[3/3] gdiplus: Make GdipInvertMatrix test pass on native

[Nikolay Sivov]

Michael Karcher wrote:
> Am Samstag, den 12.07.2008, 16:55 -0500 schrieb James Hawkins:
>   
>>>>> -    GdipCreateMatrix2(1.0/9.0, 2.0/9.0, 4.0/9.0, -1.0/9.0, -2.0, -1.0,
>>>>>           
>>> Of course there's only one value of inverted matrix.
>>>       
> Which is not representable as a finite binary fraction.
>
>   
>>> GDI+ uses floating
>>> point values for matrix elements so don't you think the result could be
>>> slightly different due different calculation algorithms?
>>>       
> As they say: Never compare floating point numbers for equality. So I
> understand your point. Especially if unrepresentable values are
> involved.
>
>   
>> If you write and test the results in Windows, you won't have to guess
>> what the results will be.
>>     
> Right. Testing against Windows is the only method of verifying whether
> Wine does the right things, but floating point arithmetic, which is
> inherently prone to rounding errors, should IMHO be accounted for by
> allowing slight variances.
>
>   
>> No I don't think the results will be
>> slightly different.  Higher-precision arithmetic doesn't mean more
>> slop.
>>     
> What do you mean with higher-precision arithmetic? Floating point
> arithmetic *always* means slop, as soon as numbers that can't be written
> as finite binary fractions are involved. In this concrete case, I
> suspect you are right. There is just one obvious algorithm[1] to invert
> a 2x2 Matrix, which is so simple that it cannot be stated in numerically
> non-equivalent ways (remember, a+(b+c) is not necessarily equal to (a
> +b)+c)), so I would expect the results to be really identical on windows
> if the input numbers are small integers. Still, the fractions with nine
> in the denominator make me worry. Couldn't we use a matrix with a
> determinant of 8 or 16 instead of nine? This would make nice floats you
> can definitely compare for equality.
>
> As a side note: I don't like the implementation of m_equalf, as it
> checks for absolute deviation instead of relative deviation. The values
> used have the same order of magnitude as 1, so it does not matter for
> this test. But: This very criterion is also used in in
> GdipIsMatrixInvertible, where I consider it highly questionable, as long
> as it is not backed by API tests.
>   
You're absolutely right. m_equalf id used as a temporary solution just 
to make the test pass with this deviation, which is acceptable in this 
particular initial data, to show that GdipInvertMatrix works in the 
main. But check  in GdipIsMatrixInvertible should be replaced, I'm fully 
agreed here. I'll try to choose appropriate method to do so (using 
Windows test results too of course).
> Nikolay: Please write a test whether the matrix
>   1.0/131072, 2.0/131072, 4.0/131072, -1/131072, 0, 0
> is invertible. According to your criterion, it is *not* invertible, as
> the determinant will be 9.0/17179869184, which is way below 1e-5, but
> this matrix still *is* invertible. What happens on Windows?
>   
On Windows it shows the following:

0.00000000, 32768.000, 65536.000, -16384.000, 0.00000000, 0.00000000

So native criterion differs.
> Regards,
>   Michael Karcher
>
> [1] Which I found (as expected) when looking at dlls/gdiplus/matrix.c
>