Thank you for all of your quick responses and advices.
And I'm sorry for my slow reply.
As was correctly pointed out, the line
f = (`y' - 1)/ln(`1')
should have been
f = (`y' - 1)/ln(`y')
So, though I wrote 'It works well all in all', it was mistaken,
too:-). I'm sorry to have posted such a careless question.
For your reference, let me explain a little bit the motivation
behind this posting.
At a glance, a more natural way to code
f = (exp(x) - 1)/x
would be:
if `1' == 0 {
di in gr "f = " 1
}
else {
local f = (exp(`1') - 1)/`1'
di in gr "f = " "`f'"
}
But, according to McCullough and Vinod (1999, p.646),
this 'natural method' tends to return biased results when
the argument is fairly small(ex. x = 9e-15). They say
'The reason the natural method fails miserably is because
the intermediate step of the calculation is imprecise: for
x ~ 0('nearly zero') the numerator is swamped by rounding and
cancellation error'.
And they recommend an alternative method, which I posted.
Reference:
McCullough, B. D. and H. D. Vinod,
The Numerical Reliability of Econometric Software,
Journal of Economic Literature,
Jun., 1999, vol 37, num 2, pp.633-665.
K.I.
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