/* Lambda matrix and vector interface.
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/* Lambda matrix and vector interface.
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Copyright (C) 2003, 2004, 2005, 2006, 2007 Free Software Foundation, Inc.
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Copyright (C) 2003, 2004, 2005, 2006, 2007 Free Software Foundation, Inc.
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Contributed by Daniel Berlin <dberlin@dberlin.org>
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Contributed by Daniel Berlin <dberlin@dberlin.org>
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This file is part of GCC.
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This file is part of GCC.
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GCC is free software; you can redistribute it and/or modify it under
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GCC is free software; you can redistribute it and/or modify it under
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the terms of the GNU General Public License as published by the Free
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the terms of the GNU General Public License as published by the Free
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Software Foundation; either version 3, or (at your option) any later
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Software Foundation; either version 3, or (at your option) any later
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version.
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version.
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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for more details.
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You should have received a copy of the GNU General Public License
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You should have received a copy of the GNU General Public License
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along with GCC; see the file COPYING3. If not see
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along with GCC; see the file COPYING3. If not see
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<http://www.gnu.org/licenses/>. */
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<http://www.gnu.org/licenses/>. */
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#ifndef LAMBDA_H
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#ifndef LAMBDA_H
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#define LAMBDA_H
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#define LAMBDA_H
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#include "vec.h"
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#include "vec.h"
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/* An integer vector. A vector formally consists of an element of a vector
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/* An integer vector. A vector formally consists of an element of a vector
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space. A vector space is a set that is closed under vector addition
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space. A vector space is a set that is closed under vector addition
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and scalar multiplication. In this vector space, an element is a list of
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and scalar multiplication. In this vector space, an element is a list of
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integers. */
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integers. */
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typedef int *lambda_vector;
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typedef int *lambda_vector;
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DEF_VEC_P(lambda_vector);
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DEF_VEC_P(lambda_vector);
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DEF_VEC_ALLOC_P(lambda_vector,heap);
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DEF_VEC_ALLOC_P(lambda_vector,heap);
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/* An integer matrix. A matrix consists of m vectors of length n (IE
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/* An integer matrix. A matrix consists of m vectors of length n (IE
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all vectors are the same length). */
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all vectors are the same length). */
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typedef lambda_vector *lambda_matrix;
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typedef lambda_vector *lambda_matrix;
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/* A transformation matrix, which is a self-contained ROWSIZE x COLSIZE
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/* A transformation matrix, which is a self-contained ROWSIZE x COLSIZE
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matrix. Rather than use floats, we simply keep a single DENOMINATOR that
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matrix. Rather than use floats, we simply keep a single DENOMINATOR that
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represents the denominator for every element in the matrix. */
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represents the denominator for every element in the matrix. */
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typedef struct
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typedef struct
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{
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{
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lambda_matrix matrix;
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lambda_matrix matrix;
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int rowsize;
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int rowsize;
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int colsize;
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int colsize;
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int denominator;
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int denominator;
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} *lambda_trans_matrix;
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} *lambda_trans_matrix;
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#define LTM_MATRIX(T) ((T)->matrix)
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#define LTM_MATRIX(T) ((T)->matrix)
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#define LTM_ROWSIZE(T) ((T)->rowsize)
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#define LTM_ROWSIZE(T) ((T)->rowsize)
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#define LTM_COLSIZE(T) ((T)->colsize)
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#define LTM_COLSIZE(T) ((T)->colsize)
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#define LTM_DENOMINATOR(T) ((T)->denominator)
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#define LTM_DENOMINATOR(T) ((T)->denominator)
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/* A vector representing a statement in the body of a loop.
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/* A vector representing a statement in the body of a loop.
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The COEFFICIENTS vector contains a coefficient for each induction variable
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The COEFFICIENTS vector contains a coefficient for each induction variable
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in the loop nest containing the statement.
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in the loop nest containing the statement.
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The DENOMINATOR represents the denominator for each coefficient in the
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The DENOMINATOR represents the denominator for each coefficient in the
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COEFFICIENT vector.
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COEFFICIENT vector.
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This structure is used during code generation in order to rewrite the old
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This structure is used during code generation in order to rewrite the old
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induction variable uses in a statement in terms of the newly created
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induction variable uses in a statement in terms of the newly created
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induction variables. */
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induction variables. */
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typedef struct
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typedef struct
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{
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{
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lambda_vector coefficients;
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lambda_vector coefficients;
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int size;
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int size;
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int denominator;
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int denominator;
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} *lambda_body_vector;
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} *lambda_body_vector;
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#define LBV_COEFFICIENTS(T) ((T)->coefficients)
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#define LBV_COEFFICIENTS(T) ((T)->coefficients)
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#define LBV_SIZE(T) ((T)->size)
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#define LBV_SIZE(T) ((T)->size)
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#define LBV_DENOMINATOR(T) ((T)->denominator)
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#define LBV_DENOMINATOR(T) ((T)->denominator)
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/* Piecewise linear expression.
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/* Piecewise linear expression.
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This structure represents a linear expression with terms for the invariants
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This structure represents a linear expression with terms for the invariants
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and induction variables of a loop.
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and induction variables of a loop.
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COEFFICIENTS is a vector of coefficients for the induction variables, one
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COEFFICIENTS is a vector of coefficients for the induction variables, one
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per loop in the loop nest.
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per loop in the loop nest.
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CONSTANT is the constant portion of the linear expression
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CONSTANT is the constant portion of the linear expression
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INVARIANT_COEFFICIENTS is a vector of coefficients for the loop invariants,
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INVARIANT_COEFFICIENTS is a vector of coefficients for the loop invariants,
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one per invariant.
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one per invariant.
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DENOMINATOR is the denominator for all of the coefficients and constants in
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DENOMINATOR is the denominator for all of the coefficients and constants in
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the expression.
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the expression.
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The linear expressions can be linked together using the NEXT field, in
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The linear expressions can be linked together using the NEXT field, in
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order to represent MAX or MIN of a group of linear expressions. */
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order to represent MAX or MIN of a group of linear expressions. */
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typedef struct lambda_linear_expression_s
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typedef struct lambda_linear_expression_s
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{
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{
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lambda_vector coefficients;
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lambda_vector coefficients;
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int constant;
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int constant;
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lambda_vector invariant_coefficients;
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lambda_vector invariant_coefficients;
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int denominator;
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int denominator;
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struct lambda_linear_expression_s *next;
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struct lambda_linear_expression_s *next;
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} *lambda_linear_expression;
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} *lambda_linear_expression;
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#define LLE_COEFFICIENTS(T) ((T)->coefficients)
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#define LLE_COEFFICIENTS(T) ((T)->coefficients)
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#define LLE_CONSTANT(T) ((T)->constant)
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#define LLE_CONSTANT(T) ((T)->constant)
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#define LLE_INVARIANT_COEFFICIENTS(T) ((T)->invariant_coefficients)
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#define LLE_INVARIANT_COEFFICIENTS(T) ((T)->invariant_coefficients)
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#define LLE_DENOMINATOR(T) ((T)->denominator)
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#define LLE_DENOMINATOR(T) ((T)->denominator)
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#define LLE_NEXT(T) ((T)->next)
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#define LLE_NEXT(T) ((T)->next)
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lambda_linear_expression lambda_linear_expression_new (int, int);
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lambda_linear_expression lambda_linear_expression_new (int, int);
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void print_lambda_linear_expression (FILE *, lambda_linear_expression, int,
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void print_lambda_linear_expression (FILE *, lambda_linear_expression, int,
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int, char);
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int, char);
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/* Loop structure. Our loop structure consists of a constant representing the
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/* Loop structure. Our loop structure consists of a constant representing the
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STEP of the loop, a set of linear expressions representing the LOWER_BOUND
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STEP of the loop, a set of linear expressions representing the LOWER_BOUND
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of the loop, a set of linear expressions representing the UPPER_BOUND of
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of the loop, a set of linear expressions representing the UPPER_BOUND of
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the loop, and a set of linear expressions representing the LINEAR_OFFSET of
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the loop, and a set of linear expressions representing the LINEAR_OFFSET of
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the loop. The linear offset is a set of linear expressions that are
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the loop. The linear offset is a set of linear expressions that are
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applied to *both* the lower bound, and the upper bound. */
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applied to *both* the lower bound, and the upper bound. */
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typedef struct lambda_loop_s
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typedef struct lambda_loop_s
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{
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{
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lambda_linear_expression lower_bound;
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lambda_linear_expression lower_bound;
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lambda_linear_expression upper_bound;
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lambda_linear_expression upper_bound;
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lambda_linear_expression linear_offset;
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lambda_linear_expression linear_offset;
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int step;
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int step;
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} *lambda_loop;
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} *lambda_loop;
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#define LL_LOWER_BOUND(T) ((T)->lower_bound)
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#define LL_LOWER_BOUND(T) ((T)->lower_bound)
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#define LL_UPPER_BOUND(T) ((T)->upper_bound)
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#define LL_UPPER_BOUND(T) ((T)->upper_bound)
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#define LL_LINEAR_OFFSET(T) ((T)->linear_offset)
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#define LL_LINEAR_OFFSET(T) ((T)->linear_offset)
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#define LL_STEP(T) ((T)->step)
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#define LL_STEP(T) ((T)->step)
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/* Loop nest structure.
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/* Loop nest structure.
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The loop nest structure consists of a set of loop structures (defined
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The loop nest structure consists of a set of loop structures (defined
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above) in LOOPS, along with an integer representing the DEPTH of the loop,
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above) in LOOPS, along with an integer representing the DEPTH of the loop,
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and an integer representing the number of INVARIANTS in the loop. Both of
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and an integer representing the number of INVARIANTS in the loop. Both of
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these integers are used to size the associated coefficient vectors in the
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these integers are used to size the associated coefficient vectors in the
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linear expression structures. */
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linear expression structures. */
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typedef struct
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typedef struct
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{
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{
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lambda_loop *loops;
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lambda_loop *loops;
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int depth;
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int depth;
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int invariants;
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int invariants;
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} *lambda_loopnest;
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} *lambda_loopnest;
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#define LN_LOOPS(T) ((T)->loops)
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#define LN_LOOPS(T) ((T)->loops)
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#define LN_DEPTH(T) ((T)->depth)
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#define LN_DEPTH(T) ((T)->depth)
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#define LN_INVARIANTS(T) ((T)->invariants)
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#define LN_INVARIANTS(T) ((T)->invariants)
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lambda_loopnest lambda_loopnest_new (int, int);
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lambda_loopnest lambda_loopnest_new (int, int);
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lambda_loopnest lambda_loopnest_transform (lambda_loopnest, lambda_trans_matrix);
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lambda_loopnest lambda_loopnest_transform (lambda_loopnest, lambda_trans_matrix);
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struct loop;
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struct loop;
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struct loops;
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struct loops;
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bool perfect_nest_p (struct loop *);
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bool perfect_nest_p (struct loop *);
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void print_lambda_loopnest (FILE *, lambda_loopnest, char);
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void print_lambda_loopnest (FILE *, lambda_loopnest, char);
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#define lambda_loop_new() (lambda_loop) ggc_alloc_cleared (sizeof (struct lambda_loop_s))
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#define lambda_loop_new() (lambda_loop) ggc_alloc_cleared (sizeof (struct lambda_loop_s))
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void print_lambda_loop (FILE *, lambda_loop, int, int, char);
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void print_lambda_loop (FILE *, lambda_loop, int, int, char);
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lambda_matrix lambda_matrix_new (int, int);
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lambda_matrix lambda_matrix_new (int, int);
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void lambda_matrix_id (lambda_matrix, int);
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void lambda_matrix_id (lambda_matrix, int);
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bool lambda_matrix_id_p (lambda_matrix, int);
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bool lambda_matrix_id_p (lambda_matrix, int);
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void lambda_matrix_copy (lambda_matrix, lambda_matrix, int, int);
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void lambda_matrix_copy (lambda_matrix, lambda_matrix, int, int);
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void lambda_matrix_negate (lambda_matrix, lambda_matrix, int, int);
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void lambda_matrix_negate (lambda_matrix, lambda_matrix, int, int);
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void lambda_matrix_transpose (lambda_matrix, lambda_matrix, int, int);
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void lambda_matrix_transpose (lambda_matrix, lambda_matrix, int, int);
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void lambda_matrix_add (lambda_matrix, lambda_matrix, lambda_matrix, int,
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void lambda_matrix_add (lambda_matrix, lambda_matrix, lambda_matrix, int,
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int);
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int);
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void lambda_matrix_add_mc (lambda_matrix, int, lambda_matrix, int,
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void lambda_matrix_add_mc (lambda_matrix, int, lambda_matrix, int,
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lambda_matrix, int, int);
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lambda_matrix, int, int);
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void lambda_matrix_mult (lambda_matrix, lambda_matrix, lambda_matrix,
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void lambda_matrix_mult (lambda_matrix, lambda_matrix, lambda_matrix,
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int, int, int);
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int, int, int);
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void lambda_matrix_delete_rows (lambda_matrix, int, int, int);
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void lambda_matrix_delete_rows (lambda_matrix, int, int, int);
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void lambda_matrix_row_exchange (lambda_matrix, int, int);
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void lambda_matrix_row_exchange (lambda_matrix, int, int);
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void lambda_matrix_row_add (lambda_matrix, int, int, int, int);
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void lambda_matrix_row_add (lambda_matrix, int, int, int, int);
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void lambda_matrix_row_negate (lambda_matrix mat, int, int);
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void lambda_matrix_row_negate (lambda_matrix mat, int, int);
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void lambda_matrix_row_mc (lambda_matrix, int, int, int);
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void lambda_matrix_row_mc (lambda_matrix, int, int, int);
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void lambda_matrix_col_exchange (lambda_matrix, int, int, int);
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void lambda_matrix_col_exchange (lambda_matrix, int, int, int);
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void lambda_matrix_col_add (lambda_matrix, int, int, int, int);
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void lambda_matrix_col_add (lambda_matrix, int, int, int, int);
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void lambda_matrix_col_negate (lambda_matrix, int, int);
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void lambda_matrix_col_negate (lambda_matrix, int, int);
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void lambda_matrix_col_mc (lambda_matrix, int, int, int);
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void lambda_matrix_col_mc (lambda_matrix, int, int, int);
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int lambda_matrix_inverse (lambda_matrix, lambda_matrix, int);
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int lambda_matrix_inverse (lambda_matrix, lambda_matrix, int);
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void lambda_matrix_hermite (lambda_matrix, int, lambda_matrix, lambda_matrix);
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void lambda_matrix_hermite (lambda_matrix, int, lambda_matrix, lambda_matrix);
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void lambda_matrix_left_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix);
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void lambda_matrix_left_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix);
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void lambda_matrix_right_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix);
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void lambda_matrix_right_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix);
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int lambda_matrix_first_nz_vec (lambda_matrix, int, int, int);
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int lambda_matrix_first_nz_vec (lambda_matrix, int, int, int);
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void lambda_matrix_project_to_null (lambda_matrix, int, int, int,
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void lambda_matrix_project_to_null (lambda_matrix, int, int, int,
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lambda_vector);
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lambda_vector);
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void print_lambda_matrix (FILE *, lambda_matrix, int, int);
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void print_lambda_matrix (FILE *, lambda_matrix, int, int);
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lambda_trans_matrix lambda_trans_matrix_new (int, int);
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lambda_trans_matrix lambda_trans_matrix_new (int, int);
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bool lambda_trans_matrix_nonsingular_p (lambda_trans_matrix);
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bool lambda_trans_matrix_nonsingular_p (lambda_trans_matrix);
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bool lambda_trans_matrix_fullrank_p (lambda_trans_matrix);
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bool lambda_trans_matrix_fullrank_p (lambda_trans_matrix);
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int lambda_trans_matrix_rank (lambda_trans_matrix);
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int lambda_trans_matrix_rank (lambda_trans_matrix);
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lambda_trans_matrix lambda_trans_matrix_basis (lambda_trans_matrix);
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lambda_trans_matrix lambda_trans_matrix_basis (lambda_trans_matrix);
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lambda_trans_matrix lambda_trans_matrix_padding (lambda_trans_matrix);
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lambda_trans_matrix lambda_trans_matrix_padding (lambda_trans_matrix);
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lambda_trans_matrix lambda_trans_matrix_inverse (lambda_trans_matrix);
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lambda_trans_matrix lambda_trans_matrix_inverse (lambda_trans_matrix);
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void print_lambda_trans_matrix (FILE *, lambda_trans_matrix);
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void print_lambda_trans_matrix (FILE *, lambda_trans_matrix);
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void lambda_matrix_vector_mult (lambda_matrix, int, int, lambda_vector,
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void lambda_matrix_vector_mult (lambda_matrix, int, int, lambda_vector,
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lambda_vector);
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lambda_vector);
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bool lambda_trans_matrix_id_p (lambda_trans_matrix);
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bool lambda_trans_matrix_id_p (lambda_trans_matrix);
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lambda_body_vector lambda_body_vector_new (int);
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lambda_body_vector lambda_body_vector_new (int);
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lambda_body_vector lambda_body_vector_compute_new (lambda_trans_matrix,
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lambda_body_vector lambda_body_vector_compute_new (lambda_trans_matrix,
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lambda_body_vector);
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lambda_body_vector);
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void print_lambda_body_vector (FILE *, lambda_body_vector);
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void print_lambda_body_vector (FILE *, lambda_body_vector);
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lambda_loopnest gcc_loopnest_to_lambda_loopnest (struct loops *,
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lambda_loopnest gcc_loopnest_to_lambda_loopnest (struct loops *,
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struct loop *,
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struct loop *,
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VEC(tree,heap) **,
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VEC(tree,heap) **,
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VEC(tree,heap) **);
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VEC(tree,heap) **);
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void lambda_loopnest_to_gcc_loopnest (struct loop *,
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void lambda_loopnest_to_gcc_loopnest (struct loop *,
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VEC(tree,heap) *, VEC(tree,heap) *,
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VEC(tree,heap) *, VEC(tree,heap) *,
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lambda_loopnest, lambda_trans_matrix);
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lambda_loopnest, lambda_trans_matrix);
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static inline void lambda_vector_negate (lambda_vector, lambda_vector, int);
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static inline void lambda_vector_negate (lambda_vector, lambda_vector, int);
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static inline void lambda_vector_mult_const (lambda_vector, lambda_vector, int, int);
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static inline void lambda_vector_mult_const (lambda_vector, lambda_vector, int, int);
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static inline void lambda_vector_add (lambda_vector, lambda_vector,
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static inline void lambda_vector_add (lambda_vector, lambda_vector,
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lambda_vector, int);
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lambda_vector, int);
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static inline void lambda_vector_add_mc (lambda_vector, int, lambda_vector, int,
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static inline void lambda_vector_add_mc (lambda_vector, int, lambda_vector, int,
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lambda_vector, int);
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lambda_vector, int);
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static inline void lambda_vector_copy (lambda_vector, lambda_vector, int);
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static inline void lambda_vector_copy (lambda_vector, lambda_vector, int);
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static inline bool lambda_vector_zerop (lambda_vector, int);
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static inline bool lambda_vector_zerop (lambda_vector, int);
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static inline void lambda_vector_clear (lambda_vector, int);
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static inline void lambda_vector_clear (lambda_vector, int);
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static inline bool lambda_vector_equal (lambda_vector, lambda_vector, int);
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static inline bool lambda_vector_equal (lambda_vector, lambda_vector, int);
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static inline int lambda_vector_min_nz (lambda_vector, int, int);
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static inline int lambda_vector_min_nz (lambda_vector, int, int);
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static inline int lambda_vector_first_nz (lambda_vector, int, int);
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static inline int lambda_vector_first_nz (lambda_vector, int, int);
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static inline void print_lambda_vector (FILE *, lambda_vector, int);
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static inline void print_lambda_vector (FILE *, lambda_vector, int);
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/* Allocate a new vector of given SIZE. */
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/* Allocate a new vector of given SIZE. */
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static inline lambda_vector
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static inline lambda_vector
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lambda_vector_new (int size)
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lambda_vector_new (int size)
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{
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{
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return GGC_CNEWVEC (int, size);
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return GGC_CNEWVEC (int, size);
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}
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}
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/* Multiply vector VEC1 of length SIZE by a constant CONST1,
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/* Multiply vector VEC1 of length SIZE by a constant CONST1,
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and store the result in VEC2. */
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and store the result in VEC2. */
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static inline void
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static inline void
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lambda_vector_mult_const (lambda_vector vec1, lambda_vector vec2,
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lambda_vector_mult_const (lambda_vector vec1, lambda_vector vec2,
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int size, int const1)
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int size, int const1)
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{
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{
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int i;
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int i;
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if (const1 == 0)
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if (const1 == 0)
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lambda_vector_clear (vec2, size);
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lambda_vector_clear (vec2, size);
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else
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else
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for (i = 0; i < size; i++)
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for (i = 0; i < size; i++)
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vec2[i] = const1 * vec1[i];
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vec2[i] = const1 * vec1[i];
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}
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}
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/* Negate vector VEC1 with length SIZE and store it in VEC2. */
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/* Negate vector VEC1 with length SIZE and store it in VEC2. */
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static inline void
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static inline void
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lambda_vector_negate (lambda_vector vec1, lambda_vector vec2,
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lambda_vector_negate (lambda_vector vec1, lambda_vector vec2,
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int size)
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int size)
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{
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{
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lambda_vector_mult_const (vec1, vec2, size, -1);
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lambda_vector_mult_const (vec1, vec2, size, -1);
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}
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}
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/* VEC3 = VEC1+VEC2, where all three the vectors are of length SIZE. */
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/* VEC3 = VEC1+VEC2, where all three the vectors are of length SIZE. */
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static inline void
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static inline void
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lambda_vector_add (lambda_vector vec1, lambda_vector vec2,
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lambda_vector_add (lambda_vector vec1, lambda_vector vec2,
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lambda_vector vec3, int size)
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lambda_vector vec3, int size)
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{
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{
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int i;
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int i;
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for (i = 0; i < size; i++)
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for (i = 0; i < size; i++)
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vec3[i] = vec1[i] + vec2[i];
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vec3[i] = vec1[i] + vec2[i];
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}
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}
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/* VEC3 = CONSTANT1*VEC1 + CONSTANT2*VEC2. All vectors have length SIZE. */
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/* VEC3 = CONSTANT1*VEC1 + CONSTANT2*VEC2. All vectors have length SIZE. */
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static inline void
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static inline void
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lambda_vector_add_mc (lambda_vector vec1, int const1,
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lambda_vector_add_mc (lambda_vector vec1, int const1,
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lambda_vector vec2, int const2,
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lambda_vector vec2, int const2,
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lambda_vector vec3, int size)
|
lambda_vector vec3, int size)
|
{
|
{
|
int i;
|
int i;
|
for (i = 0; i < size; i++)
|
for (i = 0; i < size; i++)
|
vec3[i] = const1 * vec1[i] + const2 * vec2[i];
|
vec3[i] = const1 * vec1[i] + const2 * vec2[i];
|
}
|
}
|
|
|
/* Copy the elements of vector VEC1 with length SIZE to VEC2. */
|
/* Copy the elements of vector VEC1 with length SIZE to VEC2. */
|
|
|
static inline void
|
static inline void
|
lambda_vector_copy (lambda_vector vec1, lambda_vector vec2,
|
lambda_vector_copy (lambda_vector vec1, lambda_vector vec2,
|
int size)
|
int size)
|
{
|
{
|
memcpy (vec2, vec1, size * sizeof (*vec1));
|
memcpy (vec2, vec1, size * sizeof (*vec1));
|
}
|
}
|
|
|
/* Return true if vector VEC1 of length SIZE is the zero vector. */
|
/* Return true if vector VEC1 of length SIZE is the zero vector. */
|
|
|
static inline bool
|
static inline bool
|
lambda_vector_zerop (lambda_vector vec1, int size)
|
lambda_vector_zerop (lambda_vector vec1, int size)
|
{
|
{
|
int i;
|
int i;
|
for (i = 0; i < size; i++)
|
for (i = 0; i < size; i++)
|
if (vec1[i] != 0)
|
if (vec1[i] != 0)
|
return false;
|
return false;
|
return true;
|
return true;
|
}
|
}
|
|
|
/* Clear out vector VEC1 of length SIZE. */
|
/* Clear out vector VEC1 of length SIZE. */
|
|
|
static inline void
|
static inline void
|
lambda_vector_clear (lambda_vector vec1, int size)
|
lambda_vector_clear (lambda_vector vec1, int size)
|
{
|
{
|
memset (vec1, 0, size * sizeof (*vec1));
|
memset (vec1, 0, size * sizeof (*vec1));
|
}
|
}
|
|
|
/* Return true if two vectors are equal. */
|
/* Return true if two vectors are equal. */
|
|
|
static inline bool
|
static inline bool
|
lambda_vector_equal (lambda_vector vec1, lambda_vector vec2, int size)
|
lambda_vector_equal (lambda_vector vec1, lambda_vector vec2, int size)
|
{
|
{
|
int i;
|
int i;
|
for (i = 0; i < size; i++)
|
for (i = 0; i < size; i++)
|
if (vec1[i] != vec2[i])
|
if (vec1[i] != vec2[i])
|
return false;
|
return false;
|
return true;
|
return true;
|
}
|
}
|
|
|
/* Return the minimum nonzero element in vector VEC1 between START and N.
|
/* Return the minimum nonzero element in vector VEC1 between START and N.
|
We must have START <= N. */
|
We must have START <= N. */
|
|
|
static inline int
|
static inline int
|
lambda_vector_min_nz (lambda_vector vec1, int n, int start)
|
lambda_vector_min_nz (lambda_vector vec1, int n, int start)
|
{
|
{
|
int j;
|
int j;
|
int min = -1;
|
int min = -1;
|
|
|
gcc_assert (start <= n);
|
gcc_assert (start <= n);
|
for (j = start; j < n; j++)
|
for (j = start; j < n; j++)
|
{
|
{
|
if (vec1[j])
|
if (vec1[j])
|
if (min < 0 || vec1[j] < vec1[min])
|
if (min < 0 || vec1[j] < vec1[min])
|
min = j;
|
min = j;
|
}
|
}
|
gcc_assert (min >= 0);
|
gcc_assert (min >= 0);
|
|
|
return min;
|
return min;
|
}
|
}
|
|
|
/* Return the first nonzero element of vector VEC1 between START and N.
|
/* Return the first nonzero element of vector VEC1 between START and N.
|
We must have START <= N. Returns N if VEC1 is the zero vector. */
|
We must have START <= N. Returns N if VEC1 is the zero vector. */
|
|
|
static inline int
|
static inline int
|
lambda_vector_first_nz (lambda_vector vec1, int n, int start)
|
lambda_vector_first_nz (lambda_vector vec1, int n, int start)
|
{
|
{
|
int j = start;
|
int j = start;
|
while (j < n && vec1[j] == 0)
|
while (j < n && vec1[j] == 0)
|
j++;
|
j++;
|
return j;
|
return j;
|
}
|
}
|
|
|
|
|
/* Multiply a vector by a matrix. */
|
/* Multiply a vector by a matrix. */
|
|
|
static inline void
|
static inline void
|
lambda_vector_matrix_mult (lambda_vector vect, int m, lambda_matrix mat,
|
lambda_vector_matrix_mult (lambda_vector vect, int m, lambda_matrix mat,
|
int n, lambda_vector dest)
|
int n, lambda_vector dest)
|
{
|
{
|
int i, j;
|
int i, j;
|
lambda_vector_clear (dest, n);
|
lambda_vector_clear (dest, n);
|
for (i = 0; i < n; i++)
|
for (i = 0; i < n; i++)
|
for (j = 0; j < m; j++)
|
for (j = 0; j < m; j++)
|
dest[i] += mat[j][i] * vect[j];
|
dest[i] += mat[j][i] * vect[j];
|
}
|
}
|
|
|
|
|
/* Print out a vector VEC of length N to OUTFILE. */
|
/* Print out a vector VEC of length N to OUTFILE. */
|
|
|
static inline void
|
static inline void
|
print_lambda_vector (FILE * outfile, lambda_vector vector, int n)
|
print_lambda_vector (FILE * outfile, lambda_vector vector, int n)
|
{
|
{
|
int i;
|
int i;
|
|
|
for (i = 0; i < n; i++)
|
for (i = 0; i < n; i++)
|
fprintf (outfile, "%3d ", vector[i]);
|
fprintf (outfile, "%3d ", vector[i]);
|
fprintf (outfile, "\n");
|
fprintf (outfile, "\n");
|
}
|
}
|
|
|
/* Compute the greatest common divisor of two numbers using
|
/* Compute the greatest common divisor of two numbers using
|
Euclid's algorithm. */
|
Euclid's algorithm. */
|
|
|
static inline int
|
static inline int
|
gcd (int a, int b)
|
gcd (int a, int b)
|
{
|
{
|
int x, y, z;
|
int x, y, z;
|
|
|
x = abs (a);
|
x = abs (a);
|
y = abs (b);
|
y = abs (b);
|
|
|
while (x > 0)
|
while (x > 0)
|
{
|
{
|
z = y % x;
|
z = y % x;
|
y = x;
|
y = x;
|
x = z;
|
x = z;
|
}
|
}
|
|
|
return y;
|
return y;
|
}
|
}
|
|
|
/* Compute the greatest common divisor of a VECTOR of SIZE numbers. */
|
/* Compute the greatest common divisor of a VECTOR of SIZE numbers. */
|
|
|
static inline int
|
static inline int
|
lambda_vector_gcd (lambda_vector vector, int size)
|
lambda_vector_gcd (lambda_vector vector, int size)
|
{
|
{
|
int i;
|
int i;
|
int gcd1 = 0;
|
int gcd1 = 0;
|
|
|
if (size > 0)
|
if (size > 0)
|
{
|
{
|
gcd1 = vector[0];
|
gcd1 = vector[0];
|
for (i = 1; i < size; i++)
|
for (i = 1; i < size; i++)
|
gcd1 = gcd (gcd1, vector[i]);
|
gcd1 = gcd (gcd1, vector[i]);
|
}
|
}
|
return gcd1;
|
return gcd1;
|
}
|
}
|
|
|
/* Returns true when the vector V is lexicographically positive, in
|
/* Returns true when the vector V is lexicographically positive, in
|
other words, when the first nonzero element is positive. */
|
other words, when the first nonzero element is positive. */
|
|
|
static inline bool
|
static inline bool
|
lambda_vector_lexico_pos (lambda_vector v,
|
lambda_vector_lexico_pos (lambda_vector v,
|
unsigned n)
|
unsigned n)
|
{
|
{
|
unsigned i;
|
unsigned i;
|
for (i = 0; i < n; i++)
|
for (i = 0; i < n; i++)
|
{
|
{
|
if (v[i] == 0)
|
if (v[i] == 0)
|
continue;
|
continue;
|
if (v[i] < 0)
|
if (v[i] < 0)
|
return false;
|
return false;
|
if (v[i] > 0)
|
if (v[i] > 0)
|
return true;
|
return true;
|
}
|
}
|
return true;
|
return true;
|
}
|
}
|
|
|
#endif /* LAMBDA_H */
|
#endif /* LAMBDA_H */
|
|
|
|
|
