1 /* Lambda matrix and vector interface.
2 Copyright (C) 2003, 2004, 2005, 2006, 2007 Free Software Foundation, Inc.
3 Contributed by Daniel Berlin <dberlin@dberlin.org>
5 This file is part of GCC.
7 GCC is free software; you can redistribute it and/or modify it under
8 the terms of the GNU General Public License as published by the Free
9 Software Foundation; either version 3, or (at your option) any later
12 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
13 WARRANTY; without even the implied warranty of MERCHANTABILITY or
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
17 You should have received a copy of the GNU General Public License
18 along with GCC; see the file COPYING3. If not see
19 <http://www.gnu.org/licenses/>. */
26 /* An integer vector. A vector formally consists of an element of a vector
27 space. A vector space is a set that is closed under vector addition
28 and scalar multiplication. In this vector space, an element is a list of
30 typedef int *lambda_vector;
32 DEF_VEC_P(lambda_vector);
33 DEF_VEC_ALLOC_P(lambda_vector,heap);
35 /* An integer matrix. A matrix consists of m vectors of length n (IE
36 all vectors are the same length). */
37 typedef lambda_vector *lambda_matrix;
39 /* A transformation matrix, which is a self-contained ROWSIZE x COLSIZE
40 matrix. Rather than use floats, we simply keep a single DENOMINATOR that
41 represents the denominator for every element in the matrix. */
42 typedef struct lambda_trans_matrix_s
48 } *lambda_trans_matrix;
49 #define LTM_MATRIX(T) ((T)->matrix)
50 #define LTM_ROWSIZE(T) ((T)->rowsize)
51 #define LTM_COLSIZE(T) ((T)->colsize)
52 #define LTM_DENOMINATOR(T) ((T)->denominator)
54 /* A vector representing a statement in the body of a loop.
55 The COEFFICIENTS vector contains a coefficient for each induction variable
56 in the loop nest containing the statement.
57 The DENOMINATOR represents the denominator for each coefficient in the
60 This structure is used during code generation in order to rewrite the old
61 induction variable uses in a statement in terms of the newly created
62 induction variables. */
63 typedef struct lambda_body_vector_s
65 lambda_vector coefficients;
68 } *lambda_body_vector;
69 #define LBV_COEFFICIENTS(T) ((T)->coefficients)
70 #define LBV_SIZE(T) ((T)->size)
71 #define LBV_DENOMINATOR(T) ((T)->denominator)
73 /* Piecewise linear expression.
74 This structure represents a linear expression with terms for the invariants
75 and induction variables of a loop.
76 COEFFICIENTS is a vector of coefficients for the induction variables, one
77 per loop in the loop nest.
78 CONSTANT is the constant portion of the linear expression
79 INVARIANT_COEFFICIENTS is a vector of coefficients for the loop invariants,
81 DENOMINATOR is the denominator for all of the coefficients and constants in
83 The linear expressions can be linked together using the NEXT field, in
84 order to represent MAX or MIN of a group of linear expressions. */
85 typedef struct lambda_linear_expression_s
87 lambda_vector coefficients;
89 lambda_vector invariant_coefficients;
91 struct lambda_linear_expression_s *next;
92 } *lambda_linear_expression;
94 #define LLE_COEFFICIENTS(T) ((T)->coefficients)
95 #define LLE_CONSTANT(T) ((T)->constant)
96 #define LLE_INVARIANT_COEFFICIENTS(T) ((T)->invariant_coefficients)
97 #define LLE_DENOMINATOR(T) ((T)->denominator)
98 #define LLE_NEXT(T) ((T)->next)
100 lambda_linear_expression lambda_linear_expression_new (int, int);
101 void print_lambda_linear_expression (FILE *, lambda_linear_expression, int,
104 /* Loop structure. Our loop structure consists of a constant representing the
105 STEP of the loop, a set of linear expressions representing the LOWER_BOUND
106 of the loop, a set of linear expressions representing the UPPER_BOUND of
107 the loop, and a set of linear expressions representing the LINEAR_OFFSET of
108 the loop. The linear offset is a set of linear expressions that are
109 applied to *both* the lower bound, and the upper bound. */
110 typedef struct lambda_loop_s
112 lambda_linear_expression lower_bound;
113 lambda_linear_expression upper_bound;
114 lambda_linear_expression linear_offset;
118 #define LL_LOWER_BOUND(T) ((T)->lower_bound)
119 #define LL_UPPER_BOUND(T) ((T)->upper_bound)
120 #define LL_LINEAR_OFFSET(T) ((T)->linear_offset)
121 #define LL_STEP(T) ((T)->step)
123 /* Loop nest structure.
124 The loop nest structure consists of a set of loop structures (defined
125 above) in LOOPS, along with an integer representing the DEPTH of the loop,
126 and an integer representing the number of INVARIANTS in the loop. Both of
127 these integers are used to size the associated coefficient vectors in the
128 linear expression structures. */
129 typedef struct lambda_loopnest_s
136 #define LN_LOOPS(T) ((T)->loops)
137 #define LN_DEPTH(T) ((T)->depth)
138 #define LN_INVARIANTS(T) ((T)->invariants)
140 lambda_loopnest lambda_loopnest_new (int, int);
141 lambda_loopnest lambda_loopnest_transform (lambda_loopnest, lambda_trans_matrix);
143 bool perfect_nest_p (struct loop *);
144 void print_lambda_loopnest (FILE *, lambda_loopnest, char);
146 #define lambda_loop_new() (lambda_loop) ggc_alloc_cleared (sizeof (struct lambda_loop_s))
148 void print_lambda_loop (FILE *, lambda_loop, int, int, char);
150 lambda_matrix lambda_matrix_new (int, int);
152 void lambda_matrix_id (lambda_matrix, int);
153 bool lambda_matrix_id_p (lambda_matrix, int);
154 void lambda_matrix_copy (lambda_matrix, lambda_matrix, int, int);
155 void lambda_matrix_negate (lambda_matrix, lambda_matrix, int, int);
156 void lambda_matrix_transpose (lambda_matrix, lambda_matrix, int, int);
157 void lambda_matrix_add (lambda_matrix, lambda_matrix, lambda_matrix, int,
159 void lambda_matrix_add_mc (lambda_matrix, int, lambda_matrix, int,
160 lambda_matrix, int, int);
161 void lambda_matrix_mult (lambda_matrix, lambda_matrix, lambda_matrix,
163 void lambda_matrix_delete_rows (lambda_matrix, int, int, int);
164 void lambda_matrix_row_exchange (lambda_matrix, int, int);
165 void lambda_matrix_row_add (lambda_matrix, int, int, int, int);
166 void lambda_matrix_row_negate (lambda_matrix mat, int, int);
167 void lambda_matrix_row_mc (lambda_matrix, int, int, int);
168 void lambda_matrix_col_exchange (lambda_matrix, int, int, int);
169 void lambda_matrix_col_add (lambda_matrix, int, int, int, int);
170 void lambda_matrix_col_negate (lambda_matrix, int, int);
171 void lambda_matrix_col_mc (lambda_matrix, int, int, int);
172 int lambda_matrix_inverse (lambda_matrix, lambda_matrix, int);
173 void lambda_matrix_hermite (lambda_matrix, int, lambda_matrix, lambda_matrix);
174 void lambda_matrix_left_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix);
175 void lambda_matrix_right_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix);
176 int lambda_matrix_first_nz_vec (lambda_matrix, int, int, int);
177 void lambda_matrix_project_to_null (lambda_matrix, int, int, int,
179 void print_lambda_matrix (FILE *, lambda_matrix, int, int);
181 lambda_trans_matrix lambda_trans_matrix_new (int, int);
182 bool lambda_trans_matrix_nonsingular_p (lambda_trans_matrix);
183 bool lambda_trans_matrix_fullrank_p (lambda_trans_matrix);
184 int lambda_trans_matrix_rank (lambda_trans_matrix);
185 lambda_trans_matrix lambda_trans_matrix_basis (lambda_trans_matrix);
186 lambda_trans_matrix lambda_trans_matrix_padding (lambda_trans_matrix);
187 lambda_trans_matrix lambda_trans_matrix_inverse (lambda_trans_matrix);
188 void print_lambda_trans_matrix (FILE *, lambda_trans_matrix);
189 void lambda_matrix_vector_mult (lambda_matrix, int, int, lambda_vector,
191 bool lambda_trans_matrix_id_p (lambda_trans_matrix);
193 lambda_body_vector lambda_body_vector_new (int);
194 lambda_body_vector lambda_body_vector_compute_new (lambda_trans_matrix,
196 void print_lambda_body_vector (FILE *, lambda_body_vector);
197 lambda_loopnest gcc_loopnest_to_lambda_loopnest (struct loop *,
200 void lambda_loopnest_to_gcc_loopnest (struct loop *,
201 VEC(tree,heap) *, VEC(tree,heap) *,
202 lambda_loopnest, lambda_trans_matrix);
205 static inline void lambda_vector_negate (lambda_vector, lambda_vector, int);
206 static inline void lambda_vector_mult_const (lambda_vector, lambda_vector, int, int);
207 static inline void lambda_vector_add (lambda_vector, lambda_vector,
209 static inline void lambda_vector_add_mc (lambda_vector, int, lambda_vector, int,
211 static inline void lambda_vector_copy (lambda_vector, lambda_vector, int);
212 static inline bool lambda_vector_zerop (lambda_vector, int);
213 static inline void lambda_vector_clear (lambda_vector, int);
214 static inline bool lambda_vector_equal (lambda_vector, lambda_vector, int);
215 static inline int lambda_vector_min_nz (lambda_vector, int, int);
216 static inline int lambda_vector_first_nz (lambda_vector, int, int);
217 static inline void print_lambda_vector (FILE *, lambda_vector, int);
219 /* Allocate a new vector of given SIZE. */
221 static inline lambda_vector
222 lambda_vector_new (int size)
224 return GGC_CNEWVEC (int, size);
229 /* Multiply vector VEC1 of length SIZE by a constant CONST1,
230 and store the result in VEC2. */
233 lambda_vector_mult_const (lambda_vector vec1, lambda_vector vec2,
234 int size, int const1)
239 lambda_vector_clear (vec2, size);
241 for (i = 0; i < size; i++)
242 vec2[i] = const1 * vec1[i];
245 /* Negate vector VEC1 with length SIZE and store it in VEC2. */
248 lambda_vector_negate (lambda_vector vec1, lambda_vector vec2,
251 lambda_vector_mult_const (vec1, vec2, size, -1);
254 /* VEC3 = VEC1+VEC2, where all three the vectors are of length SIZE. */
257 lambda_vector_add (lambda_vector vec1, lambda_vector vec2,
258 lambda_vector vec3, int size)
261 for (i = 0; i < size; i++)
262 vec3[i] = vec1[i] + vec2[i];
265 /* VEC3 = CONSTANT1*VEC1 + CONSTANT2*VEC2. All vectors have length SIZE. */
268 lambda_vector_add_mc (lambda_vector vec1, int const1,
269 lambda_vector vec2, int const2,
270 lambda_vector vec3, int size)
273 for (i = 0; i < size; i++)
274 vec3[i] = const1 * vec1[i] + const2 * vec2[i];
277 /* Copy the elements of vector VEC1 with length SIZE to VEC2. */
280 lambda_vector_copy (lambda_vector vec1, lambda_vector vec2,
283 memcpy (vec2, vec1, size * sizeof (*vec1));
286 /* Return true if vector VEC1 of length SIZE is the zero vector. */
289 lambda_vector_zerop (lambda_vector vec1, int size)
292 for (i = 0; i < size; i++)
298 /* Clear out vector VEC1 of length SIZE. */
301 lambda_vector_clear (lambda_vector vec1, int size)
303 memset (vec1, 0, size * sizeof (*vec1));
306 /* Return true if two vectors are equal. */
309 lambda_vector_equal (lambda_vector vec1, lambda_vector vec2, int size)
312 for (i = 0; i < size; i++)
313 if (vec1[i] != vec2[i])
318 /* Return the minimum nonzero element in vector VEC1 between START and N.
319 We must have START <= N. */
322 lambda_vector_min_nz (lambda_vector vec1, int n, int start)
327 gcc_assert (start <= n);
328 for (j = start; j < n; j++)
331 if (min < 0 || vec1[j] < vec1[min])
334 gcc_assert (min >= 0);
339 /* Return the first nonzero element of vector VEC1 between START and N.
340 We must have START <= N. Returns N if VEC1 is the zero vector. */
343 lambda_vector_first_nz (lambda_vector vec1, int n, int start)
346 while (j < n && vec1[j] == 0)
352 /* Multiply a vector by a matrix. */
355 lambda_vector_matrix_mult (lambda_vector vect, int m, lambda_matrix mat,
356 int n, lambda_vector dest)
359 lambda_vector_clear (dest, n);
360 for (i = 0; i < n; i++)
361 for (j = 0; j < m; j++)
362 dest[i] += mat[j][i] * vect[j];
366 /* Print out a vector VEC of length N to OUTFILE. */
369 print_lambda_vector (FILE * outfile, lambda_vector vector, int n)
373 for (i = 0; i < n; i++)
374 fprintf (outfile, "%3d ", vector[i]);
375 fprintf (outfile, "\n");
378 /* Compute the greatest common divisor of two numbers using
379 Euclid's algorithm. */
399 /* Compute the greatest common divisor of a VECTOR of SIZE numbers. */
402 lambda_vector_gcd (lambda_vector vector, int size)
410 for (i = 1; i < size; i++)
411 gcd1 = gcd (gcd1, vector[i]);
416 /* Returns true when the vector V is lexicographically positive, in
417 other words, when the first nonzero element is positive. */
420 lambda_vector_lexico_pos (lambda_vector v,
424 for (i = 0; i < n; i++)
436 /* Given a vector of induction variables IVS, and a vector of
437 coefficients COEFS, build a tree that is a linear combination of
438 the induction variables. */
441 build_linear_expr (tree type, lambda_vector coefs, VEC (tree, heap) *ivs)
445 tree expr = fold_convert (type, integer_zero_node);
447 for (i = 0; VEC_iterate (tree, ivs, i, iv); i++)
452 expr = fold_build2 (PLUS_EXPR, type, expr, iv);
455 expr = fold_build2 (PLUS_EXPR, type, expr,
456 fold_build2 (MULT_EXPR, type, iv,
457 build_int_cst (type, k)));
463 #endif /* LAMBDA_H */