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 ; 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].
(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 ;
(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.
Does that look like a good plan?
Snark
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