First seen when compiled with gcc-4.6.2 -g -O1
The macro `Fn_SZ' which boils down to
1/2 * (x + sqrt(x*x + c*c))
was used in a context where a negative result
blew up the following computations.
(used to compute `Egidl', which is used to
compute exp(-1 / (Egidl + small_constant)))
For large negative values of x the computation
boils down to
1/2 ( x + almost(|x|) )
where the summands almost cancel each other,
sometimes yielding a small negative result.
small_constant was too small to avoid a big
result for -1/(Egidl + small_constant)
yielding an `inf' during the exp() computation,
which was later multiplied with a `0'
yielding a NaN,
which was carried forward
during the rest of computations.
Because the error of the cancellation scales
with the magnitude of x, no larger `small_constant'
could have avoided the problem.
Presumably the problem was amplified
by a mixture of precisions (double versus extended float)
of intermediate values.
(the program wasn't compiled for sse)
( x was -2.812500e+06,
c was 1.000000e-02,
Fn_SZ result was -1.853095e-11
thus the cancellation remainder
was of relative size
6.6e-18
which is approximately
2^-57
and thus more accurate
as a `double float' could have delivered
)
Holger Vogt
rlar
dwarning