diff --git a/ChangeLog b/ChangeLog
index d2f1b3bcf8..0d7de6fed6 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,16 @@
+Tue Nov 22 10:46:57 2011  NARUSE, Yui  <naruse@ruby-lang.org>
+
+	* numeric.c (ruby_float_step): improve floating point calculations.
+	  [ruby-core:35753] [Bug #4576]
+
+	* numeric.c (ruby_float_step): correct the error of floating point
+	  numbers on the excluding case.
+	  patched by Masahiro Tanaka [ruby-core:39608]
+
+	* numeric.c (ruby_float_step): use the end value when the current
+	  value is greater than or equal to the end value.
+	  patched by Akira Tanaka [ruby-core:39612]
+
 Tue Nov 22 06:59:21 2011  Tanaka Akira  <akr@fsij.org>
 
 	* test/ruby/test_io.rb (test_fcntl_dupfd): there is no known platform
diff --git a/numeric.c b/numeric.c
index e749a396d2..c8616f5f73 100644
--- a/numeric.c
+++ b/numeric.c
@@ -1690,10 +1690,21 @@ ruby_float_step(VALUE from, VALUE to, VALUE step, int excl)
 	}
 	else {
 	    if (err>0.5) err=0.5;
-	    n = floor(n + err);
-	    if (!excl || ((long)n)*unit+beg < end) n++;
-	    for (i=0; i<n; i++) {
-		rb_yield(DBL2NUM(i*unit+beg));
+	    if (excl) {
+		if (n<=0) return TRUE;
+		if (n<1)
+		    n = 0;
+		else
+		    n = floor(n - err);
+	    }
+	    else {
+		if (n<0) return TRUE;
+		n = floor(n + err);
+	    }
+	    for (i=0; i<=n; i++) {
+		double d = i*unit+beg;
+		if (end < d) d = end;
+		rb_yield(DBL2NUM(d));
 	    }
 	}
 	return TRUE;
diff --git a/test/ruby/test_float.rb b/test/ruby/test_float.rb
index e77b9e62e0..d16384898d 100644
--- a/test/ruby/test_float.rb
+++ b/test/ruby/test_float.rb
@@ -508,4 +508,33 @@ class TestFloat < Test::Unit::TestCase
       sleep(0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1)
     end
   end
+
+  def test_step
+    1000.times do
+      a = rand
+      b = a+rand*1000
+      s = (b - a) / 10
+      assert_equal(11, (a..b).step(s).to_a.length)
+    end
+
+    (1.0..12.7).step(1.3).each do |n|
+      assert_operator(n, :<=, 12.7)
+    end
+  end
+
+  def test_step_excl
+    1000.times do
+      a = rand
+      b = a+rand*1000
+      s = (b - a) / 10
+      assert_equal(10, (a...b).step(s).to_a.length)
+    end
+
+    assert_equal([1.0, 2.9, 4.8, 6.699999999999999], (1.0...6.8).step(1.9).to_a)
+
+    e = 1+1E-12
+    (1.0 ... e).step(1E-16) do |n|
+      assert_operator(n, :<=, e)
+    end
+  end
 end