forked from OSchip/llvm-project
563 lines
15 KiB
C
563 lines
15 KiB
C
#include <isl_ctx_private.h>
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#include <isl/val.h>
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#include <isl_constraint_private.h>
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#include <isl/set.h>
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#include <isl_polynomial_private.h>
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#include <isl_morph.h>
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#include <isl_range.h>
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struct range_data {
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struct isl_bound *bound;
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int *signs;
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int sign;
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int test_monotonicity;
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int monotonicity;
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int tight;
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isl_qpolynomial *poly;
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isl_pw_qpolynomial_fold *pwf;
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isl_pw_qpolynomial_fold *pwf_tight;
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};
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static isl_stat propagate_on_domain(__isl_take isl_basic_set *bset,
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__isl_take isl_qpolynomial *poly, struct range_data *data);
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/* Check whether the polynomial "poly" has sign "sign" over "bset",
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* i.e., if sign == 1, check that the lower bound on the polynomial
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* is non-negative and if sign == -1, check that the upper bound on
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* the polynomial is non-positive.
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*/
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static isl_bool has_sign(__isl_keep isl_basic_set *bset,
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__isl_keep isl_qpolynomial *poly, int sign, int *signs)
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{
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struct range_data data_m;
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isl_size nparam;
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isl_space *space;
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isl_val *opt;
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isl_bool r;
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enum isl_fold type;
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nparam = isl_basic_set_dim(bset, isl_dim_param);
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if (nparam < 0)
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return isl_bool_error;
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bset = isl_basic_set_copy(bset);
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poly = isl_qpolynomial_copy(poly);
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bset = isl_basic_set_move_dims(bset, isl_dim_set, 0,
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isl_dim_param, 0, nparam);
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poly = isl_qpolynomial_move_dims(poly, isl_dim_in, 0,
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isl_dim_param, 0, nparam);
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space = isl_qpolynomial_get_space(poly);
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space = isl_space_params(space);
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space = isl_space_from_domain(space);
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space = isl_space_add_dims(space, isl_dim_out, 1);
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data_m.test_monotonicity = 0;
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data_m.signs = signs;
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data_m.sign = -sign;
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type = data_m.sign < 0 ? isl_fold_min : isl_fold_max;
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data_m.pwf = isl_pw_qpolynomial_fold_zero(space, type);
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data_m.tight = 0;
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data_m.pwf_tight = NULL;
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if (propagate_on_domain(bset, poly, &data_m) < 0)
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goto error;
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if (sign > 0)
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opt = isl_pw_qpolynomial_fold_min(data_m.pwf);
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else
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opt = isl_pw_qpolynomial_fold_max(data_m.pwf);
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if (!opt)
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r = isl_bool_error;
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else if (isl_val_is_nan(opt) ||
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isl_val_is_infty(opt) ||
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isl_val_is_neginfty(opt))
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r = isl_bool_false;
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else
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r = isl_bool_ok(sign * isl_val_sgn(opt) >= 0);
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isl_val_free(opt);
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return r;
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error:
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isl_pw_qpolynomial_fold_free(data_m.pwf);
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return isl_bool_error;
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}
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/* Return 1 if poly is monotonically increasing in the last set variable,
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* -1 if poly is monotonically decreasing in the last set variable,
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* 0 if no conclusion,
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* -2 on error.
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*
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* We simply check the sign of p(x+1)-p(x)
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*/
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static int monotonicity(__isl_keep isl_basic_set *bset,
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__isl_keep isl_qpolynomial *poly, struct range_data *data)
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{
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isl_ctx *ctx;
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isl_space *space;
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isl_qpolynomial *sub = NULL;
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isl_qpolynomial *diff = NULL;
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int result = 0;
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isl_bool s;
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isl_size nvar;
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nvar = isl_basic_set_dim(bset, isl_dim_set);
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if (nvar < 0)
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return -2;
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ctx = isl_qpolynomial_get_ctx(poly);
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space = isl_qpolynomial_get_domain_space(poly);
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sub = isl_qpolynomial_var_on_domain(isl_space_copy(space),
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isl_dim_set, nvar - 1);
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sub = isl_qpolynomial_add(sub,
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isl_qpolynomial_rat_cst_on_domain(space, ctx->one, ctx->one));
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diff = isl_qpolynomial_substitute(isl_qpolynomial_copy(poly),
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isl_dim_in, nvar - 1, 1, &sub);
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diff = isl_qpolynomial_sub(diff, isl_qpolynomial_copy(poly));
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s = has_sign(bset, diff, 1, data->signs);
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if (s < 0)
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goto error;
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if (s)
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result = 1;
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else {
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s = has_sign(bset, diff, -1, data->signs);
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if (s < 0)
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goto error;
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if (s)
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result = -1;
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}
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isl_qpolynomial_free(diff);
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isl_qpolynomial_free(sub);
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return result;
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error:
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isl_qpolynomial_free(diff);
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isl_qpolynomial_free(sub);
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return -2;
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}
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/* Return a positive ("sign" > 0) or negative ("sign" < 0) infinite polynomial
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* with domain space "space".
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*/
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static __isl_give isl_qpolynomial *signed_infty(__isl_take isl_space *space,
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int sign)
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{
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if (sign > 0)
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return isl_qpolynomial_infty_on_domain(space);
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else
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return isl_qpolynomial_neginfty_on_domain(space);
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}
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static __isl_give isl_qpolynomial *bound2poly(__isl_take isl_constraint *bound,
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__isl_take isl_space *space, unsigned pos, int sign)
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{
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if (!bound)
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return signed_infty(space, sign);
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isl_space_free(space);
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return isl_qpolynomial_from_constraint(bound, isl_dim_set, pos);
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}
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static int bound_is_integer(__isl_keep isl_constraint *bound, unsigned pos)
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{
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isl_int c;
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int is_int;
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if (!bound)
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return 1;
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isl_int_init(c);
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isl_constraint_get_coefficient(bound, isl_dim_set, pos, &c);
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is_int = isl_int_is_one(c) || isl_int_is_negone(c);
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isl_int_clear(c);
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return is_int;
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}
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struct isl_fixed_sign_data {
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int *signs;
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int sign;
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isl_qpolynomial *poly;
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};
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/* Add term "term" to data->poly if it has sign data->sign.
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* The sign is determined based on the signs of the parameters
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* and variables in data->signs. The integer divisions, if
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* any, are assumed to be non-negative.
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*/
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static isl_stat collect_fixed_sign_terms(__isl_take isl_term *term, void *user)
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{
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struct isl_fixed_sign_data *data = (struct isl_fixed_sign_data *)user;
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isl_int n;
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int i;
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int sign;
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isl_size nparam;
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isl_size nvar;
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isl_size exp;
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nparam = isl_term_dim(term, isl_dim_param);
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nvar = isl_term_dim(term, isl_dim_set);
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if (nparam < 0 || nvar < 0)
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return isl_stat_error;
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isl_int_init(n);
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isl_term_get_num(term, &n);
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sign = isl_int_sgn(n);
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isl_int_clear(n);
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for (i = 0; i < nparam; ++i) {
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if (data->signs[i] > 0)
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continue;
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exp = isl_term_get_exp(term, isl_dim_param, i);
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if (exp < 0)
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return isl_stat_error;
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if (exp % 2)
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sign = -sign;
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}
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for (i = 0; i < nvar; ++i) {
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if (data->signs[nparam + i] > 0)
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continue;
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exp = isl_term_get_exp(term, isl_dim_set, i);
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if (exp < 0)
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return isl_stat_error;
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if (exp % 2)
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sign = -sign;
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}
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if (sign == data->sign) {
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isl_qpolynomial *t = isl_qpolynomial_from_term(term);
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data->poly = isl_qpolynomial_add(data->poly, t);
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} else
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isl_term_free(term);
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return isl_stat_ok;
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}
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/* Construct and return a polynomial that consists of the terms
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* in "poly" that have sign "sign". The integer divisions, if
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* any, are assumed to be non-negative.
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*/
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__isl_give isl_qpolynomial *isl_qpolynomial_terms_of_sign(
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__isl_keep isl_qpolynomial *poly, int *signs, int sign)
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{
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isl_space *space;
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struct isl_fixed_sign_data data = { signs, sign };
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space = isl_qpolynomial_get_domain_space(poly);
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data.poly = isl_qpolynomial_zero_on_domain(space);
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if (isl_qpolynomial_foreach_term(poly, collect_fixed_sign_terms, &data) < 0)
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goto error;
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return data.poly;
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error:
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isl_qpolynomial_free(data.poly);
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return NULL;
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}
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/* Helper function to add a guarded polynomial to either pwf_tight or pwf,
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* depending on whether the result has been determined to be tight.
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*/
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static isl_stat add_guarded_poly(__isl_take isl_basic_set *bset,
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__isl_take isl_qpolynomial *poly, struct range_data *data)
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{
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enum isl_fold type = data->sign < 0 ? isl_fold_min : isl_fold_max;
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isl_set *set;
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isl_qpolynomial_fold *fold;
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isl_pw_qpolynomial_fold *pwf;
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bset = isl_basic_set_params(bset);
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poly = isl_qpolynomial_project_domain_on_params(poly);
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fold = isl_qpolynomial_fold_alloc(type, poly);
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set = isl_set_from_basic_set(bset);
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pwf = isl_pw_qpolynomial_fold_alloc(type, set, fold);
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if (data->tight)
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data->pwf_tight = isl_pw_qpolynomial_fold_fold(
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data->pwf_tight, pwf);
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else
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data->pwf = isl_pw_qpolynomial_fold_fold(data->pwf, pwf);
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return isl_stat_ok;
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}
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/* Plug in "sub" for the variable at position "pos" in "poly".
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*
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* If "sub" is an infinite polynomial and if the variable actually
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* appears in "poly", then calling isl_qpolynomial_substitute
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* to perform the substitution may result in a NaN result.
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* In such cases, return positive or negative infinity instead,
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* depending on whether an upper bound or a lower bound is being computed,
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* and mark the result as not being tight.
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*/
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static __isl_give isl_qpolynomial *plug_in_at_pos(
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__isl_take isl_qpolynomial *poly, int pos,
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__isl_take isl_qpolynomial *sub, struct range_data *data)
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{
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isl_bool involves, infty;
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involves = isl_qpolynomial_involves_dims(poly, isl_dim_in, pos, 1);
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if (involves < 0)
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goto error;
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if (!involves) {
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isl_qpolynomial_free(sub);
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return poly;
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}
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infty = isl_qpolynomial_is_infty(sub);
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if (infty >= 0 && !infty)
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infty = isl_qpolynomial_is_neginfty(sub);
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if (infty < 0)
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goto error;
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if (infty) {
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isl_space *space = isl_qpolynomial_get_domain_space(poly);
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data->tight = 0;
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isl_qpolynomial_free(poly);
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isl_qpolynomial_free(sub);
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return signed_infty(space, data->sign);
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}
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poly = isl_qpolynomial_substitute(poly, isl_dim_in, pos, 1, &sub);
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isl_qpolynomial_free(sub);
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return poly;
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error:
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isl_qpolynomial_free(poly);
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isl_qpolynomial_free(sub);
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return NULL;
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}
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/* Given a lower and upper bound on the final variable and constraints
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* on the remaining variables where these bounds are active,
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* eliminate the variable from data->poly based on these bounds.
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* If the polynomial has been determined to be monotonic
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* in the variable, then simply plug in the appropriate bound.
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* If the current polynomial is tight and if this bound is integer,
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* then the result is still tight. In all other cases, the results
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* may not be tight.
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* Otherwise, plug in the largest bound (in absolute value) in
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* the positive terms (if an upper bound is wanted) or the negative terms
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* (if a lower bounded is wanted) and the other bound in the other terms.
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*
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* If all variables have been eliminated, then record the result.
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* Ohterwise, recurse on the next variable.
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*/
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static isl_stat propagate_on_bound_pair(__isl_take isl_constraint *lower,
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__isl_take isl_constraint *upper, __isl_take isl_basic_set *bset,
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void *user)
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{
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struct range_data *data = (struct range_data *)user;
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int save_tight = data->tight;
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isl_qpolynomial *poly;
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isl_stat r;
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isl_size nvar, nparam;
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nvar = isl_basic_set_dim(bset, isl_dim_set);
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nparam = isl_basic_set_dim(bset, isl_dim_param);
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if (nvar < 0 || nparam < 0)
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goto error;
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if (data->monotonicity) {
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isl_qpolynomial *sub;
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isl_space *space = isl_qpolynomial_get_domain_space(data->poly);
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if (data->monotonicity * data->sign > 0) {
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if (data->tight)
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data->tight = bound_is_integer(upper, nvar);
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sub = bound2poly(upper, space, nvar, 1);
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isl_constraint_free(lower);
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} else {
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if (data->tight)
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data->tight = bound_is_integer(lower, nvar);
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sub = bound2poly(lower, space, nvar, -1);
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isl_constraint_free(upper);
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}
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poly = isl_qpolynomial_copy(data->poly);
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poly = plug_in_at_pos(poly, nvar, sub, data);
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poly = isl_qpolynomial_drop_dims(poly, isl_dim_in, nvar, 1);
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} else {
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isl_qpolynomial *l, *u;
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isl_qpolynomial *pos, *neg;
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isl_space *space = isl_qpolynomial_get_domain_space(data->poly);
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int sign = data->sign * data->signs[nparam + nvar];
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data->tight = 0;
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u = bound2poly(upper, isl_space_copy(space), nvar, 1);
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l = bound2poly(lower, space, nvar, -1);
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pos = isl_qpolynomial_terms_of_sign(data->poly, data->signs, sign);
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neg = isl_qpolynomial_terms_of_sign(data->poly, data->signs, -sign);
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pos = plug_in_at_pos(pos, nvar, u, data);
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neg = plug_in_at_pos(neg, nvar, l, data);
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poly = isl_qpolynomial_add(pos, neg);
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poly = isl_qpolynomial_drop_dims(poly, isl_dim_in, nvar, 1);
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}
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if (nvar == 0)
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r = add_guarded_poly(bset, poly, data);
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else
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r = propagate_on_domain(bset, poly, data);
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data->tight = save_tight;
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return r;
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error:
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isl_constraint_free(lower);
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isl_constraint_free(upper);
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isl_basic_set_free(bset);
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return isl_stat_error;
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}
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/* Recursively perform range propagation on the polynomial "poly"
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* defined over the basic set "bset" and collect the results in "data".
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*/
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static isl_stat propagate_on_domain(__isl_take isl_basic_set *bset,
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__isl_take isl_qpolynomial *poly, struct range_data *data)
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{
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isl_bool is_cst;
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isl_ctx *ctx;
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isl_qpolynomial *save_poly = data->poly;
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int save_monotonicity = data->monotonicity;
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isl_size d;
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d = isl_basic_set_dim(bset, isl_dim_set);
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is_cst = isl_qpolynomial_is_cst(poly, NULL, NULL);
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if (d < 0 || is_cst < 0)
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goto error;
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ctx = isl_basic_set_get_ctx(bset);
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isl_assert(ctx, d >= 1, goto error);
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if (is_cst) {
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bset = isl_basic_set_project_out(bset, isl_dim_set, 0, d);
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poly = isl_qpolynomial_drop_dims(poly, isl_dim_in, 0, d);
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return add_guarded_poly(bset, poly, data);
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}
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if (data->test_monotonicity)
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data->monotonicity = monotonicity(bset, poly, data);
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else
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data->monotonicity = 0;
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if (data->monotonicity < -1)
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goto error;
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data->poly = poly;
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if (isl_basic_set_foreach_bound_pair(bset, isl_dim_set, d - 1,
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&propagate_on_bound_pair, data) < 0)
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goto error;
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isl_basic_set_free(bset);
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isl_qpolynomial_free(poly);
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data->monotonicity = save_monotonicity;
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data->poly = save_poly;
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return isl_stat_ok;
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error:
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isl_basic_set_free(bset);
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isl_qpolynomial_free(poly);
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data->monotonicity = save_monotonicity;
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data->poly = save_poly;
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return isl_stat_error;
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}
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static isl_stat basic_guarded_poly_bound(__isl_take isl_basic_set *bset,
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void *user)
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{
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struct range_data *data = (struct range_data *)user;
|
|
isl_ctx *ctx;
|
|
isl_size nparam = isl_basic_set_dim(bset, isl_dim_param);
|
|
isl_size dim = isl_basic_set_dim(bset, isl_dim_set);
|
|
isl_size total = isl_basic_set_dim(bset, isl_dim_all);
|
|
isl_stat r;
|
|
|
|
data->signs = NULL;
|
|
|
|
if (nparam < 0 || dim < 0 || total < 0)
|
|
goto error;
|
|
|
|
ctx = isl_basic_set_get_ctx(bset);
|
|
data->signs = isl_alloc_array(ctx, int, total);
|
|
|
|
if (isl_basic_set_dims_get_sign(bset, isl_dim_set, 0, dim,
|
|
data->signs + nparam) < 0)
|
|
goto error;
|
|
if (isl_basic_set_dims_get_sign(bset, isl_dim_param, 0, nparam,
|
|
data->signs) < 0)
|
|
goto error;
|
|
|
|
r = propagate_on_domain(bset, isl_qpolynomial_copy(data->poly), data);
|
|
|
|
free(data->signs);
|
|
|
|
return r;
|
|
error:
|
|
free(data->signs);
|
|
isl_basic_set_free(bset);
|
|
return isl_stat_error;
|
|
}
|
|
|
|
static isl_stat qpolynomial_bound_on_domain_range(
|
|
__isl_take isl_basic_set *bset, __isl_take isl_qpolynomial *poly,
|
|
struct range_data *data)
|
|
{
|
|
isl_size nparam = isl_basic_set_dim(bset, isl_dim_param);
|
|
isl_size nvar = isl_basic_set_dim(bset, isl_dim_set);
|
|
isl_set *set = NULL;
|
|
|
|
if (nparam < 0 || nvar < 0)
|
|
goto error;
|
|
|
|
if (nvar == 0)
|
|
return add_guarded_poly(bset, poly, data);
|
|
|
|
set = isl_set_from_basic_set(bset);
|
|
set = isl_set_split_dims(set, isl_dim_param, 0, nparam);
|
|
set = isl_set_split_dims(set, isl_dim_set, 0, nvar);
|
|
|
|
data->poly = poly;
|
|
|
|
data->test_monotonicity = 1;
|
|
if (isl_set_foreach_basic_set(set, &basic_guarded_poly_bound, data) < 0)
|
|
goto error;
|
|
|
|
isl_set_free(set);
|
|
isl_qpolynomial_free(poly);
|
|
|
|
return isl_stat_ok;
|
|
error:
|
|
isl_set_free(set);
|
|
isl_qpolynomial_free(poly);
|
|
return isl_stat_error;
|
|
}
|
|
|
|
isl_stat isl_qpolynomial_bound_on_domain_range(__isl_take isl_basic_set *bset,
|
|
__isl_take isl_qpolynomial *poly, struct isl_bound *bound)
|
|
{
|
|
struct range_data data;
|
|
isl_stat r;
|
|
|
|
data.pwf = bound->pwf;
|
|
data.pwf_tight = bound->pwf_tight;
|
|
data.tight = bound->check_tight;
|
|
if (bound->type == isl_fold_min)
|
|
data.sign = -1;
|
|
else
|
|
data.sign = 1;
|
|
|
|
r = qpolynomial_bound_on_domain_range(bset, poly, &data);
|
|
|
|
bound->pwf = data.pwf;
|
|
bound->pwf_tight = data.pwf_tight;
|
|
|
|
return r;
|
|
}
|