#include <isl_ctx_private.h>

#include <isl_constraint_private.h>

#include <isl/set.h>

#include <isl_polynomial_private.h>

#include <isl_morph.h>

#include <isl_range.h>

struct range_data {

	struct isl_bound	*bound;

	int 		    	*signs;

	int			sign;

	int			test_monotonicity;

	int		    	monotonicity;

	int			tight;

	isl_qpolynomial	    	*poly;

	isl_pw_qpolynomial_fold *pwf;

	isl_pw_qpolynomial_fold *pwf_tight;

};

static int propagate_on_domain(__isl_take isl_basic_set *bset,

	__isl_take isl_qpolynomial *poly, struct range_data *data);

/* Check whether the polynomial "poly" has sign "sign" over "bset",

 * i.e., if sign == 1, check that the lower bound on the polynomial

 * is non-negative and if sign == -1, check that the upper bound on

 * the polynomial is non-positive.

 */

static int has_sign(__isl_keep isl_basic_set *bset,

	__isl_keep isl_qpolynomial *poly, int sign, int *signs)

{

	struct range_data data_m;

	unsigned nvar;

	unsigned nparam;

	isl_space *dim;

	isl_val *opt;

	int r;

	enum isl_fold type;

	nparam = isl_basic_set_dim(bset, isl_dim_param);

	nvar = isl_basic_set_dim(bset, isl_dim_set);

	bset = isl_basic_set_copy(bset);

	poly = isl_qpolynomial_copy(poly);

	bset = isl_basic_set_move_dims(bset, isl_dim_set, 0,

					isl_dim_param, 0, nparam);

	poly = isl_qpolynomial_move_dims(poly, isl_dim_in, 0,

					isl_dim_param, 0, nparam);

	dim = isl_qpolynomial_get_space(poly);

	dim = isl_space_params(dim);

	dim = isl_space_from_domain(dim);

	dim = isl_space_add_dims(dim, isl_dim_out, 1);

	data_m.test_monotonicity = 0;

	data_m.signs = signs;

	data_m.sign = -sign;

	type = data_m.sign < 0 ? isl_fold_min : isl_fold_max;

	data_m.pwf = isl_pw_qpolynomial_fold_zero(dim, type);

	data_m.tight = 0;

	data_m.pwf_tight = NULL;

	if (propagate_on_domain(bset, poly, &data_m) < 0)

		goto error;

	if (sign > 0)

		opt = isl_pw_qpolynomial_fold_min(data_m.pwf);

	else

		opt = isl_pw_qpolynomial_fold_max(data_m.pwf);

	if (!opt)

		r = -1;

	else if (isl_val_is_nan(opt) ||

		 isl_val_is_infty(opt) ||

		 isl_val_is_neginfty(opt))

		r = 0;

	else

		r = sign * isl_val_sgn(opt) >= 0;

	isl_val_free(opt);

	return r;

error:

	isl_pw_qpolynomial_fold_free(data_m.pwf);

	return -1;

}

/* Return  1 if poly is monotonically increasing in the last set variable,

 *        -1 if poly is monotonically decreasing in the last set variable,

 *	   0 if no conclusion,

 *	  -2 on error.

 *

 * We simply check the sign of p(x+1)-p(x)

 */

static int monotonicity(__isl_keep isl_basic_set *bset,

	__isl_keep isl_qpolynomial *poly, struct range_data *data)

{

	isl_ctx *ctx;

	isl_space *dim;

	isl_qpolynomial *sub = NULL;

	isl_qpolynomial *diff = NULL;

	int result = 0;

	int s;

	unsigned nvar;

	ctx = isl_qpolynomial_get_ctx(poly);

	dim = isl_qpolynomial_get_domain_space(poly);

	nvar = isl_basic_set_dim(bset, isl_dim_set);

	sub = isl_qpolynomial_var_on_domain(isl_space_copy(dim), isl_dim_set, nvar - 1);

	sub = isl_qpolynomial_add(sub,

		isl_qpolynomial_rat_cst_on_domain(dim, ctx->one, ctx->one));

	diff = isl_qpolynomial_substitute(isl_qpolynomial_copy(poly),

			isl_dim_in, nvar - 1, 1, &sub);

	diff = isl_qpolynomial_sub(diff, isl_qpolynomial_copy(poly));

	s = has_sign(bset, diff, 1, data->signs);

	if (s < 0)

		goto error;

	if (s)

		result = 1;

	else {

		s = has_sign(bset, diff, -1, data->signs);

		if (s < 0)

			goto error;

		if (s)

			result = -1;

	}

	isl_qpolynomial_free(diff);

	isl_qpolynomial_free(sub);

	return result;

error:

	isl_qpolynomial_free(diff);

	isl_qpolynomial_free(sub);

	return -2;

}

static __isl_give isl_qpolynomial *bound2poly(__isl_take isl_constraint *bound,

	__isl_take isl_space *dim, unsigned pos, int sign)

{

	if (!bound) {

		if (sign > 0)

			return isl_qpolynomial_infty_on_domain(dim);

		else

			return isl_qpolynomial_neginfty_on_domain(dim);

	}

	isl_space_free(dim);

	return isl_qpolynomial_from_constraint(bound, isl_dim_set, pos);

}

static int bound_is_integer(__isl_take isl_constraint *bound, unsigned pos)

{

	isl_int c;

	int is_int;

	if (!bound)

		return 1;

	isl_int_init(c);

	isl_constraint_get_coefficient(bound, isl_dim_set, pos, &c);

	is_int = isl_int_is_one(c) || isl_int_is_negone(c);

	isl_int_clear(c);

	return is_int;

}

struct isl_fixed_sign_data {

	int		*signs;

	int		sign;

	isl_qpolynomial	*poly;

};

/* Add term "term" to data->poly if it has sign data->sign.

 * The sign is determined based on the signs of the parameters

 * and variables in data->signs.  The integer divisions, if

 * any, are assumed to be non-negative.

 */

static int collect_fixed_sign_terms(__isl_take isl_term *term, void *user)

{

	struct isl_fixed_sign_data *data = (struct isl_fixed_sign_data *)user;

	isl_int n;

	int i;

	int sign;

	unsigned nparam;

	unsigned nvar;

	if (!term)

		return -1;

	nparam = isl_term_dim(term, isl_dim_param);

	nvar = isl_term_dim(term, isl_dim_set);

	isl_int_init(n);

	isl_term_get_num(term, &n);

	sign = isl_int_sgn(n);

	for (i = 0; i < nparam; ++i) {

		if (data->signs[i] > 0)

			continue;

		if (isl_term_get_exp(term, isl_dim_param, i) % 2)

			sign = -sign;

	}

	for (i = 0; i < nvar; ++i) {

		if (data->signs[nparam + i] > 0)

			continue;

		if (isl_term_get_exp(term, isl_dim_set, i) % 2)

			sign = -sign;

	}

	if (sign == data->sign) {

		isl_qpolynomial *t = isl_qpolynomial_from_term(term);

		data->poly = isl_qpolynomial_add(data->poly, t);

	} else

		isl_term_free(term);

	isl_int_clear(n);

	return 0;

}

/* Construct and return a polynomial that consists of the terms

 * in "poly" that have sign "sign".  The integer divisions, if

 * any, are assumed to be non-negative.

 */

__isl_give isl_qpolynomial *isl_qpolynomial_terms_of_sign(

	__isl_keep isl_qpolynomial *poly, int *signs, int sign)

{

	isl_space *space;

	struct isl_fixed_sign_data data = { signs, sign };

	space = isl_qpolynomial_get_domain_space(poly);

	data.poly = isl_qpolynomial_zero_on_domain(space);

	if (isl_qpolynomial_foreach_term(poly, collect_fixed_sign_terms, &data) < 0)

		goto error;

	return data.poly;

error:

	isl_qpolynomial_free(data.poly);

	return NULL;

}

/* Helper function to add a guarded polynomial to either pwf_tight or pwf,

 * depending on whether the result has been determined to be tight.

 */

static int add_guarded_poly(__isl_take isl_basic_set *bset,

	__isl_take isl_qpolynomial *poly, struct range_data *data)

{

	enum isl_fold type = data->sign < 0 ? isl_fold_min : isl_fold_max;

	isl_set *set;

	isl_qpolynomial_fold *fold;

	isl_pw_qpolynomial_fold *pwf;

	bset = isl_basic_set_params(bset);

	poly = isl_qpolynomial_project_domain_on_params(poly);

	fold = isl_qpolynomial_fold_alloc(type, poly);

	set = isl_set_from_basic_set(bset);

	pwf = isl_pw_qpolynomial_fold_alloc(type, set, fold);

	if (data->tight)

		data->pwf_tight = isl_pw_qpolynomial_fold_fold(

						data->pwf_tight, pwf);

	else

		data->pwf = isl_pw_qpolynomial_fold_fold(data->pwf, pwf);

	return 0;

}

/* Given a lower and upper bound on the final variable and constraints

 * on the remaining variables where these bounds are active,

 * eliminate the variable from data->poly based on these bounds.

 * If the polynomial has been determined to be monotonic

 * in the variable, then simply plug in the appropriate bound.

 * If the current polynomial is tight and if this bound is integer,

 * then the result is still tight.  In all other cases, the results

 * may not be tight.

 * Otherwise, plug in the largest bound (in absolute value) in

 * the positive terms (if an upper bound is wanted) or the negative terms

 * (if a lower bounded is wanted) and the other bound in the other terms.

 *

 * If all variables have been eliminated, then record the result.

 * Ohterwise, recurse on the next variable.

 */

static int propagate_on_bound_pair(__isl_take isl_constraint *lower,

	__isl_take isl_constraint *upper, __isl_take isl_basic_set *bset,

	void *user)

{

	struct range_data *data = (struct range_data *)user;

	int save_tight = data->tight;

	isl_qpolynomial *poly;

	int r;

	unsigned nvar;

	nvar = isl_basic_set_dim(bset, isl_dim_set);

	if (data->monotonicity) {

		isl_qpolynomial *sub;

		isl_space *dim = isl_qpolynomial_get_domain_space(data->poly);

		if (data->monotonicity * data->sign > 0) {

			if (data->tight)

				data->tight = bound_is_integer(upper, nvar);

			sub = bound2poly(upper, dim, nvar, 1);

			isl_constraint_free(lower);

		} else {

			if (data->tight)

				data->tight = bound_is_integer(lower, nvar);

			sub = bound2poly(lower, dim, nvar, -1);

			isl_constraint_free(upper);

		}

		poly = isl_qpolynomial_copy(data->poly);

		poly = isl_qpolynomial_substitute(poly, isl_dim_in, nvar, 1, &sub);

		poly = isl_qpolynomial_drop_dims(poly, isl_dim_in, nvar, 1);

		isl_qpolynomial_free(sub);

	} else {

		isl_qpolynomial *l, *u;

		isl_qpolynomial *pos, *neg;

		isl_space *dim = isl_qpolynomial_get_domain_space(data->poly);

		unsigned nparam = isl_basic_set_dim(bset, isl_dim_param);

		int sign = data->sign * data->signs[nparam + nvar];

		data->tight = 0;

		u = bound2poly(upper, isl_space_copy(dim), nvar, 1);

		l = bound2poly(lower, dim, nvar, -1);

		pos = isl_qpolynomial_terms_of_sign(data->poly, data->signs, sign);

		neg = isl_qpolynomial_terms_of_sign(data->poly, data->signs, -sign);

		pos = isl_qpolynomial_substitute(pos, isl_dim_in, nvar, 1, &u);

		neg = isl_qpolynomial_substitute(neg, isl_dim_in, nvar, 1, &l);

		poly = isl_qpolynomial_add(pos, neg);

		poly = isl_qpolynomial_drop_dims(poly, isl_dim_in, nvar, 1);

		isl_qpolynomial_free(u);

		isl_qpolynomial_free(l);

	}

	if (isl_basic_set_dim(bset, isl_dim_set) == 0)

		r = add_guarded_poly(bset, poly, data);

	else

		r = propagate_on_domain(bset, poly, data);

	data->tight = save_tight;

	return r;

}

/* Recursively perform range propagation on the polynomial "poly"

 * defined over the basic set "bset" and collect the results in "data".

 */

static int propagate_on_domain(__isl_take isl_basic_set *bset,

	__isl_take isl_qpolynomial *poly, struct range_data *data)

{

	isl_ctx *ctx;

	isl_qpolynomial *save_poly = data->poly;

	int save_monotonicity = data->monotonicity;

	unsigned d;

	if (!bset || !poly)

		goto error;

	ctx = isl_basic_set_get_ctx(bset);

	d = isl_basic_set_dim(bset, isl_dim_set);

	isl_assert(ctx, d >= 1, goto error);

	if (isl_qpolynomial_is_cst(poly, NULL, NULL)) {

		bset = isl_basic_set_project_out(bset, isl_dim_set, 0, d);

		poly = isl_qpolynomial_drop_dims(poly, isl_dim_in, 0, d);

		return add_guarded_poly(bset, poly, data);

	}

	if (data->test_monotonicity)

		data->monotonicity = monotonicity(bset, poly, data);

	else

		data->monotonicity = 0;

	if (data->monotonicity < -1)

		goto error;

	data->poly = poly;

	if (isl_basic_set_foreach_bound_pair(bset, isl_dim_set, d - 1,

					    &propagate_on_bound_pair, data) < 0)

		goto error;

	isl_basic_set_free(bset);

	isl_qpolynomial_free(poly);

	data->monotonicity = save_monotonicity;

	data->poly = save_poly;

	return 0;

error:

	isl_basic_set_free(bset);

	isl_qpolynomial_free(poly);

	data->monotonicity = save_monotonicity;

	data->poly = save_poly;

	return -1;

}

static int basic_guarded_poly_bound(__isl_take isl_basic_set *bset, void *user)

{

	struct range_data *data = (struct range_data *)user;

	isl_ctx *ctx;

	unsigned nparam = isl_basic_set_dim(bset, isl_dim_param);

	unsigned dim = isl_basic_set_dim(bset, isl_dim_set);

	int r;

	data->signs = NULL;

	ctx = isl_basic_set_get_ctx(bset);

	data->signs = isl_alloc_array(ctx, int,

					isl_basic_set_dim(bset, isl_dim_all));

	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 -1;

}

static int qpolynomial_bound_on_domain_range(__isl_take isl_basic_set *bset,

	__isl_take isl_qpolynomial *poly, struct range_data *data)

{

	unsigned nparam = isl_basic_set_dim(bset, isl_dim_param);

	unsigned nvar = isl_basic_set_dim(bset, isl_dim_set);

	isl_set *set = NULL;

	if (!bset)

		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 0;

error:

	isl_set_free(set);

	isl_qpolynomial_free(poly);

	return -1;

}

int 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;

	int 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;

}