This patch adds a pass that collects information that is common to all
uses of an SSA name X and back-propagates that information up the statements
that generate X.  The general idea is to use the information to simplify
instructions (rather than a pure DCE) so I've simply called it
tree-ssa-backprop.c, to go with tree-ssa-forwprop.c.

At the moment the only use of the pass is to remove unnecessry sign
operations, so that it's effectively a global version of
fold_strip_sign_ops.  I'm hoping it could be extended in future to
record which bits of an integer are significant.  There are probably
other potential uses too.

A later patch gets rid of fold_strip_sign_ops.

Tested on x86_64-linux-gnu, aarch64-linux-gnu and arm-linux-gnueabi.
OK to install?

Thanks,
Richard


gcc/
        * doc/invoke.texi (-fdump-tree-backprop, -ftree-backprop): Document.
        * Makefile.in (OBJS): Add tree-ssa-backprop.o.
        * common.opt (ftree-backprop): New option.
        * fold-const.h (negate_mathfn_p): Declare.
        * fold-const.c (negate_mathfn_p): Make public.
        * timevar.def (TV_TREE_BACKPROP): New.
        * tree-passes.h (make_pass_backprop): Declare.
        * passes.def (pass_backprop): Add.
        * tree-ssa-backprop.c: New file.

gcc/testsuite/
        * gcc.dg/tree-ssa/backprop-1.c, gcc.dg/tree-ssa/backprop-2.c,
        gcc.dg/tree-ssa/backprop-3.c, gcc.dg/tree-ssa/backprop-4.c,
        gcc.dg/tree-ssa/backprop-5.c, gcc.dg/tree-ssa/backprop-6.c: New tests.

diff --git a/gcc/Makefile.in b/gcc/Makefile.in
index 783e4c9..69e669d 100644
--- a/gcc/Makefile.in
+++ b/gcc/Makefile.in
@@ -1445,6 +1445,7 @@ OBJS = \
        tree-switch-conversion.o \
        tree-ssa-address.o \
        tree-ssa-alias.o \
+       tree-ssa-backprop.o \
        tree-ssa-ccp.o \
        tree-ssa-coalesce.o \
        tree-ssa-copy.o \
diff --git a/gcc/common.opt b/gcc/common.opt
index 5060208..5aef625 100644
--- a/gcc/common.opt
+++ b/gcc/common.opt
@@ -2364,6 +2364,10 @@ ftree-pta
 Common Report Var(flag_tree_pta) Optimization
 Perform function-local points-to analysis on trees.
 
+ftree-backprop
+Common Report Var(flag_tree_backprop) Init(1) Optimization
+Enable backward propagation of use properties at the tree level.
+
 ftree-reassoc
 Common Report Var(flag_tree_reassoc) Init(1) Optimization
 Enable reassociation on tree level
diff --git a/gcc/doc/invoke.texi b/gcc/doc/invoke.texi
index 54e9f12..fe15d08 100644
--- a/gcc/doc/invoke.texi
+++ b/gcc/doc/invoke.texi
@@ -343,6 +343,7 @@ Objective-C and Objective-C++ Dialects}.
 -fdump-tree-dse@r{[}-@var{n}@r{]} @gol
 -fdump-tree-phiprop@r{[}-@var{n}@r{]} @gol
 -fdump-tree-phiopt@r{[}-@var{n}@r{]} @gol
+-fdump-tree-backprop@r{[}-@var{n}@r{]} @gol
 -fdump-tree-forwprop@r{[}-@var{n}@r{]} @gol
 -fdump-tree-nrv -fdump-tree-vect @gol
 -fdump-tree-sink @gol
@@ -451,8 +452,8 @@ Objective-C and Objective-C++ Dialects}.
 -fstrict-overflow -fthread-jumps -ftracer -ftree-bit-ccp @gol
 -ftree-builtin-call-dce -ftree-ccp -ftree-ch @gol
 -ftree-coalesce-vars -ftree-copy-prop -ftree-dce -ftree-dominator-opts @gol
--ftree-dse -ftree-forwprop -ftree-fre -ftree-loop-if-convert @gol
--ftree-loop-if-convert-stores -ftree-loop-im @gol
+-ftree-dse -ftree-backprop -ftree-forwprop -ftree-fre @gol
+-ftree-loop-if-convert -ftree-loop-if-convert-stores -ftree-loop-im @gol
 -ftree-phiprop -ftree-loop-distribution -ftree-loop-distribute-patterns @gol
 -ftree-loop-ivcanon -ftree-loop-linear -ftree-loop-optimize @gol
 -ftree-loop-vectorize @gol
@@ -7236,6 +7237,12 @@ name is made by appending @file{.dse} to the source file 
name.
 Dump each function after optimizing PHI nodes into straightline code.  The file
 name is made by appending @file{.phiopt} to the source file name.
 
+@item backprop
+@opindex fdump-tree-backprop
+Dump each function after back-propagating use information up the definition
+chain.  The file name is made by appending @file{.backprop} to the
+source file name.
+
 @item forwprop
 @opindex fdump-tree-forwprop
 Dump each function after forward propagating single use variables.  The file
@@ -7716,6 +7723,7 @@ compilation time.
 -ftree-dce @gol
 -ftree-dominator-opts @gol
 -ftree-dse @gol
+-ftree-backprop @gol
 -ftree-forwprop @gol
 -ftree-fre @gol
 -ftree-phiprop @gol
@@ -8658,6 +8666,13 @@ enabled by default at @option{-O2} and @option{-O3}.
 Make partial redundancy elimination (PRE) more aggressive.  This flag is
 enabled by default at @option{-O3}.
 
+@item -ftree-backprop
+@opindex ftree-backprop
+Propagate information about uses of a value up the definition chain
+in order to simplify the definitions.  For example, this pass strips
+sign operations if the sign of a value never matters.  The flag is
+enabled by default at @option{-O} and higher.
+
 @item -ftree-forwprop
 @opindex ftree-forwprop
 Perform forward propagation on trees.  This flag is enabled by default
diff --git a/gcc/fold-const.c b/gcc/fold-const.c
index de45a2c..7f00e72 100644
--- a/gcc/fold-const.c
+++ b/gcc/fold-const.c
@@ -110,7 +110,6 @@ enum comparison_code {
   COMPCODE_TRUE = 15
 };
 
-static bool negate_mathfn_p (enum built_in_function);
 static bool negate_expr_p (tree);
 static tree negate_expr (tree);
 static tree split_tree (tree, enum tree_code, tree *, tree *, tree *, int);
@@ -319,7 +318,7 @@ fold_overflow_warning (const char* gmsgid, enum 
warn_strict_overflow_code wc)
 /* Return true if the built-in mathematical function specified by CODE
    is odd, i.e. -f(x) == f(-x).  */
 
-static bool
+bool
 negate_mathfn_p (enum built_in_function code)
 {
   switch (code)
diff --git a/gcc/fold-const.h b/gcc/fold-const.h
index ee74dc8..4d5b24b 100644
--- a/gcc/fold-const.h
+++ b/gcc/fold-const.h
@@ -173,6 +173,7 @@ extern tree sign_bit_p (tree, const_tree);
 extern tree exact_inverse (tree, tree);
 extern tree const_unop (enum tree_code, tree, tree);
 extern tree const_binop (enum tree_code, tree, tree, tree);
+extern bool negate_mathfn_p (enum built_in_function);
 
 /* Return OFF converted to a pointer offset type suitable as offset for
    POINTER_PLUS_EXPR.  Use location LOC for this conversion.  */
diff --git a/gcc/passes.def b/gcc/passes.def
index dc3f44c..36d2b3b 100644
--- a/gcc/passes.def
+++ b/gcc/passes.def
@@ -159,6 +159,7 @@ along with GCC; see the file COPYING3.  If not see
       /* After CCP we rewrite no longer addressed locals into SSA
         form if possible.  */
       NEXT_PASS (pass_complete_unrolli);
+      NEXT_PASS (pass_backprop);
       NEXT_PASS (pass_phiprop);
       NEXT_PASS (pass_forwprop);
       NEXT_PASS (pass_object_sizes);
diff --git a/gcc/testsuite/gcc.dg/tree-ssa/backprop-1.c 
b/gcc/testsuite/gcc.dg/tree-ssa/backprop-1.c
new file mode 100644
index 0000000..ff88ae8
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/tree-ssa/backprop-1.c
@@ -0,0 +1,22 @@
+/* { dg-do compile } */
+/* { dg-options "-O -fdump-tree-backprop-details" }  */
+
+/* Test a simple case of non-looping code in which both uses ignore
+   the sign and both definitions are sign ops.  */
+#define TEST_FUNCTION(TYPE, SUFFIX)                            \
+  TYPE                                                         \
+  test##SUFFIX (TYPE x, int sel1, int sel2)                    \
+  {                                                            \
+    TYPE input = sel1 ? -x : __builtin_fabs##SUFFIX (x);       \
+    if (sel2)                                                  \
+      return __builtin_cos##SUFFIX (input);                    \
+    else                                                       \
+      return __builtin_cosh##SUFFIX (input);                   \
+  }
+
+TEST_FUNCTION (float, f)
+TEST_FUNCTION (double, )
+TEST_FUNCTION (long double, l)
+
+/* { dg-final { scan-tree-dump-times {Deleting[^\n]* = -x} 3 "backprop" } } */
+/* { dg-final { scan-tree-dump-times {Deleting[^\n]* = ABS_EXPR <x} 3 
"backprop" } } */
diff --git a/gcc/testsuite/gcc.dg/tree-ssa/backprop-2.c 
b/gcc/testsuite/gcc.dg/tree-ssa/backprop-2.c
new file mode 100644
index 0000000..aa1233a
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/tree-ssa/backprop-2.c
@@ -0,0 +1,21 @@
+/* { dg-do compile } */
+/* { dg-options "-O -fdump-tree-backprop-details" }  */
+
+/* Test a simple case of non-looping code in which both uses ignore
+   the sign but only one definition is a sign op.  */
+#define TEST_FUNCTION(TYPE, SUFFIX)                            \
+  TYPE                                                         \
+  test##SUFFIX (TYPE x, int sel1, int sel2)                    \
+  {                                                            \
+    TYPE input = sel1 ? -x : x + 1;                            \
+    if (sel2)                                                  \
+      return __builtin_cos##SUFFIX (input);                    \
+    else                                                       \
+      return __builtin_cosh##SUFFIX (input);                   \
+  }
+
+TEST_FUNCTION (float, f)
+TEST_FUNCTION (double, )
+TEST_FUNCTION (long double, l)
+
+/* { dg-final { scan-tree-dump-times {Deleting[^\n]* = -x} 3 "backprop" } } */
diff --git a/gcc/testsuite/gcc.dg/tree-ssa/backprop-3.c 
b/gcc/testsuite/gcc.dg/tree-ssa/backprop-3.c
new file mode 100644
index 0000000..6381fff
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/tree-ssa/backprop-3.c
@@ -0,0 +1,21 @@
+/* { dg-do compile } */
+/* { dg-options "-O -fdump-tree-backprop-details" }  */
+
+/* Test a simple case of non-looping code in which one use ignores
+   the sign but another doesn't.  */
+#define TEST_FUNCTION(TYPE, SUFFIX)                            \
+  TYPE                                                         \
+  test##SUFFIX (TYPE x, int sel1, int sel2)                    \
+  {                                                            \
+    TYPE input = sel1 ? -x : __builtin_fabs##SUFFIX (x);       \
+    if (sel2)                                                  \
+      return __builtin_cos##SUFFIX (input);                    \
+    else                                                       \
+      return __builtin_sin##SUFFIX (input);                    \
+  }
+
+TEST_FUNCTION (float, f)
+TEST_FUNCTION (double, )
+TEST_FUNCTION (long double, l)
+
+/* { dg-final { scan-tree-dump-times {Deleting[^\n]* = -x} 0 "backprop" } } */
diff --git a/gcc/testsuite/gcc.dg/tree-ssa/backprop-4.c 
b/gcc/testsuite/gcc.dg/tree-ssa/backprop-4.c
new file mode 100644
index 0000000..fc96f3e
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/tree-ssa/backprop-4.c
@@ -0,0 +1,21 @@
+/* { dg-do compile } */
+/* { dg-options "-O -fdump-tree-backprop-details" }  */
+
+/* Test a simple reduction loop in which all inputs are sign ops and
+   the consumer doesn't care about the sign.  */
+#define TEST_FUNCTION(TYPE, SUFFIX)                    \
+  TYPE                                                 \
+  test##SUFFIX (TYPE x, TYPE y, TYPE *array, int n)    \
+  {                                                    \
+    x = __builtin_copysign##SUFFIX (x, y);             \
+    for (int i = 0; i < n; ++i)                                \
+      x *= -array[i];                                  \
+    return __builtin_hypot##SUFFIX (x, y);             \
+  }
+
+TEST_FUNCTION (float, f)
+TEST_FUNCTION (double, )
+TEST_FUNCTION (long double, l)
+
+/* { dg-final { scan-tree-dump-times {Deleting[^\n]* = __builtin_copysign} 3 
"backprop" } } */
+/* { dg-final { scan-tree-dump-times {Deleting[^\n]* = -} 3 "backprop" } } */
diff --git a/gcc/testsuite/gcc.dg/tree-ssa/backprop-5.c 
b/gcc/testsuite/gcc.dg/tree-ssa/backprop-5.c
new file mode 100644
index 0000000..90e18cb
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/tree-ssa/backprop-5.c
@@ -0,0 +1,20 @@
+/* { dg-do compile } */
+/* { dg-options "-O -fdump-tree-backprop-details" }  */
+
+/* Test a loop that does both a multiplication and addition.  The addition
+   should prevent any sign ops from being removed.  */
+#define TEST_FUNCTION(TYPE, SUFFIX)                    \
+  TYPE                                                 \
+  test##SUFFIX (TYPE x, TYPE y, TYPE *array, int n)    \
+  {                                                    \
+    x = __builtin_copysign##SUFFIX (x, y);             \
+    for (int i = 0; i < n; ++i)                                \
+      x = (x + 1) * array[i];                          \
+    return __builtin_hypot##SUFFIX (x, y);             \
+  }
+
+TEST_FUNCTION (float, f)
+TEST_FUNCTION (double, )
+TEST_FUNCTION (long double, l)
+
+/* { dg-final { scan-tree-dump-times {Deleting[^\n]* = __builtin_copysign} 0 
"backprop" } } */
diff --git a/gcc/testsuite/gcc.dg/tree-ssa/backprop-6.c 
b/gcc/testsuite/gcc.dg/tree-ssa/backprop-6.c
new file mode 100644
index 0000000..31f0571
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/tree-ssa/backprop-6.c
@@ -0,0 +1,30 @@
+/* { dg-do compile } */
+/* { dg-options "-O -fdump-tree-backprop-details" }  */
+
+void start (void *);
+void end (void *);
+
+/* Test that we optimize the contents of infinite loops.  */
+#define TEST_FUNCTION(TYPE, SUFFIX)                    \
+  void                                                 \
+  test##SUFFIX (TYPE *array, TYPE y, int n)            \
+  {                                                    \
+    for (;;)                                           \
+      {                                                        \
+       start (array);                                  \
+       TYPE x = -__builtin_fabs##SUFFIX (array[-1]);   \
+       for (int i = 0; i < n; ++i)                     \
+         x = -x / array[i];                            \
+       array[-1] = x * x;                              \
+       array[-2] = __builtin_fma##SUFFIX (x, x, y);    \
+       array[-3] = __builtin_pow##SUFFIX (x, 20);      \
+       end (array);                                    \
+      }                                                        \
+  }
+
+TEST_FUNCTION (float, f)
+TEST_FUNCTION (double, )
+TEST_FUNCTION (long double, l)
+
+/* { dg-final { scan-tree-dump-times {Deleting[^\n]* = -} 6 "backprop" } } */
+/* { dg-final { scan-tree-dump-times {Deleting[^\n]* = ABS_EXPR <} 3 
"backprop" } } */
diff --git a/gcc/timevar.def b/gcc/timevar.def
index ac41075..ef16226 100644
--- a/gcc/timevar.def
+++ b/gcc/timevar.def
@@ -163,6 +163,7 @@ DEFTIMEVAR (TV_TREE_PRE                  , "tree PRE")
 DEFTIMEVAR (TV_TREE_FRE                     , "tree FRE")
 DEFTIMEVAR (TV_TREE_SINK             , "tree code sinking")
 DEFTIMEVAR (TV_TREE_PHIOPT          , "tree linearize phis")
+DEFTIMEVAR (TV_TREE_BACKPROP        , "tree backward propagate")
 DEFTIMEVAR (TV_TREE_FORWPROP        , "tree forward propagate")
 DEFTIMEVAR (TV_TREE_PHIPROP         , "tree phiprop")
 DEFTIMEVAR (TV_TREE_DCE                     , "tree conservative DCE")
diff --git a/gcc/tree-pass.h b/gcc/tree-pass.h
index c37e4b2..333b5a7 100644
--- a/gcc/tree-pass.h
+++ b/gcc/tree-pass.h
@@ -497,6 +497,7 @@ extern gimple_opt_pass 
*make_pass_cleanup_cfg_post_optimizing (gcc::context
                                                               *ctxt);
 extern gimple_opt_pass *make_pass_init_datastructures (gcc::context *ctxt);
 extern gimple_opt_pass *make_pass_fixup_cfg (gcc::context *ctxt);
+extern gimple_opt_pass *make_pass_backprop (gcc::context *ctxt);
 
 extern rtl_opt_pass *make_pass_expand (gcc::context *ctxt);
 extern rtl_opt_pass *make_pass_instantiate_virtual_regs (gcc::context *ctxt);
diff --git a/gcc/tree-ssa-backprop.c b/gcc/tree-ssa-backprop.c
new file mode 100644
index 0000000..bf2dcd9
--- /dev/null
+++ b/gcc/tree-ssa-backprop.c
@@ -0,0 +1,900 @@
+/* Back-propagation of usage information to definitions.
+   Copyright (C) 2015 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 3, 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 COPYING3.  If not see
+<http://www.gnu.org/licenses/>.  */
+
+/* This pass propagates information that is common to all uses of an SSA
+   name back up through the sequence of statements that generate it,
+   simplifying the statements where possible.  Sometimes this can expose
+   fully or partially dead code, but the main focus is simplifying
+   computations.
+
+   At the moment the pass only handles one piece of information: whether the
+   sign of a value matters, and therefore whether sign-changing operations
+   can be skipped.  The pass could be extended to more interesting
+   information in future, such as which bits of an integer are significant.
+
+   For example, take the function:
+
+     double
+     f (double *a, int n, double start)
+     {
+       double x = fabs (start);
+       for (int i = 0; i < n; ++i)
+        x *= a[i];
+       return __builtin_cos (x);
+     }
+
+   cos(x) == cos(-x), so the sign of the final x doesn't matter.
+   That x is the result of a series of multiplications, and if
+   the sign of the result of a multiplication doesn't matter,
+   the signs of the inputs don't matter either.
+
+   The pass would replace the incoming value of x (i.e. fabs(start))
+   with start.  Since there are no other uses of the fabs result,
+   the call would get deleted as dead.
+
+   The algorithm is:
+
+   (1) Do a post-order traversal of the blocks in the function, walking
+       each block backwards.  For each potentially-simplifiable statement
+       that defines an SSA name X, examine all uses of X to see what
+       information is actually significant.  Record this as INFO_MAP[X].
+       Optimistically ignore for now any back-edge references to
+       unprocessed phis.
+
+   (2) Iteratively reduce the optimistic result of (1) until we reach
+       a maximal fixed point (which at the moment would mean revisiting
+       statements at most once).  First push all SSA names that used an
+       optimistic assumption about a backedge phi onto a worklist.
+       While the worklist is nonempty, pick off an SSA name X and recompute
+       INFO_MAP[X].  If the value changes, push all SSA names used in the
+       definition of X onto the worklist.
+
+   (3) Iterate over each SSA name X with info in INFO_MAP, in the
+       opposite order to (1), i.e. a forward reverse-post-order walk.
+       Try to optimize the definition of X using INFO_MAP[X] and fold
+       the result.  (This ensures that we fold definitions before uses.)
+
+   (4) Iterate over each SSA name X with info in INFO_MAP, in the same
+       order as (1), and delete any statements that are now dead.
+       (This ensures that if a sequence of statements is dead,
+       we delete the last statement first.)
+
+   Note that this pass does not deal with direct redundancies,
+   such as cos(-x)->cos(x).  match.pd handles those cases instead.  */
+
+#include "config.h"
+#include "system.h"
+#include "coretypes.h"
+#include "backend.h"
+#include "tree.h"
+#include "gimple.h"
+#include "gimple-iterator.h"
+#include "ssa.h"
+#include "fold-const.h"
+#include "tree-pass.h"
+#include "cfganal.h"
+#include "gimple-pretty-print.h"
+#include "tree-cfg.h"
+#include "tree-ssa-propagate.h"
+#include "gimple-fold.h"
+#include "alloc-pool.h"
+#include "tree-hash-traits.h"
+
+namespace {
+
+/* Information about a group of uses of an SSA name.  */
+struct usage_info
+{
+  usage_info () : flag_word (0) {}
+  usage_info &operator &= (const usage_info &);
+  usage_info operator & (const usage_info &) const;
+  bool operator == (const usage_info &) const;
+  bool operator != (const usage_info &) const;
+  bool is_useful () const;
+
+  static usage_info intersection_identity ();
+
+  union
+  {
+    struct
+    {
+      /* True if the uses treat x and -x in the same way.  */
+      unsigned int ignore_sign : 1;
+    } flags;
+    /* All the flag bits as a single int.  */
+    unsigned int flag_word;
+  };
+};
+
+/* Return an X such that X & Y == Y for all Y.  This is the most
+   optimistic assumption possible.  */
+
+usage_info
+usage_info::intersection_identity ()
+{
+  usage_info ret;
+  ret.flag_word = -1;
+  return ret;
+}
+
+/* Intersect *THIS with OTHER, so that *THIS describes all uses covered
+   by the original *THIS and OTHER.  */
+
+usage_info &
+usage_info::operator &= (const usage_info &other)
+{
+  flag_word &= other.flag_word;
+  return *this;
+}
+
+/* Return the intersection of *THIS and OTHER, i.e. a structure that
+   describes all uses covered by *THIS and OTHER.  */
+
+usage_info
+usage_info::operator & (const usage_info &other) const
+{
+  usage_info info (*this);
+  info &= other;
+  return info;
+}
+
+bool
+usage_info::operator == (const usage_info &other) const
+{
+  return flag_word == other.flag_word;
+}
+
+bool
+usage_info::operator != (const usage_info &other) const
+{
+  return !operator == (other);
+}
+
+/* Return true if *THIS is not simply the default, safe assumption.  */
+
+bool
+usage_info::is_useful () const
+{
+  return flag_word != 0;
+}
+
+/* Start a dump line about SSA name VAR.  */
+
+static void
+dump_usage_prefix (FILE *file, tree var)
+{
+  fprintf (file, "  ");
+  print_generic_expr (file, var, 0);
+  fprintf (file, ": ");
+}
+
+/* Print INFO to FILE.  */
+
+static void
+dump_usage_info (FILE *file, tree var, usage_info *info)
+{
+  if (info->flags.ignore_sign)
+    {
+      dump_usage_prefix (file, var);
+      fprintf (file, "sign bit not important\n");
+    }
+}
+
+/* Represents one execution of the pass.  */
+class backprop
+{
+public:
+  backprop (function *);
+  ~backprop ();
+
+  void execute ();
+
+private:
+  const usage_info *lookup_operand (tree);
+
+  void push_to_worklist (tree);
+  tree pop_from_worklist ();
+
+  void process_builtin_call_use (gcall *, tree, usage_info *);
+  void process_assign_use (gassign *, tree, usage_info *);
+  void process_phi_use (gphi *, usage_info *);
+  void process_use (gimple *, tree, usage_info *);
+  bool intersect_uses (tree, usage_info *);
+  void reprocess_inputs (gimple *);
+  void process_var (tree);
+  void process_block (basic_block);
+
+  void complete_change (gimple *);
+  void optimize_builtin_call (gcall *, const usage_info *);
+  void optimize_assign (gassign *, const usage_info *);
+  void optimize_phi (gphi *, const usage_info *);
+
+  typedef hash_map <tree_ssa_name_hash, usage_info *> info_map_type;
+  typedef std::pair <tree, usage_info *> var_info_pair;
+
+  /* The function we're optimizing.  */
+  function *m_fn;
+
+  /* Pool for allocating usage_info structures.  */
+  object_allocator <usage_info> m_info_pool;
+
+  /* Maps an SSA name to a description of all uses of that SSA name.
+     All the usage_infos satisfy is_useful.  */
+  info_map_type m_info_map;
+
+  /* Post-ordered list of all potentially-interesting SSA names,
+     along with information that describes all uses.  */
+  auto_vec <var_info_pair, 128> m_vars;
+
+  /* A bitmap of blocks that we have finished processing in the initial
+     post-order walk.  */
+  sbitmap m_visited_blocks;
+
+  /* A worklist of SSA names whose definitions need to be reconsidered.  */
+  auto_vec <tree, 64> m_worklist;
+
+  /* The SSA names in M_WORKLIST, identified by their SSA_NAME_VERSION.  */
+  bitmap m_worklist_names;
+};
+
+backprop::backprop (function *fn)
+  : m_fn (fn),
+    m_info_pool ("usage_info"),
+    m_visited_blocks (sbitmap_alloc (last_basic_block_for_fn (m_fn))),
+    m_worklist_names (BITMAP_ALLOC (NULL))
+{
+  bitmap_clear (m_visited_blocks);
+}
+
+backprop::~backprop ()
+{
+  BITMAP_FREE (m_worklist_names);
+  sbitmap_free (m_visited_blocks);
+  m_info_pool.release ();
+}
+
+/* Return usage information for general operand OP, or null if none.  */
+
+const usage_info *
+backprop::lookup_operand (tree op)
+{
+  if (op && TREE_CODE (op) == SSA_NAME)
+    if (usage_info **slot = m_info_map.get (op))
+      return *slot;
+  return NULL;
+}
+
+/* Add SSA name VAR to the worklist, if it isn't on the worklist already.  */
+
+void
+backprop::push_to_worklist (tree var)
+{
+  if (!bitmap_set_bit (m_worklist_names, SSA_NAME_VERSION (var)))
+    return;
+  m_worklist.safe_push (var);
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "[WORKLIST] Pushing ");
+      print_generic_expr (dump_file, var, 0);
+      fprintf (dump_file, "\n");
+    }
+}
+
+/* Remove and return the next SSA name from the worklist.  The worklist
+   is known to be nonempty.  */
+
+tree
+backprop::pop_from_worklist ()
+{
+  tree var = m_worklist.pop ();
+  bitmap_clear_bit (m_worklist_names, SSA_NAME_VERSION (var));
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "[WORKLIST] Popping ");
+      print_generic_expr (dump_file, var, 0);
+      fprintf (dump_file, "\n");
+    }
+  return var;
+}
+
+/* Make INFO describe all uses of RHS in CALL, which is a call to a
+   built-in function.  */
+
+void
+backprop::process_builtin_call_use (gcall *call, tree rhs, usage_info *info)
+{
+  enum built_in_function fn = DECL_FUNCTION_CODE (gimple_call_fndecl (call));
+  tree lhs = gimple_call_lhs (call);
+  switch (fn)
+    {
+    CASE_FLT_FN (BUILT_IN_COS):
+    CASE_FLT_FN (BUILT_IN_COSH):
+    CASE_FLT_FN (BUILT_IN_CCOS):
+    CASE_FLT_FN (BUILT_IN_CCOSH):
+    CASE_FLT_FN (BUILT_IN_HYPOT):
+      /* The signs of all inputs are ignored.  */
+      info->flags.ignore_sign = true;
+      break;
+
+    CASE_FLT_FN (BUILT_IN_COPYSIGN):
+      /* The sign of the first input is ignored.  */
+      if (rhs != gimple_call_arg (call, 1))
+       info->flags.ignore_sign = true;
+      break;
+
+    CASE_FLT_FN (BUILT_IN_POW):
+      {
+       /* The sign of the first input is ignored as long as the second
+          input is an even real.  */
+       tree power = gimple_call_arg (call, 1);
+       HOST_WIDE_INT n;
+       if (TREE_CODE (power) == REAL_CST
+           && real_isinteger (&TREE_REAL_CST (power), &n)
+           && (n & 1) == 0)
+         info->flags.ignore_sign = true;
+       break;
+      }
+
+    CASE_FLT_FN (BUILT_IN_FMA):
+      /* In X * X + Y, where Y is distinct from X, the sign of X doesn't
+        matter.  */
+      if (gimple_call_arg (call, 0) == rhs
+         && gimple_call_arg (call, 1) == rhs
+         && gimple_call_arg (call, 2) != rhs)
+       info->flags.ignore_sign = true;
+      break;
+
+    default:
+      if (negate_mathfn_p (fn))
+       /* The sign of the (single) input doesn't matter provided
+          that the sign of the output doesn't matter.  */
+       if (const usage_info *lhs_info = lookup_operand (lhs))
+         info->flags.ignore_sign = lhs_info->flags.ignore_sign;
+      break;
+    }
+}
+
+/* Make INFO describe all uses of RHS in ASSIGN.  */
+
+void
+backprop::process_assign_use (gassign *assign, tree rhs, usage_info *info)
+{
+  tree lhs = gimple_assign_lhs (assign);
+  switch (gimple_assign_rhs_code (assign))
+    {
+    case ABS_EXPR:
+      /* The sign of the input doesn't matter.  */
+      info->flags.ignore_sign = true;
+      break;
+
+    case COND_EXPR:
+      /* For A = B ? C : D, propagate information about all uses of A
+        to B and C.  */
+      if (rhs != gimple_assign_rhs1 (assign))
+       if (const usage_info *lhs_info = lookup_operand (lhs))
+         *info = *lhs_info;
+      break;
+
+    case FMA_EXPR:
+      /* In X * X + Y, where Y is distinct from X, the sign of X doesn't
+        matter.  */
+      if (gimple_assign_rhs1 (assign) == rhs
+         && gimple_assign_rhs2 (assign) == rhs
+         && gimple_assign_rhs3 (assign) != rhs)
+       info->flags.ignore_sign = true;
+      break;
+
+    case MULT_EXPR:
+      /* In X * X, the sign of X doesn't matter.  */
+      if (gimple_assign_rhs1 (assign) == rhs
+         && gimple_assign_rhs2 (assign) == rhs)
+       info->flags.ignore_sign = true;
+      /* Fall through.  */
+
+    case NEGATE_EXPR:
+    case RDIV_EXPR:
+      /* If the sign of the result doesn't matter, the sign of the inputs
+        doesn't matter either.  */
+      if (FLOAT_TYPE_P (TREE_TYPE (rhs)))
+       if (const usage_info *lhs_info = lookup_operand (lhs))
+         info->flags.ignore_sign = lhs_info->flags.ignore_sign;
+      break;
+
+    default:
+      break;
+    }
+}
+
+/* Make INFO describe the uses of PHI's result.  */
+
+void
+backprop::process_phi_use (gphi *phi, usage_info *info)
+{
+  tree result = gimple_phi_result (phi);
+  if (const usage_info *result_info = lookup_operand (result))
+    *info = *result_info;
+}
+
+/* Make INFO describe all uses of RHS in STMT.  */
+
+void
+backprop::process_use (gimple *stmt, tree rhs, usage_info *info)
+{
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "[USE] ");
+      print_generic_expr (dump_file, rhs, 0);
+      fprintf (dump_file, " in ");
+      print_gimple_stmt (dump_file, stmt, 0, TDF_SLIM);
+    }
+
+  if (gcall *call = dyn_cast <gcall *> (stmt))
+    {
+      if (gimple_call_builtin_p (call, BUILT_IN_NORMAL))
+       process_builtin_call_use (call, rhs, info);
+    }
+  else if (gassign *assign = dyn_cast <gassign *> (stmt))
+    process_assign_use (assign, rhs, info);
+  else if (gphi *phi = dyn_cast <gphi *> (stmt))
+    process_phi_use (phi, info);
+
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    dump_usage_info (dump_file, rhs, info);
+}
+
+/* Make INFO describe all uses of VAR, returning true if the result
+   is useful.  If the uses include phis that haven't been processed yet,
+   make the most optimistic assumption possible, so that we aim for
+   a maximum rather than a minimum fixed point.  */
+
+bool
+backprop::intersect_uses (tree var, usage_info *info)
+{
+  imm_use_iterator iter;
+  gimple *stmt;
+  *info = usage_info::intersection_identity ();
+  FOR_EACH_IMM_USE_STMT (stmt, iter, var)
+    {
+      if (is_a <gphi *> (stmt)
+         && !bitmap_bit_p (m_visited_blocks, gimple_bb (stmt)->index))
+       {
+         /* Skip unprocessed phis.  */
+         if (dump_file && (dump_flags & TDF_DETAILS))
+           {
+             fprintf (dump_file, "[BACKEDGE] ");
+             print_generic_expr (dump_file, var, 0);
+             fprintf (dump_file, " in ");
+             print_gimple_stmt (dump_file, stmt, 0, TDF_SLIM);
+           }
+       }
+      else
+       {
+         usage_info subinfo;
+         process_use (stmt, var, &subinfo);
+         *info &= subinfo;
+         if (!info->is_useful ())
+           {
+             BREAK_FROM_IMM_USE_STMT (iter);
+             return false;
+           }
+       }
+    }
+  return true;
+}
+
+/* Queue for reconsideration any input of STMT that has information
+   associated with it.  This is used if that information might be
+   too optimistic.  */
+
+void
+backprop::reprocess_inputs (gimple *stmt)
+{
+  use_operand_p use_p;
+  ssa_op_iter oi;
+  FOR_EACH_PHI_OR_STMT_USE (use_p, stmt, oi, SSA_OP_USE)
+    {
+      tree var = get_use_from_ptr (use_p);
+      if (lookup_operand (var))
+       push_to_worklist (var);
+    }
+}
+
+/* Say that we're recording INFO for SSA name VAR, or that we're deleting
+   existing information if INFO is null.  INTRO describes the change.  */
+
+static void
+dump_var_info (tree var, usage_info *info, const char *intro)
+{
+  fprintf (dump_file, "[DEF] %s for ", intro);
+  print_gimple_stmt (dump_file, SSA_NAME_DEF_STMT (var), 0, TDF_SLIM);
+  if (info)
+    dump_usage_info (dump_file, var, info);
+}
+
+/* Process all uses of VAR and record or update the result in
+   M_INFO_MAP and M_VARS.  */
+
+void
+backprop::process_var (tree var)
+{
+  if (has_zero_uses (var))
+    return;
+
+  usage_info info;
+  intersect_uses (var, &info);
+
+  gimple *stmt = SSA_NAME_DEF_STMT (var);
+  if (info.is_useful ())
+    {
+      bool existed;
+      usage_info *&map_info = m_info_map.get_or_insert (var, &existed);
+      if (!existed)
+       {
+         /* Recording information about VAR for the first time.  */
+         map_info = m_info_pool.allocate ();
+         *map_info = info;
+         m_vars.safe_push (var_info_pair (var, map_info));
+         if (dump_file && (dump_flags & TDF_DETAILS))
+           dump_var_info (var, map_info, "Recording new information");
+
+         /* If STMT is a phi, reprocess any backedge uses.  This is a
+            no-op for other uses, which won't have any information
+            associated with them.  */
+         if (is_a <gphi *> (stmt))
+           reprocess_inputs (stmt);
+       }
+      else if (info != *map_info)
+       {
+         /* Recording information that is less optimistic than before.  */
+         gcc_checking_assert ((info & *map_info) == info);
+         *map_info = info;
+         if (dump_file && (dump_flags & TDF_DETAILS))
+           dump_var_info (var, map_info, "Updating information");
+         reprocess_inputs (stmt);
+       }
+    }
+  else
+    {
+      if (usage_info **slot = m_info_map.get (var))
+       {
+         /* Removing previously-recorded information.  */
+         **slot = info;
+         m_info_map.remove (var);
+         if (dump_file && (dump_flags & TDF_DETAILS))
+           dump_var_info (var, NULL, "Deleting information");
+         reprocess_inputs (stmt);
+       }
+      else
+       {
+         /* If STMT is a phi, remove any information recorded for
+            its arguments.  */
+         if (is_a <gphi *> (stmt))
+           reprocess_inputs (stmt);
+       }
+    }
+}
+
+/* Process all statements and phis in BB, during the first post-order walk.  */
+
+void
+backprop::process_block (basic_block bb)
+{
+  for (gimple_stmt_iterator gsi = gsi_last_bb (bb); !gsi_end_p (gsi);
+       gsi_prev (&gsi))
+    {
+      tree lhs = gimple_get_lhs (gsi_stmt (gsi));
+      if (lhs && TREE_CODE (lhs) == SSA_NAME)
+       process_var (lhs);
+    }
+  for (gphi_iterator gpi = gsi_start_phis (bb); !gsi_end_p (gpi);
+       gsi_next (&gpi))
+    process_var (gimple_phi_result (gpi.phi ()));
+}
+
+/* Delete the definition of VAR, which has no uses.  */
+
+static void
+remove_unused_var (tree var)
+{
+  gimple *stmt = SSA_NAME_DEF_STMT (var);
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "Deleting ");
+      print_gimple_stmt (dump_file, stmt, 0, TDF_SLIM);
+    }
+  gimple_stmt_iterator gsi = gsi_for_stmt (stmt);
+  gsi_remove (&gsi, true);
+  release_ssa_name (var);
+}
+
+/* Note that we're replacing OLD_RHS with NEW_RHS in STMT.  */
+
+static void
+note_replacement (gimple *stmt, tree old_rhs, tree new_rhs)
+{
+  fprintf (dump_file, "Replacing use of ");
+  print_generic_expr (dump_file, old_rhs, 0);
+  fprintf (dump_file, " with ");
+  print_generic_expr (dump_file, new_rhs, 0);
+  fprintf (dump_file, " in ");
+  print_gimple_stmt (dump_file, stmt, 0, TDF_SLIM);
+}
+
+/* If RHS is an SSA name whose definition just changes the sign of a value,
+   return that other value, otherwise return null.  */
+
+static tree
+strip_sign_op_1 (tree rhs)
+{
+  if (TREE_CODE (rhs) != SSA_NAME)
+    return NULL_TREE;
+
+  gimple *def_stmt = SSA_NAME_DEF_STMT (rhs);
+  if (gassign *assign = dyn_cast <gassign *> (def_stmt))
+    switch (gimple_assign_rhs_code (assign))
+      {
+      case ABS_EXPR:
+      case NEGATE_EXPR:
+       return gimple_assign_rhs1 (assign);
+
+      default:
+       break;
+      }
+  else if (gcall *call = dyn_cast <gcall *> (def_stmt))
+    {
+      if (gimple_call_builtin_p (call, BUILT_IN_NORMAL))
+       switch (DECL_FUNCTION_CODE (gimple_call_fndecl (call)))
+         {
+         CASE_FLT_FN (BUILT_IN_COPYSIGN):
+           return gimple_call_arg (call, 0);
+
+         default:
+           break;
+         }
+    }
+
+  return NULL_TREE;
+}
+
+/* If RHS is an SSA name whose definition just changes the sign of a value,
+   strip all such operations and return the ultimate input to them.
+   Return null otherwise.
+
+   Although this could in principle lead to quadratic searching,
+   in practice a long sequence of sign manipulations should already
+   have been folded down.  E.g. --x -> x, abs(-x) -> abs(x).  We search
+   for more than one operation in order to catch cases like -abs(x).  */
+
+static tree
+strip_sign_op (tree rhs)
+{
+  tree new_rhs = strip_sign_op_1 (rhs);
+  if (!new_rhs)
+    return NULL_TREE;
+  while (tree next = strip_sign_op_1 (new_rhs))
+    new_rhs = next;
+  return new_rhs;
+}
+
+/* Strip all sign operations from the rvalue at *RHS_PTR in STMT.
+   Return true if something changed.  The caller is responsible
+   for the necessary bookkeeping.  */
+
+static bool
+strip_sign_op (gimple *stmt, tree *rhs_ptr)
+{
+  if (tree new_rhs = strip_sign_op (*rhs_ptr))
+    {
+      if (dump_file && (dump_flags & TDF_DETAILS))
+       note_replacement (stmt, *rhs_ptr, new_rhs);
+      *rhs_ptr = new_rhs;
+      return true;
+    }
+  return false;
+}
+
+/* STMT has been changed.  Give the fold machinery a chance to simplify
+   and canonicalize it (e.g. by ensuring that commutative operands have
+   the right order), then record the updates.  */
+
+void
+backprop::complete_change (gimple *stmt)
+{
+  gimple_stmt_iterator gsi = gsi_for_stmt (stmt);
+  if (fold_stmt (&gsi))
+    {
+      if (dump_file && (dump_flags & TDF_DETAILS))
+       {
+         fprintf (dump_file, "  which folds to: ");
+         print_gimple_stmt (dump_file, gsi_stmt (gsi), 0, TDF_SLIM);
+       }
+    }
+  update_stmt (gsi_stmt (gsi));
+}
+
+/* Optimize CALL, a call to a built-in function, on the basis that INFO
+   describes all uses of the LHS.  */
+
+void
+backprop::optimize_builtin_call (gcall *call, const usage_info *info)
+{
+  bool changed_p = false;
+  enum built_in_function fn = DECL_FUNCTION_CODE (gimple_call_fndecl (call));
+  /* If we have an f such that -f(x) = f(-x), and if the sign of the result
+     doesn't matter, strip any sign operations from the input.  */
+  if (info->flags.ignore_sign
+      && negate_mathfn_p (fn)
+      && strip_sign_op (call, gimple_call_arg_ptr (call, 0)))
+    changed_p = true;
+  if (changed_p)
+    complete_change (call);
+}
+
+/* Optimize ASSIGN on the basis that INFO describes all uses of the lhs.  */
+
+void
+backprop::optimize_assign (gassign *assign, const usage_info *info)
+{
+  bool changed_p = false;
+  switch (gimple_assign_rhs_code (assign))
+    {
+    case MULT_EXPR:
+    case RDIV_EXPR:
+      /* If the sign of the result doesn't matter, strip sign operations
+        from both inputs.  */
+      if (info->flags.ignore_sign
+         && (strip_sign_op (assign, gimple_assign_rhs1_ptr (assign))
+             || strip_sign_op (assign, gimple_assign_rhs2_ptr (assign))))
+       changed_p = true;
+      break;
+
+    case COND_EXPR:
+      /* If the sign of A ? B : C doesn't matter, strip sign operations
+        from both B and C.  */
+      if (info->flags.ignore_sign
+         && (strip_sign_op (assign, gimple_assign_rhs2_ptr (assign))
+             || strip_sign_op (assign, gimple_assign_rhs3_ptr (assign))))
+       changed_p = true;
+      break;
+
+    default:
+      break;
+    }
+  if (changed_p)
+    complete_change (assign);
+}
+
+/* Optimize PHI on the basis that INFO describes all uses of the result.  */
+
+void
+backprop::optimize_phi (gphi *phi, const usage_info *info)
+{
+  /* If the sign of the result doesn't matter, strip sign operations
+     from all arguments.  */
+  if (info->flags.ignore_sign)
+    {
+      use_operand_p use;
+      ssa_op_iter oi;
+      FOR_EACH_PHI_ARG (use, phi, oi, SSA_OP_USE)
+       if (tree new_arg = strip_sign_op (USE_FROM_PTR (use)))
+         {
+           if (dump_file && (dump_flags & TDF_DETAILS))
+             note_replacement (phi, USE_FROM_PTR (use), new_arg);
+           replace_exp (use, new_arg);
+         }
+    }
+}
+
+void
+backprop::execute ()
+{
+  /* Phase 1: Traverse the function, making optimistic assumptions
+     about any phi whose definition we haven't seen.  */
+  int *postorder = XNEWVEC (int, n_basic_blocks_for_fn (m_fn));
+  unsigned int postorder_num = post_order_compute (postorder, false, false);
+  for (unsigned int i = 0; i < postorder_num; ++i)
+    {
+      process_block (BASIC_BLOCK_FOR_FN (m_fn, postorder[i]));
+      bitmap_set_bit (m_visited_blocks, postorder[i]);
+    }
+  XDELETEVEC (postorder);
+
+  /* Phase 2: Use the initial (perhaps overly optimistic) information
+     to create a maximal fixed point solution.  */
+  while (!m_worklist.is_empty ())
+    process_var (pop_from_worklist ());
+
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    fprintf (dump_file, "\n");
+
+  /* Phase 3: Do a reverse post-order walk, using information about
+     the uses of SSA names to optimize their definitions.  */
+  for (unsigned int i = m_vars.length (); i-- > 0;)
+    {
+      usage_info *info = m_vars[i].second;
+      if (info->is_useful ())
+       {
+         tree var = m_vars[i].first;
+         gimple *stmt = SSA_NAME_DEF_STMT (var);
+         if (gcall *call = dyn_cast <gcall *> (stmt))
+           {
+             if (gimple_call_builtin_p (call, BUILT_IN_NORMAL))
+               optimize_builtin_call (call, info);
+           }
+         else if (gassign *assign = dyn_cast <gassign *> (stmt))
+           optimize_assign (assign, info);
+         else if (gphi *phi = dyn_cast <gphi *> (stmt))
+           optimize_phi (phi, info);
+       }
+    }
+
+  /* Phase 4: Do a post-order walk, deleting statements that are no
+     longer needed.  */
+  for (unsigned int i = 0; i < m_vars.length (); ++i)
+    {
+      tree var = m_vars[i].first;
+      if (has_zero_uses (var))
+       remove_unused_var (var);
+    }
+
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    fprintf (dump_file, "\n");
+}
+
+const pass_data pass_data_backprop =
+{
+  GIMPLE_PASS, /* type */
+  "backprop", /* name */
+  OPTGROUP_NONE, /* optinfo_flags */
+  TV_TREE_BACKPROP, /* tv_id */
+  ( PROP_cfg | PROP_ssa ), /* properties_required */
+  0, /* properties_provided */
+  0, /* properties_destroyed */
+  0, /* todo_flags_start */
+  0, /* todo_flags_finish */
+};
+
+class pass_backprop : public gimple_opt_pass
+{
+public:
+  pass_backprop (gcc::context *ctxt)
+    : gimple_opt_pass (pass_data_backprop, ctxt)
+  {}
+
+  /* opt_pass methods: */
+  opt_pass * clone () { return new pass_backprop (m_ctxt); }
+  virtual bool gate (function *) { return flag_tree_backprop; }
+  virtual unsigned int execute (function *);
+
+}; // class pass_backprop
+
+unsigned int
+pass_backprop::execute (function *fn)
+{
+  backprop (fn).execute ();
+  return 0;
+}
+
+} // anon namespace
+
+gimple_opt_pass *
+make_pass_backprop (gcc::context *ctxt)
+{
+  return new pass_backprop (ctxt);
+}

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