gcc/tree-ssa-math-opts.c

   1 /* Global, SSA-based optimizations using mathematical identities.
   2    Copyright (C) 2005 Free Software Foundation, Inc.
   3
   4 This file is part of GCC.
   5
   6 GCC is free software; you can redistribute it and/or modify it
   7 under the terms of the GNU General Public License as published by the
   8 Free Software Foundation; either version 2, or (at your option) any
   9 later version.
  10
  11 GCC is distributed in the hope that it will be useful, but WITHOUT
  12 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  13 FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  14 for more details.
  15
  16 You should have received a copy of the GNU General Public License
  17 along with GCC; see the file COPYING.  If not, write to the Free
  18 Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
  19 02110-1301, USA.  */
  20
  21 /* Currently, the only mini-pass in this file tries to CSE reciprocal
  22    operations.  These are common in sequences such as this one:
  23
  24         modulus = sqrt(x*x + y*y + z*z);
  25         x = x / modulus;
  26         y = y / modulus;
  27         z = z / modulus;
  28
  29    that can be optimized to
  30
  31         modulus = sqrt(x*x + y*y + z*z);
  32         rmodulus = 1.0 / modulus;
  33         x = x * rmodulus;
  34         y = y * rmodulus;
  35         z = z * rmodulus;
  36
  37    We do this for loop invariant divisors, and with this pass whenever
  38    we notice that a division has the same divisor multiple times.
  39
  40    Of course, like in PRE, we don't insert a division if a dominator
  41    already has one.  However, this cannot be done as an extension of
  42    PRE for several reasons.
  43
  44    First of all, with some experiments it was found out that the
  45    transformation is not always useful if there are only two divisions
  46    hy the same divisor.  This is probably because modern processors
  47    can pipeline the divisions; on older, in-order processors it should
  48    still be effective to optimize two divisions by the same number.
  49    We make this a param, and it shall be called N in the remainder of
  50    this comment.
  51
  52    Second, if trapping math is active, we have less freedom on where
  53    to insert divisions: we can only do so in basic blocks that already
  54    contain one.  (If divisions don't trap, instead, we can insert
  55    divisions elsewhere, which will be in blocks that are common dominators
  56    of those that have the division).
  57
  58    We really don't want to compute the reciprocal unless a division will
  59    be found.  To do this, we won't insert the division in a basic block
  60    that has less than N divisions *post-dominating* it.
  61
  62    The algorithm constructs a subset of the dominator tree, holding the
  63    blocks containing the divisions and the common dominators to them,
  64    and walk it twice.  The first walk is in post-order, and it annotates
  65    each block with the number of divisions that post-dominate it: this
  66    gives information on where divisions can be inserted profitably.
  67    The second walk is in pre-order, and it inserts divisions as explained
  68    above, and replaces divisions by multiplications.
  69
  70    In the best case, the cost of the pass is O(n_statements).  In the
  71    worst-case, the cost is due to creating the dominator tree subset,
  72    with a cost of O(n_basic_blocks ^ 2); however this can only happen
  73    for n_statements / n_basic_blocks statements.  So, the amortized cost
  74    of creating the dominator tree subset is O(n_basic_blocks) and the
  75    worst-case cost of the pass is O(n_statements * n_basic_blocks).
  76
  77    More practically, the cost will be small because there are few
  78    divisions, and they tend to be in the same basic block, so insert_bb
  79    is called very few times.
  80
  81    If we did this using domwalk.c, an efficient implementation would have
  82    to work on all the variables in a single pass, because we could not
  83    work on just a subset of the dominator tree, as we do now, and the
  84    cost would also be something like O(n_statements * n_basic_blocks).
  85    The data structures would be more complex in order to work on all the
  86    variables in a single pass.  */
  87
  88 #include "config.h"
  89 #include "system.h"
  90 #include "coretypes.h"
  91 #include "tm.h"
  92 #include "flags.h"
  93 #include "tree.h"
  94 #include "tree-flow.h"
  95 #include "real.h"
  96 #include "timevar.h"
  97 #include "tree-pass.h"
  98 #include "alloc-pool.h"
  99 #include "basic-block.h"
 100 #include "target.h"
 101
 102
 103 /* This structure represents one basic block that either computes a
 104    division, or is a common dominator for basic block that compute a
 105    division.  */
 106 struct occurrence {
 107   /* The basic block represented by this structure.  */
 108   basic_block bb;
 109
 110   /* If non-NULL, the SSA_NAME holding the definition for a reciprocal
 111      inserted in BB.  */
 112   tree recip_def;
 113
 114   /* If non-NULL, the MODIFY_EXPR for a reciprocal computation that
 115      was inserted in BB.  */
 116   tree recip_def_stmt;
 117
 118   /* Pointer to a list of "struct occurrence"s for blocks dominated
 119      by BB.  */
 120   struct occurrence *children;
 121
 122   /* Pointer to the next "struct occurrence"s in the list of blocks
 123      sharing a common dominator.  */
 124   struct occurrence *next;
 125
 126   /* The number of divisions that are in BB before compute_merit.  The
 127      number of divisions that are in BB or post-dominate it after
 128      compute_merit.  */
 129   int num_divisions;
 130
 131   /* True if the basic block has a division, false if it is a common
 132      dominator for basic blocks that do.  If it is false and trapping
 133      math is active, BB is not a candidate for inserting a reciprocal.  */
 134   bool bb_has_division;
 135 };
 136
 137
 138 /* The instance of "struct occurrence" representing the highest
 139    interesting block in the dominator tree.  */
 140 static struct occurrence *occ_head;
 141
 142 /* Allocation pool for getting instances of "struct occurrence".  */
 143 static alloc_pool occ_pool;
 144
 145
 146
 147 /* Allocate and return a new struct occurrence for basic block BB, and
 148    whose children list is headed by CHILDREN.  */
 149 static struct occurrence *
 150 occ_new (basic_block bb, struct occurrence *children)
 151 {
 152   struct occurrence *occ;
 153
 154   occ = bb->aux = pool_alloc (occ_pool);
 155   memset (occ, 0, sizeof (struct occurrence));
 156
 157   occ->bb = bb;
 158   occ->children = children;
 159   return occ;
 160 }
 161
 162
 163 /* Insert NEW_OCC into our subset of the dominator tree.  P_HEAD points to a
 164    list of "struct occurrence"s, one per basic block, having IDOM as
 165    their common dominator.
 166
 167    We try to insert NEW_OCC as deep as possible in the tree, and we also
 168    insert any other block that is a common dominator for BB and one
 169    block already in the tree.  */
 170
 171 static void
 172 insert_bb (struct occurrence *new_occ, basic_block idom,
 173            struct occurrence **p_head)
 174 {
 175   struct occurrence *occ, **p_occ;
 176
 177   for (p_occ = p_head; (occ = *p_occ) != NULL; )
 178     {
 179       basic_block bb = new_occ->bb, occ_bb = occ->bb;
 180       basic_block dom = nearest_common_dominator (CDI_DOMINATORS, occ_bb, bb);
 181       if (dom == bb)
 182         {
 183           /* BB dominates OCC_BB.  OCC becomes NEW_OCC's child: remove OCC
 184              from its list.  */
 185           *p_occ = occ->next;
 186           occ->next = new_occ->children;
 187           new_occ->children = occ;
 188
 189           /* Try the next block (it may as well be dominated by BB).  */
 190         }
 191
 192       else if (dom == occ_bb)
 193         {
 194           /* OCC_BB dominates BB.  Tail recurse to look deeper.  */
 195           insert_bb (new_occ, dom, &occ->children);
 196           return;
 197         }
 198
 199       else if (dom != idom)
 200         {
 201           gcc_assert (!dom->aux);
 202
 203           /* There is a dominator between IDOM and BB, add it and make
 204              two children out of NEW_OCC and OCC.  First, remove OCC from
 205              its list.  */
 206           *p_occ = occ->next;
 207           new_occ->next = occ;
 208           occ->next = NULL;
 209
 210           /* None of the previous blocks has DOM as a dominator: if we tail
 211              recursed, we would reexamine them uselessly. Just switch BB with
 212              DOM, and go on looking for blocks dominated by DOM.  */
 213           new_occ = occ_new (dom, new_occ);
 214         }
 215
 216       else
 217         {
 218           /* Nothing special, go on with the next element.  */
 219           p_occ = &occ->next;
 220         }
 221     }
 222
 223   /* No place was found as a child of IDOM.  Make BB a sibling of IDOM.  */
 224   new_occ->next = *p_head;
 225   *p_head = new_occ;
 226 }
 227
 228 /* Register that we found a division in BB.  */
 229
 230 static inline void
 231 register_division_in (basic_block bb)
 232 {
 233   struct occurrence *occ;
 234
 235   occ = (struct occurrence *) bb->aux;
 236   if (!occ)
 237     {
 238       occ = occ_new (bb, NULL);
 239       insert_bb (occ, ENTRY_BLOCK_PTR, &occ_head);
 240     }
 241
 242   occ->bb_has_division = true;
 243   occ->num_divisions++;
 244 }
 245
 246
 247 /* Compute the number of divisions that postdominate each block in OCC and
 248    its children.  */
 249
 250 static void
 251 compute_merit (struct occurrence *occ)
 252 {
 253   struct occurrence *occ_child;
 254   basic_block dom = occ->bb;
 255
 256   for (occ_child = occ->children; occ_child; occ_child = occ_child->next)
 257     {
 258       basic_block bb;
 259       if (occ_child->children)
 260         compute_merit (occ_child);
 261
 262       if (flag_exceptions)
 263         bb = single_noncomplex_succ (dom);
 264       else
 265         bb = dom;
 266
 267       if (dominated_by_p (CDI_POST_DOMINATORS, bb, occ_child->bb))
 268         occ->num_divisions += occ_child->num_divisions;
 269     }
 270 }
 271
 272
 273 /* Return whether USE_STMT is a floating-point division by DEF.  */
 274 static inline bool
 275 is_division_by (tree use_stmt, tree def)
 276 {
 277   return TREE_CODE (use_stmt) == MODIFY_EXPR
 278          && TREE_CODE (TREE_OPERAND (use_stmt, 1)) == RDIV_EXPR
 279          && TREE_OPERAND (TREE_OPERAND (use_stmt, 1), 1) == def;
 280 }
 281
 282 /* Return the LHS of a RDIV_EXPR that computes a reciprocal in type TYPE.  */
 283 static tree
 284 get_constant_one (tree type)
 285 {
 286   tree scalar, cst;
 287   int i;
 288
 289   gcc_assert (FLOAT_TYPE_P (type));
 290   switch (TREE_CODE (type))
 291     {
 292     case REAL_TYPE:
 293       return build_real (type, dconst1);
 294
 295     case VECTOR_TYPE:
 296       scalar = build_real (TREE_TYPE (type), dconst1);
 297
 298       /* Create 'vect_cst_ = {cst,cst,...,cst}'  */
 299       cst = NULL_TREE;
 300       for (i = TYPE_VECTOR_SUBPARTS (type); --i >= 0; )
 301         cst = tree_cons (NULL_TREE, scalar, cst);
 302
 303       return build_vector (type, cst);
 304
 305     default:
 306       /* Complex operations have been split already.  */
 307       gcc_unreachable ();
 308     }
 309 }
 310
 311 /* Walk the subset of the dominator tree rooted at OCC, setting the
 312    RECIP_DEF field to a definition of 1.0 / DEF that can be used in
 313    the given basic block.  The field may be left NULL, of course,
 314    if it is not possible or profitable to do the optimization.
 315
 316    DEF_BSI is an iterator pointing at the statement defining DEF.
 317    If RECIP_DEF is set, a dominator already has a computation that can
 318    be used.  */
 319
 320 static void
 321 insert_reciprocals (block_stmt_iterator *def_bsi, struct occurrence *occ,
 322                     tree def, tree recip_def, int threshold)
 323 {
 324   tree type, new_stmt;
 325   block_stmt_iterator bsi;
 326   struct occurrence *occ_child;
 327
 328   if (!recip_def
 329       && (occ->bb_has_division || !flag_trapping_math)
 330       && occ->num_divisions >= threshold)
 331     {
 332       /* Make a variable with the replacement and substitute it.  */
 333       type = TREE_TYPE (def);
 334       recip_def = make_rename_temp (type, "reciptmp");
 335       new_stmt = build2 (MODIFY_EXPR, void_type_node, recip_def,
 336                          fold_build2 (RDIV_EXPR, type, get_constant_one (type),
 337                                       def));
 338
 339
 340       if (occ->bb_has_division)
 341         {
 342           /* Case 1: insert before an existing division.  */
 343           bsi = bsi_after_labels (occ->bb);
 344           while (!bsi_end_p (bsi) && !is_division_by (bsi_stmt (bsi), def))
 345             bsi_next (&bsi);
 346
 347           bsi_insert_before (&bsi, new_stmt, BSI_SAME_STMT);
 348         }
 349       else if (def_bsi && occ->bb == def_bsi->bb)
 350         {
 351           /* Case 2: insert right after the definition.  Note that this will
 352              never happen if the definition statement can throw, because in
 353              that case the sole successor of the statement's basic block will
 354              dominate all the uses as well.  */
 355           bsi_insert_after (def_bsi, new_stmt, BSI_NEW_STMT);
 356         }
 357       else
 358         {
 359           /* Case 3: insert in a basic block not containing defs/uses.  */
 360           bsi = bsi_after_labels (occ->bb);
 361           bsi_insert_before (&bsi, new_stmt, BSI_SAME_STMT);
 362         }
 363
 364       occ->recip_def_stmt = new_stmt;
 365     }
 366
 367   occ->recip_def = recip_def;
 368   for (occ_child = occ->children; occ_child; occ_child = occ_child->next)
 369     insert_reciprocals (def_bsi, occ_child, def, recip_def, threshold);
 370 }
 371
 372
 373 /* Replace the division at USE_P with a multiplication by the reciprocal, if
 374    possible.  */
 375
 376 static inline void
 377 replace_reciprocal (use_operand_p use_p)
 378 {
 379   tree use_stmt = USE_STMT (use_p);
 380   basic_block bb = bb_for_stmt (use_stmt);
 381   struct occurrence *occ = (struct occurrence *) bb->aux;
 382
 383   if (occ->recip_def && use_stmt != occ->recip_def_stmt)
 384     {
 385       TREE_SET_CODE (TREE_OPERAND (use_stmt, 1), MULT_EXPR);
 386       SET_USE (use_p, occ->recip_def);
 387       fold_stmt_inplace (use_stmt);
 388       update_stmt (use_stmt);
 389     }
 390 }
 391
 392
 393 /* Free OCC and return one more "struct occurrence" to be freed.  */
 394
 395 static struct occurrence *
 396 free_bb (struct occurrence *occ)
 397 {
 398   struct occurrence *child, *next;
 399
 400   /* First get the two pointers hanging off OCC.  */
 401   next = occ->next;
 402   child = occ->children;
 403   occ->bb->aux = NULL;
 404   pool_free (occ_pool, occ);
 405
 406   /* Now ensure that we don't recurse unless it is necessary.  */
 407   if (!child)
 408     return next;
 409   else
 410     {
 411       while (next)
 412         next = free_bb (next);
 413
 414       return child;
 415     }
 416 }
 417
 418
 419 /* Look for floating-point divisions among DEF's uses, and try to
 420    replace them by multiplications with the reciprocal.  Add
 421    as many statements computing the reciprocal as needed.
 422
 423    DEF must be a GIMPLE register of a floating-point type.  */
 424
 425 static void
 426 execute_cse_reciprocals_1 (block_stmt_iterator *def_bsi, tree def)
 427 {
 428   use_operand_p use_p;
 429   imm_use_iterator use_iter;
 430   struct occurrence *occ;
 431   int count = 0, threshold;
 432
 433   gcc_assert (FLOAT_TYPE_P (TREE_TYPE (def)) && is_gimple_reg (def));
 434
 435   FOR_EACH_IMM_USE_FAST (use_p, use_iter, def)
 436     {
 437       tree use_stmt = USE_STMT (use_p);
 438       if (is_division_by (use_stmt, def))
 439         {
 440           register_division_in (bb_for_stmt (use_stmt));
 441           count++;
 442         }
 443     }
 444
 445   /* Do the expensive part only if we can hope to optimize something.  */
 446   threshold = targetm.min_divisions_for_recip_mul (TYPE_MODE (TREE_TYPE (def)));
 447   if (count >= threshold)
 448     {
 449       tree use_stmt;
 450       for (occ = occ_head; occ; occ = occ->next)
 451         {
 452           compute_merit (occ);
 453           insert_reciprocals (def_bsi, occ, def, NULL, threshold);
 454         }
 455
 456       FOR_EACH_IMM_USE_STMT (use_stmt, use_iter, def)
 457         {
 458           if (is_division_by (use_stmt, def))
 459             {
 460               FOR_EACH_IMM_USE_ON_STMT (use_p, use_iter)
 461                 replace_reciprocal (use_p);
 462             }
 463         }
 464     }
 465
 466   for (occ = occ_head; occ; )
 467     occ = free_bb (occ);
 468
 469   occ_head = NULL;
 470 }
 471
 472
 473 static bool
 474 gate_cse_reciprocals (void)
 475 {
 476   return optimize && !optimize_size && flag_unsafe_math_optimizations;
 477 }
 478
 479
 480 /* Go through all the floating-point SSA_NAMEs, and call
 481    execute_cse_reciprocals_1 on each of them.  */
 482 static unsigned int
 483 execute_cse_reciprocals (void)
 484 {
 485   basic_block bb;
 486   tree arg;
 487
 488   occ_pool = create_alloc_pool ("dominators for recip",
 489                                 sizeof (struct occurrence),
 490                                 n_basic_blocks / 3 + 1);
 491
 492   calculate_dominance_info (CDI_DOMINATORS | CDI_POST_DOMINATORS);
 493
 494 #ifdef ENABLE_CHECKING
 495   FOR_EACH_BB (bb)
 496     gcc_assert (!bb->aux);
 497 #endif
 498
 499   for (arg = DECL_ARGUMENTS (cfun->decl); arg; arg = TREE_CHAIN (arg))
 500     if (default_def (arg)
 501         && FLOAT_TYPE_P (TREE_TYPE (arg))
 502         && is_gimple_reg (arg))
 503       execute_cse_reciprocals_1 (NULL, default_def (arg));
 504
 505   FOR_EACH_BB (bb)
 506     {
 507       block_stmt_iterator bsi;
 508       tree phi, def;
 509
 510       for (phi = phi_nodes (bb); phi; phi = PHI_CHAIN (phi))
 511         {
 512           def = PHI_RESULT (phi);
 513           if (FLOAT_TYPE_P (TREE_TYPE (def))
 514               && is_gimple_reg (def))
 515             execute_cse_reciprocals_1 (NULL, def);
 516         }
 517
 518       for (bsi = bsi_after_labels (bb); !bsi_end_p (bsi); bsi_next (&bsi))
 519         {
 520           tree stmt = bsi_stmt (bsi);
 521           if (TREE_CODE (stmt) == MODIFY_EXPR
 522               && (def = SINGLE_SSA_TREE_OPERAND (stmt, SSA_OP_DEF)) != NULL
 523               && FLOAT_TYPE_P (TREE_TYPE (def))
 524               && TREE_CODE (def) == SSA_NAME)
 525             execute_cse_reciprocals_1 (&bsi, def);
 526         }
 527     }
 528
 529   free_dominance_info (CDI_DOMINATORS | CDI_POST_DOMINATORS);
 530   free_alloc_pool (occ_pool);
 531   return 0;
 532 }
 533
 534 struct tree_opt_pass pass_cse_reciprocals =
 535 {
 536   "recip",                              /* name */
 537   gate_cse_reciprocals,                 /* gate */
 538   execute_cse_reciprocals,              /* execute */
 539   NULL,                                 /* sub */
 540   NULL,                                 /* next */
 541   0,                                    /* static_pass_number */
 542   0,                                    /* tv_id */
 543   PROP_ssa,                             /* properties_required */
 544   0,                                    /* properties_provided */
 545   0,                                    /* properties_destroyed */
 546   0,                                    /* todo_flags_start */
 547   TODO_dump_func | TODO_update_ssa | TODO_verify_ssa
 548     | TODO_verify_stmts,                /* todo_flags_finish */
 549   0                                     /* letter */
 550 };