Re: Re: Slowdown

*To*: mathgroup at smc.vnet.net*Subject*: [mg53236] Re: [mg53221] Re: Slowdown*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sun, 2 Jan 2005 04:12:45 -0500 (EST)*References*: <cr33tt$je6$1@smc.vnet.net> <200501010733.CAA01134@smc.vnet.net> <E11A8158-5BF2-11D9-8DF3-000A95B4967A@mimuw.edu.pl>*Sender*: owner-wri-mathgroup at wolfram.com

There was some confusion in the names I used in my earlier message so here are the results again. They look even more "weird": In[1]:= L=weirdness[]; Do[L=weirdness[L,i],{i,10^4}]//Timing Out[2]= {0.07 Second,Null} In[3]:= L=weirdness$1[]; Do[L=weirdness$1[L,i],{i,10^4}]//Timing Out[4]= {0.06 Second,Null} In[5]:= L=weirdness$25[]; Do[L=weirdness$25[L,i],{i,10^4}]//Timing Out[6]= {14.76 Second,Null} In[7]:= L=weirdness[]; Do[L=weirdness[L,i],{i,10^4}]//Timing Out[8]= {0.07 Second,Null} In[9]:= $Version Out[9]= 5.1 for Mac OS X (October 25, 2004) Andrzej On 1 Jan 2005, at 21:44, Andrzej Kozlowski wrote: > On 1 Jan 2005, at 16:33, David Bailey wrote: > >> Maxim wrote: >>> Consider: >>> >>> In[1]:= >>> Module[{f, L}, >>> L = f[]; >>> Do[L = f[L, i], {i, 10^4}] >>> ] // Timing >>> >>> Module[{weirdness, L}, >>> L = weirdness[]; >>> Do[L = weirdness[L, i], {i, 10^4}] >>> ] // Timing >>> >>> Out[1]= >>> {0.015*Second, Null} >>> >>> Out[2]= >>> {3.063*Second, Null} >>> >>> Here the timings differ by a factor of 200. Besides, the timing grows >>> linearly in the first case and quadratically in the second >>> (therefore, for >>> n=10^5 there will be an approximately 2000 times slowdown). We can >>> only >>> guess that something goes wrong with the symbol name hashing. >>> >>> Maxim Rytin >>> m.r at inbox.ru >>> >> Hi Maxim, >> >> I found those timings very interesting. I remember doing some timing >> experiments a long time ago - trying to see if when you constructed a >> complicated structure - as you are obviously doing - the time went up >> quadratically. I expected it would, because each time a new expression >> is created, the system has to check that nothing has changed inside >> the >> existing expression, which is getting ever bigger. Although it is >> clear >> to a human in most cases that this is so, it is obviously not easy to >> get a machine to do this efficiently. In fact, all my experiments >> indicated that adding a new layer to a large structure was no more >> expensive that adding one to a tiny structure! >> >> This led me to speculate that maybe Mathematica holds some sort of an >> array of bits generated by hash to test to see if a large expression >> could have changed (say because of a variable assignment) since it was >> created. If this idea is close to the truth, then you would expect >> there >> to be exceptional situations where the hash values would clash and >> cause >> a quadratic time dependency. This could hardly be called "something >> going wrong", however - anything that uses a hash strategy will run >> slowly in some situations. >> >> Your phenomenon is quite robust, in that it can be set up as a >> function >> that can be used to test any symbol: >> >> test[x_]:=Timing[Module[{x,L}, >> L=weirdness[]; >> Do[L=weirdness[L,i],{i,10^4}]]][[1]] >> >> Sure enough test[weirdness] is very slow. Moreover, it is slow every >> time you run it, even though each time the Module is run a DIFFERENT >> local variable will be created. Therefore, I set Mathematica going >> creating 9-letter random variables and testing each in turn - looking >> for another 'weird' variable. So far, I have found no others - so the >> phenomenon you have discovered must be quite rare. >> >> After searching random variables for a bit test[weirdness] seems to >> become even more expensive, but curiously, after a really long search, >> 'weirdness' lost its weirdness - I guess something gets restructured >> when a very large number of symbols get created. >> >> My tests were done on a Windows XP machine, is the variable >> 'weirdness' >> just as weird on other platforms, I wonder? >> >> It would be interesting if we could tempt someone from WRI to comment! >> >> David Bailey >> dbaileyconsultancy.co.uk >> >> > > > The problem does not actually seem to involve Module itself, rather > it appears connected with variable names of the form > weirdness$somenumber. Here is what I see: > > In[1]:= > L=weirdness[]; > Do[L=weirdness[L,i],{i,10^4}]//Timing > > Out[2]= > {0.07 Second,Null} > > In[3]:= > L=weirdness$1[]; > Do[L=weirdness$25[L,i],{i,10^4}]//Timing > > Out[4]= > {17.92 Second,Null} > > In[5]:= > L=weirdness$25[]; > Do[L=weirdness$25[L,i],{i,10^4}]//Timing > > Out[6]= > {13.26 Second,Null} > > In[7]:= > $Version > > Out[7]= > 5.1 for Mac OS X (October 25, 2004) > > > Andrzej Kozlowski > Chiba, Japan > http://www.akikoz.net/~andrzej/ > http://www.mimuw.edu.pl/~akoz/ >

**References**:**Re: Slowdown***From:*David Bailey <dave@Remove_Thisdbailey.co.uk>