1 /* Lambda matrix and vector interface.
2 Copyright (C) 2003, 2004, 2005, 2006 Free Software Foundation, Inc.
3 Contributed by Daniel Berlin <dberlin@dberlin.org>
4
5 This file is part of GCC.
6
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 2, or (at your option) any later
10 version.
11
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
15 for more details.
16
17 You should have received a copy of the GNU General Public License
18 along with GCC; see the file COPYING. If not, write to the Free
19 Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
20 02110-1301, USA. */
21
22 #ifndef LAMBDA_H
23 #define LAMBDA_H
24
25 #include "vec.h"
26
27 /* An integer vector. A vector formally consists of an element of a vector
28 space. A vector space is a set that is closed under vector addition
29 and scalar multiplication. In this vector space, an element is a list of
30 integers. */
31 typedef int *lambda_vector;
32
33 DEF_VEC_P(lambda_vector);
34 DEF_VEC_ALLOC_P(lambda_vector,heap);
35
36 /* An integer matrix. A matrix consists of m vectors of length n (IE
37 all vectors are the same length). */
38 typedef lambda_vector *lambda_matrix;
39
40 /* A transformation matrix, which is a self-contained ROWSIZE x COLSIZE
41 matrix. Rather than use floats, we simply keep a single DENOMINATOR that
42 represents the denominator for every element in the matrix. */
43 typedef struct
44 {
45 lambda_matrix matrix;
46 int rowsize;
47 int colsize;
48 int denominator;
49 } *lambda_trans_matrix;
50 #define LTM_MATRIX(T) ((T)->matrix)
51 #define LTM_ROWSIZE(T) ((T)->rowsize)
52 #define LTM_COLSIZE(T) ((T)->colsize)
53 #define LTM_DENOMINATOR(T) ((T)->denominator)
54
55 /* A vector representing a statement in the body of a loop.
56 The COEFFICIENTS vector contains a coefficient for each induction variable
57 in the loop nest containing the statement.
58 The DENOMINATOR represents the denominator for each coefficient in the
59 COEFFICIENT vector.
60
61 This structure is used during code generation in order to rewrite the old
62 induction variable uses in a statement in terms of the newly created
63 induction variables. */
64 typedef struct
65 {
66 lambda_vector coefficients;
67 int size;
68 int denominator;
69 } *lambda_body_vector;
70 #define LBV_COEFFICIENTS(T) ((T)->coefficients)
71 #define LBV_SIZE(T) ((T)->size)
72 #define LBV_DENOMINATOR(T) ((T)->denominator)
73
74 /* Piecewise linear expression.
75 This structure represents a linear expression with terms for the invariants
76 and induction variables of a loop.
77 COEFFICIENTS is a vector of coefficients for the induction variables, one
78 per loop in the loop nest.
79 CONSTANT is the constant portion of the linear expression
80 INVARIANT_COEFFICIENTS is a vector of coefficients for the loop invariants,
81 one per invariant.
82 DENOMINATOR is the denominator for all of the coefficients and constants in
83 the expression.
84 The linear expressions can be linked together using the NEXT field, in
85 order to represent MAX or MIN of a group of linear expressions. */
86 typedef struct lambda_linear_expression_s
87 {
88 lambda_vector coefficients;
89 int constant;
90 lambda_vector invariant_coefficients;
91 int denominator;
92 struct lambda_linear_expression_s *next;
93 } *lambda_linear_expression;
94
95 #define LLE_COEFFICIENTS(T) ((T)->coefficients)
96 #define LLE_CONSTANT(T) ((T)->constant)
97 #define LLE_INVARIANT_COEFFICIENTS(T) ((T)->invariant_coefficients)
98 #define LLE_DENOMINATOR(T) ((T)->denominator)
99 #define LLE_NEXT(T) ((T)->next)
100
101 lambda_linear_expression lambda_linear_expression_new (int, int);
102 void print_lambda_linear_expression (FILE *, lambda_linear_expression, int,
103 int, char);
104
105 /* Loop structure. Our loop structure consists of a constant representing the
106 STEP of the loop, a set of linear expressions representing the LOWER_BOUND
107 of the loop, a set of linear expressions representing the UPPER_BOUND of
108 the loop, and a set of linear expressions representing the LINEAR_OFFSET of
109 the loop. The linear offset is a set of linear expressions that are
110 applied to *both* the lower bound, and the upper bound. */
111 typedef struct lambda_loop_s
112 {
113 lambda_linear_expression lower_bound;
114 lambda_linear_expression upper_bound;
115 lambda_linear_expression linear_offset;
116 int step;
117 } *lambda_loop;
118
119 #define LL_LOWER_BOUND(T) ((T)->lower_bound)
120 #define LL_UPPER_BOUND(T) ((T)->upper_bound)
121 #define LL_LINEAR_OFFSET(T) ((T)->linear_offset)
122 #define LL_STEP(T) ((T)->step)
123
124 /* Loop nest structure.
125 The loop nest structure consists of a set of loop structures (defined
126 above) in LOOPS, along with an integer representing the DEPTH of the loop,
127 and an integer representing the number of INVARIANTS in the loop. Both of
128 these integers are used to size the associated coefficient vectors in the
129 linear expression structures. */
130 typedef struct
131 {
132 lambda_loop *loops;
133 int depth;
134 int invariants;
135 } *lambda_loopnest;
136
137 #define LN_LOOPS(T) ((T)->loops)
138 #define LN_DEPTH(T) ((T)->depth)
139 #define LN_INVARIANTS(T) ((T)->invariants)
140
141 lambda_loopnest lambda_loopnest_new (int, int);
142 lambda_loopnest lambda_loopnest_transform (lambda_loopnest, lambda_trans_matrix);
143 struct loop;
144 struct loops;
145 bool perfect_nest_p (struct loop *);
146 void print_lambda_loopnest (FILE *, lambda_loopnest, char);
147
148 #define lambda_loop_new() (lambda_loop) ggc_alloc_cleared (sizeof (struct lambda_loop_s))
149
150 void print_lambda_loop (FILE *, lambda_loop, int, int, char);
151
152 lambda_matrix lambda_matrix_new (int, int);
153
154 void lambda_matrix_id (lambda_matrix, int);
155 bool lambda_matrix_id_p (lambda_matrix, int);
156 void lambda_matrix_copy (lambda_matrix, lambda_matrix, int, int);
157 void lambda_matrix_negate (lambda_matrix, lambda_matrix, int, int);
158 void lambda_matrix_transpose (lambda_matrix, lambda_matrix, int, int);
159 void lambda_matrix_add (lambda_matrix, lambda_matrix, lambda_matrix, int,
160 int);
161 void lambda_matrix_add_mc (lambda_matrix, int, lambda_matrix, int,
162 lambda_matrix, int, int);
163 void lambda_matrix_mult (lambda_matrix, lambda_matrix, lambda_matrix,
164 int, int, int);
165 void lambda_matrix_delete_rows (lambda_matrix, int, int, int);
166 void lambda_matrix_row_exchange (lambda_matrix, int, int);
167 void lambda_matrix_row_add (lambda_matrix, int, int, int, int);
168 void lambda_matrix_row_negate (lambda_matrix mat, int, int);
169 void lambda_matrix_row_mc (lambda_matrix, int, int, int);
170 void lambda_matrix_col_exchange (lambda_matrix, int, int, int);
171 void lambda_matrix_col_add (lambda_matrix, int, int, int, int);
172 void lambda_matrix_col_negate (lambda_matrix, int, int);
173 void lambda_matrix_col_mc (lambda_matrix, int, int, int);
174 int lambda_matrix_inverse (lambda_matrix, lambda_matrix, int);
175 void lambda_matrix_hermite (lambda_matrix, int, lambda_matrix, lambda_matrix);
176 void lambda_matrix_left_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix);
177 void lambda_matrix_right_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix);
178 int lambda_matrix_first_nz_vec (lambda_matrix, int, int, int);
179 void lambda_matrix_project_to_null (lambda_matrix, int, int, int,
180 lambda_vector);
181 void print_lambda_matrix (FILE *, lambda_matrix, int, int);
182
183 lambda_trans_matrix lambda_trans_matrix_new (int, int);
184 bool lambda_trans_matrix_nonsingular_p (lambda_trans_matrix);
185 bool lambda_trans_matrix_fullrank_p (lambda_trans_matrix);
186 int lambda_trans_matrix_rank (lambda_trans_matrix);
187 lambda_trans_matrix lambda_trans_matrix_basis (lambda_trans_matrix);
188 lambda_trans_matrix lambda_trans_matrix_padding (lambda_trans_matrix);
189 lambda_trans_matrix lambda_trans_matrix_inverse (lambda_trans_matrix);
190 void print_lambda_trans_matrix (FILE *, lambda_trans_matrix);
191 void lambda_matrix_vector_mult (lambda_matrix, int, int, lambda_vector,
192 lambda_vector);
193 bool lambda_trans_matrix_id_p (lambda_trans_matrix);
194
195 lambda_body_vector lambda_body_vector_new (int);
196 lambda_body_vector lambda_body_vector_compute_new (lambda_trans_matrix,
197 lambda_body_vector);
198 void print_lambda_body_vector (FILE *, lambda_body_vector);
199 lambda_loopnest gcc_loopnest_to_lambda_loopnest (struct loops *,
200 struct loop *,
201 VEC(tree,heap) **,
202 VEC(tree,heap) **);
203 void lambda_loopnest_to_gcc_loopnest (struct loop *,
204 VEC(tree,heap) *, VEC(tree,heap) *,
205 lambda_loopnest, lambda_trans_matrix);
206
207
208 static inline void lambda_vector_negate (lambda_vector, lambda_vector, int);
209 static inline void lambda_vector_mult_const (lambda_vector, lambda_vector, int, int);
210 static inline void lambda_vector_add (lambda_vector, lambda_vector,
211 lambda_vector, int);
212 static inline void lambda_vector_add_mc (lambda_vector, int, lambda_vector, int,
213 lambda_vector, int);
214 static inline void lambda_vector_copy (lambda_vector, lambda_vector, int);
215 static inline bool lambda_vector_zerop (lambda_vector, int);
216 static inline void lambda_vector_clear (lambda_vector, int);
217 static inline bool lambda_vector_equal (lambda_vector, lambda_vector, int);
218 static inline int lambda_vector_min_nz (lambda_vector, int, int);
219 static inline int lambda_vector_first_nz (lambda_vector, int, int);
220 static inline void print_lambda_vector (FILE *, lambda_vector, int);
221
222 /* Allocate a new vector of given SIZE. */
223
224 static inline lambda_vector
lambda_vector_new(int size)225 lambda_vector_new (int size)
226 {
227 return GGC_CNEWVEC (int, size);
228 }
229
230
231
232 /* Multiply vector VEC1 of length SIZE by a constant CONST1,
233 and store the result in VEC2. */
234
235 static inline void
lambda_vector_mult_const(lambda_vector vec1,lambda_vector vec2,int size,int const1)236 lambda_vector_mult_const (lambda_vector vec1, lambda_vector vec2,
237 int size, int const1)
238 {
239 int i;
240
241 if (const1 == 0)
242 lambda_vector_clear (vec2, size);
243 else
244 for (i = 0; i < size; i++)
245 vec2[i] = const1 * vec1[i];
246 }
247
248 /* Negate vector VEC1 with length SIZE and store it in VEC2. */
249
250 static inline void
lambda_vector_negate(lambda_vector vec1,lambda_vector vec2,int size)251 lambda_vector_negate (lambda_vector vec1, lambda_vector vec2,
252 int size)
253 {
254 lambda_vector_mult_const (vec1, vec2, size, -1);
255 }
256
257 /* VEC3 = VEC1+VEC2, where all three the vectors are of length SIZE. */
258
259 static inline void
lambda_vector_add(lambda_vector vec1,lambda_vector vec2,lambda_vector vec3,int size)260 lambda_vector_add (lambda_vector vec1, lambda_vector vec2,
261 lambda_vector vec3, int size)
262 {
263 int i;
264 for (i = 0; i < size; i++)
265 vec3[i] = vec1[i] + vec2[i];
266 }
267
268 /* VEC3 = CONSTANT1*VEC1 + CONSTANT2*VEC2. All vectors have length SIZE. */
269
270 static inline void
lambda_vector_add_mc(lambda_vector vec1,int const1,lambda_vector vec2,int const2,lambda_vector vec3,int size)271 lambda_vector_add_mc (lambda_vector vec1, int const1,
272 lambda_vector vec2, int const2,
273 lambda_vector vec3, int size)
274 {
275 int i;
276 for (i = 0; i < size; i++)
277 vec3[i] = const1 * vec1[i] + const2 * vec2[i];
278 }
279
280 /* Copy the elements of vector VEC1 with length SIZE to VEC2. */
281
282 static inline void
lambda_vector_copy(lambda_vector vec1,lambda_vector vec2,int size)283 lambda_vector_copy (lambda_vector vec1, lambda_vector vec2,
284 int size)
285 {
286 memcpy (vec2, vec1, size * sizeof (*vec1));
287 }
288
289 /* Return true if vector VEC1 of length SIZE is the zero vector. */
290
291 static inline bool
lambda_vector_zerop(lambda_vector vec1,int size)292 lambda_vector_zerop (lambda_vector vec1, int size)
293 {
294 int i;
295 for (i = 0; i < size; i++)
296 if (vec1[i] != 0)
297 return false;
298 return true;
299 }
300
301 /* Clear out vector VEC1 of length SIZE. */
302
303 static inline void
lambda_vector_clear(lambda_vector vec1,int size)304 lambda_vector_clear (lambda_vector vec1, int size)
305 {
306 memset (vec1, 0, size * sizeof (*vec1));
307 }
308
309 /* Return true if two vectors are equal. */
310
311 static inline bool
lambda_vector_equal(lambda_vector vec1,lambda_vector vec2,int size)312 lambda_vector_equal (lambda_vector vec1, lambda_vector vec2, int size)
313 {
314 int i;
315 for (i = 0; i < size; i++)
316 if (vec1[i] != vec2[i])
317 return false;
318 return true;
319 }
320
321 /* Return the minimum nonzero element in vector VEC1 between START and N.
322 We must have START <= N. */
323
324 static inline int
lambda_vector_min_nz(lambda_vector vec1,int n,int start)325 lambda_vector_min_nz (lambda_vector vec1, int n, int start)
326 {
327 int j;
328 int min = -1;
329
330 gcc_assert (start <= n);
331 for (j = start; j < n; j++)
332 {
333 if (vec1[j])
334 if (min < 0 || vec1[j] < vec1[min])
335 min = j;
336 }
337 gcc_assert (min >= 0);
338
339 return min;
340 }
341
342 /* Return the first nonzero element of vector VEC1 between START and N.
343 We must have START <= N. Returns N if VEC1 is the zero vector. */
344
345 static inline int
lambda_vector_first_nz(lambda_vector vec1,int n,int start)346 lambda_vector_first_nz (lambda_vector vec1, int n, int start)
347 {
348 int j = start;
349 while (j < n && vec1[j] == 0)
350 j++;
351 return j;
352 }
353
354
355 /* Multiply a vector by a matrix. */
356
357 static inline void
lambda_vector_matrix_mult(lambda_vector vect,int m,lambda_matrix mat,int n,lambda_vector dest)358 lambda_vector_matrix_mult (lambda_vector vect, int m, lambda_matrix mat,
359 int n, lambda_vector dest)
360 {
361 int i, j;
362 lambda_vector_clear (dest, n);
363 for (i = 0; i < n; i++)
364 for (j = 0; j < m; j++)
365 dest[i] += mat[j][i] * vect[j];
366 }
367
368
369 /* Print out a vector VEC of length N to OUTFILE. */
370
371 static inline void
print_lambda_vector(FILE * outfile,lambda_vector vector,int n)372 print_lambda_vector (FILE * outfile, lambda_vector vector, int n)
373 {
374 int i;
375
376 for (i = 0; i < n; i++)
377 fprintf (outfile, "%3d ", vector[i]);
378 fprintf (outfile, "\n");
379 }
380
381 /* Compute the greatest common divisor of two numbers using
382 Euclid's algorithm. */
383
384 static inline int
gcd(int a,int b)385 gcd (int a, int b)
386 {
387 int x, y, z;
388
389 x = abs (a);
390 y = abs (b);
391
392 while (x > 0)
393 {
394 z = y % x;
395 y = x;
396 x = z;
397 }
398
399 return y;
400 }
401
402 /* Compute the greatest common divisor of a VECTOR of SIZE numbers. */
403
404 static inline int
lambda_vector_gcd(lambda_vector vector,int size)405 lambda_vector_gcd (lambda_vector vector, int size)
406 {
407 int i;
408 int gcd1 = 0;
409
410 if (size > 0)
411 {
412 gcd1 = vector[0];
413 for (i = 1; i < size; i++)
414 gcd1 = gcd (gcd1, vector[i]);
415 }
416 return gcd1;
417 }
418
419 /* Returns true when the vector V is lexicographically positive, in
420 other words, when the first nonzero element is positive. */
421
422 static inline bool
lambda_vector_lexico_pos(lambda_vector v,unsigned n)423 lambda_vector_lexico_pos (lambda_vector v,
424 unsigned n)
425 {
426 unsigned i;
427 for (i = 0; i < n; i++)
428 {
429 if (v[i] == 0)
430 continue;
431 if (v[i] < 0)
432 return false;
433 if (v[i] > 0)
434 return true;
435 }
436 return true;
437 }
438
439 #endif /* LAMBDA_H */
440
441