% Script roundoff2.m
% loss of significance in subtraction
% not easy to see the loss os significance in matlab.
% To do it convert to base 2 or hex reprentation of IEEE

%    0 123456789012 3456789012345678901234567890123456789012345678901234
%    s mmmmmmmmmmmm mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
%    | |            |
%    | |            +--------+
%    | 12-bit exponent       |
%    |                       | 
%    sign bit                52 bit mantissa in 51 bits
%                            the hidden bit is always 1

f1 = @(x) sqrt(1 + x) - 1;

num2hex(f1(0.123456789012345E-1))
num2hex(f1(0.123456789012345E-5))
num2hex(f1(0.123456789012345E-10))
num2hex(f1(0.123456789012345E-12))
num2hex(f1(0.123456789012345E-15))