8. (Machine Epsilon)

Machine epsilon gives an upper bound on the relative error due to rounding in floatingpoint arithmetic. In C++11, epsilon is the difference between 1.0 and the next representable value of the given floating-point type.

Answer the following questions:

a) Write a small C function to compute epsilon:

double epsilon = 1.0;

while ((1.0 + 0.5*epsilon) != 1.0)

{

epsilon *= 0.5;

}

Generalise this function for other types.

b) Compare the value from part

a) with the value produced by:

std::numeric_limits::epsilon().