Re: four approaches to do a simple sum

*To*: mathgroup at smc.vnet.net*Subject*: [mg57212] Re: [mg57171] four approaches to do a simple sum*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sat, 21 May 2005 02:39:25 -0400 (EDT)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

I don't know the answer to your question but Tr is even faster. longlist=Table[Random[],{1000000}]; Timing[Plus@@longlist] {1.39 Second,499953.} Timing[Fold[Plus,0,longlist]] {0.53 Second,499953.} Timing[Tr[longlist]] {0.03 Second,499953.} Bob Hanlon > > From: Hui Fang <fangh73 at xmu.edu.cn> To: mathgroup at smc.vnet.net > Date: 2005/05/20 Fri AM 04:43:04 EDT > Subject: [mg57212] [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 > >