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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


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