MATLAB: How do the OverflowMode and RoundMode properties interact during fixed point conversion in MATLAB (R2011b)

fixedoverflowmodepointroundmode

The below commands are executed in MATLAB to perform fixed point conversion:

a = fi(0.999,'OverflowMode','wrap','RoundMode','ceil','Signedness','Unsigned','WordLength',8,'FractionLength',8)
b = fi(0.999,'OverflowMode','wrap','RoundMode','floor','Signedness','Unsigned','WordLength',8,'FractionLength',8)

This gives the output:

a = 0, b = 0.9961

In what order are the OverflowMode and RoundMode properties processed?

Best Answer

In the first case, since the 'OverflowMode' is 'wrap', the output will be zero once the limit is exceeded (for WordLength = 8, the limit is 255). Now, consider the Fixed point representation for 0.999:

(0.999*(2^8)) = 255.744

For 'RoundMode' = 'ceil', the final value is 256, which wraps around to zero according to the OverflowMode property. For 'RoundMode' = 'floor', the final value is 255, which gives output = 0.9961 (because 255/256 = 0.9961).

During fixed point conversion, we first need to round off the number to the nearest ceil or floor, and only then check for overflow. This is because, for the overflow check, we need to compare two integers (the input and the maximum integer that can be stored for the given wordlength and fraction length). In order to obtain an integer value for the given floating point input, we first need to perform rounding.

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MATLAB: Does the fixed point conversion output from Simulink differ from the output in MATLAB (R2011b)

The MATLAB and Simulink outputs are different because the settings used for fixed point conversion are different. In the Datatype Conversion block in Simulink, select the 'Saturate on integer overflow' check box and simulate the model again. This should give the same output as obtained from MATLAB.

To illustrate this difference in MATLAB, execute the following commands:

z = fi(1,'OverflowMode','wrap','RoundMode','ceil','Signedness','Unsigned','WordLength',8,'FractionLength',8)

This will give z = 0, (the same output that was originally observed in Simulink).

Now, execute the below command:

z = fi(1,'OverflowMode','saturate','RoundMode','ceil','Signedness','Unsigned','WordLength',8,'FractionLength',8)

This will give z = 0.9961, (which is the output observed in Simulink after selecting the 'Saturate on integer overflow' checkbox).

Note that in MATLAB, the OverflowMode property for FIMATH is 'saturate' by default. In Simulink, this option ('Saturate on integer overflow') is unchecked by default.

MATLAB: How to specify the length of a product of two fixed-point numbers with Fixed-Point Toolbox

To cast a variable into another, you should use subscripted assignment. The rounding and overflow characteristics are taken from the left-hand-side variable's fimath settings.

% set fixed point variable display behavior
p = fipref;
p.NumericTypeDisplay = 'short';
p.FimathDisplay = 'none';
p.LoggingMode = 'on';
format compact
% Set integer and fractional number of bits
DataWordLength = 4
DataFracLength = 3 
MultWordLength = 8
MultFracLength = 7
AccWordLength = 10
AccFracLength = 8
% Apply bit widths to named types
Tdata = numerictype('WordLength', DataWordLength, 'FractionLength', DataFracLength)
Tmult = numerictype('WordLength', MultWordLength, 'FractionLength', MultFracLength)
Taccum = numerictype('WordLength', AccWordLength, 'FractionLength', AccFracLength)
% Accumulator sum/mult characteristics
F = fimath('ProductMode','SpecifyPrecision', ...
      'ProductWordLength',AccWordLength, 'ProductFractionLength',AccFracLength, ...
      'SumMode','SpecifyPrecision', 'SumWordLength', AccWordLength, ...
      'SumFractionLength',AccFracLength)
% experiment
Fdata = fimath('ProductMode','SpecifyPrecision', ...
      'ProductWordLength',DataWordLength, 'ProductFractionLength',DataFracLength, ...
      'SumMode','SpecifyPrecision', 'SumWordLength', DataWordLength, ...
      'SumFractionLength',DataFracLength)
% set data values
x = fi(-1, Tdata, F)
y = fi(-1, Tdata, F)
z = fi(-1, Tdata, Fdata)
acc = fi(0, Taccum, F)
mult = fi(0, Tmult, F)
% multiply two numbers
mult(:) = x * y
acc(:) = x * y
% Now try to move the data from "acc" into a variable that has the same
% size as x or y.
z(:) = acc

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Related Solutions

MATLAB: Does the fixed point conversion output from Simulink differ from the output in MATLAB (R2011b)

MATLAB: How to specify the length of a product of two fixed-point numbers with Fixed-Point Toolbox

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