diff --git a/math.c b/math.c
index a781167d5e..eefcec3c93 100644
--- a/math.c
+++ b/math.c
@@ -283,7 +283,9 @@ math_sinh(VALUE obj, VALUE x)
 double
 tanh(double x)
 {
-    return sinh(x) / cosh(x);
+    const double c = cosh(x);
+    if (!isinf(c)) return sinh(x) / c;
+    return x > 0 ? 1.0 : -1.0;
 }
 #endif
 
diff --git a/test/ruby/test_math.rb b/test/ruby/test_math.rb
index ac9ab3c961..f226287442 100644
--- a/test/ruby/test_math.rb
+++ b/test/ruby/test_math.rb
@@ -111,6 +111,8 @@ class TestMath < Test::Unit::TestCase
     check(Math.sinh(0) / Math.cosh(0), Math.tanh(0))
     check(Math.sinh(1) / Math.cosh(1), Math.tanh(1))
     check(Math.sinh(2) / Math.cosh(2), Math.tanh(2))
+    check(+1.0, Math.tanh(+1000.0))
+    check(-1.0, Math.tanh(-1000.0))
   end
 
   def test_acosh