Since you've extended this thread some more, I'll mention that the
current version of the code that I am working on runs a little bit more
than twice as fast as that version. It's posted at

http://www.math.lsa.umich.edu/~bober/partitions_c.cc

if anyone is interested in testing it. (But don't waste too much time
testing right now, because it is likely to change.)

It's not quite ready for inclusion, but, eventually, maybe Bill Hart's
prediction about it only taking 10 seconds to compute p(10^9) on
sage.math will come true.

On Fri, 2007-08-03 at 23:21 -0500, Alec Mihailovs wrote:
> From: "William Stein" <[EMAIL PROTECTED]>
> 
> > Thanks.  I've fixed this for sage >= 2.7.3 in the attached patch.
> 
> Just upgraded SAGE to 2.7.3 and number_of_partitions works twice as fast as 
> in 2.7.2 with algorithm='bober' for 10^9 - it took 112 sec in 2.7.2 and only 
> 56 sec in 2.7.3. This is in Ubuntu 7.04 on Dual Core 64-bit 2.6GHz Athlon 
> with 2 GB RAM. By the way, to compare with other systems, SAGE 2.7.2 
> installation took about 53 minutes.
> 
> I noticed the following interesting thing with time measuring: assigning 
> number_of_partitions to a variable (that shouldn't take time at all), took 
> about 10% or more of total time. For example,
> 
> sage: time number_of_partitions(10^7)
> 
> took about 0.8 sec while
> 
> sage: time a=number_of_partitions(10^7)
> 
> took slightly more than 1 sec. For 10^8 the corresponding times were 5 sec 
> and 5.45 sec.
> 
> That seems odd, isn't it?
> 
> Alec
> 
> 
> 
>  
> 
> 
> > 
> 
> 


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