Re: Re: fastest way to add up a billion numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg73973] Re: [mg73907] Re: fastest way to add up a billion numbers*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sat, 3 Mar 2007 23:53:18 -0500 (EST)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <es92b2$3oj$1@smc.vnet.net> <200703030555.AAA02643@smc.vnet.net>*Reply-to*: murray at math.umass.edu

I wonder what the timing for a sum of the form Sum[n,{n,nstart,nend}] really indicates. I suspect that Mathematica is not actually summing but rather just uses Gauss' well-known closed-form formula for such a sum of consecutive positive integers. dimitris wrote: > There is recent post of mine asking something relevant here. > > You can find also a relevant thread here: > > http://forums.wolfram.com/mathgroup/archive/2005/May/msg00600.html > > One billion numbers? > Here is what I get to my PC > > In[3]:= > Range[10^9] >>From In[3]:= > No more memory available. > Mathematica kernel has shut down. > Try quitting other applications and then retry. > > In[1]:= > Table[i, {i, 1, 10^9}]; > >>From In[1]:= > No more memory available. > Mathematica kernel has shut down. > Try quitting other applications and then retry. > > Anyway... > > lst = Range[10^6]; > > Timing[Plus @@ lst] > {0.34299999999999997*Second, 500000500000} > > Timing[Total[lst]] > {0.2659999999999999*Second, 500000500000} > > Timing[Fold[Plus, 0, lst]] > {0.703*Second, 500000500000} > > Timing[lst /. {x_, y___} -> x + y] > {0.45300000000000007*Second, 500000500000} > > Timing[Tr[lst]] > {0.3899999999999997*Second, 500000500000} > > Timing[Sum[lst[[i]], {i, 1, 10^6}]] > {1.4379999999999997*Second, 500000500000} > > > But for your case I should simply suggest > > Timing[Sum[i,{i,1,10^9}]] > {0.047 Second,500000000500000000} > > > Regards > Dimitris > > > > > =CF/=C7 Raj =DD=E3=F1=E1=F8=E5: >> hi! >> >> Could somebody tell me what would be the fastest way to add up a >> billion numbers(from 1 to 10^9 i.e the first billion numbers) in >> Mathematica? >> >> Ofcourse the answer is n(n+1)/2, but is there any other way in >> Mathematica other than the following one: >> >> Total@@Range[10^9] >> >> Thanks, >> >> Raj > > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**Follow-Ups**:**Re: Re: Re: fastest way to add up a billion numbers***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**References**:**Re: fastest way to add up a billion numbers***From:*"dimitris" <dimmechan@yahoo.com>