IEEE 754 Floating Point Binary Representations

Just to gather up a whole bunch of stuff I had to slog through and make this more googleable, allow me to summarize some various trivia having to do with bitwise representation of IEEE 754 floating point values across platforms. This is primarily useful if you need to read and write floating point values from byte arrays or binary network streams across platforms, particularly if you have to interact with Steve Ballmer's Insanity.

First, there is no official standard for endian-ness when transmitting IEEE floating point data over the wire. That means that Java ends up defaulting to in DataInputStream and DataOutputStream to big-endian format (to match the fact that everything is big-endian), C# defaults to host-endian format (always little-endian in practice, as the Mono guys have learned.) for BinaryReader and BinaryWriter. First point of fun.

Secondly, IEEE 754 floating point representation defines an entire range of values to represent NaN, not a single value. Java takes the approach to make things byte compatible in the wire format by always emitting a single constant value for all NaN values (where all the meaningless bits are set to 0), while C# allows whatever cruft happens to be in the value on the CPU to flow through to your binary representation. And don't assume in C# that double.NaN has all those set to 0. It doesn't. In practice, double.NaN in C# is full of cruft.

This is fine if you read in the value and call IsNaN on it, but not so great if you want to check that your serialized/deserialized byte arrays are fine. For that, you need to mask out to ensure that you're always writing a canonical representation of your NaN values.

A useful C# block if you find yourself having to deal with this stuff is the following (using this will ensure that your binary representations are always bit-equivalent with the Java formats):

    

      

        

  

    
    


        


  


  

        

          

          
private const long DOUBLE_NAN_REPRESENTATION = 0x7ff8000000000000L;

        
        

          

          
private const int FLOAT_NAN_REPRESENTATION = 0x7fc00000;

        
        

          

          
private static void WriteDouble(double value, BinaryWriter writer)

        
        

          

          
{

        
        

          

          
  if (double.IsNaN(value))

        
        

          

          
  {

        
        

          

          
    writer.Write(System.Net.IPAddress.HostToNetworkOrder(DOUBLE_NAN_REPRESENTATION));

        
        

          

          
  }

        
        

          

          
  else

        
        

          

          
  {

        
        

          

          
    WriteBigEndianBytes(BitConverter.GetBytes(value), writer);

        
        

          

          
  }

        
        

          

          
}

        
        

          

          
private static void WriteFloat(float value, BinaryWriter writer)

        
        

          

          
{

        
        

          

          
  if (float.IsNaN(value))

        
        

          

          
  {

        
        

          

          
    writer.Write(System.Net.IPAddress.HostToNetworkOrder(FLOAT_NAN_REPRESENTATION));

        
        

          

          
  }

        
        

          

          
  else

        
        

          

          
  {

        
        

          

          
    WriteBigEndianBytes(BitConverter.GetBytes(value), writer);

        
        

          

          
  }

        
        

          

          
}

        
        

          

          
private static void WriteBigEndianBytes(byte[] bytes, BinaryWriter writer)

        
        

          

          
{

        
        

          

          
  if (BitConverter.IsLittleEndian) { Array.Reverse(bytes); }

        
        

          

          
  writer.Write(bytes);

        
        

          

          
}

        
        

          

          
private static double ReadDouble(BinaryReader reader)

        
        

          

          
{

        
        

          

          
  byte[] bytes = reader.ReadBytes(8);

        
        

          

          
  if (BitConverter.IsLittleEndian) { Array.Reverse(bytes); }

        
        

          

          
  return BitConverter.ToDouble(bytes, 0);

        
        

          

          
}

        
        

          

          
private static float ReadFloat(BinaryReader reader)

        
        

          

          
{

        
        

          

          
  byte[] bytes = reader.ReadBytes(4);

        
        

          

          
  if (BitConverter.IsLittleEndian) { Array.Reverse(bytes); }

        
        

          

          
  return BitConverter.ToSingle(bytes, 0);

        
        

          

          
}
        
  



    

  


      
      

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          ieee754encoding.cs
        
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