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.
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?
--
Joel
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