Detailed explanation of code that determines the Machine Epsilon for single and double precision numbers?

The following code was used to determine the machine epsilon for single and double precision numbers:

numprec=double(1.0); % Define 1.0 with double precision
numprec=single(1.0); % Define 1.0 with single precision
while(1 < 1 + numprec)
numprec=numprec*0.5;
end
numprec=numprec*2

Questions: Why do we consider addition to 1? Explain in detail what the code does.

Answer 1

[Walter Roberson]

Machine epsilon is, by tradition, measured with relationship to 1.

The code is looping through finding the largest number numprec such that 1 differs from 1+numprec . That is the basic definition of machine epsilon.

https://en.wikipedia.org/wiki/IEEE_floating_point#Formats

[Steven Lord]

You may also find section 1.7 of Cleve's Numerical Computing with MATLAB informative.