#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;
+
/* An integer matrix. A matrix consists of m vectors of length n (IE
all vectors are the same length). */
typedef lambda_vector *lambda_matrix;
+/* 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_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
+ COEFFICIENT vector.
+
+ 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_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)
+
+lambda_linear_expression lambda_linear_expression_new (int, int);
+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_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);
+lambda_loopnest lambda_loopnest_transform (lambda_loopnest, lambda_trans_matrix);
+struct loop;
+struct loops;
+bool perfect_nest_p (struct loop *);
+bool lambda_transform_legal_p (lambda_trans_matrix, int, varray_type);
+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);
lambda_vector);
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,
lambda_vector);
+bool lambda_trans_matrix_id_p (lambda_trans_matrix);
+
+lambda_body_vector lambda_body_vector_new (int);
+lambda_body_vector lambda_body_vector_compute_new (lambda_trans_matrix,
+ lambda_body_vector);
+void print_lambda_body_vector (FILE *, lambda_body_vector);
+lambda_loopnest gcc_loopnest_to_lambda_loopnest (struct loops *,
+ struct loop *,
+ VEC(tree) **,
+ VEC(tree) **,
+ bool);
+void lambda_loopnest_to_gcc_loopnest (struct loop *, VEC(tree) *,
+ VEC(tree) *,
+ lambda_loopnest,
+ lambda_trans_matrix);
+
static inline void lambda_vector_negate (lambda_vector, lambda_vector, int);
static inline void lambda_vector_mult_const (lambda_vector, lambda_vector, int, int);
return true;
}
-/* Return the minimum non-zero 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. */
static inline int
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