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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/id.h>
#include <isl/space.h>
#include <isl/constraint.h>
#include <isl/ilp.h>
#include <isl/val.h>
#include <isl_ast_build_expr.h>
#include <isl_ast_private.h>
#include <isl_ast_build_private.h>
#include <isl_sort.h>
/* Compute the "opposite" of the (numerator of the) argument of a div
* with denominator "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_expr_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_expr_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_expr_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_expr_op_minus, expr2)
*
* Otherwise, we return
*
* (isl_ast_expr_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_expr_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_expr_op_minus, expr)
*
* Otherwise, we return
*
* (isl_ast_expr_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_expr_op_sub, expr, e)
*
* except when expr is trivially zero, in which case we create
*
* (isl_ast_expr_op_minus, e)
*
* instead.
*
* If "*v" is positive, we simply create
*
* (isl_ast_expr_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;
};
/* Does
*
* arg mod data->d
*
* represent (a special case of) a test for some linear expression
* being even?
*
* In particular, is it of the form
*
* (lin - 1) mod 2
*
* ?
*/
static isl_bool is_even_test(struct isl_extract_mod_data *data,
__isl_keep isl_aff *arg)
{
isl_bool res;
isl_val *cst;
res = isl_val_eq_si(data->d, 2);
if (res < 0 || !res)
return res;
cst = isl_aff_get_constant_val(arg);
res = isl_val_eq_si(cst, -1);
isl_val_free(cst);
return res;
}
/* Given that data->v * div_i in data->aff is equal to
*
* f * (term - (arg mod d))
*
* with data->d * f = data->v and "arg" non-negative on data->build, add
*
* f * term
*
* to data->add and
*
* abs(f) * (arg mod d)
*
* to data->neg or data->pos depending on the sign of -f.
*
* In the special case that "arg mod d" is of the form "(lin - 1) mod 2",
* with "lin" some linear expression, first replace
*
* f * (term - ((lin - 1) mod 2))
*
* by
*
* -f * (1 - term - (lin mod 2))
*
* These two are equal because
*
* ((lin - 1) mod 2) + (lin mod 2) = 1
*
* Also, if "lin - 1" is non-negative, then "lin" is non-negative too.
*/
static int extract_term_and_mod(struct isl_extract_mod_data *data,
__isl_take isl_aff *term, __isl_take isl_aff *arg)
{
isl_bool even;
isl_ast_expr *expr;
int s;
even = is_even_test(data, arg);
if (even < 0) {
arg = isl_aff_free(arg);
} else if (even) {
term = oppose_div_arg(term, isl_val_copy(data->d));
data->v = isl_val_neg(data->v);
arg = isl_aff_set_constant_si(arg, 0);
}
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(term, 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;
isl_size n[2];
int parallel = 1, opposite = 1;
for (t = 0; t < 2; ++t) {
n[t] = isl_constraint_dim(c, c_type[t]);
if (n[t] < 0)
return isl_stat_error;
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;
isl_stat r;
isl_size n;
if (!data->build)
goto error;
n = isl_aff_dim(data->div, isl_dim_div);
if (n < 0)
goto error;
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_expr_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;
isl_size 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);
if (n < 0)
return isl_aff_free(aff);
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;
isl_size n;
isl_aff *rat = NULL;
isl_local_space *ls = NULL;
isl_ast_expr *rat_expr;
isl_val *v, *d;
enum isl_dim_type t[] = { isl_dim_param, isl_dim_in, isl_dim_div };
enum isl_dim_type l[] = { isl_dim_param, isl_dim_set, isl_dim_div };
if (!aff)
return NULL;
d = isl_aff_get_denominator_val(aff);
if (!d)
goto error;
if (isl_val_is_one(d)) {
isl_val_free(d);
return aff;
}
aff = isl_aff_scale_val(aff, isl_val_copy(d));
ls = isl_aff_get_domain_local_space(aff);
rat = isl_aff_zero_on_domain(isl_local_space_copy(ls));
for (i = 0; i < 3; ++i) {
n = isl_aff_dim(aff, t[i]);
if (n < 0)
goto error;
for (j = 0; j < n; ++j) {
isl_aff *rat_j;
v = isl_aff_get_coefficient_val(aff, t[i], j);
if (!v)
goto error;
if (isl_val_is_divisible_by(v, d)) {
isl_val_free(v);
continue;
}
rat_j = isl_aff_var_on_domain(isl_local_space_copy(ls),
l[i], j);
rat_j = isl_aff_scale_val(rat_j, v);
rat = isl_aff_add(rat, rat_j);
}
}
v = isl_aff_get_constant_val(aff);
if (isl_val_is_divisible_by(v, d)) {
isl_val_free(v);
} else {
isl_aff *rat_0;
rat_0 = isl_aff_val_on_domain(isl_local_space_copy(ls), v);
rat = isl_aff_add(rat, rat_0);
}
isl_local_space_free(ls);
aff = isl_aff_sub(aff, isl_aff_copy(rat));
aff = isl_aff_scale_down_val(aff, isl_val_copy(d));
rat_expr = isl_ast_expr_from_aff(rat, build);
rat_expr = isl_ast_expr_div(rat_expr, isl_ast_expr_from_val(d));
*expr = ast_expr_add(*expr, rat_expr);
return aff;
error:
isl_aff_free(rat);
isl_local_space_free(ls);
isl_aff_free(aff);
isl_val_free(d);
return NULL;
}
/* Construct an isl_ast_expr that evaluates the affine expression "aff",
* The result is simplified in terms of build->domain.
*
* We first extract hidden modulo computations from the affine expression
* and then add terms for each variable with a non-zero coefficient.
* Finally, if the affine expression has a non-trivial denominator,
* we divide the resulting isl_ast_expr by this denominator.
*/
__isl_give isl_ast_expr *isl_ast_expr_from_aff(__isl_take isl_aff *aff,
__isl_keep isl_ast_build *build)
{
int i, j;
isl_size n;
isl_val *v;
isl_ctx *ctx = isl_aff_get_ctx(aff);
isl_ast_expr *expr, *expr_neg;
enum isl_dim_type t[] = { isl_dim_param, isl_dim_in, isl_dim_div };
enum isl_dim_type l[] = { isl_dim_param, isl_dim_set, isl_dim_div };
isl_local_space *ls;
struct isl_ast_add_term_data data;
if (!aff)
return NULL;
expr = isl_ast_expr_alloc_int_si(ctx, 0);
expr_neg = isl_ast_expr_alloc_int_si(ctx, 0);
aff = extract_rational(aff, &expr, build);
aff = extract_modulos(aff, &expr, &expr_neg, build);
expr = ast_expr_sub(expr, expr_neg);
ls = isl_aff_get_domain_local_space(aff);
data.build = build;
data.cst = isl_aff_get_constant_val(aff);
for (i = 0; i < 3; ++i) {
n = isl_aff_dim(aff, t[i]);
if (n < 0)
expr = isl_ast_expr_free(expr);
for (j = 0; j < n; ++j) {
v = isl_aff_get_coefficient_val(aff, t[i], j);
if (!v)
expr = isl_ast_expr_free(expr);
if (isl_val_is_zero(v)) {
isl_val_free(v);
continue;
}
expr = isl_ast_expr_add_term(expr,
ls, l[i], j, v, &data);
}
}
expr = isl_ast_expr_add_int(expr, data.cst);
isl_local_space_free(ls);
isl_aff_free(aff);
return expr;
}
/* Add terms to "expr" for each variable in "aff" with a coefficient
* with sign equal to "sign".
* The result is simplified in terms of data->build->domain.
*/
static __isl_give isl_ast_expr *add_signed_terms(__isl_take isl_ast_expr *expr,
__isl_keep isl_aff *aff, int sign, struct isl_ast_add_term_data *data)
{
int i, j;
isl_val *v;
enum isl_dim_type t[] = { isl_dim_param, isl_dim_in, isl_dim_div };
enum isl_dim_type l[] = { isl_dim_param, isl_dim_set, isl_dim_div };
isl_local_space *ls;
ls = isl_aff_get_domain_local_space(aff);
for (i = 0; i < 3; ++i) {
isl_size n = isl_aff_dim(aff, t[i]);
if (n < 0)
expr = isl_ast_expr_free(expr);
for (j = 0; j < n; ++j) {
v = isl_aff_get_coefficient_val(aff, t[i], j);
if (sign * isl_val_sgn(v) <= 0) {
isl_val_free(v);
continue;
}
v = isl_val_abs(v);
expr = isl_ast_expr_add_term(expr,
ls, l[i], j, v, data);
}
}
isl_local_space_free(ls);
return expr;
}
/* Should the constant term "v" be considered positive?
*
* A positive constant will be added to "pos" by the caller,
* while a negative constant will be added to "neg".
* If either "pos" or "neg" is exactly zero, then we prefer
* to add the constant "v" to that side, irrespective of the sign of "v".
* This results in slightly shorter expressions and may reduce the risk
* of overflows.
*/
static int constant_is_considered_positive(__isl_keep isl_val *v,
__isl_keep isl_ast_expr *pos, __isl_keep isl_ast_expr *neg)
{
if (ast_expr_is_zero(pos))
return 1;
if (ast_expr_is_zero(neg))
return 0;
return isl_val_is_pos(v);
}
/* Check if the equality
*
* aff = 0
*
* represents a stride constraint on the integer division "pos".
*
* In particular, if the integer division "pos" is equal to
*
* floor(e/d)
*
* then check if aff is equal to
*
* e - d floor(e/d)
*
* or its opposite.
*
* If so, the equality is exactly
*
* e mod d = 0
*
* Note that in principle we could also accept
*
* e - d floor(e'/d)
*
* where e and e' differ by a constant.
*/
static int is_stride_constraint(__isl_keep isl_aff *aff, int pos)
{
isl_aff *div;
isl_val *c, *d;
int eq;
div = isl_aff_get_div(aff, pos);
c = isl_aff_get_coefficient_val(aff, isl_dim_div, pos);
d = isl_aff_get_denominator_val(div);
eq = isl_val_abs_eq(c, d);
if (eq >= 0 && eq) {
aff = isl_aff_copy(aff);
aff = isl_aff_set_coefficient_si(aff, isl_dim_div, pos, 0);
div = isl_aff_scale_val(div, d);
if (isl_val_is_pos(c))
div = isl_aff_neg(div);
eq = isl_aff_plain_is_equal(div, aff);
isl_aff_free(aff);
} else
isl_val_free(d);
isl_val_free(c);
isl_aff_free(div);
return eq;
}
/* Are all coefficients of "aff" (zero or) negative?
*/
static isl_bool all_negative_coefficients(__isl_keep isl_aff *aff)
{
int i;
isl_size n;
n = isl_aff_dim(aff, isl_dim_param);
if (n < 0)
return isl_bool_error;
for (i = 0; i < n; ++i)
if (isl_aff_coefficient_sgn(aff, isl_dim_param, i) > 0)
return isl_bool_false;
n = isl_aff_dim(aff, isl_dim_in);
if (n < 0)
return isl_bool_error;
for (i = 0; i < n; ++i)
if (isl_aff_coefficient_sgn(aff, isl_dim_in, i) > 0)
return isl_bool_false;
return isl_bool_true;
}
/* Give an equality of the form
*
* aff = e - d floor(e/d) = 0
*
* or
*
* aff = -e + d floor(e/d) = 0
*
* with the integer division "pos" equal to floor(e/d),
* construct the AST expression
*
* (isl_ast_expr_op_eq,
* (isl_ast_expr_op_zdiv_r, expr(e), expr(d)), expr(0))
*
* If e only has negative coefficients, then construct
*
* (isl_ast_expr_op_eq,
* (isl_ast_expr_op_zdiv_r, expr(-e), expr(d)), expr(0))
*
* instead.
*/
static __isl_give isl_ast_expr *extract_stride_constraint(
__isl_take isl_aff *aff, int pos, __isl_keep isl_ast_build *build)
{
isl_bool all_neg;
isl_ctx *ctx;
isl_val *c;
isl_ast_expr *expr, *cst;
if (!aff)
return NULL;
ctx = isl_aff_get_ctx(aff);
c = isl_aff_get_coefficient_val(aff, isl_dim_div, pos);
aff = isl_aff_set_coefficient_si(aff, isl_dim_div, pos, 0);
all_neg = all_negative_coefficients(aff);
if (all_neg < 0)
aff = isl_aff_free(aff);
else if (all_neg)
aff = isl_aff_neg(aff);
cst = isl_ast_expr_from_val(isl_val_abs(c));
expr = isl_ast_expr_from_aff(aff, build);
expr = isl_ast_expr_alloc_binary(isl_ast_expr_op_zdiv_r, expr, cst);
cst = isl_ast_expr_alloc_int_si(ctx, 0);
expr = isl_ast_expr_alloc_binary(isl_ast_expr_op_eq, expr, cst);
return expr;
}
/* Construct an isl_ast_expr that evaluates the condition "constraint",
* The result is simplified in terms of build->domain.
*
* We first check if the constraint is an equality of the form
*
* e - d floor(e/d) = 0
*
* i.e.,
*
* e mod d = 0
*
* If so, we convert it to
*
* (isl_ast_expr_op_eq,
* (isl_ast_expr_op_zdiv_r, expr(e), expr(d)), expr(0))
*
* Otherwise, let the constraint by either "a >= 0" or "a == 0".
* We first extract hidden modulo computations from "a"
* and then collect all the terms with a positive coefficient in cons_pos
* and the terms with a negative coefficient in cons_neg.
*
* The result is then of the form
*
* (isl_ast_expr_op_ge, expr(pos), expr(-neg)))
*
* or
*
* (isl_ast_expr_op_eq, expr(pos), expr(-neg)))
*
* However, if the first expression is an integer constant (and the second
* is not), then we swap the two expressions. This ensures that we construct,
* e.g., "i <= 5" rather than "5 >= i".
*
* Furthermore, is there are no terms with positive coefficients (or no terms
* with negative coefficients), then the constant term is added to "pos"
* (or "neg"), ignoring the sign of the constant term.
*/
static __isl_give isl_ast_expr *isl_ast_expr_from_constraint(
__isl_take isl_constraint *constraint, __isl_keep isl_ast_build *build)
{
int i;
isl_size n;
isl_ctx *ctx;
isl_ast_expr *expr_pos;
isl_ast_expr *expr_neg;
isl_ast_expr *expr;
isl_aff *aff;
int eq;
enum isl_ast_expr_op_type type;
struct isl_ast_add_term_data data;
if (!constraint)
return NULL;
aff = isl_constraint_get_aff(constraint);
eq = isl_constraint_is_equality(constraint);
isl_constraint_free(constraint);
n = isl_aff_dim(aff, isl_dim_div);
if (n < 0)
aff = isl_aff_free(aff);
if (eq && n > 0)
for (i = 0; i < n; ++i) {
int is_stride;
is_stride = is_stride_constraint(aff, i);
if (is_stride < 0)
goto error;
if (is_stride)
return extract_stride_constraint(aff, i, build);
}
ctx = isl_aff_get_ctx(aff);
expr_pos = isl_ast_expr_alloc_int_si(ctx, 0);
expr_neg = isl_ast_expr_alloc_int_si(ctx, 0);
aff = extract_modulos(aff, &expr_pos, &expr_neg, build);
data.build = build;
data.cst = isl_aff_get_constant_val(aff);
expr_pos = add_signed_terms(expr_pos, aff, 1, &data);
data.cst = isl_val_neg(data.cst);
expr_neg = add_signed_terms(expr_neg, aff, -1, &data);
data.cst = isl_val_neg(data.cst);
if (constant_is_considered_positive(data.cst, expr_pos, expr_neg)) {
expr_pos = isl_ast_expr_add_int(expr_pos, data.cst);
} else {
data.cst = isl_val_neg(data.cst);
expr_neg = isl_ast_expr_add_int(expr_neg, data.cst);
}
if (isl_ast_expr_get_type(expr_pos) == isl_ast_expr_int &&
isl_ast_expr_get_type(expr_neg) != isl_ast_expr_int) {
type = eq ? isl_ast_expr_op_eq : isl_ast_expr_op_le;
expr = isl_ast_expr_alloc_binary(type, expr_neg, expr_pos);
} else {
type = eq ? isl_ast_expr_op_eq : isl_ast_expr_op_ge;
expr = isl_ast_expr_alloc_binary(type, expr_pos, expr_neg);
}
isl_aff_free(aff);
return expr;
error:
isl_aff_free(aff);
return NULL;
}
/* Wrapper around isl_constraint_cmp_last_non_zero for use
* as a callback to isl_constraint_list_sort.
* If isl_constraint_cmp_last_non_zero cannot tell the constraints
* apart, then use isl_constraint_plain_cmp instead.
*/
static int cmp_constraint(__isl_keep isl_constraint *a,
__isl_keep isl_constraint *b, void *user)
{
int cmp;
cmp = isl_constraint_cmp_last_non_zero(a, b);
if (cmp != 0)
return cmp;
return isl_constraint_plain_cmp(a, b);
}
/* Construct an isl_ast_expr that evaluates the conditions defining "bset".
* The result is simplified in terms of build->domain.
*
* If "bset" is not bounded by any constraint, then we construct
* the expression "1", i.e., "true".
*
* Otherwise, we sort the constraints, putting constraints that involve
* integer divisions after those that do not, and construct an "and"
* of the ast expressions of the individual constraints.
*
* Each constraint is added to the generated constraints of the build
* after it has been converted to an AST expression so that it can be used
* to simplify the following constraints. This may change the truth value
* of subsequent constraints that do not satisfy the earlier constraints,
* but this does not affect the outcome of the conjunction as it is
* only true if all the conjuncts are true (no matter in what order
* they are evaluated). In particular, the constraints that do not
* involve integer divisions may serve to simplify some constraints
* that do involve integer divisions.
*/
__isl_give isl_ast_expr *isl_ast_build_expr_from_basic_set(
__isl_keep isl_ast_build *build, __isl_take isl_basic_set *bset)
{
int i;
isl_size n;
isl_constraint *c;
isl_constraint_list *list;
isl_ast_expr *res;
isl_set *set;
list = isl_basic_set_get_constraint_list(bset);
isl_basic_set_free(bset);
list = isl_constraint_list_sort(list, &cmp_constraint, NULL);
n = isl_constraint_list_n_constraint(list);
if (n < 0)
build = NULL;
if (n == 0) {
isl_ctx *ctx = isl_constraint_list_get_ctx(list);
isl_constraint_list_free(list);
return isl_ast_expr_alloc_int_si(ctx, 1);
}
build = isl_ast_build_copy(build);
c = isl_constraint_list_get_constraint(list, 0);
bset = isl_basic_set_from_constraint(isl_constraint_copy(c));
set = isl_set_from_basic_set(bset);
res = isl_ast_expr_from_constraint(c, build);
build = isl_ast_build_restrict_generated(build, set);
for (i = 1; i < n; ++i) {
isl_ast_expr *expr;
c = isl_constraint_list_get_constraint(list, i);
bset = isl_basic_set_from_constraint(isl_constraint_copy(c));
set = isl_set_from_basic_set(bset);
expr = isl_ast_expr_from_constraint(c, build);
build = isl_ast_build_restrict_generated(build, set);
res = isl_ast_expr_and(res, expr);
}
isl_constraint_list_free(list);
isl_ast_build_free(build);
return res;
}
/* Construct an isl_ast_expr that evaluates the conditions defining "set".
* The result is simplified in terms of build->domain.
*
* If "set" is an (obviously) empty set, then return the expression "0".
*
* If there are multiple disjuncts in the description of the set,
* then subsequent disjuncts are simplified in a context where
* the previous disjuncts have been removed from build->domain.
* In particular, constraints that ensure that there is no overlap
* with these previous disjuncts, can be removed.
* This is mostly useful for disjuncts that are only defined by
* a single constraint (relative to the build domain) as the opposite
* of that single constraint can then be removed from the other disjuncts.
* In order not to increase the number of disjuncts in the build domain
* after subtracting the previous disjuncts of "set", the simple hull
* is computed after taking the difference with each of these disjuncts.
* This means that constraints that prevent overlap with a union
* of multiple previous disjuncts are not removed.
*
* "set" lives in the internal schedule space.
*/
__isl_give isl_ast_expr *isl_ast_build_expr_from_set_internal(
__isl_keep isl_ast_build *build, __isl_take isl_set *set)
{
int i;
isl_size n;
isl_basic_set *bset;
isl_basic_set_list *list;
isl_set *domain;
isl_ast_expr *res;
list = isl_set_get_basic_set_list(set);
isl_set_free(set);
n = isl_basic_set_list_n_basic_set(list);
if (n < 0)
build = NULL;
if (n == 0) {
isl_ctx *ctx = isl_ast_build_get_ctx(build);
isl_basic_set_list_free(list);
return isl_ast_expr_from_val(isl_val_zero(ctx));
}
domain = isl_ast_build_get_domain(build);
bset = isl_basic_set_list_get_basic_set(list, 0);
set = isl_set_from_basic_set(isl_basic_set_copy(bset));
res = isl_ast_build_expr_from_basic_set(build, bset);
for (i = 1; i < n; ++i) {
isl_ast_expr *expr;
isl_set *rest;
rest = isl_set_subtract(isl_set_copy(domain), set);
rest = isl_set_from_basic_set(isl_set_simple_hull(rest));
domain = isl_set_intersect(domain, rest);
bset = isl_basic_set_list_get_basic_set(list, i);
set = isl_set_from_basic_set(isl_basic_set_copy(bset));
bset = isl_basic_set_gist(bset,
isl_set_simple_hull(isl_set_copy(domain)));
expr = isl_ast_build_expr_from_basic_set(build, bset);
res = isl_ast_expr_or(res, expr);
}
isl_set_free(domain);
isl_set_free(set);
isl_basic_set_list_free(list);
return res;
}
/* Construct an isl_ast_expr that evaluates the conditions defining "set".
* The result is simplified in terms of build->domain.
*
* If "set" is an (obviously) empty set, then return the expression "0".
*
* "set" lives in the external schedule space.
*
* The internal AST expression generation assumes that there are
* no unknown divs, so make sure an explicit representation is available.
* Since the set comes from the outside, it may have constraints that
* are redundant with respect to the build domain. Remove them first.
*/
__isl_give isl_ast_expr *isl_ast_build_expr_from_set(
__isl_keep isl_ast_build *build, __isl_take isl_set *set)
{
isl_bool needs_map;
needs_map = isl_ast_build_need_schedule_map(build);
if (needs_map < 0) {
set = isl_set_free(set);
} else if (needs_map) {
isl_multi_aff *ma;
ma = isl_ast_build_get_schedule_map_multi_aff(build);
set = isl_set_preimage_multi_aff(set, ma);
}
set = isl_set_compute_divs(set);
set = isl_ast_build_compute_gist(build, set);
return isl_ast_build_expr_from_set_internal(build, set);
}
/* State of data about previous pieces in
* isl_ast_build_expr_from_pw_aff_internal.
*
* isl_state_none: no data about previous pieces
* isl_state_single: data about a single previous piece
* isl_state_min: data represents minimum of several pieces
* isl_state_max: data represents maximum of several pieces
*/
enum isl_from_pw_aff_state {
isl_state_none,
isl_state_single,
isl_state_min,
isl_state_max
};
/* Internal date structure representing a single piece in the input of
* isl_ast_build_expr_from_pw_aff_internal.
*
* If "state" is isl_state_none, then "set_list" and "aff_list" are not used.
* If "state" is isl_state_single, then "set_list" and "aff_list" contain the
* single previous subpiece.
* If "state" is isl_state_min, then "set_list" and "aff_list" contain
* a sequence of several previous subpieces that are equal to the minimum
* of the entries in "aff_list" over the union of "set_list"
* If "state" is isl_state_max, then "set_list" and "aff_list" contain
* a sequence of several previous subpieces that are equal to the maximum
* of the entries in "aff_list" over the union of "set_list"
*
* During the construction of the pieces, "set" is NULL.
* After the construction, "set" is set to the union of the elements
* in "set_list", at which point "set_list" is set to NULL.
*/
struct isl_from_pw_aff_piece {
enum isl_from_pw_aff_state state;
isl_set *set;
isl_set_list *set_list;
isl_aff_list *aff_list;
};
/* Internal data structure for isl_ast_build_expr_from_pw_aff_internal.
*
* "build" specifies the domain against which the result is simplified.
* "dom" is the domain of the entire isl_pw_aff.
*
* "n" is the number of pieces constructed already.
* In particular, during the construction of the pieces, "n" points to
* the piece that is being constructed. After the construction of the
* pieces, "n" is set to the total number of pieces.
* "max" is the total number of allocated entries.
* "p" contains the individual pieces.
*/
struct isl_from_pw_aff_data {
isl_ast_build *build;
isl_set *dom;
int n;
int max;
struct isl_from_pw_aff_piece *p;
};
/* Initialize "data" based on "build" and "pa".
*/
static isl_stat isl_from_pw_aff_data_init(struct isl_from_pw_aff_data *data,
__isl_keep isl_ast_build *build, __isl_keep isl_pw_aff *pa)
{
isl_size n;
isl_ctx *ctx;
ctx = isl_pw_aff_get_ctx(pa);
n = isl_pw_aff_n_piece(pa);
if (n < 0)
return isl_stat_error;
if (n == 0)
isl_die(ctx, isl_error_invalid,
"cannot handle void expression", return isl_stat_error);
data->max = n;
data->p = isl_calloc_array(ctx, struct isl_from_pw_aff_piece, n);
if (!data->p)
return isl_stat_error;
data->build = build;
data->dom = isl_pw_aff_domain(isl_pw_aff_copy(pa));
data->n = 0;
return isl_stat_ok;
}
/* Free all memory allocated for "data".
*/
static void isl_from_pw_aff_data_clear(struct isl_from_pw_aff_data *data)
{
int i;
isl_set_free(data->dom);
if (!data->p)
return;
for (i = 0; i < data->max; ++i) {
isl_set_free(data->p[i].set);
isl_set_list_free(data->p[i].set_list);
isl_aff_list_free(data->p[i].aff_list);
}
free(data->p);
}
/* Initialize the current entry of "data" to an unused piece.
*/
static void set_none(struct isl_from_pw_aff_data *data)
{
data->p[data->n].state = isl_state_none;
data->p[data->n].set_list = NULL;
data->p[data->n].aff_list = NULL;
}
/* Store "set" and "aff" in the current entry of "data" as a single subpiece.
*/
static void set_single(struct isl_from_pw_aff_data *data,
__isl_take isl_set *set, __isl_take isl_aff *aff)
{
data->p[data->n].state = isl_state_single;
data->p[data->n].set_list = isl_set_list_from_set(set);
data->p[data->n].aff_list = isl_aff_list_from_aff(aff);
}
/* Extend the current entry of "data" with "set" and "aff"
* as a minimum expression.
*/
static isl_stat extend_min(struct isl_from_pw_aff_data *data,
__isl_take isl_set *set, __isl_take isl_aff *aff)
{
int n = data->n;
data->p[n].state = isl_state_min;
data->p[n].set_list = isl_set_list_add(data->p[n].set_list, set);
data->p[n].aff_list = isl_aff_list_add(data->p[n].aff_list, aff);
if (!data->p[n].set_list || !data->p[n].aff_list)
return isl_stat_error;
return isl_stat_ok;
}
/* Extend the current entry of "data" with "set" and "aff"
* as a maximum expression.
*/
static isl_stat extend_max(struct isl_from_pw_aff_data *data,
__isl_take isl_set *set, __isl_take isl_aff *aff)
{
int n = data->n;
data->p[n].state = isl_state_max;
data->p[n].set_list = isl_set_list_add(data->p[n].set_list, set);
data->p[n].aff_list = isl_aff_list_add(data->p[n].aff_list, aff);
if (!data->p[n].set_list || !data->p[n].aff_list)
return isl_stat_error;
return isl_stat_ok;
}
/* Extend the domain of the current entry of "data", which is assumed
* to contain a single subpiece, with "set". If "replace" is set,
* then also replace the affine function by "aff". Otherwise,
* simply free "aff".
*/
static isl_stat extend_domain(struct isl_from_pw_aff_data *data,
__isl_take isl_set *set, __isl_take isl_aff *aff, int replace)
{
int n = data->n;
isl_set *set_n;
set_n = isl_set_list_get_set(data->p[n].set_list, 0);
set_n = isl_set_union(set_n, set);
data->p[n].set_list =
isl_set_list_set_set(data->p[n].set_list, 0, set_n);
if (replace)
data->p[n].aff_list =
isl_aff_list_set_aff(data->p[n].aff_list, 0, aff);
else
isl_aff_free(aff);
if (!data->p[n].set_list || !data->p[n].aff_list)
return isl_stat_error;
return isl_stat_ok;
}
/* Construct an isl_ast_expr from "list" within "build".
* If "state" is isl_state_single, then "list" contains a single entry and
* an isl_ast_expr is constructed for that entry.
* Otherwise a min or max expression is constructed from "list"
* depending on "state".
*/
static __isl_give isl_ast_expr *ast_expr_from_aff_list(
__isl_take isl_aff_list *list, enum isl_from_pw_aff_state state,
__isl_keep isl_ast_build *build)
{
int i;
isl_size n;
isl_aff *aff;
isl_ast_expr *expr = NULL;
enum isl_ast_expr_op_type op_type;
if (state == isl_state_single) {
aff = isl_aff_list_get_aff(list, 0);
isl_aff_list_free(list);
return isl_ast_expr_from_aff(aff, build);
}
n = isl_aff_list_n_aff(list);
if (n < 0)
goto error;
op_type = state == isl_state_min ? isl_ast_expr_op_min
: isl_ast_expr_op_max;
expr = isl_ast_expr_alloc_op(isl_ast_build_get_ctx(build), op_type, n);
if (!expr)
goto error;
for (i = 0; i < n; ++i) {
isl_ast_expr *expr_i;
aff = isl_aff_list_get_aff(list, i);
expr_i = isl_ast_expr_from_aff(aff, build);
if (!expr_i)
goto error;
expr->u.op.args[i] = expr_i;
}
isl_aff_list_free(list);
return expr;
error:
isl_aff_list_free(list);
isl_ast_expr_free(expr);
return NULL;
}
/* Extend the expression in "next" to take into account
* the piece at position "pos" in "data", allowing for a further extension
* for the next piece(s).
* In particular, "next" is set to a select operation that selects
* an isl_ast_expr corresponding to data->aff_list on data->set and
* to an expression that will be filled in by later calls.
* Return a pointer to this location.
* Afterwards, the state of "data" is set to isl_state_none.
*
* The constraints of data->set are added to the generated
* constraints of the build such that they can be exploited to simplify
* the AST expression constructed from data->aff_list.
*/
static isl_ast_expr **add_intermediate_piece(struct isl_from_pw_aff_data *data,
int pos, isl_ast_expr **next)
{
isl_ctx *ctx;
isl_ast_build *build;
isl_ast_expr *ternary, *arg;
isl_set *set, *gist;
set = data->p[pos].set;
data->p[pos].set = NULL;
ctx = isl_ast_build_get_ctx(data->build);
ternary = isl_ast_expr_alloc_op(ctx, isl_ast_expr_op_select, 3);
gist = isl_set_gist(isl_set_copy(set), isl_set_copy(data->dom));
arg = isl_ast_build_expr_from_set_internal(data->build, gist);
ternary = isl_ast_expr_set_op_arg(ternary, 0, arg);
build = isl_ast_build_copy(data->build);
build = isl_ast_build_restrict_generated(build, set);
arg = ast_expr_from_aff_list(data->p[pos].aff_list,
data->p[pos].state, build);
data->p[pos].aff_list = NULL;
isl_ast_build_free(build);
ternary = isl_ast_expr_set_op_arg(ternary, 1, arg);
data->p[pos].state = isl_state_none;
if (!ternary)
return NULL;
*next = ternary;
return &ternary->u.op.args[2];
}
/* Extend the expression in "next" to take into account
* the final piece, located at position "pos" in "data".
* In particular, "next" is set to evaluate data->aff_list
* and the domain is ignored.
* Return isl_stat_ok on success and isl_stat_error on failure.
*
* The constraints of data->set are however added to the generated
* constraints of the build such that they can be exploited to simplify
* the AST expression constructed from data->aff_list.
*/
static isl_stat add_last_piece(struct isl_from_pw_aff_data *data,
int pos, isl_ast_expr **next)
{
isl_ast_build *build;
if (data->p[pos].state == isl_state_none)
isl_die(isl_ast_build_get_ctx(data->build), isl_error_invalid,
"cannot handle void expression", return isl_stat_error);
build = isl_ast_build_copy(data->build);
build = isl_ast_build_restrict_generated(build, data->p[pos].set);
data->p[pos].set = NULL;
*next = ast_expr_from_aff_list(data->p[pos].aff_list,
data->p[pos].state, build);
data->p[pos].aff_list = NULL;
isl_ast_build_free(build);
data->p[pos].state = isl_state_none;
if (!*next)
return isl_stat_error;
return isl_stat_ok;
}
/* Return -1 if the piece "p1" should be sorted before "p2"
* and 1 if it should be sorted after "p2".
* Return 0 if they do not need to be sorted in a specific order.
*
* Pieces are sorted according to the number of disjuncts
* in their domains.
*/
static int sort_pieces_cmp(const void *p1, const void *p2, void *arg)
{
const struct isl_from_pw_aff_piece *piece1 = p1;
const struct isl_from_pw_aff_piece *piece2 = p2;
isl_size n1, n2;
n1 = isl_set_n_basic_set(piece1->set);
n2 = isl_set_n_basic_set(piece2->set);
return n1 - n2;
}
/* Construct an isl_ast_expr from the pieces in "data".
* Return the result or NULL on failure.
*
* When this function is called, data->n points to the current piece.
* If this is an effective piece, then first increment data->n such
* that data->n contains the number of pieces.
* The "set_list" fields are subsequently replaced by the corresponding
* "set" fields, after which the pieces are sorted according to
* the number of disjuncts in these "set" fields.
*
* Construct intermediate AST expressions for the initial pieces and
* finish off with the final pieces.
*/
static isl_ast_expr *build_pieces(struct isl_from_pw_aff_data *data)
{
int i;
isl_ast_expr *res = NULL;
isl_ast_expr **next = &res;
if (data->p[data->n].state != isl_state_none)
data->n++;
if (data->n == 0)
isl_die(isl_ast_build_get_ctx(data->build), isl_error_invalid,
"cannot handle void expression", return NULL);
for (i = 0; i < data->n; ++i) {
data->p[i].set = isl_set_list_union(data->p[i].set_list);
if (data->p[i].state != isl_state_single)
data->p[i].set = isl_set_coalesce(data->p[i].set);
data->p[i].set_list = NULL;
}
if (isl_sort(data->p, data->n, sizeof(data->p[0]),
&sort_pieces_cmp, NULL) < 0)
return isl_ast_expr_free(res);
for (i = 0; i + 1 < data->n; ++i) {
next = add_intermediate_piece(data, i, next);
if (!next)
return isl_ast_expr_free(res);
}
if (add_last_piece(data, data->n - 1, next) < 0)
return isl_ast_expr_free(res);
return res;
}
/* Is the domain of the current entry of "data", which is assumed
* to contain a single subpiece, a subset of "set"?
*/
static isl_bool single_is_subset(struct isl_from_pw_aff_data *data,
__isl_keep isl_set *set)
{
isl_bool subset;
isl_set *set_n;
set_n = isl_set_list_get_set(data->p[data->n].set_list, 0);
subset = isl_set_is_subset(set_n, set);
isl_set_free(set_n);
return subset;
}
/* Is "aff" a rational expression, i.e., does it have a denominator
* different from one?
*/
static isl_bool aff_is_rational(__isl_keep isl_aff *aff)
{
isl_bool rational;
isl_val *den;
den = isl_aff_get_denominator_val(aff);
rational = isl_bool_not(isl_val_is_one(den));
isl_val_free(den);
return rational;
}
/* Does "list" consist of a single rational affine expression?
*/
static isl_bool is_single_rational_aff(__isl_keep isl_aff_list *list)
{
isl_size n;
isl_bool rational;
isl_aff *aff;
n = isl_aff_list_n_aff(list);
if (n < 0)
return isl_bool_error;
if (n != 1)
return isl_bool_false;
aff = isl_aff_list_get_aff(list, 0);
rational = aff_is_rational(aff);
isl_aff_free(aff);
return rational;
}
/* Can the list of subpieces in the last piece of "data" be extended with
* "set" and "aff" based on "test"?
* In particular, is it the case for each entry (set_i, aff_i) that
*
* test(aff, aff_i) holds on set_i, and
* test(aff_i, aff) holds on set?
*
* "test" returns the set of elements where the tests holds, meaning
* that test(aff_i, aff) holds on set if set is a subset of test(aff_i, aff).
*
* This function is used to detect min/max expressions.
* If the ast_build_detect_min_max option is turned off, then
* do not even try and perform any detection and return false instead.
*
* Rational affine expressions are not considered for min/max expressions
* since the combined expression will be defined on the union of the domains,
* while a rational expression may only yield integer values
* on its own definition domain.
*/
static isl_bool extends(struct isl_from_pw_aff_data *data,
__isl_keep isl_set *set, __isl_keep isl_aff *aff,
__isl_give isl_basic_set *(*test)(__isl_take isl_aff *aff1,
__isl_take isl_aff *aff2))
{
int i;
isl_size n;
isl_bool is_rational;
isl_ctx *ctx;
isl_set *dom;
is_rational = aff_is_rational(aff);
if (is_rational >= 0 && !is_rational)
is_rational = is_single_rational_aff(data->p[data->n].aff_list);
if (is_rational < 0 || is_rational)
return isl_bool_not(is_rational);
ctx = isl_ast_build_get_ctx(data->build);
if (!isl_options_get_ast_build_detect_min_max(ctx))
return isl_bool_false;
n = isl_set_list_n_set(data->p[data->n].set_list);
if (n < 0)
return isl_bool_error;
dom = isl_ast_build_get_domain(data->build);
set = isl_set_intersect(dom, isl_set_copy(set));
for (i = 0; i < n ; ++i) {
isl_aff *aff_i;
isl_set *valid;
isl_set *dom, *required;
isl_bool is_valid;
aff_i = isl_aff_list_get_aff(data->p[data->n].aff_list, i);
valid = isl_set_from_basic_set(test(isl_aff_copy(aff), aff_i));
required = isl_set_list_get_set(data->p[data->n].set_list, i);
dom = isl_ast_build_get_domain(data->build);
required = isl_set_intersect(dom, required);
is_valid = isl_set_is_subset(required, valid);
isl_set_free(required);
isl_set_free(valid);
if (is_valid < 0 || !is_valid) {
isl_set_free(set);
return is_valid;
}
aff_i = isl_aff_list_get_aff(data->p[data->n].aff_list, i);
valid = isl_set_from_basic_set(test(aff_i, isl_aff_copy(aff)));
is_valid = isl_set_is_subset(set, valid);
isl_set_free(valid);
if (is_valid < 0 || !is_valid) {
isl_set_free(set);
return is_valid;
}
}
isl_set_free(set);
return isl_bool_true;
}
/* Can the list of pieces in "data" be extended with "set" and "aff"
* to form/preserve a minimum expression?
* In particular, is it the case for each entry (set_i, aff_i) that
*
* aff >= aff_i on set_i, and
* aff_i >= aff on set?
*/
static isl_bool extends_min(struct isl_from_pw_aff_data *data,
__isl_keep isl_set *set, __isl_keep isl_aff *aff)
{
return extends(data, set, aff, &isl_aff_ge_basic_set);
}
/* Can the list of pieces in "data" be extended with "set" and "aff"
* to form/preserve a maximum expression?
* In particular, is it the case for each entry (set_i, aff_i) that
*
* aff <= aff_i on set_i, and
* aff_i <= aff on set?
*/
static isl_bool extends_max(struct isl_from_pw_aff_data *data,
__isl_keep isl_set *set, __isl_keep isl_aff *aff)
{
return extends(data, set, aff, &isl_aff_le_basic_set);
}
/* This function is called during the construction of an isl_ast_expr
* that evaluates an isl_pw_aff.
* If the last piece of "data" contains a single subpiece and
* if its affine function is equal to "aff" on a part of the domain
* that includes either "set" or the domain of that single subpiece,
* then extend the domain of that single subpiece with "set".
* If it was the original domain of the single subpiece where
* the two affine functions are equal, then also replace
* the affine function of the single subpiece by "aff".
* If the last piece of "data" contains either a single subpiece
* or a minimum, then check if this minimum expression can be extended
* with (set, aff).
* If so, extend the sequence and return.
* Perform the same operation for maximum expressions.
* If no such extension can be performed, then move to the next piece
* in "data" (if the current piece contains any data), and then store
* the current subpiece in the current piece of "data" for later handling.
*/
static isl_stat ast_expr_from_pw_aff(__isl_take isl_set *set,
__isl_take isl_aff *aff, void *user)
{
struct isl_from_pw_aff_data *data = user;
isl_bool test;
enum isl_from_pw_aff_state state;
state = data->p[data->n].state;
if (state == isl_state_single) {
isl_aff *aff0;
isl_set *eq;
isl_bool subset1, subset2 = isl_bool_false;
aff0 = isl_aff_list_get_aff(data->p[data->n].aff_list, 0);
eq = isl_aff_eq_set(isl_aff_copy(aff), aff0);
subset1 = isl_set_is_subset(set, eq);
if (subset1 >= 0 && !subset1)
subset2 = single_is_subset(data, eq);
isl_set_free(eq);
if (subset1 < 0 || subset2 < 0)
goto error;
if (subset1)
return extend_domain(data, set, aff, 0);
if (subset2)
return extend_domain(data, set, aff, 1);
}
if (state == isl_state_single || state == isl_state_min) {
test = extends_min(data, set, aff);
if (test < 0)
goto error;
if (test)
return extend_min(data, set, aff);
}
if (state == isl_state_single || state == isl_state_max) {
test = extends_max(data, set, aff);
if (test < 0)
goto error;
if (test)
return extend_max(data, set, aff);
}
if (state != isl_state_none)
data->n++;
set_single(data, set, aff);
return isl_stat_ok;
error:
isl_set_free(set);
isl_aff_free(aff);
return isl_stat_error;
}
/* Construct an isl_ast_expr that evaluates "pa".
* The result is simplified in terms of build->domain.
*
* The domain of "pa" lives in the internal schedule space.
*/
__isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff_internal(
__isl_keep isl_ast_build *build, __isl_take isl_pw_aff *pa)
{
struct isl_from_pw_aff_data data = { NULL };
isl_ast_expr *res = NULL;
pa = isl_ast_build_compute_gist_pw_aff(build, pa);
pa = isl_pw_aff_coalesce(pa);
if (!pa)
return NULL;
if (isl_from_pw_aff_data_init(&data, build, pa) < 0)
goto error;
set_none(&data);
if (isl_pw_aff_foreach_piece(pa, &ast_expr_from_pw_aff, &data) >= 0)
res = build_pieces(&data);
isl_pw_aff_free(pa);
isl_from_pw_aff_data_clear(&data);
return res;
error:
isl_pw_aff_free(pa);
isl_from_pw_aff_data_clear(&data);
return NULL;
}
/* Construct an isl_ast_expr that evaluates "pa".
* The result is simplified in terms of build->domain.
*
* The domain of "pa" lives in the external schedule space.
*/
__isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
__isl_keep isl_ast_build *build, __isl_take isl_pw_aff *pa)
{
isl_ast_expr *expr;
isl_bool needs_map;
needs_map = isl_ast_build_need_schedule_map(build);
if (needs_map < 0) {
pa = isl_pw_aff_free(pa);
} else if (needs_map) {
isl_multi_aff *ma;
ma = isl_ast_build_get_schedule_map_multi_aff(build);
pa = isl_pw_aff_pullback_multi_aff(pa, ma);
}
expr = isl_ast_build_expr_from_pw_aff_internal(build, pa);
return expr;
}
/* Set the ids of the input dimensions of "mpa" to the iterator ids
* of "build".
*
* The domain of "mpa" is assumed to live in the internal schedule domain.
*/
static __isl_give isl_multi_pw_aff *set_iterator_names(
__isl_keep isl_ast_build *build, __isl_take isl_multi_pw_aff *mpa)
{
int i;
isl_size n;
n = isl_multi_pw_aff_dim(mpa, isl_dim_in);
if (n < 0)
return isl_multi_pw_aff_free(mpa);
for (i = 0; i < n; ++i) {
isl_id *id;
id = isl_ast_build_get_iterator_id(build, i);
mpa = isl_multi_pw_aff_set_dim_id(mpa, isl_dim_in, i, id);
}
return mpa;
}
/* Construct an isl_ast_expr of type "type" with as first argument "arg0" and
* the remaining arguments derived from "mpa".
* That is, construct a call or access expression that calls/accesses "arg0"
* with arguments/indices specified by "mpa".
*/
static __isl_give isl_ast_expr *isl_ast_build_with_arguments(
__isl_keep isl_ast_build *build, enum isl_ast_expr_op_type type,
__isl_take isl_ast_expr *arg0, __isl_take isl_multi_pw_aff *mpa)
{
int i;
isl_size n;
isl_ctx *ctx;
isl_ast_expr *expr;
ctx = isl_ast_build_get_ctx(build);
n = isl_multi_pw_aff_dim(mpa, isl_dim_out);
expr = n >= 0 ? isl_ast_expr_alloc_op(ctx, type, 1 + n) : NULL;
expr = isl_ast_expr_set_op_arg(expr, 0, arg0);
for (i = 0; i < n; ++i) {
isl_pw_aff *pa;
isl_ast_expr *arg;
pa = isl_multi_pw_aff_get_pw_aff(mpa, i);
arg = isl_ast_build_expr_from_pw_aff_internal(build, pa);
expr = isl_ast_expr_set_op_arg(expr, 1 + i, arg);
}
isl_multi_pw_aff_free(mpa);
return expr;
}
static __isl_give isl_ast_expr *isl_ast_build_from_multi_pw_aff_internal(
__isl_keep isl_ast_build *build, enum isl_ast_expr_op_type type,
__isl_take isl_multi_pw_aff *mpa);
/* Construct an isl_ast_expr that accesses the member specified by "mpa".
* The range of "mpa" is assumed to be wrapped relation.
* The domain of this wrapped relation specifies the structure being
* accessed, while the range of this wrapped relation spacifies the
* member of the structure being accessed.
*
* The domain of "mpa" is assumed to live in the internal schedule domain.
*/
static __isl_give isl_ast_expr *isl_ast_build_from_multi_pw_aff_member(
__isl_keep isl_ast_build *build, __isl_take isl_multi_pw_aff *mpa)
{
isl_id *id;
isl_multi_pw_aff *domain;
isl_ast_expr *domain_expr, *expr;
enum isl_ast_expr_op_type type = isl_ast_expr_op_access;
domain = isl_multi_pw_aff_copy(mpa);
domain = isl_multi_pw_aff_range_factor_domain(domain);
domain_expr = isl_ast_build_from_multi_pw_aff_internal(build,
type, domain);
mpa = isl_multi_pw_aff_range_factor_range(mpa);
if (!isl_multi_pw_aff_has_tuple_id(mpa, isl_dim_out))
isl_die(isl_ast_build_get_ctx(build), isl_error_invalid,
"missing field name", goto error);
id = isl_multi_pw_aff_get_tuple_id(mpa, isl_dim_out);
expr = isl_ast_expr_from_id(id);
expr = isl_ast_expr_alloc_binary(isl_ast_expr_op_member,
domain_expr, expr);
return isl_ast_build_with_arguments(build, type, expr, mpa);
error:
isl_multi_pw_aff_free(mpa);
return NULL;
}
/* Construct an isl_ast_expr of type "type" that calls or accesses
* the element specified by "mpa".
* The first argument is obtained from the output tuple name.
* The remaining arguments are given by the piecewise affine expressions.
*
* If the range of "mpa" is a mapped relation, then we assume it
* represents an access to a member of a structure.
*
* The domain of "mpa" is assumed to live in the internal schedule domain.
*/
static __isl_give isl_ast_expr *isl_ast_build_from_multi_pw_aff_internal(
__isl_keep isl_ast_build *build, enum isl_ast_expr_op_type type,
__isl_take isl_multi_pw_aff *mpa)
{
isl_ctx *ctx;
isl_id *id;
isl_ast_expr *expr;
if (!mpa)
goto error;
if (type == isl_ast_expr_op_access &&
isl_multi_pw_aff_range_is_wrapping(mpa))
return isl_ast_build_from_multi_pw_aff_member(build, mpa);
mpa = set_iterator_names(build, mpa);
if (!build || !mpa)
goto error;
ctx = isl_ast_build_get_ctx(build);
if (isl_multi_pw_aff_has_tuple_id(mpa, isl_dim_out))
id = isl_multi_pw_aff_get_tuple_id(mpa, isl_dim_out);
else
id = isl_id_alloc(ctx, "", NULL);
expr = isl_ast_expr_from_id(id);
return isl_ast_build_with_arguments(build, type, expr, mpa);
error:
isl_multi_pw_aff_free(mpa);
return NULL;
}
/* Construct an isl_ast_expr of type "type" that calls or accesses
* the element specified by "pma".
* The first argument is obtained from the output tuple name.
* The remaining arguments are given by the piecewise affine expressions.
*
* The domain of "pma" is assumed to live in the internal schedule domain.
*/
static __isl_give isl_ast_expr *isl_ast_build_from_pw_multi_aff_internal(
__isl_keep isl_ast_build *build, enum isl_ast_expr_op_type type,
__isl_take isl_pw_multi_aff *pma)
{
isl_multi_pw_aff *mpa;
mpa = isl_multi_pw_aff_from_pw_multi_aff(pma);
return isl_ast_build_from_multi_pw_aff_internal(build, type, mpa);
}
/* Construct an isl_ast_expr of type "type" that calls or accesses
* the element specified by "mpa".
* The first argument is obtained from the output tuple name.
* The remaining arguments are given by the piecewise affine expressions.
*
* The domain of "mpa" is assumed to live in the external schedule domain.
*/
static __isl_give isl_ast_expr *isl_ast_build_from_multi_pw_aff(
__isl_keep isl_ast_build *build, enum isl_ast_expr_op_type type,
__isl_take isl_multi_pw_aff *mpa)
{
isl_bool is_domain;
isl_bool needs_map;
isl_ast_expr *expr;
isl_space *space_build, *space_mpa;
space_build = isl_ast_build_get_space(build, 0);
space_mpa = isl_multi_pw_aff_get_space(mpa);
is_domain = isl_space_tuple_is_equal(space_build, isl_dim_set,
space_mpa, isl_dim_in);
isl_space_free(space_build);
isl_space_free(space_mpa);
if (is_domain < 0)
goto error;
if (!is_domain)
isl_die(isl_ast_build_get_ctx(build), isl_error_invalid,
"spaces don't match", goto error);
needs_map = isl_ast_build_need_schedule_map(build);
if (needs_map < 0)
goto error;
if (needs_map) {
isl_multi_aff *ma;
ma = isl_ast_build_get_schedule_map_multi_aff(build);
mpa = isl_multi_pw_aff_pullback_multi_aff(mpa, ma);
}
expr = isl_ast_build_from_multi_pw_aff_internal(build, type, mpa);
return expr;
error:
isl_multi_pw_aff_free(mpa);
return NULL;
}
/* Construct an isl_ast_expr that calls the domain element specified by "mpa".
* The name of the function is obtained from the output tuple name.
* The arguments are given by the piecewise affine expressions.
*
* The domain of "mpa" is assumed to live in the external schedule domain.
*/
__isl_give isl_ast_expr *isl_ast_build_call_from_multi_pw_aff(
__isl_keep isl_ast_build *build, __isl_take isl_multi_pw_aff *mpa)
{
return isl_ast_build_from_multi_pw_aff(build,
isl_ast_expr_op_call, mpa);
}
/* Construct an isl_ast_expr that accesses the array element specified by "mpa".
* The name of the array is obtained from the output tuple name.
* The index expressions are given by the piecewise affine expressions.
*
* The domain of "mpa" is assumed to live in the external schedule domain.
*/
__isl_give isl_ast_expr *isl_ast_build_access_from_multi_pw_aff(
__isl_keep isl_ast_build *build, __isl_take isl_multi_pw_aff *mpa)
{
return isl_ast_build_from_multi_pw_aff(build,
isl_ast_expr_op_access, mpa);
}
/* Construct an isl_ast_expr of type "type" that calls or accesses
* the element specified by "pma".
* The first argument is obtained from the output tuple name.
* The remaining arguments are given by the piecewise affine expressions.
*
* The domain of "pma" is assumed to live in the external schedule domain.
*/
static __isl_give isl_ast_expr *isl_ast_build_from_pw_multi_aff(
__isl_keep isl_ast_build *build, enum isl_ast_expr_op_type type,
__isl_take isl_pw_multi_aff *pma)
{
isl_multi_pw_aff *mpa;
mpa = isl_multi_pw_aff_from_pw_multi_aff(pma);
return isl_ast_build_from_multi_pw_aff(build, type, mpa);
}
/* Construct an isl_ast_expr that calls the domain element specified by "pma".
* The name of the function is obtained from the output tuple name.
* The arguments are given by the piecewise affine expressions.
*
* The domain of "pma" is assumed to live in the external schedule domain.
*/
__isl_give isl_ast_expr *isl_ast_build_call_from_pw_multi_aff(
__isl_keep isl_ast_build *build, __isl_take isl_pw_multi_aff *pma)
{
return isl_ast_build_from_pw_multi_aff(build,
isl_ast_expr_op_call, pma);
}
/* Construct an isl_ast_expr that accesses the array element specified by "pma".
* The name of the array is obtained from the output tuple name.
* The index expressions are given by the piecewise affine expressions.
*
* The domain of "pma" is assumed to live in the external schedule domain.
*/
__isl_give isl_ast_expr *isl_ast_build_access_from_pw_multi_aff(
__isl_keep isl_ast_build *build, __isl_take isl_pw_multi_aff *pma)
{
return isl_ast_build_from_pw_multi_aff(build,
isl_ast_expr_op_access, pma);
}
/* Construct an isl_ast_expr that calls the domain element
* specified by "executed".
*
* "executed" is assumed to be single-valued, with a domain that lives
* in the internal schedule space.
*/
__isl_give isl_ast_node *isl_ast_build_call_from_executed(
__isl_keep isl_ast_build *build, __isl_take isl_map *executed)
{
isl_pw_multi_aff *iteration;
isl_ast_expr *expr;
iteration = isl_pw_multi_aff_from_map(executed);
iteration = isl_ast_build_compute_gist_pw_multi_aff(build, iteration);
iteration = isl_pw_multi_aff_intersect_domain(iteration,
isl_ast_build_get_domain(build));
expr = isl_ast_build_from_pw_multi_aff_internal(build,
isl_ast_expr_op_call, iteration);
return isl_ast_node_alloc_user(expr);
}
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