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/* Lambda matrix and vector interface.
Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009
Free Software Foundation, Inc.
Contributed by Daniel Berlin <>
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
for more details.
You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING3. If not see
<>. */
#ifndef LAMBDA_H
#define LAMBDA_H
#include "vec.h"
/* An integer vector. A vector formally consists of an element of a vector
space. A vector space is a set that is closed under vector addition
and scalar multiplication. In this vector space, an element is a list of
integers. */
typedef int *lambda_vector;
typedef VEC(lambda_vector, heap) *lambda_vector_vec_p;
DEF_VEC_P (lambda_vector_vec_p);
DEF_VEC_ALLOC_P (lambda_vector_vec_p, heap);
/* An integer matrix. A matrix consists of m vectors of length n (IE
all vectors are the same length). */
typedef lambda_vector *lambda_matrix;
DEF_VEC_P (lambda_matrix);
DEF_VEC_ALLOC_P (lambda_matrix, heap);
/* A transformation matrix, which is a self-contained ROWSIZE x COLSIZE
matrix. Rather than use floats, we simply keep a single DENOMINATOR that
represents the denominator for every element in the matrix. */
typedef struct lambda_trans_matrix_s
lambda_matrix matrix;
int rowsize;
int colsize;
int denominator;
} *lambda_trans_matrix;
#define LTM_MATRIX(T) ((T)->matrix)
#define LTM_ROWSIZE(T) ((T)->rowsize)
#define LTM_COLSIZE(T) ((T)->colsize)
#define LTM_DENOMINATOR(T) ((T)->denominator)
/* A vector representing a statement in the body of a loop.
The COEFFICIENTS vector contains a coefficient for each induction variable
in the loop nest containing the statement.
The DENOMINATOR represents the denominator for each coefficient in the
This structure is used during code generation in order to rewrite the old
induction variable uses in a statement in terms of the newly created
induction variables. */
typedef struct lambda_body_vector_s
lambda_vector coefficients;
int size;
int denominator;
} *lambda_body_vector;
#define LBV_COEFFICIENTS(T) ((T)->coefficients)
#define LBV_SIZE(T) ((T)->size)
#define LBV_DENOMINATOR(T) ((T)->denominator)
/* Piecewise linear expression.
This structure represents a linear expression with terms for the invariants
and induction variables of a loop.
COEFFICIENTS is a vector of coefficients for the induction variables, one
per loop in the loop nest.
CONSTANT is the constant portion of the linear expression
INVARIANT_COEFFICIENTS is a vector of coefficients for the loop invariants,
one per invariant.
DENOMINATOR is the denominator for all of the coefficients and constants in
the expression.
The linear expressions can be linked together using the NEXT field, in
order to represent MAX or MIN of a group of linear expressions. */
typedef struct lambda_linear_expression_s
lambda_vector coefficients;
int constant;
lambda_vector invariant_coefficients;
int denominator;
struct lambda_linear_expression_s *next;
} *lambda_linear_expression;
#define LLE_COEFFICIENTS(T) ((T)->coefficients)
#define LLE_CONSTANT(T) ((T)->constant)
#define LLE_INVARIANT_COEFFICIENTS(T) ((T)->invariant_coefficients)
#define LLE_DENOMINATOR(T) ((T)->denominator)
#define LLE_NEXT(T) ((T)->next)
struct obstack;
lambda_linear_expression lambda_linear_expression_new (int, int,
struct obstack *);
void print_lambda_linear_expression (FILE *, lambda_linear_expression, int,
int, char);
/* Loop structure. Our loop structure consists of a constant representing the
STEP of the loop, a set of linear expressions representing the LOWER_BOUND
of the loop, a set of linear expressions representing the UPPER_BOUND of
the loop, and a set of linear expressions representing the LINEAR_OFFSET of
the loop. The linear offset is a set of linear expressions that are
applied to *both* the lower bound, and the upper bound. */
typedef struct lambda_loop_s
lambda_linear_expression lower_bound;
lambda_linear_expression upper_bound;
lambda_linear_expression linear_offset;
int step;
} *lambda_loop;
#define LL_LOWER_BOUND(T) ((T)->lower_bound)
#define LL_UPPER_BOUND(T) ((T)->upper_bound)
#define LL_LINEAR_OFFSET(T) ((T)->linear_offset)
#define LL_STEP(T) ((T)->step)
/* Loop nest structure.
The loop nest structure consists of a set of loop structures (defined
above) in LOOPS, along with an integer representing the DEPTH of the loop,
and an integer representing the number of INVARIANTS in the loop. Both of
these integers are used to size the associated coefficient vectors in the
linear expression structures. */
typedef struct lambda_loopnest_s
lambda_loop *loops;
int depth;
int invariants;
} *lambda_loopnest;
#define LN_LOOPS(T) ((T)->loops)
#define LN_DEPTH(T) ((T)->depth)
#define LN_INVARIANTS(T) ((T)->invariants)
lambda_loopnest lambda_loopnest_new (int, int, struct obstack *);
lambda_loopnest lambda_loopnest_transform (lambda_loopnest,
struct obstack *);
struct loop;
bool perfect_nest_p (struct loop *);
void print_lambda_loopnest (FILE *, lambda_loopnest, char);
#define lambda_loop_new() (lambda_loop) ggc_alloc_cleared (sizeof (struct lambda_loop_s))
void print_lambda_loop (FILE *, lambda_loop, int, int, char);
lambda_matrix lambda_matrix_new (int, int);
void lambda_matrix_id (lambda_matrix, int);
bool lambda_matrix_id_p (lambda_matrix, int);
void lambda_matrix_copy (lambda_matrix, lambda_matrix, int, int);
void lambda_matrix_negate (lambda_matrix, lambda_matrix, int, int);
void lambda_matrix_transpose (lambda_matrix, lambda_matrix, int, int);
void lambda_matrix_add (lambda_matrix, lambda_matrix, lambda_matrix, int,
void lambda_matrix_add_mc (lambda_matrix, int, lambda_matrix, int,
lambda_matrix, int, int);
void lambda_matrix_mult (lambda_matrix, lambda_matrix, lambda_matrix,
int, int, int);
void lambda_matrix_delete_rows (lambda_matrix, int, int, int);
void lambda_matrix_row_exchange (lambda_matrix, int, int);
void lambda_matrix_row_add (lambda_matrix, int, int, int, int);
void lambda_matrix_row_negate (lambda_matrix mat, int, int);
void lambda_matrix_row_mc (lambda_matrix, int, int, int);
void lambda_matrix_col_exchange (lambda_matrix, int, int, int);
void lambda_matrix_col_add (lambda_matrix, int, int, int, int);
void lambda_matrix_col_negate (lambda_matrix, int, int);
void lambda_matrix_col_mc (lambda_matrix, int, int, int);
int lambda_matrix_inverse (lambda_matrix, lambda_matrix, int);
void lambda_matrix_hermite (lambda_matrix, int, lambda_matrix, lambda_matrix);
void lambda_matrix_left_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix);
void lambda_matrix_right_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix);
int lambda_matrix_first_nz_vec (lambda_matrix, int, int, int);
void lambda_matrix_project_to_null (lambda_matrix, int, int, int,
void print_lambda_matrix (FILE *, lambda_matrix, int, int);
lambda_trans_matrix lambda_trans_matrix_new (int, int);
bool lambda_trans_matrix_nonsingular_p (lambda_trans_matrix);
bool lambda_trans_matrix_fullrank_p (lambda_trans_matrix);
int lambda_trans_matrix_rank (lambda_trans_matrix);
lambda_trans_matrix lambda_trans_matrix_basis (lambda_trans_matrix);
lambda_trans_matrix lambda_trans_matrix_padding (lambda_trans_matrix);
lambda_trans_matrix lambda_trans_matrix_inverse (lambda_trans_matrix);
void print_lambda_trans_matrix (FILE *, lambda_trans_matrix);
void lambda_matrix_vector_mult (lambda_matrix, int, int, lambda_vector,
bool lambda_trans_matrix_id_p (lambda_trans_matrix);
lambda_body_vector lambda_body_vector_new (int, struct obstack *);
lambda_body_vector lambda_body_vector_compute_new (lambda_trans_matrix,
struct obstack *);
void print_lambda_body_vector (FILE *, lambda_body_vector);
lambda_loopnest gcc_loopnest_to_lambda_loopnest (struct loop *,
VEC(tree,heap) **,
VEC(tree,heap) **,
struct obstack *);
void lambda_loopnest_to_gcc_loopnest (struct loop *,
VEC(tree,heap) *, VEC(tree,heap) *,
VEC(gimple,heap) **,
lambda_loopnest, lambda_trans_matrix,
struct obstack *);
void remove_iv (gimple);
tree find_induction_var_from_exit_cond (struct loop *);
static inline void lambda_vector_negate (lambda_vector, lambda_vector, int);
static inline void lambda_vector_mult_const (lambda_vector, lambda_vector, int, int);
static inline void lambda_vector_add (lambda_vector, lambda_vector,
lambda_vector, int);
static inline void lambda_vector_add_mc (lambda_vector, int, lambda_vector, int,
lambda_vector, int);
static inline void lambda_vector_copy (lambda_vector, lambda_vector, int);
static inline bool lambda_vector_zerop (lambda_vector, int);
static inline void lambda_vector_clear (lambda_vector, int);
static inline bool lambda_vector_equal (lambda_vector, lambda_vector, int);
static inline int lambda_vector_min_nz (lambda_vector, int, int);
static inline int lambda_vector_first_nz (lambda_vector, int, int);
static inline void print_lambda_vector (FILE *, lambda_vector, int);
/* Allocate a new vector of given SIZE. */
static inline lambda_vector
lambda_vector_new (int size)
return GGC_CNEWVEC (int, size);
/* Multiply vector VEC1 of length SIZE by a constant CONST1,
and store the result in VEC2. */
static inline void
lambda_vector_mult_const (lambda_vector vec1, lambda_vector vec2,
int size, int const1)
int i;
if (const1 == 0)
lambda_vector_clear (vec2, size);
for (i = 0; i < size; i++)
vec2[i] = const1 * vec1[i];
/* Negate vector VEC1 with length SIZE and store it in VEC2. */
static inline void
lambda_vector_negate (lambda_vector vec1, lambda_vector vec2,
int size)
lambda_vector_mult_const (vec1, vec2, size, -1);
/* VEC3 = VEC1+VEC2, where all three the vectors are of length SIZE. */
static inline void
lambda_vector_add (lambda_vector vec1, lambda_vector vec2,
lambda_vector vec3, int size)
int i;
for (i = 0; i < size; i++)
vec3[i] = vec1[i] + vec2[i];
/* VEC3 = CONSTANT1*VEC1 + CONSTANT2*VEC2. All vectors have length SIZE. */
static inline void
lambda_vector_add_mc (lambda_vector vec1, int const1,
lambda_vector vec2, int const2,
lambda_vector vec3, int size)
int i;
for (i = 0; i < size; i++)
vec3[i] = const1 * vec1[i] + const2 * vec2[i];
/* Copy the elements of vector VEC1 with length SIZE to VEC2. */
static inline void
lambda_vector_copy (lambda_vector vec1, lambda_vector vec2,
int size)
memcpy (vec2, vec1, size * sizeof (*vec1));
/* Return true if vector VEC1 of length SIZE is the zero vector. */
static inline bool
lambda_vector_zerop (lambda_vector vec1, int size)
int i;
for (i = 0; i < size; i++)
if (vec1[i] != 0)
return false;
return true;
/* Clear out vector VEC1 of length SIZE. */
static inline void
lambda_vector_clear (lambda_vector vec1, int size)
memset (vec1, 0, size * sizeof (*vec1));
/* Return true if two vectors are equal. */
static inline bool
lambda_vector_equal (lambda_vector vec1, lambda_vector vec2, int size)
int i;
for (i = 0; i < size; i++)
if (vec1[i] != vec2[i])
return false;
return true;
/* Return the minimum nonzero element in vector VEC1 between START and N.
We must have START <= N. */
static inline int
lambda_vector_min_nz (lambda_vector vec1, int n, int start)
int j;
int min = -1;
gcc_assert (start <= n);
for (j = start; j < n; j++)
if (vec1[j])
if (min < 0 || vec1[j] < vec1[min])
min = j;
gcc_assert (min >= 0);
return min;
/* 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. */
static inline int
lambda_vector_first_nz (lambda_vector vec1, int n, int start)
int j = start;
while (j < n && vec1[j] == 0)
return j;
/* Multiply a vector by a matrix. */
static inline void
lambda_vector_matrix_mult (lambda_vector vect, int m, lambda_matrix mat,
int n, lambda_vector dest)
int i, j;
lambda_vector_clear (dest, n);
for (i = 0; i < n; i++)
for (j = 0; j < m; j++)
dest[i] += mat[j][i] * vect[j];
/* Compare two vectors returning an integer less than, equal to, or
greater than zero if the first argument is considered to be respectively
less than, equal to, or greater than the second.
We use the lexicographic order. */
static inline int
lambda_vector_compare (lambda_vector vec1, int length1, lambda_vector vec2,
int length2)
int min_length;
int i;
if (length1 < length2)
min_length = length1;
min_length = length2;
for (i = 0; i < min_length; i++)
if (vec1[i] < vec2[i])
return -1;
else if (vec1[i] > vec2[i])
return 1;
return length1 - length2;
/* Print out a vector VEC of length N to OUTFILE. */
static inline void
print_lambda_vector (FILE * outfile, lambda_vector vector, int n)
int i;
for (i = 0; i < n; i++)
fprintf (outfile, "%3d ", vector[i]);
fprintf (outfile, "\n");
/* Compute the greatest common divisor of two numbers using
Euclid's algorithm. */
static inline int
gcd (int a, int b)
int x, y, z;
x = abs (a);
y = abs (b);
while (x > 0)
z = y % x;
y = x;
x = z;
return y;
/* Compute the greatest common divisor of a VECTOR of SIZE numbers. */
static inline int
lambda_vector_gcd (lambda_vector vector, int size)
int i;
int gcd1 = 0;
if (size > 0)
gcd1 = vector[0];
for (i = 1; i < size; i++)
gcd1 = gcd (gcd1, vector[i]);
return gcd1;
/* Returns true when the vector V is lexicographically positive, in
other words, when the first nonzero element is positive. */
static inline bool
lambda_vector_lexico_pos (lambda_vector v,
unsigned n)
unsigned i;
for (i = 0; i < n; i++)
if (v[i] == 0)
if (v[i] < 0)
return false;
if (v[i] > 0)
return true;
return true;
/* Given a vector of induction variables IVS, and a vector of
coefficients COEFS, build a tree that is a linear combination of
the induction variables. */
static inline tree
build_linear_expr (tree type, lambda_vector coefs, VEC (tree, heap) *ivs)
unsigned i;
tree iv;
tree expr = fold_convert (type, integer_zero_node);
for (i = 0; VEC_iterate (tree, ivs, i, iv); i++)
int k = coefs[i];
if (k == 1)
expr = fold_build2 (PLUS_EXPR, type, expr, iv);
else if (k != 0)
expr = fold_build2 (PLUS_EXPR, type, expr,
fold_build2 (MULT_EXPR, type, iv,
build_int_cst (type, k)));
return expr;
/* Returns the dependence level for a vector DIST of size LENGTH.
LEVEL = 0 means a lexicographic dependence, i.e. a dependence due
to the sequence of statements, not carried by any loop. */
static inline unsigned
dependence_level (lambda_vector dist_vect, int length)
int i;
for (i = 0; i < length; i++)
if (dist_vect[i] != 0)
return i + 1;
return 0;
#endif /* LAMBDA_H */