/* * Copyright 2011 INRIA Saclay * Copyright 2011 Sven Verdoolaege * Copyright 2012 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 __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 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); } void *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; } int isl_aff_plain_is_zero(__isl_keep isl_aff *aff) { if (!aff) return -1; return isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1) < 0; } int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2) { int equal; if (!aff1 || !aff2) return -1; 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); } int isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v) { if (!aff) return -1; isl_int_set(*v, aff->v->el[0]); return 0; } int isl_aff_get_constant(__isl_keep isl_aff *aff, isl_int *v) { if (!aff) return -1; isl_int_set(*v, aff->v->el[1]); return 0; } 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); pos += isl_local_space_offset(aff->ls, type); isl_int_set(*v, aff->v->el[1 + pos]); return 0; } __isl_give isl_aff *isl_aff_set_denominator(__isl_take isl_aff *aff, isl_int v) { 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; } __isl_give isl_aff *isl_aff_set_constant(__isl_take isl_aff *aff, isl_int v) { 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; } __isl_give isl_aff *isl_aff_add_constant(__isl_take isl_aff *aff, isl_int v) { if (isl_int_is_zero(v)) 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; } __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". */ __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; 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". */ __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; } __isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v) { 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; } __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)); 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; } __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 >= isl_local_space_dim(aff->ls, type)) isl_die(aff->v->ctx, isl_error_invalid, "position out of bounds", return isl_aff_free(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_si(aff->v->el[1 + pos], v); return aff; } __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)); 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; } __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); } __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *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); 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); } /* 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 = 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. */ __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_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); 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 * * 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; } /* Given f, return ceil(f). * If f is an integer expression, then just return f. * Otherwise, create a new div d = [-f] and return the expression -d. */ __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff) { if (!aff) return NULL; if (isl_int_is_one(aff->v->el[0])) return aff; aff = isl_aff_neg(aff); aff = isl_aff_floor(aff); aff = isl_aff_neg(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; } __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; 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 (aff1->ls->div->n_row == 0 && aff2->ls->div->n_row == 0) return add_expanded(aff1, aff2); exp1 = isl_alloc_array(ctx, int, aff1->ls->div->n_row); exp2 = isl_alloc_array(ctx, int, aff2->ls->div->n_row); if (!exp1 || !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)); } __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff, isl_int f) { isl_int gcd; 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); 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; } __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f) { isl_int gcd; 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; } __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) return isl_id_free(id); 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; } /* 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)); if (!aff->ls) 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(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. */ __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff) { isl_constraint *ineq; isl_basic_set *bset; ineq = isl_inequality_from_aff(aff); bset = isl_basic_set_from_constraint(ineq); bset = isl_basic_set_simplify(bset); return bset; } /* 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. */ __isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff) { isl_constraint *ineq; isl_basic_set *bset; ineq = isl_equality_from_aff(aff); bset = isl_basic_set_from_constraint(ineq); bset = isl_basic_set_simplify(bset); return bset; } /* 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); } __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_MOVE_DIMS #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", return isl_pw_aff_free(pwaff)); return map_from_pw_aff(pwaff); } /* 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", return isl_pw_aff_free(pwaff)); return map_from_pw_aff(pwaff); } /* 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; bset = isl_aff_nonneg_basic_set(isl_aff_copy(pwaff->p[i].aff)); 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). */ 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; bset = isl_aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff)); 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; } __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; */ __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; 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); } 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; } __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1, __isl_take isl_aff *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 piecewise constant. */ __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1, __isl_take isl_aff *aff2) { int is_cst; int neg; 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", return isl_pw_aff_list_free(list)); 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; } /* 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); } #undef BASE #define BASE aff #include /* 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)); } __isl_give isl_multi_aff *isl_multi_aff_add(__isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2) { int i; isl_ctx *ctx; maff1 = isl_multi_aff_cow(maff1); if (!maff1 || !maff2) goto error; ctx = isl_multi_aff_get_ctx(maff1); if (!isl_space_is_equal(maff1->space, maff2->space)) isl_die(ctx, isl_error_invalid, "spaces don't match", goto error); for (i = 0; i < maff1->n; ++i) { maff1->p[i] = isl_aff_add(maff1->p[i], isl_aff_copy(maff2->p[i])); if (!maff1->p[i]) goto error; } isl_multi_aff_free(maff2); return maff1; error: isl_multi_aff_free(maff1); isl_multi_aff_free(maff2); return NULL; } /* Given two multi-affine expressions A -> B and C -> D, * construct a multi-affine expression [A -> C] -> [B -> D]. */ __isl_give isl_multi_aff *isl_multi_aff_product( __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2) { int i; isl_aff *aff; isl_space *space; isl_multi_aff *res; int in1, in2, out1, out2; in1 = isl_multi_aff_dim(ma1, isl_dim_in); in2 = isl_multi_aff_dim(ma2, isl_dim_in); out1 = isl_multi_aff_dim(ma1, isl_dim_out); out2 = isl_multi_aff_dim(ma2, isl_dim_out); space = isl_space_product(isl_multi_aff_get_space(ma1), isl_multi_aff_get_space(ma2)); res = isl_multi_aff_alloc(isl_space_copy(space)); space = isl_space_domain(space); for (i = 0; i < out1; ++i) { aff = isl_multi_aff_get_aff(ma1, i); aff = isl_aff_insert_dims(aff, isl_dim_in, in1, in2); aff = isl_aff_reset_domain_space(aff, isl_space_copy(space)); res = isl_multi_aff_set_aff(res, i, aff); } for (i = 0; i < out2; ++i) { aff = isl_multi_aff_get_aff(ma2, i); aff = isl_aff_insert_dims(aff, isl_dim_in, 0, in1); aff = isl_aff_reset_domain_space(aff, isl_space_copy(space)); res = isl_multi_aff_set_aff(res, out1 + i, aff); } isl_space_free(space); isl_multi_aff_free(ma1); isl_multi_aff_free(ma2); return res; } /* 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; } __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; } int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1, __isl_keep isl_multi_aff *maff2) { int i; int equal; if (!maff1 || !maff2) return -1; if (maff1->n != maff2->n) return 0; equal = isl_space_is_equal(maff1->space, maff2->space); if (equal < 0 || !equal) return equal; for (i = 0; i < maff1->n; ++i) { equal = isl_aff_plain_is_equal(maff1->p[i], maff2->p[i]); if (equal < 0 || !equal) return equal; } return 1; } /* 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_MOVE_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); } __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[i].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", return isl_pw_multi_aff_free(pma)); return isl_map_from_pw_multi_aff(pma); } /* 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. * * 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. * * 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 i; unsigned offset; unsigned total; 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); offset = isl_basic_map_offset(bmap, isl_dim_out); total = isl_basic_map_total_dim(bmap); for (i = 0; i < bmap->n_eq; ++i) { if (isl_int_is_zero(bmap->eq[i][offset])) continue; if (isl_seq_first_non_zero(bmap->eq[i] + offset + 1, 1 + total - (offset + 1)) != -1) continue; break; } if (i >= 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; if (isl_int_is_neg(bmap->eq[i][offset])) isl_seq_cpy(aff->v->el + 1, bmap->eq[i], offset); else isl_seq_neg(aff->v->el + 1, bmap->eq[i], offset); isl_seq_clr(aff->v->el + 1 + offset, aff->v->size - (1 + offset)); isl_int_abs(aff->v->el[0], bmap->eq[i][offset]); isl_basic_map_free(bmap); aff = isl_aff_remove_unused_divs(aff); aff = isl_aff_floor(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; } /* 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. */ 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); 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. * * 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. */ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(__isl_take isl_map *map) { int i; int sv; isl_pw_multi_aff *pma; isl_basic_map *hull; 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); isl_basic_map_free(hull); if (sv < 0) goto error; 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; } __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); } /* 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; 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); if (isl_set_plain_is_empty(common)) { isl_set_free(common); 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; } /* 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 || !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_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_match(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_match(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; } #undef BASE #define BASE pw_aff #include