Hello Pasquale,
In R2020a, we introduced an improvement to how we quantize the net slope, specifically when using small (less than 16-bit) fixed-point types.
In R2019b and earlier, we would use the input wordlength to perform the quantization.
Let us look at an example quantization (which will be used below).
We wish to quantize the value 1.6 into a power of 2 scaled fixed-point value (this is so we can emit code consisting of an integer multiplication followed by a shift right)
If we use the input wordlength (11-bits in your case), we get this:
>> a = fi(1.6,0,11)
a =
1.599609375
DataTypeMode: Fixed-point: binary point scaling
Signedness: Unsigned
WordLength: 11
FractionLength: 10
Instead, we may be able to use a larger wordlength for quantization which can yield a more accurate representation, with only a small impact on the code efficiency:
>> b = fi(1.6,0,20)
b =
1.60000038146973
DataTypeMode: Fixed-point: binary point scaling
Signedness: Unsigned
WordLength: 20
FractionLength: 19
Now, let's lay out the formula for a fixed-point cast, where we will solve for the output stored integer Qout:
Qin * 0.0025 - 1 = Qout * 0.1
We can normalize the slopes into a Slope Adjustment Factor and a Fixed Exponent:
Qin * 1.28 * 2^-9 - 1 = Qout * 1.6 * 2^-4
Solving for the output stored integer (Qout):
Qout = Qin * 1.28 / 1.6 * 2^-5 - 2^4/1.6
This can be reduced to:
Qout = Qin * 0.8 * 2^-5 - 10
We can now do another normalization:
Qout = Qin * 1.6 * 2^-6 - 10
Now, we need to decide how to handle the 1.6 term.
We cannot accurately represent 1.6
If we go with the smaller quantization (older releases), we get a less accurate value that is slightly under the ideal value of 1.6.
If we go with the larger quantization (newer releases), we get a more accurate value that is slightly above the ideal value of 1.6.
If we plug in the value for Qin used in your model:
Qout = 1900 * 1.6 * 2^-6 -10 = 37.5
However, we cannot use 1.6, we have to use a quantized value:
Smaller quantization (R2019b and earlier):
Qout = 1900 * 1.599609375 * 2^-6 -10 = 37.4884033203125
Larger quantization (R2020a and later):
Qout = 1900 * 1.60000038146973 * 2^-6 -10 = 37.5000113248826
With a "nearest" style of rounding, they will round to different integer values, since they reside on different sides of the "half mark".
