MATLAB: Does ’round’ mode of the QUANTIZER function of the Fixed Point toolbox give different results from ROUND in MATLAB

inconsistentquantizeround

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.

Best Answer

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).
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