On Sunday, 5 February 2012 21:03:46 UTC+8, Snark wrote:
>
> Hi,
>
> this thread is getting... long. Let me try to refocus it on more
> constructive grounds.
>
> Let's list the problematic expressions:
> 1. gamma(float(6))
> 2. SR(10.0r).gamma()
> 3. float(maxima("1.7e17"))
> 4. binomial(0.5r,5)
>
> The following is known :
> (a) 1,3 and 4 give test-passing results with "#tol rel", so even if
> wrong, they're not dead-wrong ;
>
> (b) 1, 2 and 4 are all the same bug in various disguise : the libc
> lgammal function isn't good enough ;
>
more precisely, the (e)glibc gamma function is not good. (lgammal isn't too
good either, but it's a different story).
Let me post your link to a good implementation of gamma(), in netbsd's libc:
http://cvsweb.netbsd.org/bsdweb.cgi/~checkout~/src/lib/libm/noieee_src/n_gamma.c?rev=1.7&content-type=text/plain&only_with_tag=MAIN
(and it states the error bounds, by the way!)
> this is explicit in 1 and 2, and
> implicit in 4 where for floats the computation is by a quotient of gamma
> calls [aside: that is probably a wrong way to do things].
>
I'm sure there is research done on how to do this numerically in a proper
way...
> (c) 3 is a different problem, and although "#tol rel" makes it pass the
> tests, the fact that it needs it to pass is bad.
>
> So my proposition is the following:
>
> (1) I'll try to fix the implementation of lgammal upstream ;
>
gammal, and gamma, the first thing, perhaps. Not sure if lgammal can be
fixed easily, actually.
> (2) I'll try to investigate the maxima string-to-float conversion ;
>
> (3) the sage developpers should still decide and make public some
> statement as to what they consider a correct numerical approximation,
> because that thread only made obvious that there's a need for a
> reference document.
>
This is a very good idea. The link to netbsd's implementation show that's
it's doable...
> Does that look like a good plan?
>
> Snark
>
Dima
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