gcc/lambda.h

   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>
   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 3, 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 COPYING3.  If not see
  19 <http://www.gnu.org/licenses/>.  */
  20
  21 #ifndef LAMBDA_H
  22 #define LAMBDA_H
  23
  24 #include "vec.h"
  25
  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
  29    integers.  */
  30 typedef int *lambda_vector;
  31 DEF_VEC_P(lambda_vector);
  32 DEF_VEC_ALLOC_P(lambda_vector,heap);
  33
  34 typedef VEC(lambda_vector, heap) *lambda_vector_vec_p;
  35 DEF_VEC_P (lambda_vector_vec_p);
  36 DEF_VEC_ALLOC_P (lambda_vector_vec_p, heap);
  37
  38 /* An integer matrix.  A matrix consists of m vectors of length n (IE
  39    all vectors are the same length).  */
  40 typedef lambda_vector *lambda_matrix;
  41
  42 DEF_VEC_P (lambda_matrix);
  43 DEF_VEC_ALLOC_P (lambda_matrix, heap);
  44
  45 /* A transformation matrix, which is a self-contained ROWSIZE x COLSIZE
  46    matrix.  Rather than use floats, we simply keep a single DENOMINATOR that
  47    represents the denominator for every element in the matrix.  */
  48 typedef struct lambda_trans_matrix_s
  49 {
  50   lambda_matrix matrix;
  51   int rowsize;
  52   int colsize;
  53   int denominator;
  54 } *lambda_trans_matrix;
  55 #define LTM_MATRIX(T) ((T)->matrix)
  56 #define LTM_ROWSIZE(T) ((T)->rowsize)
  57 #define LTM_COLSIZE(T) ((T)->colsize)
  58 #define LTM_DENOMINATOR(T) ((T)->denominator)
  59
  60 /* A vector representing a statement in the body of a loop.
  61    The COEFFICIENTS vector contains a coefficient for each induction variable
  62    in the loop nest containing the statement.
  63    The DENOMINATOR represents the denominator for each coefficient in the
  64    COEFFICIENT vector.
  65
  66    This structure is used during code generation in order to rewrite the old
  67    induction variable uses in a statement in terms of the newly created
  68    induction variables.  */
  69 typedef struct lambda_body_vector_s
  70 {
  71   lambda_vector coefficients;
  72   int size;
  73   int denominator;
  74 } *lambda_body_vector;
  75 #define LBV_COEFFICIENTS(T) ((T)->coefficients)
  76 #define LBV_SIZE(T) ((T)->size)
  77 #define LBV_DENOMINATOR(T) ((T)->denominator)
  78
  79 /* Piecewise linear expression.
  80    This structure represents a linear expression with terms for the invariants
  81    and induction variables of a loop.
  82    COEFFICIENTS is a vector of coefficients for the induction variables, one
  83    per loop in the loop nest.
  84    CONSTANT is the constant portion of the linear expression
  85    INVARIANT_COEFFICIENTS is a vector of coefficients for the loop invariants,
  86    one per invariant.
  87    DENOMINATOR is the denominator for all of the coefficients and constants in
  88    the expression.
  89    The linear expressions can be linked together using the NEXT field, in
  90    order to represent MAX or MIN of a group of linear expressions.  */
  91 typedef struct lambda_linear_expression_s
  92 {
  93   lambda_vector coefficients;
  94   int constant;
  95   lambda_vector invariant_coefficients;
  96   int denominator;
  97   struct lambda_linear_expression_s *next;
  98 } *lambda_linear_expression;
  99
 100 #define LLE_COEFFICIENTS(T) ((T)->coefficients)
 101 #define LLE_CONSTANT(T) ((T)->constant)
 102 #define LLE_INVARIANT_COEFFICIENTS(T) ((T)->invariant_coefficients)
 103 #define LLE_DENOMINATOR(T) ((T)->denominator)
 104 #define LLE_NEXT(T) ((T)->next)
 105
 106 struct obstack;
 107
 108 lambda_linear_expression lambda_linear_expression_new (int, int,
 109                                                        struct obstack *);
 110 void print_lambda_linear_expression (FILE *, lambda_linear_expression, int,
 111                                      int, char);
 112
 113 /* Loop structure.  Our loop structure consists of a constant representing the
 114    STEP of the loop, a set of linear expressions representing the LOWER_BOUND
 115    of the loop, a set of linear expressions representing the UPPER_BOUND of
 116    the loop, and a set of linear expressions representing the LINEAR_OFFSET of
 117    the loop.  The linear offset is a set of linear expressions that are
 118    applied to *both* the lower bound, and the upper bound.  */
 119 typedef struct lambda_loop_s
 120 {
 121   lambda_linear_expression lower_bound;
 122   lambda_linear_expression upper_bound;
 123   lambda_linear_expression linear_offset;
 124   int step;
 125 } *lambda_loop;
 126
 127 #define LL_LOWER_BOUND(T) ((T)->lower_bound)
 128 #define LL_UPPER_BOUND(T) ((T)->upper_bound)
 129 #define LL_LINEAR_OFFSET(T) ((T)->linear_offset)
 130 #define LL_STEP(T)   ((T)->step)
 131
 132 /* Loop nest structure.
 133    The loop nest structure consists of a set of loop structures (defined
 134    above) in LOOPS, along with an integer representing the DEPTH of the loop,
 135    and an integer representing the number of INVARIANTS in the loop.  Both of
 136    these integers are used to size the associated coefficient vectors in the
 137    linear expression structures.  */
 138 typedef struct lambda_loopnest_s
 139 {
 140   lambda_loop *loops;
 141   int depth;
 142   int invariants;
 143 } *lambda_loopnest;
 144
 145 #define LN_LOOPS(T) ((T)->loops)
 146 #define LN_DEPTH(T) ((T)->depth)
 147 #define LN_INVARIANTS(T) ((T)->invariants)
 148
 149 lambda_loopnest lambda_loopnest_new (int, int, struct obstack *);
 150 lambda_loopnest lambda_loopnest_transform (lambda_loopnest,
 151                                            lambda_trans_matrix,
 152                                            struct obstack *);
 153 struct loop;
 154 bool perfect_nest_p (struct loop *);
 155 void print_lambda_loopnest (FILE *, lambda_loopnest, char);
 156
 157 #define lambda_loop_new() (lambda_loop) ggc_alloc_cleared (sizeof (struct lambda_loop_s))
 158
 159 void print_lambda_loop (FILE *, lambda_loop, int, int, char);
 160
 161 lambda_matrix lambda_matrix_new (int, int);
 162
 163 void lambda_matrix_id (lambda_matrix, int);
 164 bool lambda_matrix_id_p (lambda_matrix, int);
 165 void lambda_matrix_copy (lambda_matrix, lambda_matrix, int, int);
 166 void lambda_matrix_negate (lambda_matrix, lambda_matrix, int, int);
 167 void lambda_matrix_transpose (lambda_matrix, lambda_matrix, int, int);
 168 void lambda_matrix_add (lambda_matrix, lambda_matrix, lambda_matrix, int,
 169                         int);
 170 void lambda_matrix_add_mc (lambda_matrix, int, lambda_matrix, int,
 171                            lambda_matrix, int, int);
 172 void lambda_matrix_mult (lambda_matrix, lambda_matrix, lambda_matrix,
 173                          int, int, int);
 174 void lambda_matrix_delete_rows (lambda_matrix, int, int, int);
 175 void lambda_matrix_row_exchange (lambda_matrix, int, int);
 176 void lambda_matrix_row_add (lambda_matrix, int, int, int, int);
 177 void lambda_matrix_row_negate (lambda_matrix mat, int, int);
 178 void lambda_matrix_row_mc (lambda_matrix, int, int, int);
 179 void lambda_matrix_col_exchange (lambda_matrix, int, int, int);
 180 void lambda_matrix_col_add (lambda_matrix, int, int, int, int);
 181 void lambda_matrix_col_negate (lambda_matrix, int, int);
 182 void lambda_matrix_col_mc (lambda_matrix, int, int, int);
 183 int lambda_matrix_inverse (lambda_matrix, lambda_matrix, int);
 184 void lambda_matrix_hermite (lambda_matrix, int, lambda_matrix, lambda_matrix);
 185 void lambda_matrix_left_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix);
 186 void lambda_matrix_right_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix);
 187 int lambda_matrix_first_nz_vec (lambda_matrix, int, int, int);
 188 void lambda_matrix_project_to_null (lambda_matrix, int, int, int,
 189                                     lambda_vector);
 190 void print_lambda_matrix (FILE *, lambda_matrix, int, int);
 191
 192 lambda_trans_matrix lambda_trans_matrix_new (int, int);
 193 bool lambda_trans_matrix_nonsingular_p (lambda_trans_matrix);
 194 bool lambda_trans_matrix_fullrank_p (lambda_trans_matrix);
 195 int lambda_trans_matrix_rank (lambda_trans_matrix);
 196 lambda_trans_matrix lambda_trans_matrix_basis (lambda_trans_matrix);
 197 lambda_trans_matrix lambda_trans_matrix_padding (lambda_trans_matrix);
 198 lambda_trans_matrix lambda_trans_matrix_inverse (lambda_trans_matrix);
 199 void print_lambda_trans_matrix (FILE *, lambda_trans_matrix);
 200 void lambda_matrix_vector_mult (lambda_matrix, int, int, lambda_vector,
 201                                 lambda_vector);
 202 bool lambda_trans_matrix_id_p (lambda_trans_matrix);
 203
 204 lambda_body_vector lambda_body_vector_new (int, struct obstack *);
 205 lambda_body_vector lambda_body_vector_compute_new (lambda_trans_matrix,
 206                                                    lambda_body_vector,
 207                                                    struct obstack *);
 208 void print_lambda_body_vector (FILE *, lambda_body_vector);
 209 lambda_loopnest gcc_loopnest_to_lambda_loopnest (struct loop *,
 210                                                  VEC(tree,heap) **,
 211                                                  VEC(tree,heap) **,
 212                                                  struct obstack *);
 213 void lambda_loopnest_to_gcc_loopnest (struct loop *,
 214                                       VEC(tree,heap) *, VEC(tree,heap) *,
 215                                       VEC(gimple,heap) **,
 216                                       lambda_loopnest, lambda_trans_matrix,
 217                                       struct obstack *);
 218 void remove_iv (gimple);
 219 tree find_induction_var_from_exit_cond (struct loop *);
 220
 221 static inline void lambda_vector_negate (lambda_vector, lambda_vector, int);
 222 static inline void lambda_vector_mult_const (lambda_vector, lambda_vector, int, int);
 223 static inline void lambda_vector_add (lambda_vector, lambda_vector,
 224                                       lambda_vector, int);
 225 static inline void lambda_vector_add_mc (lambda_vector, int, lambda_vector, int,
 226                                          lambda_vector, int);
 227 static inline void lambda_vector_copy (lambda_vector, lambda_vector, int);
 228 static inline bool lambda_vector_zerop (lambda_vector, int);
 229 static inline void lambda_vector_clear (lambda_vector, int);
 230 static inline bool lambda_vector_equal (lambda_vector, lambda_vector, int);
 231 static inline int lambda_vector_min_nz (lambda_vector, int, int);
 232 static inline int lambda_vector_first_nz (lambda_vector, int, int);
 233 static inline void print_lambda_vector (FILE *, lambda_vector, int);
 234
 235 /* Allocate a new vector of given SIZE.  */
 236
 237 static inline lambda_vector
 238 lambda_vector_new (int size)
 239 {
 240   return GGC_CNEWVEC (int, size);
 241 }
 242
 243
 244
 245 /* Multiply vector VEC1 of length SIZE by a constant CONST1,
 246    and store the result in VEC2.  */
 247
 248 static inline void
 249 lambda_vector_mult_const (lambda_vector vec1, lambda_vector vec2,
 250                           int size, int const1)
 251 {
 252   int i;
 253
 254   if (const1 == 0)
 255     lambda_vector_clear (vec2, size);
 256   else
 257     for (i = 0; i < size; i++)
 258       vec2[i] = const1 * vec1[i];
 259 }
 260
 261 /* Negate vector VEC1 with length SIZE and store it in VEC2.  */
 262
 263 static inline void
 264 lambda_vector_negate (lambda_vector vec1, lambda_vector vec2,
 265                       int size)
 266 {
 267   lambda_vector_mult_const (vec1, vec2, size, -1);
 268 }
 269
 270 /* VEC3 = VEC1+VEC2, where all three the vectors are of length SIZE.  */
 271
 272 static inline void
 273 lambda_vector_add (lambda_vector vec1, lambda_vector vec2,
 274                    lambda_vector vec3, int size)
 275 {
 276   int i;
 277   for (i = 0; i < size; i++)
 278     vec3[i] = vec1[i] + vec2[i];
 279 }
 280
 281 /* VEC3 = CONSTANT1*VEC1 + CONSTANT2*VEC2.  All vectors have length SIZE.  */
 282
 283 static inline void
 284 lambda_vector_add_mc (lambda_vector vec1, int const1,
 285                       lambda_vector vec2, int const2,
 286                       lambda_vector vec3, int size)
 287 {
 288   int i;
 289   for (i = 0; i < size; i++)
 290     vec3[i] = const1 * vec1[i] + const2 * vec2[i];
 291 }
 292
 293 /* Copy the elements of vector VEC1 with length SIZE to VEC2.  */
 294
 295 static inline void
 296 lambda_vector_copy (lambda_vector vec1, lambda_vector vec2,
 297                     int size)
 298 {
 299   memcpy (vec2, vec1, size * sizeof (*vec1));
 300 }
 301
 302 /* Return true if vector VEC1 of length SIZE is the zero vector.  */
 303
 304 static inline bool
 305 lambda_vector_zerop (lambda_vector vec1, int size)
 306 {
 307   int i;
 308   for (i = 0; i < size; i++)
 309     if (vec1[i] != 0)
 310       return false;
 311   return true;
 312 }
 313
 314 /* Clear out vector VEC1 of length SIZE.  */
 315
 316 static inline void
 317 lambda_vector_clear (lambda_vector vec1, int size)
 318 {
 319   memset (vec1, 0, size * sizeof (*vec1));
 320 }
 321
 322 /* Return true if two vectors are equal.  */
 323
 324 static inline bool
 325 lambda_vector_equal (lambda_vector vec1, lambda_vector vec2, int size)
 326 {
 327   int i;
 328   for (i = 0; i < size; i++)
 329     if (vec1[i] != vec2[i])
 330       return false;
 331   return true;
 332 }
 333
 334 /* Return the minimum nonzero element in vector VEC1 between START and N.
 335    We must have START <= N.  */
 336
 337 static inline int
 338 lambda_vector_min_nz (lambda_vector vec1, int n, int start)
 339 {
 340   int j;
 341   int min = -1;
 342
 343   gcc_assert (start <= n);
 344   for (j = start; j < n; j++)
 345     {
 346       if (vec1[j])
 347         if (min < 0 || vec1[j] < vec1[min])
 348           min = j;
 349     }
 350   gcc_assert (min >= 0);
 351
 352   return min;
 353 }
 354
 355 /* Return the first nonzero element of vector VEC1 between START and N.
 356    We must have START <= N.   Returns N if VEC1 is the zero vector.  */
 357
 358 static inline int
 359 lambda_vector_first_nz (lambda_vector vec1, int n, int start)
 360 {
 361   int j = start;
 362   while (j < n && vec1[j] == 0)
 363     j++;
 364   return j;
 365 }
 366
 367
 368 /* Multiply a vector by a matrix.  */
 369
 370 static inline void
 371 lambda_vector_matrix_mult (lambda_vector vect, int m, lambda_matrix mat,
 372                            int n, lambda_vector dest)
 373 {
 374   int i, j;
 375   lambda_vector_clear (dest, n);
 376   for (i = 0; i < n; i++)
 377     for (j = 0; j < m; j++)
 378       dest[i] += mat[j][i] * vect[j];
 379 }
 380
 381 /* Compare two vectors returning an integer less than, equal to, or
 382    greater than zero if the first argument is considered to be respectively
 383    less than, equal to, or greater than the second.
 384    We use the lexicographic order.  */
 385
 386 static inline int
 387 lambda_vector_compare (lambda_vector vec1, int length1, lambda_vector vec2,
 388                        int length2)
 389 {
 390   int min_length;
 391   int i;
 392
 393   if (length1 < length2)
 394     min_length = length1;
 395   else
 396     min_length = length2;
 397
 398   for (i = 0; i < min_length; i++)
 399     if (vec1[i] < vec2[i])
 400       return -1;
 401     else if (vec1[i] > vec2[i])
 402       return 1;
 403     else
 404       continue;
 405
 406   return length1 - length2;
 407 }
 408
 409 /* Print out a vector VEC of length N to OUTFILE.  */
 410
 411 static inline void
 412 print_lambda_vector (FILE * outfile, lambda_vector vector, int n)
 413 {
 414   int i;
 415
 416   for (i = 0; i < n; i++)
 417     fprintf (outfile, "%3d ", vector[i]);
 418   fprintf (outfile, "\n");
 419 }
 420
 421 /* Compute the greatest common divisor of two numbers using
 422    Euclid's algorithm.  */
 423
 424 static inline int
 425 gcd (int a, int b)
 426 {
 427   int x, y, z;
 428
 429   x = abs (a);
 430   y = abs (b);
 431
 432   while (x > 0)
 433     {
 434       z = y % x;
 435       y = x;
 436       x = z;
 437     }
 438
 439   return y;
 440 }
 441
 442 /* Compute the greatest common divisor of a VECTOR of SIZE numbers.  */
 443
 444 static inline int
 445 lambda_vector_gcd (lambda_vector vector, int size)
 446 {
 447   int i;
 448   int gcd1 = 0;
 449
 450   if (size > 0)
 451     {
 452       gcd1 = vector[0];
 453       for (i = 1; i < size; i++)
 454         gcd1 = gcd (gcd1, vector[i]);
 455     }
 456   return gcd1;
 457 }
 458
 459 /* Returns true when the vector V is lexicographically positive, in
 460    other words, when the first nonzero element is positive.  */
 461
 462 static inline bool
 463 lambda_vector_lexico_pos (lambda_vector v,
 464                           unsigned n)
 465 {
 466   unsigned i;
 467   for (i = 0; i < n; i++)
 468     {
 469       if (v[i] == 0)
 470         continue;
 471       if (v[i] < 0)
 472         return false;
 473       if (v[i] > 0)
 474         return true;
 475     }
 476   return true;
 477 }
 478
 479 /* Given a vector of induction variables IVS, and a vector of
 480    coefficients COEFS, build a tree that is a linear combination of
 481    the induction variables.  */
 482
 483 static inline tree
 484 build_linear_expr (tree type, lambda_vector coefs, VEC (tree, heap) *ivs)
 485 {
 486   unsigned i;
 487   tree iv;
 488   tree expr = fold_convert (type, integer_zero_node);
 489
 490   for (i = 0; VEC_iterate (tree, ivs, i, iv); i++)
 491     {
 492       int k = coefs[i];
 493
 494       if (k == 1)
 495         expr = fold_build2 (PLUS_EXPR, type, expr, iv);
 496
 497       else if (k != 0)
 498         expr = fold_build2 (PLUS_EXPR, type, expr,
 499                             fold_build2 (MULT_EXPR, type, iv,
 500                                          build_int_cst (type, k)));
 501     }
 502
 503   return expr;
 504 }
 505
 506 /* Returns the dependence level for a vector DIST of size LENGTH.
 507    LEVEL = 0 means a lexicographic dependence, i.e. a dependence due
 508    to the sequence of statements, not carried by any loop.  */
 509
 510
 511 static inline unsigned
 512 dependence_level (lambda_vector dist_vect, int length)
 513 {
 514   int i;
 515
 516   for (i = 0; i < length; i++)
 517     if (dist_vect[i] != 0)
 518       return i + 1;
 519
 520   return 0;
 521 }
 522
 523 #endif /* LAMBDA_H  */