is_zero; int neg; if (!aff1 || !aff2) goto error; if (isl_aff_is_nan(aff1)) { isl_aff_free(aff2); return aff1; } if (isl_aff_is_nan(aff2)) { isl_aff_free(aff1); return aff2; } is_cst = isl_aff_is_cst(aff2); if (is_cst < 0) goto error; if (!is_cst) isl_die(isl_aff_get_ctx(aff2), isl_error_invalid, "second argument should be a constant", goto error); is_zero = isl_aff_plain_is_zero(aff2); if (is_zero < 0) goto error; if (is_zero) return set_nan_free(aff1, aff2); neg = isl_int_is_neg(aff2->v->el[1]); if (neg) { isl_int_neg(aff2->v->el[0], aff2->v->el[0]); isl_int_neg(aff2->v->el[1], aff2->v->el[1]); } aff1 = isl_aff_scale(aff1, aff2->v->el[0]); aff1 = isl_aff_scale_down(aff1, aff2->v->el[1]); if (neg) { isl_int_neg(aff2->v->el[0], aff2->v->el[0]); isl_int_neg(aff2->v->el[1], aff2->v->el[1]); } isl_aff_free(aff2); return aff1; error: isl_aff_free(aff1); isl_aff_free(aff2); return NULL; } __isl_give isl_pw_aff *isl_pw_aff_add(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { isl_pw_aff_align_params_bin(&pwaff1, &pwaff2); return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_add); } __isl_give isl_pw_aff *isl_pw_aff_union_add(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return isl_pw_aff_union_add_(pwaff1, pwaff2); } __isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { isl_pw_aff_align_params_bin(&pwaff1, &pwaff2); return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_mul); } /* Divide "pa1" by "pa2", assuming "pa2" is a piecewise constant. */ __isl_give isl_pw_aff *isl_pw_aff_div(__isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2) { int is_cst; is_cst = isl_pw_aff_is_cst(pa2); if (is_cst < 0) goto error; if (!is_cst) isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid, "second argument should be a piecewise constant", goto error); isl_pw_aff_align_params_bin(&pa1, &pa2); return isl_pw_aff_on_shared_domain(pa1, pa2, &isl_aff_div); error: isl_pw_aff_free(pa1); isl_pw_aff_free(pa2); return NULL; } /* Compute the quotient of the integer division of "pa1" by "pa2" * with rounding towards zero. * "pa2" is assumed to be a piecewise constant. * * In particular, return * * pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2) * */ __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(__isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2) { int is_cst; isl_set *cond; isl_pw_aff *f, *c; is_cst = isl_pw_aff_is_cst(pa2); if (is_cst < 0) goto error; if (!is_cst) isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid, "second argument should be a piecewise constant", goto error); pa1 = isl_pw_aff_div(pa1, pa2); cond = isl_pw_aff_nonneg_set(isl_pw_aff_copy(pa1)); f = isl_pw_aff_floor(isl_pw_aff_copy(pa1)); c = isl_pw_aff_ceil(pa1); return isl_pw_aff_cond(isl_set_indicator_function(cond), f, c); error: isl_pw_aff_free(pa1); isl_pw_aff_free(pa2); return NULL; } /* Compute the remainder of the integer division of "pa1" by "pa2" * with rounding towards zero. * "pa2" is assumed to be a piecewise constant. * * In particular, return * * pa1 - pa2 * (pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2)) * */ __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(__isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2) { int is_cst; isl_pw_aff *res; is_cst = isl_pw_aff_is_cst(pa2); if (is_cst < 0) goto error; if (!is_cst) isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid, "second argument should be a piecewise constant", goto error); res = isl_pw_aff_tdiv_q(isl_pw_aff_copy(pa1), isl_pw_aff_copy(pa2)); res = isl_pw_aff_mul(pa2, res); res = isl_pw_aff_sub(pa1, res); return res; error: isl_pw_aff_free(pa1); isl_pw_aff_free(pa2); return NULL; } /* Does either of "pa1" or "pa2" involve any NaN2? */ static isl_bool either_involves_nan(__isl_keep isl_pw_aff *pa1, __isl_keep isl_pw_aff *pa2) { isl_bool has_nan; has_nan = isl_pw_aff_involves_nan(pa1); if (has_nan < 0 || has_nan) return has_nan; return isl_pw_aff_involves_nan(pa2); } /* Replace "pa1" and "pa2" (at least one of which involves a NaN) * by a NaN on their shared domain. * * In principle, the result could be refined to only being NaN * on the parts of this domain where at least one of "pa1" or "pa2" is NaN. */ static __isl_give isl_pw_aff *replace_by_nan(__isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2) { isl_local_space *ls; isl_set *dom; isl_pw_aff *pa; dom = isl_set_intersect(isl_pw_aff_domain(pa1), isl_pw_aff_domain(pa2)); ls = isl_local_space_from_space(isl_set_get_space(dom)); pa = isl_pw_aff_nan_on_domain(ls); pa = isl_pw_aff_intersect_domain(pa, dom); return pa; } static __isl_give isl_pw_aff *pw_aff_min(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { isl_set *le; isl_set *dom; dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)), isl_pw_aff_domain(isl_pw_aff_copy(pwaff2))); le = isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1), isl_pw_aff_copy(pwaff2)); dom = isl_set_subtract(dom, isl_set_copy(le)); return isl_pw_aff_select(le, pwaff1, dom, pwaff2); } static __isl_give isl_pw_aff *pw_aff_max(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { isl_set *ge; isl_set *dom; dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)), isl_pw_aff_domain(isl_pw_aff_copy(pwaff2))); ge = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1), isl_pw_aff_copy(pwaff2)); dom = isl_set_subtract(dom, isl_set_copy(ge)); return isl_pw_aff_select(ge, pwaff1, dom, pwaff2); } /* Return an expression for the minimum (if "max" is not set) or * the maximum (if "max" is set) of "pa1" and "pa2". * If either expression involves any NaN, then return a NaN * on the shared domain as result. */ static __isl_give isl_pw_aff *pw_aff_min_max(__isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2, int max) { isl_bool has_nan; has_nan = either_involves_nan(pa1, pa2); if (has_nan < 0) pa1 = isl_pw_aff_free(pa1); else if (has_nan) return replace_by_nan(pa1, pa2); isl_pw_aff_align_params_bin(&pa1, &pa2); if (max) return pw_aff_max(pa1, pa2); else return pw_aff_min(pa1, pa2); } /* Return an expression for the minimum of "pwaff1" and "pwaff2". */ __isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return pw_aff_min_max(pwaff1, pwaff2, 0); } /* Return an expression for the maximum of "pwaff1" and "pwaff2". */ __isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return pw_aff_min_max(pwaff1, pwaff2, 1); } static __isl_give isl_pw_aff *pw_aff_list_reduce( __isl_take isl_pw_aff_list *list, __isl_give isl_pw_aff *(*fn)(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2)) { int i; isl_ctx *ctx; isl_pw_aff *res; if (!list) return NULL; ctx = isl_pw_aff_list_get_ctx(list); if (list->n < 1) isl_die(ctx, isl_error_invalid, "list should contain at least one element", goto error); res = isl_pw_aff_copy(list->p[0]); for (i = 1; i < list->n; ++i) res = fn(res, isl_pw_aff_copy(list->p[i])); isl_pw_aff_list_free(list); return res; error: isl_pw_aff_list_free(list); return NULL; } /* Return an isl_pw_aff that maps each element in the intersection of the * domains of the elements of list to the minimal corresponding affine * expression. */ __isl_give isl_pw_aff *isl_pw_aff_list_min(__isl_take isl_pw_aff_list *list) { return pw_aff_list_reduce(list, &isl_pw_aff_min); } /* Return an isl_pw_aff that maps each element in the intersection of the * domains of the elements of list to the maximal corresponding affine * expression. */ __isl_give isl_pw_aff *isl_pw_aff_list_max(__isl_take isl_pw_aff_list *list) { return pw_aff_list_reduce(list, &isl_pw_aff_max); } /* Mark the domains of "pwaff" as rational. */ __isl_give isl_pw_aff *isl_pw_aff_set_rational(__isl_take isl_pw_aff *pwaff) { int i; pwaff = isl_pw_aff_cow(pwaff); if (!pwaff) return NULL; if (pwaff->n == 0) return pwaff; for (i = 0; i < pwaff->n; ++i) { pwaff->p[i].set = isl_set_set_rational(pwaff->p[i].set); if (!pwaff->p[i].set) return isl_pw_aff_free(pwaff); } return pwaff; } /* Mark the domains of the elements of "list" as rational. */ __isl_give isl_pw_aff_list *isl_pw_aff_list_set_rational( __isl_take isl_pw_aff_list *list) { int i, n; if (!list) return NULL; if (list->n == 0) return list; n = list->n; for (i = 0; i < n; ++i) { isl_pw_aff *pa; pa = isl_pw_aff_list_get_pw_aff(list, i); pa = isl_pw_aff_set_rational(pa); list = isl_pw_aff_list_set_pw_aff(list, i, pa); } return list; } /* Do the parameters of "aff" match those of "space"? */ isl_bool isl_aff_matching_params(__isl_keep isl_aff *aff, __isl_keep isl_space *space) { isl_space *aff_space; isl_bool match; if (!aff || !space) return isl_bool_error; aff_space = isl_aff_get_domain_space(aff); match = isl_space_has_equal_params(space, aff_space); isl_space_free(aff_space); return match; } /* Check that the domain space of "aff" matches "space". */ isl_stat isl_aff_check_match_domain_space(__isl_keep isl_aff *aff, __isl_keep isl_space *space) { isl_space *aff_space; isl_bool match; if (!aff || !space) return isl_stat_error; aff_space = isl_aff_get_domain_space(aff); match = isl_space_has_equal_params(space, aff_space); if (match < 0) goto error; if (!match) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "parameters don't match", goto error); match = isl_space_tuple_is_equal(space, isl_dim_in, aff_space, isl_dim_set); if (match < 0) goto error; if (!match) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "domains don't match", goto error); isl_space_free(aff_space); return isl_stat_ok; error: isl_space_free(aff_space); return isl_stat_error; } /* Return the shared (universe) domain of the elements of "ma". * * Since an isl_multi_aff (and an isl_aff) is always total, * the domain is always the universe set in its domain space. * This is a helper function for use in the generic isl_multi_*_bind. */ static __isl_give isl_basic_set *isl_multi_aff_domain( __isl_take isl_multi_aff *ma) { isl_space *space; space = isl_multi_aff_get_space(ma); isl_multi_aff_free(ma); return isl_basic_set_universe(isl_space_domain(space)); } #undef BASE #define BASE aff #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #undef DOMBASE #define DOMBASE set #include #undef DOMBASE #define DOMBASE basic_set #include /* Construct an isl_multi_aff living in "space" that corresponds * to the affine transformation matrix "mat". */ __isl_give isl_multi_aff *isl_multi_aff_from_aff_mat( __isl_take isl_space *space, __isl_take isl_mat *mat) { isl_ctx *ctx; isl_local_space *ls = NULL; isl_multi_aff *ma = NULL; isl_size n_row, n_col, n_out, total; int i; if (!space || !mat) goto error; ctx = isl_mat_get_ctx(mat); n_row = isl_mat_rows(mat); n_col = isl_mat_cols(mat); n_out = isl_space_dim(space, isl_dim_out); total = isl_space_dim(space, isl_dim_all); if (n_row < 0 || n_col < 0 || n_out < 0 || total < 0) goto error; if (n_row < 1) isl_die(ctx, isl_error_invalid, "insufficient number of rows", goto error); if (n_col < 1) isl_die(ctx, isl_error_invalid, "insufficient number of columns", goto error); if (1 + n_out != n_row || 2 + total != n_row + n_col) isl_die(ctx, isl_error_invalid, "dimension mismatch", goto error); ma = isl_multi_aff_zero(isl_space_copy(space)); space = isl_space_domain(space); ls = isl_local_space_from_space(isl_space_copy(space)); for (i = 0; i < n_row - 1; ++i) { isl_vec *v; isl_aff *aff; v = isl_vec_alloc(ctx, 1 + n_col); if (!v) goto error; isl_int_set(v->el[0], mat->row[0][0]); isl_seq_cpy(v->el + 1, mat->row[1 + i], n_col); v = isl_vec_normalize(v); aff = isl_aff_alloc_vec(isl_local_space_copy(ls), v); ma = isl_multi_aff_set_aff(ma, i, aff); } isl_space_free(space); isl_local_space_free(ls); isl_mat_free(mat); return ma; error: isl_space_free(space); isl_local_space_free(ls); isl_mat_free(mat); isl_multi_aff_free(ma); return NULL; } /* Return the constant terms of the affine expressions of "ma". */ __isl_give isl_multi_val *isl_multi_aff_get_constant_multi_val( __isl_keep isl_multi_aff *ma) { int i; isl_size n; isl_space *space; isl_multi_val *mv; n = isl_multi_aff_size(ma); if (n < 0) return NULL; space = isl_space_range(isl_multi_aff_get_space(ma)); space = isl_space_drop_all_params(space); mv = isl_multi_val_zero(space); for (i = 0; i < n; ++i) { isl_aff *aff; isl_val *val; aff = isl_multi_aff_get_at(ma, i); val = isl_aff_get_constant_val(aff); isl_aff_free(aff); mv = isl_multi_val_set_at(mv, i, val); } return mv; } /* Remove any internal structure of the domain of "ma". * If there is any such internal structure in the input, * then the name of the corresponding space is also removed. */ __isl_give isl_multi_aff *isl_multi_aff_flatten_domain( __isl_take isl_multi_aff *ma) { isl_space *space; if (!ma) return NULL; if (!ma->space->nested[0]) return ma; space = isl_multi_aff_get_space(ma); space = isl_space_flatten_domain(space); ma = isl_multi_aff_reset_space(ma, space); return ma; } /* Given a map space, return an isl_multi_aff that maps a wrapped copy * of the space to its domain. */ __isl_give isl_multi_aff *isl_multi_aff_domain_map(__isl_take isl_space *space) { int i; isl_size n_in; isl_local_space *ls; isl_multi_aff *ma; if (!space) return NULL; if (!isl_space_is_map(space)) isl_die(isl_space_get_ctx(space), isl_error_invalid, "not a map space", goto error); n_in = isl_space_dim(space, isl_dim_in); if (n_in < 0) goto error; space = isl_space_domain_map(space); ma = isl_multi_aff_alloc(isl_space_copy(space)); if (n_in == 0) { isl_space_free(space); return ma; } space = isl_space_domain(space); ls = isl_local_space_from_space(space); for (i = 0; i < n_in; ++i) { isl_aff *aff; aff = isl_aff_var_on_domain(isl_local_space_copy(ls), isl_dim_set, i); ma = isl_multi_aff_set_aff(ma, i, aff); } isl_local_space_free(ls); return ma; error: isl_space_free(space); return NULL; } /* This function performs the same operation as isl_multi_aff_domain_map, * but is considered as a function on an isl_space when exported. */ __isl_give isl_multi_aff *isl_space_domain_map_multi_aff( __isl_take isl_space *space) { return isl_multi_aff_domain_map(space); } /* Given a map space, return an isl_multi_aff that maps a wrapped copy * of the space to its range. */ __isl_give isl_multi_aff *isl_multi_aff_range_map(__isl_take isl_space *space) { int i; isl_size n_in, n_out; isl_local_space *ls; isl_multi_aff *ma; if (!space) return NULL; if (!isl_space_is_map(space)) isl_die(isl_space_get_ctx(space), isl_error_invalid, "not a map space", goto error); n_in = isl_space_dim(space, isl_dim_in); n_out = isl_space_dim(space, isl_dim_out); if (n_in < 0 || n_out < 0) goto error; space = isl_space_range_map(space); ma = isl_multi_aff_alloc(isl_space_copy(space)); if (n_out == 0) { isl_space_free(space); return ma; } space = isl_space_domain(space); ls = isl_local_space_from_space(space); for (i = 0; i < n_out; ++i) { isl_aff *aff; aff = isl_aff_var_on_domain(isl_local_space_copy(ls), isl_dim_set, n_in + i); ma = isl_multi_aff_set_aff(ma, i, aff); } isl_local_space_free(ls); return ma; error: isl_space_free(space); return NULL; } /* This function performs the same operation as isl_multi_aff_range_map, * but is considered as a function on an isl_space when exported. */ __isl_give isl_multi_aff *isl_space_range_map_multi_aff( __isl_take isl_space *space) { return isl_multi_aff_range_map(space); } /* Given a map space, return an isl_pw_multi_aff that maps a wrapped copy * of the space to its domain. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_domain_map( __isl_take isl_space *space) { return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_domain_map(space)); } /* This function performs the same operation as isl_pw_multi_aff_domain_map, * but is considered as a function on an isl_space when exported. */ __isl_give isl_pw_multi_aff *isl_space_domain_map_pw_multi_aff( __isl_take isl_space *space) { return isl_pw_multi_aff_domain_map(space); } /* Given a map space, return an isl_pw_multi_aff that maps a wrapped copy * of the space to its range. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map( __isl_take isl_space *space) { return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_range_map(space)); } /* This function performs the same operation as isl_pw_multi_aff_range_map, * but is considered as a function on an isl_space when exported. */ __isl_give isl_pw_multi_aff *isl_space_range_map_pw_multi_aff( __isl_take isl_space *space) { return isl_pw_multi_aff_range_map(space); } /* Given the space of a set and a range of set dimensions, * construct an isl_multi_aff that projects out those dimensions. */ __isl_give isl_multi_aff *isl_multi_aff_project_out_map( __isl_take isl_space *space, enum isl_dim_type type, unsigned first, unsigned n) { int i; isl_size dim; isl_local_space *ls; isl_multi_aff *ma; if (!space) return NULL; if (!isl_space_is_set(space)) isl_die(isl_space_get_ctx(space), isl_error_unsupported, "expecting set space", goto error); if (type != isl_dim_set) isl_die(isl_space_get_ctx(space), isl_error_invalid, "only set dimensions can be projected out", goto error); if (isl_space_check_range(space, type, first, n) < 0) goto error; dim = isl_space_dim(space, isl_dim_set); if (dim < 0) goto error; space = isl_space_from_domain(space); space = isl_space_add_dims(space, isl_dim_out, dim - n); if (dim == n) return isl_multi_aff_alloc(space); ma = isl_multi_aff_alloc(isl_space_copy(space)); space = isl_space_domain(space); ls = isl_local_space_from_space(space); for (i = 0; i < first; ++i) { isl_aff *aff; aff = isl_aff_var_on_domain(isl_local_space_copy(ls), isl_dim_set, i); ma = isl_multi_aff_set_aff(ma, i, aff); } for (i = 0; i < dim - (first + n); ++i) { isl_aff *aff; aff = isl_aff_var_on_domain(isl_local_space_copy(ls), isl_dim_set, first + n + i); ma = isl_multi_aff_set_aff(ma, first + i, aff); } isl_local_space_free(ls); return ma; error: isl_space_free(space); return NULL; } /* Given the space of a set and a range of set dimensions, * construct an isl_pw_multi_aff that projects out those dimensions. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_project_out_map( __isl_take isl_space *space, enum isl_dim_type type, unsigned first, unsigned n) { isl_multi_aff *ma; ma = isl_multi_aff_project_out_map(space, type, first, n); return isl_pw_multi_aff_from_multi_aff(ma); } /* This function performs the same operation as isl_pw_multi_aff_from_multi_aff, * but is considered as a function on an isl_multi_aff when exported. */ __isl_give isl_pw_multi_aff *isl_multi_aff_to_pw_multi_aff( __isl_take isl_multi_aff *ma) { return isl_pw_multi_aff_from_multi_aff(ma); } /* Create a piecewise multi-affine expression in the given space that maps each * input dimension to the corresponding output dimension. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity( __isl_take isl_space *space) { return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_identity(space)); } /* Create a piecewise multi expression that maps elements in the given space * to themselves. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity_on_domain_space( __isl_take isl_space *space) { isl_multi_aff *ma; ma = isl_multi_aff_identity_on_domain_space(space); return isl_pw_multi_aff_from_multi_aff(ma); } /* This function performs the same operation as * isl_pw_multi_aff_identity_on_domain_space, * but is considered as a function on an isl_space when exported. */ __isl_give isl_pw_multi_aff *isl_space_identity_pw_multi_aff_on_domain( __isl_take isl_space *space) { return isl_pw_multi_aff_identity_on_domain_space(space); } /* Exploit the equalities in "eq" to simplify the affine expressions. */ static __isl_give isl_multi_aff *isl_multi_aff_substitute_equalities( __isl_take isl_multi_aff *maff, __isl_take isl_basic_set *eq) { int i; maff = isl_multi_aff_cow(maff); if (!maff || !eq) goto error; for (i = 0; i < maff->n; ++i) { maff->u.p[i] = isl_aff_substitute_equalities(maff->u.p[i], isl_basic_set_copy(eq)); if (!maff->u.p[i]) goto error; } isl_basic_set_free(eq); return maff; error: isl_basic_set_free(eq); isl_multi_aff_free(maff); return NULL; } __isl_give isl_multi_aff *isl_multi_aff_scale(__isl_take isl_multi_aff *maff, isl_int f) { int i; maff = isl_multi_aff_cow(maff); if (!maff) return NULL; for (i = 0; i < maff->n; ++i) { maff->u.p[i] = isl_aff_scale(maff->u.p[i], f); if (!maff->u.p[i]) return isl_multi_aff_free(maff); } return maff; } __isl_give isl_multi_aff *isl_multi_aff_add_on_domain(__isl_keep isl_set *dom, __isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2) { maff1 = isl_multi_aff_add(maff1, maff2); maff1 = isl_multi_aff_gist(maff1, isl_set_copy(dom)); return maff1; } isl_bool isl_multi_aff_is_empty(__isl_keep isl_multi_aff *maff) { if (!maff) return isl_bool_error; return isl_bool_false; } /* Return the set of domain elements where "ma1" is lexicographically * smaller than or equal to "ma2". */ __isl_give isl_set *isl_multi_aff_lex_le_set(__isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2) { return isl_multi_aff_lex_ge_set(ma2, ma1); } /* Return the set of domain elements where "ma1" is lexicographically * smaller than "ma2". */ __isl_give isl_set *isl_multi_aff_lex_lt_set(__isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2) { return isl_multi_aff_lex_gt_set(ma2, ma1); } /* Return the set of domain elements where "ma1" is lexicographically * greater than to "ma2". If "equal" is set, then include the domain * elements where they are equal. * Do this for the case where there are no entries. * In this case, "ma1" cannot be greater than "ma2", * but it is (greater than or) equal to "ma2". */ static __isl_give isl_set *isl_multi_aff_lex_gte_set_0d( __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2, int equal) { isl_space *space; space = isl_multi_aff_get_domain_space(ma1); isl_multi_aff_free(ma1); isl_multi_aff_free(ma2); if (equal) return isl_set_universe(space); else return isl_set_empty(space); } /* Return the set where entry "i" of "ma1" and "ma2" * satisfy the relation prescribed by "cmp". */ static __isl_give isl_set *isl_multi_aff_order_at(__isl_keep isl_multi_aff *ma1, __isl_keep isl_multi_aff *ma2, int i, __isl_give isl_set *(*cmp)(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2)) { isl_aff *aff1, *aff2; aff1 = isl_multi_aff_get_at(ma1, i); aff2 = isl_multi_aff_get_at(ma2, i); return cmp(aff1, aff2); } /* Return the set of domain elements where "ma1" is lexicographically * greater than to "ma2". If "equal" is set, then include the domain * elements where they are equal. * * In particular, for all but the final entry, * include the set of elements where this entry is strictly greater in "ma1" * and all previous entries are equal. * The final entry is also allowed to be equal in the two functions * if "equal" is set. * * The case where there are no entries is handled separately. */ static __isl_give isl_set *isl_multi_aff_lex_gte_set( __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2, int equal) { int i; isl_size n; isl_space *space; isl_set *res; isl_set *equal_set; isl_set *gte; if (isl_multi_aff_check_equal_space(ma1, ma2) < 0) goto error; n = isl_multi_aff_size(ma1); if (n < 0) goto error; if (n == 0) return isl_multi_aff_lex_gte_set_0d(ma1, ma2, equal); space = isl_multi_aff_get_domain_space(ma1); res = isl_set_empty(isl_space_copy(space)); equal_set = isl_set_universe(space); for (i = 0; i + 1 < n; ++i) { isl_bool empty; isl_set *gt, *eq; gt = isl_multi_aff_order_at(ma1, ma2, i, &isl_aff_gt_set); gt = isl_set_intersect(gt, isl_set_copy(equal_set)); res = isl_set_union(res, gt); eq = isl_multi_aff_order_at(ma1, ma2, i, &isl_aff_eq_set); equal_set = isl_set_intersect(equal_set, eq); empty = isl_set_is_empty(equal_set); if (empty >= 0 && empty) break; } if (equal) gte = isl_multi_aff_order_at(ma1, ma2, n - 1, &isl_aff_ge_set); else gte = isl_multi_aff_order_at(ma1, ma2, n - 1, &isl_aff_gt_set); isl_multi_aff_free(ma1); isl_multi_aff_free(ma2); gte = isl_set_intersect(gte, equal_set); return isl_set_union(res, gte); error: isl_multi_aff_free(ma1); isl_multi_aff_free(ma2); return NULL; } /* Return the set of domain elements where "ma1" is lexicographically * greater than or equal to "ma2". */ __isl_give isl_set *isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2) { return isl_multi_aff_lex_gte_set(ma1, ma2, 1); } /* Return the set of domain elements where "ma1" is lexicographically * greater than "ma2". */ __isl_give isl_set *isl_multi_aff_lex_gt_set(__isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2) { return isl_multi_aff_lex_gte_set(ma1, ma2, 0); } #define isl_multi_aff_zero_in_space isl_multi_aff_zero #undef PW #define PW isl_pw_multi_aff #undef BASE #define BASE multi_aff #undef EL_IS_ZERO #define EL_IS_ZERO is_empty #undef ZERO #define ZERO empty #undef IS_ZERO #define IS_ZERO is_empty #undef FIELD #define FIELD maff #undef DEFAULT_IS_ZERO #define DEFAULT_IS_ZERO 0 #include #include #include #include #include #include #include #include #include #include #include #include #undef BASE #define BASE pw_multi_aff #include #include "isl_union_locals_templ.c" #include #undef BASE #define BASE multi_aff #include /* Generic function for extracting a factor from a product "pma". * "check_space" checks that the space is that of the right kind of product. * "space_factor" extracts the factor from the space. * "multi_aff_factor" extracts the factor from the constituent functions. */ static __isl_give isl_pw_multi_aff *pw_multi_aff_factor( __isl_take isl_pw_multi_aff *pma, isl_stat (*check_space)(__isl_keep isl_pw_multi_aff *pma), __isl_give isl_space *(*space_factor)(__isl_take isl_space *space), __isl_give isl_multi_aff *(*multi_aff_factor)( __isl_take isl_multi_aff *ma)) { int i; isl_space *space; if (check_space(pma) < 0) return isl_pw_multi_aff_free(pma); space = isl_pw_multi_aff_take_space(pma); space = space_factor(space); for (i = 0; pma && i < pma->n; ++i) { isl_multi_aff *ma; ma = isl_pw_multi_aff_take_base_at(pma, i); ma = multi_aff_factor(ma); pma = isl_pw_multi_aff_restore_base_at(pma, i, ma); } pma = isl_pw_multi_aff_restore_space(pma, space); return pma; } /* Is the range of "pma" a wrapped relation? */ static isl_bool isl_pw_multi_aff_range_is_wrapping( __isl_keep isl_pw_multi_aff *pma) { return isl_space_range_is_wrapping(isl_pw_multi_aff_peek_space(pma)); } /* Check that the range of "pma" is a product. */ static isl_stat pw_multi_aff_check_range_product( __isl_keep isl_pw_multi_aff *pma) { isl_bool wraps; wraps = isl_pw_multi_aff_range_is_wrapping(pma); if (wraps < 0) return isl_stat_error; if (!wraps) isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid, "range is not a product", return isl_stat_error); return isl_stat_ok; } /* Given a function A -> [B -> C], extract the function A -> B. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_factor_domain( __isl_take isl_pw_multi_aff *pma) { return pw_multi_aff_factor(pma, &pw_multi_aff_check_range_product, &isl_space_range_factor_domain, &isl_multi_aff_range_factor_domain); } /* Given a function A -> [B -> C], extract the function A -> C. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_factor_range( __isl_take isl_pw_multi_aff *pma) { return pw_multi_aff_factor(pma, &pw_multi_aff_check_range_product, &isl_space_range_factor_range, &isl_multi_aff_range_factor_range); } /* Given two piecewise multi affine expressions, return a piecewise * multi-affine expression defined on the union of the definition domains * of the inputs that is equal to the lexicographic maximum of the two * inputs on each cell. If only one of the two inputs is defined on * a given cell, then it is considered to be the maximum. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { isl_pw_multi_aff_align_params_bin(&pma1, &pma2); return isl_pw_multi_aff_union_opt_cmp(pma1, pma2, &isl_multi_aff_lex_ge_set); } /* Given two piecewise multi affine expressions, return a piecewise * multi-affine expression defined on the union of the definition domains * of the inputs that is equal to the lexicographic minimum of the two * inputs on each cell. If only one of the two inputs is defined on * a given cell, then it is considered to be the minimum. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { isl_pw_multi_aff_align_params_bin(&pma1, &pma2); return isl_pw_multi_aff_union_opt_cmp(pma1, pma2, &isl_multi_aff_lex_le_set); } __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { isl_pw_multi_aff_align_params_bin(&pma1, &pma2); return isl_pw_multi_aff_on_shared_domain(pma1, pma2, &isl_multi_aff_add); } /* Subtract "pma2" from "pma1" and return the result. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { isl_pw_multi_aff_align_params_bin(&pma1, &pma2); return isl_pw_multi_aff_on_shared_domain(pma1, pma2, &isl_multi_aff_sub); } __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { return isl_pw_multi_aff_union_add_(pma1, pma2); } /* Compute the sum of "upa1" and "upa2" on the union of their domains, * with the actual sum on the shared domain and * the defined expression on the symmetric difference of the domains. */ __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add( __isl_take isl_union_pw_aff *upa1, __isl_take isl_union_pw_aff *upa2) { return isl_union_pw_aff_union_add_(upa1, upa2); } /* Compute the sum of "upma1" and "upma2" on the union of their domains, * with the actual sum on the shared domain and * the defined expression on the symmetric difference of the domains. */ __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_union_add( __isl_take isl_union_pw_multi_aff *upma1, __isl_take isl_union_pw_multi_aff *upma2) { return isl_union_pw_multi_aff_union_add_(upma1, upma2); } /* Given two piecewise multi-affine expressions A -> B and C -> D, * construct a piecewise multi-affine expression [A -> C] -> [B -> D]. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { int i, j, n; isl_space *space; isl_pw_multi_aff *res; if (isl_pw_multi_aff_align_params_bin(&pma1, &pma2) < 0) goto error; n = pma1->n * pma2->n; space = isl_space_product(isl_space_copy(pma1->dim), isl_space_copy(pma2->dim)); res = isl_pw_multi_aff_alloc_size(space, n); for (i = 0; i < pma1->n; ++i) { for (j = 0; j < pma2->n; ++j) { isl_set *domain; isl_multi_aff *ma; domain = isl_set_product(isl_set_copy(pma1->p[i].set), isl_set_copy(pma2->p[j].set)); ma = isl_multi_aff_product( isl_multi_aff_copy(pma1->p[i].maff), isl_multi_aff_copy(pma2->p[j].maff)); res = isl_pw_multi_aff_add_piece(res, domain, ma); } } isl_pw_multi_aff_free(pma1); isl_pw_multi_aff_free(pma2); return res; error: isl_pw_multi_aff_free(pma1); isl_pw_multi_aff_free(pma2); return NULL; } /* Subtract the initial "n" elements in "ma" with coefficients in "c" and * denominator "denom". * "denom" is allowed to be negative, in which case the actual denominator * is -denom and the expressions are added instead. */ static __isl_give isl_aff *subtract_initial(__isl_take isl_aff *aff, __isl_keep isl_multi_aff *ma, int n, isl_int *c, isl_int denom) { int i, first; int sign; isl_int d; first = isl_seq_first_non_zero(c, n); if (first == -1) return aff; sign = isl_int_sgn(denom); isl_int_init(d); isl_int_abs(d, denom); for (i = first; i < n; ++i) { isl_aff *aff_i; if (isl_int_is_zero(c[i])) continue; aff_i = isl_multi_aff_get_aff(ma, i); aff_i = isl_aff_scale(aff_i, c[i]); aff_i = isl_aff_scale_down(aff_i, d); if (sign >= 0) aff = isl_aff_sub(aff, aff_i); else aff = isl_aff_add(aff, aff_i); } isl_int_clear(d); return aff; } /* Extract an affine expression that expresses the output dimension "pos" * of "bmap" in terms of the parameters and input dimensions from * equality "eq". * Note that this expression may involve integer divisions defined * in terms of parameters and input dimensions. * The equality may also involve references to earlier (but not later) * output dimensions. These are replaced by the corresponding elements * in "ma". * * If the equality is of the form * * f(i) + h(j) + a x + g(i) = 0, * * with f(i) a linear combinations of the parameters and input dimensions, * g(i) a linear combination of integer divisions defined in terms of the same * and h(j) a linear combinations of earlier output dimensions, * then the affine expression is * * (-f(i) - g(i))/a - h(j)/a * * If the equality is of the form * * f(i) + h(j) - a x + g(i) = 0, * * then the affine expression is * * (f(i) + g(i))/a - h(j)/(-a) * * * If "div" refers to an integer division (i.e., it is smaller than * the number of integer divisions), then the equality constraint * does involve an integer division (the one at position "div") that * is defined in terms of output dimensions. However, this integer * division can be eliminated by exploiting a pair of constraints * x >= l and x <= l + n, with n smaller than the coefficient of "div" * in the equality constraint. "ineq" refers to inequality x >= l, i.e., * -l + x >= 0. * In particular, let * * x = e(i) + m floor(...) * * with e(i) the expression derived above and floor(...) the integer * division involving output dimensions. * From * * l <= x <= l + n, * * we have * * 0 <= x - l <= n * * This means * * e(i) + m floor(...) - l = (e(i) + m floor(...) - l) mod m * = (e(i) - l) mod m * * Therefore, * * x - l = (e(i) - l) mod m * * or * * x = ((e(i) - l) mod m) + l * * The variable "shift" below contains the expression -l, which may * also involve a linear combination of earlier output dimensions. */ static __isl_give isl_aff *extract_aff_from_equality( __isl_keep isl_basic_map *bmap, int pos, int eq, int div, int ineq, __isl_keep isl_multi_aff *ma) { unsigned o_out; isl_size n_div, n_out; isl_ctx *ctx; isl_local_space *ls; isl_aff *aff, *shift; isl_val *mod; ctx = isl_basic_map_get_ctx(bmap); ls = isl_basic_map_get_local_space(bmap); ls = isl_local_space_domain(ls); aff = isl_aff_alloc(isl_local_space_copy(ls)); if (!aff) goto error; o_out = isl_basic_map_offset(bmap, isl_dim_out); n_out = isl_basic_map_dim(bmap, isl_dim_out); n_div = isl_basic_map_dim(bmap, isl_dim_div); if (n_out < 0 || n_div < 0) goto error; if (isl_int_is_neg(bmap->eq[eq][o_out + pos])) { isl_seq_cpy(aff->v->el + 1, bmap->eq[eq], o_out); isl_seq_cpy(aff->v->el + 1 + o_out, bmap->eq[eq] + o_out + n_out, n_div); } else { isl_seq_neg(aff->v->el + 1, bmap->eq[eq], o_out); isl_seq_neg(aff->v->el + 1 + o_out, bmap->eq[eq] + o_out + n_out, n_div); } if (div < n_div) isl_int_set_si(aff->v->el[1 + o_out + div], 0); isl_int_abs(aff->v->el[0], bmap->eq[eq][o_out + pos]); aff = subtract_initial(aff, ma, pos, bmap->eq[eq] + o_out, bmap->eq[eq][o_out + pos]); if (div < n_div) { shift = isl_aff_alloc(isl_local_space_copy(ls)); if (!shift) goto error; isl_seq_cpy(shift->v->el + 1, bmap->ineq[ineq], o_out); isl_seq_cpy(shift->v->el + 1 + o_out, bmap->ineq[ineq] + o_out + n_out, n_div); isl_int_set_si(shift->v->el[0], 1); shift = subtract_initial(shift, ma, pos, bmap->ineq[ineq] + o_out, ctx->negone); aff = isl_aff_add(aff, isl_aff_copy(shift)); mod = isl_val_int_from_isl_int(ctx, bmap->eq[eq][o_out + n_out + div]); mod = isl_val_abs(mod); aff = isl_aff_mod_val(aff, mod); aff = isl_aff_sub(aff, shift); } isl_local_space_free(ls); return aff; error: isl_local_space_free(ls); isl_aff_free(aff); return NULL; } /* Given a basic map with output dimensions defined * in terms of the parameters input dimensions and earlier * output dimensions using an equality (and possibly a pair on inequalities), * extract an isl_aff that expresses output dimension "pos" in terms * of the parameters and input dimensions. * Note that this expression may involve integer divisions defined * in terms of parameters and input dimensions. * "ma" contains the expressions corresponding to earlier output dimensions. * * This function shares some similarities with * isl_basic_map_has_defining_equality and isl_constraint_get_bound. */ static __isl_give isl_aff *extract_isl_aff_from_basic_map( __isl_keep isl_basic_map *bmap, int pos, __isl_keep isl_multi_aff *ma) { int eq, div, ineq; isl_aff *aff; if (!bmap) return NULL; eq = isl_basic_map_output_defining_equality(bmap, pos, &div, &ineq); if (eq >= bmap->n_eq) isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid, "unable to find suitable equality", return NULL); aff = extract_aff_from_equality(bmap, pos, eq, div, ineq, ma); aff = isl_aff_remove_unused_divs(aff); return aff; } /* Given a basic map where each output dimension is defined * in terms of the parameters and input dimensions using an equality, * extract an isl_multi_aff that expresses the output dimensions in terms * of the parameters and input dimensions. */ static __isl_give isl_multi_aff *extract_isl_multi_aff_from_basic_map( __isl_take isl_basic_map *bmap) { int i; isl_size n_out; isl_multi_aff *ma; if (!bmap) return NULL; ma = isl_multi_aff_alloc(isl_basic_map_get_space(bmap)); n_out = isl_basic_map_dim(bmap, isl_dim_out); if (n_out < 0) ma = isl_multi_aff_free(ma); for (i = 0; i < n_out; ++i) { isl_aff *aff; aff = extract_isl_aff_from_basic_map(bmap, i, ma); ma = isl_multi_aff_set_aff(ma, i, aff); } isl_basic_map_free(bmap); return ma; } /* Given a basic set where each set dimension is defined * in terms of the parameters using an equality, * extract an isl_multi_aff that expresses the set dimensions in terms * of the parameters. */ __isl_give isl_multi_aff *isl_multi_aff_from_basic_set_equalities( __isl_take isl_basic_set *bset) { return extract_isl_multi_aff_from_basic_map(bset); } /* Create an isl_pw_multi_aff that is equivalent to * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain). * The given basic map is such that each output dimension is defined * in terms of the parameters and input dimensions using an equality. * * Since some applications expect the result of isl_pw_multi_aff_from_map * to only contain integer affine expressions, we compute the floor * of the expression before returning. * * Remove all constraints involving local variables without * an explicit representation (resulting in the removal of those * local variables) prior to the actual extraction to ensure * that the local spaces in which the resulting affine expressions * are created do not contain any unknown local variables. * Removing such constraints is safe because constraints involving * unknown local variables are not used to determine whether * a basic map is obviously single-valued. */ static __isl_give isl_pw_multi_aff *plain_pw_multi_aff_from_map( __isl_take isl_set *domain, __isl_take isl_basic_map *bmap) { isl_multi_aff *ma; bmap = isl_basic_map_drop_constraints_involving_unknown_divs(bmap); ma = extract_isl_multi_aff_from_basic_map(bmap); ma = isl_multi_aff_floor(ma); return isl_pw_multi_aff_alloc(domain, ma); } /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map. * This obviously only works if the input "map" is single-valued. * If so, we compute the lexicographic minimum of the image in the form * of an isl_pw_multi_aff. Since the image is unique, it is equal * to its lexicographic minimum. * If the input is not single-valued, we produce an error. */ static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_base( __isl_take isl_map *map) { int i; int sv; isl_pw_multi_aff *pma; sv = isl_map_is_single_valued(map); if (sv < 0) goto error; if (!sv) isl_die(isl_map_get_ctx(map), isl_error_invalid, "map is not single-valued", goto error); map = isl_map_make_disjoint(map); if (!map) return NULL; pma = isl_pw_multi_aff_empty(isl_map_get_space(map)); for (i = 0; i < map->n; ++i) { isl_pw_multi_aff *pma_i; isl_basic_map *bmap; bmap = isl_basic_map_copy(map->p[i]); pma_i = isl_basic_map_lexmin_pw_multi_aff(bmap); pma = isl_pw_multi_aff_add_disjoint(pma, pma_i); } isl_map_free(map); return pma; error: isl_map_free(map); return NULL; } /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map, * taking into account that the output dimension at position "d" * can be represented as * * x = floor((e(...) + c1) / m) * * given that constraint "i" is of the form * * e(...) + c1 - m x >= 0 * * * Let "map" be of the form * * A -> B * * We construct a mapping * * A -> [A -> x = floor(...)] * * apply that to the map, obtaining * * [A -> x = floor(...)] -> B * * and equate dimension "d" to x. * We then compute a isl_pw_multi_aff representation of the resulting map * and plug in the mapping above. */ static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_div( __isl_take isl_map *map, __isl_take isl_basic_map *hull, int d, int i) { isl_ctx *ctx; isl_space *space = NULL; isl_local_space *ls; isl_multi_aff *ma; isl_aff *aff; isl_vec *v; isl_map *insert; int offset; isl_size n; isl_size n_in; isl_pw_multi_aff *pma; isl_bool is_set; is_set = isl_map_is_set(map); if (is_set < 0) goto error; offset = isl_basic_map_offset(hull, isl_dim_out); ctx = isl_map_get_ctx(map); space = isl_space_domain(isl_map_get_space(map)); n_in = isl_space_dim(space, isl_dim_set); n = isl_space_dim(space, isl_dim_all); if (n_in < 0 || n < 0) goto error; v = isl_vec_alloc(ctx, 1 + 1 + n); if (v) { isl_int_neg(v->el[0], hull->ineq[i][offset + d]); isl_seq_cpy(v->el + 1, hull->ineq[i], 1 + n); } isl_basic_map_free(hull); ls = isl_local_space_from_space(isl_space_copy(space)); aff = isl_aff_alloc_vec(ls, v); aff = isl_aff_floor(aff); if (is_set) { isl_space_free(space); ma = isl_multi_aff_from_aff(aff); } else { ma = isl_multi_aff_identity(isl_space_map_from_set(space)); ma = isl_multi_aff_range_product(ma, isl_multi_aff_from_aff(aff)); } insert = isl_map_from_multi_aff_internal(isl_multi_aff_copy(ma)); map = isl_map_apply_domain(map, insert); map = isl_map_equate(map, isl_dim_in, n_in, isl_dim_out, d); pma = isl_pw_multi_aff_from_map(map); pma = isl_pw_multi_aff_pullback_multi_aff(pma, ma); return pma; error: isl_space_free(space); isl_map_free(map); isl_basic_map_free(hull); return NULL; } /* Is constraint "c" of the form * * e(...) + c1 - m x >= 0 * * or * * -e(...) + c2 + m x >= 0 * * where m > 1 and e only depends on parameters and input dimensions? * * "offset" is the offset of the output dimensions * "pos" is the position of output dimension x. */ static int is_potential_div_constraint(isl_int *c, int offset, int d, int total) { if (isl_int_is_zero(c[offset + d])) return 0; if (isl_int_is_one(c[offset + d])) return 0; if (isl_int_is_negone(c[offset + d])) return 0; if (isl_seq_first_non_zero(c + offset, d) != -1) return 0; if (isl_seq_first_non_zero(c + offset + d + 1, total - (offset + d + 1)) != -1) return 0; return 1; } /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map. * * As a special case, we first check if there is any pair of constraints, * shared by all the basic maps in "map" that force a given dimension * to be equal to the floor of some affine combination of the input dimensions. * * In particular, if we can find two constraints * * e(...) + c1 - m x >= 0 i.e., m x <= e(...) + c1 * * and * * -e(...) + c2 + m x >= 0 i.e., m x >= e(...) - c2 * * where m > 1 and e only depends on parameters and input dimensions, * and such that * * c1 + c2 < m i.e., -c2 >= c1 - (m - 1) * * then we know that we can take * * x = floor((e(...) + c1) / m) * * without having to perform any computation. * * Note that we know that * * c1 + c2 >= 1 * * If c1 + c2 were 0, then we would have detected an equality during * simplification. If c1 + c2 were negative, then we would have detected * a contradiction. */ static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_check_div( __isl_take isl_map *map) { int d; isl_size dim; int i, j, n; int offset; isl_size total; isl_int sum; isl_basic_map *hull; hull = isl_map_unshifted_simple_hull(isl_map_copy(map)); dim = isl_map_dim(map, isl_dim_out); total = isl_basic_map_dim(hull, isl_dim_all); if (dim < 0 || total < 0) goto error; isl_int_init(sum); offset = isl_basic_map_offset(hull, isl_dim_out); n = hull->n_ineq; for (d = 0; d < dim; ++d) { for (i = 0; i < n; ++i) { if (!is_potential_div_constraint(hull->ineq[i], offset, d, 1 + total)) continue; for (j = i + 1; j < n; ++j) { if (!isl_seq_is_neg(hull->ineq[i] + 1, hull->ineq[j] + 1, total)) continue; isl_int_add(sum, hull->ineq[i][0], hull->ineq[j][0]); if (isl_int_abs_lt(sum, hull->ineq[i][offset + d])) break; } if (j >= n) continue; isl_int_clear(sum); if (isl_int_is_pos(hull->ineq[j][offset + d])) j = i; return pw_multi_aff_from_map_div(map, hull, d, j); } } isl_int_clear(sum); isl_basic_map_free(hull); return pw_multi_aff_from_map_base(map); error: isl_map_free(map); isl_basic_map_free(hull); return NULL; } /* Given an affine expression * * [A -> B] -> f(A,B) * * construct an isl_multi_aff * * [A -> B] -> B' * * such that dimension "d" in B' is set to "aff" and the remaining * dimensions are set equal to the corresponding dimensions in B. * "n_in" is the dimension of the space A. * "n_out" is the dimension of the space B. * * If "is_set" is set, then the affine expression is of the form * * [B] -> f(B) * * and we construct an isl_multi_aff * * B -> B' */ static __isl_give isl_multi_aff *range_map(__isl_take isl_aff *aff, int d, unsigned n_in, unsigned n_out, int is_set) { int i; isl_multi_aff *ma; isl_space *space, *space2; isl_local_space *ls; space = isl_aff_get_domain_space(aff); ls = isl_local_space_from_space(isl_space_copy(space)); space2 = isl_space_copy(space); if (!is_set) space2 = isl_space_range(isl_space_unwrap(space2)); space = isl_space_map_from_domain_and_range(space, space2); ma = isl_multi_aff_alloc(space); ma = isl_multi_aff_set_aff(ma, d, aff); for (i = 0; i < n_out; ++i) { if (i == d) continue; aff = isl_aff_var_on_domain(isl_local_space_copy(ls), isl_dim_set, n_in + i); ma = isl_multi_aff_set_aff(ma, i, aff); } isl_local_space_free(ls); return ma; } /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map, * taking into account that the dimension at position "d" can be written as * * x = m a + f(..) (1) * * where m is equal to "gcd". * "i" is the index of the equality in "hull" that defines f(..). * In particular, the equality is of the form * * f(..) - x + m g(existentials) = 0 * * or * * -f(..) + x + m g(existentials) = 0 * * We basically plug (1) into "map", resulting in a map with "a" * in the range instead of "x". The corresponding isl_pw_multi_aff * defining "a" is then plugged back into (1) to obtain a definition for "x". * * Specifically, given the input map * * A -> B * * We first wrap it into a set * * [A -> B] * * and define (1) on top of the corresponding space, resulting in "aff". * We use this to create an isl_multi_aff that maps the output position "d" * from "a" to "x", leaving all other (intput and output) dimensions unchanged. * We plug this into the wrapped map, unwrap the result and compute the * corresponding isl_pw_multi_aff. * The result is an expression * * A -> T(A) * * We adjust that to * * A -> [A -> T(A)] * * so that we can plug that into "aff", after extending the latter to * a mapping * * [A -> B] -> B' * * * If "map" is actually a set, then there is no "A" space, meaning * that we do not need to perform any wrapping, and that the result * of the recursive call is of the form * * [T] * * which is plugged into a mapping of the form * * B -> B' */ static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_stride( __isl_take isl_map *map, __isl_take isl_basic_map *hull, int d, int i, isl_int gcd) { isl_set *set; isl_space *space; isl_local_space *ls; isl_aff *aff; isl_multi_aff *ma; isl_pw_multi_aff *pma, *id; isl_size n_in; unsigned o_out; isl_size n_out; isl_bool is_set; is_set = isl_map_is_set(map); if (is_set < 0) goto error; n_in = isl_basic_map_dim(hull, isl_dim_in); n_out = isl_basic_map_dim(hull, isl_dim_out); if (n_in < 0 || n_out < 0) goto error; o_out = isl_basic_map_offset(hull, isl_dim_out); if (is_set) set = map; else set = isl_map_wrap(map); space = isl_space_map_from_set(isl_set_get_space(set)); ma = isl_multi_aff_identity(space); ls = isl_local_space_from_space(isl_set_get_space(set)); aff = isl_aff_alloc(ls); if (aff) { isl_int_set_si(aff->v->el[0], 1); if (isl_int_is_one(hull->eq[i][o_out + d])) isl_seq_neg(aff->v->el + 1, hull->eq[i], aff->v->size - 1); else isl_seq_cpy(aff->v->el + 1, hull->eq[i], aff->v->size - 1); isl_int_set(aff->v->el[1 + o_out + d], gcd); } ma = isl_multi_aff_set_aff(ma, n_in + d, isl_aff_copy(aff)); set = isl_set_preimage_multi_aff(set, ma); ma = range_map(aff, d, n_in, n_out, is_set); if (is_set) map = set; else map = isl_set_unwrap(set); pma = isl_pw_multi_aff_from_map(map); if (!is_set) { space = isl_pw_multi_aff_get_domain_space(pma); space = isl_space_map_from_set(space); id = isl_pw_multi_aff_identity(space); pma = isl_pw_multi_aff_range_product(id, pma); } id = isl_pw_multi_aff_from_multi_aff(ma); pma = isl_pw_multi_aff_pullback_pw_multi_aff(id, pma); isl_basic_map_free(hull); return pma; error: isl_map_free(map); isl_basic_map_free(hull); return NULL; } /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map. * "hull" contains the equalities valid for "map". * * Check if any of the output dimensions is "strided". * That is, we check if it can be written as * * x = m a + f(..) * * with m greater than 1, a some combination of existentially quantified * variables and f an expression in the parameters and input dimensions. * If so, we remove the stride in pw_multi_aff_from_map_stride. * * Otherwise, we continue with pw_multi_aff_from_map_check_div for a further * special case. */ static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_check_strides( __isl_take isl_map *map, __isl_take isl_basic_map *hull) { int i, j; isl_size n_out; unsigned o_out; isl_size n_div; unsigned o_div; isl_int gcd; n_div = isl_basic_map_dim(hull, isl_dim_div); n_out = isl_basic_map_dim(hull, isl_dim_out); if (n_div < 0 || n_out < 0) goto error; if (n_div == 0) { isl_basic_map_free(hull); return pw_multi_aff_from_map_check_div(map); } isl_int_init(gcd); o_div = isl_basic_map_offset(hull, isl_dim_div); o_out = isl_basic_map_offset(hull, isl_dim_out); for (i = 0; i < n_out; ++i) { for (j = 0; j < hull->n_eq; ++j) { isl_int *eq = hull->eq[j]; isl_pw_multi_aff *res; if (!isl_int_is_one(eq[o_out + i]) && !isl_int_is_negone(eq[o_out + i])) continue; if (isl_seq_first_non_zero(eq + o_out, i) != -1) continue; if (isl_seq_first_non_zero(eq + o_out + i + 1, n_out - (i + 1)) != -1) continue; isl_seq_gcd(eq + o_div, n_div, &gcd); if (isl_int_is_zero(gcd)) continue; if (isl_int_is_one(gcd)) continue; res = pw_multi_aff_from_map_stride(map, hull, i, j, gcd); isl_int_clear(gcd); return res; } } isl_int_clear(gcd); isl_basic_map_free(hull); return pw_multi_aff_from_map_check_div(map); error: isl_map_free(map); isl_basic_map_free(hull); return NULL; } /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map. * * As a special case, we first check if all output dimensions are uniquely * defined in terms of the parameters and input dimensions over the entire * domain. If so, we extract the desired isl_pw_multi_aff directly * from the affine hull of "map" and its domain. * * Otherwise, continue with pw_multi_aff_from_map_check_strides for more * special cases. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(__isl_take isl_map *map) { isl_bool sv; isl_size n; isl_basic_map *hull; n = isl_map_n_basic_map(map); if (n < 0) goto error; if (n == 1) { hull = isl_map_unshifted_simple_hull(isl_map_copy(map)); hull = isl_basic_map_plain_affine_hull(hull); sv = isl_basic_map_plain_is_single_valued(hull); if (sv >= 0 && sv) return plain_pw_multi_aff_from_map(isl_map_domain(map), hull); isl_basic_map_free(hull); } map = isl_map_detect_equalities(map); hull = isl_map_unshifted_simple_hull(isl_map_copy(map)); sv = isl_basic_map_plain_is_single_valued(hull); if (sv >= 0 && sv) return plain_pw_multi_aff_from_map(isl_map_domain(map), hull); if (sv >= 0) return pw_multi_aff_from_map_check_strides(map, hull); isl_basic_map_free(hull); error: isl_map_free(map); return NULL; } /* This function performs the same operation as isl_pw_multi_aff_from_map, * but is considered as a function on an isl_map when exported. */ __isl_give isl_pw_multi_aff *isl_map_as_pw_multi_aff(__isl_take isl_map *map) { return isl_pw_multi_aff_from_map(map); } __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(__isl_take isl_set *set) { return isl_pw_multi_aff_from_map(set); } /* This function performs the same operation as isl_pw_multi_aff_from_set, * but is considered as a function on an isl_set when exported. */ __isl_give isl_pw_multi_aff *isl_set_as_pw_multi_aff(__isl_take isl_set *set) { return isl_pw_multi_aff_from_set(set); } /* Convert "map" into an isl_pw_multi_aff (if possible) and * add it to *user. */ static isl_stat pw_multi_aff_from_map(__isl_take isl_map *map, void *user) { isl_union_pw_multi_aff **upma = user; isl_pw_multi_aff *pma; pma = isl_pw_multi_aff_from_map(map); *upma = isl_union_pw_multi_aff_add_pw_multi_aff(*upma, pma); return *upma ? isl_stat_ok : isl_stat_error; } /* Create an isl_union_pw_multi_aff with the given isl_aff on a universe * domain. */ __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_aff( __isl_take isl_aff *aff) { isl_multi_aff *ma; isl_pw_multi_aff *pma; ma = isl_multi_aff_from_aff(aff); pma = isl_pw_multi_aff_from_multi_aff(ma); return isl_union_pw_multi_aff_from_pw_multi_aff(pma); } /* Try and create an isl_union_pw_multi_aff that is equivalent * to the given isl_union_map. * The isl_union_map is required to be single-valued in each space. * Otherwise, an error is produced. */ __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_union_map( __isl_take isl_union_map *umap) { isl_space *space; isl_union_pw_multi_aff *upma; space = isl_union_map_get_space(umap); upma = isl_union_pw_multi_aff_empty(space); if (isl_union_map_foreach_map(umap, &pw_multi_aff_from_map, &upma) < 0) upma = isl_union_pw_multi_aff_free(upma); isl_union_map_free(umap); return upma; } /* This function performs the same operation as * isl_union_pw_multi_aff_from_union_map, * but is considered as a function on an isl_union_map when exported. */ __isl_give isl_union_pw_multi_aff *isl_union_map_as_union_pw_multi_aff( __isl_take isl_union_map *umap) { return isl_union_pw_multi_aff_from_union_map(umap); } /* Try and create an isl_union_pw_multi_aff that is equivalent * to the given isl_union_set. * The isl_union_set is required to be a singleton in each space. * Otherwise, an error is produced. */ __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_union_set( __isl_take isl_union_set *uset) { return isl_union_pw_multi_aff_from_union_map(uset); } /* Return the piecewise affine expression "set ? 1 : 0". */ __isl_give isl_pw_aff *isl_set_indicator_function(__isl_take isl_set *set) { isl_pw_aff *pa; isl_space *space = isl_set_get_space(set); isl_local_space *ls = isl_local_space_from_space(space); isl_aff *zero = isl_aff_zero_on_domain(isl_local_space_copy(ls)); isl_aff *one = isl_aff_zero_on_domain(ls); one = isl_aff_add_constant_si(one, 1); pa = isl_pw_aff_alloc(isl_set_copy(set), one); set = isl_set_complement(set); pa = isl_pw_aff_add_disjoint(pa, isl_pw_aff_alloc(set, zero)); return pa; } /* Plug in "subs" for dimension "type", "pos" of "aff". * * Let i be the dimension to replace and let "subs" be of the form * * f/d * * and "aff" of the form * * (a i + g)/m * * The result is * * (a f + d g')/(m d) * * where g' is the result of plugging in "subs" in each of the integer * divisions in g. */ __isl_give isl_aff *isl_aff_substitute(__isl_take isl_aff *aff, enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs) { isl_ctx *ctx; isl_int v; isl_size n_div; aff = isl_aff_cow(aff); if (!aff || !subs) return isl_aff_free(aff); ctx = isl_aff_get_ctx(aff); if (!isl_space_is_equal(aff->ls->dim, subs->ls->dim)) isl_die(ctx, isl_error_invalid, "spaces don't match", return isl_aff_free(aff)); n_div = isl_aff_domain_dim(subs, isl_dim_div); if (n_div < 0) return isl_aff_free(aff); if (n_div != 0) isl_die(ctx, isl_error_unsupported, "cannot handle divs yet", return isl_aff_free(aff)); aff->ls = isl_local_space_substitute(aff->ls, type, pos, subs); if (!aff->ls) return isl_aff_free(aff); aff->v = isl_vec_cow(aff->v); if (!aff->v) return isl_aff_free(aff); pos += isl_local_space_offset(aff->ls, type); isl_int_init(v); isl_seq_substitute(aff->v->el, pos, subs->v->el, aff->v->size, subs->v->size, v); isl_int_clear(v); return aff; } /* Plug in "subs" for dimension "type", "pos" in each of the affine * expressions in "maff". */ __isl_give isl_multi_aff *isl_multi_aff_substitute( __isl_take isl_multi_aff *maff, enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs) { int i; maff = isl_multi_aff_cow(maff); if (!maff || !subs) return isl_multi_aff_free(maff); if (type == isl_dim_in) type = isl_dim_set; for (i = 0; i < maff->n; ++i) { maff->u.p[i] = isl_aff_substitute(maff->u.p[i], type, pos, subs); if (!maff->u.p[i]) return isl_multi_aff_free(maff); } return maff; } /* Plug in "subs" for input dimension "pos" of "pma". * * pma is of the form * * A_i(v) -> M_i(v) * * while subs is of the form * * v' = B_j(v) -> S_j * * Each pair i,j such that C_ij = A_i \cap B_i is non-empty * has a contribution in the result, in particular * * C_ij(S_j) -> M_i(S_j) * * Note that plugging in S_j in C_ij may also result in an empty set * and this contribution should simply be discarded. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_substitute( __isl_take isl_pw_multi_aff *pma, unsigned pos, __isl_keep isl_pw_aff *subs) { int i, j, n; isl_pw_multi_aff *res; if (!pma || !subs) return isl_pw_multi_aff_free(pma); n = pma->n * subs->n; res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma->dim), n); for (i = 0; i < pma->n; ++i) { for (j = 0; j < subs->n; ++j) { isl_set *common; isl_multi_aff *res_ij; int empty; common = isl_set_intersect( isl_set_copy(pma->p[i].set), isl_set_copy(subs->p[j].set)); common = isl_set_substitute(common, pos, subs->p[j].aff); empty = isl_set_plain_is_empty(common); if (empty < 0 || empty) { isl_set_free(common); if (empty < 0) goto error; continue; } res_ij = isl_multi_aff_substitute( isl_multi_aff_copy(pma->p[i].maff), isl_dim_in, pos, subs->p[j].aff); res = isl_pw_multi_aff_add_piece(res, common, res_ij); } } isl_pw_multi_aff_free(pma); return res; error: isl_pw_multi_aff_free(pma); isl_pw_multi_aff_free(res); return NULL; } /* Compute the preimage of a range of dimensions in the affine expression "src" * under "ma" and put the result in "dst". The number of dimensions in "src" * that precede the range is given by "n_before". The number of dimensions * in the range is given by the number of output dimensions of "ma". * The number of dimensions that follow the range is given by "n_after". * If "has_denom" is set (to one), * then "src" and "dst" have an extra initial denominator. * "n_div_ma" is the number of existentials in "ma" * "n_div_bset" is the number of existentials in "src" * The resulting "dst" (which is assumed to have been allocated by * the caller) contains coefficients for both sets of existentials, * first those in "ma" and then those in "src". * f, c1, c2 and g are temporary objects that have been initialized * by the caller. * * Let src represent the expression * * (a(p) + f_u u + b v + f_w w + c(divs))/d * * and let ma represent the expressions * * v_i = (r_i(p) + s_i(y) + t_i(divs'))/m_i * * We start out with the following expression for dst: * * (a(p) + f_u u + 0 y + f_w w + 0 divs' + c(divs) + f \sum_i b_i v_i)/d * * with the multiplication factor f initially equal to 1 * and f \sum_i b_i v_i kept separately. * For each x_i that we substitute, we multiply the numerator * (and denominator) of dst by c_1 = m_i and add the numerator * of the x_i expression multiplied by c_2 = f b_i, * after removing the common factors of c_1 and c_2. * The multiplication factor f also needs to be multiplied by c_1 * for the next x_j, j > i. */ isl_stat isl_seq_preimage(isl_int *dst, isl_int *src, __isl_keep isl_multi_aff *ma, int n_before, int n_after, int n_div_ma, int n_div_bmap, isl_int f, isl_int c1, isl_int c2, isl_int g, int has_denom) { int i; isl_size n_param, n_in, n_out; int o_dst, o_src; n_param = isl_multi_aff_dim(ma, isl_dim_param); n_in = isl_multi_aff_dim(ma, isl_dim_in); n_out = isl_multi_aff_dim(ma, isl_dim_out); if (n_param < 0 || n_in < 0 || n_out < 0) return isl_stat_error; isl_seq_cpy(dst, src, has_denom + 1 + n_param + n_before); o_dst = o_src = has_denom + 1 + n_param + n_before; isl_seq_clr(dst + o_dst, n_in); o_dst += n_in; o_src += n_out; isl_seq_cpy(dst + o_dst, src + o_src, n_after); o_dst += n_after; o_src += n_after; isl_seq_clr(dst + o_dst, n_div_ma); o_dst += n_div_ma; isl_seq_cpy(dst + o_dst, src + o_src, n_div_bmap); isl_int_set_si(f, 1); for (i = 0; i < n_out; ++i) { int offset = has_denom + 1 + n_param + n_before + i; if (isl_int_is_zero(src[offset])) continue; isl_int_set(c1, ma->u.p[i]->v->el[0]); isl_int_mul(c2, f, src[offset]); isl_int_gcd(g, c1, c2); isl_int_divexact(c1, c1, g); isl_int_divexact(c2, c2, g); isl_int_mul(f, f, c1); o_dst = has_denom; o_src = 1; isl_seq_combine(dst + o_dst, c1, dst + o_dst, c2, ma->u.p[i]->v->el + o_src, 1 + n_param); o_dst += 1 + n_param; o_src += 1 + n_param; isl_seq_scale(dst + o_dst, dst + o_dst, c1, n_before); o_dst += n_before; isl_seq_combine(dst + o_dst, c1, dst + o_dst, c2, ma->u.p[i]->v->el + o_src, n_in); o_dst += n_in; o_src += n_in; isl_seq_scale(dst + o_dst, dst + o_dst, c1, n_after); o_dst += n_after; isl_seq_combine(dst + o_dst, c1, dst + o_dst, c2, ma->u.p[i]->v->el + o_src, n_div_ma); o_dst += n_div_ma; o_src += n_div_ma; isl_seq_scale(dst + o_dst, dst + o_dst, c1, n_div_bmap); if (has_denom) isl_int_mul(dst[0], dst[0], c1); } return isl_stat_ok; } /* Compute the pullback of "aff" by the function represented by "ma". * In other words, plug in "ma" in "aff". The result is an affine expression * defined over the domain space of "ma". * * If "aff" is represented by * * (a(p) + b x + c(divs))/d * * and ma is represented by * * x = D(p) + F(y) + G(divs') * * then the result is * * (a(p) + b D(p) + b F(y) + b G(divs') + c(divs))/d * * The divs in the local space of the input are similarly adjusted * through a call to isl_local_space_preimage_multi_aff. */ __isl_give isl_aff *isl_aff_pullback_multi_aff(__isl_take isl_aff *aff, __isl_take isl_multi_aff *ma) { isl_aff *res = NULL; isl_local_space *ls; isl_size n_div_aff, n_div_ma; isl_int f, c1, c2, g; ma = isl_multi_aff_align_divs(ma); if (!aff || !ma) goto error; n_div_aff = isl_aff_dim(aff, isl_dim_div); n_div_ma = ma->n ? isl_aff_dim(ma->u.p[0], isl_dim_div) : 0; if (n_div_aff < 0 || n_div_ma < 0) goto error; ls = isl_aff_get_domain_local_space(aff); ls = isl_local_space_preimage_multi_aff(ls, isl_multi_aff_copy(ma)); res = isl_aff_alloc(ls); if (!res) goto error; isl_int_init(f); isl_int_init(c1); isl_int_init(c2); isl_int_init(g); if (isl_seq_preimage(res->v->el, aff->v->el, ma, 0, 0, n_div_ma, n_div_aff, f, c1, c2, g, 1) < 0) res = isl_aff_free(res); isl_int_clear(f); isl_int_clear(c1); isl_int_clear(c2); isl_int_clear(g); isl_aff_free(aff); isl_multi_aff_free(ma); res = isl_aff_normalize(res); return res; error: isl_aff_free(aff); isl_multi_aff_free(ma); isl_aff_free(res); return NULL; } /* Compute the pullback of "aff1" by the function represented by "aff2". * In other words, plug in "aff2" in "aff1". The result is an affine expression * defined over the domain space of "aff1". * * The domain of "aff1" should match the range of "aff2", which means * that it should be single-dimensional. */ __isl_give isl_aff *isl_aff_pullback_aff(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { isl_multi_aff *ma; ma = isl_multi_aff_from_aff(aff2); return isl_aff_pullback_multi_aff(aff1, ma); } /* Compute the pullback of "ma1" by the function represented by "ma2". * In other words, plug in "ma2" in "ma1". */ __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff( __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2) { int i; isl_space *space = NULL; isl_multi_aff_align_params_bin(&ma1, &ma2); ma2 = isl_multi_aff_align_divs(ma2); ma1 = isl_multi_aff_cow(ma1); if (!ma1 || !ma2) goto error; space = isl_space_join(isl_multi_aff_get_space(ma2), isl_multi_aff_get_space(ma1)); for (i = 0; i < ma1->n; ++i) { ma1->u.p[i] = isl_aff_pullback_multi_aff(ma1->u.p[i], isl_multi_aff_copy(ma2)); if (!ma1->u.p[i]) goto error; } ma1 = isl_multi_aff_reset_space(ma1, space); isl_multi_aff_free(ma2); return ma1; error: isl_space_free(space); isl_multi_aff_free(ma2); isl_multi_aff_free(ma1); return NULL; } /* Extend the local space of "dst" to include the divs * in the local space of "src". * * If "src" does not have any divs or if the local spaces of "dst" and * "src" are the same, then no extension is required. */ __isl_give isl_aff *isl_aff_align_divs(__isl_take isl_aff *dst, __isl_keep isl_aff *src) { isl_ctx *ctx; isl_size src_n_div, dst_n_div; int *exp1 = NULL; int *exp2 = NULL; isl_bool equal; isl_mat *div; if (!src || !dst) return isl_aff_free(dst); ctx = isl_aff_get_ctx(src); equal = isl_local_space_has_equal_space(src->ls, dst->ls); if (equal < 0) return isl_aff_free(dst); if (!equal) isl_die(ctx, isl_error_invalid, "spaces don't match", goto error); src_n_div = isl_aff_domain_dim(src, isl_dim_div); dst_n_div = isl_aff_domain_dim(dst, isl_dim_div); if (src_n_div == 0) return dst; equal = isl_local_space_is_equal(src->ls, dst->ls); if (equal < 0 || src_n_div < 0 || dst_n_div < 0) return isl_aff_free(dst); if (equal) return dst; exp1 = isl_alloc_array(ctx, int, src_n_div); exp2 = isl_alloc_array(ctx, int, dst_n_div); if (!exp1 || (dst_n_div && !exp2)) goto error; div = isl_merge_divs(src->ls->div, dst->ls->div, exp1, exp2); dst = isl_aff_expand_divs(dst, div, exp2); free(exp1); free(exp2); return dst; error: free(exp1); free(exp2); return isl_aff_free(dst); } /* Adjust the local spaces of the affine expressions in "maff" * such that they all have the save divs. */ __isl_give isl_multi_aff *isl_multi_aff_align_divs( __isl_take isl_multi_aff *maff) { int i; if (!maff) return NULL; if (maff->n == 0) return maff; maff = isl_multi_aff_cow(maff); if (!maff) return NULL; for (i = 1; i < maff->n; ++i) maff->u.p[0] = isl_aff_align_divs(maff->u.p[0], maff->u.p[i]); for (i = 1; i < maff->n; ++i) { maff->u.p[i] = isl_aff_align_divs(maff->u.p[i], maff->u.p[0]); if (!maff->u.p[i]) return isl_multi_aff_free(maff); } return maff; } __isl_give isl_aff *isl_aff_lift(__isl_take isl_aff *aff) { aff = isl_aff_cow(aff); if (!aff) return NULL; aff->ls = isl_local_space_lift(aff->ls); if (!aff->ls) return isl_aff_free(aff); return aff; } /* Lift "maff" to a space with extra dimensions such that the result * has no more existentially quantified variables. * If "ls" is not NULL, then *ls is assigned the local space that lies * at the basis of the lifting applied to "maff". */ __isl_give isl_multi_aff *isl_multi_aff_lift(__isl_take isl_multi_aff *maff, __isl_give isl_local_space **ls) { int i; isl_space *space; isl_size n_div; if (ls) *ls = NULL; if (!maff) return NULL; if (maff->n == 0) { if (ls) { isl_space *space = isl_multi_aff_get_domain_space(maff); *ls = isl_local_space_from_space(space); if (!*ls) return isl_multi_aff_free(maff); } return maff; } maff = isl_multi_aff_cow(maff); maff = isl_multi_aff_align_divs(maff); if (!maff) return NULL; n_div = isl_aff_dim(maff->u.p[0], isl_dim_div); if (n_div < 0) return isl_multi_aff_free(maff); space = isl_multi_aff_get_space(maff); space = isl_space_lift(isl_space_domain(space), n_div); space = isl_space_extend_domain_with_range(space, isl_multi_aff_get_space(maff)); if (!space) return isl_multi_aff_free(maff); isl_space_free(maff->space); maff->space = space; if (ls) { *ls = isl_aff_get_domain_local_space(maff->u.p[0]); if (!*ls) return isl_multi_aff_free(maff); } for (i = 0; i < maff->n; ++i) { maff->u.p[i] = isl_aff_lift(maff->u.p[i]); if (!maff->u.p[i]) goto error; } return maff; error: if (ls) isl_local_space_free(*ls); return isl_multi_aff_free(maff); } #undef TYPE #define TYPE isl_pw_multi_aff static #include "check_type_range_templ.c" /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma". */ __isl_give isl_pw_aff *isl_pw_multi_aff_get_at( __isl_keep isl_pw_multi_aff *pma, int pos) { int i; isl_size n_out; isl_space *space; isl_pw_aff *pa; if (isl_pw_multi_aff_check_range(pma, isl_dim_out, pos, 1) < 0) return NULL; n_out = isl_pw_multi_aff_dim(pma, isl_dim_out); if (n_out < 0) return NULL; space = isl_pw_multi_aff_get_space(pma); space = isl_space_drop_dims(space, isl_dim_out, pos + 1, n_out - pos - 1); space = isl_space_drop_dims(space, isl_dim_out, 0, pos); pa = isl_pw_aff_alloc_size(space, pma->n); for (i = 0; i < pma->n; ++i) { isl_aff *aff; aff = isl_multi_aff_get_aff(pma->p[i].maff, pos); pa = isl_pw_aff_add_piece(pa, isl_set_copy(pma->p[i].set), aff); } return pa; } /* This is an alternative name for the function above. */ __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff( __isl_keep isl_pw_multi_aff *pma, int pos) { return isl_pw_multi_aff_get_at(pma, pos); } /* Return an isl_pw_multi_aff with the given "set" as domain and * an unnamed zero-dimensional range. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain( __isl_take isl_set *set) { isl_multi_aff *ma; isl_space *space; space = isl_set_get_space(set); space = isl_space_from_domain(space); ma = isl_multi_aff_zero(space); return isl_pw_multi_aff_alloc(set, ma); } /* Add an isl_pw_multi_aff with the given "set" as domain and * an unnamed zero-dimensional range to *user. */ static isl_stat add_pw_multi_aff_from_domain(__isl_take isl_set *set, void *user) { isl_union_pw_multi_aff **upma = user; isl_pw_multi_aff *pma; pma = isl_pw_multi_aff_from_domain(set); *upma = isl_union_pw_multi_aff_add_pw_multi_aff(*upma, pma); return isl_stat_ok; } /* Return an isl_union_pw_multi_aff with the given "uset" as domain and * an unnamed zero-dimensional range. */ __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_domain( __isl_take isl_union_set *uset) { isl_space *space; isl_union_pw_multi_aff *upma; if (!uset) return NULL; space = isl_union_set_get_space(uset); upma = isl_union_pw_multi_aff_empty(space); if (isl_union_set_foreach_set(uset, &add_pw_multi_aff_from_domain, &upma) < 0) goto error; isl_union_set_free(uset); return upma; error: isl_union_set_free(uset); isl_union_pw_multi_aff_free(upma); return NULL; } /* Local data for bin_entry and the callback "fn". */ struct isl_union_pw_multi_aff_bin_data { isl_union_pw_multi_aff *upma2; isl_union_pw_multi_aff *res; isl_pw_multi_aff *pma; isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma, void *user); }; /* Given an isl_pw_multi_aff from upma1, store it in data->pma * and call data->fn for each isl_pw_multi_aff in data->upma2. */ static isl_stat bin_entry(__isl_take isl_pw_multi_aff *pma, void *user) { struct isl_union_pw_multi_aff_bin_data *data = user; isl_stat r; data->pma = pma; r = isl_union_pw_multi_aff_foreach_pw_multi_aff(data->upma2, data->fn, data); isl_pw_multi_aff_free(pma); return r; } /* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2". * The isl_pw_multi_aff from upma1 is stored in data->pma (where data is * passed as user field) and the isl_pw_multi_aff from upma2 is available * as *entry. The callback should adjust data->res if desired. */ static __isl_give isl_union_pw_multi_aff *bin_op( __isl_take isl_union_pw_multi_aff *upma1, __isl_take isl_union_pw_multi_aff *upma2, isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma, void *user)) { isl_space *space; struct isl_union_pw_multi_aff_bin_data data = { NULL, NULL, NULL, fn }; space = isl_union_pw_multi_aff_get_space(upma2); upma1 = isl_union_pw_multi_aff_align_params(upma1, space); space = isl_union_pw_multi_aff_get_space(upma1); upma2 = isl_union_pw_multi_aff_align_params(upma2, space); if (!upma1 || !upma2) goto error; data.upma2 = upma2; data.res = isl_union_pw_multi_aff_alloc_same_size(upma1); if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma1, &bin_entry, &data) < 0) goto error; isl_union_pw_multi_aff_free(upma1); isl_union_pw_multi_aff_free(upma2); return data.res; error: isl_union_pw_multi_aff_free(upma1); isl_union_pw_multi_aff_free(upma2); isl_union_pw_multi_aff_free(data.res); return NULL; } /* Given two isl_pw_multi_affs A -> B and C -> D, * construct an isl_pw_multi_aff (A * C) -> [B -> D]. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_product( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { isl_space *space; isl_pw_multi_aff_align_params_bin(&pma1, &pma2); space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1), isl_pw_multi_aff_get_space(pma2)); return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space, &isl_multi_aff_range_product); } /* Given two isl_pw_multi_affs A -> B and C -> D, * construct an isl_pw_multi_aff (A * C) -> (B, D). */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_flat_range_product( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { isl_space *space; isl_pw_multi_aff_align_params_bin(&pma1, &pma2); space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1), isl_pw_multi_aff_get_space(pma2)); space = isl_space_flatten_range(space); return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space, &isl_multi_aff_flat_range_product); } /* If data->pma and "pma2" have the same domain space, then use "range_product" * to compute some form of range product and add the result to data->res. */ static isl_stat gen_range_product_entry(__isl_take isl_pw_multi_aff *pma2, __isl_give isl_pw_multi_aff *(*range_product)( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2), void *user) { struct isl_union_pw_multi_aff_bin_data *data = user; isl_bool match; isl_space *space1, *space2; space1 = isl_pw_multi_aff_peek_space(data->pma); space2 = isl_pw_multi_aff_peek_space(pma2); match = isl_space_tuple_is_equal(space1, isl_dim_in, space2, isl_dim_in); if (match < 0 || !match) { isl_pw_multi_aff_free(pma2); return match < 0 ? isl_stat_error : isl_stat_ok; } pma2 = range_product(isl_pw_multi_aff_copy(data->pma), pma2); data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma2); return isl_stat_ok; } /* If data->pma and "pma2" have the same domain space, then compute * their flat range product and add the result to data->res. */ static isl_stat flat_range_product_entry(__isl_take isl_pw_multi_aff *pma2, void *user) { return gen_range_product_entry(pma2, &isl_pw_multi_aff_flat_range_product, user); } /* Given two isl_union_pw_multi_affs A -> B and C -> D, * construct an isl_union_pw_multi_aff (A * C) -> (B, D). */ __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_flat_range_product( __isl_take isl_union_pw_multi_aff *upma1, __isl_take isl_union_pw_multi_aff *upma2) { return bin_op(upma1, upma2, &flat_range_product_entry); } /* If data->pma and "pma2" have the same domain space, then compute * their range product and add the result to data->res. */ static isl_stat range_product_entry(__isl_take isl_pw_multi_aff *pma2, void *user) { return gen_range_product_entry(pma2, &isl_pw_multi_aff_range_product, user); } /* Given two isl_union_pw_multi_affs A -> B and C -> D, * construct an isl_union_pw_multi_aff (A * C) -> [B -> D]. */ __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_range_product( __isl_take isl_union_pw_multi_aff *upma1, __isl_take isl_union_pw_multi_aff *upma2) { return bin_op(upma1, upma2, &range_product_entry); } /* Replace the affine expressions at position "pos" in "pma" by "pa". * The parameters are assumed to have been aligned. * * The implementation essentially performs an isl_pw_*_on_shared_domain, * except that it works on two different isl_pw_* types. */ static __isl_give isl_pw_multi_aff *pw_multi_aff_set_pw_aff( __isl_take isl_pw_multi_aff *pma, unsigned pos, __isl_take isl_pw_aff *pa) { int i, j, n; isl_pw_multi_aff *res = NULL; if (!pma || !pa) goto error; if (!isl_space_tuple_is_equal(pma->dim, isl_dim_in, pa->dim, isl_dim_in)) isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid, "domains don't match", goto error); if (isl_pw_multi_aff_check_range(pma, isl_dim_out, pos, 1) < 0) goto error; n = pma->n * pa->n; res = isl_pw_multi_aff_alloc_size(isl_pw_multi_aff_get_space(pma), n); for (i = 0; i < pma->n; ++i) { for (j = 0; j < pa->n; ++j) { isl_set *common; isl_multi_aff *res_ij; int empty; common = isl_set_intersect(isl_set_copy(pma->p[i].set), isl_set_copy(pa->p[j].set)); empty = isl_set_plain_is_empty(common); if (empty < 0 || empty) { isl_set_free(common); if (empty < 0) goto error; continue; } res_ij = isl_multi_aff_set_aff( isl_multi_aff_copy(pma->p[i].maff), pos, isl_aff_copy(pa->p[j].aff)); res_ij = isl_multi_aff_gist(res_ij, isl_set_copy(common)); res = isl_pw_multi_aff_add_piece(res, common, res_ij); } } isl_pw_multi_aff_free(pma); isl_pw_aff_free(pa); return res; error: isl_pw_multi_aff_free(pma); isl_pw_aff_free(pa); return isl_pw_multi_aff_free(res); } /* Replace the affine expressions at position "pos" in "pma" by "pa". */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff( __isl_take isl_pw_multi_aff *pma, unsigned pos, __isl_take isl_pw_aff *pa) { isl_bool equal_params; if (!pma || !pa) goto error; equal_params = isl_space_has_equal_params(pma->dim, pa->dim); if (equal_params < 0) goto error; if (equal_params) return pw_multi_aff_set_pw_aff(pma, pos, pa); if (isl_pw_multi_aff_check_named_params(pma) < 0 || isl_pw_aff_check_named_params(pa) < 0) goto error; pma = isl_pw_multi_aff_align_params(pma, isl_pw_aff_get_space(pa)); pa = isl_pw_aff_align_params(pa, isl_pw_multi_aff_get_space(pma)); return pw_multi_aff_set_pw_aff(pma, pos, pa); error: isl_pw_multi_aff_free(pma); isl_pw_aff_free(pa); return NULL; } /* Do the parameters of "pa" match those of "space"? */ isl_bool isl_pw_aff_matching_params(__isl_keep isl_pw_aff *pa, __isl_keep isl_space *space) { isl_space *pa_space; isl_bool match; if (!pa || !space) return isl_bool_error; pa_space = isl_pw_aff_get_space(pa); match = isl_space_has_equal_params(space, pa_space); isl_space_free(pa_space); return match; } /* Check that the domain space of "pa" matches "space". */ isl_stat isl_pw_aff_check_match_domain_space(__isl_keep isl_pw_aff *pa, __isl_keep isl_space *space) { isl_space *pa_space; isl_bool match; if (!pa || !space) return isl_stat_error; pa_space = isl_pw_aff_get_space(pa); match = isl_space_has_equal_params(space, pa_space); if (match < 0) goto error; if (!match) isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid, "parameters don't match", goto error); match = isl_space_tuple_is_equal(space, isl_dim_in, pa_space, isl_dim_in); if (match < 0) goto error; if (!match) isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid, "domains don't match", goto error); isl_space_free(pa_space); return isl_stat_ok; error: isl_space_free(pa_space); return isl_stat_error; } #undef BASE #define BASE pw_aff #undef DOMBASE #define DOMBASE set #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include /* Is every element of "mpa" defined over a single universe domain? */ isl_bool isl_multi_pw_aff_isa_multi_aff(__isl_keep isl_multi_pw_aff *mpa) { return isl_multi_pw_aff_every(mpa, &isl_pw_aff_isa_aff); } /* Given that every element of "mpa" is defined over a single universe domain, * return the corresponding base expressions. */ __isl_give isl_multi_aff *isl_multi_pw_aff_as_multi_aff( __isl_take isl_multi_pw_aff *mpa) { int i; isl_size n; isl_multi_aff *ma; n = isl_multi_pw_aff_size(mpa); if (n < 0) mpa = isl_multi_pw_aff_free(mpa); ma = isl_multi_aff_alloc(isl_multi_pw_aff_get_space(mpa)); for (i = 0; i < n; ++i) { isl_aff *aff; aff = isl_pw_aff_as_aff(isl_multi_pw_aff_get_at(mpa, i)); ma = isl_multi_aff_set_aff(ma, i, aff); } isl_multi_pw_aff_free(mpa); return ma; } /* If "mpa" has an explicit domain, then intersect the domain of "map" * with this explicit domain. */ __isl_give isl_map *isl_map_intersect_multi_pw_aff_explicit_domain( __isl_take isl_map *map, __isl_keep isl_multi_pw_aff *mpa) { isl_set *dom; if (!isl_multi_pw_aff_has_explicit_domain(mpa)) return map; dom = isl_multi_pw_aff_domain(isl_multi_pw_aff_copy(mpa)); map = isl_map_intersect_domain(map, dom); return map; } /* Are all elements of "mpa" piecewise constants? */ isl_bool isl_multi_pw_aff_is_cst(__isl_keep isl_multi_pw_aff *mpa) { return isl_multi_pw_aff_every(mpa, &isl_pw_aff_is_cst); } /* Does "mpa" have a non-trivial explicit domain? * * The explicit domain, if present, is trivial if it represents * an (obviously) universe set. */ isl_bool isl_multi_pw_aff_has_non_trivial_domain( __isl_keep isl_multi_pw_aff *mpa) { if (!mpa) return isl_bool_error; if (!isl_multi_pw_aff_has_explicit_domain(mpa)) return isl_bool_false; return isl_bool_not(isl_set_plain_is_universe(mpa->u.dom)); } #undef BASE #define BASE set #include "isl_opt_mpa_templ.c" /* Compute the minima of the set dimensions as a function of the * parameters, but independently of the other set dimensions. */ __isl_give isl_multi_pw_aff *isl_set_min_multi_pw_aff(__isl_take isl_set *set) { return set_opt_mpa(set, &isl_set_dim_min); } /* Compute the maxima of the set dimensions as a function of the * parameters, but independently of the other set dimensions. */ __isl_give isl_multi_pw_aff *isl_set_max_multi_pw_aff(__isl_take isl_set *set) { return set_opt_mpa(set, &isl_set_dim_max); } #undef BASE #define BASE map #include "isl_opt_mpa_templ.c" /* Compute the minima of the output dimensions as a function of the * parameters and input dimensions, but independently of * the other output dimensions. */ __isl_give isl_multi_pw_aff *isl_map_min_multi_pw_aff(__isl_take isl_map *map) { return map_opt_mpa(map, &isl_map_dim_min); } /* Compute the maxima of the output dimensions as a function of the * parameters and input dimensions, but independently of * the other output dimensions. */ __isl_give isl_multi_pw_aff *isl_map_max_multi_pw_aff(__isl_take isl_map *map) { return map_opt_mpa(map, &isl_map_dim_max); } /* Scale the elements of "pma" by the corresponding elements of "mv". */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_multi_val( __isl_take isl_pw_multi_aff *pma, __isl_take isl_multi_val *mv) { int i; isl_bool equal_params; pma = isl_pw_multi_aff_cow(pma); if (!pma || !mv) goto error; if (!isl_space_tuple_is_equal(pma->dim, isl_dim_out, mv->space, isl_dim_set)) isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid, "spaces don't match", goto error); equal_params = isl_space_has_equal_params(pma->dim, mv->space); if (equal_params < 0) goto error; if (!equal_params) { pma = isl_pw_multi_aff_align_params(pma, isl_multi_val_get_space(mv)); mv = isl_multi_val_align_params(mv, isl_pw_multi_aff_get_space(pma)); if (!pma || !mv) goto error; } for (i = 0; i < pma->n; ++i) { pma->p[i].maff = isl_multi_aff_scale_multi_val(pma->p[i].maff, isl_multi_val_copy(mv)); if (!pma->p[i].maff) goto error; } isl_multi_val_free(mv); return pma; error: isl_multi_val_free(mv); isl_pw_multi_aff_free(pma); return NULL; } /* This function is called for each entry of an isl_union_pw_multi_aff. * If the space of the entry matches that of data->mv, * then apply isl_pw_multi_aff_scale_multi_val and return the result. * Otherwise, return an empty isl_pw_multi_aff. */ static __isl_give isl_pw_multi_aff *union_pw_multi_aff_scale_multi_val_entry( __isl_take isl_pw_multi_aff *pma, void *user) { isl_multi_val *mv = user; if (!pma) return NULL; if (!isl_space_tuple_is_equal(pma->dim, isl_dim_out, mv->space, isl_dim_set)) { isl_space *space = isl_pw_multi_aff_get_space(pma); isl_pw_multi_aff_free(pma); return isl_pw_multi_aff_empty(space); } return isl_pw_multi_aff_scale_multi_val(pma, isl_multi_val_copy(mv)); } /* Scale the elements of "upma" by the corresponding elements of "mv", * for those entries that match the space of "mv". */ __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_multi_val( __isl_take isl_union_pw_multi_aff *upma, __isl_take isl_multi_val *mv) { struct isl_union_pw_multi_aff_transform_control control = { .fn = &union_pw_multi_aff_scale_multi_val_entry, .fn_user = mv, }; upma = isl_union_pw_multi_aff_align_params(upma, isl_multi_val_get_space(mv)); mv = isl_multi_val_align_params(mv, isl_union_pw_multi_aff_get_space(upma)); if (!upma || !mv) goto error; return isl_union_pw_multi_aff_transform(upma, &control); isl_multi_val_free(mv); return upma; error: isl_multi_val_free(mv); isl_union_pw_multi_aff_free(upma); return NULL; } /* Construct and return a piecewise multi affine expression * in the given space with value zero in each of the output dimensions and * a universe domain. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(__isl_take isl_space *space) { return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_zero(space)); } /* Construct and return a piecewise multi affine expression * that is equal to the given piecewise affine expression. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff( __isl_take isl_pw_aff *pa) { int i; isl_space *space; isl_pw_multi_aff *pma; if (!pa) return NULL; space = isl_pw_aff_get_space(pa); pma = isl_pw_multi_aff_alloc_size(space, pa->n); for (i = 0; i < pa->n; ++i) { isl_set *set; isl_multi_aff *ma; set = isl_set_copy(pa->p[i].set); ma = isl_multi_aff_from_aff(isl_aff_copy(pa->p[i].aff)); pma = isl_pw_multi_aff_add_piece(pma, set, ma); } isl_pw_aff_free(pa); return pma; } /* Construct and return a piecewise multi affine expression * that is equal to the given multi piecewise affine expression * on the shared domain of the piecewise affine expressions, * in the special case of a 0D multi piecewise affine expression. * * Create a piecewise multi affine expression with the explicit domain of * the 0D multi piecewise affine expression as domain. */ static __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_multi_pw_aff_0D( __isl_take isl_multi_pw_aff *mpa) { isl_space *space; isl_set *dom; isl_multi_aff *ma; space = isl_multi_pw_aff_get_space(mpa); dom = isl_multi_pw_aff_get_explicit_domain(mpa); isl_multi_pw_aff_free(mpa); ma = isl_multi_aff_zero(space); return isl_pw_multi_aff_alloc(dom, ma); } /* Construct and return a piecewise multi affine expression * that is equal to the given multi piecewise affine expression * on the shared domain of the piecewise affine expressions. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_multi_pw_aff( __isl_take isl_multi_pw_aff *mpa) { int i; isl_space *space; isl_pw_aff *pa; isl_pw_multi_aff *pma; if (!mpa) return NULL; if (mpa->n == 0) return isl_pw_multi_aff_from_multi_pw_aff_0D(mpa); space = isl_multi_pw_aff_get_space(mpa); pa = isl_multi_pw_aff_get_pw_aff(mpa, 0); pma = isl_pw_multi_aff_from_pw_aff(pa); for (i = 1; i < mpa->n; ++i) { isl_pw_multi_aff *pma_i; pa = isl_multi_pw_aff_get_pw_aff(mpa, i); pma_i = isl_pw_multi_aff_from_pw_aff(pa); pma = isl_pw_multi_aff_range_product(pma, pma_i); } pma = isl_pw_multi_aff_reset_space(pma, space); isl_multi_pw_aff_free(mpa); return pma; } /* Convenience function that constructs an isl_multi_pw_aff * directly from an isl_aff. */ __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_aff(__isl_take isl_aff *aff) { return isl_multi_pw_aff_from_pw_aff(isl_pw_aff_from_aff(aff)); } /* Construct and return a multi piecewise affine expression * that is equal to the given multi affine expression. */ __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_multi_aff( __isl_take isl_multi_aff *ma) { int i; isl_size n; isl_multi_pw_aff *mpa; n = isl_multi_aff_dim(ma, isl_dim_out); if (n < 0) ma = isl_multi_aff_free(ma); if (!ma) return NULL; mpa = isl_multi_pw_aff_alloc(isl_multi_aff_get_space(ma)); for (i = 0; i < n; ++i) { isl_pw_aff *pa; pa = isl_pw_aff_from_aff(isl_multi_aff_get_aff(ma, i)); mpa = isl_multi_pw_aff_set_pw_aff(mpa, i, pa); } isl_multi_aff_free(ma); return mpa; } /* This function performs the same operation as isl_multi_pw_aff_from_multi_aff, * but is considered as a function on an isl_multi_aff when exported. */ __isl_give isl_multi_pw_aff *isl_multi_aff_to_multi_pw_aff( __isl_take isl_multi_aff *ma) { return isl_multi_pw_aff_from_multi_aff(ma); } /* Construct and return a multi piecewise affine expression * that is equal to the given piecewise multi affine expression. * * If the resulting multi piecewise affine expression has * an explicit domain, then assign it the domain of the input. * In other cases, the domain is stored in the individual elements. */ __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_multi_aff( __isl_take isl_pw_multi_aff *pma) { int i; isl_size n; isl_space *space; isl_multi_pw_aff *mpa; n = isl_pw_multi_aff_dim(pma, isl_dim_out); if (n < 0) pma = isl_pw_multi_aff_free(pma); space = isl_pw_multi_aff_get_space(pma); mpa = isl_multi_pw_aff_alloc(space); for (i = 0; i < n; ++i) { isl_pw_aff *pa; pa = isl_pw_multi_aff_get_pw_aff(pma, i); mpa = isl_multi_pw_aff_set_pw_aff(mpa, i, pa); } if (isl_multi_pw_aff_has_explicit_domain(mpa)) { isl_set *dom; dom = isl_pw_multi_aff_domain(isl_pw_multi_aff_copy(pma)); mpa = isl_multi_pw_aff_intersect_domain(mpa, dom); } isl_pw_multi_aff_free(pma); return mpa; } /* This function performs the same operation as * isl_multi_pw_aff_from_pw_multi_aff, * but is considered as a function on an isl_pw_multi_aff when exported. */ __isl_give isl_multi_pw_aff *isl_pw_multi_aff_to_multi_pw_aff( __isl_take isl_pw_multi_aff *pma) { return isl_multi_pw_aff_from_pw_multi_aff(pma); } /* Do "pa1" and "pa2" represent the same function? * * We first check if they are obviously equal. * If not, we convert them to maps and check if those are equal. * * If "pa1" or "pa2" contain any NaNs, then they are considered * not to be the same. A NaN is not equal to anything, not even * to another NaN. */ isl_bool isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1, __isl_keep isl_pw_aff *pa2) { isl_bool equal; isl_bool has_nan; isl_map *map1, *map2; if (!pa1 || !pa2) return isl_bool_error; equal = isl_pw_aff_plain_is_equal(pa1, pa2); if (equal < 0 || equal) return equal; has_nan = either_involves_nan(pa1, pa2); if (has_nan < 0) return isl_bool_error; if (has_nan) return isl_bool_false; map1 = isl_map_from_pw_aff_internal(isl_pw_aff_copy(pa1)); map2 = isl_map_from_pw_aff_internal(isl_pw_aff_copy(pa2)); equal = isl_map_is_equal(map1, map2); isl_map_free(map1); isl_map_free(map2); return equal; } /* Do "mpa1" and "mpa2" represent the same function? * * Note that we cannot convert the entire isl_multi_pw_aff * to a map because the domains of the piecewise affine expressions * may not be the same. */ isl_bool isl_multi_pw_aff_is_equal(__isl_keep isl_multi_pw_aff *mpa1, __isl_keep isl_multi_pw_aff *mpa2) { int i; isl_bool equal, equal_params; if (!mpa1 || !mpa2) return isl_bool_error; equal_params = isl_space_has_equal_params(mpa1->space, mpa2->space); if (equal_params < 0) return isl_bool_error; if (!equal_params) { if (!isl_space_has_named_params(mpa1->space)) return isl_bool_false; if (!isl_space_has_named_params(mpa2->space)) return isl_bool_false; mpa1 = isl_multi_pw_aff_copy(mpa1); mpa2 = isl_multi_pw_aff_copy(mpa2); mpa1 = isl_multi_pw_aff_align_params(mpa1, isl_multi_pw_aff_get_space(mpa2)); mpa2 = isl_multi_pw_aff_align_params(mpa2, isl_multi_pw_aff_get_space(mpa1)); equal = isl_multi_pw_aff_is_equal(mpa1, mpa2); isl_multi_pw_aff_free(mpa1); isl_multi_pw_aff_free(mpa2); return equal; } equal = isl_space_is_equal(mpa1->space, mpa2->space); if (equal < 0 || !equal) return equal; for (i = 0; i < mpa1->n; ++i) { equal = isl_pw_aff_is_equal(mpa1->u.p[i], mpa2->u.p[i]); if (equal < 0 || !equal) return equal; } return isl_bool_true; } /* Do "pma1" and "pma2" represent the same function? * * First check if they are obviously equal. * If not, then convert them to maps and check if those are equal. * * If "pa1" or "pa2" contain any NaNs, then they are considered * not to be the same. A NaN is not equal to anything, not even * to another NaN. */ isl_bool isl_pw_multi_aff_is_equal(__isl_keep isl_pw_multi_aff *pma1, __isl_keep isl_pw_multi_aff *pma2) { isl_bool equal; isl_bool has_nan; isl_map *map1, *map2; if (!pma1 || !pma2) return isl_bool_error; equal = isl_pw_multi_aff_plain_is_equal(pma1, pma2); if (equal < 0 || equal) return equal; has_nan = isl_pw_multi_aff_involves_nan(pma1); if (has_nan >= 0 && !has_nan) has_nan = isl_pw_multi_aff_involves_nan(pma2); if (has_nan < 0 || has_nan) return isl_bool_not(has_nan); map1 = isl_map_from_pw_multi_aff_internal(isl_pw_multi_aff_copy(pma1)); map2 = isl_map_from_pw_multi_aff_internal(isl_pw_multi_aff_copy(pma2)); equal = isl_map_is_equal(map1, map2); isl_map_free(map1); isl_map_free(map2); return equal; } /* Compute the pullback of "mpa" by the function represented by "ma". * In other words, plug in "ma" in "mpa". * * The parameters of "mpa" and "ma" are assumed to have been aligned. * * If "mpa" has an explicit domain, then it is this domain * that needs to undergo a pullback, i.e., a preimage. */ static __isl_give isl_multi_pw_aff *isl_multi_pw_aff_pullback_multi_aff_aligned( __isl_take isl_multi_pw_aff *mpa, __isl_take isl_multi_aff *ma) { int i; isl_space *space = NULL; mpa = isl_multi_pw_aff_cow(mpa); if (!mpa || !ma) goto error; space = isl_space_join(isl_multi_aff_get_space(ma), isl_multi_pw_aff_get_space(mpa)); if (!space) goto error; for (i = 0; i < mpa->n; ++i) { mpa->u.p[i] = isl_pw_aff_pullback_multi_aff(mpa->u.p[i], isl_multi_aff_copy(ma)); if (!mpa->u.p[i]) goto error; } if (isl_multi_pw_aff_has_explicit_domain(mpa)) { mpa->u.dom = isl_set_preimage_multi_aff(mpa->u.dom, isl_multi_aff_copy(ma)); if (!mpa->u.dom) goto error; } isl_multi_aff_free(ma); isl_space_free(mpa->space); mpa->space = space; return mpa; error: isl_space_free(space); isl_multi_pw_aff_free(mpa); isl_multi_aff_free(ma); return NULL; } /* Compute the pullback of "mpa" by the function represented by "ma". * In other words, plug in "ma" in "mpa". */ __isl_give isl_multi_pw_aff *isl_multi_pw_aff_pullback_multi_aff( __isl_take isl_multi_pw_aff *mpa, __isl_take isl_multi_aff *ma) { isl_bool equal_params; if (!mpa || !ma) goto error; equal_params = isl_space_has_equal_params(mpa->space, ma->space); if (equal_params < 0) goto error; if (equal_params) return isl_multi_pw_aff_pullback_multi_aff_aligned(mpa, ma); mpa = isl_multi_pw_aff_align_params(mpa, isl_multi_aff_get_space(ma)); ma = isl_multi_aff_align_params(ma, isl_multi_pw_aff_get_space(mpa)); return isl_multi_pw_aff_pullback_multi_aff_aligned(mpa, ma); error: isl_multi_pw_aff_free(mpa); isl_multi_aff_free(ma); return NULL; } /* Compute the pullback of "mpa" by the function represented by "pma". * In other words, plug in "pma" in "mpa". * * The parameters of "mpa" and "mpa" are assumed to have been aligned. * * If "mpa" has an explicit domain, then it is this domain * that needs to undergo a pullback, i.e., a preimage. */ static __isl_give isl_multi_pw_aff * isl_multi_pw_aff_pullback_pw_multi_aff_aligned( __isl_take isl_multi_pw_aff *mpa, __isl_take isl_pw_multi_aff *pma) { int i; isl_space *space = NULL; mpa = isl_multi_pw_aff_cow(mpa); if (!mpa || !pma) goto error; space = isl_space_join(isl_pw_multi_aff_get_space(pma), isl_multi_pw_aff_get_space(mpa)); for (i = 0; i < mpa->n; ++i) { mpa->u.p[i] = isl_pw_aff_pullback_pw_multi_aff_aligned( mpa->u.p[i], isl_pw_multi_aff_copy(pma)); if (!mpa->u.p[i]) goto error; } if (isl_multi_pw_aff_has_explicit_domain(mpa)) { mpa->u.dom = isl_set_preimage_pw_multi_aff(mpa->u.dom, isl_pw_multi_aff_copy(pma)); if (!mpa->u.dom) goto error; } isl_pw_multi_aff_free(pma); isl_space_free(mpa->space); mpa->space = space; return mpa; error: isl_space_free(space); isl_multi_pw_aff_free(mpa); isl_pw_multi_aff_free(pma); return NULL; } /* Compute the pullback of "mpa" by the function represented by "pma". * In other words, plug in "pma" in "mpa". */ __isl_give isl_multi_pw_aff *isl_multi_pw_aff_pullback_pw_multi_aff( __isl_take isl_multi_pw_aff *mpa, __isl_take isl_pw_multi_aff *pma) { isl_bool equal_params; if (!mpa || !pma) goto error; equal_params = isl_space_has_equal_params(mpa->space, pma->dim); if (equal_params < 0) goto error; if (equal_params) return isl_multi_pw_aff_pullback_pw_multi_aff_aligned(mpa, pma); mpa = isl_multi_pw_aff_align_params(mpa, isl_pw_multi_aff_get_space(pma)); pma = isl_pw_multi_aff_align_params(pma, isl_multi_pw_aff_get_space(mpa)); return isl_multi_pw_aff_pullback_pw_multi_aff_aligned(mpa, pma); error: isl_multi_pw_aff_free(mpa); isl_pw_multi_aff_free(pma); return NULL; } /* Apply "aff" to "mpa". The range of "mpa" needs to be compatible * with the domain of "aff". The domain of the result is the same * as that of "mpa". * "mpa" and "aff" are assumed to have been aligned. * * We first extract the parametric constant from "aff", defined * over the correct domain. * Then we add the appropriate combinations of the members of "mpa". * Finally, we add the integer divisions through recursive calls. */ static __isl_give isl_pw_aff *isl_multi_pw_aff_apply_aff_aligned( __isl_take isl_multi_pw_aff *mpa, __isl_take isl_aff *aff) { int i; isl_size n_in, n_div, n_mpa_in; isl_space *space; isl_val *v; isl_pw_aff *pa; isl_aff *tmp; n_in = isl_aff_dim(aff, isl_dim_in); n_div = isl_aff_dim(aff, isl_dim_div); n_mpa_in = isl_multi_pw_aff_dim(mpa, isl_dim_in); if (n_in < 0 || n_div < 0 || n_mpa_in < 0) goto error; space = isl_space_domain(isl_multi_pw_aff_get_space(mpa)); tmp = isl_aff_copy(aff); tmp = isl_aff_drop_dims(tmp, isl_dim_div, 0, n_div); tmp = isl_aff_drop_dims(tmp, isl_dim_in, 0, n_in); tmp = isl_aff_add_dims(tmp, isl_dim_in, n_mpa_in); tmp = isl_aff_reset_domain_space(tmp, space); pa = isl_pw_aff_from_aff(tmp); for (i = 0; i < n_in; ++i) { isl_pw_aff *pa_i; if (!isl_aff_involves_dims(aff, isl_dim_in, i, 1)) continue; v = isl_aff_get_coefficient_val(aff, isl_dim_in, i); pa_i = isl_multi_pw_aff_get_pw_aff(mpa, i); pa_i = isl_pw_aff_scale_val(pa_i, v); pa = isl_pw_aff_add(pa, pa_i); } for (i = 0; i < n_div; ++i) { isl_aff *div; isl_pw_aff *pa_i; if (!isl_aff_involves_dims(aff, isl_dim_div, i, 1)) continue; div = isl_aff_get_div(aff, i); pa_i = isl_multi_pw_aff_apply_aff_aligned( isl_multi_pw_aff_copy(mpa), div); pa_i = isl_pw_aff_floor(pa_i); v = isl_aff_get_coefficient_val(aff, isl_dim_div, i); pa_i = isl_pw_aff_scale_val(pa_i, v); pa = isl_pw_aff_add(pa, pa_i); } isl_multi_pw_aff_free(mpa); isl_aff_free(aff); return pa; error: isl_multi_pw_aff_free(mpa); isl_aff_free(aff); return NULL; } /* Apply "aff" to "mpa". The range of "mpa" needs to be compatible * with the domain of "aff". The domain of the result is the same * as that of "mpa". */ __isl_give isl_pw_aff *isl_multi_pw_aff_apply_aff( __isl_take isl_multi_pw_aff *mpa, __isl_take isl_aff *aff) { isl_bool equal_params; if (!aff || !mpa) goto error; equal_params = isl_space_has_equal_params(aff->ls->dim, mpa->space); if (equal_params < 0) goto error; if (equal_params) return isl_multi_pw_aff_apply_aff_aligned(mpa, aff); aff = isl_aff_align_params(aff, isl_multi_pw_aff_get_space(mpa)); mpa = isl_multi_pw_aff_align_params(mpa, isl_aff_get_space(aff)); return isl_multi_pw_aff_apply_aff_aligned(mpa, aff); error: isl_aff_free(aff); isl_multi_pw_aff_free(mpa); return NULL; } /* Apply "pa" to "mpa". The range of "mpa" needs to be compatible * with the domain of "pa". The domain of the result is the same * as that of "mpa". * "mpa" and "pa" are assumed to have been aligned. * * We consider each piece in turn. Note that the domains of the * pieces are assumed to be disjoint and they remain disjoint * after taking the preimage (over the same function). */ static __isl_give isl_pw_aff *isl_multi_pw_aff_apply_pw_aff_aligned( __isl_take isl_multi_pw_aff *mpa, __isl_take isl_pw_aff *pa) { isl_space *space; isl_pw_aff *res; int i; if (!mpa || !pa) goto error; space = isl_space_join(isl_multi_pw_aff_get_space(mpa), isl_pw_aff_get_space(pa)); res = isl_pw_aff_empty(space); for (i = 0; i < pa->n; ++i) { isl_pw_aff *pa_i; isl_set *domain; pa_i = isl_multi_pw_aff_apply_aff_aligned( isl_multi_pw_aff_copy(mpa), isl_aff_copy(pa->p[i].aff)); domain = isl_set_copy(pa->p[i].set); domain = isl_set_preimage_multi_pw_aff(domain, isl_multi_pw_aff_copy(mpa)); pa_i = isl_pw_aff_intersect_domain(pa_i, domain); res = isl_pw_aff_add_disjoint(res, pa_i); } isl_pw_aff_free(pa); isl_multi_pw_aff_free(mpa); return res; error: isl_pw_aff_free(pa); isl_multi_pw_aff_free(mpa); return NULL; } /* Apply "pa" to "mpa". The range of "mpa" needs to be compatible * with the domain of "pa". The domain of the result is the same * as that of "mpa". */ __isl_give isl_pw_aff *isl_multi_pw_aff_apply_pw_aff( __isl_take isl_multi_pw_aff *mpa, __isl_take isl_pw_aff *pa) { isl_bool equal_params; if (!pa || !mpa) goto error; equal_params = isl_space_has_equal_params(pa->dim, mpa->space); if (equal_params < 0) goto error; if (equal_params) return isl_multi_pw_aff_apply_pw_aff_aligned(mpa, pa); pa = isl_pw_aff_align_params(pa, isl_multi_pw_aff_get_space(mpa)); mpa = isl_multi_pw_aff_align_params(mpa, isl_pw_aff_get_space(pa)); return isl_multi_pw_aff_apply_pw_aff_aligned(mpa, pa); error: isl_pw_aff_free(pa); isl_multi_pw_aff_free(mpa); return NULL; } /* Compute the pullback of "pa" by the function represented by "mpa". * In other words, plug in "mpa" in "pa". * "pa" and "mpa" are assumed to have been aligned. * * The pullback is computed by applying "pa" to "mpa". */ static __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff_aligned( __isl_take isl_pw_aff *pa, __isl_take isl_multi_pw_aff *mpa) { return isl_multi_pw_aff_apply_pw_aff_aligned(mpa, pa); } /* Compute the pullback of "pa" by the function represented by "mpa". * In other words, plug in "mpa" in "pa". * * The pullback is computed by applying "pa" to "mpa". */ __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff( __isl_take isl_pw_aff *pa, __isl_take isl_multi_pw_aff *mpa) { return isl_multi_pw_aff_apply_pw_aff(mpa, pa); } /* Compute the pullback of "mpa1" by the function represented by "mpa2". * In other words, plug in "mpa2" in "mpa1". * * We pullback each member of "mpa1" in turn. * * If "mpa1" has an explicit domain, then it is this domain * that needs to undergo a pullback instead, i.e., a preimage. */ __isl_give isl_multi_pw_aff *isl_multi_pw_aff_pullback_multi_pw_aff( __isl_take isl_multi_pw_aff *mpa1, __isl_take isl_multi_pw_aff *mpa2) { int i; isl_space *space = NULL; isl_multi_pw_aff_align_params_bin(&mpa1, &mpa2); mpa1 = isl_multi_pw_aff_cow(mpa1); if (!mpa1 || !mpa2) goto error; space = isl_space_join(isl_multi_pw_aff_get_space(mpa2), isl_multi_pw_aff_get_space(mpa1)); for (i = 0; i < mpa1->n; ++i) { mpa1->u.p[i] = isl_pw_aff_pullback_multi_pw_aff_aligned( mpa1->u.p[i], isl_multi_pw_aff_copy(mpa2)); if (!mpa1->u.p[i]) goto error; } if (isl_multi_pw_aff_has_explicit_domain(mpa1)) { mpa1->u.dom = isl_set_preimage_multi_pw_aff(mpa1->u.dom, isl_multi_pw_aff_copy(mpa2)); if (!mpa1->u.dom) goto error; } mpa1 = isl_multi_pw_aff_reset_space(mpa1, space); isl_multi_pw_aff_free(mpa2); return mpa1; error: isl_space_free(space); isl_multi_pw_aff_free(mpa1); isl_multi_pw_aff_free(mpa2); return NULL; } /* Align the parameters of "mpa1" and "mpa2", check that the ranges * of "mpa1" and "mpa2" live in the same space, construct map space * between the domain spaces of "mpa1" and "mpa2" and call "order" * with this map space as extract argument. */ static __isl_give isl_map *isl_multi_pw_aff_order_map( __isl_take isl_multi_pw_aff *mpa1, __isl_take isl_multi_pw_aff *mpa2, __isl_give isl_map *(*order)(__isl_keep isl_multi_pw_aff *mpa1, __isl_keep isl_multi_pw_aff *mpa2, __isl_take isl_space *space)) { int match; isl_space *space1, *space2; isl_map *res; mpa1 = isl_multi_pw_aff_align_params(mpa1, isl_multi_pw_aff_get_space(mpa2)); mpa2 = isl_multi_pw_aff_align_params(mpa2, isl_multi_pw_aff_get_space(mpa1)); if (!mpa1 || !mpa2) goto error; match = isl_space_tuple_is_equal(mpa1->space, isl_dim_out, mpa2->space, isl_dim_out); if (match < 0) goto error; if (!match) isl_die(isl_multi_pw_aff_get_ctx(mpa1), isl_error_invalid, "range spaces don't match", goto error); space1 = isl_space_domain(isl_multi_pw_aff_get_space(mpa1)); space2 = isl_space_domain(isl_multi_pw_aff_get_space(mpa2)); space1 = isl_space_map_from_domain_and_range(space1, space2); res = order(mpa1, mpa2, space1); isl_multi_pw_aff_free(mpa1); isl_multi_pw_aff_free(mpa2); return res; error: isl_multi_pw_aff_free(mpa1); isl_multi_pw_aff_free(mpa2); return NULL; } /* Return a map containing pairs of elements in the domains of "mpa1" and "mpa2" * where the function values are equal. "space" is the space of the result. * The parameters of "mpa1" and "mpa2" are assumed to have been aligned. * * "mpa1" and "mpa2" are equal when each of the pairs of elements * in the sequences are equal. */ static __isl_give isl_map *isl_multi_pw_aff_eq_map_on_space( __isl_keep isl_multi_pw_aff *mpa1, __isl_keep isl_multi_pw_aff *mpa2, __isl_take isl_space *space) { int i; isl_size n; isl_map *res; n = isl_multi_pw_aff_dim(mpa1, isl_dim_out); if (n < 0) space = isl_space_free(space); res = isl_map_universe(space); for (i = 0; i < n; ++i) { isl_pw_aff *pa1, *pa2; isl_map *map; pa1 = isl_multi_pw_aff_get_pw_aff(mpa1, i); pa2 = isl_multi_pw_aff_get_pw_aff(mpa2, i); map = isl_pw_aff_eq_map(pa1, pa2); res = isl_map_intersect(res, map); } return res; } /* Return a map containing pairs of elements in the domains of "mpa1" and "mpa2" * where the function values are equal. */ __isl_give isl_map *isl_multi_pw_aff_eq_map(__isl_take isl_multi_pw_aff *mpa1, __isl_take isl_multi_pw_aff *mpa2) { return isl_multi_pw_aff_order_map(mpa1, mpa2, &isl_multi_pw_aff_eq_map_on_space); } /* Intersect "map" with the result of applying "order" * on two copies of "mpa". */ static __isl_give isl_map *isl_map_order_at_multi_pw_aff( __isl_take isl_map *map, __isl_take isl_multi_pw_aff *mpa, __isl_give isl_map *(*order)(__isl_take isl_multi_pw_aff *mpa1, __isl_take isl_multi_pw_aff *mpa2)) { return isl_map_intersect(map, order(mpa, isl_multi_pw_aff_copy(mpa))); } /* Return the subset of "map" where the domain and the range * have equal "mpa" values. */ __isl_give isl_map *isl_map_eq_at_multi_pw_aff(__isl_take isl_map *map, __isl_take isl_multi_pw_aff *mpa) { return isl_map_order_at_multi_pw_aff(map, mpa, &isl_multi_pw_aff_eq_map); } /* Return a map containing pairs of elements in the domains of "mpa1" and "mpa2" * where the function values of "mpa1" lexicographically satisfies * "strict_base"/"base" compared to that of "mpa2". * "space" is the space of the result. * The parameters of "mpa1" and "mpa2" are assumed to have been aligned. * * "mpa1" lexicographically satisfies "strict_base"/"base" compared to "mpa2" * if, for some i, the i-th element of "mpa1" satisfies "strict_base"/"base" * when compared to the i-th element of "mpa2" while all previous elements are * pairwise equal. * In particular, if i corresponds to the final elements * then they need to satisfy "base", while "strict_base" needs to be satisfied * for other values of i. * If "base" is a strict order, then "base" and "strict_base" are the same. */ static __isl_give isl_map *isl_multi_pw_aff_lex_map_on_space( __isl_keep isl_multi_pw_aff *mpa1, __isl_keep isl_multi_pw_aff *mpa2, __isl_give isl_map *(*strict_base)(__isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2), __isl_give isl_map *(*base)(__isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2), __isl_take isl_space *space) { int i; isl_size n; isl_map *res, *rest; n = isl_multi_pw_aff_dim(mpa1, isl_dim_out); if (n < 0) space = isl_space_free(space); res = isl_map_empty(isl_space_copy(space)); rest = isl_map_universe(space); for (i = 0; i < n; ++i) { int last; isl_pw_aff *pa1, *pa2; isl_map *map; last = i == n - 1; pa1 = isl_multi_pw_aff_get_pw_aff(mpa1, i); pa2 = isl_multi_pw_aff_get_pw_aff(mpa2, i); map = last ? base(pa1, pa2) : strict_base(pa1, pa2); map = isl_map_intersect(map, isl_map_copy(rest)); res = isl_map_union(res, map); if (last) continue; pa1 = isl_multi_pw_aff_get_pw_aff(mpa1, i); pa2 = isl_multi_pw_aff_get_pw_aff(mpa2, i); map = isl_pw_aff_eq_map(pa1, pa2); rest = isl_map_intersect(rest, map); } isl_map_free(rest); return res; } #undef ORDER #define ORDER le #undef STRICT_ORDER #define STRICT_ORDER lt #include "isl_aff_lex_templ.c" #undef ORDER #define ORDER lt #undef STRICT_ORDER #define STRICT_ORDER lt #include "isl_aff_lex_templ.c" #undef ORDER #define ORDER ge #undef STRICT_ORDER #define STRICT_ORDER gt #include "isl_aff_lex_templ.c" #undef ORDER #define ORDER gt #undef STRICT_ORDER #define STRICT_ORDER gt #include "isl_aff_lex_templ.c" /* Compare two isl_affs. * * Return -1 if "aff1" is "smaller" than "aff2", 1 if "aff1" is "greater" * than "aff2" and 0 if they are equal. * * The order is fairly arbitrary. We do consider expressions that only involve * earlier dimensions as "smaller". */ int isl_aff_plain_cmp(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2) { int cmp; int last1, last2; if (aff1 == aff2) return 0; if (!aff1) return -1; if (!aff2) return 1; cmp = isl_local_space_cmp(aff1->ls, aff2->ls); if (cmp != 0) return cmp; last1 = isl_seq_last_non_zero(aff1->v->el + 1, aff1->v->size - 1); last2 = isl_seq_last_non_zero(aff2->v->el + 1, aff1->v->size - 1); if (last1 != last2) return last1 - last2; return isl_seq_cmp(aff1->v->el, aff2->v->el, aff1->v->size); } /* Compare two isl_pw_affs. * * Return -1 if "pa1" is "smaller" than "pa2", 1 if "pa1" is "greater" * than "pa2" and 0 if they are equal. * * The order is fairly arbitrary. We do consider expressions that only involve * earlier dimensions as "smaller". */ int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1, __isl_keep isl_pw_aff *pa2) { int i; int cmp; if (pa1 == pa2) return 0; if (!pa1) return -1; if (!pa2) return 1; cmp = isl_space_cmp(pa1->dim, pa2->dim); if (cmp != 0) return cmp; if (pa1->n != pa2->n) return pa1->n - pa2->n; for (i = 0; i < pa1->n; ++i) { cmp = isl_set_plain_cmp(pa1->p[i].set, pa2->p[i].set); if (cmp != 0) return cmp; cmp = isl_aff_plain_cmp(pa1->p[i].aff, pa2->p[i].aff); if (cmp != 0) return cmp; } return 0; } /* Return a piecewise affine expression that is equal to "v" on "domain". */ __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(__isl_take isl_set *domain, __isl_take isl_val *v) { isl_space *space; isl_local_space *ls; isl_aff *aff; space = isl_set_get_space(domain); ls = isl_local_space_from_space(space); aff = isl_aff_val_on_domain(ls, v); return isl_pw_aff_alloc(domain, aff); } /* Return a piecewise affine expression that is equal to the parameter * with identifier "id" on "domain". */ __isl_give isl_pw_aff *isl_pw_aff_param_on_domain_id( __isl_take isl_set *domain, __isl_take isl_id *id) { isl_space *space; isl_aff *aff; space = isl_set_get_space(domain); space = isl_space_add_param_id(space, isl_id_copy(id)); domain = isl_set_align_params(domain, isl_space_copy(space)); aff = isl_aff_param_on_domain_space_id(space, id); return isl_pw_aff_alloc(domain, aff); } /* Return a multi affine expression that is equal to "mv" on domain * space "space". */ __isl_give isl_multi_aff *isl_multi_aff_multi_val_on_domain_space( __isl_take isl_space *space, __isl_take isl_multi_val *mv) { int i; isl_size n; isl_space *space2; isl_local_space *ls; isl_multi_aff *ma; n = isl_multi_val_dim(mv, isl_dim_set); if (!space || n < 0) goto error; space2 = isl_multi_val_get_space(mv); space2 = isl_space_align_params(space2, isl_space_copy(space)); space = isl_space_align_params(space, isl_space_copy(space2)); space = isl_space_map_from_domain_and_range(space, space2); ma = isl_multi_aff_alloc(isl_space_copy(space)); ls = isl_local_space_from_space(isl_space_domain(space)); for (i = 0; i < n; ++i) { isl_val *v; isl_aff *aff; v = isl_multi_val_get_val(mv, i); aff = isl_aff_val_on_domain(isl_local_space_copy(ls), v); ma = isl_multi_aff_set_aff(ma, i, aff); } isl_local_space_free(ls); isl_multi_val_free(mv); return ma; error: isl_space_free(space); isl_multi_val_free(mv); return NULL; } /* This is an alternative name for the function above. */ __isl_give isl_multi_aff *isl_multi_aff_multi_val_on_space( __isl_take isl_space *space, __isl_take isl_multi_val *mv) { return isl_multi_aff_multi_val_on_domain_space(space, mv); } /* This function performs the same operation as * isl_multi_aff_multi_val_on_domain_space, * but is considered as a function on an isl_space when exported. */ __isl_give isl_multi_aff *isl_space_multi_aff_on_domain_multi_val( __isl_take isl_space *space, __isl_take isl_multi_val *mv) { return isl_multi_aff_multi_val_on_domain_space(space, mv); } /* Return a piecewise multi-affine expression * that is equal to "mv" on "domain". */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_multi_val_on_domain( __isl_take isl_set *domain, __isl_take isl_multi_val *mv) { isl_space *space; isl_multi_aff *ma; space = isl_set_get_space(domain); ma = isl_multi_aff_multi_val_on_space(space, mv); return isl_pw_multi_aff_alloc(domain, ma); } /* This function performs the same operation as * isl_pw_multi_aff_multi_val_on_domain, * but is considered as a function on an isl_set when exported. */ __isl_give isl_pw_multi_aff *isl_set_pw_multi_aff_on_domain_multi_val( __isl_take isl_set *domain, __isl_take isl_multi_val *mv) { return isl_pw_multi_aff_multi_val_on_domain(domain, mv); } /* Internal data structure for isl_union_pw_multi_aff_multi_val_on_domain. * mv is the value that should be attained on each domain set * res collects the results */ struct isl_union_pw_multi_aff_multi_val_on_domain_data { isl_multi_val *mv; isl_union_pw_multi_aff *res; }; /* Create an isl_pw_multi_aff equal to data->mv on "domain" * and add it to data->res. */ static isl_stat pw_multi_aff_multi_val_on_domain(__isl_take isl_set *domain, void *user) { struct isl_union_pw_multi_aff_multi_val_on_domain_data *data = user; isl_pw_multi_aff *pma; isl_multi_val *mv; mv = isl_multi_val_copy(data->mv); pma = isl_pw_multi_aff_multi_val_on_domain(domain, mv); data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma); return data->res ? isl_stat_ok : isl_stat_error; } /* Return a union piecewise multi-affine expression * that is equal to "mv" on "domain". */ __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_multi_val_on_domain( __isl_take isl_union_set *domain, __isl_take isl_multi_val *mv) { struct isl_union_pw_multi_aff_multi_val_on_domain_data data; isl_space *space; space = isl_union_set_get_space(domain); data.res = isl_union_pw_multi_aff_empty(space); data.mv = mv; if (isl_union_set_foreach_set(domain, &pw_multi_aff_multi_val_on_domain, &data) < 0) data.res = isl_union_pw_multi_aff_free(data.res); isl_union_set_free(domain); isl_multi_val_free(mv); return data.res; } /* Compute the pullback of data->pma by the function represented by "pma2", * provided the spaces match, and add the results to data->res. */ static isl_stat pullback_entry(__isl_take isl_pw_multi_aff *pma2, void *user) { struct isl_union_pw_multi_aff_bin_data *data = user; if (!isl_space_tuple_is_equal(data->pma->dim, isl_dim_in, pma2->dim, isl_dim_out)) { isl_pw_multi_aff_free(pma2); return isl_stat_ok; } pma2 = isl_pw_multi_aff_pullback_pw_multi_aff( isl_pw_multi_aff_copy(data->pma), pma2); data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma2); if (!data->res) return isl_stat_error; return isl_stat_ok; } /* Compute the pullback of "upma1" by the function represented by "upma2". */ __isl_give isl_union_pw_multi_aff * isl_union_pw_multi_aff_pullback_union_pw_multi_aff( __isl_take isl_union_pw_multi_aff *upma1, __isl_take isl_union_pw_multi_aff *upma2) { return bin_op(upma1, upma2, &pullback_entry); } /* Apply "upma2" to "upma1". * * That is, compute the pullback of "upma2" by "upma1". */ __isl_give isl_union_pw_multi_aff * isl_union_pw_multi_aff_apply_union_pw_multi_aff( __isl_take isl_union_pw_multi_aff *upma1, __isl_take isl_union_pw_multi_aff *upma2) { return isl_union_pw_multi_aff_pullback_union_pw_multi_aff(upma2, upma1); } #undef TYPE #define TYPE isl_pw_multi_aff static #include "isl_copy_tuple_id_templ.c" /* Given a function "pma1" of the form A[B -> C] -> D and * a function "pma2" of the form E -> B, * replace the domain of the wrapped relation inside the domain of "pma1" * by the preimage with respect to "pma2". * In other words, plug in "pma2" in this nested domain. * The result is of the form A[E -> C] -> D. * * In particular, extend E -> B to A[E -> C] -> A[B -> C] and * plug that into "pma1". */ __isl_give isl_pw_multi_aff * isl_pw_multi_aff_preimage_domain_wrapped_domain_pw_multi_aff( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { isl_space *pma1_space, *pma2_space; isl_space *space; isl_pw_multi_aff *id; pma1_space = isl_pw_multi_aff_peek_space(pma1); pma2_space = isl_pw_multi_aff_peek_space(pma2); if (isl_space_check_domain_is_wrapping(pma1_space) < 0) goto error; if (isl_space_check_wrapped_tuple_is_equal(pma1_space, isl_dim_in, isl_dim_in, pma2_space, isl_dim_out) < 0) goto error; space = isl_space_domain(isl_space_copy(pma1_space)); space = isl_space_range(isl_space_unwrap(space)); id = isl_pw_multi_aff_identity_on_domain_space(space); pma2 = isl_pw_multi_aff_product(pma2, id); pma2 = isl_pw_multi_aff_copy_tuple_id(pma2, isl_dim_in, pma1_space, isl_dim_in); pma2 = isl_pw_multi_aff_copy_tuple_id(pma2, isl_dim_out, pma1_space, isl_dim_in); return isl_pw_multi_aff_pullback_pw_multi_aff(pma1, pma2); error: isl_pw_multi_aff_free(pma1); isl_pw_multi_aff_free(pma2); return NULL; } /* If data->pma and "pma2" are such that * data->pma is of the form A[B -> C] -> D and * "pma2" is of the form E -> B, * then replace the domain of the wrapped relation * inside the domain of data->pma by the preimage with respect to "pma2" and * add the result to data->res. */ static isl_stat preimage_domain_wrapped_domain_entry( __isl_take isl_pw_multi_aff *pma2, void *user) { struct isl_union_pw_multi_aff_bin_data *data = user; isl_space *pma1_space, *pma2_space; isl_bool match; pma1_space = isl_pw_multi_aff_peek_space(data->pma); pma2_space = isl_pw_multi_aff_peek_space(pma2); match = isl_space_domain_is_wrapping(pma1_space); if (match >= 0 && match) match = isl_space_wrapped_tuple_is_equal(pma1_space, isl_dim_in, isl_dim_in, pma2_space, isl_dim_out); if (match < 0 || !match) { isl_pw_multi_aff_free(pma2); return match < 0 ? isl_stat_error : isl_stat_ok; } pma2 = isl_pw_multi_aff_preimage_domain_wrapped_domain_pw_multi_aff( isl_pw_multi_aff_copy(data->pma), pma2); data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma2); return isl_stat_non_null(data->res); } /* For each pair of functions A[B -> C] -> D in "upma1" and * E -> B in "upma2", * replace the domain of the wrapped relation inside the domain of the first * by the preimage with respect to the second and collect the results. * In other words, plug in the second function in this nested domain. * The results are of the form A[E -> C] -> D. */ __isl_give isl_union_pw_multi_aff * isl_union_pw_multi_aff_preimage_domain_wrapped_domain_union_pw_multi_aff( __isl_take isl_union_pw_multi_aff *upma1, __isl_take isl_union_pw_multi_aff *upma2) { return bin_op(upma1, upma2, &preimage_domain_wrapped_domain_entry); } /* Check that the domain space of "upa" matches "space". * * This function is called from isl_multi_union_pw_aff_set_union_pw_aff and * can in principle never fail since the space "space" is that * of the isl_multi_union_pw_aff and is a set space such that * there is no domain space to match. * * We check the parameters and double-check that "space" is * indeed that of a set. */ static isl_stat isl_union_pw_aff_check_match_domain_space( __isl_keep isl_union_pw_aff *upa, __isl_keep isl_space *space) { isl_space *upa_space; isl_bool match; if (!upa || !space) return isl_stat_error; match = isl_space_is_set(space); if (match < 0) return isl_stat_error; if (!match) isl_die(isl_space_get_ctx(space), isl_error_invalid, "expecting set space", return isl_stat_error); upa_space = isl_union_pw_aff_get_space(upa); match = isl_space_has_equal_params(space, upa_space); if (match < 0) goto error; if (!match) isl_die(isl_space_get_ctx(space), isl_error_invalid, "parameters don't match", goto error); isl_space_free(upa_space); return isl_stat_ok; error: isl_space_free(upa_space); return isl_stat_error; } /* Do the parameters of "upa" match those of "space"? */ static isl_bool isl_union_pw_aff_matching_params( __isl_keep isl_union_pw_aff *upa, __isl_keep isl_space *space) { isl_space *upa_space; isl_bool match; if (!upa || !space) return isl_bool_error; upa_space = isl_union_pw_aff_get_space(upa); match = isl_space_has_equal_params(space, upa_space); isl_space_free(upa_space); return match; } /* Internal data structure for isl_union_pw_aff_reset_domain_space. * space represents the new parameters. * res collects the results. */ struct isl_union_pw_aff_reset_params_data { isl_space *space; isl_union_pw_aff *res; }; /* Replace the parameters of "pa" by data->space and * add the result to data->res. */ static isl_stat reset_params(__isl_take isl_pw_aff *pa, void *user) { struct isl_union_pw_aff_reset_params_data *data = user; isl_space *space; space = isl_pw_aff_get_space(pa); space = isl_space_replace_params(space, data->space); pa = isl_pw_aff_reset_space(pa, space); data->res = isl_union_pw_aff_add_pw_aff(data->res, pa); return data->res ? isl_stat_ok : isl_stat_error; } /* Replace the domain space of "upa" by "space". * Since a union expression does not have a (single) domain space, * "space" is necessarily a parameter space. * * Since the order and the names of the parameters determine * the hash value, we need to create a new hash table. */ static __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_domain_space( __isl_take isl_union_pw_aff *upa, __isl_take isl_space *space) { struct isl_union_pw_aff_reset_params_data data = { space }; isl_bool match; match = isl_union_pw_aff_matching_params(upa, space); if (match < 0) upa = isl_union_pw_aff_free(upa); else if (match) { isl_space_free(space); return upa; } data.res = isl_union_pw_aff_empty(isl_space_copy(space)); if (isl_union_pw_aff_foreach_pw_aff(upa, &reset_params, &data) < 0) data.res = isl_union_pw_aff_free(data.res); isl_union_pw_aff_free(upa); isl_space_free(space); return data.res; } /* Return the floor of "pa". */ static __isl_give isl_pw_aff *floor_entry(__isl_take isl_pw_aff *pa, void *user) { return isl_pw_aff_floor(pa); } /* Given f, return floor(f). */ __isl_give isl_union_pw_aff *isl_union_pw_aff_floor( __isl_take isl_union_pw_aff *upa) { return isl_union_pw_aff_transform_inplace(upa, &floor_entry, NULL); } /* Compute * * upa mod m = upa - m * floor(upa/m) * * with m an integer value. */ __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val( __isl_take isl_union_pw_aff *upa, __isl_take isl_val *m) { isl_union_pw_aff *res; if (!upa || !m) goto error; if (!isl_val_is_int(m)) isl_die(isl_val_get_ctx(m), isl_error_invalid, "expecting integer modulo", goto error); if (!isl_val_is_pos(m)) isl_die(isl_val_get_ctx(m), isl_error_invalid, "expecting positive modulo", goto error); res = isl_union_pw_aff_copy(upa); upa = isl_union_pw_aff_scale_down_val(upa, isl_val_copy(m)); upa = isl_union_pw_aff_floor(upa); upa = isl_union_pw_aff_scale_val(upa, m); res = isl_union_pw_aff_sub(res, upa); return res; error: isl_val_free(m); isl_union_pw_aff_free(upa); return NULL; } /* Internal data structure for isl_union_pw_multi_aff_get_union_pw_aff. * pos is the output position that needs to be extracted. * res collects the results. */ struct isl_union_pw_multi_aff_get_union_pw_aff_data { int pos; isl_union_pw_aff *res; }; /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma" * (assuming it has such a dimension) and add it to data->res. */ static isl_stat get_union_pw_aff(__isl_take isl_pw_multi_aff *pma, void *user) { struct isl_union_pw_multi_aff_get_union_pw_aff_data *data = user; isl_size n_out; isl_pw_aff *pa; n_out = isl_pw_multi_aff_dim(pma, isl_dim_out); if (n_out < 0) return isl_stat_error; if (data->pos >= n_out) { isl_pw_multi_aff_free(pma); return isl_stat_ok; } pa = isl_pw_multi_aff_get_pw_aff(pma, data->pos); isl_pw_multi_aff_free(pma); data->res = isl_union_pw_aff_add_pw_aff(data->res, pa); return data->res ? isl_stat_ok : isl_stat_error; } /* Extract an isl_union_pw_aff corresponding to * output dimension "pos" of "upma". */ __isl_give isl_union_pw_aff *isl_union_pw_multi_aff_get_union_pw_aff( __isl_keep isl_union_pw_multi_aff *upma, int pos) { struct isl_union_pw_multi_aff_get_union_pw_aff_data data; isl_space *space; if (!upma) return NULL; if (pos < 0) isl_die(isl_union_pw_multi_aff_get_ctx(upma), isl_error_invalid, "cannot extract at negative position", return NULL); space = isl_union_pw_multi_aff_get_space(upma); data.res = isl_union_pw_aff_empty(space); data.pos = pos; if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma, &get_union_pw_aff, &data) < 0) data.res = isl_union_pw_aff_free(data.res); return data.res; } /* Return a union piecewise affine expression * that is equal to "aff" on "domain". */ __isl_give isl_union_pw_aff *isl_union_pw_aff_aff_on_domain( __isl_take isl_union_set *domain, __isl_take isl_aff *aff) { isl_pw_aff *pa; pa = isl_pw_aff_from_aff(aff); return isl_union_pw_aff_pw_aff_on_domain(domain, pa); } /* Return a union piecewise affine expression * that is equal to the parameter identified by "id" on "domain". * * Make sure the parameter appears in the space passed to * isl_aff_param_on_domain_space_id. */ __isl_give isl_union_pw_aff *isl_union_pw_aff_param_on_domain_id( __isl_take isl_union_set *domain, __isl_take isl_id *id) { isl_space *space; isl_aff *aff; space = isl_union_set_get_space(domain); space = isl_space_add_param_id(space, isl_id_copy(id)); aff = isl_aff_param_on_domain_space_id(space, id); return isl_union_pw_aff_aff_on_domain(domain, aff); } /* Internal data structure for isl_union_pw_aff_pw_aff_on_domain. * "pa" is the piecewise symbolic value that the resulting isl_union_pw_aff * needs to attain. * "res" collects the results. */ struct isl_union_pw_aff_pw_aff_on_domain_data { isl_pw_aff *pa; isl_union_pw_aff *res; }; /* Construct a piecewise affine expression that is equal to data->pa * on "domain" and add the result to data->res. */ static isl_stat pw_aff_on_domain(__isl_take isl_set *domain, void *user) { struct isl_union_pw_aff_pw_aff_on_domain_data *data = user; isl_pw_aff *pa; isl_size dim; pa = isl_pw_aff_copy(data->pa); dim = isl_set_dim(domain, isl_dim_set); if (dim < 0) pa = isl_pw_aff_free(pa); pa = isl_pw_aff_from_range(pa); pa = isl_pw_aff_add_dims(pa, isl_dim_in, dim); pa = isl_pw_aff_reset_domain_space(pa, isl_set_get_space(domain)); pa = isl_pw_aff_intersect_domain(pa, domain); data->res = isl_union_pw_aff_add_pw_aff(data->res, pa); return data->res ? isl_stat_ok : isl_stat_error; } /* Return a union piecewise affine expression * that is equal to "pa" on "domain", assuming "domain" and "pa" * have been aligned. * * Construct an isl_pw_aff on each of the sets in "domain" and * collect the results. */ static __isl_give isl_union_pw_aff *isl_union_pw_aff_pw_aff_on_domain_aligned( __isl_take isl_union_set *domain, __isl_take isl_pw_aff *pa) { struct isl_union_pw_aff_pw_aff_on_domain_data data; isl_space *space; space = isl_union_set_get_space(domain); data.res = isl_union_pw_aff_empty(space); data.pa = pa; if (isl_union_set_foreach_set(domain, &pw_aff_on_domain, &data) < 0) data.res = isl_union_pw_aff_free(data.res); isl_union_set_free(domain); isl_pw_aff_free(pa); return data.res; } /* Return a union piecewise affine expression * that is equal to "pa" on "domain". * * Check that "pa" is a parametric expression, * align the parameters if needed and call * isl_union_pw_aff_pw_aff_on_domain_aligned. */ __isl_give isl_union_pw_aff *isl_union_pw_aff_pw_aff_on_domain( __isl_take isl_union_set *domain, __isl_take isl_pw_aff *pa) { isl_bool is_set; isl_bool equal_params; isl_space *domain_space, *pa_space; pa_space = isl_pw_aff_peek_space(pa); is_set = isl_space_is_set(pa_space); if (is_set < 0) goto error; if (!is_set) isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid, "expecting parametric expression", goto error); domain_space = isl_union_set_get_space(domain); pa_space = isl_pw_aff_get_space(pa); equal_params = isl_space_has_equal_params(domain_space, pa_space); if (equal_params >= 0 && !equal_params) { isl_space *space; space = isl_space_align_params(domain_space, pa_space); pa = isl_pw_aff_align_params(pa, isl_space_copy(space)); domain = isl_union_set_align_params(domain, space); } else { isl_space_free(domain_space); isl_space_free(pa_space); } if (equal_params < 0) goto error; return isl_union_pw_aff_pw_aff_on_domain_aligned(domain, pa); error: isl_union_set_free(domain); isl_pw_aff_free(pa); return NULL; } /* Internal data structure for isl_union_pw_aff_val_on_domain. * "v" is the value that the resulting isl_union_pw_aff needs to attain. * "res" collects the results. */ struct isl_union_pw_aff_val_on_domain_data { isl_val *v; isl_union_pw_aff *res; }; /* Construct a piecewise affine expression that is equal to data->v * on "domain" and add the result to data->res. */ static isl_stat pw_aff_val_on_domain(__isl_take isl_set *domain, void *user) { struct isl_union_pw_aff_val_on_domain_data *data = user; isl_pw_aff *pa; isl_val *v; v = isl_val_copy(data->v); pa = isl_pw_aff_val_on_domain(domain, v); data->res = isl_union_pw_aff_add_pw_aff(data->res, pa); return data->res ? isl_stat_ok : isl_stat_error; } /* Return a union piecewise affine expression * that is equal to "v" on "domain". * * Construct an isl_pw_aff on each of the sets in "domain" and * collect the results. */ __isl_give isl_union_pw_aff *isl_union_pw_aff_val_on_domain( __isl_take isl_union_set *domain, __isl_take isl_val *v) { struct isl_union_pw_aff_val_on_domain_data data; isl_space *space; space = isl_union_set_get_space(domain); data.res = isl_union_pw_aff_empty(space); data.v = v; if (isl_union_set_foreach_set(domain, &pw_aff_val_on_domain, &data) < 0) data.res = isl_union_pw_aff_free(data.res); isl_union_set_free(domain); isl_val_free(v); return data.res; } /* Construct a piecewise multi affine expression * that is equal to "pa" and add it to upma. */ static isl_stat pw_multi_aff_from_pw_aff_entry(__isl_take isl_pw_aff *pa, void *user) { isl_union_pw_multi_aff **upma = user; isl_pw_multi_aff *pma; pma = isl_pw_multi_aff_from_pw_aff(pa); *upma = isl_union_pw_multi_aff_add_pw_multi_aff(*upma, pma); return *upma ? isl_stat_ok : isl_stat_error; } /* Construct and return a union piecewise multi affine expression * that is equal to the given union piecewise affine expression. */ __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_union_pw_aff( __isl_take isl_union_pw_aff *upa) { isl_space *space; isl_union_pw_multi_aff *upma; if (!upa) return NULL; space = isl_union_pw_aff_get_space(upa); upma = isl_union_pw_multi_aff_empty(space); if (isl_union_pw_aff_foreach_pw_aff(upa, &pw_multi_aff_from_pw_aff_entry, &upma) < 0) upma = isl_union_pw_multi_aff_free(upma); isl_union_pw_aff_free(upa); return upma; } /* Compute the set of elements in the domain of "pa" where it is zero and * add this set to "uset". */ static isl_stat zero_union_set(__isl_take isl_pw_aff *pa, void *user) { isl_union_set **uset = (isl_union_set **)user; *uset = isl_union_set_add_set(*uset, isl_pw_aff_zero_set(pa)); return *uset ? isl_stat_ok : isl_stat_error; } /* Return a union set containing those elements in the domain * of "upa" where it is zero. */ __isl_give isl_union_set *isl_union_pw_aff_zero_union_set( __isl_take isl_union_pw_aff *upa) { isl_union_set *zero; zero = isl_union_set_empty(isl_union_pw_aff_get_space(upa)); if (isl_union_pw_aff_foreach_pw_aff(upa, &zero_union_set, &zero) < 0) zero = isl_union_set_free(zero); isl_union_pw_aff_free(upa); return zero; } /* Internal data structure for isl_union_pw_aff_bind_id, * storing the parameter that needs to be bound and * the accumulated results. */ struct isl_bind_id_data { isl_id *id; isl_union_set *bound; }; /* Bind the piecewise affine function "pa" to the parameter data->id, * adding the resulting elements in the domain where the expression * is equal to the parameter to data->bound. */ static isl_stat bind_id(__isl_take isl_pw_aff *pa, void *user) { struct isl_bind_id_data *data = user; isl_set *bound; bound = isl_pw_aff_bind_id(pa, isl_id_copy(data->id)); data->bound = isl_union_set_add_set(data->bound, bound); return data->bound ? isl_stat_ok : isl_stat_error; } /* Bind the union piecewise affine function "upa" to the parameter "id", * returning the elements in the domain where the expression * is equal to the parameter. */ __isl_give isl_union_set *isl_union_pw_aff_bind_id( __isl_take isl_union_pw_aff *upa, __isl_take isl_id *id) { struct isl_bind_id_data data = { id }; data.bound = isl_union_set_empty(isl_union_pw_aff_get_space(upa)); if (isl_union_pw_aff_foreach_pw_aff(upa, &bind_id, &data) < 0) data.bound = isl_union_set_free(data.bound); isl_union_pw_aff_free(upa); isl_id_free(id); return data.bound; } /* Internal data structure for isl_union_pw_aff_pullback_union_pw_multi_aff. * upma is the function that is plugged in. * pa is the current part of the function in which upma is plugged in. * res collects the results. */ struct isl_union_pw_aff_pullback_upma_data { isl_union_pw_multi_aff *upma; isl_pw_aff *pa; isl_union_pw_aff *res; }; /* Check if "pma" can be plugged into data->pa. * If so, perform the pullback and add the result to data->res. */ static isl_stat pa_pb_pma(__isl_take isl_pw_multi_aff *pma, void *user) { struct isl_union_pw_aff_pullback_upma_data *data = user; isl_pw_aff *pa; if (!isl_space_tuple_is_equal(data->pa->dim, isl_dim_in, pma->dim, isl_dim_out)) { isl_pw_multi_aff_free(pma); return isl_stat_ok; } pa = isl_pw_aff_copy(data->pa); pa = isl_pw_aff_pullback_pw_multi_aff(pa, pma); data->res = isl_union_pw_aff_add_pw_aff(data->res, pa); return data->res ? isl_stat_ok : isl_stat_error; } /* Check if any of the elements of data->upma can be plugged into pa, * add if so add the result to data->res. */ static isl_stat upa_pb_upma(__isl_take isl_pw_aff *pa, void *user) { struct isl_union_pw_aff_pullback_upma_data *data = user; isl_stat r; data->pa = pa; r = isl_union_pw_multi_aff_foreach_pw_multi_aff(data->upma, &pa_pb_pma, data); isl_pw_aff_free(pa); return r; } /* Compute the pullback of "upa" by the function represented by "upma". * In other words, plug in "upma" in "upa". The result contains * expressions defined over the domain space of "upma". * * Run over all pairs of elements in "upa" and "upma", perform * the pullback when appropriate and collect the results. * If the hash value were based on the domain space rather than * the function space, then we could run through all elements * of "upma" and directly pick out the corresponding element of "upa". */ __isl_give isl_union_pw_aff *isl_union_pw_aff_pullback_union_pw_multi_aff( __isl_take isl_union_pw_aff *upa, __isl_take isl_union_pw_multi_aff *upma) { struct isl_union_pw_aff_pullback_upma_data data = { NULL, NULL }; isl_space *space; space = isl_union_pw_multi_aff_get_space(upma); upa = isl_union_pw_aff_align_params(upa, space); space = isl_union_pw_aff_get_space(upa); upma = isl_union_pw_multi_aff_align_params(upma, space); if (!upa || !upma) goto error; data.upma = upma; data.res = isl_union_pw_aff_alloc_same_size(upa); if (isl_union_pw_aff_foreach_pw_aff(upa, &upa_pb_upma, &data) < 0) data.res = isl_union_pw_aff_free(data.res); isl_union_pw_aff_free(upa); isl_union_pw_multi_aff_free(upma); return data.res; error: isl_union_pw_aff_free(upa); isl_union_pw_multi_aff_free(upma); return NULL; } #undef BASE #define BASE union_pw_aff #undef DOMBASE #define DOMBASE union_set #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include /* Does "mupa" have a non-trivial explicit domain? * * The explicit domain, if present, is trivial if it represents * an (obviously) universe parameter set. */ isl_bool isl_multi_union_pw_aff_has_non_trivial_domain( __isl_keep isl_multi_union_pw_aff *mupa) { isl_bool is_params, trivial; isl_set *set; if (!mupa) return isl_bool_error; if (!isl_multi_union_pw_aff_has_explicit_domain(mupa)) return isl_bool_false; is_params = isl_union_set_is_params(mupa->u.dom); if (is_params < 0 || !is_params) return isl_bool_not(is_params); set = isl_set_from_union_set(isl_union_set_copy(mupa->u.dom)); trivial = isl_set_plain_is_universe(set); isl_set_free(set); return isl_bool_not(trivial); } /* Construct a multiple union piecewise affine expression * in the given space with value zero in each of the output dimensions. * * Since there is no canonical zero value for * a union piecewise affine expression, we can only construct * a zero-dimensional "zero" value. */ __isl_give isl_multi_union_pw_aff *isl_multi_union_pw_aff_zero( __isl_take isl_space *space) { isl_bool params; isl_size dim; if (!space) return NULL; params = isl_space_is_params(space); if (params < 0) goto error; if (params) isl_die(isl_space_get_ctx(space), isl_error_invalid, "expecting proper set space", goto error); if (!isl_space_is_set(space)) isl_die(isl_space_get_ctx(space), isl_error_invalid, "expecting set space", goto error); dim = isl_space_dim(space, isl_dim_out); if (dim < 0) goto error; if (dim != 0) isl_die(isl_space_get_ctx(space), isl_error_invalid, "expecting 0D space", goto error); return isl_multi_union_pw_aff_alloc(space); error: isl_space_free(space); return NULL; } /* Construct and return a multi union piecewise affine expression * that is equal to the given multi affine expression. */ __isl_give isl_multi_union_pw_aff *isl_multi_union_pw_aff_from_multi_aff( __isl_take isl_multi_aff *ma) { isl_multi_pw_aff *mpa; mpa = isl_multi_pw_aff_from_multi_aff(ma); return isl_multi_union_pw_aff_from_multi_pw_aff(mpa); } /* This function performs the same operation as * isl_multi_union_pw_aff_from_multi_aff, but is considered as a function on an * isl_multi_aff when exported. */ __isl_give isl_multi_union_pw_aff *isl_multi_aff_to_multi_union_pw_aff( __isl_take isl_multi_aff *ma) { return isl_multi_union_pw_aff_from_multi_aff(ma); } /* Construct and return a multi union piecewise affine expression * that is equal to the given multi piecewise affine expression. */ __isl_give isl_multi_union_pw_aff *isl_multi_union_pw_aff_from_multi_pw_aff( __isl_take isl_multi_pw_aff *mpa) { int i; isl_size n; isl_space *space; isl_multi_union_pw_aff *mupa; n = isl_multi_pw_aff_dim(mpa, isl_dim_out); if (n < 0) mpa = isl_multi_pw_aff_free(mpa); if (!mpa) return NULL; space = isl_multi_pw_aff_get_space(mpa); space = isl_space_range(space); mupa = isl_multi_union_pw_aff_alloc(space); for (i = 0; i < n; ++i) { isl_pw_aff *pa; isl_union_pw_aff *upa; pa = isl_multi_pw_aff_get_pw_aff(mpa, i); upa = isl_union_pw_aff_from_pw_aff(pa); mupa = isl_multi_union_pw_aff_restore_check_space(mupa, i, upa); } isl_multi_pw_aff_free(mpa); return mupa; } /* Extract the range space of "pma" and assign it to *space. * If *space has already been set (through a previous call to this function), * then check that the range space is the same. */ static isl_stat extract_space(__isl_take isl_pw_multi_aff *pma, void *user) { isl_space **space = user; isl_space *pma_space; isl_bool equal; pma_space = isl_space_range(isl_pw_multi_aff_get_space(pma)); isl_pw_multi_aff_free(pma); if (!pma_space) return isl_stat_error; if (!*space) { *space = pma_space; return isl_stat_ok; } equal = isl_space_is_equal(pma_space, *space); isl_space_free(pma_space); if (equal < 0) return isl_stat_error; if (!equal) isl_die(isl_space_get_ctx(*space), isl_error_invalid, "range spaces not the same", return isl_stat_error); return isl_stat_ok; } /* Construct and return a multi union piecewise affine expression * that is equal to the given union piecewise multi affine expression. * * In order to be able to perform the conversion, the input * needs to be non-empty and may only involve a single range space. * * If the resulting multi union piecewise affine expression has * an explicit domain, then assign it the domain of the input. * In other cases, the domain is stored in the individual elements. */ __isl_give isl_multi_union_pw_aff * isl_multi_union_pw_aff_from_union_pw_multi_aff( __isl_take isl_union_pw_multi_aff *upma) { isl_space *space = NULL; isl_multi_union_pw_aff *mupa; int i; isl_size n; n = isl_union_pw_multi_aff_n_pw_multi_aff(upma); if (n < 0) goto error; if (n == 0) isl_die(isl_union_pw_multi_aff_get_ctx(upma), isl_error_invalid, "cannot extract range space from empty input", goto error); if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma, &extract_space, &space) < 0) goto error; if (!space) goto error; n = isl_space_dim(space, isl_dim_set); if (n < 0) space = isl_space_free(space); mupa = isl_multi_union_pw_aff_alloc(space); for (i = 0; i < n; ++i) { isl_union_pw_aff *upa; upa = isl_union_pw_multi_aff_get_union_pw_aff(upma, i); mupa = isl_multi_union_pw_aff_set_union_pw_aff(mupa, i, upa); } if (isl_multi_union_pw_aff_has_explicit_domain(mupa)) { isl_union_set *dom; isl_union_pw_multi_aff *copy; copy = isl_union_pw_multi_aff_copy(upma); dom = isl_union_pw_multi_aff_domain(copy); mupa = isl_multi_union_pw_aff_intersect_domain(mupa, dom); } isl_union_pw_multi_aff_free(upma); return mupa; error: isl_space_free(space); isl_union_pw_multi_aff_free(upma); return NULL; } /* This function performs the same operation as * isl_multi_union_pw_aff_from_union_pw_multi_aff, * but is considered as a function on an isl_union_pw_multi_aff when exported. */ __isl_give isl_multi_union_pw_aff * isl_union_pw_multi_aff_as_multi_union_pw_aff( __isl_take isl_union_pw_multi_aff *upma) { return isl_multi_union_pw_aff_from_union_pw_multi_aff(upma); } /* Try and create an isl_multi_union_pw_aff that is equivalent * to the given isl_union_map. * The isl_union_map is required to be single-valued in each space. * Moreover, it cannot be empty and all range spaces need to be the same. * Otherwise, an error is produced. */ __isl_give isl_multi_union_pw_aff *isl_multi_union_pw_aff_from_union_map( __isl_take isl_union_map *umap) { isl_union_pw_multi_aff *upma; upma = isl_union_pw_multi_aff_from_union_map(umap); return isl_multi_union_pw_aff_from_union_pw_multi_aff(upma); } /* This function performs the same operation as * isl_multi_union_pw_aff_from_union_map, * but is considered as a function on an isl_union_map when exported. */ __isl_give isl_multi_union_pw_aff *isl_union_map_as_multi_union_pw_aff( __isl_take isl_union_map *umap) { return isl_multi_union_pw_aff_from_union_map(umap); } /* Return a multiple union piecewise affine expression * that is equal to "mv" on "domain", assuming "domain" and "mv" * have been aligned. * * If the resulting multi union piecewise affine expression has * an explicit domain, then assign it the input domain. * In other cases, the domain is stored in the individual elements. */ static __isl_give isl_multi_union_pw_aff * isl_multi_union_pw_aff_multi_val_on_domain_aligned( __isl_take isl_union_set *domain, __isl_take isl_multi_val *mv) { int i; isl_size n; isl_space *space; isl_multi_union_pw_aff *mupa; n = isl_multi_val_dim(mv, isl_dim_set); if (!domain || n < 0) goto error; space = isl_multi_val_get_space(mv); mupa = isl_multi_union_pw_aff_alloc(space); for (i = 0; i < n; ++i) { isl_val *v; isl_union_pw_aff *upa; v = isl_multi_val_get_val(mv, i); upa = isl_union_pw_aff_val_on_domain(isl_union_set_copy(domain), v); mupa = isl_multi_union_pw_aff_set_union_pw_aff(mupa, i, upa); } if (isl_multi_union_pw_aff_has_explicit_domain(mupa)) mupa = isl_multi_union_pw_aff_intersect_domain(mupa, isl_union_set_copy(domain)); isl_union_set_free(domain); isl_multi_val_free(mv); return mupa; error: isl_union_set_free(domain); isl_multi_val_free(mv); return NULL; } /* Return a multiple union piecewise affine expression * that is equal to "mv" on "domain". */ __isl_give isl_multi_union_pw_aff *isl_multi_union_pw_aff_multi_val_on_domain( __isl_take isl_union_set *domain, __isl_take isl_multi_val *mv) { isl_bool equal_params; if (!domain || !mv) goto error; equal_params = isl_space_has_equal_params(domain->dim, mv->space); if (equal_params < 0) goto error; if (equal_params) return isl_multi_union_pw_aff_multi_val_on_domain_aligned( domain, mv); domain = isl_union_set_align_params(domain, isl_multi_val_get_space(mv)); mv = isl_multi_val_align_params(mv, isl_union_set_get_space(domain)); return isl_multi_union_pw_aff_multi_val_on_domain_aligned(domain, mv); error: isl_union_set_free(domain); isl_multi_val_free(mv); return NULL; } /* Return a multiple union piecewise affine expression * that is equal to "ma" on "domain". */ __isl_give isl_multi_union_pw_aff *isl_multi_union_pw_aff_multi_aff_on_domain( __isl_take isl_union_set *domain, __isl_take isl_multi_aff *ma) { isl_pw_multi_aff *pma; pma = isl_pw_multi_aff_from_multi_aff(ma); return isl_multi_union_pw_aff_pw_multi_aff_on_domain(domain, pma); } /* Return a multiple union piecewise affine expression * that is equal to "pma" on "domain", assuming "domain" and "pma" * have been aligned. * * If the resulting multi union piecewise affine expression has * an explicit domain, then assign it the input domain. * In other cases, the domain is stored in the individual elements. */ static __isl_give isl_multi_union_pw_aff * isl_multi_union_pw_aff_pw_multi_aff_on_domain_aligned( __isl_take isl_union_set *domain, __isl_take isl_pw_multi_aff *pma) { int i; isl_size n; isl_space *space; isl_multi_union_pw_aff *mupa; n = isl_pw_multi_aff_dim(pma, isl_dim_set); if (!domain || n < 0) goto error; space = isl_pw_multi_aff_get_space(pma); mupa = isl_multi_union_pw_aff_alloc(space); for (i = 0; i < n; ++i) { isl_pw_aff *pa; isl_union_pw_aff *upa; pa = isl_pw_multi_aff_get_pw_aff(pma, i); upa = isl_union_pw_aff_pw_aff_on_domain( isl_union_set_copy(domain), pa); mupa = isl_multi_union_pw_aff_set_union_pw_aff(mupa, i, upa); } if (isl_multi_union_pw_aff_has_explicit_domain(mupa)) mupa = isl_multi_union_pw_aff_intersect_domain(mupa, isl_union_set_copy(domain)); isl_union_set_free(domain); isl_pw_multi_aff_free(pma); return mupa; error: isl_union_set_free(domain); isl_pw_multi_aff_free(pma); return NULL; } /* Return a multiple union piecewise affine expression * that is equal to "pma" on "domain". */ __isl_give isl_multi_union_pw_aff * isl_multi_union_pw_aff_pw_multi_aff_on_domain(__isl_take isl_union_set *domain, __isl_take isl_pw_multi_aff *pma) { isl_bool equal_params; isl_space *space; space = isl_pw_multi_aff_peek_space(pma); equal_params = isl_union_set_space_has_equal_params(domain, space); if (equal_params < 0) goto error; if (equal_params) return isl_multi_union_pw_aff_pw_multi_aff_on_domain_aligned( domain, pma); domain = isl_union_set_align_params(domain, isl_pw_multi_aff_get_space(pma)); pma = isl_pw_multi_aff_align_params(pma, isl_union_set_get_space(domain)); return isl_multi_union_pw_aff_pw_multi_aff_on_domain_aligned(domain, pma); error: isl_union_set_free(domain); isl_pw_multi_aff_free(pma); return NULL; } /* Return a union set containing those elements in the domains * of the elements of "mupa" where they are all zero. * * If there are no elements, then simply return the entire domain. */ __isl_give isl_union_set *isl_multi_union_pw_aff_zero_union_set( __isl_take isl_multi_union_pw_aff *mupa) { int i; isl_size n; isl_union_pw_aff *upa; isl_union_set *zero; n = isl_multi_union_pw_aff_dim(mupa, isl_dim_set); if (n < 0) mupa = isl_multi_union_pw_aff_free(mupa); if (!mupa) return NULL; if (n == 0) return isl_multi_union_pw_aff_domain(mupa); upa = isl_multi_union_pw_aff_get_union_pw_aff(mupa, 0); zero = isl_union_pw_aff_zero_union_set(upa); for (i = 1; i < n; ++i) { isl_union_set *zero_i; upa = isl_multi_union_pw_aff_get_union_pw_aff(mupa, i); zero_i = isl_union_pw_aff_zero_union_set(upa); zero = isl_union_set_intersect(zero, zero_i); } isl_multi_union_pw_aff_free(mupa); return zero; } /* Construct a union map mapping the shared domain * of the union piecewise affine expressions to the range of "mupa" * in the special case of a 0D multi union piecewise affine expression. * * Construct a map between the explicit domain of "mupa" and * the range space. * Note that this assumes that the domain consists of explicit elements. */ static __isl_give isl_union_map *isl_union_map_from_multi_union_pw_aff_0D( __isl_take isl_multi_union_pw_aff *mupa) { isl_bool is_params; isl_space *space; isl_union_set *dom, *ran; space = isl_multi_union_pw_aff_get_space(mupa); dom = isl_multi_union_pw_aff_domain(mupa); ran = isl_union_set_from_set(isl_set_universe(space)); is_params = isl_union_set_is_params(dom); if (is_params < 0) dom = isl_union_set_free(dom); else if (is_params) isl_die(isl_union_set_get_ctx(dom), isl_error_invalid, "cannot create union map from expression without " "explicit domain elements", dom = isl_union_set_free(dom)); return isl_union_map_from_domain_and_range(dom, ran); } /* Construct a union map mapping the shared domain * of the union piecewise affine expressions to the range of "mupa" * with each dimension in the range equated to the * corresponding union piecewise affine expression. * * If the input is zero-dimensional, then construct a mapping * from its explicit domain. */ __isl_give isl_union_map *isl_union_map_from_multi_union_pw_aff( __isl_take isl_multi_union_pw_aff *mupa) { int i; isl_size n; isl_space *space; isl_union_map *umap; isl_union_pw_aff *upa; n = isl_multi_union_pw_aff_dim(mupa, isl_dim_set); if (n < 0) mupa = isl_multi_union_pw_aff_free(mupa); if (!mupa) return NULL; if (n == 0) return isl_union_map_from_multi_union_pw_aff_0D(mupa); upa = isl_multi_union_pw_aff_get_union_pw_aff(mupa, 0); umap = isl_union_map_from_union_pw_aff(upa); for (i = 1; i < n; ++i) { isl_union_map *umap_i; upa = isl_multi_union_pw_aff_get_union_pw_aff(mupa, i); umap_i = isl_union_map_from_union_pw_aff(upa); umap = isl_union_map_flat_range_product(umap, umap_i); } space = isl_multi_union_pw_aff_get_space(mupa); umap = isl_union_map_reset_range_space(umap, space); isl_multi_union_pw_aff_free(mupa); return umap; } /* Internal data structure for isl_union_pw_multi_aff_reset_range_space. * "range" is the space from which to set the range space. * "res" collects the results. */ struct isl_union_pw_multi_aff_reset_range_space_data { isl_space *range; isl_union_pw_multi_aff *res; }; /* Replace the range space of "pma" by the range space of data->range and * add the result to data->res. */ static isl_stat reset_range_space(__isl_take isl_pw_multi_aff *pma, void *user) { struct isl_union_pw_multi_aff_reset_range_space_data *data = user; isl_space *space; space = isl_pw_multi_aff_get_space(pma); space = isl_space_domain(space); space = isl_space_extend_domain_with_range(space, isl_space_copy(data->range)); pma = isl_pw_multi_aff_reset_space(pma, space); data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma); return data->res ? isl_stat_ok : isl_stat_error; } /* Replace the range space of all the piecewise affine expressions in "upma" by * the range space of "space". * * This assumes that all these expressions have the same output dimension. * * Since the spaces of the expressions change, so do their hash values. * We therefore need to create a new isl_union_pw_multi_aff. * Note that the hash value is currently computed based on the entire * space even though there can only be a single expression with a given * domain space. */ static __isl_give isl_union_pw_multi_aff * isl_union_pw_multi_aff_reset_range_space( __isl_take isl_union_pw_multi_aff *upma, __isl_take isl_space *space) { struct isl_union_pw_multi_aff_reset_range_space_data data = { space }; isl_space *space_upma; space_upma = isl_union_pw_multi_aff_get_space(upma); data.res = isl_union_pw_multi_aff_empty(space_upma); if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma, &reset_range_space, &data) < 0) data.res = isl_union_pw_multi_aff_free(data.res); isl_space_free(space); isl_union_pw_multi_aff_free(upma); return data.res; } /* Construct and return a union piecewise multi affine expression * that is equal to the given multi union piecewise affine expression, * in the special case of a 0D multi union piecewise affine expression. * * Construct a union piecewise multi affine expression * on top of the explicit domain of the input. */ __isl_give isl_union_pw_multi_aff * isl_union_pw_multi_aff_from_multi_union_pw_aff_0D( __isl_take isl_multi_union_pw_aff *mupa) { isl_space *space; isl_multi_val *mv; isl_union_set *domain; space = isl_multi_union_pw_aff_get_space(mupa); mv = isl_multi_val_zero(space); domain = isl_multi_union_pw_aff_domain(mupa); return isl_union_pw_multi_aff_multi_val_on_domain(domain, mv); } /* Construct and return a union piecewise multi affine expression * that is equal to the given multi union piecewise affine expression. * * If the input is zero-dimensional, then * construct a union piecewise multi affine expression * on top of the explicit domain of the input. */ __isl_give isl_union_pw_multi_aff * isl_union_pw_multi_aff_from_multi_union_pw_aff( __isl_take isl_multi_union_pw_aff *mupa) { int i; isl_size n; isl_space *space; isl_union_pw_multi_aff *upma; isl_union_pw_aff *upa; n = isl_multi_union_pw_aff_dim(mupa, isl_dim_set); if (n < 0) mupa = isl_multi_union_pw_aff_free(mupa); if (!mupa) return NULL; if (n == 0) return isl_union_pw_multi_aff_from_multi_union_pw_aff_0D(mupa); space = isl_multi_union_pw_aff_get_space(mupa); upa = isl_multi_union_pw_aff_get_union_pw_aff(mupa, 0); upma = isl_union_pw_multi_aff_from_union_pw_aff(upa); for (i = 1; i < n; ++i) { isl_union_pw_multi_aff *upma_i; upa = isl_multi_union_pw_aff_get_union_pw_aff(mupa, i); upma_i = isl_union_pw_multi_aff_from_union_pw_aff(upa); upma = isl_union_pw_multi_aff_flat_range_product(upma, upma_i); } upma = isl_union_pw_multi_aff_reset_range_space(upma, space); isl_multi_union_pw_aff_free(mupa); return upma; } /* Intersect the range of "mupa" with "range", * in the special case where "mupa" is 0D. * * Intersect the domain of "mupa" with the constraints on the parameters * of "range". */ static __isl_give isl_multi_union_pw_aff *mupa_intersect_range_0D( __isl_take isl_multi_union_pw_aff *mupa, __isl_take isl_set *range) { range = isl_set_params(range); mupa = isl_multi_union_pw_aff_intersect_params(mupa, range); return mupa; } /* Intersect the range of "mupa" with "range". * That is, keep only those domain elements that have a function value * in "range". */ __isl_give isl_multi_union_pw_aff *isl_multi_union_pw_aff_intersect_range( __isl_take isl_multi_union_pw_aff *mupa, __isl_take isl_set *range) { isl_union_pw_multi_aff *upma; isl_union_set *domain; isl_space *space; isl_size n; int match; n = isl_multi_union_pw_aff_dim(mupa, isl_dim_set); if (n < 0 || !range) goto error; space = isl_set_get_space(range); match = isl_space_tuple_is_equal(mupa->space, isl_dim_set, space, isl_dim_set); isl_space_free(space); if (match < 0) goto error; if (!match) isl_die(isl_multi_union_pw_aff_get_ctx(mupa), isl_error_invalid, "space don't match", goto error); if (n == 0) return mupa_intersect_range_0D(mupa, range); upma = isl_union_pw_multi_aff_from_multi_union_pw_aff( isl_multi_union_pw_aff_copy(mupa)); domain = isl_union_set_from_set(range); domain = isl_union_set_preimage_union_pw_multi_aff(domain, upma); mupa = isl_multi_union_pw_aff_intersect_domain(mupa, domain); return mupa; error: isl_multi_union_pw_aff_free(mupa); isl_set_free(range); return NULL; } /* Return the shared domain of the elements of "mupa", * in the special case where "mupa" is zero-dimensional. * * Return the explicit domain of "mupa". * Note that this domain may be a parameter set, either * because "mupa" is meant to live in a set space or * because no explicit domain has been set. */ __isl_give isl_union_set *isl_multi_union_pw_aff_domain_0D( __isl_take isl_multi_union_pw_aff *mupa) { isl_union_set *dom; dom = isl_multi_union_pw_aff_get_explicit_domain(mupa); isl_multi_union_pw_aff_free(mupa); return dom; } /* Return the shared domain of the elements of "mupa". * * If "mupa" is zero-dimensional, then return its explicit domain. */ __isl_give isl_union_set *isl_multi_union_pw_aff_domain( __isl_take isl_multi_union_pw_aff *mupa) { int i; isl_size n; isl_union_pw_aff *upa; isl_union_set *dom; n = isl_multi_union_pw_aff_dim(mupa, isl_dim_set); if (n < 0) mupa = isl_multi_union_pw_aff_free(mupa); if (!mupa) return NULL; if (n == 0) return isl_multi_union_pw_aff_domain_0D(mupa); upa = isl_multi_union_pw_aff_get_union_pw_aff(mupa, 0); dom = isl_union_pw_aff_domain(upa); for (i = 1; i < n; ++i) { isl_union_set *dom_i; upa = isl_multi_union_pw_aff_get_union_pw_aff(mupa, i); dom_i = isl_union_pw_aff_domain(upa); dom = isl_union_set_intersect(dom, dom_i); } isl_multi_union_pw_aff_free(mupa); return dom; } /* Apply "aff" to "mupa". The space of "mupa" is equal to the domain of "aff". * In particular, the spaces have been aligned. * The result is defined over the shared domain of the elements of "mupa" * * We first extract the parametric constant part of "aff" and * define that over the shared domain. * Then we iterate over all input dimensions of "aff" and add the corresponding * multiples of the elements of "mupa". * Finally, we consider the integer divisions, calling the function * recursively to obtain an isl_union_pw_aff corresponding to the * integer division argument. */ static __isl_give isl_union_pw_aff *multi_union_pw_aff_apply_aff( __isl_take isl_multi_union_pw_aff *mupa, __isl_take isl_aff *aff) { int i; isl_size n_in, n_div; isl_union_pw_aff *upa; isl_union_set *uset; isl_val *v; isl_aff *cst; n_in = isl_aff_dim(aff, isl_dim_in); n_div = isl_aff_dim(aff, isl_dim_div); if (n_in < 0 || n_div < 0) goto error; uset = isl_multi_union_pw_aff_domain(isl_multi_union_pw_aff_copy(mupa)); cst = isl_aff_copy(aff); cst = isl_aff_drop_dims(cst, isl_dim_div, 0, n_div); cst = isl_aff_drop_dims(cst, isl_dim_in, 0, n_in); cst = isl_aff_project_domain_on_params(cst); upa = isl_union_pw_aff_aff_on_domain(uset, cst); for (i = 0; i < n_in; ++i) { isl_union_pw_aff *upa_i; if (!isl_aff_involves_dims(aff, isl_dim_in, i, 1)) continue; v = isl_aff_get_coefficient_val(aff, isl_dim_in, i); upa_i = isl_multi_union_pw_aff_get_union_pw_aff(mupa, i); upa_i = isl_union_pw_aff_scale_val(upa_i, v); upa = isl_union_pw_aff_add(upa, upa_i); } for (i = 0; i < n_div; ++i) { isl_aff *div; isl_union_pw_aff *upa_i; if (!isl_aff_involves_dims(aff, isl_dim_div, i, 1)) continue; div = isl_aff_get_div(aff, i); upa_i = multi_union_pw_aff_apply_aff( isl_multi_union_pw_aff_copy(mupa), div); upa_i = isl_union_pw_aff_floor(upa_i); v = isl_aff_get_coefficient_val(aff, isl_dim_div, i); upa_i = isl_union_pw_aff_scale_val(upa_i, v); upa = isl_union_pw_aff_add(upa, upa_i); } isl_multi_union_pw_aff_free(mupa); isl_aff_free(aff); return upa; error: isl_multi_union_pw_aff_free(mupa); isl_aff_free(aff); return NULL; } /* Apply "aff" to "mupa". The space of "mupa" needs to be compatible * with the domain of "aff". * Furthermore, the dimension of this space needs to be greater than zero. * The result is defined over the shared domain of the elements of "mupa" * * We perform these checks and then hand over control to * multi_union_pw_aff_apply_aff. */ __isl_give isl_union_pw_aff *isl_multi_union_pw_aff_apply_aff( __isl_take isl_multi_union_pw_aff *mupa, __isl_take isl_aff *aff) { isl_size dim; isl_space *space1, *space2; isl_bool equal; mupa = isl_multi_union_pw_aff_align_params(mupa, isl_aff_get_space(aff)); aff = isl_aff_align_params(aff, isl_multi_union_pw_aff_get_space(mupa)); if (!mupa || !aff) goto error; space1 = isl_multi_union_pw_aff_get_space(mupa); space2 = isl_aff_get_domain_space(aff); equal = isl_space_is_equal(space1, space2); isl_space_free(space1); isl_space_free(space2); if (equal < 0) goto error; if (!equal) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "spaces don't match", goto error); dim = isl_aff_dim(aff, isl_dim_in); if (dim < 0) goto error; if (dim == 0) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "cannot determine domains", goto error); return multi_union_pw_aff_apply_aff(mupa, aff); error: isl_multi_union_pw_aff_free(mupa); isl_aff_free(aff); return NULL; } /* Apply "ma" to "mupa", in the special case where "mupa" is 0D. * The space of "mupa" is known to be compatible with the domain of "ma". * * Construct an isl_multi_union_pw_aff that is equal to "ma" * on the domain of "mupa". */ static __isl_give isl_multi_union_pw_aff *mupa_apply_multi_aff_0D( __isl_take isl_multi_union_pw_aff *mupa, __isl_take isl_multi_aff *ma) { isl_union_set *dom; dom = isl_multi_union_pw_aff_domain(mupa); ma = isl_multi_aff_project_domain_on_params(ma); return isl_multi_union_pw_aff_multi_aff_on_domain(dom, ma); } /* Apply "ma" to "mupa". The space of "mupa" needs to be compatible * with the domain of "ma". * The result is defined over the shared domain of the elements of "mupa" */ __isl_give isl_multi_union_pw_aff *isl_multi_union_pw_aff_apply_multi_aff( __isl_take isl_multi_union_pw_aff *mupa, __isl_take isl_multi_aff *ma) { isl_space *space1, *space2; isl_multi_union_pw_aff *res; isl_bool equal; int i; isl_size n_in, n_out; mupa = isl_multi_union_pw_aff_align_params(mupa, isl_multi_aff_get_space(ma)); ma = isl_multi_aff_align_params(ma, isl_multi_union_pw_aff_get_space(mupa)); n_in = isl_multi_aff_dim(ma, isl_dim_in); n_out = isl_multi_aff_dim(ma, isl_dim_out); if (!mupa || n_in < 0 || n_out < 0) goto error; space1 = isl_multi_union_pw_aff_get_space(mupa); space2 = isl_multi_aff_get_domain_space(ma); equal = isl_space_is_equal(space1, space2); isl_space_free(space1); isl_space_free(space2); if (equal < 0) goto error; if (!equal) isl_die(isl_multi_aff_get_ctx(ma), isl_error_invalid, "spaces don't match", goto error); if (n_in == 0) return mupa_apply_multi_aff_0D(mupa, ma); space1 = isl_space_range(isl_multi_aff_get_space(ma)); res = isl_multi_union_pw_aff_alloc(space1); for (i = 0; i < n_out; ++i) { isl_aff *aff; isl_union_pw_aff *upa; aff = isl_multi_aff_get_aff(ma, i); upa = multi_union_pw_aff_apply_aff( isl_multi_union_pw_aff_copy(mupa), aff); res = isl_multi_union_pw_aff_set_union_pw_aff(res, i, upa); } isl_multi_aff_free(ma); isl_multi_union_pw_aff_free(mupa); return res; error: isl_multi_union_pw_aff_free(mupa); isl_multi_aff_free(ma); return NULL; } /* Apply "pa" to "mupa", in the special case where "mupa" is 0D. * The space of "mupa" is known to be compatible with the domain of "pa". * * Construct an isl_multi_union_pw_aff that is equal to "pa" * on the domain of "mupa". */ static __isl_give isl_union_pw_aff *isl_multi_union_pw_aff_apply_pw_aff_0D( __isl_take isl_multi_union_pw_aff *mupa, __isl_take isl_pw_aff *pa) { isl_union_set *dom; dom = isl_multi_union_pw_aff_domain(mupa); pa = isl_pw_aff_project_domain_on_params(pa); return isl_union_pw_aff_pw_aff_on_domain(dom, pa); } /* Apply "pa" to "mupa". The space of "mupa" needs to be compatible * with the domain of "pa". * Furthermore, the dimension of this space needs to be greater than zero. * The result is defined over the shared domain of the elements of "mupa" */ __isl_give isl_union_pw_aff *isl_multi_union_pw_aff_apply_pw_aff( __isl_take isl_multi_union_pw_aff *mupa, __isl_take isl_pw_aff *pa) { int i; isl_bool equal; isl_size n_in; isl_space *space, *space2; isl_union_pw_aff *upa; mupa = isl_multi_union_pw_aff_align_params(mupa, isl_pw_aff_get_space(pa)); pa = isl_pw_aff_align_params(pa, isl_multi_union_pw_aff_get_space(mupa)); if (!mupa || !pa) goto error; space = isl_multi_union_pw_aff_get_space(mupa); space2 = isl_pw_aff_get_domain_space(pa); equal = isl_space_is_equal(space, space2); isl_space_free(space); isl_space_free(space2); if (equal < 0) goto error; if (!equal) isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid, "spaces don't match", goto error); n_in = isl_pw_aff_dim(pa, isl_dim_in); if (n_in < 0) goto error; if (n_in == 0) return isl_multi_union_pw_aff_apply_pw_aff_0D(mupa, pa); space = isl_space_params(isl_multi_union_pw_aff_get_space(mupa)); upa = isl_union_pw_aff_empty(space); for (i = 0; i < pa->n; ++i) { isl_aff *aff; isl_set *domain; isl_multi_union_pw_aff *mupa_i; isl_union_pw_aff *upa_i; mupa_i = isl_multi_union_pw_aff_copy(mupa); domain = isl_set_copy(pa->p[i].set); mupa_i = isl_multi_union_pw_aff_intersect_range(mupa_i, domain); aff = isl_aff_copy(pa->p[i].aff); upa_i = multi_union_pw_aff_apply_aff(mupa_i, aff); upa = isl_union_pw_aff_union_add(upa, upa_i); } isl_multi_union_pw_aff_free(mupa); isl_pw_aff_free(pa); return upa; error: isl_multi_union_pw_aff_free(mupa); isl_pw_aff_free(pa); return NULL; } /* Apply "pma" to "mupa", in the special case where "mupa" is 0D. * The space of "mupa" is known to be compatible with the domain of "pma". * * Construct an isl_multi_union_pw_aff that is equal to "pma" * on the domain of "mupa". */ static __isl_give isl_multi_union_pw_aff *mupa_apply_pw_multi_aff_0D( __isl_take isl_multi_union_pw_aff *mupa, __isl_take isl_pw_multi_aff *pma) { isl_union_set *dom; dom = isl_multi_union_pw_aff_domain(mupa); pma = isl_pw_multi_aff_project_domain_on_params(pma); return isl_multi_union_pw_aff_pw_multi_aff_on_domain(dom, pma); } /* Apply "pma" to "mupa". The space of "mupa" needs to be compatible * with the domain of "pma". * The result is defined over the shared domain of the elements of "mupa" */ __isl_give isl_multi_union_pw_aff *isl_multi_union_pw_aff_apply_pw_multi_aff( __isl_take isl_multi_union_pw_aff *mupa, __isl_take isl_pw_multi_aff *pma) { isl_space *space1, *space2; isl_multi_union_pw_aff *res; isl_bool equal; int i; isl_size n_in, n_out; mupa = isl_multi_union_pw_aff_align_params(mupa, isl_pw_multi_aff_get_space(pma)); pma = isl_pw_multi_aff_align_params(pma, isl_multi_union_pw_aff_get_space(mupa)); if (!mupa || !pma) goto error; space1 = isl_multi_union_pw_aff_get_space(mupa); space2 = isl_pw_multi_aff_get_domain_space(pma); equal = isl_space_is_equal(space1, space2); isl_space_free(space1); isl_space_free(space2); if (equal < 0) goto error; if (!equal) isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid, "spaces don't match", goto error); n_in = isl_pw_multi_aff_dim(pma, isl_dim_in); n_out = isl_pw_multi_aff_dim(pma, isl_dim_out); if (n_in < 0 || n_out < 0) goto error; if (n_in == 0) return mupa_apply_pw_multi_aff_0D(mupa, pma); space1 = isl_space_range(isl_pw_multi_aff_get_space(pma)); res = isl_multi_union_pw_aff_alloc(space1); for (i = 0; i < n_out; ++i) { isl_pw_aff *pa; isl_union_pw_aff *upa; pa = isl_pw_multi_aff_get_pw_aff(pma, i); upa = isl_multi_union_pw_aff_apply_pw_aff( isl_multi_union_pw_aff_copy(mupa), pa); res = isl_multi_union_pw_aff_set_union_pw_aff(res, i, upa); } isl_pw_multi_aff_free(pma); isl_multi_union_pw_aff_free(mupa); return res; error: isl_multi_union_pw_aff_free(mupa); isl_pw_multi_aff_free(pma); return NULL; } /* Replace the explicit domain of "mupa" by its preimage under "upma". * If the explicit domain only keeps track of constraints on the parameters, * then only update those constraints. */ static __isl_give isl_multi_union_pw_aff *preimage_explicit_domain( __isl_take isl_multi_union_pw_aff *mupa, __isl_keep isl_union_pw_multi_aff *upma) { isl_bool is_params; if (isl_multi_union_pw_aff_check_has_explicit_domain(mupa) < 0) return isl_multi_union_pw_aff_free(mupa); mupa = isl_multi_union_pw_aff_cow(mupa); if (!mupa) return NULL; is_params = isl_union_set_is_params(mupa->u.dom); if (is_params < 0) return isl_multi_union_pw_aff_free(mupa); upma = isl_union_pw_multi_aff_copy(upma); if (is_params) mupa->u.dom = isl_union_set_intersect_params(mupa->u.dom, isl_union_set_params(isl_union_pw_multi_aff_domain(upma))); else mupa->u.dom = isl_union_set_preimage_union_pw_multi_aff( mupa->u.dom, upma); if (!mupa->u.dom) return isl_multi_union_pw_aff_free(mupa); return mupa; } /* Compute the pullback of "mupa" by the function represented by "upma". * In other words, plug in "upma" in "mupa". The result contains * expressions defined over the domain space of "upma". * * Run over all elements of "mupa" and plug in "upma" in each of them. * * If "mupa" has an explicit domain, then it is this domain * that needs to undergo a pullback instead, i.e., a preimage. */ __isl_give isl_multi_union_pw_aff * isl_multi_union_pw_aff_pullback_union_pw_multi_aff( __isl_take isl_multi_union_pw_aff *mupa, __isl_take isl_union_pw_multi_aff *upma) { int i; isl_size n; mupa = isl_multi_union_pw_aff_align_params(mupa, isl_union_pw_multi_aff_get_space(upma)); upma = isl_union_pw_multi_aff_align_params(upma, isl_multi_union_pw_aff_get_space(mupa)); mupa = isl_multi_union_pw_aff_cow(mupa); n = isl_multi_union_pw_aff_dim(mupa, isl_dim_set); if (n < 0 || !upma) goto error; for (i = 0; i < n; ++i) { isl_union_pw_aff *upa; upa = isl_multi_union_pw_aff_get_union_pw_aff(mupa, i); upa = isl_union_pw_aff_pullback_union_pw_multi_aff(upa, isl_union_pw_multi_aff_copy(upma)); mupa = isl_multi_union_pw_aff_set_union_pw_aff(mupa, i, upa); } if (isl_multi_union_pw_aff_has_explicit_domain(mupa)) mupa = preimage_explicit_domain(mupa, upma); isl_union_pw_multi_aff_free(upma); return mupa; error: isl_multi_union_pw_aff_free(mupa); isl_union_pw_multi_aff_free(upma); return NULL; } /* Extract the sequence of elements in "mupa" with domain space "space" * (ignoring parameters). * * For the elements of "mupa" that are not defined on the specified space, * the corresponding element in the result is empty. */ __isl_give isl_multi_pw_aff *isl_multi_union_pw_aff_extract_multi_pw_aff( __isl_keep isl_multi_union_pw_aff *mupa, __isl_take isl_space *space) { int i; isl_size n; isl_space *space_mpa; isl_multi_pw_aff *mpa; n = isl_multi_union_pw_aff_dim(mupa, isl_dim_set); if (n < 0 || !space) goto error; space_mpa = isl_multi_union_pw_aff_get_space(mupa); space = isl_space_replace_params(space, space_mpa); space_mpa = isl_space_map_from_domain_and_range(isl_space_copy(space), space_mpa); mpa = isl_multi_pw_aff_alloc(space_mpa); space = isl_space_from_domain(space); space = isl_space_add_dims(space, isl_dim_out, 1); for (i = 0; i < n; ++i) { isl_union_pw_aff *upa; isl_pw_aff *pa; upa = isl_multi_union_pw_aff_get_union_pw_aff(mupa, i); pa = isl_union_pw_aff_extract_pw_aff(upa, isl_space_copy(space)); mpa = isl_multi_pw_aff_set_pw_aff(mpa, i, pa); isl_union_pw_aff_free(upa); } isl_space_free(space); return mpa; error: isl_space_free(space); return NULL; } /* Data structure that specifies how isl_union_pw_multi_aff_un_op * should modify the base expressions in the input. * * If "filter" is not NULL, then only the base expressions that satisfy "filter" * are taken into account. * "fn" is applied to each entry in the input. */ struct isl_union_pw_multi_aff_un_op_control { isl_bool (*filter)(__isl_keep isl_pw_multi_aff *part); __isl_give isl_pw_multi_aff *(*fn)(__isl_take isl_pw_multi_aff *pma); }; /* Wrapper for isl_union_pw_multi_aff_un_op filter functions (which do not take * a second argument) for use as an isl_union_pw_multi_aff_transform * filter function (which does take a second argument). * Simply call control->filter without the second argument. */ static isl_bool isl_union_pw_multi_aff_un_op_filter_drop_user( __isl_take isl_pw_multi_aff *pma, void *user) { struct isl_union_pw_multi_aff_un_op_control *control = user; return control->filter(pma); } /* Wrapper for isl_union_pw_multi_aff_un_op base functions (which do not take * a second argument) for use as an isl_union_pw_multi_aff_transform * base function (which does take a second argument). * Simply call control->fn without the second argument. */ static __isl_give isl_pw_multi_aff *isl_union_pw_multi_aff_un_op_drop_user( __isl_take isl_pw_multi_aff *pma, void *user) { struct isl_union_pw_multi_aff_un_op_control *control = user; return control->fn(pma); } /* Construct an isl_union_pw_multi_aff that is obtained by * modifying "upma" according to "control". * * isl_union_pw_multi_aff_transform performs essentially * the same operation, but takes a filter and a callback function * of a different form (with an extra argument). * Call isl_union_pw_multi_aff_transform with wrappers * that remove this extra argument. */ static __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_un_op( __isl_take isl_union_pw_multi_aff *upma, struct isl_union_pw_multi_aff_un_op_control *control) { struct isl_union_pw_multi_aff_transform_control t_control = { .filter = &isl_union_pw_multi_aff_un_op_filter_drop_user, .filter_user = control, .fn = &isl_union_pw_multi_aff_un_op_drop_user, .fn_user = control, }; return isl_union_pw_multi_aff_transform(upma, &t_control); } /* For each function in "upma" of the form A -> [B -> C], * extract the function A -> B and collect the results. */ __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_range_factor_domain( __isl_take isl_union_pw_multi_aff *upma) { struct isl_union_pw_multi_aff_un_op_control control = { .filter = &isl_pw_multi_aff_range_is_wrapping, .fn = &isl_pw_multi_aff_range_factor_domain, }; return isl_union_pw_multi_aff_un_op(upma, &control); } /* For each function in "upma" of the form A -> [B -> C], * extract the function A -> C and collect the results. */ __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_range_factor_range( __isl_take isl_union_pw_multi_aff *upma) { struct isl_union_pw_multi_aff_un_op_control control = { .filter = &isl_pw_multi_aff_range_is_wrapping, .fn = &isl_pw_multi_aff_range_factor_range, }; return isl_union_pw_multi_aff_un_op(upma, &control); } /* Evaluate the affine function "aff" in the void point "pnt". * In particular, return the value NaN. */ static __isl_give isl_val *eval_void(__isl_take isl_aff *aff, __isl_take isl_point *pnt) { isl_ctx *ctx; ctx = isl_point_get_ctx(pnt); isl_aff_free(aff); isl_point_free(pnt); return isl_val_nan(ctx); } /* Evaluate the affine expression "aff" * in the coordinates (with denominator) "pnt". */ static __isl_give isl_val *eval(__isl_keep isl_vec *aff, __isl_keep isl_vec *pnt) { isl_int n, d; isl_ctx *ctx; isl_val *v; if (!aff || !pnt) return NULL; ctx = isl_vec_get_ctx(aff); isl_int_init(n); isl_int_init(d); isl_seq_inner_product(aff->el + 1, pnt->el, pnt->size, &n); isl_int_mul(d, aff->el[0], pnt->el[0]); v = isl_val_rat_from_isl_int(ctx, n, d); v = isl_val_normalize(v); isl_int_clear(n); isl_int_clear(d); return v; } /* Check that the domain space of "aff" is equal to "space". */ static isl_stat isl_aff_check_has_domain_space(__isl_keep isl_aff *aff, __isl_keep isl_space *space) { isl_bool ok; ok = isl_space_is_equal(isl_aff_peek_domain_space(aff), space); if (ok < 0) return isl_stat_error; if (!ok) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "incompatible spaces", return isl_stat_error); return isl_stat_ok; } /* Evaluate the affine function "aff" in "pnt". */ __isl_give isl_val *isl_aff_eval(__isl_take isl_aff *aff, __isl_take isl_point *pnt) { isl_bool is_void; isl_val *v; isl_local_space *ls; if (isl_aff_check_has_domain_space(aff, isl_point_peek_space(pnt)) < 0) goto error; is_void = isl_point_is_void(pnt); if (is_void < 0) goto error; if (is_void) return eval_void(aff, pnt); ls = isl_aff_get_domain_local_space(aff); pnt = isl_local_space_lift_point(ls, pnt); v = eval(aff->v, isl_point_peek_vec(pnt)); isl_aff_free(aff); isl_point_free(pnt); return v; error: isl_aff_free(aff); isl_point_free(pnt); return NULL; }