LCM framework

Jeffrey A Law law@hurl.cygnus.com
Wed Mar 10 22:01:00 GMT 1999


This is the basic LCM optimizer framework.  Once I'm done with the gcse.c
cleanups, gcse.c will be converted to use the LCM optimizer.



Index: Makefile.in
===================================================================
RCS file: /egcs/carton/cvsfiles/egcs/gcc/Makefile.in,v
retrieving revision 1.240
diff -c -3 -p -r1.240 Makefile.in
*** Makefile.in	1999/03/09 06:40:48	1.240
--- Makefile.in	1999/03/11 05:57:13
*************** OBJS = toplev.o version.o tree.o print-t
*** 676,682 ****
   integrate.o jump.o cse.o loop.o unroll.o flow.o stupid.o combine.o varray.o \
   regclass.o regmove.o local-alloc.o global.o reload.o reload1.o caller-save.o \
   insn-peep.o reorg.o $(SCHED_PREFIX)sched.o final.o recog.o reg-stack.o \
!  insn-opinit.o insn-recog.o insn-extract.o insn-output.o insn-emit.o \
   profile.o insn-attrtab.o $(out_object_file) getpwd.o $(EXTRA_OBJS) convert.o \
   mbchar.o dyn-string.o splay-tree.o graph.o sbitmap.o resource.o
  
--- 676,682 ----
   integrate.o jump.o cse.o loop.o unroll.o flow.o stupid.o combine.o varray.o \
   regclass.o regmove.o local-alloc.o global.o reload.o reload1.o caller-save.o \
   insn-peep.o reorg.o $(SCHED_PREFIX)sched.o final.o recog.o reg-stack.o \
!  insn-opinit.o insn-recog.o insn-extract.o insn-output.o insn-emit.o lcm.o \
   profile.o insn-attrtab.o $(out_object_file) getpwd.o $(EXTRA_OBJS) convert.o \
   mbchar.o dyn-string.o splay-tree.o graph.o sbitmap.o resource.o
  
*************** gcse.o : gcse.c $(CONFIG_H) system.h $(R
*** 1505,1510 ****
--- 1505,1512 ----
     real.h insn-config.h $(RECOG_H) $(EXPR_H) $(BASIC_BLOCK_H) output.h
  resource.o : resource.c $(CONFIG_H) $(RTL_H) hard-reg-set.h system.h \
     $(BASIC_BLOCK_H) $(REGS_H) flags.h output.h resource.h
+ lcm.o : lcm.c $(CONFIG_H) system.h $(RTL_H) $(REGS_H) hard-reg-set.h flags.h \
+    real.h insn-config.h $(RECOG_H) $(EXPR_H) $(BASIC_BLOCK_H)
  profile.o : profile.c $(CONFIG_H) system.h $(RTL_H) flags.h insn-flags.h \
     gcov-io.h $(TREE_H) output.h $(REGS_H) toplev.h insn-config.h
  loop.o : loop.c $(CONFIG_H) system.h $(RTL_H) flags.h loop.h insn-config.h \
*** /dev/null	Wed Mar 10 19:02:39 1999
--- lcm.c	Wed Mar 10 22:54:14 1999
***************
*** 0 ****
--- 1,799 ----
+ /* Generic partial redundancy elimination with lazy code motion
+    support.
+    Copyright (C) 1998 Free Software Foundation, Inc.
+ 
+ This file is part of GNU CC.
+ 
+ GNU CC 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.
+ 
+ GNU CC 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 GNU CC; see the file COPYING.  If not, write to
+ the Free Software Foundation, 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA.  */
+ 
+ /* These routines are meant to be used by various optimization
+    passes which can be modeled as lazy code motion problems. 
+    Including, but not limited to:
+ 
+ 	* Traditional partial redundancy elimination.
+ 
+ 	* Placement of caller/caller register save/restores.
+ 
+ 	* Load/store motion.
+ 
+ 	* Copy motion.
+ 
+ 	* Conversion of flat register files to a stacked register
+ 	model.
+ 
+ 	* Dead load/store elimination.
+ 
+   These routines accept as input:
+ 
+ 	* Basic block information (number of blocks, lists of
+ 	predecessors and successors).  Note the granularity
+ 	does not need to be basic block, they could be statements
+ 	or functions.
+ 
+ 	* Bitmaps of local properties (computed, transparent and
+ 	anticipatable expressions).
+ 
+   The output of these routines is bitmap of redundant computations
+   and a bitmap of optimal placement points.  */
+ 
+ 
+ #include "config.h"
+ #include "system.h"
+ 
+ #include "rtl.h"
+ #include "regs.h"
+ #include "hard-reg-set.h"
+ #include "flags.h"
+ #include "real.h"
+ #include "insn-config.h"
+ #include "recog.h"
+ #include "basic-block.h"
+ 
+ static void compute_antinout 	PROTO ((int, int_list_ptr *, sbitmap *,
+ 					sbitmap *, sbitmap *, sbitmap *));
+ static void compute_earlyinout	PROTO ((int, int, int_list_ptr *, sbitmap *,
+ 					sbitmap *, sbitmap *, sbitmap *));
+ static void compute_delayinout  PROTO ((int, int, int_list_ptr *, sbitmap *,
+ 					sbitmap *, sbitmap *,
+ 					sbitmap *, sbitmap *));
+ static void compute_latein	PROTO ((int, int, int_list_ptr *, sbitmap *,
+ 					sbitmap *, sbitmap *));
+ static void compute_isoinout	PROTO ((int, int_list_ptr *, sbitmap *,
+ 					sbitmap *, sbitmap *, sbitmap *));
+ static void compute_optimal	PROTO ((int, sbitmap *,
+ 					sbitmap *, sbitmap *));
+ static void compute_redundant	PROTO ((int, int, sbitmap *,
+ 					sbitmap *, sbitmap *, sbitmap *));
+ 
+ /* Similarly, but for the reversed flowgraph.  */
+ static void compute_avinout 	PROTO ((int, int_list_ptr *, sbitmap *,
+ 					sbitmap *, sbitmap *, sbitmap *));
+ static void compute_fartherinout	PROTO ((int, int, int_list_ptr *,
+ 						sbitmap *, sbitmap *,
+ 						sbitmap *, sbitmap *));
+ static void compute_earlierinout  PROTO ((int, int, int_list_ptr *, sbitmap *,
+ 					  sbitmap *, sbitmap *,
+ 					  sbitmap *, sbitmap *));
+ static void compute_firstout	PROTO ((int, int, int_list_ptr *, sbitmap *,
+ 					sbitmap *, sbitmap *));
+ static void compute_rev_isoinout PROTO ((int, int_list_ptr *, sbitmap *,
+ 					 sbitmap *, sbitmap *, sbitmap *));
+ 
+ /* Given local properties TRANSP, ANTLOC, return the redundant and optimal
+    computation points for expressions.
+ 
+    To reduce overall memory consumption, we allocate memory immediately
+    before its needed and deallocate it as soon as possible.  */
+ void
+ pre_lcm (n_blocks, n_exprs, s_preds, s_succs, transp,
+ 	 antloc, redundant, optimal)
+      int n_blocks;
+      int n_exprs;
+      int_list_ptr *s_preds;
+      int_list_ptr *s_succs;
+      sbitmap *transp;
+      sbitmap *antloc;
+      sbitmap *redundant;
+      sbitmap *optimal;
+ {
+   sbitmap *antin, *antout, *earlyin, *earlyout, *delayin, *delayout;
+   sbitmap *latein, *isoin, *isoout;
+ 
+   /* Compute global anticipatability.  ANTOUT is not needed except to
+      compute ANTIN, so free its memory as soon as we return from
+      compute_antinout.  */
+   antin = sbitmap_vector_alloc (n_blocks, n_exprs);
+   antout = sbitmap_vector_alloc (n_blocks, n_exprs);
+   compute_antinout (n_blocks, s_succs, antloc,
+ 		    transp, antin, antout);
+   free (antout);
+   antout = NULL;
+ 
+   /* Compute earliestness.  EARLYOUT is not needed except to compute
+      EARLYIN, so free its memory as soon as we return from
+      compute_earlyinout.  */
+   earlyin = sbitmap_vector_alloc (n_blocks, n_exprs);
+   earlyout = sbitmap_vector_alloc (n_blocks, n_exprs);
+   compute_earlyinout (n_blocks, n_exprs, s_preds, transp, antin,
+ 		      earlyin, earlyout);
+   free (earlyout);
+   earlyout = NULL;
+ 
+   /* Compute delayedness.  DELAYOUT is not needed except to compute
+      DELAYIN, so free its memory as soon as we return from
+      compute_delayinout.  We also no longer need ANTIN and EARLYIN.  */
+   delayin = sbitmap_vector_alloc (n_blocks, n_exprs);
+   delayout = sbitmap_vector_alloc (n_blocks, n_exprs);
+   compute_delayinout (n_blocks, n_exprs, s_preds, antloc,
+ 		      antin, earlyin, delayin, delayout);
+   free (delayout);
+   delayout = NULL;
+   free (antin);
+   antin = NULL;
+   free (earlyin);
+   earlyin = NULL;
+ 
+   /* Compute latestness.  We no longer need DELAYIN after we compute
+      LATEIN.  */
+   latein = sbitmap_vector_alloc (n_blocks, n_exprs);
+   compute_latein (n_blocks, n_exprs, s_succs, antloc, delayin, latein);
+   free (delayin);
+   delayin = NULL;
+ 
+   /* Compute isolatedness.  ISOIN is not needed except to compute
+      ISOOUT, so free its memory as soon as we return from
+      compute_isoinout.  */
+   isoin = sbitmap_vector_alloc (n_blocks, n_exprs);
+   isoout = sbitmap_vector_alloc (n_blocks, n_exprs);
+   compute_isoinout (n_blocks, s_succs, antloc, latein, isoin, isoout);
+   free (isoin);
+   isoin = NULL;
+ 
+   /* Now compute optimal placement points and the redundant expressions.  */
+   compute_optimal (n_blocks, latein, isoout, optimal);
+   compute_redundant (n_blocks, n_exprs, antloc, latein, isoout, redundant);
+   free (latein);
+   latein = NULL;
+   free (isoout);
+   isoout = NULL;
+ }
+ 
+ /* Given local properties TRANSP, AVLOC, return the redundant and optimal
+    computation points for expressions on the reverse flowgraph.
+ 
+    To reduce overall memory consumption, we allocate memory immediately
+    before its needed and deallocate it as soon as possible.  */
+ 
+ void
+ pre_rev_lcm (n_blocks, n_exprs, s_preds, s_succs, transp,
+ 	     avloc, redundant, optimal)
+      int n_blocks;
+      int n_exprs;
+      int_list_ptr *s_preds;
+      int_list_ptr *s_succs;
+      sbitmap *transp;
+      sbitmap *avloc;
+      sbitmap *redundant;
+      sbitmap *optimal;
+ {
+   sbitmap *avin, *avout, *fartherin, *fartherout, *earlierin, *earlierout;
+   sbitmap *firstout, *rev_isoin, *rev_isoout;
+ 
+   /* Compute global availability.  AVIN is not needed except to
+      compute AVOUT, so free its memory as soon as we return from
+      compute_avinout.  */
+   avin = sbitmap_vector_alloc (n_blocks, n_exprs);
+   avout = sbitmap_vector_alloc (n_blocks, n_exprs);
+   compute_avinout (n_blocks, s_preds, avloc, transp, avin, avout);
+   free (avin);
+   avin = NULL;
+ 
+   /* Compute fartherness.  FARTHERIN is not needed except to compute
+      FARTHEROUT, so free its memory as soon as we return from
+      compute_earlyinout.  */
+   fartherin = sbitmap_vector_alloc (n_blocks, n_exprs);
+   fartherout = sbitmap_vector_alloc (n_blocks, n_exprs);
+   compute_fartherinout (n_blocks, n_exprs, s_succs, transp,
+ 			avout, fartherin, fartherout);
+   free (fartherin);
+   fartherin = NULL;
+ 
+   /* Compute earlierness.  EARLIERIN is not needed except to compute
+      EARLIEROUT, so free its memory as soon as we return from
+      compute_delayinout.  We also no longer need AVOUT and FARTHEROUT.  */
+   earlierin = sbitmap_vector_alloc (n_blocks, n_exprs);
+   earlierout = sbitmap_vector_alloc (n_blocks, n_exprs);
+   compute_earlierinout (n_blocks, n_exprs, s_succs, avloc,
+ 		        avout, fartherout, earlierin, earlierout);
+   free (earlierin);
+   earlierin = NULL;
+   free (avout);
+   avout = NULL;
+   free (fartherout);
+   fartherout = NULL;
+ 
+   /* Compute firstness.  We no longer need EARLIEROUT after we compute
+      FIRSTOUT.  */
+   firstout = sbitmap_vector_alloc (n_blocks, n_exprs);
+   compute_firstout (n_blocks, n_exprs, s_preds, avloc, earlierout, firstout);
+   free (earlierout);
+   earlierout = NULL;
+ 
+   /* Compute rev_isolatedness.  ISOIN is not needed except to compute
+      ISOOUT, so free its memory as soon as we return from
+      compute_isoinout.  */
+   rev_isoin = sbitmap_vector_alloc (n_blocks, n_exprs);
+   rev_isoout = sbitmap_vector_alloc (n_blocks, n_exprs);
+   compute_rev_isoinout (n_blocks, s_preds, avloc, firstout,
+ 			rev_isoin, rev_isoout);
+   free (rev_isoout);
+   rev_isoout = NULL;
+ 
+   /* Now compute optimal placement points and the redundant expressions.  */
+   compute_optimal (n_blocks, firstout, rev_isoin, optimal);
+   compute_redundant (n_blocks, n_exprs, avloc, firstout, rev_isoin, redundant);
+   free (firstout);
+   firstout = NULL;
+   free (rev_isoin);
+   rev_isoin = NULL;
+ }
+ 
+ /* Compute expression anticipatability at entrance and exit of each block.  */
+ 
+ static void
+ compute_antinout (n_blocks, s_succs, antloc, transp, antin, antout)
+      int n_blocks;
+      int_list_ptr *s_succs;
+      sbitmap *antloc;
+      sbitmap *transp;
+      sbitmap *antin;
+      sbitmap *antout;
+ {
+   int bb, changed, passes;
+   sbitmap old_changed, new_changed;
+ 
+   sbitmap_zero (antout[n_blocks - 1]);
+   sbitmap_vector_ones (antin, n_blocks);
+ 
+   old_changed = sbitmap_alloc (n_blocks);
+   new_changed = sbitmap_alloc (n_blocks);
+   sbitmap_ones (old_changed);
+ 
+   passes = 0;
+   changed = 1;
+   while (changed)
+     {
+       changed = 0;
+       sbitmap_zero (new_changed);
+       /* We scan the blocks in the reverse order to speed up
+ 	 the convergence.  */
+       for (bb = n_blocks - 1; bb >= 0; bb--)
+ 	{
+ 	  int_list_ptr ps;
+ 
+ 	  /* If none of the successors of this block have changed,
+ 	     then this block is not going to change.  */
+ 	  for (ps = s_succs[bb] ; ps; ps = ps->next)
+ 	    {
+ 	      if (INT_LIST_VAL (ps) == EXIT_BLOCK
+ 		  || INT_LIST_VAL (ps) == ENTRY_BLOCK)
+ 		break;
+ 
+ 	      if (TEST_BIT (old_changed, INT_LIST_VAL (ps))
+ 		  || TEST_BIT (new_changed, INT_LIST_VAL (ps)))
+ 		break;
+ 	    }
+ 
+ 	  if (!ps)
+ 	    continue;
+ 
+ 	  if (bb != n_blocks - 1)
+ 	    sbitmap_intersect_of_successors (antout[bb], antin,
+ 					     bb, s_succs);
+  	  if (sbitmap_a_or_b_and_c (antin[bb], antloc[bb],
+ 				    transp[bb], antout[bb]))
+ 	    {
+ 	      changed = 1;
+ 	      SET_BIT (new_changed, bb);
+ 	    }
+ 	}
+       sbitmap_copy (old_changed, new_changed);
+       passes++;
+     }
+   free (old_changed);
+   free (new_changed);
+ }
+ 
+ /* Compute expression earliestness at entrance and exit of each block.
+ 
+    From Advanced Compiler Design and Implementation pp411.
+ 
+    An expression is earliest at the entrance to basic block BB if no
+    block from entry to block BB both evaluates the expression and
+    produces the same value as evaluating it at the entry to block BB
+    does.  Similarly for earlistness at basic block BB exit.  */
+ 
+ static void
+ compute_earlyinout (n_blocks, n_exprs, s_preds, transp, antin,
+ 		    earlyin, earlyout)
+      int n_blocks;
+      int n_exprs;
+      int_list_ptr *s_preds;
+      sbitmap *transp;
+      sbitmap *antin;
+      sbitmap *earlyin;
+      sbitmap *earlyout;
+ {
+   int bb, changed, passes;
+   sbitmap temp_bitmap;
+   sbitmap old_changed, new_changed;
+ 
+   temp_bitmap = sbitmap_alloc (n_exprs);
+ 
+   sbitmap_vector_zero (earlyout, n_blocks);
+   sbitmap_ones (earlyin[0]);
+ 
+   old_changed = sbitmap_alloc (n_blocks);
+   new_changed = sbitmap_alloc (n_blocks);
+   sbitmap_ones (old_changed);
+ 
+   passes = 0;
+   changed = 1;
+   while (changed)
+     {
+       changed = 0;
+       sbitmap_zero (new_changed);
+       for (bb = 0; bb < n_blocks; bb++)
+ 	{
+ 	  int_list_ptr ps;
+ 
+ 	  /* If none of the predecessors of this block have changed,
+ 	     then this block is not going to change.  */
+ 	  for (ps = s_preds[bb] ; ps; ps = ps->next)
+ 	    {
+ 	      if (INT_LIST_VAL (ps) == EXIT_BLOCK
+ 		  || INT_LIST_VAL (ps) == ENTRY_BLOCK)
+ 		break;
+ 
+ 	      if (TEST_BIT (old_changed, INT_LIST_VAL (ps))
+ 		  || TEST_BIT (new_changed, INT_LIST_VAL (ps)))
+ 		break;
+ 	    }
+ 
+ 	  if (!ps)
+ 	    continue;
+ 
+ 	  if (bb != 0)
+ 	    sbitmap_union_of_predecessors (earlyin[bb], earlyout,
+ 					   bb, s_preds);
+ 	  sbitmap_not (temp_bitmap, transp[bb]);
+ 	  if (sbitmap_union_of_diff (earlyout[bb], temp_bitmap,
+ 				     earlyin[bb], antin[bb]))
+ 	    {
+ 	      changed = 1;
+ 	      SET_BIT (new_changed, bb);
+ 	    }
+ 	}
+       sbitmap_copy (old_changed, new_changed);
+       passes++;
+     }
+   free (old_changed);
+   free (new_changed);
+   free (temp_bitmap);
+ }
+ 
+ /* Compute expression delayedness at entrance and exit of each block.
+ 
+    From Advanced Compiler Design and Implementation pp411.
+ 
+    An expression is delayed at the entrance to BB if it is anticipatable
+    and earliest at that point and if all subsequent computations of
+    the expression are in block BB.   */
+ 
+ static void
+ compute_delayinout (n_blocks, n_exprs, s_preds, antloc,
+ 		    antin, earlyin, delayin, delayout)
+      int n_blocks;
+      int n_exprs;
+      int_list_ptr *s_preds;
+      sbitmap *antloc;
+      sbitmap *antin;
+      sbitmap *earlyin;
+      sbitmap *delayin;
+      sbitmap *delayout;
+ {
+   int bb, changed, passes;
+   sbitmap *anti_and_early;
+   sbitmap temp_bitmap;
+ 
+   temp_bitmap = sbitmap_alloc (n_exprs);
+ 
+   /* This is constant throughout the flow equations below, so compute
+      it once to save time.  */
+   anti_and_early = sbitmap_vector_alloc (n_blocks, n_exprs);
+   for (bb = 0; bb < n_blocks; bb++)
+     sbitmap_a_and_b (anti_and_early[bb], antin[bb], earlyin[bb]);
+   
+   sbitmap_vector_zero (delayout, n_blocks);
+   sbitmap_copy (delayin[0], anti_and_early[0]);
+ 
+   passes = 0;
+   changed = 1;
+   while (changed)
+     {
+       changed = 0;
+       for (bb = 0; bb < n_blocks; bb++)
+ 	{
+ 	  if (bb != 0)
+ 	    {
+ 	      sbitmap_intersect_of_predecessors (temp_bitmap, delayout,
+ 						 bb, s_preds);
+ 	      changed |= sbitmap_a_or_b (delayin[bb],
+ 					 anti_and_early[bb],
+ 					 temp_bitmap);
+ 	    }
+ 	  sbitmap_not (temp_bitmap, antloc[bb]);
+ 	  changed |= sbitmap_a_and_b (delayout[bb],
+ 				      temp_bitmap,
+ 				      delayin[bb]);
+ 	}
+       passes++;
+     }
+ 
+   /* We're done with this, so go ahead and free it's memory now instead
+      of waiting until the end of pre.  */
+   free (anti_and_early);
+   free (temp_bitmap);
+ }
+ 
+ /* Compute latestness.
+ 
+    From Advanced Compiler Design and Implementation pp412.
+ 
+    An expression is latest at the entrance to block BB if that is an optimal
+    point for computing the expression and if on every path from block BB's
+    entrance to the exit block, any optimal computation point for the 
+    expression occurs after one of the points at which the expression was
+    computed in the original flowgraph.  */
+ 
+ static void
+ compute_latein (n_blocks, n_exprs, s_succs, antloc, delayin, latein)
+      int n_blocks;
+      int n_exprs;
+      int_list_ptr *s_succs;
+      sbitmap *antloc;
+      sbitmap *delayin;
+      sbitmap *latein;
+ {
+   int bb;
+   sbitmap temp_bitmap;
+ 
+   temp_bitmap = sbitmap_alloc (n_exprs);
+ 
+   for (bb = 0; bb < n_blocks; bb++)
+     {
+       /* The last block is succeeded only by the exit block; therefore,
+ 	 temp_bitmap will not be set by the following call!  */
+       if (bb == n_blocks - 1)
+ 	{
+           sbitmap_intersect_of_successors (temp_bitmap, delayin,
+ 				           bb, s_succs);
+ 	  sbitmap_not (temp_bitmap, temp_bitmap);
+ 	}
+       else
+ 	sbitmap_ones (temp_bitmap);
+       sbitmap_a_and_b_or_c (latein[bb], delayin[bb],
+ 			    antloc[bb], temp_bitmap);
+     }
+   free (temp_bitmap);
+ }
+ 
+ /* Compute isolated.
+ 
+    From Advanced Compiler Design and Implementation pp413.
+ 
+    A computationally optimal placement for the evaluation of an expression
+    is defined to be isolated if and only if on every path from a successor
+    of the block in which it is computed to the exit block, every original
+    computation of the expression is preceded by the optimal placement point.  */
+ 
+ static void
+ compute_isoinout (n_blocks, s_succs, antloc, latein, isoin, isoout)
+      int n_blocks;
+      int_list_ptr *s_succs;
+      sbitmap *antloc;
+      sbitmap *latein;
+      sbitmap *isoin;
+      sbitmap *isoout;
+ {
+   int bb, changed, passes;
+ 
+   sbitmap_vector_zero (isoin, n_blocks);
+   sbitmap_zero (isoout[n_blocks - 1]);
+ 
+   passes = 0;
+   changed = 1;
+   while (changed)
+     {
+       changed = 0;
+       for (bb = n_blocks - 1; bb >= 0; bb--)
+ 	{
+ 	  if (bb != n_blocks - 1)
+ 	    sbitmap_intersect_of_successors (isoout[bb], isoin,
+ 					     bb, s_succs);
+ 	  changed |= sbitmap_union_of_diff (isoin[bb], latein[bb],
+ 					    isoout[bb], antloc[bb]);
+ 	}
+       passes++;
+     }
+ }
+ 
+ /* Compute the set of expressions which have optimal computational points
+    in each basic block.  This is the set of expressions that are latest, but
+    that are not isolated in the block.  */
+ 
+ static void
+ compute_optimal (n_blocks, latein, isoout, optimal)
+      int n_blocks;
+      sbitmap *latein;
+      sbitmap *isoout;
+      sbitmap *optimal;
+ {
+   int bb;
+ 
+   for (bb = 0; bb < n_blocks; bb++)
+     sbitmap_difference (optimal[bb], latein[bb], isoout[bb]);
+ }
+ 
+ /* Compute the set of expressions that are redundant in a block.  They are
+    the expressions that are used in the block and that are neither isolated
+    or latest.  */
+ 
+ static void
+ compute_redundant (n_blocks, n_exprs, antloc, latein, isoout, redundant)
+      int n_blocks;
+      int n_exprs;
+      sbitmap *antloc;
+      sbitmap *latein;
+      sbitmap *isoout;
+      sbitmap *redundant;
+ {
+   int bb;
+   sbitmap temp_bitmap;
+ 
+   temp_bitmap = sbitmap_alloc (n_exprs);
+ 
+   for (bb = 0; bb < n_blocks; bb++)
+     {
+       sbitmap_a_or_b (temp_bitmap, latein[bb], isoout[bb]);
+       sbitmap_difference (redundant[bb], antloc[bb], temp_bitmap);
+     }
+   free (temp_bitmap);
+ }
+ 
+ /* Compute expression availability at entrance and exit of each block.  */
+ 
+ static void
+ compute_avinout (n_blocks, s_preds, avloc, transp, avin, avout)
+      int n_blocks;
+      int_list_ptr *s_preds;
+      sbitmap *avloc;
+      sbitmap *transp;
+      sbitmap *avin;
+      sbitmap *avout;
+ {
+   int bb, changed, passes;
+ 
+   sbitmap_zero (avin[0]);
+   sbitmap_vector_ones (avout, n_blocks);
+ 
+   passes = 0;
+   changed = 1;
+   while (changed)
+     {
+       changed = 0;
+       for (bb = 0; bb < n_blocks; bb++)
+ 	{
+ 	  if (bb != 0)
+ 	    sbitmap_intersect_of_predecessors (avin[bb], avout,
+ 					       bb, s_preds);
+ 	  changed |= sbitmap_a_or_b_and_c (avout[bb], avloc[bb],
+ 					   transp[bb], avin[bb]);
+ 	}
+       passes++;
+     }
+ }
+ 
+ /* Compute expression latestness.
+ 
+    This is effectively the same as earliestness computed on the reverse
+    flow graph.  */
+ 
+ static void
+ compute_fartherinout (n_blocks, n_exprs, s_succs,
+ 		      transp, avout, fartherin, fartherout)
+      int n_blocks;
+      int n_exprs;
+      int_list_ptr *s_succs;
+      sbitmap *transp;
+      sbitmap *avout;
+      sbitmap *fartherin;
+      sbitmap *fartherout;
+ {
+   int bb, changed, passes;
+   sbitmap temp_bitmap;
+ 
+   temp_bitmap = sbitmap_alloc (n_exprs);
+ 
+   sbitmap_vector_zero (fartherin, n_blocks);
+   sbitmap_ones (fartherout[n_blocks - 1]);
+ 
+   passes = 0;
+   changed = 1;
+   while (changed)
+     {
+       changed = 0;
+       for (bb = n_blocks - 1; bb >= 0; bb--)
+ 	{
+ 	  if (bb != n_blocks - 1)
+ 	    sbitmap_union_of_successors (fartherout[bb], fartherin,
+ 					 bb, s_succs);
+ 	  sbitmap_not (temp_bitmap, transp[bb]);
+ 	  changed |= sbitmap_union_of_diff (fartherin[bb], temp_bitmap,
+ 					    fartherout[bb], avout[bb]);
+ 	}
+       passes++;
+     }
+ 
+   free (temp_bitmap);
+ }
+ 
+ /* Compute expression earlierness at entrance and exit of each block.
+ 
+    This is effectively the same as delayedness computed on the reverse
+    flow graph.  */
+ 
+ static void
+ compute_earlierinout (n_blocks, n_exprs, s_succs, avloc,
+ 		      avout, fartherout, earlierin, earlierout)
+      int n_blocks;
+      int n_exprs;
+      int_list_ptr *s_succs;
+      sbitmap *avloc;
+      sbitmap *avout;
+      sbitmap *fartherout;
+      sbitmap *earlierin;
+      sbitmap *earlierout;
+ {
+   int bb, changed, passes;
+   sbitmap *av_and_farther;
+   sbitmap temp_bitmap;
+ 
+   temp_bitmap = sbitmap_alloc (n_exprs);
+ 
+   /* This is constant throughout the flow equations below, so compute
+      it once to save time.  */
+   av_and_farther = sbitmap_vector_alloc (n_blocks, n_exprs);
+   for (bb = 0; bb < n_blocks; bb++)
+     sbitmap_a_and_b (av_and_farther[bb], avout[bb], fartherout[bb]);
+   
+   sbitmap_vector_zero (earlierin, n_blocks);
+   sbitmap_copy (earlierout[n_blocks - 1], av_and_farther[n_blocks - 1]);
+ 
+   passes = 0;
+   changed = 1;
+   while (changed)
+     {
+       changed = 0;
+       for (bb = n_blocks - 1; bb >= 0; bb--)
+ 	{
+ 	  if (bb != n_blocks - 1)
+ 	    {
+ 	      sbitmap_intersect_of_successors (temp_bitmap, earlierin,
+ 					       bb, s_succs);
+ 	      changed |= sbitmap_a_or_b (earlierout[bb],
+ 					 av_and_farther[bb],
+ 					 temp_bitmap);
+ 	    }
+ 	  sbitmap_not (temp_bitmap, avloc[bb]);
+ 	  changed |= sbitmap_a_and_b (earlierin[bb],
+ 				      temp_bitmap,
+ 				      earlierout[bb]);
+ 	}
+       passes++;
+     }
+ 
+   /* We're done with this, so go ahead and free it's memory now instead
+      of waiting until the end of pre.  */
+   free (av_and_farther);
+   free (temp_bitmap);
+ }
+ 
+ /* Compute firstness. 
+ 
+    This is effectively the same as latestness computed on the reverse
+    flow graph.  */
+ 
+ static void
+ compute_firstout (n_blocks, n_exprs, s_preds, avloc, earlierout, firstout)
+      int n_blocks;
+      int n_exprs;
+      int_list_ptr *s_preds;
+      sbitmap *avloc;
+      sbitmap *earlierout;
+      sbitmap *firstout;
+ {
+   int bb;
+   sbitmap temp_bitmap;
+ 
+   temp_bitmap = sbitmap_alloc (n_exprs);
+ 
+   for (bb = 0; bb < n_blocks; bb++)
+     {
+       /* The first block is preceded only by the entry block; therefore,
+ 	 temp_bitmap will not be set by the following call!  */
+       if (bb != 0)
+ 	{
+ 	  sbitmap_intersect_of_predecessors (temp_bitmap, earlierout,
+ 					     bb, s_preds);
+ 	  sbitmap_not (temp_bitmap, temp_bitmap);
+ 	}
+       else
+ 	{
+ 	  sbitmap_ones (temp_bitmap);
+ 	}
+       sbitmap_a_and_b_or_c (firstout[bb], earlierout[bb],
+ 			    avloc[bb], temp_bitmap);
+     }
+   free (temp_bitmap);
+ }
+ 
+ /* Compute reverse isolated.
+ 
+    This is effectively the same as isolatedness computed on the reverse
+    flow graph.  */
+ 
+ static void
+ compute_rev_isoinout (n_blocks, s_preds, avloc, firstout,
+ 		      rev_isoin, rev_isoout)
+      int n_blocks;
+      int_list_ptr *s_preds;
+      sbitmap *avloc;
+      sbitmap *firstout;
+      sbitmap *rev_isoin;
+      sbitmap *rev_isoout;
+ {
+   int bb, changed, passes;
+ 
+   sbitmap_vector_zero (rev_isoout, n_blocks);
+   sbitmap_zero (rev_isoin[0]);
+ 
+   passes = 0;
+   changed = 1;
+   while (changed)
+     {
+       changed = 0;
+       for (bb = 0; bb < n_blocks; bb++)
+ 	{
+ 	  if (bb != 0)
+ 	    sbitmap_intersect_of_predecessors (rev_isoin[bb], rev_isoout,
+ 					       bb, s_preds);
+ 	  changed |= sbitmap_union_of_diff (rev_isoout[bb], firstout[bb],
+ 					    rev_isoin[bb], avloc[bb]);
+ 	}
+       passes++;
+     }
+ }


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