NumericTypeScope

Create a fi object and set the DataTypeOverride to ScaledDoubles.

a = fi(magic(10),1,8,2);
b = fi([a; 2.^(-5:4)],1,8,3);

fp = fipref;
initialDTOSetting = fp.DataTypeOverride;
fp.DataTypeOverride = 'ScaledDoubles';

Create a NumericTypeScope object. You can use the reset method to ensure that all stored information is cleared from the NumericTypeScope object h.

h = NumericTypeScope;
reset(h)

Use the step method to process your data and visualize the dynamic range of the fi object b.

step(h,b);

Closing the NumericTypeScope window does not delete the object from your workspace. Close the NumericTypeScope window and reopen it using the show function.

show(h);

The NumericTypeScope displays a log2 histogram which shows that the values appear both outside of the range and below the precision of the data type of the variable. Pause on one bar of the histogram to view the percentage of the total values that are represented by that bar.

In this case, the data type of b is numerictype(1,8,3). The numerictype(1,8,3) data type provides 5 integer bits, including the signed bit, and 3 fractional bits. Thus, this data type can represent only values between -2^4 and 2^4 - 2^-3 (from -16 to 15.8750). Given the range and precision of this data type, values greater than 2^4 fall outside the range and values less than 2^-3 fall below the precision of the data type.

The NumericTypeScope shows that values requiring bits 5, 6, and 7 are outside the range and values requiring fractional bits 4 and 5 are below precision. Given this information, you can prevent values that are outside range and below precision by changing the data type of the variable b to numerictype(0,13,5).

Given this information, you can prevent values that are outside range and below precision by changing the data type of the variable b to numerictype(0,13,5). In the NumericTypeScope, enter numerictype(0,13,5) in the Proposed Data Type box.

Return to the original data type override setting.

fp.DataTypeOverride = initialDTOSetting;

View the dynamic range and determine an appropriate numeric type for a fi object with a DataTypeMode of Scaled double: binary point scaling.

Create a numerictype object with a DataTypeMode of Scaled double: binary point scaling. Then, use that numerictype object to construct your fi objects.

T = numerictype;
T.DataTypeMode = 'Scaled double: binary point scaling';
T.WordLength = 8;
T.FractionLength = 6;

a = fi(sin(0:100)*3.5, T);
b = fi(cos(0:100)*1.75,T);
acc = fi(0,T);

Create a NumericTypeScope object h. Then, use the step function in a for loop to view the dynamic range of the accumulator object, acc.

h = NumericTypeScope;
for i = 1:length(a)
    acc(:) = a(i)*0.7+b(i);
    step(h,acc)
end

This dynamic range analysis shows that you can represent the entire range of data in the accumulator with 5 bits, two to the left of the binary point (integer bits) and three to the right of it (fractional bits). You can verify that this data type is able to represent all the values by changing the WordLength and FractionLength properties of the numerictype object T. Then, use T to redefine the accumulator.

T.WordLength = 5;
T.FractionLength = 2;
acc = fi(0,T);

To view the dynamic range analysis based on this new data type, reset the NumericTypeScope object h, and rerun the loop.

reset(h)
for i = 1:length(a)
    acc(:) = a(i)*0.7 + b(i);
    step(h,acc)
end

Clear the information stored in the NumericTypeScope object h.

reset(h);