Why does 'round' mode of the QUANTIZER function of the Fixed Point toolbox give different results from ROUND in MATLAB?

I am using the Quantizer object as follows:

   Q=quantizer([12 0],'fixed','round','saturate');

   round([-1.5 1.5])

Here, I get the output as:

 ans =

     -2     2

Now, if I use the QUANTIZE function as:

   quantize(Q,[-1.5 1.5])

Here, I get the output as:

 ans =

     -1     2

I would like to know why it is not quantizing with a 'Roundmode' of 'round' consistent with MATLAB's round function.

This occurred when I was trying to make my MATLAB fixed point code "bit-true" with a Xilinx Blockset model in Simulink.

Answer 1

[MathWorks Support Team]

This is expected behavior, and one that is more natural for two's-complement integers.

Rounding on the half-way point is always up (towards positive infinity) in fixed-point mode with roundmode='round'. Otherwise it would give an uneven step across zero.

The algorithm is "add half a bit and truncate."

    floor([-1.5 1.5]+.5)

You would get the output:

   ans =

     -1     2

As a further example, see the following example:

    x=(-3:.25:3)'; q=quantizer([12 0],'round');

    [x quantize(q,x) floor(x+.5) round(x)]

IEEE 754 floating-point is sign-magnitude, and the round on the half-way point goes towards the larger absolute value (towards positive infinity if the number is positive, towards negative infinity if the number is negative).