gcc/lambda.h

   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 bool lambda_transform_legal_p (lambda_trans_matrix, int, varray_type);
 147 void print_lambda_loopnest (FILE *, lambda_loopnest, char);
 148
 149 #define lambda_loop_new() (lambda_loop) ggc_alloc_cleared (sizeof (struct lambda_loop_s))
 150
 151 void print_lambda_loop (FILE *, lambda_loop, int, int, char);
 152
 153 lambda_matrix lambda_matrix_new (int, int);
 154
 155 void lambda_matrix_id (lambda_matrix, int);
 156 bool lambda_matrix_id_p (lambda_matrix, int);
 157 void lambda_matrix_copy (lambda_matrix, lambda_matrix, int, int);
 158 void lambda_matrix_negate (lambda_matrix, lambda_matrix, int, int);
 159 void lambda_matrix_transpose (lambda_matrix, lambda_matrix, int, int);
 160 void lambda_matrix_add (lambda_matrix, lambda_matrix, lambda_matrix, int,
 161                         int);
 162 void lambda_matrix_add_mc (lambda_matrix, int, lambda_matrix, int,
 163                            lambda_matrix, int, int);
 164 void lambda_matrix_mult (lambda_matrix, lambda_matrix, lambda_matrix,
 165                          int, int, int);
 166 void lambda_matrix_delete_rows (lambda_matrix, int, int, int);
 167 void lambda_matrix_row_exchange (lambda_matrix, int, int);
 168 void lambda_matrix_row_add (lambda_matrix, int, int, int, int);
 169 void lambda_matrix_row_negate (lambda_matrix mat, int, int);
 170 void lambda_matrix_row_mc (lambda_matrix, int, int, int);
 171 void lambda_matrix_col_exchange (lambda_matrix, int, int, int);
 172 void lambda_matrix_col_add (lambda_matrix, int, int, int, int);
 173 void lambda_matrix_col_negate (lambda_matrix, int, int);
 174 void lambda_matrix_col_mc (lambda_matrix, int, int, int);
 175 int lambda_matrix_inverse (lambda_matrix, lambda_matrix, int);
 176 void lambda_matrix_hermite (lambda_matrix, int, lambda_matrix, lambda_matrix);
 177 void lambda_matrix_left_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix);
 178 void lambda_matrix_right_hermite (lambda_matrix, int, int, lambda_matrix, lambda_matrix);
 179 int lambda_matrix_first_nz_vec (lambda_matrix, int, int, int);
 180 void lambda_matrix_project_to_null (lambda_matrix, int, int, int,
 181                                     lambda_vector);
 182 void print_lambda_matrix (FILE *, lambda_matrix, int, int);
 183
 184 lambda_trans_matrix lambda_trans_matrix_new (int, int);
 185 bool lambda_trans_matrix_nonsingular_p (lambda_trans_matrix);
 186 bool lambda_trans_matrix_fullrank_p (lambda_trans_matrix);
 187 int lambda_trans_matrix_rank (lambda_trans_matrix);
 188 lambda_trans_matrix lambda_trans_matrix_basis (lambda_trans_matrix);
 189 lambda_trans_matrix lambda_trans_matrix_padding (lambda_trans_matrix);
 190 lambda_trans_matrix lambda_trans_matrix_inverse (lambda_trans_matrix);
 191 void print_lambda_trans_matrix (FILE *, lambda_trans_matrix);
 192 void lambda_matrix_vector_mult (lambda_matrix, int, int, lambda_vector,
 193                                 lambda_vector);
 194 bool lambda_trans_matrix_id_p (lambda_trans_matrix);
 195
 196 lambda_body_vector lambda_body_vector_new (int);
 197 lambda_body_vector lambda_body_vector_compute_new (lambda_trans_matrix,
 198                                                    lambda_body_vector);
 199 void print_lambda_body_vector (FILE *, lambda_body_vector);
 200 lambda_loopnest gcc_loopnest_to_lambda_loopnest (struct loops *,
 201                                                  struct loop *,
 202                                                  VEC(tree,heap) **,
 203                                                  VEC(tree,heap) **,
 204                                                  bool);
 205 void lambda_loopnest_to_gcc_loopnest (struct loop *,
 206                                       VEC(tree,heap) *, VEC(tree,heap) *,
 207                                       lambda_loopnest, lambda_trans_matrix);
 208
 209
 210 static inline void lambda_vector_negate (lambda_vector, lambda_vector, int);
 211 static inline void lambda_vector_mult_const (lambda_vector, lambda_vector, int, int);
 212 static inline void lambda_vector_add (lambda_vector, lambda_vector,
 213                                       lambda_vector, int);
 214 static inline void lambda_vector_add_mc (lambda_vector, int, lambda_vector, int,
 215                                          lambda_vector, int);
 216 static inline void lambda_vector_copy (lambda_vector, lambda_vector, int);
 217 static inline bool lambda_vector_zerop (lambda_vector, int);
 218 static inline void lambda_vector_clear (lambda_vector, int);
 219 static inline bool lambda_vector_equal (lambda_vector, lambda_vector, int);
 220 static inline int lambda_vector_min_nz (lambda_vector, int, int);
 221 static inline int lambda_vector_first_nz (lambda_vector, int, int);
 222 static inline void print_lambda_vector (FILE *, lambda_vector, int);
 223
 224 /* Allocate a new vector of given SIZE.  */
 225
 226 static inline lambda_vector
 227 lambda_vector_new (int size)
 228 {
 229   return GGC_CNEWVEC (int, size);
 230 }
 231
 232
 233
 234 /* Multiply vector VEC1 of length SIZE by a constant CONST1,
 235    and store the result in VEC2.  */
 236
 237 static inline void
 238 lambda_vector_mult_const (lambda_vector vec1, lambda_vector vec2,
 239                           int size, int const1)
 240 {
 241   int i;
 242
 243   if (const1 == 0)
 244     lambda_vector_clear (vec2, size);
 245   else
 246     for (i = 0; i < size; i++)
 247       vec2[i] = const1 * vec1[i];
 248 }
 249
 250 /* Negate vector VEC1 with length SIZE and store it in VEC2.  */
 251
 252 static inline void
 253 lambda_vector_negate (lambda_vector vec1, lambda_vector vec2,
 254                       int size)
 255 {
 256   lambda_vector_mult_const (vec1, vec2, size, -1);
 257 }
 258
 259 /* VEC3 = VEC1+VEC2, where all three the vectors are of length SIZE.  */
 260
 261 static inline void
 262 lambda_vector_add (lambda_vector vec1, lambda_vector vec2,
 263                    lambda_vector vec3, int size)
 264 {
 265   int i;
 266   for (i = 0; i < size; i++)
 267     vec3[i] = vec1[i] + vec2[i];
 268 }
 269
 270 /* VEC3 = CONSTANT1*VEC1 + CONSTANT2*VEC2.  All vectors have length SIZE.  */
 271
 272 static inline void
 273 lambda_vector_add_mc (lambda_vector vec1, int const1,
 274                       lambda_vector vec2, int const2,
 275                       lambda_vector vec3, int size)
 276 {
 277   int i;
 278   for (i = 0; i < size; i++)
 279     vec3[i] = const1 * vec1[i] + const2 * vec2[i];
 280 }
 281
 282 /* Copy the elements of vector VEC1 with length SIZE to VEC2.  */
 283
 284 static inline void
 285 lambda_vector_copy (lambda_vector vec1, lambda_vector vec2,
 286                     int size)
 287 {
 288   memcpy (vec2, vec1, size * sizeof (*vec1));
 289 }
 290
 291 /* Return true if vector VEC1 of length SIZE is the zero vector.  */
 292
 293 static inline bool
 294 lambda_vector_zerop (lambda_vector vec1, int size)
 295 {
 296   int i;
 297   for (i = 0; i < size; i++)
 298     if (vec1[i] != 0)
 299       return false;
 300   return true;
 301 }
 302
 303 /* Clear out vector VEC1 of length SIZE.  */
 304
 305 static inline void
 306 lambda_vector_clear (lambda_vector vec1, int size)
 307 {
 308   memset (vec1, 0, size * sizeof (*vec1));
 309 }
 310
 311 /* Return true if two vectors are equal.  */
 312
 313 static inline bool
 314 lambda_vector_equal (lambda_vector vec1, lambda_vector vec2, int size)
 315 {
 316   int i;
 317   for (i = 0; i < size; i++)
 318     if (vec1[i] != vec2[i])
 319       return false;
 320   return true;
 321 }
 322
 323 /* Return the minimum nonzero element in vector VEC1 between START and N.
 324    We must have START <= N.  */
 325
 326 static inline int
 327 lambda_vector_min_nz (lambda_vector vec1, int n, int start)
 328 {
 329   int j;
 330   int min = -1;
 331
 332   gcc_assert (start <= n);
 333   for (j = start; j < n; j++)
 334     {
 335       if (vec1[j])
 336         if (min < 0 || vec1[j] < vec1[min])
 337           min = j;
 338     }
 339   gcc_assert (min >= 0);
 340
 341   return min;
 342 }
 343
 344 /* Return the first nonzero element of vector VEC1 between START and N.
 345    We must have START <= N.   Returns N if VEC1 is the zero vector.  */
 346
 347 static inline int
 348 lambda_vector_first_nz (lambda_vector vec1, int n, int start)
 349 {
 350   int j = start;
 351   while (j < n && vec1[j] == 0)
 352     j++;
 353   return j;
 354 }
 355
 356
 357 /* Multiply a vector by a matrix.  */
 358
 359 static inline void
 360 lambda_vector_matrix_mult (lambda_vector vect, int m, lambda_matrix mat,
 361                            int n, lambda_vector dest)
 362 {
 363   int i, j;
 364   lambda_vector_clear (dest, n);
 365   for (i = 0; i < n; i++)
 366     for (j = 0; j < m; j++)
 367       dest[i] += mat[j][i] * vect[j];
 368 }
 369
 370
 371 /* Print out a vector VEC of length N to OUTFILE.  */
 372
 373 static inline void
 374 print_lambda_vector (FILE * outfile, lambda_vector vector, int n)
 375 {
 376   int i;
 377
 378   for (i = 0; i < n; i++)
 379     fprintf (outfile, "%3d ", vector[i]);
 380   fprintf (outfile, "\n");
 381 }
 382
 383 /* Compute the greatest common divisor of two numbers using
 384    Euclid's algorithm.  */
 385
 386 static inline int
 387 gcd (int a, int b)
 388 {
 389   int x, y, z;
 390
 391   x = abs (a);
 392   y = abs (b);
 393
 394   while (x > 0)
 395     {
 396       z = y % x;
 397       y = x;
 398       x = z;
 399     }
 400
 401   return y;
 402 }
 403
 404 /* Compute the greatest common divisor of a VECTOR of SIZE numbers.  */
 405
 406 static inline int
 407 lambda_vector_gcd (lambda_vector vector, int size)
 408 {
 409   int i;
 410   int gcd1 = 0;
 411
 412   if (size > 0)
 413     {
 414       gcd1 = vector[0];
 415       for (i = 1; i < size; i++)
 416         gcd1 = gcd (gcd1, vector[i]);
 417     }
 418   return gcd1;
 419 }
 420
 421 /* Returns true when the vector V is lexicographically positive, in
 422    other words, when the first nonzero element is positive.  */
 423
 424 static inline bool
 425 lambda_vector_lexico_pos (lambda_vector v,
 426                           unsigned n)
 427 {
 428   unsigned i;
 429   for (i = 0; i < n; i++)
 430     {
 431       if (v[i] == 0)
 432         continue;
 433       if (v[i] < 0)
 434         return false;
 435       if (v[i] > 0)
 436         return true;
 437     }
 438   return true;
 439 }
 440
 441 #endif /* LAMBDA_H  */
 442