#4432: [with patch, needs work] symbolic gamma and factorial
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Reporter: whuss | Owner: whuss
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.2.1
Component: calculus | Resolution:
Keywords: |
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Comment (by whuss):
Michael,[[BR]]
I probably have to read the Mercurial documentation.
I'm not sure if I measure the performance correctly, but if I do
{{{
def f(n):
s = 0
for i in xrange(n):
s += factorial(2^i)
return s.ndigits()
def g(n):
s = 0
for i in xrange(n):
s += gamma((1.8)^i)
return s
def h(n):
set_random_seed(0)
s = 0
for i in xrange(n):
s += gamma(random())
return s
timeit('f(22)')
timeit('g(22)')
timeit('h(10^4)')
}}}
I get the following:
on sage-3.2 without the patch
{{{
5 loops, best of 3: 10.9 s per loop
125 loops, best of 3: 4.16 ms per loop
5 loops, best of 3: 5.38 s per loop
}}}
with trac_4432.patch
{{{
5 loops, best of 3: 10.9 s per loop
125 loops, best of 3: 4.18 ms per loop
5 loops, best of 3: 1.67 s per loop
}}}
with trac_4432.patch + trac_4432-gamma.patch
{{{
5 loops, best of 3: 10.9 s per loop
125 loops, best of 3: 4.17 ms per loop
5 loops, best of 3: 5.45 s per loop
}}}
So trac_4432.patch is much faster for small values of the gamma function
because we are not computing over the complex numbers.
Also only with trac_4432.patch
{{{
plot(gamma, 1, 4)
}}}
works. But this also doesn't work with the current code.
Greetings,[[BR]]
Wilfried
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4432#comment:10>
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