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+/* Lambda matrix and vector interface.
+ Copyright (C) 2003, 2004, 2005, 2006 Free Software Foundation, Inc.
+ Contributed by Daniel Berlin <dberlin@dberlin.org>
+
+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 2, or (at your option) any later
+version.
+
+GCC is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or
+FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
+for more details.
+
+You should have received a copy of the GNU General Public License
+along with GCC; see the file COPYING. If not, write to the Free
+Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
+02110-1301, USA. */
+
+#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;
+
+DEF_VEC_P(lambda_vector);
+DEF_VEC_ALLOC_P(lambda_vector,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;
+
+/* 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 *);
+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,
+ 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,
+ 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,heap) **,
+ VEC(tree,heap) **);
+void lambda_loopnest_to_gcc_loopnest (struct loop *,
+ VEC(tree,heap) *, VEC(tree,heap) *,
+ 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);
+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);
+ else
+ 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)
+ j++;
+ 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];
+}
+
+
+/* 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)
+ continue;
+ if (v[i] < 0)
+ return false;
+ if (v[i] > 0)
+ return true;
+ }
+ return true;
+}
+
+#endif /* LAMBDA_H */
+