source: trunk/src/gcc/gcc/predict.c@ 2

/* Branch prediction routines for the GNU compiler.
   Copyright (C) 2000, 2001, 2002 Free Software Foundation, Inc.

This file is part of GCC.

GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 2, or (at your option) any later
version.

GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING.  If not, write to the Free
Software Foundation, 59 Temple Place - Suite 330, Boston, MA
02111-1307, USA.  */

/* References:

   [1] "Branch Prediction for Free"
       Ball and Larus; PLDI '93.
   [2] "Static Branch Frequency and Program Profile Analysis"
       Wu and Larus; MICRO-27.
   [3] "Corpus-based Static Branch Prediction"
       Calder, Grunwald, Lindsay, Martin, Mozer, and Zorn; PLDI '95.  */


#include "config.h"
#include "system.h"
#include "tree.h"
#include "rtl.h"
#include "tm_p.h"
#include "hard-reg-set.h"
#include "basic-block.h"
#include "insn-config.h"
#include "regs.h"
#include "flags.h"
#include "output.h"
#include "function.h"
#include "except.h"
#include "toplev.h"
#include "recog.h"
#include "expr.h"
#include "predict.h"

/* Random guesstimation given names.  */
#define PROB_NEVER              (0)
#define PROB_VERY_UNLIKELY      (REG_BR_PROB_BASE / 10 - 1)
#define PROB_UNLIKELY           (REG_BR_PROB_BASE * 4 / 10 - 1)
#define PROB_EVEN               (REG_BR_PROB_BASE / 2)
#define PROB_LIKELY             (REG_BR_PROB_BASE - PROB_UNLIKELY)
#define PROB_VERY_LIKELY        (REG_BR_PROB_BASE - PROB_VERY_UNLIKELY)
#define PROB_ALWAYS             (REG_BR_PROB_BASE)

static void combine_predictions_for_insn PARAMS ((rtx, basic_block));
static void dump_prediction              PARAMS ((enum br_predictor, int,
                                                  basic_block, int));
static void estimate_loops_at_level      PARAMS ((struct loop *loop));
static void propagate_freq               PARAMS ((basic_block));
static void estimate_bb_frequencies      PARAMS ((struct loops *));
static void counts_to_freqs              PARAMS ((void));

/* Information we hold about each branch predictor.
   Filled using information from predict.def.  */

struct predictor_info
{
  const char *const name;       /* Name used in the debugging dumps.  */
  const int hitrate;            /* Expected hitrate used by
                                   predict_insn_def call.  */
  const int flags;
};

/* Use given predictor without Dempster-Shaffer theory if it matches
   using first_match heuristics.  */
#define PRED_FLAG_FIRST_MATCH 1

/* Recompute hitrate in percent to our representation.  */

#define HITRATE(VAL) ((int) ((VAL) * REG_BR_PROB_BASE + 50) / 100)

#define DEF_PREDICTOR(ENUM, NAME, HITRATE, FLAGS) {NAME, HITRATE, FLAGS},
static const struct predictor_info predictor_info[]= {
#include "predict.def"

  /* Upper bound on predictors.  */
  {NULL, 0, 0}
};
#undef DEF_PREDICTOR

void
predict_insn (insn, predictor, probability)
     rtx insn;
     int probability;
     enum br_predictor predictor;
{
  if (!any_condjump_p (insn))
    abort ();

  REG_NOTES (insn)
    = gen_rtx_EXPR_LIST (REG_BR_PRED,
                         gen_rtx_CONCAT (VOIDmode,
                                         GEN_INT ((int) predictor),
                                         GEN_INT ((int) probability)),
                         REG_NOTES (insn));
}

/* Predict insn by given predictor.  */

void
predict_insn_def (insn, predictor, taken)
     rtx insn;
     enum br_predictor predictor;
     enum prediction taken;
{
   int probability = predictor_info[(int) predictor].hitrate;

   if (taken != TAKEN)
     probability = REG_BR_PROB_BASE - probability;

   predict_insn (insn, predictor, probability);
}

/* Predict edge E with given probability if possible.  */

void
predict_edge (e, predictor, probability)
     edge e;
     int probability;
     enum br_predictor predictor;
{
  rtx last_insn;
  last_insn = e->src->end;

  /* We can store the branch prediction information only about
     conditional jumps.  */
  if (!any_condjump_p (last_insn))
    return;

  /* We always store probability of branching.  */
  if (e->flags & EDGE_FALLTHRU)
    probability = REG_BR_PROB_BASE - probability;

  predict_insn (last_insn, predictor, probability);
}

/* Predict edge E by given predictor if possible.  */

void
predict_edge_def (e, predictor, taken)
     edge e;
     enum br_predictor predictor;
     enum prediction taken;
{
   int probability = predictor_info[(int) predictor].hitrate;

   if (taken != TAKEN)
     probability = REG_BR_PROB_BASE - probability;

   predict_edge (e, predictor, probability);
}

/* Invert all branch predictions or probability notes in the INSN.  This needs
   to be done each time we invert the condition used by the jump.  */

void
invert_br_probabilities (insn)
     rtx insn;
{
  rtx note;

  for (note = REG_NOTES (insn); note; note = XEXP (note, 1))
    if (REG_NOTE_KIND (note) == REG_BR_PROB)
      XEXP (note, 0) = GEN_INT (REG_BR_PROB_BASE - INTVAL (XEXP (note, 0)));
    else if (REG_NOTE_KIND (note) == REG_BR_PRED)
      XEXP (XEXP (note, 0), 1)
        = GEN_INT (REG_BR_PROB_BASE - INTVAL (XEXP (XEXP (note, 0), 1)));
}

/* Dump information about the branch prediction to the output file.  */

static void
dump_prediction (predictor, probability, bb, used)
     enum br_predictor predictor;
     int probability;
     basic_block bb;
     int used;
{
  edge e = bb->succ;

  if (!rtl_dump_file)
    return;

  while (e->flags & EDGE_FALLTHRU)
    e = e->succ_next;

  fprintf (rtl_dump_file, "  %s heuristics%s: %.1f%%",
           predictor_info[predictor].name,
           used ? "" : " (ignored)", probability * 100.0 / REG_BR_PROB_BASE);

  if (bb->count)
    {
      fprintf (rtl_dump_file, "  exec ");
      fprintf (rtl_dump_file, HOST_WIDEST_INT_PRINT_DEC, bb->count);
      fprintf (rtl_dump_file, " hit ");
      fprintf (rtl_dump_file, HOST_WIDEST_INT_PRINT_DEC, e->count);
      fprintf (rtl_dump_file, " (%.1f%%)", e->count * 100.0 / bb->count);
    }

  fprintf (rtl_dump_file, "\n");
}

/* Combine all REG_BR_PRED notes into single probability and attach REG_BR_PROB
   note if not already present.  Remove now useless REG_BR_PRED notes.  */

static void
combine_predictions_for_insn (insn, bb)
     rtx insn;
     basic_block bb;
{
  rtx prob_note = find_reg_note (insn, REG_BR_PROB, 0);
  rtx *pnote = &REG_NOTES (insn);
  rtx note;
  int best_probability = PROB_EVEN;
  int best_predictor = END_PREDICTORS;
  int combined_probability = REG_BR_PROB_BASE / 2;
  int d;
  bool first_match = false;
  bool found = false;

  if (rtl_dump_file)
    fprintf (rtl_dump_file, "Predictions for insn %i bb %i\n", INSN_UID (insn),
             bb->index);

  /* We implement "first match" heuristics and use probability guessed
     by predictor with smallest index.  In the future we will use better
     probability combination techniques.  */
  for (note = REG_NOTES (insn); note; note = XEXP (note, 1))
    if (REG_NOTE_KIND (note) == REG_BR_PRED)
      {
        int predictor = INTVAL (XEXP (XEXP (note, 0), 0));
        int probability = INTVAL (XEXP (XEXP (note, 0), 1));

        found = true;
        if (best_predictor > predictor)
          best_probability = probability, best_predictor = predictor;

        d = (combined_probability * probability
             + (REG_BR_PROB_BASE - combined_probability)
             * (REG_BR_PROB_BASE - probability));

        /* Use FP math to avoid overflows of 32bit integers.  */
        if (d == 0)
          /* If one probability is 0% and one 100%, avoid division by zero.  */
          combined_probability = REG_BR_PROB_BASE / 2;
        else
          combined_probability = (((double) combined_probability) * probability
                                  * REG_BR_PROB_BASE / d + 0.5);
      }

  /* Decide which heuristic to use.  In case we didn't match anything,
     use no_prediction heuristic, in case we did match, use either
     first match or Dempster-Shaffer theory depending on the flags.  */

  if (predictor_info [best_predictor].flags & PRED_FLAG_FIRST_MATCH)
    first_match = true;

  if (!found)
    dump_prediction (PRED_NO_PREDICTION, combined_probability, bb, true);
  else
    {
      dump_prediction (PRED_DS_THEORY, combined_probability, bb, !first_match);
      dump_prediction (PRED_FIRST_MATCH, best_probability, bb, first_match);
    }

  if (first_match)
    combined_probability = best_probability;
  dump_prediction (PRED_COMBINED, combined_probability, bb, true);

  while (*pnote)
    {
      if (REG_NOTE_KIND (*pnote) == REG_BR_PRED)
        {
          int predictor = INTVAL (XEXP (XEXP (*pnote, 0), 0));
          int probability = INTVAL (XEXP (XEXP (*pnote, 0), 1));

          dump_prediction (predictor, probability, bb,
                           !first_match || best_predictor == predictor);
          *pnote = XEXP (*pnote, 1);
        }
      else
        pnote = &XEXP (*pnote, 1);
    }

  if (!prob_note)
    {
      REG_NOTES (insn)
        = gen_rtx_EXPR_LIST (REG_BR_PROB,
                             GEN_INT (combined_probability), REG_NOTES (insn));

      /* Save the prediction into CFG in case we are seeing non-degenerated
         conditional jump.  */
      if (bb->succ->succ_next)
        {
          BRANCH_EDGE (bb)->probability = combined_probability;
          FALLTHRU_EDGE (bb)->probability
            = REG_BR_PROB_BASE - combined_probability;
        }
    }
}

/* Statically estimate the probability that a branch will be taken.
   ??? In the next revision there will be a number of other predictors added
   from the above references. Further, each heuristic will be factored out
   into its own function for clarity (and to facilitate the combination of
   predictions).  */

void
estimate_probability (loops_info)
     struct loops *loops_info;
{
  sbitmap *dominators, *post_dominators;
  int i;
  int found_noreturn = 0;

  dominators = sbitmap_vector_alloc (n_basic_blocks, n_basic_blocks);
  post_dominators = sbitmap_vector_alloc (n_basic_blocks, n_basic_blocks);
  calculate_dominance_info (NULL, dominators, CDI_DOMINATORS);
  calculate_dominance_info (NULL, post_dominators, CDI_POST_DOMINATORS);

  /* Try to predict out blocks in a loop that are not part of a
     natural loop.  */
  for (i = 0; i < loops_info->num; i++)
    {
      int j;
      int exits;
      struct loop *loop = &loops_info->array[i];

      flow_loop_scan (loops_info, loop, LOOP_EXIT_EDGES);
      exits = loop->num_exits;

      for (j = loop->first->index; j <= loop->last->index; ++j)
        if (TEST_BIT (loop->nodes, j))
          {
            int header_found = 0;
            edge e;

            /* Loop branch heuristics - predict an edge back to a
               loop's head as taken.  */
            for (e = BASIC_BLOCK(j)->succ; e; e = e->succ_next)
              if (e->dest == loop->header
                  && e->src == loop->latch)
                {
                  header_found = 1;
                  predict_edge_def (e, PRED_LOOP_BRANCH, TAKEN);
                }

            /* Loop exit heuristics - predict an edge exiting the loop if the
               conditinal has no loop header successors as not taken.  */
            if (!header_found)
              for (e = BASIC_BLOCK(j)->succ; e; e = e->succ_next)
                if (e->dest->index < 0
                    || !TEST_BIT (loop->nodes, e->dest->index))
                  predict_edge
                    (e, PRED_LOOP_EXIT,
                     (REG_BR_PROB_BASE
                      - predictor_info [(int) PRED_LOOP_EXIT].hitrate)
                     / exits);
          }
    }

  /* Attempt to predict conditional jumps using a number of heuristics.  */
  for (i = 0; i < n_basic_blocks; i++)
    {
      basic_block bb = BASIC_BLOCK (i);
      rtx last_insn = bb->end;
      rtx cond, earliest;
      edge e;

      /* If block has no successor, predict all possible paths to it as
         improbable, as the block contains a call to a noreturn function and
         thus can be executed only once.  */
      if (bb->succ == NULL && !found_noreturn)
        {
          int y;

          /* ??? Postdominator claims each noreturn block to be postdominated
             by each, so we need to run only once.  This needs to be changed
             once postdominace algorithm is updated to say something more
             sane.  */
          found_noreturn = 1;
          for (y = 0; y < n_basic_blocks; y++)
            if (!TEST_BIT (post_dominators[y], i))
              for (e = BASIC_BLOCK (y)->succ; e; e = e->succ_next)
                if (e->dest->index >= 0
                    && TEST_BIT (post_dominators[e->dest->index], i))
                  predict_edge_def (e, PRED_NORETURN, NOT_TAKEN);
        }

      if (GET_CODE (last_insn) != JUMP_INSN || ! any_condjump_p (last_insn))
        continue;

      for (e = bb->succ; e; e = e->succ_next)
        {
          /* Predict edges to blocks that return immediately to be
             improbable.  These are usually used to signal error states.  */
          if (e->dest == EXIT_BLOCK_PTR
              || (e->dest->succ && !e->dest->succ->succ_next
                  && e->dest->succ->dest == EXIT_BLOCK_PTR))
            predict_edge_def (e, PRED_ERROR_RETURN, NOT_TAKEN);

          /* Look for block we are guarding (ie we dominate it,
             but it doesn't postdominate us).  */
          if (e->dest != EXIT_BLOCK_PTR && e->dest != bb
              && TEST_BIT (dominators[e->dest->index], e->src->index)
              && !TEST_BIT (post_dominators[e->src->index], e->dest->index))
            {
              rtx insn;

              /* The call heuristic claims that a guarded function call
                 is improbable.  This is because such calls are often used
                 to signal exceptional situations such as printing error
                 messages.  */
              for (insn = e->dest->head; insn != NEXT_INSN (e->dest->end);
                   insn = NEXT_INSN (insn))
                if (GET_CODE (insn) == CALL_INSN
                    /* Constant and pure calls are hardly used to signalize
                       something exceptional.  */
                    && ! CONST_OR_PURE_CALL_P (insn))
                  {
                    predict_edge_def (e, PRED_CALL, NOT_TAKEN);
                    break;
                  }
            }
        }

      cond = get_condition (last_insn, &earliest);
      if (! cond)
        continue;

      /* Try "pointer heuristic."
         A comparison ptr == 0 is predicted as false.
         Similarly, a comparison ptr1 == ptr2 is predicted as false.  */
      if (GET_RTX_CLASS (GET_CODE (cond)) == '<'
          && ((REG_P (XEXP (cond, 0)) && REG_POINTER (XEXP (cond, 0)))
              || (REG_P (XEXP (cond, 1)) && REG_POINTER (XEXP (cond, 1)))))
        {
          if (GET_CODE (cond) == EQ)
            predict_insn_def (last_insn, PRED_POINTER, NOT_TAKEN);
          else if (GET_CODE (cond) == NE)
            predict_insn_def (last_insn, PRED_POINTER, TAKEN);
        }
      else

      /* Try "opcode heuristic."
         EQ tests are usually false and NE tests are usually true. Also,
         most quantities are positive, so we can make the appropriate guesses
         about signed comparisons against zero.  */
        switch (GET_CODE (cond))
          {
          case CONST_INT:
            /* Unconditional branch.  */
            predict_insn_def (last_insn, PRED_UNCONDITIONAL,
                              cond == const0_rtx ? NOT_TAKEN : TAKEN);
            break;

          case EQ:
          case UNEQ:
            /* Floating point comparisons appears to behave in a very
               inpredictable way because of special role of = tests in
               FP code.  */
            if (FLOAT_MODE_P (GET_MODE (XEXP (cond, 0))))
              ;
            /* Comparisons with 0 are often used for booleans and there is
               nothing usefull to predict about them.  */
            else if (XEXP (cond, 1) == const0_rtx
                     || XEXP (cond, 0) == const0_rtx)
              ;
            else
              predict_insn_def (last_insn, PRED_OPCODE_NONEQUAL, NOT_TAKEN);
            break;

          case NE:
          case LTGT:
            /* Floating point comparisons appears to behave in a very
               inpredictable way because of special role of = tests in
               FP code.  */
            if (FLOAT_MODE_P (GET_MODE (XEXP (cond, 0))))
              ;
            /* Comparisons with 0 are often used for booleans and there is
               nothing usefull to predict about them.  */
            else if (XEXP (cond, 1) == const0_rtx
                     || XEXP (cond, 0) == const0_rtx)
              ;
            else
              predict_insn_def (last_insn, PRED_OPCODE_NONEQUAL, TAKEN);
            break;

          case ORDERED:
            predict_insn_def (last_insn, PRED_FPOPCODE, TAKEN);
            break;

          case UNORDERED:
            predict_insn_def (last_insn, PRED_FPOPCODE, NOT_TAKEN);
            break;

          case LE:
          case LT:
            if (XEXP (cond, 1) == const0_rtx || XEXP (cond, 1) == const1_rtx
                || XEXP (cond, 1) == constm1_rtx)
              predict_insn_def (last_insn, PRED_OPCODE_POSITIVE, NOT_TAKEN);
            break;

          case GE:
          case GT:
            if (XEXP (cond, 1) == const0_rtx || XEXP (cond, 1) == const1_rtx
                || XEXP (cond, 1) == constm1_rtx)
              predict_insn_def (last_insn, PRED_OPCODE_POSITIVE, TAKEN);
            break;

          default:
            break;
          }
    }

  /* Attach the combined probability to each conditional jump.  */
  for (i = 0; i < n_basic_blocks; i++)
    if (GET_CODE (BLOCK_END (i)) == JUMP_INSN
        && any_condjump_p (BLOCK_END (i)))
      combine_predictions_for_insn (BLOCK_END (i), BASIC_BLOCK (i));

  sbitmap_vector_free (post_dominators);
  sbitmap_vector_free (dominators);

  estimate_bb_frequencies (loops_info);
}


/* __builtin_expect dropped tokens into the insn stream describing expected
   values of registers.  Generate branch probabilities based off these
   values.  */

void
expected_value_to_br_prob ()
{
  rtx insn, cond, ev = NULL_RTX, ev_reg = NULL_RTX;

  for (insn = get_insns (); insn ; insn = NEXT_INSN (insn))
    {
      switch (GET_CODE (insn))
        {
        case NOTE:
          /* Look for expected value notes.  */
          if (NOTE_LINE_NUMBER (insn) == NOTE_INSN_EXPECTED_VALUE)
            {
              ev = NOTE_EXPECTED_VALUE (insn);
              ev_reg = XEXP (ev, 0);
              delete_insn (insn);
            }
          continue;

        case CODE_LABEL:
          /* Never propagate across labels.  */
          ev = NULL_RTX;
          continue;

        case JUMP_INSN:
          /* Look for simple conditional branches.  If we haven't got an
             expected value yet, no point going further.  */
          if (GET_CODE (insn) != JUMP_INSN || ev == NULL_RTX
              || ! any_condjump_p (insn))
            continue;
          break;

        default:
          /* Look for insns that clobber the EV register.  */
          if (ev && reg_set_p (ev_reg, insn))
            ev = NULL_RTX;
          continue;
        }

      /* Collect the branch condition, hopefully relative to EV_REG.  */
      /* ???  At present we'll miss things like
                (expected_value (eq r70 0))
                (set r71 -1)
                (set r80 (lt r70 r71))
                (set pc (if_then_else (ne r80 0) ...))
         as canonicalize_condition will render this to us as
                (lt r70, r71)
         Could use cselib to try and reduce this further.  */
      cond = XEXP (SET_SRC (pc_set (insn)), 0);
      cond = canonicalize_condition (insn, cond, 0, NULL, ev_reg);
      if (! cond || XEXP (cond, 0) != ev_reg
          || GET_CODE (XEXP (cond, 1)) != CONST_INT)
        continue;

      /* Substitute and simplify.  Given that the expression we're
         building involves two constants, we should wind up with either
         true or false.  */
      cond = gen_rtx_fmt_ee (GET_CODE (cond), VOIDmode,
                             XEXP (ev, 1), XEXP (cond, 1));
      cond = simplify_rtx (cond);

      /* Turn the condition into a scaled branch probability.  */
      if (cond != const_true_rtx && cond != const0_rtx)
        abort ();
      predict_insn_def (insn, PRED_BUILTIN_EXPECT,
                        cond == const_true_rtx ? TAKEN : NOT_TAKEN);
    }
}


/* This is used to carry information about basic blocks.  It is
   attached to the AUX field of the standard CFG block.  */

typedef struct block_info_def
{
  /* Estimated frequency of execution of basic_block.  */
  volatile double frequency;

  /* To keep queue of basic blocks to process.  */
  basic_block next;

  /* True if block needs to be visited in prop_freqency.  */
  int tovisit:1;

  /* Number of predecessors we need to visit first.  */
  int npredecessors;
} *block_info;

/* Similar information for edges.  */
typedef struct edge_info_def
{
  /* In case edge is an loopback edge, the probability edge will be reached
     in case header is.  Estimated number of iterations of the loop can be
     then computed as 1 / (1 - back_edge_prob).

     Volatile is needed to avoid differences in the optimized and unoptimized
     builds on machines where FP registers are wider than double.  */
  volatile double back_edge_prob;
  /* True if the edge is an loopback edge in the natural loop.  */
  int back_edge:1;
} *edge_info;

#define BLOCK_INFO(B)   ((block_info) (B)->aux)
#define EDGE_INFO(E)    ((edge_info) (E)->aux)

/* Helper function for estimate_bb_frequencies.
   Propagate the frequencies for loops headed by HEAD.  */

static void
propagate_freq (head)
     basic_block head;
{
  basic_block bb = head;
  basic_block last = bb;
  edge e;
  basic_block nextbb;
  int n;

  /* For each basic block we need to visit count number of his predecessors
     we need to visit first.  */
  for (n = 0; n < n_basic_blocks; n++)
    {
      basic_block bb = BASIC_BLOCK (n);
      if (BLOCK_INFO (bb)->tovisit)
        {
          int count = 0;

          for (e = bb->pred; e; e = e->pred_next)
            if (BLOCK_INFO (e->src)->tovisit && !(e->flags & EDGE_DFS_BACK))
              count++;
            else if (BLOCK_INFO (e->src)->tovisit
                     && rtl_dump_file && !EDGE_INFO (e)->back_edge)
              fprintf (rtl_dump_file,
                       "Irreducible region hit, ignoring edge to %i->%i\n",
                       e->src->index, bb->index);
          BLOCK_INFO (bb)->npredecessors = count;
        }
    }

  BLOCK_INFO (head)->frequency = 1;
  for (; bb; bb = nextbb)
    {
      double cyclic_probability = 0, frequency = 0;

      nextbb = BLOCK_INFO (bb)->next;
      BLOCK_INFO (bb)->next = NULL;

      /* Compute frequency of basic block.  */
      if (bb != head)
        {
#ifdef ENABLE_CHECKING
          for (e = bb->pred; e; e = e->pred_next)
            if (BLOCK_INFO (e->src)->tovisit && !(e->flags & EDGE_DFS_BACK))
              abort ();
#endif

          for (e = bb->pred; e; e = e->pred_next)
            if (EDGE_INFO (e)->back_edge)
              cyclic_probability += EDGE_INFO (e)->back_edge_prob;
            else if (!(e->flags & EDGE_DFS_BACK))
              frequency += (e->probability
                            * BLOCK_INFO (e->src)->frequency /
                            REG_BR_PROB_BASE);

          if (cyclic_probability > 1.0 - 1.0 / REG_BR_PROB_BASE)
            cyclic_probability = 1.0 - 1.0 / REG_BR_PROB_BASE;

          BLOCK_INFO (bb)->frequency = frequency / (1 - cyclic_probability);
        }

      BLOCK_INFO (bb)->tovisit = 0;

      /* Compute back edge frequencies.  */
      for (e = bb->succ; e; e = e->succ_next)
        if (e->dest == head)
          EDGE_INFO (e)->back_edge_prob
            = ((e->probability * BLOCK_INFO (bb)->frequency)
               / REG_BR_PROB_BASE);

      /* Propagate to successor blocks.  */
      for (e = bb->succ; e; e = e->succ_next)
        if (!(e->flags & EDGE_DFS_BACK)
            && BLOCK_INFO (e->dest)->npredecessors)
          {
            BLOCK_INFO (e->dest)->npredecessors--;
            if (!BLOCK_INFO (e->dest)->npredecessors)
              {
                if (!nextbb)
                  nextbb = e->dest;
                else
                  BLOCK_INFO (last)->next = e->dest;

                last = e->dest;
              }
           }
    }
}

/* Estimate probabilities of loopback edges in loops at same nest level.  */

static void
estimate_loops_at_level (first_loop)
     struct loop *first_loop;
{
  struct loop *l, *loop = first_loop;

  for (loop = first_loop; loop; loop = loop->next)
    {
      int n;
      edge e;

      estimate_loops_at_level (loop->inner);

      /* Find current loop back edge and mark it.  */
      for (e = loop->latch->succ; e->dest != loop->header; e = e->succ_next)
        ;

      EDGE_INFO (e)->back_edge = 1;

      /* In case the loop header is shared, ensure that it is the last
         one sharing the same header, so we avoid redundant work.  */
      if (loop->shared)
        {
          for (l = loop->next; l; l = l->next)
            if (l->header == loop->header)
              break;

          if (l)
            continue;
        }

      /* Now merge all nodes of all loops with given header as not visited.  */
      for (l = loop->shared ? first_loop : loop; l != loop->next; l = l->next)
        if (loop->header == l->header)
          EXECUTE_IF_SET_IN_SBITMAP (l->nodes, 0, n,
                                     BLOCK_INFO (BASIC_BLOCK (n))->tovisit = 1
                                     );

      propagate_freq (loop->header);
    }
}

/* Convert counts measured by profile driven feedback to frequencies.  */

static void
counts_to_freqs ()
{
  HOST_WIDEST_INT count_max = 1;
  int i;

  for (i = 0; i < n_basic_blocks; i++)
    count_max = MAX (BASIC_BLOCK (i)->count, count_max);

  for (i = -2; i < n_basic_blocks; i++)
    {
      basic_block bb;

      if (i == -2)
        bb = ENTRY_BLOCK_PTR;
      else if (i == -1)
        bb = EXIT_BLOCK_PTR;
      else
        bb = BASIC_BLOCK (i);

      bb->frequency = (bb->count * BB_FREQ_MAX + count_max / 2) / count_max;
    }
}

/* Return true if function is likely to be expensive, so there is no point to
   optimize performance of prologue, epilogue or do inlining at the expense
   of code size growth.  THRESHOLD is the limit of number of isntructions
   function can execute at average to be still considered not expensive.  */

bool
expensive_function_p (threshold)
        int threshold;
{
  unsigned int sum = 0;
  int i;
  unsigned int limit;

  /* We can not compute accurately for large thresholds due to scaled
     frequencies.  */
  if (threshold > BB_FREQ_MAX)
    abort ();

  /* Frequencies are out of range.  This either means that function contains
     internal loop executing more than BB_FREQ_MAX times or profile feedback
     is available and function has not been executed at all.  */
  if (ENTRY_BLOCK_PTR->frequency == 0)
    return true;
    
  /* Maximally BB_FREQ_MAX^2 so overflow won't happen.  */
  limit = ENTRY_BLOCK_PTR->frequency * threshold;
  for (i = 0; i < n_basic_blocks; i++)
    {
      basic_block bb = BASIC_BLOCK (i);
      rtx insn;

      for (insn = bb->head; insn != NEXT_INSN (bb->end);
           insn = NEXT_INSN (insn))
        if (active_insn_p (insn))
          {
            sum += bb->frequency;
            if (sum > limit)
              return true;
        }
    }

  return false;
}

/* Estimate basic blocks frequency by given branch probabilities.  */

static void
estimate_bb_frequencies (loops)
     struct loops *loops;
{
  int i;
  double freq_max = 0;

  mark_dfs_back_edges ();
  if (flag_branch_probabilities)
    {
      counts_to_freqs ();
      return;
    }

  /* Fill in the probability values in flowgraph based on the REG_BR_PROB
     notes.  */
  for (i = 0; i < n_basic_blocks; i++)
    {
      rtx last_insn = BLOCK_END (i);
      int probability;
      edge fallthru, branch;

      if (GET_CODE (last_insn) != JUMP_INSN || !any_condjump_p (last_insn)
          /* Avoid handling of conditional jumps jumping to fallthru edge.  */
          || BASIC_BLOCK (i)->succ->succ_next == NULL)
        {
          /* We can predict only conditional jumps at the moment.
             Expect each edge to be equally probable.
             ?? In the future we want to make abnormal edges improbable.  */
          int nedges = 0;
          edge e;

          for (e = BASIC_BLOCK (i)->succ; e; e = e->succ_next)
            {
              nedges++;
              if (e->probability != 0)
                break;
            }
          if (!e)
            for (e = BASIC_BLOCK (i)->succ; e; e = e->succ_next)
              e->probability = (REG_BR_PROB_BASE + nedges / 2) / nedges;
        }
      else
        {
          probability = INTVAL (XEXP (find_reg_note (last_insn,
                                                     REG_BR_PROB, 0), 0));
          fallthru = BASIC_BLOCK (i)->succ;
          if (!fallthru->flags & EDGE_FALLTHRU)
            fallthru = fallthru->succ_next;
          branch = BASIC_BLOCK (i)->succ;
          if (branch->flags & EDGE_FALLTHRU)
            branch = branch->succ_next;

          branch->probability = probability;
          fallthru->probability = REG_BR_PROB_BASE - probability;
        }
    }

  ENTRY_BLOCK_PTR->succ->probability = REG_BR_PROB_BASE;

  /* Set up block info for each basic block.  */
  alloc_aux_for_blocks (sizeof (struct block_info_def));
  alloc_aux_for_edges (sizeof (struct edge_info_def));
  for (i = -2; i < n_basic_blocks; i++)
    {
      edge e;
      basic_block bb;

      if (i == -2)
        bb = ENTRY_BLOCK_PTR;
      else if (i == -1)
        bb = EXIT_BLOCK_PTR;
      else
        bb = BASIC_BLOCK (i);

      BLOCK_INFO (bb)->tovisit = 0;
      for (e = bb->succ; e; e = e->succ_next)
        EDGE_INFO (e)->back_edge_prob = ((double) e->probability
                                         / REG_BR_PROB_BASE);
    }

  /* First compute probabilities locally for each loop from innermost
     to outermost to examine probabilities for back edges.  */
  estimate_loops_at_level (loops->tree_root);

  /* Now fake loop around whole function to finalize probabilities.  */
  for (i = 0; i < n_basic_blocks; i++)
    BLOCK_INFO (BASIC_BLOCK (i))->tovisit = 1;

  BLOCK_INFO (ENTRY_BLOCK_PTR)->tovisit = 1;
  BLOCK_INFO (EXIT_BLOCK_PTR)->tovisit = 1;
  propagate_freq (ENTRY_BLOCK_PTR);

  for (i = 0; i < n_basic_blocks; i++)
    if (BLOCK_INFO (BASIC_BLOCK (i))->frequency > freq_max)
      freq_max = BLOCK_INFO (BASIC_BLOCK (i))->frequency;

  for (i = -2; i < n_basic_blocks; i++)
    {
      basic_block bb;
      volatile double tmp;

      if (i == -2)
        bb = ENTRY_BLOCK_PTR;
      else if (i == -1)
        bb = EXIT_BLOCK_PTR;
      else
        bb = BASIC_BLOCK (i);

      /* ??? Prevent rounding differences due to optimization on x86.  */
      tmp = BLOCK_INFO (bb)->frequency * BB_FREQ_MAX;
      tmp /= freq_max;
      tmp += 0.5;
      bb->frequency = tmp;
    }

  free_aux_for_blocks ();
  free_aux_for_edges ();
}