diff --git a/gcc/fold-const.cc b/gcc/fold-const.cc
index 7b26896..f7f174d 100644
--- a/gcc/fold-const.cc
+++ b/gcc/fold-const.cc
@@ -15076,16 +15076,27 @@ tree_binary_nonnegative_warnv_p (enum tree_code code, tree type, tree op0,
       break;
 
     case MULT_EXPR:
-      if (FLOAT_TYPE_P (type) || TYPE_OVERFLOW_UNDEFINED (type))
+      if (FLOAT_TYPE_P (type))
 	{
-	  /* x * x is always non-negative for floating point x
-	     or without overflow.  */
+	  /* x * x is non-negative for floating point x except
+	     that -NaN*-NaN may return -NaN.  PR middle-end/111701.  */
+	  if (operand_equal_p (op0, op1, 0))
+	    {
+	      if (!tree_expr_maybe_signaling_nan_p (op0) || RECURSE (op0))
+		return true;
+	    }
+	  else if (RECURSE (op0) && RECURSE (op1))
+	    return true;
+	}
+
+      if (ANY_INTEGRAL_TYPE_P (type)
+	  && TYPE_OVERFLOW_UNDEFINED (type))
+	{
+	  /* x * x is always non-negative without overflow.  */
 	  if (operand_equal_p (op0, op1, 0)
 	      || (RECURSE (op0) && RECURSE (op1)))
 	    {
-	      if (ANY_INTEGRAL_TYPE_P (type)
-		  && TYPE_OVERFLOW_UNDEFINED (type))
-		*strict_overflow_p = true;
+	      *strict_overflow_p = true;
 	      return true;
 	    }
 	}
diff --git a/gcc/testsuite/gcc.dg/pr111701-1.c b/gcc/testsuite/gcc.dg/pr111701-1.c
new file mode 100644
index 0000000..5cbfac2
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/pr111701-1.c
@@ -0,0 +1,14 @@
+/* { dg-do compile } */
+/* { dg-options "-O2 -fsignaling-nans -fdump-tree-optimized" } */
+
+int foo(double x)
+{
+    return __builtin_signbit(x*x);
+}
+
+int bar(float x)
+{
+    return __builtin_signbit(x*x);
+}
+
+/* { dg-final { scan-tree-dump-times " \\* " 2 "optimized" } } */
diff --git a/gcc/testsuite/gcc.dg/pr111701-2.c b/gcc/testsuite/gcc.dg/pr111701-2.c
new file mode 100644
index 0000000..f79c7ba
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/pr111701-2.c
@@ -0,0 +1,14 @@
+/* { dg-do compile } */
+/* { dg-options "-O2 -fdump-tree-optimized" } */
+
+int foo(double x)
+{
+    return __builtin_signbit(x*x);
+}
+
+int bar(float x)
+{
+    return __builtin_signbit(x*x);
+}
+
+/* { dg-final { scan-tree-dump-not " \\* " "optimized" } } */