Fold comparisons between sqrt and zero

The expression:

      signbit(sqrt(x))

is always 0 for -ffast-math.  The signbit fold first converts it to:

      sqrt(x) < 0

and whether we realise that this is false depends on a race between two
folders: the sqrt comparison folder, which wants to convert it to

      x < 0*0

and the generic tree_expr_nonnegative_p rule for ... < 0, which would
give the hoped-for 0.

The sqrt code already handles comparisons with negative values specially,
so this patch simply extends that idea to comparisons with zero.

Tested on x86_64-linux-gnu, aarch64-linux-gnu and arm-linux-gnueabi.

gcc/
	* match.pd: Handle sqrt(x) cmp 0 specially.

gcc/testsuite/
	* gcc.dg/torture/builtin-sqrt-cmp-1.c: New test.

From-SVN: r229422

4 files changed, 80 insertions, 0 deletions

diff --git a/gcc/ChangeLog b/gcc/ChangeLog
index a293321..a909966 100644
--- a/gcc/ChangeLog
+++ b/gcc/ChangeLog
@@ -1,3 +1,7 @@
+2015-10-27  Richard Sandiford  <richard.sandiford@arm.com>
+
+	* match.pd: Handle sqrt(x) cmp 0 specially.
+
 2015-10-27  Ilya Enkovich  <enkovich.gnu@gmail.com>
 
 	* tree-vect-generic.c (expand_vector_operations_1): Check
diff --git a/gcc/match.pd b/gcc/match.pd
index 26491d2..b8e6b46 100644
--- a/gcc/match.pd
+++ b/gcc/match.pd
@@ -1973,6 +1973,25 @@ DEFINE_INT_AND_FLOAT_ROUND_FN (RINT)
 	{ constant_boolean_node (true, type); })
        /* sqrt(x) > y is the same as x >= 0, if y is negative.  */
        (ge @0 { build_real (TREE_TYPE (@0), dconst0); })))
+     (if (real_equal (TREE_REAL_CST_PTR (@1), &dconst0))
+      (switch
+       /* sqrt(x) < 0 is always false.  */
+       (if (cmp == LT_EXPR)
+	{ constant_boolean_node (false, type); })
+       /* sqrt(x) >= 0 is always true if we don't care about NaNs.  */
+       (if (cmp == GE_EXPR && !HONOR_NANS (@0))
+	{ constant_boolean_node (true, type); })
+       /* sqrt(x) <= 0 -> x == 0.  */
+       (if (cmp == LE_EXPR)
+	(eq @0 @1))
+       /* Otherwise sqrt(x) cmp 0 -> x cmp 0.  Here cmp can be >=, >,
+          == or !=.  In the last case:
+
+	    (sqrt(x) != 0) == (NaN != 0) == true == (x != 0)
+
+	  if x is negative or NaN.  Due to -funsafe-math-optimizations,
+	  the results for other x follow from natural arithmetic.  */
+       (cmp @0 @1)))
      (if (cmp == GT_EXPR || cmp == GE_EXPR)
       (with
        {
diff --git a/gcc/testsuite/ChangeLog b/gcc/testsuite/ChangeLog
index 8721999..cfc9f7a 100644
--- a/gcc/testsuite/ChangeLog
+++ b/gcc/testsuite/ChangeLog
@@ -1,5 +1,9 @@
 2015-10-27  Richard Sandiford  <richard.sandiford@arm.com>
 
+	* gcc.dg/torture/builtin-sqrt-cmp-1.c: New test.
+
+2015-10-27  Richard Sandiford  <richard.sandiford@arm.com>
+
 	* gcc.dg/builtins-52.c: Add -O to dg-options.
 
 2015-10-27  Richard Sandiford  <richard.sandiford@arm.com>
diff --git a/gcc/testsuite/gcc.dg/torture/builtin-sqrt-cmp-1.c b/gcc/testsuite/gcc.dg/torture/builtin-sqrt-cmp-1.c
new file mode 100644
index 0000000..3f4a708
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/torture/builtin-sqrt-cmp-1.c
@@ -0,0 +1,53 @@
+/* { dg-do link } */
+/* { dg-options "-ffast-math" } */
+/* { dg-skip-if "" { *-*-* } { "-O0" } { "" } } */
+
+extern double sqrt (double);
+extern float sqrtf (float);
+extern long double sqrtl (long double);
+
+/* All references to link_error should go away at compile-time.  */
+extern void link_error (void);
+
+#define TEST_ONE(SUFFIX, TYPE)			\
+  void __attribute__ ((noinline, noclone))	\
+  test##SUFFIX (TYPE f, int *res)		\
+  {						\
+    TYPE sqrt_res = sqrt##SUFFIX (f);		\
+    res[0] = sqrt_res < 0;			\
+    if (res[0])					\
+      link_error ();				\
+    res[1] = sqrt_res <= 0;			\
+    if (res[1] != (f == 0))			\
+      link_error ();				\
+    res[2] = (sqrt_res == 0);			\
+    if (res[2] != (f == 0))			\
+      link_error ();				\
+    res[3] = (sqrt_res != 0);			\
+    if (res[3] != (f != 0))			\
+      link_error ();				\
+    res[4] = (sqrt_res > 0);			\
+    if (res[4] != (f > 0))			\
+      link_error ();				\
+    res[5] = (sqrt_res >= 0);			\
+    if (!res[5])				\
+      link_error ();				\
+  }
+
+volatile float f;
+volatile double d;
+volatile long double ld;
+
+TEST_ONE (f, float)
+TEST_ONE (, double)
+TEST_ONE (l, long double)
+
+int
+main ()
+{
+  int res[6];
+  testf (f, res);
+  test (d, res);
+  testl (ld, res);
+  return 0;
+}