% m12_floating.m - playing with floating point and symbolic arithmetic

    1/4096
    4096*ans
    1/49
    49*ans
    ans - 1
    2^-53
  
    sqrt(1/2)
    ans^2 - 1/2
    sqrt(1/4)
    ans^2 - 1/4
  
    sin(0)
    pi
    sin(pi)
    sin(1000*pi)
    sin(1e20*pi)
  
    1/0
    1/Inf
    1/Inf + 2/3
    0/0
    3*NaN
    2^1023
    2^1024
    2^-1024
    2^-1074
    2^-1075
  
    str2sym('1/49')      % using Matlab's Symbolic Toolbox
    whos
    49*ans - 1
    str2sym('sqrt(1/2)')
    ans^2 - 1/2
    str2sym('pi')
    str2sym('100000000000000000000*pi')
    sin(ans)
    123/456 + 789/987
    str2sym('123/456 + 789/987')
    a = ans
    double(a)
    vpa(a)
    vpa(a,50)
    A = randn(60);
    tic, e = eig(A); toc 
    AA = vpa(A);
    whos
    tic, ee = eig(AA); toc 
    help symbolic