Re: odd behaviour with 2x2 matrix floating-point multiplication

[Jordi Gutiérrez Hermoso]

On Sun, 2014-12-14 at 23:05 -0800, s.jo wrote:
> I found some errors in my Cygwin system:

Hardly an error,

    http://wiki.octave.org/FAQ#Why_is_this_floating_point_computation_wrong.3F

if you are writing code that depends on checking exact zeros instead
of almost zeros, your code is buggy. Yes, your code may have a bug.
You cannot depend on exact equality except in very narrow cases.

> Can other users check this example to see if all cygwin release has same
> problem?

For your case, I cannot reproduce what you consider a problem:

    octave:1> a = randn
    a = -1.6148
    octave:2> b = randn
    b = -0.73621
    octave:3> a^2 + b^2
    ans =  3.1497
    octave:4> a^2 + b^2 == a*a + b*b
    ans =  1
    octave:5> [a,b; -b a]*[a;b]
    ans =

       3.14966
       0.00000

    octave:6> [a,b; -b a]*[a;b] == [a^2 + b^2; 0]
    ans =

       1
       1

The fact that you're seeing errors of the order of 1e-18, which is
smaller than eps(1), makes me think that your BLAS compilation is
probably storing some floats in registers, giving you a different
precision.

- Jordi G. H.