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 5This file is part of GCC. 6 7GCC is free software; you can redistribute it and/or modify it under 8the terms of the GNU General Public License as published by the Free 9Software Foundation; either version 2, or (at your option) any later 10version. 11 12GCC is distributed in the hope that it will be useful, but WITHOUT ANY 13WARRANTY; without even the implied warranty of MERCHANTABILITY or 14FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 15for more details. 16 17You should have received a copy of the GNU General Public License 18along with GCC; see the file COPYING. If not, write to the Free 19Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 2002110-1301, 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. */ 31typedef int *lambda_vector; 32 33DEF_VEC_P(lambda_vector); 34DEF_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). */ 38typedef 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. */ 43typedef 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. */ 64typedef 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. */ 86typedef 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 101lambda_linear_expression lambda_linear_expression_new (int, int); 102void 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. */ 111typedef 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. */ 130typedef 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 141lambda_loopnest lambda_loopnest_new (int, int); 142lambda_loopnest lambda_loopnest_transform (lambda_loopnest, lambda_trans_matrix); 143struct loop; 144struct loops; 145bool perfect_nest_p (struct loop *); 146void print_lambda_loopnest (FILE *, lambda_loopnest, char); 147 148#define lambda_loop_new() (lambda_loop) ggc_alloc_cleared (sizeof (struct lambda_loop_s)) 149 150void print_lambda_loop (FILE *, lambda_loop, int, int, char); 151 152lambda_matrix lambda_matrix_new (int, int); 153 154void lambda_matrix_id (lambda_matrix, int); 155bool lambda_matrix_id_p (lambda_matrix, int); 156void lambda_matrix_copy (lambda_matrix, lambda_matrix, int, int); 157void lambda_matrix_negate (lambda_matrix, lambda_matrix, int, int); 158void lambda_matrix_transpose (lambda_matrix, lambda_matrix, int, int); 159void lambda_matrix_add (lambda_matrix, lambda_matrix, lambda_matrix, int, 160 int); 161void lambda_matrix_add_mc (lambda_matrix, int, lambda_matrix, int, 162 lambda_matrix, int, int); 163void lambda_matrix_mult (lambda_matrix, lambda_matrix, lambda_matrix, 164 int, int, int); 165void lambda_matrix_delete_rows (lambda_matrix, int, int, int); 166void lambda_matrix_row_exchange (lambda_matrix, int, int); 167void lambda_matrix_row_add (lambda_matrix, int, int, int, int); 168void lambda_matrix_row_negate (lambda_matrix mat, int, int); 169void lambda_matrix_row_mc (lambda_matrix, int, int, int); 170void lambda_matrix_col_exchange (lambda_matrix, int, int, int); 171void lambda_matrix_col_add (lambda_matrix, int, int, int, int); 172void lambda_matrix_col_negate (lambda_matrix, int, int); 173void lambda_matrix_col_mc (lambda_matrix, int, int, int); 174int lambda_matrix_inverse (lambda_matrix, lambda_matrix, int); 175void lambda_matrix_hermite (lambda_matrix, int, lambda_matrix, lambda_matrix); 176void lambda_matrix_left_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix); 177void lambda_matrix_right_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix); 178int lambda_matrix_first_nz_vec (lambda_matrix, int, int, int); 179void lambda_matrix_project_to_null (lambda_matrix, int, int, int, 180 lambda_vector); 181void print_lambda_matrix (FILE *, lambda_matrix, int, int); 182 183lambda_trans_matrix lambda_trans_matrix_new (int, int); 184bool lambda_trans_matrix_nonsingular_p (lambda_trans_matrix); 185bool lambda_trans_matrix_fullrank_p (lambda_trans_matrix); 186int lambda_trans_matrix_rank (lambda_trans_matrix); 187lambda_trans_matrix lambda_trans_matrix_basis (lambda_trans_matrix); 188lambda_trans_matrix lambda_trans_matrix_padding (lambda_trans_matrix); 189lambda_trans_matrix lambda_trans_matrix_inverse (lambda_trans_matrix); 190void print_lambda_trans_matrix (FILE *, lambda_trans_matrix); 191void lambda_matrix_vector_mult (lambda_matrix, int, int, lambda_vector, 192 lambda_vector); 193bool lambda_trans_matrix_id_p (lambda_trans_matrix); 194 195lambda_body_vector lambda_body_vector_new (int); 196lambda_body_vector lambda_body_vector_compute_new (lambda_trans_matrix, 197 lambda_body_vector); 198void print_lambda_body_vector (FILE *, lambda_body_vector); 199lambda_loopnest gcc_loopnest_to_lambda_loopnest (struct loops *, 200 struct loop *, 201 VEC(tree,heap) **, 202 VEC(tree,heap) **); 203void lambda_loopnest_to_gcc_loopnest (struct loop *, 204 VEC(tree,heap) *, VEC(tree,heap) *, 205 lambda_loopnest, lambda_trans_matrix); 206 207 208static inline void lambda_vector_negate (lambda_vector, lambda_vector, int); 209static inline void lambda_vector_mult_const (lambda_vector, lambda_vector, int, int); 210static inline void lambda_vector_add (lambda_vector, lambda_vector, 211 lambda_vector, int); 212static inline void lambda_vector_add_mc (lambda_vector, int, lambda_vector, int, 213 lambda_vector, int); 214static inline void lambda_vector_copy (lambda_vector, lambda_vector, int); 215static inline bool lambda_vector_zerop (lambda_vector, int); 216static inline void lambda_vector_clear (lambda_vector, int); 217static inline bool lambda_vector_equal (lambda_vector, lambda_vector, int); 218static inline int lambda_vector_min_nz (lambda_vector, int, int); 219static inline int lambda_vector_first_nz (lambda_vector, int, int); 220static inline void print_lambda_vector (FILE *, lambda_vector, int); 221 222/* Allocate a new vector of given SIZE. */ 223 224static inline lambda_vector 225lambda_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 235static inline void 236lambda_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 250static inline void 251lambda_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 259static inline void 260lambda_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 270static inline void 271lambda_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 282static inline void 283lambda_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 291static inline bool 292lambda_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 303static inline void 304lambda_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 311static inline bool 312lambda_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 324static inline int 325lambda_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 345static inline int 346lambda_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 357static inline void 358lambda_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 371static inline void 372print_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 384static inline int 385gcd (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 404static inline int 405lambda_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 422static inline bool 423lambda_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