μ-Law algorithm implementation - audio

Question

Here is Mu-Law encoder taken from NAudio. The question is how is this formula same with the code? I can understand that MuLawCompressTable is actually the Log but I dont get the thing about mantissa why it is taken as is.
private const int cBias = 0x84;
private const int cClip = 32635;
private static readonly byte[] MuLawCompressTable = new byte[256]
{
0,0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7
};
public static byte LinearToMuLawSample(short sample)
{
//We get the sign
int sign = (sample >> 8) & 0x80;
if (sign != 0)
sample = (short)-sample;
if (sample > cClip)
sample = cClip;
sample = (short)(sample + cBias);
int exponent = (int)MuLawCompressTable[(sample >> 7) & 0xFF];
int mantissa = (sample >> (exponent + 3)) & 0x0F;
int compressedByte = ~(sign | (exponent << 4) | mantissa);
return (byte)compressedByte;
}

Answer 1

They are different. See the Wikipedia page on mu-law, http://en.wikipedia.org/wiki/Mulaw
There are two forms of this algorithm—an analog version, and a quantized digital version.
You quote the formula for the "analog" version - a compressive mapping from -1..1 to -1..1, which emphasizes the basic idea of mu-law, i.e. that the quantized value encodes more detail (uses a smaller quantization step) for smaller values, so the introduced quantization error is roughly proportional to the overall amplitude of the signal.
The "digital" version is a piecewise-linear approximation to this basic idea, with some additional shifts to further simplify processing.
Here's a plot comparing the two. You can see the stairsteps in the green line (mu_digital) corresponding to the discrete 7-bit values, and you also spot the different linear sections approximating the smooth blue line.