Re: four approaches to do a simple sum

*To*: mathgroup at smc.vnet.net*Subject*: [mg57213] Re: [mg57171] four approaches to do a simple sum*From*: "Caffa Vittorio Dr." <Caffa at iabg.de>*Date*: Sat, 21 May 2005 02:39:26 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

By the way: Timing[Fold[Plus, 0, longlist]] {0.22 Second, 499831.} Timing[Total[longlist]] {0.01 Second, 499831.} Cheers, Vittorio >-----Original Message----- >From: Hui Fang [mailto:fangh73 at xmu.edu.cn] To: mathgroup at smc.vnet.net >Sent: Friday, May 20, 2005 10:43 AM >Subject: [mg57213] [mg57171] four approaches to do a simple sum > >Here I have a long list, length of 1 million, and I used 4 ways to get >the sum of all elements. > >In[1] = longlist=Table[Random[], {1000000}]; > >Method 1: >In[2] = Timing[sum=0; For[i=1,i<=Length[longlist],sum+=longlist[[i]]]; sum] >Out[2] = {6.219 Second, 500358} > >Method 2: >In[3] = Sum[longlist[[i]],{i,1,1000000}] >Out[3] = {1.718 Second, 500358} > >Method 3: >In[4] = Timing[Plus@@longlist] >Out[4] = {0.407 Second, 500358} > >Method 4: >In[5] = Fold[Plus,0,longlist] >Out[5] = {0.156 Second, 500358} > >The computing time gets shorter and shorter from top to bottom. It's >easy to understand why the first two methods are slow because they >involved an extra variable i for loop control and basically violates the >principle for list manipulation "Never take a list apart". >What I don't understand is why method 4 is faster than method 3. >Any explanation?Or do you have an even faster method? >Thanks a lot! > >Hui Fang