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 /* Walk the subset of the dominator tree rooted at OCC, setting the
 283    RECIP_DEF field to a definition of 1.0 / DEF that can be used in
 284    the given basic block.  The field may be left NULL, of course,
 285    if it is not possible or profitable to do the optimization.
 286
 287    DEF_BSI is an iterator pointing at the statement defining DEF.
 288    If RECIP_DEF is set, a dominator already has a computation that can
 289    be used.  */
 290
 291 static void
 292 insert_reciprocals (block_stmt_iterator *def_bsi, struct occurrence *occ,
 293                     tree def, tree recip_def, int threshold)
 294 {
 295   tree type, new_stmt;
 296   block_stmt_iterator bsi;
 297   struct occurrence *occ_child;
 298
 299   if (!recip_def
 300       && (occ->bb_has_division || !flag_trapping_math)
 301       && occ->num_divisions >= threshold)
 302     {
 303       /* Make a variable with the replacement and substitute it.  */
 304       type = TREE_TYPE (def);
 305       recip_def = make_rename_temp (type, "reciptmp");
 306       new_stmt = build2 (MODIFY_EXPR, void_type_node, recip_def,
 307                          fold_build2 (RDIV_EXPR, type, build_one_cst (type),
 308                                       def));
 309
 310
 311       if (occ->bb_has_division)
 312         {
 313           /* Case 1: insert before an existing division.  */
 314           bsi = bsi_after_labels (occ->bb);
 315           while (!bsi_end_p (bsi) && !is_division_by (bsi_stmt (bsi), def))
 316             bsi_next (&bsi);
 317
 318           bsi_insert_before (&bsi, new_stmt, BSI_SAME_STMT);
 319         }
 320       else if (def_bsi && occ->bb == def_bsi->bb)
 321         {
 322           /* Case 2: insert right after the definition.  Note that this will
 323              never happen if the definition statement can throw, because in
 324              that case the sole successor of the statement's basic block will
 325              dominate all the uses as well.  */
 326           bsi_insert_after (def_bsi, new_stmt, BSI_NEW_STMT);
 327         }
 328       else
 329         {
 330           /* Case 3: insert in a basic block not containing defs/uses.  */
 331           bsi = bsi_after_labels (occ->bb);
 332           bsi_insert_before (&bsi, new_stmt, BSI_SAME_STMT);
 333         }
 334
 335       occ->recip_def_stmt = new_stmt;
 336     }
 337
 338   occ->recip_def = recip_def;
 339   for (occ_child = occ->children; occ_child; occ_child = occ_child->next)
 340     insert_reciprocals (def_bsi, occ_child, def, recip_def, threshold);
 341 }
 342
 343
 344 /* Replace the division at USE_P with a multiplication by the reciprocal, if
 345    possible.  */
 346
 347 static inline void
 348 replace_reciprocal (use_operand_p use_p)
 349 {
 350   tree use_stmt = USE_STMT (use_p);
 351   basic_block bb = bb_for_stmt (use_stmt);
 352   struct occurrence *occ = (struct occurrence *) bb->aux;
 353
 354   if (occ->recip_def && use_stmt != occ->recip_def_stmt)
 355     {
 356       TREE_SET_CODE (TREE_OPERAND (use_stmt, 1), MULT_EXPR);
 357       SET_USE (use_p, occ->recip_def);
 358       fold_stmt_inplace (use_stmt);
 359       update_stmt (use_stmt);
 360     }
 361 }
 362
 363
 364 /* Free OCC and return one more "struct occurrence" to be freed.  */
 365
 366 static struct occurrence *
 367 free_bb (struct occurrence *occ)
 368 {
 369   struct occurrence *child, *next;
 370
 371   /* First get the two pointers hanging off OCC.  */
 372   next = occ->next;
 373   child = occ->children;
 374   occ->bb->aux = NULL;
 375   pool_free (occ_pool, occ);
 376
 377   /* Now ensure that we don't recurse unless it is necessary.  */
 378   if (!child)
 379     return next;
 380   else
 381     {
 382       while (next)
 383         next = free_bb (next);
 384
 385       return child;
 386     }
 387 }
 388
 389
 390 /* Look for floating-point divisions among DEF's uses, and try to
 391    replace them by multiplications with the reciprocal.  Add
 392    as many statements computing the reciprocal as needed.
 393
 394    DEF must be a GIMPLE register of a floating-point type.  */
 395
 396 static void
 397 execute_cse_reciprocals_1 (block_stmt_iterator *def_bsi, tree def)
 398 {
 399   use_operand_p use_p;
 400   imm_use_iterator use_iter;
 401   struct occurrence *occ;
 402   int count = 0, threshold;
 403
 404   gcc_assert (FLOAT_TYPE_P (TREE_TYPE (def)) && is_gimple_reg (def));
 405
 406   FOR_EACH_IMM_USE_FAST (use_p, use_iter, def)
 407     {
 408       tree use_stmt = USE_STMT (use_p);
 409       if (is_division_by (use_stmt, def))
 410         {
 411           register_division_in (bb_for_stmt (use_stmt));
 412           count++;
 413         }
 414     }
 415
 416   /* Do the expensive part only if we can hope to optimize something.  */
 417   threshold = targetm.min_divisions_for_recip_mul (TYPE_MODE (TREE_TYPE (def)));
 418   if (count >= threshold)
 419     {
 420       tree use_stmt;
 421       for (occ = occ_head; occ; occ = occ->next)
 422         {
 423           compute_merit (occ);
 424           insert_reciprocals (def_bsi, occ, def, NULL, threshold);
 425         }
 426
 427       FOR_EACH_IMM_USE_STMT (use_stmt, use_iter, def)
 428         {
 429           if (is_division_by (use_stmt, def))
 430             {
 431               FOR_EACH_IMM_USE_ON_STMT (use_p, use_iter)
 432                 replace_reciprocal (use_p);
 433             }
 434         }
 435     }
 436
 437   for (occ = occ_head; occ; )
 438     occ = free_bb (occ);
 439
 440   occ_head = NULL;
 441 }
 442
 443
 444 static bool
 445 gate_cse_reciprocals (void)
 446 {
 447   return optimize && !optimize_size && flag_unsafe_math_optimizations;
 448 }
 449
 450
 451 /* Go through all the floating-point SSA_NAMEs, and call
 452    execute_cse_reciprocals_1 on each of them.  */
 453 static unsigned int
 454 execute_cse_reciprocals (void)
 455 {
 456   basic_block bb;
 457   tree arg;
 458
 459   occ_pool = create_alloc_pool ("dominators for recip",
 460                                 sizeof (struct occurrence),
 461                                 n_basic_blocks / 3 + 1);
 462
 463   calculate_dominance_info (CDI_DOMINATORS);
 464   calculate_dominance_info (CDI_POST_DOMINATORS);
 465
 466 #ifdef ENABLE_CHECKING
 467   FOR_EACH_BB (bb)
 468     gcc_assert (!bb->aux);
 469 #endif
 470
 471   for (arg = DECL_ARGUMENTS (cfun->decl); arg; arg = TREE_CHAIN (arg))
 472     if (default_def (arg)
 473         && FLOAT_TYPE_P (TREE_TYPE (arg))
 474         && is_gimple_reg (arg))
 475       execute_cse_reciprocals_1 (NULL, default_def (arg));
 476
 477   FOR_EACH_BB (bb)
 478     {
 479       block_stmt_iterator bsi;
 480       tree phi, def;
 481
 482       for (phi = phi_nodes (bb); phi; phi = PHI_CHAIN (phi))
 483         {
 484           def = PHI_RESULT (phi);
 485           if (FLOAT_TYPE_P (TREE_TYPE (def))
 486               && is_gimple_reg (def))
 487             execute_cse_reciprocals_1 (NULL, def);
 488         }
 489
 490       for (bsi = bsi_after_labels (bb); !bsi_end_p (bsi); bsi_next (&bsi))
 491         {
 492           tree stmt = bsi_stmt (bsi);
 493           if (TREE_CODE (stmt) == MODIFY_EXPR
 494               && (def = SINGLE_SSA_TREE_OPERAND (stmt, SSA_OP_DEF)) != NULL
 495               && FLOAT_TYPE_P (TREE_TYPE (def))
 496               && TREE_CODE (def) == SSA_NAME)
 497             execute_cse_reciprocals_1 (&bsi, def);
 498         }
 499     }
 500
 501   free_dominance_info (CDI_DOMINATORS);
 502   free_dominance_info (CDI_POST_DOMINATORS);
 503   free_alloc_pool (occ_pool);
 504   return 0;
 505 }
 506
 507 struct tree_opt_pass pass_cse_reciprocals =
 508 {
 509   "recip",                              /* name */
 510   gate_cse_reciprocals,                 /* gate */
 511   execute_cse_reciprocals,              /* execute */
 512   NULL,                                 /* sub */
 513   NULL,                                 /* next */
 514   0,                                    /* static_pass_number */
 515   0,                                    /* tv_id */
 516   PROP_ssa,                             /* properties_required */
 517   0,                                    /* properties_provided */
 518   0,                                    /* properties_destroyed */
 519   0,                                    /* todo_flags_start */
 520   TODO_dump_func | TODO_update_ssa | TODO_verify_ssa
 521     | TODO_verify_stmts,                /* todo_flags_finish */
 522   0                                     /* letter */
 523 };