There was some discussion a month or two back about different algorithms for prime_pi. IIRC, Mathematica's was the fastest, Sage's was second fastest and Maple's method was dumb and just counted them like a 10 year old could do.
I pointed out a link to those with accounts on sage.math.users of a discussion on the newsgroup comp.unix.solaris about how to get maximum performance from a Sun T5240 (the same machine as 't2'). It was quite a technical discussion about why old machines can be faster or slower, depending how the program is written. Someone wrote a program which computed the primes under 10,000 in C, and compared the speed of his old machine to his high spec Sun T5240 and showed the old machine was quicker. (BTW, 't2' has 16 cores and 128 virtual processors) A Sun employee, Andrew Gabriel, who I happen to know, then re-wrote the program for him in a way to exploit the Sun T5240 properly. William re-run the program yesterday and found the time drop from 21 seconds to 0.6 seconds when he used 128 threads. It then occurred to me that perhaps Maple's dumb method of computing number of primes under n might be silly on most machines, but might if re-written to use a parallel machine properly, it could be the most sensible way to do it. But I've no idea how the dumb method compares with the Sage implementation or Mathematica. Obviously if the dumb method is 3 orders of magnitude slower, then I doubt much could be done with it, for now at least, though I can see machines with 1000 virtual processors wont be long, and might actually exist now. It would be very interesting to see if Mathematica could do anything very quick on t2. Clearly the hardware is capable of high performance - it's just we are not getting it because most of the programs we are using on t2 at the minute don't exploit the machine properly. Perhaps Mathematica might switch to a better method on parallel machines. For those interested, the link is here. http://groups.google.co.uk/group/comp.unix.solaris/browse_thread/thread/7041af61bab6cfd/718b4fb647765119?hl=en&ie=UTF-8&q=Single-threaded+T5240+performance&pli=1 You might want to try the program on your dual and quad processor machines, but you are not likely to get the speeds possible on t2. Dave PS Mathematica 6 failed to determine the number of CPUs the machine had on Solaris SPARC and always assumed one. I found the reason for this, and posted the details to sci.math.symbolic someone from which WRI thanked me for, http://groups.google.cl/group/sci.math.symbolic/browse_thread/thread/c07a8230fbf01bc1/837b00dfbaaa31aa PPS sci.math.symoblic is a much quicker way to get help on MMA issues than the Mathematica newsgroup, as the latter is moderated with only one moderator. Even Wolfram Research employees can't post to that without his approval ! --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
