tests pass, but results don't match !?

[Brian Gough]

Daniel Rohe writes:
 > I've compiled gsl-0.8 on SuSE-7.1 and apparently all tests pass.
 > looking quickly over the results I found e.g. the following:
 > 
 > PASS: zgbmv(case 809) real (0.751079 observed vs 0.75108 expected)
 > PASS: plain, tsuda function, 2d, abserr[7] vs sd (0.00995764 observed vs
 > 0.00726095 expected)
 > PASS: miser, product, 3d, abserr[5] vs sd (0.00905003 observed vs
 > 0.00890616 expected)
 > PASS: vegas, product, 2d, result[7] (0.9999 observed vs 1 expected)
 > PASS: vegas, product, 2d, abserr[7] (obs 0.000233065 vs exp 0.01)
 > 
 > Although these differences are not necessarily relevant, I don't have a
 > really good feeling about this!
 > Maybe someone can tell me that I don't need to worry about it.

Thanks for checking.  

The differences are within normal variation.  The first case is ok
once rounding is taken into account.  Looking in the debugger the
underlying values are 0.75107950000000001 and 0.7510794999999999,
which just happen to get rounded in different directions by printf's
%g format.

The next cases are from the monte carlo routines, which have
statistical fluctations, so exact agreement in the test output is not
possible there.  The program checks that the result and abserr (error
estimate) are self-consistent and that the result is within 5 sigma of
the expected value -- in these cases they are I think.

regards
Brian Gough