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

*To*: mathgroup at smc.vnet.net*Subject*: [mg73991] Re: [mg73973] Re: [mg73907] Re: fastest way to add up a billion numbers*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Mon, 5 Mar 2007 04:46:49 -0500 (EST)*References*: <es92b2$3oj$1@smc.vnet.net> <200703030555.AAA02643@smc.vnet.net> <200703040453.XAA25305@smc.vnet.net>

If you compare these three timing (and particularly the last one) you will see that your suspision is wrong. In[1]:= Timing[Sum[i, {i, 1, 10^9}]] Out[1]= {0.11999199999999999*Second, 500000000500000000} In[2]:= Timing[NSum[i, {i, 1, 10^9}]] Out[2]= {0.0862520000000001*Second, 5.000000005*^17} In[3]:= Timing[Sum[i, {i, 1, n}] /. n -> 10^9] Out[3]= {0.02608200000000005*Second, 500000000500000000} Only the last method (the fastest) does what you suspected (which is why I do not think it a "legitimate" solution to the posted problem). The fastest method that actually adds up numbers uses NSum (which of course gives only an approaximate answer). Andrzej Kozlowski On 4 Mar 2007, at 05:53, Murray Eisenberg wrote: > 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: Re: fastest way to add***From:*Daniel Lichtblau <danl@wolfram.com>

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

**Re: Re: fastest way to add up a billion numbers***From:*Murray Eisenberg <murray@math.umass.edu>