On Sep 10, 2007, at 4:44 PM, Joel B. Mohler wrote:
> > Hi, > > David Harvey raised a speed question on > http://sagetrac.org/sage_trac/ticket/628 > It's a legitimate concern, but as far as I can tell, it's a completely > orthogonal issue to that specific patch thanks to Pablo's clever > coding (all > of the exceptional code only occurs if we aren't on the fast path > anyhow). > The issue is basically that we want the binomial function to be as > fast as > possible for 2 integer arguments. I've observed similar potential > issues > with the moebius function. Sure, you're right, it's orthogonal. And as you point out, it's all over the place. > There are an awful lot of python name lookups before we actually > get to the > arithmetic work (in pari). I guess the only real way to fix that > is to write > some cython and call pari directly. I think this would be > worthwhile. I'm > wondering though if there isn't a way to make this moderately easy > in these > cases. > > I suggest having a cython'ed function which takes parameters to > coerce and a > function pointer (?). It coerces the parameters (quickly) to > Integers (or > some agreed upon format, mpz, etc) and passes them down to the > function > pointer which is then guaranteed an appropriate data format and can > just do > the arithmetic. If the coercion fails, an exception is thrown. > The value of > this intermediary is that the "isinstance(int,long,Integer)" is > only coded > once and can thus be maintained and made as quick as possible. > This idea is > very sketchy in my mind so I think it might need some refinement. > > The binomial function then gets a prefix something like: > > try: > call_fast_integer_function( x, m, _binomial_raw ) > except CoercionError: > # compute binomial slowly .... > > The principle refinement needed is: How can > call_fast_integer_function > bewritten generically? What is _binomial_raw -- a c-function, a > cython > function? I'm not too comfortable with this suggestion... it's too specific to integer arguments. When someone calls e.g. binomial(x, y), is it possible to make that call go directly to cython? We can't avoid the initial "binomial" name lookup, that's fine with me, but is it possible to make that call land directly in some function cdef binomial_cython(x, m): ... ? david --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
