Arithmetic precision with doubles in Matlab

Question

I am having a bit of trouble understanding how the precision of these doubles affects the outcome of arithmetic operations in Matlab. I thought that since both a & b are

Answer 1

To add to what the other answers have said, you can use the MATLAB function EPS to visualize the precision issue you are running into. For a given double-precision floating-point number, the function EPS will tell you the distance from it to the next largest representable floating point number:

>> a = 1.22e-45;
>> b = 1;
>> eps(b)

ans =

  2.2204e-016

Note that the next floating point number that is larger than 1 is 1.00000000000000022204..., and the value of a doesn't even come close to half the distance between the two numbers. Hence a+b ends up staying 1.

Incidentally, you can also see why a is considered non-zero even though it is so small by looking at the smallest representable double-precision floating-point value using the function REALMIN:

>> realmin

ans =

  2.2251e-308  %# MUCH smaller than a!