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Timing puzzle

  • To: mathgroup at smc.vnet.net
  • Subject: [mg130424] Timing puzzle
  • From: carlos%colorado.edu at gtempaccount.com
  • Date: Wed, 10 Apr 2013 00:53:07 -0400 (EDT)
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  • Delivered-to: l-mathgroup@wolfram.com
  • Delivered-to: mathgroup-newout@smc.vnet.net
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I am writing a graphics package that often creates objects with thousands of polygons, possibly up to 10^5. Out of curiosity I tested 5 ways of dynamically creating a plot list, using AppendTo, Append, Join, etc., and did the following timing test of 5 ways to do it:

ClearAll[poly,p,n]; poly={}; n00;
p[arg_]:= {mygraphic[mycolor[Random[],Random[],Random[]]],
                mygraphic[mypoly[{{Random[],Random[]},
                 {Random[],Random[]},{Random[],Random[]}}]]};
Print[Timing[Do[AppendTo[poly,p[i]],{i,1,n}]][[1]]]; 
ClearAll[poly]; poly={};
Print[Timing[Do[poly=Append[poly,p[i]],{i,1,n}]][[1]]];  
ClearAll[poly]; poly={};
Print[Timing[Do[poly=Join[poly,{p[i]}],{i,1,n}]][[1]]];
ClearAll[poly]; poly={};
Print[Timing[Do[poly={poly,{p[i]}},{i,1,n}];poly=Flatten[poly]][[1]]];
ClearAll[poly]; poly=Table[0,{n}];
Print[Timing[Do[poly[[i]]=p[i],{i,1,n}]][[1]]];

Running with n00 on a MacPro under Mac OSX 10.6.8 gives these times:

0.911327 Second
0.891656 Second
0.927267 Second
0.504454 Second
0.009575 Second

Question: why is the last method much faster?  I thought that appending an object to a list should take about the same time as storing an array entry.  When I worked with linked lists several decades ago (using assembly code on a CDC 7600) all I had to do is retrieve the object address,  manipulate registers, store in a pointer array, and presto! it was done.



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