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 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
 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
 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
 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
 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
 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
 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
 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
 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
 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
 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
 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
 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
 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
 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
 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
 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