odd behaviour with 2x2 matrix floating-point multiplication

[s.jo]

Dear all,

I found some errors in my Cygwin system:

+ ## Generate two floating numbers:
+ a = randn
a =   -0.314598019079378
+ b = randn
b =    0.687235082446626
+ ##
+ ## Check
+ a * a + b * b
ans =     0.57126397215409
+ -b * a + a * b
ans =                    0
+ ##
+ ## Matrix operation
+ [a, b; -b, a] * [a; b]
ans =

       0.57126397215409
   -5.62429876976855e-18

+ ##
+ ## Element-wise operation
+ [a, b] * [a; b]
ans =     0.57126397215409
+ [-b, a] * [a; b]
ans =                    0
+ ##
+ ## Compare
+ [a, b; -b, a] * [a; b] == [a * a + b * b; -b * a + a * b]
ans =

                      1
                      0


As above example, two floating-point numbers a and b show different result
when I calculate directly -b * a + a * b and do it again with matrix
operation:
The first result is 0, but the second is -5.62429876976855e-18.

One of non-cygwin systema works well, Dan told.
I am not sure if it is a problem with my cygwin-octave 3.8.2.

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

Best regards,

jo





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