/* * Copyright 2011 INRIA Saclay * Copyright 2011 Sven Verdoolaege * Copyright 2012-2014 Ecole Normale Superieure * * 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 */ #include #define ISL_DIM_H #include #include #include #include #include #include #include #include #include #include #include #include #include #undef BASE #define BASE aff #include #undef BASE #define BASE pw_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; unsigned 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); 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_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 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)); } /* 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); if (!aff) return NULL; isl_seq_clr(aff->v->el, aff->v->size); return aff; } /* 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 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 (pos >= isl_local_space_dim(ls, type)) isl_die(isl_space_get_ctx(space), isl_error_invalid, "position out of bounds", 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)); } __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_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; } /* Externally, an isl_aff has a map space, but internally, the * ls field corresponds to the domain of that space. */ int isl_aff_dim(__isl_keep isl_aff *aff, enum isl_dim_type type) { if (!aff) return 0; if (type == isl_dim_out) return 1; if (type == isl_dim_in) type = isl_dim_set; return isl_local_space_dim(aff->ls, type); } __isl_give isl_space *isl_aff_get_domain_space(__isl_keep isl_aff *aff) { return aff ? isl_local_space_get_space(aff->ls) : NULL; } __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; } __isl_give isl_local_space *isl_aff_get_domain_local_space( __isl_keep isl_aff *aff) { return aff ? isl_local_space_copy(aff->ls) : NULL; } __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; } /* 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 *dim) { aff = isl_aff_cow(aff); if (!aff || !dim) goto error; aff->ls = isl_local_space_reset_space(aff->ls, dim); if (!aff->ls) return isl_aff_free(aff); return aff; error: isl_aff_free(aff); isl_space_free(dim); 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 reodering. * 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_vec *res; int i; if (!vec || !r) goto error; res = isl_vec_alloc(vec->ctx, 2 + isl_space_dim(r->dim, isl_dim_all) + n_div); 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) { if (!aff || !model) goto error; if (!isl_space_match(aff->ls->dim, isl_dim_param, model, isl_dim_param)) { isl_reordering *exp; model = isl_space_drop_dims(model, isl_dim_in, 0, isl_space_dim(model, isl_dim_in)); model = isl_space_drop_dims(model, isl_dim_out, 0, isl_space_dim(model, isl_dim_out)); exp = isl_parameter_alignment_reordering(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; } /* Is "aff" obviously equal to zero? * * If the denominator is zero, then "aff" is not equal to zero. */ int isl_aff_plain_is_zero(__isl_keep isl_aff *aff) { if (!aff) return -1; if (isl_int_is_zero(aff->v->el[0])) return 0; return isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1) < 0; } /* Does "aff" represent NaN? */ int isl_aff_is_nan(__isl_keep isl_aff *aff) { if (!aff) return -1; return isl_seq_first_non_zero(aff->v->el, 2) < 0; } /* Does "pa" involve any NaNs? */ int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa) { int i; if (!pa) return -1; if (pa->n == 0) return 0; for (i = 0; i < pa->n; ++i) { int is_nan = isl_aff_is_nan(pa->p[i].aff); if (is_nan < 0 || is_nan) return is_nan; } return 0; } /* Are "aff1" and "aff2" obviously equal? * * NaN is not equal to anything, not even to another NaN. */ int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2) { int equal; if (!aff1 || !aff2) return -1; if (isl_aff_is_nan(aff1) || isl_aff_is_nan(aff2)) return 0; 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. */ int isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v) { if (!aff) return -1; if (isl_aff_is_nan(aff)) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "cannot get denominator of NaN", return -1); isl_int_set(*v, aff->v->el[0]); return 0; } /* 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" in "v". * * We cannot return anything meaningful in case of a NaN. */ int isl_aff_get_constant(__isl_keep isl_aff *aff, isl_int *v) { if (!aff) return -1; if (isl_aff_is_nan(aff)) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "cannot get constant term of NaN", return -1); isl_int_set(*v, aff->v->el[1]); return 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" in "v". * * We cannot return anything meaningful in case of a NaN. */ int isl_aff_get_coefficient(__isl_keep isl_aff *aff, enum isl_dim_type type, int pos, isl_int *v) { if (!aff) return -1; if (type == isl_dim_out) isl_die(aff->v->ctx, isl_error_invalid, "output/set dimension does not have a coefficient", return -1); if (type == isl_dim_in) type = isl_dim_set; if (pos >= isl_local_space_dim(aff->ls, type)) isl_die(aff->v->ctx, isl_error_invalid, "position out of bounds", return -1); if (isl_aff_is_nan(aff)) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "cannot get coefficient of NaN", return -1); pos += isl_local_space_offset(aff->ls, type); isl_int_set(*v, aff->v->el[1 + pos]); return 0; } /* 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 (pos >= isl_local_space_dim(aff->ls, type)) isl_die(ctx, isl_error_invalid, "position out of bounds", 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); } /* Replace the denominator of "aff" by "v". * * A NaN is unaffected by this operation. */ __isl_give isl_aff *isl_aff_set_denominator(__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[0], v); 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(__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". * * A NaN is unaffected by this operation. */ __isl_give isl_aff *isl_aff_add_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_is_zero(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 value", goto error); 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; } __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 (pos >= isl_local_space_dim(aff->ls, type)) isl_die(aff->v->ctx, isl_error_invalid, "position out of bounds", 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 (pos < 0 || pos >= isl_local_space_dim(aff->ls, type)) isl_die(aff->v->ctx, isl_error_invalid, "position out of bounds", 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 (pos >= isl_local_space_dim(aff->ls, type)) isl_die(aff->v->ctx, isl_error_invalid, "position out of bounds", 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); 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 (pos >= isl_local_space_dim(aff->ls, type)) isl_die(aff->v->ctx, isl_error_invalid, "position out of bounds", 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 (pos >= isl_local_space_dim(aff->ls, type)) isl_die(aff->v->ctx, isl_error_invalid, "position out of bounds", 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; int off; int n; if (!aff) return NULL; n = isl_local_space_dim(aff->ls, isl_dim_div); off = isl_local_space_offset(aff->ls, isl_dim_div); 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; } /* Given two affine expressions "p" of length p_len (including the * denominator and the constant term) and "subs" of length subs_len, * plug in "subs" for the variable at position "pos". * The variables of "subs" and "p" are assumed to match up to subs_len, * but "p" may have additional variables. * "v" is an initialized isl_int that can be used internally. * * In particular, if "p" represents the expression * * (a i + g)/m * * with i the variable at position "pos" and "subs" represents the expression * * f/d * * then the result represents the expression * * (a f + d g)/(m d) * */ void isl_seq_substitute(isl_int *p, int pos, isl_int *subs, int p_len, int subs_len, isl_int v) { isl_int_set(v, p[1 + pos]); isl_int_set_si(p[1 + pos], 0); isl_seq_combine(p + 1, subs[0], p + 1, v, subs + 1, subs_len - 1); isl_seq_scale(p + subs_len, p + subs_len, subs[0], p_len - subs_len); isl_int_mul(p[0], p[0], subs[0]); } /* 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, n; int len; isl_int v; isl_vec *vec; isl_local_space *ls; unsigned pos; if (!aff) return NULL; n = isl_local_space_dim(aff->ls, isl_dim_div); 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); pos = isl_local_space_offset(aff->ls, isl_dim_div) + i; isl_seq_substitute(vec->el, pos, 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, n; int off; if (!aff) return NULL; n = isl_local_space_dim(aff->ls, isl_dim_div); off = isl_local_space_offset(aff->ls, isl_dim_div); 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) { unsigned off = isl_local_space_offset(aff->ls, isl_dim_div); isl_local_space *ls; isl_vec *v; 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) { unsigned off = isl_local_space_offset(aff->ls, isl_dim_div); 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) { int i, j, n; unsigned off; if (!aff) return NULL; off = isl_local_space_offset(aff->ls, isl_dim_div); n = isl_aff_dim(aff, isl_dim_div); 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 of "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. * * 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) */ __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff, isl_int m) { isl_aff *res; res = isl_aff_copy(aff); aff = isl_aff_scale_down(aff, m); aff = isl_aff_floor(aff); aff = isl_aff_scale(aff, m); res = isl_aff_sub(res, aff); return res; } /* 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) { int i, j; int old_n_div; int new_n_div; int offset; aff = isl_aff_cow(aff); if (!aff || !div) goto error; old_n_div = isl_local_space_dim(aff->ls, isl_dim_div); new_n_div = isl_mat_rows(div); if (new_n_div < old_n_div) isl_die(isl_mat_get_ctx(div), isl_error_invalid, "not an expansion", goto error); aff->v = isl_vec_extend(aff->v, aff->v->size + new_n_div - old_n_div); if (!aff->v) goto error; offset = 1 + isl_local_space_offset(aff->ls, isl_dim_div); j = old_n_div - 1; for (i = new_n_div - 1; i >= 0; --i) { if (j >= 0 && exp[j] == i) { if (i != j) isl_int_swap(aff->v->el[offset + i], aff->v->el[offset + j]); j--; } else isl_int_set_si(aff->v->el[offset + i], 0); } aff->ls = isl_local_space_replace_divs(aff->ls, isl_mat_copy(div)); if (!aff->ls) goto error; isl_mat_free(div); 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); return aff1; error: isl_aff_free(aff1); isl_aff_free(aff2); return NULL; } /* 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; int 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) 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_out) 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 total; 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; total = 1 + isl_space_dim(eq->dim, isl_dim_all); n_div = eq->n_div; for (i = 0; i < eq->n_eq; ++i) { j = isl_seq_last_non_zero(eq->eq[i], total + n_div); if (j < 0 || j == 0 || j >= total) continue; isl_seq_elim(aff->v->el + 1, eq->eq[i], j, total, &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. */ static __isl_give isl_aff *isl_aff_substitute_equalities( __isl_take isl_aff *aff, __isl_take isl_basic_set *eq) { int n_div; if (!aff || !eq) goto error; n_div = isl_local_space_dim(aff->ls, isl_dim_div); 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_basic_set *hull; int n_div; if (!aff) goto error; n_div = isl_local_space_dim(aff->ls, isl_dim_div); if (n_div > 0) { isl_basic_set *bset; isl_local_space *ls; context = isl_set_add_dims(context, isl_dim_set, n_div); ls = isl_aff_get_domain_local_space(aff); bset = isl_basic_set_from_local_space(ls); bset = isl_basic_set_lift(bset); bset = isl_basic_set_flatten(bset); context = isl_set_intersect(context, isl_set_from_basic_set(bset)); } hull = isl_set_affine_hull(context); return isl_aff_substitute_equalities_lifted(aff, hull); error: isl_aff_free(aff); isl_set_free(context); return NULL; } __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 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) { 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); } /* 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); 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 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) { 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); } /* 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 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); } __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; } int isl_aff_is_empty(__isl_keep isl_aff *aff) { if (!aff) return -1; return 0; } /* 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. */ int isl_aff_involves_dims(__isl_keep isl_aff *aff, enum isl_dim_type type, unsigned first, unsigned n) { int i; isl_ctx *ctx; int *active = NULL; int involves = 0; if (!aff) return -1; if (n == 0) return 0; ctx = isl_aff_get_ctx(aff); if (first + n > isl_aff_dim(aff, type)) isl_die(ctx, isl_error_invalid, "range out of bounds", return -1); 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 = 1; break; } free(active); return involves; error: free(active); return -1; } __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 (first + n > isl_local_space_dim(aff->ls, type)) isl_die(ctx, isl_error_invalid, "range out of bounds", 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; } /* 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; unsigned n; int involves; n = isl_aff_dim(aff, isl_dim_in); involves = isl_aff_involves_dims(aff, isl_dim_in, 0, n); if (involves < 0) return isl_aff_free(aff); if (involves) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "affine expression involves some of the domain dimensions", return isl_aff_free(aff)); aff = isl_aff_drop_dims(aff, isl_dim_in, 0, n); space = isl_aff_get_domain_space(aff); space = isl_space_params(space); aff = isl_aff_reset_domain_space(aff, space); 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 (first > isl_local_space_dim(aff->ls, type)) isl_die(ctx, isl_error_invalid, "position out of bounds", 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) { unsigned pos; pos = isl_aff_dim(aff, type); return isl_aff_insert_dims(aff, type, pos, n); } __isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff, enum isl_dim_type type, unsigned n) { unsigned pos; pos = isl_pw_aff_dim(pwaff, type); return isl_pw_aff_insert_dims(pwaff, 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; 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", 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", 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 (src_pos + n > isl_local_space_dim(aff->ls, src_type)) isl_die(isl_aff_get_ctx(aff), isl_error_invalid, "range out of bounds", 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", isl_aff_free(aff)); aff = isl_aff_cow(aff); if (!aff) return NULL; g_src_pos = 1 + isl_local_space_offset(aff->ls, src_type) + src_pos; g_dst_pos = 1 + isl_local_space_offset(aff->ls, dst_type) + 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; } __isl_give isl_pw_aff *isl_pw_aff_from_aff(__isl_take isl_aff *aff) { isl_set *dom = isl_set_universe(isl_aff_get_domain_space(aff)); return isl_pw_aff_alloc(dom, aff); } #undef PW #define PW isl_pw_aff #undef EL #define EL isl_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 #define NO_EVAL #define NO_OPT #define NO_LIFT #define NO_MORPH #include static __isl_give isl_set *align_params_pw_pw_set_and( __isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2, __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2)) { if (!pwaff1 || !pwaff2) goto error; if (isl_space_match(pwaff1->dim, isl_dim_param, pwaff2->dim, isl_dim_param)) return fn(pwaff1, pwaff2); if (!isl_space_has_named_params(pwaff1->dim) || !isl_space_has_named_params(pwaff2->dim)) isl_die(isl_pw_aff_get_ctx(pwaff1), isl_error_invalid, "unaligned unnamed parameters", goto error); pwaff1 = isl_pw_aff_align_params(pwaff1, isl_pw_aff_get_space(pwaff2)); pwaff2 = isl_pw_aff_align_params(pwaff2, isl_pw_aff_get_space(pwaff1)); return fn(pwaff1, pwaff2); error: isl_pw_aff_free(pwaff1); isl_pw_aff_free(pwaff2); return NULL; } /* 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 better (according to cmp) * 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. */ static __isl_give isl_pw_aff *pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2, __isl_give isl_basic_set *(*cmp)(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2)) { int i, j, n; isl_pw_aff *res; isl_ctx *ctx; isl_set *set; if (!pwaff1 || !pwaff2) goto error; ctx = isl_space_get_ctx(pwaff1->dim); if (!isl_space_is_equal(pwaff1->dim, pwaff2->dim)) isl_die(ctx, isl_error_invalid, "arguments should live in same space", goto error); if (isl_pw_aff_is_empty(pwaff1)) { isl_pw_aff_free(pwaff1); return pwaff2; } if (isl_pw_aff_is_empty(pwaff2)) { isl_pw_aff_free(pwaff2); return pwaff1; } n = 2 * (pwaff1->n + 1) * (pwaff2->n + 1); res = isl_pw_aff_alloc_size(isl_space_copy(pwaff1->dim), n); for (i = 0; i < pwaff1->n; ++i) { set = isl_set_copy(pwaff1->p[i].set); for (j = 0; j < pwaff2->n; ++j) { struct isl_set *common; isl_set *better; common = isl_set_intersect( isl_set_copy(pwaff1->p[i].set), isl_set_copy(pwaff2->p[j].set)); better = isl_set_from_basic_set(cmp( isl_aff_copy(pwaff2->p[j].aff), isl_aff_copy(pwaff1->p[i].aff))); better = isl_set_intersect(common, better); if (isl_set_plain_is_empty(better)) { isl_set_free(better); continue; } set = isl_set_subtract(set, isl_set_copy(better)); res = isl_pw_aff_add_piece(res, better, isl_aff_copy(pwaff2->p[j].aff)); } res = isl_pw_aff_add_piece(res, set, isl_aff_copy(pwaff1->p[i].aff)); } for (j = 0; j < pwaff2->n; ++j) { set = isl_set_copy(pwaff2->p[j].set); for (i = 0; i < pwaff1->n; ++i) set = isl_set_subtract(set, isl_set_copy(pwaff1->p[i].set)); res = isl_pw_aff_add_piece(res, set, isl_aff_copy(pwaff2->p[j].aff)); } isl_pw_aff_free(pwaff1); isl_pw_aff_free(pwaff2); return res; error: isl_pw_aff_free(pwaff1); isl_pw_aff_free(pwaff2); return NULL; } /* 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. */ static __isl_give isl_pw_aff *pw_aff_union_max(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_ge_basic_set); } __isl_give isl_pw_aff *isl_pw_aff_union_max(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_union_max); } /* 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. */ static __isl_give isl_pw_aff *pw_aff_union_min(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_le_basic_set); } __isl_give isl_pw_aff *isl_pw_aff_union_min(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_union_min); } __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); } /* Construct a map with as domain the domain of pwaff and * one-dimensional range corresponding to the affine expressions. */ static __isl_give isl_map *map_from_pw_aff(__isl_take isl_pw_aff *pwaff) { int i; isl_space *dim; isl_map *map; if (!pwaff) return NULL; dim = isl_pw_aff_get_space(pwaff); map = isl_map_empty(dim); for (i = 0; i < pwaff->n; ++i) { isl_basic_map *bmap; isl_map *map_i; bmap = isl_basic_map_from_aff(isl_aff_copy(pwaff->p[i].aff)); map_i = isl_map_from_basic_map(bmap); map_i = isl_map_intersect_domain(map_i, isl_set_copy(pwaff->p[i].set)); map = isl_map_union_disjoint(map, map_i); } isl_pw_aff_free(pwaff); return map; } /* Construct a map with as domain the domain of pwaff and * one-dimensional range corresponding to the affine expressions. */ __isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff) { if (!pwaff) return NULL; if (isl_space_is_set(pwaff->dim)) isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid, "space of input is not a map", goto error); return map_from_pw_aff(pwaff); error: isl_pw_aff_free(pwaff); return NULL; } /* Construct a one-dimensional set with as parameter domain * the domain of pwaff and the single set dimension * corresponding to the affine expressions. */ __isl_give isl_set *isl_set_from_pw_aff(__isl_take isl_pw_aff *pwaff) { if (!pwaff) return NULL; if (!isl_space_is_set(pwaff->dim)) isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid, "space of input is not a set", goto error); return map_from_pw_aff(pwaff); error: isl_pw_aff_free(pwaff); return 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) { 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; int rational; rational = isl_set_has_rational(pwaff->p[i].set); bset = aff_nonneg_basic_set(isl_aff_copy(pwaff->p[i].aff), rational); set_i = isl_set_from_basic_set(bset); set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set)); 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 pwaff where it is zero (if complement is 0) or not zero * (if complement is 1). * * The pieces with a NaN never belong to the result since * NaN is neither zero nor non-zero. */ static __isl_give isl_set *pw_aff_zero_set(__isl_take isl_pw_aff *pwaff, int complement) { 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, *zero; int rational; if (isl_aff_is_nan(pwaff->p[i].aff)) continue; rational = isl_set_has_rational(pwaff->p[i].set); bset = aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff), rational); zero = isl_set_from_basic_set(bset); set_i = isl_set_copy(pwaff->p[i].set); if (complement) set_i = isl_set_subtract(set_i, zero); else set_i = isl_set_intersect(set_i, zero); 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 pwaff where it is zero. */ __isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff) { return pw_aff_zero_set(pwaff, 0); } /* 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_zero_set(pwaff, 1); } /* 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 *dim = isl_set_get_space(set1); isl_aff *aff; aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim)); 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. */ static __isl_give isl_set *pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return pw_aff_gte_set(pwaff1, pwaff2, 0, 1); } __isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_eq_set); } /* Return a set containing those elements in the shared domain * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2. */ static __isl_give isl_set *pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return pw_aff_gte_set(pwaff1, pwaff2, 0, 0); } __isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ge_set); } /* Return a set containing those elements in the shared domain * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2. */ static __isl_give isl_set *pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return pw_aff_gte_set(pwaff1, pwaff2, 1, 0); } __isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_gt_set); } __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 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. */ static __isl_give isl_set *pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { isl_set *set_lt, *set_gt; 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_set *isl_pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ne_set); } __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; } /* Divide "pa" by "f". */ __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(__isl_take isl_pw_aff *pa, __isl_take isl_val *f) { int i; if (!pa || !f) goto error; if (isl_val_is_one(f)) { isl_val_free(f); return pa; } if (!isl_val_is_rat(f)) isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid, "expecting rational factor", goto error); if (!isl_val_is_pos(f)) isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid, "factor needs to be positive", goto error); pa = isl_pw_aff_cow(pa); if (!pa) return NULL; if (pa->n == 0) return pa; for (i = 0; i < pa->n; ++i) { pa->p[i].aff = isl_aff_scale_down_val(pa->p[i].aff, isl_val_copy(f)); if (!pa->p[i].aff) goto error; } isl_val_free(f); return pa; error: isl_pw_aff_free(pa); isl_val_free(f); return NULL; } __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. */ __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; 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); } 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; } int isl_aff_is_cst(__isl_keep isl_aff *aff) { if (!aff) return -1; return isl_seq_first_non_zero(aff->v->el + 2, aff->v->size - 2) == -1; } /* Check whether pwaff is a piecewise constant. */ int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff) { int i; if (!pwaff) return -1; for (i = 0; i < pwaff->n; ++i) { int is_cst = isl_aff_is_cst(pwaff->p[i].aff); if (is_cst < 0 || !is_cst) return is_cst; } return 1; } /* 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. */ __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { int is_cst; 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); if (!aff2) goto error; 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; } static __isl_give isl_pw_aff *pw_aff_add(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_add); } __isl_give isl_pw_aff *isl_pw_aff_add(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_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); } static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_mul); } __isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_mul); } static __isl_give isl_pw_aff *pw_aff_div(__isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2) { return isl_pw_aff_on_shared_domain(pa1, pa2, &isl_aff_div); } /* 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); return isl_pw_aff_align_params_pw_pw_and(pa1, pa2, &pw_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; } 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); } __isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_min); } 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); } __isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2) { return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_max); } 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"? */ int isl_aff_matching_params(__isl_keep isl_aff *aff, __isl_keep isl_space *space) { isl_space *aff_space; int match; if (!aff || !space) return -1; aff_space = isl_aff_get_domain_space(aff); match = isl_space_match(space, isl_dim_param, aff_space, isl_dim_param); isl_space_free(aff_space); return match; } /* Check that the domain space of "aff" matches "space". * * Return 0 on success and -1 on error. */ int isl_aff_check_match_domain_space(__isl_keep isl_aff *aff, __isl_keep isl_space *space) { isl_space *aff_space; int match; if (!aff || !space) return -1; aff_space = isl_aff_get_domain_space(aff); match = isl_space_match(space, isl_dim_param, aff_space, isl_dim_param); 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 0; error: isl_space_free(aff_space); return -1; } #undef BASE #define BASE aff #define NO_INTERSECT_DOMAIN #define NO_DOMAIN #include #undef NO_DOMAIN #undef NO_INTERSECT_DOMAIN /* 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, 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); 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; } /* 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, 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); 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; } /* 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, 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); dim = isl_space_dim(space, isl_dim_set); if (first + n > dim) isl_die(isl_space_get_ctx(space), isl_error_invalid, "range out of bounds", 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); } /* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe * domain. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_multi_aff( __isl_take isl_multi_aff *ma) { isl_set *dom = isl_set_universe(isl_multi_aff_get_domain_space(ma)); return isl_pw_multi_aff_alloc(dom, 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)); } /* Add "ma2" to "ma1" and return the result. * * The parameters of "ma1" and "ma2" are assumed to have been aligned. */ static __isl_give isl_multi_aff *isl_multi_aff_add_aligned( __isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2) { return isl_multi_aff_bin_op(maff1, maff2, &isl_aff_add); } /* Add "ma2" to "ma1" and return the result. */ __isl_give isl_multi_aff *isl_multi_aff_add(__isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2) { return isl_multi_aff_align_params_multi_multi_and(ma1, ma2, &isl_multi_aff_add_aligned); } /* Subtract "ma2" from "ma1" and return the result. * * The parameters of "ma1" and "ma2" are assumed to have been aligned. */ static __isl_give isl_multi_aff *isl_multi_aff_sub_aligned( __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2) { return isl_multi_aff_bin_op(ma1, ma2, &isl_aff_sub); } /* Subtract "ma2" from "ma1" and return the result. */ __isl_give isl_multi_aff *isl_multi_aff_sub(__isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2) { return isl_multi_aff_align_params_multi_multi_and(ma1, ma2, &isl_multi_aff_sub_aligned); } /* 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->p[i] = isl_aff_substitute_equalities(maff->p[i], isl_basic_set_copy(eq)); if (!maff->p[i]) goto error; } isl_basic_set_free(eq); return maff; error: isl_basic_set_free(eq); isl_multi_aff_free(maff); return NULL; } /* Given f, return floor(f). */ __isl_give isl_multi_aff *isl_multi_aff_floor(__isl_take isl_multi_aff *ma) { int i; ma = isl_multi_aff_cow(ma); if (!ma) return NULL; for (i = 0; i < ma->n; ++i) { ma->p[i] = isl_aff_floor(ma->p[i]); if (!ma->p[i]) return isl_multi_aff_free(ma); } return ma; } __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->p[i] = isl_aff_scale(maff->p[i], f); if (!maff->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; } int isl_multi_aff_is_empty(__isl_keep isl_multi_aff *maff) { if (!maff) return -1; return 0; } /* 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 * 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) { isl_space *space; isl_map *map1, *map2; isl_map *map, *ge; map1 = isl_map_from_multi_aff(ma1); map2 = isl_map_from_multi_aff(ma2); map = isl_map_range_product(map1, map2); space = isl_space_range(isl_map_get_space(map)); space = isl_space_domain(isl_space_unwrap(space)); ge = isl_map_lex_ge(space); map = isl_map_intersect_range(map, isl_map_wrap(ge)); return isl_map_domain(map); } #undef PW #define PW isl_pw_multi_aff #undef EL #define EL isl_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 #define NO_NEG #define NO_EVAL #define NO_OPT #define NO_INVOLVES_DIMS #define NO_INSERT_DIMS #define NO_LIFT #define NO_MORPH #include #undef UNION #define UNION isl_union_pw_multi_aff #undef PART #define PART isl_pw_multi_aff #undef PARTS #define PARTS pw_multi_aff #define ALIGN_DOMAIN #define NO_EVAL #include /* Given a function "cmp" that returns the set of elements where * "ma1" is "better" than "ma2", return the intersection of this * set with "dom1" and "dom2". */ static __isl_give isl_set *shared_and_better(__isl_keep isl_set *dom1, __isl_keep isl_set *dom2, __isl_keep isl_multi_aff *ma1, __isl_keep isl_multi_aff *ma2, __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)) { isl_set *common; isl_set *better; int is_empty; common = isl_set_intersect(isl_set_copy(dom1), isl_set_copy(dom2)); is_empty = isl_set_plain_is_empty(common); if (is_empty >= 0 && is_empty) return common; if (is_empty < 0) return isl_set_free(common); better = cmp(isl_multi_aff_copy(ma1), isl_multi_aff_copy(ma2)); better = isl_set_intersect(common, better); return better; } /* Given a function "cmp" that returns the set of elements where * "ma1" is "better" than "ma2", return a piecewise multi affine * expression defined on the union of the definition domains * of "pma1" and "pma2" that maps to the "best" of "pma1" and * "pma2" on each cell. If only one of the two input functions * is defined on a given cell, then it is considered the best. */ static __isl_give isl_pw_multi_aff *pw_multi_aff_union_opt( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2, __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)) { int i, j, n; isl_pw_multi_aff *res = NULL; isl_ctx *ctx; isl_set *set = NULL; if (!pma1 || !pma2) goto error; ctx = isl_space_get_ctx(pma1->dim); if (!isl_space_is_equal(pma1->dim, pma2->dim)) isl_die(ctx, isl_error_invalid, "arguments should live in the same space", goto error); if (isl_pw_multi_aff_is_empty(pma1)) { isl_pw_multi_aff_free(pma1); return pma2; } if (isl_pw_multi_aff_is_empty(pma2)) { isl_pw_multi_aff_free(pma2); return pma1; } n = 2 * (pma1->n + 1) * (pma2->n + 1); res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma1->dim), n); for (i = 0; i < pma1->n; ++i) { set = isl_set_copy(pma1->p[i].set); for (j = 0; j < pma2->n; ++j) { isl_set *better; int is_empty; better = shared_and_better(pma2->p[j].set, pma1->p[i].set, pma2->p[j].maff, pma1->p[i].maff, cmp); is_empty = isl_set_plain_is_empty(better); if (is_empty < 0 || is_empty) { isl_set_free(better); if (is_empty < 0) goto error; continue; } set = isl_set_subtract(set, isl_set_copy(better)); res = isl_pw_multi_aff_add_piece(res, better, isl_multi_aff_copy(pma2->p[j].maff)); } res = isl_pw_multi_aff_add_piece(res, set, isl_multi_aff_copy(pma1->p[i].maff)); } for (j = 0; j < pma2->n; ++j) { set = isl_set_copy(pma2->p[j].set); for (i = 0; i < pma1->n; ++i) set = isl_set_subtract(set, isl_set_copy(pma1->p[i].set)); res = isl_pw_multi_aff_add_piece(res, set, isl_multi_aff_copy(pma2->p[j].maff)); } 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); isl_set_free(set); return isl_pw_multi_aff_free(res); } static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmax( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { return pw_multi_aff_union_opt(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 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) { return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2, &pw_multi_aff_union_lexmax); } static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmin( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_le_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) { return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2, &pw_multi_aff_union_lexmin); } static __isl_give isl_pw_multi_aff *pw_multi_aff_add( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { return isl_pw_multi_aff_on_shared_domain(pma1, pma2, &isl_multi_aff_add); } __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) { return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2, &pw_multi_aff_add); } static __isl_give isl_pw_multi_aff *pw_multi_aff_sub( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { return isl_pw_multi_aff_on_shared_domain(pma1, pma2, &isl_multi_aff_sub); } /* 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) { return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2, &pw_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); } /* Given two piecewise multi-affine expressions A -> B and C -> D, * construct a piecewise multi-affine expression [A -> C] -> [B -> D]. */ static __isl_give isl_pw_multi_aff *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 (!pma1 || !pma2) 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; } __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) { return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2, &pw_multi_aff_product); } /* Construct a map mapping the domain of the piecewise multi-affine expression * to its range, with each dimension in the range equated to the * corresponding affine expression on its cell. */ __isl_give isl_map *isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma) { int i; isl_map *map; if (!pma) return NULL; map = isl_map_empty(isl_pw_multi_aff_get_space(pma)); for (i = 0; i < pma->n; ++i) { isl_multi_aff *maff; isl_basic_map *bmap; isl_map *map_i; maff = isl_multi_aff_copy(pma->p[i].maff); bmap = isl_basic_map_from_multi_aff(maff); map_i = isl_map_from_basic_map(bmap); map_i = isl_map_intersect_domain(map_i, isl_set_copy(pma->p[i].set)); map = isl_map_union_disjoint(map, map_i); } isl_pw_multi_aff_free(pma); return map; } __isl_give isl_set *isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma) { if (!pma) return NULL; if (!isl_space_is_set(pma->dim)) isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid, "isl_pw_multi_aff cannot be converted into an isl_set", goto error); return isl_map_from_pw_multi_aff(pma); error: isl_pw_multi_aff_free(pma); return NULL; } /* Given a basic map with a single output dimension that is defined * in terms of the parameters and input dimensions using an equality, * extract an isl_aff that expresses the output dimension in terms * of the parameters and input dimensions. * Note that this expression may involve integer divisions defined * in terms of parameters and input 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_take isl_basic_map *bmap) { int eq; unsigned offset; unsigned n_div; isl_local_space *ls; isl_aff *aff; if (!bmap) return NULL; if (isl_basic_map_dim(bmap, isl_dim_out) != 1) isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid, "basic map should have a single output dimension", goto error); eq = isl_basic_map_output_defining_equality(bmap, 0); if (eq >= bmap->n_eq) isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid, "unable to find suitable equality", goto error); ls = isl_basic_map_get_local_space(bmap); aff = isl_aff_alloc(isl_local_space_domain(ls)); if (!aff) goto error; offset = isl_basic_map_offset(bmap, isl_dim_out); n_div = isl_basic_map_dim(bmap, isl_dim_div); if (isl_int_is_neg(bmap->eq[eq][offset])) { isl_seq_cpy(aff->v->el + 1, bmap->eq[eq], offset); isl_seq_cpy(aff->v->el + 1 + offset, bmap->eq[eq] + offset + 1, n_div); } else { isl_seq_neg(aff->v->el + 1, bmap->eq[eq], offset); isl_seq_neg(aff->v->el + 1 + offset, bmap->eq[eq] + offset + 1, n_div); } isl_int_abs(aff->v->el[0], bmap->eq[eq][offset]); isl_basic_map_free(bmap); aff = isl_aff_remove_unused_divs(aff); return aff; error: isl_basic_map_free(bmap); return NULL; } /* 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; unsigned 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); for (i = 0; i < n_out; ++i) { isl_basic_map *bmap_i; isl_aff *aff; bmap_i = isl_basic_map_copy(bmap); bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out, i + 1, n_out - (1 + i)); bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out, 0, i); aff = extract_isl_aff_from_basic_map(bmap_i); 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. */ 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; 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; isl_local_space *ls; isl_multi_aff *ma; isl_aff *aff; isl_vec *v; isl_map *insert; int offset; int n; int n_in; isl_pw_multi_aff *pma; int is_set; is_set = isl_map_is_set(map); 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); 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(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; } /* 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 dimemnsions? * * "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 dimemnsions, * 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, dim; int i, j, n; int offset, total; isl_int sum; isl_basic_map *hull; hull = isl_map_unshifted_simple_hull(isl_map_copy(map)); if (!hull) goto error; isl_int_init(sum); dim = isl_map_dim(map, isl_dim_out); offset = isl_basic_map_offset(hull, isl_dim_out); total = 1 + isl_basic_map_total_dim(hull); 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, total)) continue; for (j = i + 1; j < n; ++j) { if (!isl_seq_is_neg(hull->ineq[i] + 1, hull->ineq[j] + 1, total - 1)) 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 fro "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; unsigned n_in; unsigned o_out; unsigned n_out; int is_set; is_set = isl_map_is_set(map); n_in = isl_basic_map_dim(hull, isl_dim_in); n_out = isl_basic_map_dim(hull, isl_dim_out); 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(set); 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; } /* 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, we check if any of the output dimensions is "strided". * That is, we check if can be written as * * x = m a + f(..) * * with m greater than 1, a some combination of existentiall quantified * variables and f and 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. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(__isl_take isl_map *map) { int i, j; int sv; isl_basic_map *hull; unsigned n_out; unsigned o_out; unsigned n_div; unsigned o_div; isl_int gcd; if (!map) return NULL; hull = isl_map_affine_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) hull = isl_basic_map_free(hull); if (!hull) goto error; n_div = isl_basic_map_dim(hull, isl_dim_div); o_div = isl_basic_map_offset(hull, isl_dim_div); if (n_div == 0) { isl_basic_map_free(hull); return pw_multi_aff_from_map_check_div(map); } isl_int_init(gcd); n_out = isl_basic_map_dim(hull, isl_dim_out); 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); return NULL; } __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); } /* Convert "map" into an isl_pw_multi_aff (if possible) and * add it to *user. */ static int 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 ? 0 : -1; } /* 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; } /* 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; 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)); if (isl_local_space_dim(subs->ls, isl_dim_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->p[i] = isl_aff_substitute(maff->p[i], type, pos, subs); if (!maff->p[i]) return isl_multi_aff_free(maff); } return maff; } /* Plug in "subs" for dimension "type", "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, enum isl_dim_type type, 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, type, 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), type, 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. */ void 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; int 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); 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->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->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->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->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); } } /* 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; int 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->p[0], isl_dim_div) : 0; 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); isl_seq_preimage(res->v->el, aff->v->el, ma, 0, 0, n_div_ma, n_div_aff, f, c1, c2, g, 1); 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". * * The parameters of "ma1" and "ma2" are assumed to have been aligned. */ static __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff_aligned( __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2) { int i; isl_space *space = NULL; 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->p[i] = isl_aff_pullback_multi_aff(ma1->p[i], isl_multi_aff_copy(ma2)); if (!ma1->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; } /* 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) { return isl_multi_aff_align_params_multi_multi_and(ma1, ma2, &isl_multi_aff_pullback_multi_aff_aligned); } /* Extend the local space of "dst" to include the divs * in the local space of "src". */ __isl_give isl_aff *isl_aff_align_divs(__isl_take isl_aff *dst, __isl_keep isl_aff *src) { isl_ctx *ctx; int *exp1 = NULL; int *exp2 = NULL; isl_mat *div; if (!src || !dst) return isl_aff_free(dst); ctx = isl_aff_get_ctx(src); if (!isl_space_is_equal(src->ls->dim, dst->ls->dim)) isl_die(ctx, isl_error_invalid, "spaces don't match", goto error); if (src->ls->div->n_row == 0) return dst; exp1 = isl_alloc_array(ctx, int, src->ls->div->n_row); exp2 = isl_alloc_array(ctx, int, dst->ls->div->n_row); if (!exp1 || (dst->ls->div->n_row && !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->p[0] = isl_aff_align_divs(maff->p[0], maff->p[i]); for (i = 1; i < maff->n; ++i) { maff->p[i] = isl_aff_align_divs(maff->p[i], maff->p[0]); if (!maff->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; unsigned 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->p[0], isl_dim_div); 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->p[0]); if (!*ls) return isl_multi_aff_free(maff); } for (i = 0; i < maff->n; ++i) { maff->p[i] = isl_aff_lift(maff->p[i]); if (!maff->p[i]) goto error; } return maff; error: if (ls) isl_local_space_free(*ls); return isl_multi_aff_free(maff); } /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma". */ __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff( __isl_keep isl_pw_multi_aff *pma, int pos) { int i; int n_out; isl_space *space; isl_pw_aff *pa; if (!pma) return NULL; n_out = isl_pw_multi_aff_dim(pma, isl_dim_out); if (pos < 0 || pos >= n_out) isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid, "index out of bounds", 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; } /* 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 int 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 0; } /* 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; } /* Convert "pma" to an isl_map and add it to *umap. */ static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma, void *user) { isl_union_map **umap = user; isl_map *map; map = isl_map_from_pw_multi_aff(pma); *umap = isl_union_map_add_map(*umap, map); return 0; } /* Construct a union map mapping the domain of the union * piecewise multi-affine expression to its range, with each dimension * in the range equated to the corresponding affine expression on its cell. */ __isl_give isl_union_map *isl_union_map_from_union_pw_multi_aff( __isl_take isl_union_pw_multi_aff *upma) { isl_space *space; isl_union_map *umap; if (!upma) return NULL; space = isl_union_pw_multi_aff_get_space(upma); umap = isl_union_map_empty(space); if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma, &map_from_pw_multi_aff, &umap) < 0) goto error; isl_union_pw_multi_aff_free(upma); return umap; error: isl_union_pw_multi_aff_free(upma); isl_union_map_free(umap); 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; int (*fn)(void **entry, 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 int bin_entry(void **entry, void *user) { struct isl_union_pw_multi_aff_bin_data *data = user; isl_pw_multi_aff *pma = *entry; data->pma = pma; if (isl_hash_table_foreach(data->upma2->dim->ctx, &data->upma2->table, data->fn, data) < 0) return -1; return 0; } /* 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, int (*fn)(void **entry, 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(isl_space_copy(upma1->dim), upma1->table.n); if (isl_hash_table_foreach(upma1->dim->ctx, &upma1->table, &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 aligned isl_pw_multi_affs A -> B and C -> D, * construct an isl_pw_multi_aff (A * C) -> [B -> D]. */ static __isl_give isl_pw_multi_aff *pw_multi_aff_range_product( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { isl_space *space; 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_range_product( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2, &pw_multi_aff_range_product); } /* Given two aligned isl_pw_multi_affs A -> B and C -> D, * construct an isl_pw_multi_aff (A * C) -> (B, D). */ static __isl_give isl_pw_multi_aff *pw_multi_aff_flat_range_product( __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2) { isl_space *space; 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); } /* 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) { return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2, &pw_multi_aff_flat_range_product); } /* If data->pma and *entry have the same domain space, then compute * their flat range product and the result to data->res. */ static int flat_range_product_entry(void **entry, void *user) { struct isl_union_pw_multi_aff_bin_data *data = user; isl_pw_multi_aff *pma2 = *entry; if (!isl_space_tuple_is_equal(data->pma->dim, isl_dim_in, pma2->dim, isl_dim_in)) return 0; pma2 = isl_pw_multi_aff_flat_range_product( isl_pw_multi_aff_copy(data->pma), isl_pw_multi_aff_copy(pma2)); data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma2); return 0; } /* 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); } /* 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 (pos >= isl_pw_multi_aff_dim(pma, isl_dim_out)) isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid, "index out of bounds", 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) { if (!pma || !pa) goto error; if (isl_space_match(pma->dim, isl_dim_param, pa->dim, isl_dim_param)) return pw_multi_aff_set_pw_aff(pma, pos, pa); if (!isl_space_has_named_params(pma->dim) || !isl_space_has_named_params(pa->dim)) isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid, "unaligned unnamed parameters", 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"? */ int isl_pw_aff_matching_params(__isl_keep isl_pw_aff *pa, __isl_keep isl_space *space) { isl_space *pa_space; int match; if (!pa || !space) return -1; pa_space = isl_pw_aff_get_space(pa); match = isl_space_match(space, isl_dim_param, pa_space, isl_dim_param); isl_space_free(pa_space); return match; } /* Check that the domain space of "pa" matches "space". * * Return 0 on success and -1 on error. */ int isl_pw_aff_check_match_domain_space(__isl_keep isl_pw_aff *pa, __isl_keep isl_space *space) { isl_space *pa_space; int match; if (!pa || !space) return -1; pa_space = isl_pw_aff_get_space(pa); match = isl_space_match(space, isl_dim_param, pa_space, isl_dim_param); 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 0; error: isl_space_free(pa_space); return -1; } #undef BASE #define BASE pw_aff #include /* 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; 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); if (!isl_space_match(pma->dim, isl_dim_param, mv->space, isl_dim_param)) { 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; } /* Internal data structure for isl_union_pw_multi_aff_scale_multi_val. * mv contains the mv argument. * res collects the results. */ struct isl_union_pw_multi_aff_scale_multi_val_data { isl_multi_val *mv; isl_union_pw_multi_aff *res; }; /* 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 add the result * to data->res. */ static int union_pw_multi_aff_scale_multi_val_entry(void **entry, void *user) { struct isl_union_pw_multi_aff_scale_multi_val_data *data = user; isl_pw_multi_aff *pma = *entry; if (!pma) return -1; if (!isl_space_tuple_is_equal(pma->dim, isl_dim_out, data->mv->space, isl_dim_set)) return 0; pma = isl_pw_multi_aff_copy(pma); pma = isl_pw_multi_aff_scale_multi_val(pma, isl_multi_val_copy(data->mv)); data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma); if (!data->res) return -1; return 0; } /* 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_scale_multi_val_data data; 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; data.mv = mv; data.res = isl_union_pw_multi_aff_alloc(isl_space_copy(upma->dim), upma->table.n); if (isl_hash_table_foreach(upma->dim->ctx, &upma->table, &union_pw_multi_aff_scale_multi_val_entry, &data) < 0) goto error; isl_multi_val_free(mv); isl_union_pw_multi_aff_free(upma); return data.res; 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 a set or map mapping the shared (parameter) domain * of the piecewise affine expressions to the range of "mpa" * with each dimension in the range equated to the * corresponding piecewise affine expression. */ static __isl_give isl_map *map_from_multi_pw_aff( __isl_take isl_multi_pw_aff *mpa) { int i; isl_space *space; isl_map *map; if (!mpa) return NULL; if (isl_space_dim(mpa->space, isl_dim_out) != mpa->n) isl_die(isl_multi_pw_aff_get_ctx(mpa), isl_error_internal, "invalid space", goto error); space = isl_multi_pw_aff_get_domain_space(mpa); map = isl_map_universe(isl_space_from_domain(space)); for (i = 0; i < mpa->n; ++i) { isl_pw_aff *pa; isl_map *map_i; pa = isl_pw_aff_copy(mpa->p[i]); map_i = map_from_pw_aff(pa); map = isl_map_flat_range_product(map, map_i); } map = isl_map_reset_space(map, isl_multi_pw_aff_get_space(mpa)); isl_multi_pw_aff_free(mpa); return map; error: isl_multi_pw_aff_free(mpa); return NULL; } /* Construct a map mapping the shared domain * of the piecewise affine expressions to the range of "mpa" * with each dimension in the range equated to the * corresponding piecewise affine expression. */ __isl_give isl_map *isl_map_from_multi_pw_aff(__isl_take isl_multi_pw_aff *mpa) { if (!mpa) return NULL; if (isl_space_is_set(mpa->space)) isl_die(isl_multi_pw_aff_get_ctx(mpa), isl_error_internal, "space of input is not a map", goto error); return map_from_multi_pw_aff(mpa); error: isl_multi_pw_aff_free(mpa); return NULL; } /* Construct a set mapping the shared parameter domain * of the piecewise affine expressions to the space of "mpa" * with each dimension in the range equated to the * corresponding piecewise affine expression. */ __isl_give isl_set *isl_set_from_multi_pw_aff(__isl_take isl_multi_pw_aff *mpa) { if (!mpa) return NULL; if (!isl_space_is_set(mpa->space)) isl_die(isl_multi_pw_aff_get_ctx(mpa), isl_error_internal, "space of input is not a set", goto error); return map_from_multi_pw_aff(mpa); error: isl_multi_pw_aff_free(mpa); return NULL; } /* 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; space = isl_multi_pw_aff_get_space(mpa); if (mpa->n == 0) { isl_multi_pw_aff_free(mpa); return isl_pw_multi_aff_zero(space); } 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; } /* 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, n; isl_multi_pw_aff *mpa; if (!ma) return NULL; n = isl_multi_aff_dim(ma, isl_dim_out); 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; } /* Construct and return a multi piecewise affine expression * that is equal to the given piecewise multi affine expression. */ __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_multi_aff( __isl_take isl_pw_multi_aff *pma) { int i, n; isl_space *space; isl_multi_pw_aff *mpa; if (!pma) return NULL; n = isl_pw_multi_aff_dim(pma, isl_dim_out); 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); } isl_pw_multi_aff_free(pma); return mpa; } /* 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. */ int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1, __isl_keep isl_pw_aff *pa2) { int equal; isl_map *map1, *map2; if (!pa1 || !pa2) return -1; equal = isl_pw_aff_plain_is_equal(pa1, pa2); if (equal < 0 || equal) return equal; map1 = map_from_pw_aff(isl_pw_aff_copy(pa1)); map2 = map_from_pw_aff(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. */ int isl_multi_pw_aff_is_equal(__isl_keep isl_multi_pw_aff *mpa1, __isl_keep isl_multi_pw_aff *mpa2) { int i; int equal; if (!mpa1 || !mpa2) return -1; if (!isl_space_match(mpa1->space, isl_dim_param, mpa2->space, isl_dim_param)) { if (!isl_space_has_named_params(mpa1->space)) return 0; if (!isl_space_has_named_params(mpa2->space)) return 0; 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->p[i], mpa2->p[i]); if (equal < 0 || !equal) return equal; } return 1; } /* Coalesce the elements of "mpa". * * Note that such coalescing does not change the meaning of "mpa" * so there is no need to cow. We do need to be careful not to * destroy any other copies of "mpa" in case of failure. */ __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce( __isl_take isl_multi_pw_aff *mpa) { int i; if (!mpa) return NULL; for (i = 0; i < mpa->n; ++i) { isl_pw_aff *pa = isl_pw_aff_copy(mpa->p[i]); pa = isl_pw_aff_coalesce(pa); if (!pa) return isl_multi_pw_aff_free(mpa); isl_pw_aff_free(mpa->p[i]); mpa->p[i] = pa; } return mpa; } /* 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. */ 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->p[i] = isl_pw_aff_pullback_multi_aff(mpa->p[i], isl_multi_aff_copy(ma)); if (!mpa->p[i]) 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) { if (!mpa || !ma) goto error; if (isl_space_match(mpa->space, isl_dim_param, ma->space, isl_dim_param)) 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. */ 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->p[i] = isl_pw_aff_pullback_pw_multi_aff_aligned(mpa->p[i], isl_pw_multi_aff_copy(pma)); if (!mpa->p[i]) 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) { if (!mpa || !pma) goto error; if (isl_space_match(mpa->space, isl_dim_param, pma->dim, isl_dim_param)) 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, n_param, n_in, n_div; isl_space *space; isl_val *v; isl_pw_aff *pa; isl_aff *tmp; n_param = isl_aff_dim(aff, isl_dim_param); n_in = isl_aff_dim(aff, isl_dim_in); n_div = isl_aff_dim(aff, isl_dim_div); 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, isl_space_dim(space, isl_dim_set)); 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; } /* 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) { if (!aff || !mpa) goto error; if (isl_space_match(aff->ls->dim, isl_dim_param, mpa->space, isl_dim_param)) 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) { if (!pa || !mpa) goto error; if (isl_space_match(pa->dim, isl_dim_param, mpa->space, isl_dim_param)) 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". * * The parameters of "mpa1" and "mpa2" are assumed to have been aligned. * * We pullback each member of "mpa1" in turn. */ static __isl_give isl_multi_pw_aff * isl_multi_pw_aff_pullback_multi_pw_aff_aligned( __isl_take isl_multi_pw_aff *mpa1, __isl_take isl_multi_pw_aff *mpa2) { int i; isl_space *space = NULL; 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->p[i] = isl_pw_aff_pullback_multi_pw_aff_aligned( mpa1->p[i], isl_multi_pw_aff_copy(mpa2)); if (!mpa1->p[i]) 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; } /* Compute the pullback of "mpa1" by the function represented by "mpa2". * In other words, plug in "mpa2" in "mpa1". */ __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) { return isl_multi_pw_aff_align_params_multi_multi_and(mpa1, mpa2, &isl_multi_pw_aff_pullback_multi_pw_aff_aligned); } /* 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; }