diff --git a/gcc/ChangeLog b/gcc/ChangeLog
index a8650439eef..9fcea2965a7 100644
--- a/gcc/ChangeLog
+++ b/gcc/ChangeLog
@@ -1,3 +1,10 @@
+2015-10-13  Richard Sandiford  <richard.sandiford@arm.com>
+
+	* real.h (real_isinteger): Declare.
+	* real.c (real_isinteger): New function.
+	* match.pd: Simplify pow(|x|,y) and pow(-x,y) to pow(x,y)
+	if y is an even integer.
+
 2015-10-11  Jan Hubicka  <hubicka@ucw.cz>
 
 	revert:
diff --git a/gcc/match.pd b/gcc/match.pd
index b02dd03430d..6714796943e 100644
--- a/gcc/match.pd
+++ b/gcc/match.pd
@@ -309,12 +309,19 @@ along with GCC; see the file COPYING3.  If not see
        && TYPE_OVERFLOW_UNDEFINED (type))
    @0)))
 
-/* Simplify cos (-x) -> cos (x).  */
 (for op (negate abs)
-(for coss (COS COSH)
- (simplify
-  (coss (op @0))
-   (coss @0))))
+ /* Simplify cos(-x) and cos(|x|) -> cos(x).  Similarly for cosh.  */
+ (for coss (COS COSH)
+  (simplify
+   (coss (op @0))
+    (coss @0)))
+ /* Simplify pow(-x, y) and pow(|x|,y) -> pow(x,y) if y is an even integer.  */
+ (for pows (POW)
+  (simplify
+   (pows (op @0) REAL_CST@1)
+   (with { HOST_WIDE_INT n; }
+    (if (real_isinteger (&TREE_REAL_CST (@1), &n) && (n & 1) == 0)
+     (pows @0 @1))))))
 
 /* X % Y is smaller than Y.  */
 (for cmp (lt ge)
diff --git a/gcc/real.c b/gcc/real.c
index f633ffd2e88..85ac83d3fdc 100644
--- a/gcc/real.c
+++ b/gcc/real.c
@@ -4997,6 +4997,24 @@ real_isinteger (const REAL_VALUE_TYPE *c, machine_mode mode)
   return real_identical (c, &cint);
 }
 
+/* Check whether C is an integer that fits in a HOST_WIDE_INT,
+   storing it in *INT_OUT if so.  */
+
+bool
+real_isinteger (const REAL_VALUE_TYPE *c, HOST_WIDE_INT *int_out)
+{
+  REAL_VALUE_TYPE cint;
+
+  HOST_WIDE_INT n = real_to_integer (c);
+  real_from_integer (&cint, VOIDmode, n, SIGNED);
+  if (real_identical (c, &cint))
+    {
+      *int_out = n;
+      return true;
+    }
+  return false;
+}
+
 /* Write into BUF the maximum representable finite floating-point
    number, (1 - b**-p) * b**emax for a given FP format FMT as a hex
    float string.  LEN is the size of BUF, and the buffer must be large
diff --git a/gcc/real.h b/gcc/real.h
index 706859b6c64..e65b5263e11 100644
--- a/gcc/real.h
+++ b/gcc/real.h
@@ -467,7 +467,8 @@ extern void real_round (REAL_VALUE_TYPE *, machine_mode,
 extern void real_copysign (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
 
 /* Check whether the real constant value given is an integer.  */
-extern bool real_isinteger (const REAL_VALUE_TYPE *c, machine_mode mode);
+extern bool real_isinteger (const REAL_VALUE_TYPE *, machine_mode);
+extern bool real_isinteger (const REAL_VALUE_TYPE *, HOST_WIDE_INT *);
 
 /* Write into BUF the maximum representable finite floating-point
    number, (1 - b**-p) * b**emax for a given FP format FMT as a hex