Re: Timing puzzle

*To*: mathgroup at smc.vnet.net*Subject*: [mg130437] Re: Timing puzzle*From*: awnl <awnl at gmx-topmail.de>*Date*: Thu, 11 Apr 2013 04:11:28 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <kk2qvl$bip$1@smc.vnet.net>

Hi, > 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. the answer is pretty obvious: Lists in Mathematica are - despite their name - not linked lists but arrays. It can be argued whether that was a good decision or not, but you certainly have to live with that fact and remember it if efficiency matters... You should check your results of case 4, this is a well known "Mathematica emulation" of linked lists and should be much faster: on my computer (Windows 7, Mathematica 9) with n=10000 it is just as fast as the Do loop which sets the preallocated table entries... hth, albert