diff --git a/lib/flt/bin_num.rb b/lib/flt/bin_num.rb
index 4675239..61f5858 100644
--- a/lib/flt/bin_num.rb
+++ b/lib/flt/bin_num.rb
@@ -206,7 +206,7 @@ def number_of_digits
   # Specific to_f conversion TODO: check if it represents an optimization
   if Float::RADIX==2
     def to_f
-      if special?
+      if special? || zero?
         super
       else
         ::Math.ldexp(@sign*@coeff, @exp)
diff --git a/lib/flt/num.rb b/lib/flt/num.rb
index 171214d..227c664 100644
--- a/lib/flt/num.rb
+++ b/lib/flt/num.rb
@@ -2703,10 +2703,24 @@ def to_f
       else
         0.0/0.0
       end
+    elsif zero?
+      @sign*0.0
     else
-      # to_rational.to_f
-      # to_s.to_f
-      (@sign*@coeff*(num_class.radix.to_f**@exp)).to_f
+      f = nil
+      f ||= to_s.to_f if num_class.radix == 10 # very precise, but slow
+      unless f
+        c = @coeff.to_f
+        if c.finite?
+          # This is fast to compute but may introduce roundoff error, and overflow or yield NaN
+          f = if @exp >= 0
+                @sign*c*(num_class.radix.to_f**@exp)
+              else
+                @sign*c/(num_class.radix.to_f**(-@exp))
+              end
+        end
+        f = nil unless f && f.finite?
+      end
+      f ||= to_r.to_f # not so slow, also may introduce roundoff error due to arithmetic
     end
   end
 
diff --git a/test/test_to_rf.rb b/test/test_to_rf.rb
index b574c52..46003a5 100644
--- a/test/test_to_rf.rb
+++ b/test/test_to_rf.rb
@@ -31,6 +31,131 @@ def test_to_f
       assert d.to_f.is_a?(Float)
       assert_equal f, d.to_f
     end
+    assert DecNum.nan.to_f.nan?
+    assert DecNum.infinity.to_f.infinite?
+    assert DecNum.infinity.to_f > 0
+    assert DecNum.infinity(-1).to_f.infinite?
+    assert DecNum.infinity(-1).to_f < 0
+    assert 1.0/DecNum('-0').to_f < 0
+    assert 1.0/DecNum('+0').to_f > 0
+
+    data  = []
+    [10, 100, 1000, 10000].each do |n_digits|
+      data << DecNum('+0.'+'1'*n_digits)
+      data << DecNum('-0.'+'1'*n_digits)
+    end
+
+    srand 1023022
+    data = []
+    DecNum.context(:precision=>15, :elimit=>90) do
+      data += [DecNum('1.448997445238699'), DecNum('1E23'),DecNum('-6.22320623338259E+16'),
+               DecNum('-3.83501075447972E-10'), DecNum('1.448997445238699')]
+      data += %w{
+        1E23
+        1.448997445238699
+        -6.22320623338259E+16
+        -3.83501075447972E-10
+        1.448997445238699
+        1.23E-30
+        1.23456789E-20
+        1.23456789E-30
+        1.234567890123456789
+        0.9999999999999995559107901499
+        0.9999999999999996114219413812
+        0.9999999999999996669330926125
+        0.9999999999999997224442438437
+        0.9999999999999997779553950750
+        0.9999999999999998334665463062
+        0.9999999999999998889776975375
+        0.9999999999999999444888487687
+        1
+        1.000000000000000111022302463
+        1.000000000000000222044604925
+        1.000000000000000333066907388
+        1.000000000000000444089209850
+        1.000000000000000555111512313
+        1.000000000000000666133814775
+        1.000000000000000777156117238
+        1.000000000000000888178419700
+      }.map{ |num| DecNum(num) }
+      data += Array.new(10000){random_num(DecNum)}
+    end
+
+    assert_equal 2, Float::RADIX
+
+    data.each do |x|
+      expected = Flt::Num.convert_exact(x, 2, Flt::BinNum::FloatContext).to_f
+      assert_equal expected, x.to_s.to_f
+
+      relative_error_limit = Float::EPSILON
+      rel_err = (x.to_f - expected).abs/expected.abs
+      assert  expected.abs*relative_error_limit > (x.to_f - expected).abs, "#{x.to_f} != #{expected} (#{x})"
+    end
   end
 
+  def test_to_f_bin
+    BinNum.context(BinNum::FloatContext) do
+      ['0.1', '-0.1', '0.0', '1234567.1234567', '-1234567.1234567', '1.234E7', '1.234E-7'].each do |n|
+        f = Float(n)
+        b = BinNum(n, :fixed)
+        assert b.to_f.is_a?(Float)
+        assert_equal f, b.to_f
+      end
+      assert BinNum.nan.to_f.nan?
+      assert BinNum.infinity.to_f.infinite?
+      assert BinNum.infinity.to_f > 0
+      assert BinNum.infinity(-1).to_f.infinite?
+      assert BinNum.infinity(-1).to_f < 0
+      assert 1.0/BinNum('-0', :fixed).to_f < 0
+      assert 1.0/BinNum('+0', :fixed).to_f > 0
+
+      data  = []
+      [10, 100, 1000, 10000].each do |n_digits|
+        data << BinNum('+0.'+'1'*n_digits)
+        data << BinNum('-0.'+'1'*n_digits)
+      end
+
+      srand 1023022
+      data = []
+        data += [BinNum('1.448997445238699', :fixed), BinNum('1E23', :fixed),BinNum('-6.22320623338259E+16', :fixed),
+                BinNum('-3.83501075447972E-10', :fixed), BinNum('1.448997445238699', :fixed)]
+        data += %w{
+          1E23
+          1.448997445238699
+          -6.22320623338259E+16
+          -3.83501075447972E-10
+          1.448997445238699
+          1.23E-30
+          1.23456789E-20
+          1.23456789E-30
+          1.234567890123456789
+          0.9999999999999995559107901499
+          0.9999999999999996114219413812
+          0.9999999999999996669330926125
+          0.9999999999999997224442438437
+          0.9999999999999997779553950750
+          0.9999999999999998334665463062
+          0.9999999999999998889776975375
+          0.9999999999999999444888487687
+          1
+          1.000000000000000111022302463
+          1.000000000000000222044604925
+          1.000000000000000333066907388
+          1.000000000000000444089209850
+          1.000000000000000555111512313
+          1.000000000000000666133814775
+          1.000000000000000777156117238
+          1.000000000000000888178419700
+        }.map{ |num| BinNum(num, :fixed) }
+        data += Array.new(10000){random_num(BinNum)}
+
+      data.each do |x|
+        expected = x.to_decimal_exact(exact: true).to_s.to_f
+        assert_equal expected, x.to_f
+      end
+    end
+
+  end
+
+
 end
\ No newline at end of file