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isl_ast_build_expr.c
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isl_ast_build_expr.c
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/*
* Copyright 2012-2014 Ecole Normale Superieure
* Copyright 2014 INRIA Rocquencourt
*
* Use of this software is governed by the MIT license
*
* Written by Sven Verdoolaege,
* Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
* and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
* B.P. 105 - 78153 Le Chesnay, France
*/
#include <isl/constraint.h>
#include <isl/ilp.h>
#include <isl_ast_build_expr.h>
#include <isl_ast_private.h>
#include <isl_ast_build_private.h>
/* Compute the "opposite" of the (numerator of the) argument of a div
* with denonimator "d".
*
* In particular, compute
*
* -aff + (d - 1)
*/
static __isl_give isl_aff *oppose_div_arg(__isl_take isl_aff *aff,
__isl_take isl_val *d)
{
aff = isl_aff_neg(aff);
aff = isl_aff_add_constant_val(aff, d);
aff = isl_aff_add_constant_si(aff, -1);
return aff;
}
/* Internal data structure used inside isl_ast_expr_add_term.
* The domain of "build" is used to simplify the expressions.
* "build" needs to be set by the caller of isl_ast_expr_add_term.
* "cst" is the constant term of the expression in which the added term
* appears. It may be modified by isl_ast_expr_add_term.
*
* "v" is the coefficient of the term that is being constructed and
* is set internally by isl_ast_expr_add_term.
*/
struct isl_ast_add_term_data {
isl_ast_build *build;
isl_val *cst;
isl_val *v;
};
/* Given the numerator "aff" of the argument of an integer division
* with denominator "d", check if it can be made non-negative over
* data->build->domain by stealing part of the constant term of
* the expression in which the integer division appears.
*
* In particular, the outer expression is of the form
*
* v * floor(aff/d) + cst
*
* We already know that "aff" itself may attain negative values.
* Here we check if aff + d*floor(cst/v) is non-negative, such
* that we could rewrite the expression to
*
* v * floor((aff + d*floor(cst/v))/d) + cst - v*floor(cst/v)
*
* Note that aff + d*floor(cst/v) can only possibly be non-negative
* if data->cst and data->v have the same sign.
* Similarly, if floor(cst/v) is zero, then there is no point in
* checking again.
*/
static int is_non_neg_after_stealing(__isl_keep isl_aff *aff,
__isl_keep isl_val *d, struct isl_ast_add_term_data *data)
{
isl_aff *shifted;
isl_val *shift;
int is_zero;
int non_neg;
if (isl_val_sgn(data->cst) != isl_val_sgn(data->v))
return 0;
shift = isl_val_div(isl_val_copy(data->cst), isl_val_copy(data->v));
shift = isl_val_floor(shift);
is_zero = isl_val_is_zero(shift);
if (is_zero < 0 || is_zero) {
isl_val_free(shift);
return is_zero < 0 ? -1 : 0;
}
shift = isl_val_mul(shift, isl_val_copy(d));
shifted = isl_aff_copy(aff);
shifted = isl_aff_add_constant_val(shifted, shift);
non_neg = isl_ast_build_aff_is_nonneg(data->build, shifted);
isl_aff_free(shifted);
return non_neg;
}
/* Given the numerator "aff' of the argument of an integer division
* with denominator "d", steal part of the constant term of
* the expression in which the integer division appears to make it
* non-negative over data->build->domain.
*
* In particular, the outer expression is of the form
*
* v * floor(aff/d) + cst
*
* We know that "aff" itself may attain negative values,
* but that aff + d*floor(cst/v) is non-negative.
* Find the minimal positive value that we need to add to "aff"
* to make it positive and adjust data->cst accordingly.
* That is, compute the minimal value "m" of "aff" over
* data->build->domain and take
*
* s = ceil(m/d)
*
* such that
*
* aff + d * s >= 0
*
* and rewrite the expression to
*
* v * floor((aff + s*d)/d) + (cst - v*s)
*/
static __isl_give isl_aff *steal_from_cst(__isl_take isl_aff *aff,
__isl_keep isl_val *d, struct isl_ast_add_term_data *data)
{
isl_set *domain;
isl_val *shift, *t;
domain = isl_ast_build_get_domain(data->build);
shift = isl_set_min_val(domain, aff);
isl_set_free(domain);
shift = isl_val_neg(shift);
shift = isl_val_div(shift, isl_val_copy(d));
shift = isl_val_ceil(shift);
t = isl_val_copy(shift);
t = isl_val_mul(t, isl_val_copy(data->v));
data->cst = isl_val_sub(data->cst, t);
shift = isl_val_mul(shift, isl_val_copy(d));
return isl_aff_add_constant_val(aff, shift);
}
/* Create an isl_ast_expr evaluating the div at position "pos" in "ls".
* The result is simplified in terms of data->build->domain.
* This function may change (the sign of) data->v.
*
* "ls" is known to be non-NULL.
*
* Let the div be of the form floor(e/d).
* If the ast_build_prefer_pdiv option is set then we check if "e"
* is non-negative, so that we can generate
*
* (pdiv_q, expr(e), expr(d))
*
* instead of
*
* (fdiv_q, expr(e), expr(d))
*
* If the ast_build_prefer_pdiv option is set and
* if "e" is not non-negative, then we check if "-e + d - 1" is non-negative.
* If so, we can rewrite
*
* floor(e/d) = -ceil(-e/d) = -floor((-e + d - 1)/d)
*
* and still use pdiv_q, while changing the sign of data->v.
*
* Otherwise, we check if
*
* e + d*floor(cst/v)
*
* is non-negative and if so, replace floor(e/d) by
*
* floor((e + s*d)/d) - s
*
* with s the minimal shift that makes the argument non-negative.
*/
static __isl_give isl_ast_expr *var_div(struct isl_ast_add_term_data *data,
__isl_keep isl_local_space *ls, int pos)
{
isl_ctx *ctx = isl_local_space_get_ctx(ls);
isl_aff *aff;
isl_ast_expr *num, *den;
isl_val *d;
enum isl_ast_op_type type;
aff = isl_local_space_get_div(ls, pos);
d = isl_aff_get_denominator_val(aff);
aff = isl_aff_scale_val(aff, isl_val_copy(d));
den = isl_ast_expr_from_val(isl_val_copy(d));
type = isl_ast_op_fdiv_q;
if (isl_options_get_ast_build_prefer_pdiv(ctx)) {
int non_neg = isl_ast_build_aff_is_nonneg(data->build, aff);
if (non_neg >= 0 && !non_neg) {
isl_aff *opp = oppose_div_arg(isl_aff_copy(aff),
isl_val_copy(d));
non_neg = isl_ast_build_aff_is_nonneg(data->build, opp);
if (non_neg >= 0 && non_neg) {
data->v = isl_val_neg(data->v);
isl_aff_free(aff);
aff = opp;
} else
isl_aff_free(opp);
}
if (non_neg >= 0 && !non_neg) {
non_neg = is_non_neg_after_stealing(aff, d, data);
if (non_neg >= 0 && non_neg)
aff = steal_from_cst(aff, d, data);
}
if (non_neg < 0)
aff = isl_aff_free(aff);
else if (non_neg)
type = isl_ast_op_pdiv_q;
}
isl_val_free(d);
num = isl_ast_expr_from_aff(aff, data->build);
return isl_ast_expr_alloc_binary(type, num, den);
}
/* Create an isl_ast_expr evaluating the specified dimension of "ls".
* The result is simplified in terms of data->build->domain.
* This function may change (the sign of) data->v.
*
* The isl_ast_expr is constructed based on the type of the dimension.
* - divs are constructed by var_div
* - set variables are constructed from the iterator isl_ids in data->build
* - parameters are constructed from the isl_ids in "ls"
*/
static __isl_give isl_ast_expr *var(struct isl_ast_add_term_data *data,
__isl_keep isl_local_space *ls, enum isl_dim_type type, int pos)
{
isl_ctx *ctx = isl_local_space_get_ctx(ls);
isl_id *id;
if (type == isl_dim_div)
return var_div(data, ls, pos);
if (type == isl_dim_set) {
id = isl_ast_build_get_iterator_id(data->build, pos);
return isl_ast_expr_from_id(id);
}
if (!isl_local_space_has_dim_id(ls, type, pos))
isl_die(ctx, isl_error_internal, "unnamed dimension",
return NULL);
id = isl_local_space_get_dim_id(ls, type, pos);
return isl_ast_expr_from_id(id);
}
/* Does "expr" represent the zero integer?
*/
static int ast_expr_is_zero(__isl_keep isl_ast_expr *expr)
{
if (!expr)
return -1;
if (expr->type != isl_ast_expr_int)
return 0;
return isl_val_is_zero(expr->u.v);
}
/* Create an expression representing the sum of "expr1" and "expr2",
* provided neither of the two expressions is identically zero.
*/
static __isl_give isl_ast_expr *ast_expr_add(__isl_take isl_ast_expr *expr1,
__isl_take isl_ast_expr *expr2)
{
if (!expr1 || !expr2)
goto error;
if (ast_expr_is_zero(expr1)) {
isl_ast_expr_free(expr1);
return expr2;
}
if (ast_expr_is_zero(expr2)) {
isl_ast_expr_free(expr2);
return expr1;
}
return isl_ast_expr_add(expr1, expr2);
error:
isl_ast_expr_free(expr1);
isl_ast_expr_free(expr2);
return NULL;
}
/* Subtract expr2 from expr1.
*
* If expr2 is zero, we simply return expr1.
* If expr1 is zero, we return
*
* (isl_ast_op_minus, expr2)
*
* Otherwise, we return
*
* (isl_ast_op_sub, expr1, expr2)
*/
static __isl_give isl_ast_expr *ast_expr_sub(__isl_take isl_ast_expr *expr1,
__isl_take isl_ast_expr *expr2)
{
if (!expr1 || !expr2)
goto error;
if (ast_expr_is_zero(expr2)) {
isl_ast_expr_free(expr2);
return expr1;
}
if (ast_expr_is_zero(expr1)) {
isl_ast_expr_free(expr1);
return isl_ast_expr_neg(expr2);
}
return isl_ast_expr_sub(expr1, expr2);
error:
isl_ast_expr_free(expr1);
isl_ast_expr_free(expr2);
return NULL;
}
/* Return an isl_ast_expr that represents
*
* v * (aff mod d)
*
* v is assumed to be non-negative.
* The result is simplified in terms of build->domain.
*/
static __isl_give isl_ast_expr *isl_ast_expr_mod(__isl_keep isl_val *v,
__isl_keep isl_aff *aff, __isl_keep isl_val *d,
__isl_keep isl_ast_build *build)
{
isl_ast_expr *expr;
isl_ast_expr *c;
if (!aff)
return NULL;
expr = isl_ast_expr_from_aff(isl_aff_copy(aff), build);
c = isl_ast_expr_from_val(isl_val_copy(d));
expr = isl_ast_expr_alloc_binary(isl_ast_op_pdiv_r, expr, c);
if (!isl_val_is_one(v)) {
c = isl_ast_expr_from_val(isl_val_copy(v));
expr = isl_ast_expr_mul(c, expr);
}
return expr;
}
/* Create an isl_ast_expr that scales "expr" by "v".
*
* If v is 1, we simply return expr.
* If v is -1, we return
*
* (isl_ast_op_minus, expr)
*
* Otherwise, we return
*
* (isl_ast_op_mul, expr(v), expr)
*/
static __isl_give isl_ast_expr *scale(__isl_take isl_ast_expr *expr,
__isl_take isl_val *v)
{
isl_ast_expr *c;
if (!expr || !v)
goto error;
if (isl_val_is_one(v)) {
isl_val_free(v);
return expr;
}
if (isl_val_is_negone(v)) {
isl_val_free(v);
expr = isl_ast_expr_neg(expr);
} else {
c = isl_ast_expr_from_val(v);
expr = isl_ast_expr_mul(c, expr);
}
return expr;
error:
isl_val_free(v);
isl_ast_expr_free(expr);
return NULL;
}
/* Add an expression for "*v" times the specified dimension of "ls"
* to expr.
* If the dimension is an integer division, then this function
* may modify data->cst in order to make the numerator non-negative.
* The result is simplified in terms of data->build->domain.
*
* Let e be the expression for the specified dimension,
* multiplied by the absolute value of "*v".
* If "*v" is negative, we create
*
* (isl_ast_op_sub, expr, e)
*
* except when expr is trivially zero, in which case we create
*
* (isl_ast_op_minus, e)
*
* instead.
*
* If "*v" is positive, we simply create
*
* (isl_ast_op_add, expr, e)
*
*/
static __isl_give isl_ast_expr *isl_ast_expr_add_term(
__isl_take isl_ast_expr *expr,
__isl_keep isl_local_space *ls, enum isl_dim_type type, int pos,
__isl_take isl_val *v, struct isl_ast_add_term_data *data)
{
isl_ast_expr *term;
if (!expr)
return NULL;
data->v = v;
term = var(data, ls, type, pos);
v = data->v;
if (isl_val_is_neg(v) && !ast_expr_is_zero(expr)) {
v = isl_val_neg(v);
term = scale(term, v);
return ast_expr_sub(expr, term);
} else {
term = scale(term, v);
return ast_expr_add(expr, term);
}
}
/* Add an expression for "v" to expr.
*/
static __isl_give isl_ast_expr *isl_ast_expr_add_int(
__isl_take isl_ast_expr *expr, __isl_take isl_val *v)
{
isl_ast_expr *expr_int;
if (!expr || !v)
goto error;
if (isl_val_is_zero(v)) {
isl_val_free(v);
return expr;
}
if (isl_val_is_neg(v) && !ast_expr_is_zero(expr)) {
v = isl_val_neg(v);
expr_int = isl_ast_expr_from_val(v);
return ast_expr_sub(expr, expr_int);
} else {
expr_int = isl_ast_expr_from_val(v);
return ast_expr_add(expr, expr_int);
}
error:
isl_ast_expr_free(expr);
isl_val_free(v);
return NULL;
}
/* Internal data structure used inside extract_modulos.
*
* If any modulo expressions are detected in "aff", then the
* expression is removed from "aff" and added to either "pos" or "neg"
* depending on the sign of the coefficient of the modulo expression
* inside "aff".
*
* "add" is an expression that needs to be added to "aff" at the end of
* the computation. It is NULL as long as no modulos have been extracted.
*
* "i" is the position in "aff" of the div under investigation
* "v" is the coefficient in "aff" of the div
* "div" is the argument of the div, with the denominator removed
* "d" is the original denominator of the argument of the div
*
* "nonneg" is an affine expression that is non-negative over "build"
* and that can be used to extract a modulo expression from "div".
* In particular, if "sign" is 1, then the coefficients of "nonneg"
* are equal to those of "div" modulo "d". If "sign" is -1, then
* the coefficients of "nonneg" are opposite to those of "div" modulo "d".
* If "sign" is 0, then no such affine expression has been found (yet).
*/
struct isl_extract_mod_data {
isl_ast_build *build;
isl_aff *aff;
isl_ast_expr *pos;
isl_ast_expr *neg;
isl_aff *add;
int i;
isl_val *v;
isl_val *d;
isl_aff *div;
isl_aff *nonneg;
int sign;
};
/* Given that data->v * div_i in data->aff is equal to
*
* f * (term - (arg mod d))
*
* with data->d * f = data->v, add
*
* f * term
*
* to data->add and
*
* abs(f) * (arg mod d)
*
* to data->neg or data->pos depending on the sign of -f.
*/
static int extract_term_and_mod(struct isl_extract_mod_data *data,
__isl_take isl_aff *term, __isl_take isl_aff *arg)
{
isl_ast_expr *expr;
int s;
data->v = isl_val_div(data->v, isl_val_copy(data->d));
s = isl_val_sgn(data->v);
data->v = isl_val_abs(data->v);
expr = isl_ast_expr_mod(data->v, arg, data->d, data->build);
isl_aff_free(arg);
if (s > 0)
data->neg = ast_expr_add(data->neg, expr);
else
data->pos = ast_expr_add(data->pos, expr);
data->aff = isl_aff_set_coefficient_si(data->aff,
isl_dim_div, data->i, 0);
if (s < 0)
data->v = isl_val_neg(data->v);
term = isl_aff_scale_val(data->div, isl_val_copy(data->v));
if (!data->add)
data->add = term;
else
data->add = isl_aff_add(data->add, term);
if (!data->add)
return -1;
return 0;
}
/* Given that data->v * div_i in data->aff is of the form
*
* f * d * floor(div/d)
*
* with div nonnegative on data->build, rewrite it as
*
* f * (div - (div mod d)) = f * div - f * (div mod d)
*
* and add
*
* f * div
*
* to data->add and
*
* abs(f) * (div mod d)
*
* to data->neg or data->pos depending on the sign of -f.
*/
static int extract_mod(struct isl_extract_mod_data *data)
{
return extract_term_and_mod(data, isl_aff_copy(data->div),
isl_aff_copy(data->div));
}
/* Given that data->v * div_i in data->aff is of the form
*
* f * d * floor(div/d) (1)
*
* check if div is non-negative on data->build and, if so,
* extract the corresponding modulo from data->aff.
* If not, then check if
*
* -div + d - 1
*
* is non-negative on data->build. If so, replace (1) by
*
* -f * d * floor((-div + d - 1)/d)
*
* and extract the corresponding modulo from data->aff.
*
* This function may modify data->div.
*/
static int extract_nonneg_mod(struct isl_extract_mod_data *data)
{
int mod;
mod = isl_ast_build_aff_is_nonneg(data->build, data->div);
if (mod < 0)
goto error;
if (mod)
return extract_mod(data);
data->div = oppose_div_arg(data->div, isl_val_copy(data->d));
mod = isl_ast_build_aff_is_nonneg(data->build, data->div);
if (mod < 0)
goto error;
if (mod) {
data->v = isl_val_neg(data->v);
return extract_mod(data);
}
return 0;
error:
data->aff = isl_aff_free(data->aff);
return -1;
}
/* Is the affine expression of constraint "c" "simpler" than data->nonneg
* for use in extracting a modulo expression?
*
* We currently only consider the constant term of the affine expression.
* In particular, we prefer the affine expression with the smallest constant
* term.
* This means that if there are two constraints, say x >= 0 and -x + 10 >= 0,
* then we would pick x >= 0
*
* More detailed heuristics could be used if it turns out that there is a need.
*/
static int mod_constraint_is_simpler(struct isl_extract_mod_data *data,
__isl_keep isl_constraint *c)
{
isl_val *v1, *v2;
int simpler;
if (!data->nonneg)
return 1;
v1 = isl_val_abs(isl_constraint_get_constant_val(c));
v2 = isl_val_abs(isl_aff_get_constant_val(data->nonneg));
simpler = isl_val_lt(v1, v2);
isl_val_free(v1);
isl_val_free(v2);
return simpler;
}
/* Check if the coefficients of "c" are either equal or opposite to those
* of data->div modulo data->d. If so, and if "c" is "simpler" than
* data->nonneg, then replace data->nonneg by the affine expression of "c"
* and set data->sign accordingly.
*
* Both "c" and data->div are assumed not to involve any integer divisions.
*
* Before we start the actual comparison, we first quickly check if
* "c" and data->div have the same non-zero coefficients.
* If not, then we assume that "c" is not of the desired form.
* Note that while the coefficients of data->div can be reasonably expected
* not to involve any coefficients that are multiples of d, "c" may
* very well involve such coefficients. This means that we may actually
* miss some cases.
*
* If the constant term is "too large", then the constraint is rejected,
* where "too large" is fairly arbitrarily set to 1 << 15.
* We do this to avoid picking up constraints that bound a variable
* by a very large number, say the largest or smallest possible
* variable in the representation of some integer type.
*/
static isl_stat check_parallel_or_opposite(__isl_take isl_constraint *c,
void *user)
{
struct isl_extract_mod_data *data = user;
enum isl_dim_type c_type[2] = { isl_dim_param, isl_dim_set };
enum isl_dim_type a_type[2] = { isl_dim_param, isl_dim_in };
int i, t;
int n[2];
int parallel = 1, opposite = 1;
for (t = 0; t < 2; ++t) {
n[t] = isl_constraint_dim(c, c_type[t]);
for (i = 0; i < n[t]; ++i) {
int a, b;
a = isl_constraint_involves_dims(c, c_type[t], i, 1);
b = isl_aff_involves_dims(data->div, a_type[t], i, 1);
if (a != b)
parallel = opposite = 0;
}
}
if (parallel || opposite) {
isl_val *v;
v = isl_val_abs(isl_constraint_get_constant_val(c));
if (isl_val_cmp_si(v, 1 << 15) > 0)
parallel = opposite = 0;
isl_val_free(v);
}
for (t = 0; t < 2; ++t) {
for (i = 0; i < n[t]; ++i) {
isl_val *v1, *v2;
if (!parallel && !opposite)
break;
v1 = isl_constraint_get_coefficient_val(c,
c_type[t], i);
v2 = isl_aff_get_coefficient_val(data->div,
a_type[t], i);
if (parallel) {
v1 = isl_val_sub(v1, isl_val_copy(v2));
parallel = isl_val_is_divisible_by(v1, data->d);
v1 = isl_val_add(v1, isl_val_copy(v2));
}
if (opposite) {
v1 = isl_val_add(v1, isl_val_copy(v2));
opposite = isl_val_is_divisible_by(v1, data->d);
}
isl_val_free(v1);
isl_val_free(v2);
}
}
if ((parallel || opposite) && mod_constraint_is_simpler(data, c)) {
isl_aff_free(data->nonneg);
data->nonneg = isl_constraint_get_aff(c);
data->sign = parallel ? 1 : -1;
}
isl_constraint_free(c);
if (data->sign != 0 && data->nonneg == NULL)
return isl_stat_error;
return isl_stat_ok;
}
/* Given that data->v * div_i in data->aff is of the form
*
* f * d * floor(div/d) (1)
*
* see if we can find an expression div' that is non-negative over data->build
* and that is related to div through
*
* div' = div + d * e
*
* or
*
* div' = -div + d - 1 + d * e
*
* with e some affine expression.
* If so, we write (1) as
*
* f * div + f * (div' mod d)
*
* or
*
* -f * (-div + d - 1) - f * (div' mod d)
*
* exploiting (in the second case) the fact that
*
* f * d * floor(div/d) = -f * d * floor((-div + d - 1)/d)
*
*
* We first try to find an appropriate expression for div'
* from the constraints of data->build->domain (which is therefore
* guaranteed to be non-negative on data->build), where we remove
* any integer divisions from the constraints and skip this step
* if "div" itself involves any integer divisions.
* If we cannot find an appropriate expression this way, then
* we pass control to extract_nonneg_mod where check
* if div or "-div + d -1" themselves happen to be
* non-negative on data->build.
*
* While looking for an appropriate constraint in data->build->domain,
* we ignore the constant term, so after finding such a constraint,
* we still need to fix up the constant term.
* In particular, if a is the constant term of "div"
* (or d - 1 - the constant term of "div" if data->sign < 0)
* and b is the constant term of the constraint, then we need to find
* a non-negative constant c such that
*
* b + c \equiv a mod d
*
* We therefore take
*
* c = (a - b) mod d
*
* and add it to b to obtain the constant term of div'.
* If this constant term is "too negative", then we add an appropriate
* multiple of d to make it positive.
*
*
* Note that the above is a only a very simple heuristic for finding an
* appropriate expression. We could try a bit harder by also considering
* sums of constraints that involve disjoint sets of variables or
* we could consider arbitrary linear combinations of constraints,
* although that could potentially be much more expensive as it involves
* the solution of an LP problem.
*
* In particular, if v_i is a column vector representing constraint i,
* w represents div and e_i is the i-th unit vector, then we are looking
* for a solution of the constraints
*
* \sum_i lambda_i v_i = w + \sum_i alpha_i d e_i
*
* with \lambda_i >= 0 and alpha_i of unrestricted sign.
* If we are not just interested in a non-negative expression, but
* also in one with a minimal range, then we don't just want
* c = \sum_i lambda_i v_i to be non-negative over the domain,
* but also beta - c = \sum_i mu_i v_i, where beta is a scalar
* that we want to minimize and we now also have to take into account
* the constant terms of the constraints.
* Alternatively, we could first compute the dual of the domain
* and plug in the constraints on the coefficients.
*/
static int try_extract_mod(struct isl_extract_mod_data *data)
{
isl_basic_set *hull;
isl_val *v1, *v2;
int r, n;
if (!data->build)
goto error;
n = isl_aff_dim(data->div, isl_dim_div);
if (isl_aff_involves_dims(data->div, isl_dim_div, 0, n))
return extract_nonneg_mod(data);
hull = isl_set_simple_hull(isl_set_copy(data->build->domain));
hull = isl_basic_set_remove_divs(hull);
data->sign = 0;
data->nonneg = NULL;
r = isl_basic_set_foreach_constraint(hull, &check_parallel_or_opposite,
data);
isl_basic_set_free(hull);
if (!data->sign || r < 0) {
isl_aff_free(data->nonneg);
if (r < 0)
goto error;
return extract_nonneg_mod(data);
}
v1 = isl_aff_get_constant_val(data->div);
v2 = isl_aff_get_constant_val(data->nonneg);
if (data->sign < 0) {
v1 = isl_val_neg(v1);
v1 = isl_val_add(v1, isl_val_copy(data->d));
v1 = isl_val_sub_ui(v1, 1);
}
v1 = isl_val_sub(v1, isl_val_copy(v2));
v1 = isl_val_mod(v1, isl_val_copy(data->d));
v1 = isl_val_add(v1, v2);
v2 = isl_val_div(isl_val_copy(v1), isl_val_copy(data->d));
v2 = isl_val_ceil(v2);
if (isl_val_is_neg(v2)) {
v2 = isl_val_mul(v2, isl_val_copy(data->d));
v1 = isl_val_sub(v1, isl_val_copy(v2));
}
data->nonneg = isl_aff_set_constant_val(data->nonneg, v1);
isl_val_free(v2);
if (data->sign < 0) {
data->div = oppose_div_arg(data->div, isl_val_copy(data->d));
data->v = isl_val_neg(data->v);
}
return extract_term_and_mod(data,
isl_aff_copy(data->div), data->nonneg);
error:
data->aff = isl_aff_free(data->aff);
return -1;
}
/* Check if "data->aff" involves any (implicit) modulo computations based
* on div "data->i".
* If so, remove them from aff and add expressions corresponding
* to those modulo computations to data->pos and/or data->neg.
*
* "aff" is assumed to be an integer affine expression.
*
* In particular, check if (v * div_j) is of the form
*
* f * m * floor(a / m)
*
* and, if so, rewrite it as
*
* f * (a - (a mod m)) = f * a - f * (a mod m)
*
* and extract out -f * (a mod m).
* In particular, if f > 0, we add (f * (a mod m)) to *neg.
* If f < 0, we add ((-f) * (a mod m)) to *pos.
*
* Note that in order to represent "a mod m" as
*
* (isl_ast_op_pdiv_r, a, m)
*
* we need to make sure that a is non-negative.
* If not, we check if "-a + m - 1" is non-negative.
* If so, we can rewrite
*
* floor(a/m) = -ceil(-a/m) = -floor((-a + m - 1)/m)
*
* and still extract a modulo.
*/
static int extract_modulo(struct isl_extract_mod_data *data)
{
data->div = isl_aff_get_div(data->aff, data->i);
data->d = isl_aff_get_denominator_val(data->div);
if (isl_val_is_divisible_by(data->v, data->d)) {
data->div = isl_aff_scale_val(data->div, isl_val_copy(data->d));
if (try_extract_mod(data) < 0)
data->aff = isl_aff_free(data->aff);
}
isl_aff_free(data->div);
isl_val_free(data->d);
return 0;
}
/* Check if "aff" involves any (implicit) modulo computations.
* If so, remove them from aff and add expressions corresponding
* to those modulo computations to *pos and/or *neg.
* We only do this if the option ast_build_prefer_pdiv is set.
*
* "aff" is assumed to be an integer affine expression.
*
* A modulo expression is of the form
*
* a mod m = a - m * floor(a / m)
*
* To detect them in aff, we look for terms of the form
*
* f * m * floor(a / m)
*
* rewrite them as
*
* f * (a - (a mod m)) = f * a - f * (a mod m)
*
* and extract out -f * (a mod m).
* In particular, if f > 0, we add (f * (a mod m)) to *neg.
* If f < 0, we add ((-f) * (a mod m)) to *pos.
*/
static __isl_give isl_aff *extract_modulos(__isl_take isl_aff *aff,
__isl_keep isl_ast_expr **pos, __isl_keep isl_ast_expr **neg,
__isl_keep isl_ast_build *build)
{
struct isl_extract_mod_data data = { build, aff, *pos, *neg };
isl_ctx *ctx;
int n;
if (!aff)
return NULL;
ctx = isl_aff_get_ctx(aff);
if (!isl_options_get_ast_build_prefer_pdiv(ctx))
return aff;
n = isl_aff_dim(data.aff, isl_dim_div);
for (data.i = 0; data.i < n; ++data.i) {
data.v = isl_aff_get_coefficient_val(data.aff,
isl_dim_div, data.i);
if (!data.v)
return isl_aff_free(aff);
if (isl_val_is_zero(data.v) ||
isl_val_is_one(data.v) || isl_val_is_negone(data.v)) {
isl_val_free(data.v);
continue;
}
if (extract_modulo(&data) < 0)
data.aff = isl_aff_free(data.aff);
isl_val_free(data.v);
if (!data.aff)
break;
}
if (data.add)
data.aff = isl_aff_add(data.aff, data.add);
*pos = data.pos;
*neg = data.neg;
return data.aff;
}
/* Check if aff involves any non-integer coefficients.
* If so, split aff into
*
* aff = aff1 + (aff2 / d)
*
* with both aff1 and aff2 having only integer coefficients.
* Return aff1 and add (aff2 / d) to *expr.
*/
static __isl_give isl_aff *extract_rational(__isl_take isl_aff *aff,
__isl_keep isl_ast_expr **expr, __isl_keep isl_ast_build *build)
{
int i, j, n;
isl_aff *rat = NULL;