isl_local_space_substitute_seq: take argument for the number of divs to modify

[isl.git] / isl_ast_build_expr.c

/*
 * Copyright 2012      Ecole Normale Superieure
 *
 * Use of this software is governed by the MIT license
 *
 * Written by Sven Verdoolaege,
 * Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
 */

#include <isl/ilp.h>
#include <isl_ast_build_expr.h>
#include <isl_ast_private.h>
#include <isl_ast_build_private.h>

/* Compute the minimum of the integer affine expression "obj" over the points
 * in build->domain and put the result in *opt.
 */
enum isl_lp_result isl_ast_build_min(__isl_keep isl_ast_build *build,
        __isl_keep isl_aff *obj, isl_int *opt)
{
        if (!build)
                return isl_lp_error;

        return isl_set_min(build->domain, obj, opt);
}

/* Compute the maximum of the integer affine expression "obj" over the points
 * in build->domain and put the result in *opt.
 */
enum isl_lp_result isl_ast_build_max(__isl_keep isl_ast_build *build,
        __isl_keep isl_aff *obj, isl_int *opt)
{
        if (!build)
                return isl_lp_error;

        return isl_set_max(build->domain, obj, opt);
}

/* 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_int d)
{
        aff = isl_aff_neg(aff);
        aff = isl_aff_add_constant(aff, d);
        aff = isl_aff_add_constant_si(aff, -1);

        return aff;
}

/* Create an isl_ast_expr evaluating the div at position "pos" in "ls".
 * The result is simplified in terms of build->domain.
 *
 * "v" points to the coefficient of the div in the expression where it
 * appears and may be updated by this function.
 * "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.
 */
static __isl_give isl_ast_expr *var_div(isl_int *v,
        __isl_keep isl_local_space *ls,
        int pos, __isl_keep isl_ast_build *build)
{
        isl_ctx *ctx = isl_local_space_get_ctx(ls);
        isl_aff *aff;
        isl_ast_expr *num, *den;
        isl_int d;
        enum isl_ast_op_type type;

        aff = isl_local_space_get_div(ls, pos);
        isl_int_init(d);
        isl_aff_get_denominator(aff, &d);
        aff = isl_aff_scale(aff, d);
        den = isl_ast_expr_alloc_int(ctx, 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(build, aff);
                if (non_neg >= 0 && !non_neg) {
                        isl_aff *opp = oppose_div_arg(isl_aff_copy(aff), d);
                        non_neg = isl_ast_build_aff_is_nonneg(build, opp);
                        if (non_neg >= 0 && non_neg) {
                                isl_int_neg(*v, *v);
                                isl_aff_free(aff);
                                aff = opp;
                        } else
                                isl_aff_free(opp);
                }
                if (non_neg < 0)
                        aff = isl_aff_free(aff);
                else if (non_neg)
                        type = isl_ast_op_pdiv_q;
        }

        isl_int_clear(d);
        num = isl_ast_expr_from_aff(aff, 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 build->domain.
 *
 * "v" points to the coefficient of the specified dimension
 * in the expression where it appears and may be updated by this function.
 *
 * 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 "build"
 * - parameters are constructed from the isl_ids in "ls"
 */
static __isl_give isl_ast_expr *var(isl_int *v, __isl_keep isl_local_space *ls,
        enum isl_dim_type type, int pos, __isl_keep isl_ast_build *build)
{
        isl_ctx *ctx = isl_local_space_get_ctx(ls);
        isl_id *id;

        if (type == isl_dim_div)
                return var_div(v, ls, pos, build);

        if (type == isl_dim_set) {
                id = isl_ast_build_get_iterator_id(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_int_is_zero(expr->u.i);
}

/* 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_int v,
        __isl_keep isl_aff *aff, isl_int d, __isl_keep isl_ast_build *build)
{
        isl_ctx *ctx;
        isl_ast_expr *expr;
        isl_ast_expr *c;

        if (!aff)
                return NULL;

        ctx = isl_aff_get_ctx(aff);
        expr = isl_ast_expr_from_aff(isl_aff_copy(aff), build);

        c = isl_ast_expr_alloc_int(ctx, d);
        expr = isl_ast_expr_alloc_binary(isl_ast_op_pdiv_r, expr, c);

        if (!isl_int_is_one(v)) {
                c = isl_ast_expr_alloc_int(ctx, 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_int v)
{
        isl_ctx *ctx;
        isl_ast_expr *c;

        if (!expr)
                return NULL;
        if (isl_int_is_one(v))
                return expr;

        if (isl_int_is_negone(v)) {
                expr = isl_ast_expr_neg(expr);
        } else {
                ctx = isl_ast_expr_get_ctx(expr);
                c = isl_ast_expr_alloc_int(ctx, v);
                expr = isl_ast_expr_mul(c, expr);
        }

        return expr;
}

/* Add an expression for "*v" times the specified dimension of "ls"
 * to expr.
 *
 * 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_int *v, __isl_keep isl_ast_build *build)
{
        isl_ast_expr *term;

        if (!expr)
                return NULL;

        term = var(v, ls, type, pos, build);

        if (isl_int_is_neg(*v) && !ast_expr_is_zero(expr)) {
                isl_int_neg(*v, *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_int v)
{
        isl_ctx *ctx;
        isl_ast_expr *expr_int;

        if (!expr)
                return NULL;

        if (isl_int_is_zero(v))
                return expr;

        ctx = isl_ast_expr_get_ctx(expr);
        if (isl_int_is_neg(v) && !ast_expr_is_zero(expr)) {
                isl_int_neg(v, v);
                expr_int = isl_ast_expr_alloc_int(ctx, v);
                return ast_expr_sub(expr, expr_int);
        } else {
                expr_int = isl_ast_expr_alloc_int(ctx, v);
                return ast_expr_add(expr, expr_int);
        }
}

/* Check if "aff" involves any (implicit) modulo computations based
 * on div "j".
 * If so, remove them from aff and add expressions corresponding
 * to those modulo computations to *pos and/or *neg.
 * "v" is the coefficient of div "j".
 *
 * In particular, check if (v * div_j) / d is of the form
 *
 *      (f * m * floor(a / m)) / d
 *
 * and, if so, rewrite it as
 *
 *      (f * (a - (a mod m))) / d = (f * a) / d - (f * (a mod m)) / d
 *
 * 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.
 *
 * The caller is responsible for dividing *neg and/or *pos by d.
 */
static __isl_give isl_aff *extract_modulo(__isl_take isl_aff *aff,
        __isl_keep isl_ast_expr **pos, __isl_keep isl_ast_expr **neg,
        __isl_keep isl_ast_build *build, int j, isl_int v)
{
        isl_ast_expr *expr;
        isl_aff *div;
        int s;
        int mod;
        isl_int d;

        isl_int_init(d);
        div = isl_aff_get_div(aff, j);
        isl_aff_get_denominator(div, &d);
        mod = isl_int_is_divisible_by(v, d);
        if (mod) {
                div = isl_aff_scale(div, d);
                mod = isl_ast_build_aff_is_nonneg(build, div);
                if (mod >= 0 && !mod) {
                        isl_aff *opp = oppose_div_arg(isl_aff_copy(div), d);
                        mod = isl_ast_build_aff_is_nonneg(build, opp);
                        if (mod >= 0 && mod) {
                                isl_aff_free(div);
                                div = opp;
                                isl_int_neg(v, v);
                        } else
                                isl_aff_free(opp);
                }
        }
        if (mod < 0) {
                isl_aff_free(div);
                isl_int_clear(d);
                return isl_aff_free(aff);
        } else if (!mod) {
                isl_aff_free(div);
                isl_int_clear(d);
                return aff;
        }
        isl_int_divexact(v, v, d);
        s = isl_int_sgn(v);
        isl_int_abs(v, v);
        expr = isl_ast_expr_mod(v, div, d, build);
        if (s > 0)
                *neg = ast_expr_add(*neg, expr);
        else
                *pos = ast_expr_add(*pos, expr);
        aff = isl_aff_set_coefficient_si(aff, isl_dim_div, j, 0);
        if (s < 0)
                isl_int_neg(v, v);
        div = isl_aff_scale(div, v);
        isl_aff_get_denominator(aff, &d);
        div = isl_aff_scale_down(div, d);
        aff = isl_aff_add(aff, div);
        isl_int_clear(d);

        return aff;
}

/* 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.
 *
 * 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)) / d
 *
 * rewrite them as
 *
 *      (f * (a - (a mod m))) / d = (f * a) / d - (f * (a mod m)) / d
 *
 * 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.
 *
 * The caller is responsible for dividing *neg and/or *pos by d.
 */
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)
{
        isl_ctx *ctx;
        int j, n;
        isl_int v;

        if (!aff)
                return NULL;

        ctx = isl_aff_get_ctx(aff);
        if (!isl_options_get_ast_build_prefer_pdiv(ctx))
                return aff;

        isl_int_init(v);

        n = isl_aff_dim(aff, isl_dim_div);
        for (j = 0; j < n; ++j) {
                isl_aff_get_coefficient(aff, isl_dim_div, j, &v);
                if (isl_int_is_zero(v) ||
                    isl_int_is_one(v) || isl_int_is_negone(v))
                        continue;
                aff = extract_modulo(aff, pos, neg, build, j, v);
                if (!aff)
                        break;
        }

        isl_int_clear(v);

        return aff;
}

/* 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_int v;
        int n;
        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;

        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_modulos(aff, &expr, &expr_neg, build);
        expr = ast_expr_sub(expr, expr_neg);

        isl_int_init(v);
        ls = isl_aff_get_domain_local_space(aff);

        for (i = 0; i < 3; ++i) {
                n = isl_aff_dim(aff, t[i]);
                for (j = 0; j < n; ++j) {
                        isl_aff_get_coefficient(aff, t[i], j, &v);
                        if (isl_int_is_zero(v))
                                continue;
                        expr = isl_ast_expr_add_term(expr,
                                                        ls, l[i], j, &v, build);
                }
        }

        isl_aff_get_constant(aff, &v);
        expr = isl_ast_expr_add_int(expr, v);

        isl_aff_get_denominator(aff, &v);
        if (!isl_int_is_one(v)) {
                isl_ast_expr *d;
                d = isl_ast_expr_alloc_int(ctx, v);
                expr = isl_ast_expr_div(expr, d);
        }

        isl_local_space_free(ls);
        isl_int_clear(v);
        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 build->domain.
 */
static __isl_give isl_ast_expr *add_signed_terms(__isl_take isl_ast_expr *expr,
        __isl_keep isl_aff *aff, int sign, __isl_keep isl_ast_build *build)
{
        int i, j;
        isl_int 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;

        isl_int_init(v);
        ls = isl_aff_get_domain_local_space(aff);

        for (i = 0; i < 3; ++i) {
                int n = isl_aff_dim(aff, t[i]);
                for (j = 0; j < n; ++j) {
                        isl_aff_get_coefficient(aff, t[i], j, &v);
                        if (sign * isl_int_sgn(v) <= 0)
                                continue;
                        isl_int_abs(v, v);
                        expr = isl_ast_expr_add_term(expr,
                                                ls, l[i], j, &v, build);
                }
        }

        isl_aff_get_constant(aff, &v);
        if (sign * isl_int_sgn(v) > 0) {
                isl_int_abs(v, v);
                expr = isl_ast_expr_add_int(expr, v);
        }

        isl_local_space_free(ls);
        isl_int_clear(v);

        return expr;
}

/* Construct an isl_ast_expr that evaluates the condition "constraint",
 * The result is simplified in terms of build->domain.
 *
 * 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_op_ge, expr(pos), expr(-neg)))
 *
 * or
 *
 *      (isl_ast_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".
 */
static __isl_give isl_ast_expr *isl_ast_expr_from_constraint(
        __isl_take isl_constraint *constraint, __isl_keep isl_ast_build *build)
{
        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_op_type type;

        if (!constraint)
                return NULL;

        aff = isl_constraint_get_aff(constraint);

        ctx = isl_constraint_get_ctx(constraint);
        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);

        expr_pos = add_signed_terms(expr_pos, aff, 1, build);
        expr_neg = add_signed_terms(expr_neg, aff, -1, build);

        eq = isl_constraint_is_equality(constraint);

        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_op_eq : isl_ast_op_le;
                expr = isl_ast_expr_alloc_binary(type, expr_neg, expr_pos);
        } else {
                type = eq ? isl_ast_op_eq : isl_ast_op_ge;
                expr = isl_ast_expr_alloc_binary(type, expr_pos, expr_neg);
        }

        isl_constraint_free(constraint);
        isl_aff_free(aff);
        return expr;
}

struct isl_expr_from_basic_data {
        isl_ast_build *build;
        int first;
        isl_ast_expr *res;
};

/* Construct an isl_ast_expr that evaluates the condition "c",
 * except if it is a div constraint, and add it to the data->res.
 * The result is simplified in terms of data->build->domain.
 */
static int expr_from_basic_set(__isl_take isl_constraint *c, void *user)
{
        struct isl_expr_from_basic_data *data = user;
        isl_ast_expr *expr;

        if (isl_constraint_is_div_constraint(c)) {
                isl_constraint_free(c);
                return 0;
        }

        expr = isl_ast_expr_from_constraint(c, data->build);
        if (data->first)
                data->res = expr;
        else
                data->res = isl_ast_expr_and(data->res, expr);

        data->first = 0;

        if (!data->res)
                return -1;
        return 0;
}

/* Construct an isl_ast_expr that evaluates the conditions defining "bset".
 * The result is simplified in terms of build->domain.
 *
 * We filter out the div constraints during printing, so we do not know
 * in advance how many constraints are going to be printed.
 *
 * If it turns out that there was no constraint, then we contruct
 * the expression "1", i.e., "true".
 */
__isl_give isl_ast_expr *isl_ast_build_expr_from_basic_set(
         __isl_keep isl_ast_build *build, __isl_take isl_basic_set *bset)
{
        struct isl_expr_from_basic_data data = { build, 1, NULL };

        if (isl_basic_set_foreach_constraint(bset,
                                            &expr_from_basic_set, &data) < 0) {
                data.res = isl_ast_expr_free(data.res);
        } else if (data.res == NULL) {
                isl_ctx *ctx = isl_basic_set_get_ctx(bset);
                data.res = isl_ast_expr_alloc_int_si(ctx, 1);
        }

        isl_basic_set_free(bset);
        return data.res;
}

struct isl_expr_from_set_data {
        isl_ast_build *build;
        int first;
        isl_ast_expr *res;
};

/* Construct an isl_ast_expr that evaluates the conditions defining "bset"
 * and add it to data->res.
 * The result is simplified in terms of data->build->domain.
 */
static int expr_from_set(__isl_take isl_basic_set *bset, void *user)
{
        struct isl_expr_from_set_data *data = user;
        isl_ast_expr *expr;

        expr = isl_ast_build_expr_from_basic_set(data->build, bset);
        if (data->first)
                data->res = expr;
        else
                data->res = isl_ast_expr_or(data->res, expr);

        data->first = 0;

        if (!data->res)
                return -1;
        return 0;
}

/* Construct an isl_ast_expr that evaluates the conditions defining "set".
 * The result is simplified in terms of build->domain.
 */
__isl_give isl_ast_expr *isl_ast_build_expr_from_set(
        __isl_keep isl_ast_build *build, __isl_take isl_set *set)
{
        struct isl_expr_from_set_data data = { build, 1, NULL };

        if (isl_set_foreach_basic_set(set, &expr_from_set, &data) < 0)
                data.res = isl_ast_expr_free(data.res);

        isl_set_free(set);
        return data.res;
}

struct isl_from_pw_aff_data {
        isl_ast_build *build;
        int n;
        isl_ast_expr **next;
        isl_set *dom;
};

/* This function is called during the construction of an isl_ast_expr
 * that evaluates an isl_pw_aff.
 * Adjust data->next to take into account this piece.
 *
 * data->n is the number of pairs of set and aff to go.
 * data->dom is the domain of the entire isl_pw_aff.
 *
 * If this is the last pair, then data->next is set to evaluate aff
 * and the domain is ignored.
 * Otherwise, data->next is set to a select operation that selects
 * an isl_ast_expr correponding to "aff" on "set" and to an expression
 * that will be filled in by later calls otherwise.
 */
static int 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_ctx *ctx;

        ctx = isl_set_get_ctx(set);
        data->n--;
        if (data->n == 0) {
                *data->next = isl_ast_expr_from_aff(aff, data->build);
                isl_set_free(set);
                if (!*data->next)
                        return -1;
        } else {
                isl_ast_expr *ternary, *arg;

                ternary = isl_ast_expr_alloc_op(ctx, isl_ast_op_select, 3);
                set = isl_set_gist(set, isl_set_copy(data->dom));
                arg = isl_ast_build_expr_from_set(data->build, set);
                ternary = isl_ast_expr_set_op_arg(ternary, 0, arg);
                arg = isl_ast_expr_from_aff(aff, data->build);
                ternary = isl_ast_expr_set_op_arg(ternary, 1, arg);
                if (!ternary)
                        return -1;

                *data->next = ternary;
                data->next = &ternary->u.op.args[2];
        }

        return 0;
}

/* 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;
        isl_ast_expr *res = NULL;

        if (!pa)
                return NULL;

        data.build = build;
        data.n = isl_pw_aff_n_piece(pa);
        data.next = &res;
        data.dom = isl_pw_aff_domain(isl_pw_aff_copy(pa));

        if (isl_pw_aff_foreach_piece(pa, &ast_expr_from_pw_aff, &data) < 0)
                res = isl_ast_expr_free(res);
        else if (!res)
                isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid,
                        "cannot handle void expression", res = NULL);

        isl_pw_aff_free(pa);
        isl_set_free(data.dom);
        return res;
}

/* 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;

        if (isl_ast_build_need_schedule_map(build)) {
                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 "pma" to the iterator ids
 * of "build".
 *
 * The domain of "pma" is assumed to live in the internal schedule domain.
 */
static __isl_give isl_pw_multi_aff *set_iterator_names(
        __isl_keep isl_ast_build *build, __isl_take isl_pw_multi_aff *pma)
{
        int i, n;

        n = isl_pw_multi_aff_dim(pma, isl_dim_in);
        for (i = 0; i < n; ++i) {
                isl_id *id;

                id = isl_ast_build_get_iterator_id(build, i);
                pma = isl_pw_multi_aff_set_dim_id(pma, isl_dim_in, i, id);
        }

        return pma;
}

/* 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 internal schedule domain.
 */
static __isl_give isl_ast_expr *isl_ast_build_call_from_pw_multi_aff_internal(
        __isl_keep isl_ast_build *build, __isl_take isl_pw_multi_aff *pma)
{
        int i, n;
        isl_ctx *ctx;
        isl_id *id;
        isl_ast_expr *expr;

        pma = set_iterator_names(build, pma);
        if (!build || !pma)
                return isl_pw_multi_aff_free(pma);

        ctx = isl_ast_build_get_ctx(build);
        n = isl_pw_multi_aff_dim(pma, isl_dim_out);
        expr = isl_ast_expr_alloc_op(ctx, isl_ast_op_call, 1 + n);

        if (isl_pw_multi_aff_has_tuple_id(pma, isl_dim_out))
                id = isl_pw_multi_aff_get_tuple_id(pma, isl_dim_out);
        else
                id = isl_id_alloc(ctx, "", NULL);

        expr = isl_ast_expr_set_op_arg(expr, 0, isl_ast_expr_from_id(id));
        for (i = 0; i < n; ++i) {
                isl_pw_aff *pa;
                isl_ast_expr *arg;

                pa = isl_pw_multi_aff_get_pw_aff(pma, i);
                arg = isl_ast_build_expr_from_pw_aff_internal(build, pa);
                expr = isl_ast_expr_set_op_arg(expr, 1 + i, arg);
        }

        isl_pw_multi_aff_free(pma);
        return expr;
}

/* 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)
{
        int is_domain;
        isl_ast_expr *expr;
        isl_space *space_build, *space_pma;

        space_build = isl_ast_build_get_space(build, 0);
        space_pma = isl_pw_multi_aff_get_space(pma);
        is_domain = isl_space_tuple_match(space_build, isl_dim_set,
                                        space_pma, isl_dim_in);
        isl_space_free(space_build);
        isl_space_free(space_pma);
        if (is_domain < 0)
                return isl_pw_multi_aff_free(pma);
        if (!is_domain)
                isl_die(isl_ast_build_get_ctx(build), isl_error_invalid,
                        "spaces don't match",
                        return isl_pw_multi_aff_free(pma));

        if (isl_ast_build_need_schedule_map(build)) {
                isl_multi_aff *ma;
                ma = isl_ast_build_get_schedule_map_multi_aff(build);
                pma = isl_pw_multi_aff_pullback_multi_aff(pma, ma);
        }

        expr = isl_ast_build_call_from_pw_multi_aff_internal(build, pma);
        return expr;
}

/* 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_call_from_pw_multi_aff_internal(build, iteration);
        return isl_ast_node_alloc_user(expr);
}