isl_equalities.c File Reference

#include "isl_mat.h"
#include "isl_seq.h"
#include "isl_map_private.h"
#include "isl_equalities.h"

Go to the source code of this file.

Functions
static struct isl_mat *	particular_solution (struct isl_ctx *ctx, struct isl_mat *B, struct isl_vec *d)
static struct isl_mat *	parameter_compression_1 (struct isl_ctx *ctx, struct isl_mat *B, struct isl_vec *d)
static struct isl_mat *	parameter_compression_multi (struct isl_ctx *ctx, struct isl_mat *B, struct isl_vec *d)
struct isl_mat *	isl_mat_parameter_compression (struct isl_ctx *ctx, struct isl_mat *B, struct isl_vec *d)
struct isl_mat *	isl_mat_variable_compression (struct isl_ctx *ctx, struct isl_mat *B, struct isl_mat **T2)
static struct isl_basic_set *	compress_variables (struct isl_ctx *ctx, struct isl_basic_set *bset, struct isl_mat **T, struct isl_mat **T2)
struct isl_basic_set *	isl_basic_set_remove_equalities (struct isl_basic_set *bset, struct isl_mat **T, struct isl_mat **T2)
int	isl_basic_set_dim_residue_class (struct isl_basic_set *bset, int pos, isl_int *modulo, isl_int *residue)

---

Function Documentation

static struct isl_mat* particular_solution	(	struct isl_ctx *	ctx,
		struct isl_mat *	B,
		struct isl_vec *	d
	)			[static, read]

Definition at line 52 of file isl_equalities.c.

{
        int i, j;
        struct isl_mat *M = NULL;
        struct isl_mat *C = NULL;
        struct isl_mat *U = NULL;
        struct isl_mat *H = NULL;
        struct isl_mat *cst = NULL;
        struct isl_mat *T = NULL;

        M = isl_mat_alloc(ctx, B->n_row, B->n_row + B->n_col - 1);
        C = isl_mat_alloc(ctx, 1 + B->n_row, 1);
        if (!M || !C)
                goto error;
        isl_int_set_si(C->row[0][0], 1);
        for (i = 0; i < B->n_row; ++i) {
                isl_seq_clr(M->row[i], B->n_row);
                isl_int_set(M->row[i][i], d->block.data[i]);
                isl_int_neg(C->row[1 + i][0], B->row[i][0]);
                isl_int_fdiv_r(C->row[1+i][0], C->row[1+i][0], M->row[i][i]);
                for (j = 0; j < B->n_col - 1; ++j)
                        isl_int_fdiv_r(M->row[i][B->n_row + j],
                                        B->row[i][1 + j], M->row[i][i]);
        }
        M = isl_mat_left_hermite(ctx, M, 0, &U, NULL);
        if (!M || !U)
                goto error;
        H = isl_mat_sub_alloc(ctx, M->row, 0, B->n_row, 0, B->n_row);
        H = isl_mat_lin_to_aff(ctx, H);
        C = isl_mat_inverse_product(ctx, H, C);
        if (!C)
                goto error;
        for (i = 0; i < B->n_row; ++i) {
                if (!isl_int_is_divisible_by(C->row[1+i][0], C->row[0][0]))
                        break;
                isl_int_divexact(C->row[1+i][0], C->row[1+i][0], C->row[0][0]);
        }
        if (i < B->n_row)
                cst = isl_mat_alloc(ctx, B->n_row, 0);
        else
                cst = isl_mat_sub_alloc(ctx, C->row, 1, B->n_row, 0, 1);
        T = isl_mat_sub_alloc(ctx, U->row, B->n_row, B->n_col - 1, 0, B->n_row);
        cst = isl_mat_product(ctx, T, cst);
        isl_mat_free(ctx, M);
        isl_mat_free(ctx, C);
        isl_mat_free(ctx, U);
        return cst;
error:
        isl_mat_free(ctx, M);
        isl_mat_free(ctx, C);
        isl_mat_free(ctx, U);
        return NULL;
}

static struct isl_mat* parameter_compression_1	(	struct isl_ctx *	ctx,
		struct isl_mat *	B,
		struct isl_vec *	d
	)			[static, read]

Definition at line 115 of file isl_equalities.c.

{
        struct isl_mat *U;

        U = isl_mat_alloc(ctx, B->n_col - 1, B->n_col - 1);
        if (!U)
                return NULL;
        isl_seq_cpy(U->row[0], B->row[0] + 1, B->n_col - 1);
        U = isl_mat_unimodular_complete(ctx, U, 1);
        U = isl_mat_right_inverse(ctx, U);
        if (!U)
                return NULL;
        isl_mat_col_mul(U, 0, d->block.data[0], 0);
        U = isl_mat_lin_to_aff(ctx, U);
        return U;
error:
        isl_mat_free(ctx, U);
        return NULL;
}

static struct isl_mat* parameter_compression_multi	(	struct isl_ctx *	ctx,
		struct isl_mat *	B,
		struct isl_vec *	d
	)			[static, read]

Definition at line 149 of file isl_equalities.c.

{
        int i, j, k;
        int ok;
        isl_int D;
        struct isl_mat *A = NULL, *U = NULL;
        struct isl_mat *T;
        unsigned size;

        isl_int_init(D);

        isl_vec_lcm(ctx, d, &D);

        size = B->n_col - 1;
        A = isl_mat_alloc(ctx, size, B->n_row * size);
        U = isl_mat_alloc(ctx, size, size);
        if (!U || !A)
                goto error;
        for (i = 0; i < B->n_row; ++i) {
                isl_seq_cpy(U->row[0], B->row[i] + 1, size);
                U = isl_mat_unimodular_complete(ctx, U, 1);
                if (!U)
                        goto error;
                isl_int_divexact(D, D, d->block.data[i]);
                for (k = 0; k < U->n_col; ++k)
                        isl_int_mul(A->row[k][i*size+0], D, U->row[0][k]);
                isl_int_mul(D, D, d->block.data[i]);
                for (j = 1; j < U->n_row; ++j)
                        for (k = 0; k < U->n_col; ++k)
                                isl_int_mul(A->row[k][i*size+j],
                                                D, U->row[j][k]);
        }
        A = isl_mat_left_hermite(ctx, A, 0, NULL, NULL);
        T = isl_mat_sub_alloc(ctx, A->row, 0, A->n_row, 0, A->n_row);
        T = isl_mat_lin_to_aff(ctx, T);
        isl_int_set(T->row[0][0], D);
        T = isl_mat_right_inverse(ctx, T);
        isl_assert(ctx, isl_int_is_one(T->row[0][0]), goto error);
        T = isl_mat_transpose(ctx, T);
        isl_mat_free(ctx, A);
        isl_mat_free(ctx, U);

        isl_int_clear(D);
        return T;
error:
        isl_mat_free(ctx, A);
        isl_mat_free(ctx, U);
        isl_int_clear(D);
        return NULL;
}

struct isl_mat* isl_mat_parameter_compression	(	struct isl_ctx *	ctx,
		struct isl_mat *	B,
		struct isl_vec *	d
	)			[read]

Definition at line 295 of file isl_equalities.c.

{
        int i;
        struct isl_mat *cst = NULL;
        struct isl_mat *T = NULL;
        isl_int D;

        if (!B || !d)
                goto error;
        isl_assert(ctx, B->n_row == d->size, goto error);
        cst = particular_solution(ctx, B, d);
        if (!cst)
                goto error;
        if (cst->n_col == 0) {
                T = isl_mat_alloc(ctx, B->n_col, 0);
                isl_mat_free(ctx, cst);
                isl_mat_free(ctx, B);
                isl_vec_free(ctx, d);
                return T;
        }
        isl_int_init(D);
        /* Replace a*g*row = 0 mod g*m by row = 0 mod m */
        for (i = 0; i < B->n_row; ++i) {
                isl_seq_gcd(B->row[i] + 1, B->n_col - 1, &D);
                if (isl_int_is_one(D))
                        continue;
                if (isl_int_is_zero(D)) {
                        B = isl_mat_drop_rows(ctx, B, i, 1);
                        d = isl_vec_cow(ctx, d);
                        if (!B || !d)
                                goto error2;
                        isl_seq_cpy(d->block.data+i, d->block.data+i+1,
                                                        d->size - (i+1));
                        d->size--;
                        i--;
                        continue;
                }
                B = isl_mat_cow(ctx, B);
                if (!B)
                        goto error2;
                isl_seq_scale_down(B->row[i] + 1, B->row[i] + 1, D, B->n_col-1);
                isl_int_gcd(D, D, d->block.data[i]);
                d = isl_vec_cow(ctx, d);
                if (!d)
                        goto error2;
                isl_int_divexact(d->block.data[i], d->block.data[i], D);
        }
        isl_int_clear(D);
        if (B->n_row == 0)
                T = isl_mat_identity(ctx, B->n_col);
        else if (B->n_row == 1)
                T = parameter_compression_1(ctx, B, d);
        else
                T = parameter_compression_multi(ctx, B, d);
        T = isl_mat_left_hermite(ctx, T, 0, NULL, NULL);
        if (!T)
                goto error;
        isl_mat_sub_copy(ctx, T->row + 1, cst->row, cst->n_row, 0, 0, 1);
        isl_mat_free(ctx, cst);
        isl_mat_free(ctx, B);
        isl_vec_free(ctx, d);
        return T;
error2:
        isl_int_clear(D);
error:
        isl_mat_free(ctx, cst);
        isl_mat_free(ctx, B);
        isl_vec_free(ctx, d);
        return NULL;
}

struct isl_mat* isl_mat_variable_compression	(	struct isl_ctx *	ctx,
		struct isl_mat *	B,
		struct isl_mat **	T2
	)			[read]

Definition at line 408 of file isl_equalities.c.

{
        int i;
        struct isl_mat *H = NULL, *C = NULL, *H1, *U = NULL, *U1, *U2, *TC;
        unsigned dim;

        if (T2)
                *T2 = NULL;
        if (!B)
                goto error;

        dim = B->n_col - 1;
        H = isl_mat_sub_alloc(ctx, B->row, 0, B->n_row, 1, dim);
        H = isl_mat_left_hermite(ctx, H, 0, &U, T2);
        if (!H || !U || (T2 && !*T2))
                goto error;
        if (T2) {
                *T2 = isl_mat_drop_rows(ctx, *T2, 0, B->n_row);
                *T2 = isl_mat_lin_to_aff(ctx, *T2);
                if (!*T2)
                        goto error;
        }
        C = isl_mat_alloc(ctx, 1+B->n_row, 1);
        if (!C)
                goto error;
        isl_int_set_si(C->row[0][0], 1);
        isl_mat_sub_neg(ctx, C->row+1, B->row, B->n_row, 0, 0, 1);
        H1 = isl_mat_sub_alloc(ctx, H->row, 0, H->n_row, 0, H->n_row);
        H1 = isl_mat_lin_to_aff(ctx, H1);
        TC = isl_mat_inverse_product(ctx, H1, C);
        if (!TC)
                goto error;
        isl_mat_free(ctx, H);
        if (!isl_int_is_one(TC->row[0][0])) {
                for (i = 0; i < B->n_row; ++i) {
                        if (!isl_int_is_divisible_by(TC->row[1+i][0], TC->row[0][0])) {
                                isl_mat_free(ctx, B);
                                isl_mat_free(ctx, TC);
                                isl_mat_free(ctx, U);
                                if (T2) {
                                        isl_mat_free(ctx, *T2);
                                        *T2 = NULL;
                                }
                                return isl_mat_alloc(ctx, 1 + dim, 0);
                        }
                        isl_seq_scale_down(TC->row[1+i], TC->row[1+i], TC->row[0][0], 1);
                }
                isl_int_set_si(TC->row[0][0], 1);
        }
        U1 = isl_mat_sub_alloc(ctx, U->row, 0, U->n_row, 0, B->n_row);
        U1 = isl_mat_lin_to_aff(ctx, U1);
        U2 = isl_mat_sub_alloc(ctx, U->row, 0, U->n_row,
                                B->n_row, U->n_row - B->n_row);
        U2 = isl_mat_lin_to_aff(ctx, U2);
        isl_mat_free(ctx, U);
        TC = isl_mat_product(ctx, U1, TC);
        TC = isl_mat_aff_direct_sum(ctx, TC, U2);

        isl_mat_free(ctx, B);

        return TC;
error:
        isl_mat_free(ctx, B);
        isl_mat_free(ctx, H);
        isl_mat_free(ctx, U);
        if (T2) {
                isl_mat_free(ctx, *T2);
                *T2 = NULL;
        }
        return NULL;
}

static struct isl_basic_set* compress_variables	(	struct isl_ctx *	ctx,
		struct isl_basic_set *	bset,
		struct isl_mat **	T,
		struct isl_mat **	T2
	)			[static, read]

Definition at line 488 of file isl_equalities.c.

{
        struct isl_mat *B, *TC;
        unsigned dim;

        if (T)
                *T = NULL;
        if (T2)
                *T2 = NULL;
        if (!bset)
                goto error;
        isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
        isl_assert(ctx, bset->n_div == 0, goto error);
        dim = isl_basic_set_n_dim(bset);
        isl_assert(ctx, bset->n_eq <= dim, goto error);
        if (bset->n_eq == 0)
                return bset;

        B = isl_mat_sub_alloc(ctx, bset->eq, 0, bset->n_eq, 0, 1 + dim);
        TC = isl_mat_variable_compression(ctx, B, T2);
        if (!TC)
                goto error;
        if (TC->n_col == 0) {
                isl_mat_free(ctx, TC);
                if (T2) {
                        isl_mat_free(ctx, *T2);
                        *T2 = NULL;
                }
                return isl_basic_set_set_to_empty(bset);
        }

        bset = isl_basic_set_preimage(bset, T ? isl_mat_copy(ctx, TC) : TC);
        if (T)
                *T = TC;
        return bset;
error:
        isl_basic_set_free(bset);
        return NULL;
}

struct isl_basic_set* isl_basic_set_remove_equalities	(	struct isl_basic_set *	bset,
		struct isl_mat **	T,
		struct isl_mat **	T2
	)			[read]

Definition at line 529 of file isl_equalities.c.

{
        if (T)
                *T = NULL;
        if (T2)
                *T2 = NULL;
        if (!bset)
                return NULL;
        isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
        bset = isl_basic_set_gauss(bset, NULL);
        if (ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY))
                return bset;
        bset = compress_variables(bset->ctx, bset, T, T2);
        return bset;
error:
        isl_basic_set_free(bset);
        *T = NULL;
        return NULL;
}

int isl_basic_set_dim_residue_class	(	struct isl_basic_set *	bset,
		int	pos,
		isl_int *	modulo,
		isl_int *	residue
	)

Definition at line 554 of file isl_equalities.c.

{
        struct isl_ctx *ctx;
        struct isl_mat *H = NULL, *U = NULL, *C, *H1, *U1;
        unsigned total;
        unsigned nparam;

        if (!bset || !modulo || !residue)
                return -1;

        ctx = bset->ctx;
        total = isl_basic_set_total_dim(bset);
        nparam = isl_basic_set_n_param(bset);
        H = isl_mat_sub_alloc(ctx, bset->eq, 0, bset->n_eq, 1, total);
        H = isl_mat_left_hermite(ctx, H, 0, &U, NULL);
        if (!H)
                return -1;

        isl_seq_gcd(U->row[nparam + pos]+bset->n_eq,
                        total-bset->n_eq, modulo);
        if (isl_int_is_zero(*modulo) || isl_int_is_one(*modulo)) {
                isl_int_set_si(*residue, 0);
                isl_mat_free(ctx, H);
                isl_mat_free(ctx, U);
                return 0;
        }

        C = isl_mat_alloc(ctx, 1+bset->n_eq, 1);
        if (!C)
                goto error;
        isl_int_set_si(C->row[0][0], 1);
        isl_mat_sub_neg(ctx, C->row+1, bset->eq, bset->n_eq, 0, 0, 1);
        H1 = isl_mat_sub_alloc(ctx, H->row, 0, H->n_row, 0, H->n_row);
        H1 = isl_mat_lin_to_aff(ctx, H1);
        C = isl_mat_inverse_product(ctx, H1, C);
        isl_mat_free(ctx, H);
        U1 = isl_mat_sub_alloc(ctx, U->row, nparam+pos, 1, 0, bset->n_eq);
        U1 = isl_mat_lin_to_aff(ctx, U1);
        isl_mat_free(ctx, U);
        C = isl_mat_product(ctx, U1, C);
        if (!C)
                goto error;
        if (!isl_int_is_divisible_by(C->row[1][0], C->row[0][0])) {
                bset = isl_basic_set_copy(bset);
                bset = isl_basic_set_set_to_empty(bset);
                isl_basic_set_free(bset);
                isl_int_set_si(*modulo, 0);
                isl_int_set_si(*residue, 0);
                return 0;
        }
        isl_int_divexact(*residue, C->row[1][0], C->row[0][0]);
        isl_int_fdiv_r(*residue, *residue, *modulo);
        isl_mat_free(ctx, C);
        return 0;
error:
        isl_mat_free(ctx, H);
        isl_mat_free(ctx, U);
        return -1;
}