How do I get real integer overflows in MATLAB/Octave?

Question

I'm working on a verification-tool for some VHDL-Code in MATLAB/Octave. Therefore I need data types which generate "real" overflows:

intmax('int32') + 1
ans = -2147483648

Later on, it would be helpful if I can define the bit width of a variable, but that is not so important right now.

When I build a C-like example, where a variable gets increased until it's smaller than zero, it spins forever and ever:

test = int32(2^30);
while (test > 0)
    test = test + int32(1);
end

Another approach I tried was a custom "overflow"-routine which was called every time after a number is changed. This approach was painfully slow, not practicable and not working in all cases at all. Any suggestions?

Answer 1

In MATLAB, one option you have is to overload the methods that handle arithmetic operations for integer data types, creating your own custom overflow behavior that will result in a "wrap-around" of the integer value. As stated in the documentation:

You can define or overload your own methods for int* (as you can for any object) by placing the appropriately named method in an @int* folder within a folder on your path. Type help datatypes for the names of the methods you can overload.

This page of the documentation lists the equivalent methods for the arithmetic operators. The binary addition operation A+B is actually handled by the function plus(A,B). Therefore, you can create a folder called @int32 (placed in another folder on your MATLAB path) and put a function plus.m in there that will be used instead of the built-in method for int32 data types.

Here's an example of how you could design your overloaded plus function in order to create the overflow/underflow behavior you want:

function C = plus(A,B)
%# NOTE: This code sample is designed to work for scalar values of
%#       the inputs. If one or more of the inputs is non-scalar,
%#       the code below will need to be vectorized to accommodate,
%#       and error checking of the input sizes will be needed.

  if (A > 0) && (B > (intmax-A))  %# An overflow condition

    C = builtin('plus',intmin,...
                B-(intmax-A)-1);  %# Wraps around to negative

  elseif (A < 0) && (B < (intmin-A))  %# An underflow condition

    C = builtin('plus',intmax,...
                B-(intmin-A-1));  %# Wraps around to positive

  else

    C = builtin('plus',A,B);  %# No problems; call the built-in plus.m

  end

end

Notice that I call the built-in plus method (using the BUILTIN function) to perform addition of int32 values that I know will not suffer overflow/underflow problems. If I were to instead perform the integer addition using the operation A+B it would result in a recursive call to my overloaded plus method, which could lead to additional computational overhead or (in the worst-case scenario where the last line was C = A+B;) infinite recursion.

Here's a test, showing the wrap-around overflow behavior in action:

>> A = int32(2147483642);  %# A value close to INTMAX
>> for i = 1:10, A = A+1; disp(A); end
  2147483643

  2147483644

  2147483645

  2147483646

  2147483647   %# INTMAX

 -2147483648   %# INTMIN

 -2147483647

 -2147483646

 -2147483645

 -2147483644