help with numeric speed optimization
in [Lisp]
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From: verec on 12 Aug 2006 18:06 On 2006-08-12 22:28:15 +0100, Wade Humeniuk <whumeniu+anti+spam(a)telus.net> said: > This version is better than the last > > (defun pi/2-opt () > (declare (optimize (speed 3) (safety 0) (debug 0) (float 0))) > (loop with sum of-type double-float = #.(realpart (+ (exp (- (expt > -10.0d0 2.0d0))) > (exp (- (expt > 10.0d0 2.0d0))))) > for x of-type double-float from -9.99d0 below 10.0d0 by 0.01d0 > do (incf sum (* 2d0 (exp (- (* x x))))) > finally (return (* sum 0.005d0)))) > > CL-USER 1 > (time (dotimes (i 10000) (pi/2-opt))) > Timing the evaluation of (DOTIMES (I 10000) (PI/2-OPT)) > ; Loading fasl file C:\Program > Files\Xanalys\LispWorks\lib\4-3-0-0\modules\util\callcoun.fsl > > user time = 1.231 > system time = 0.000 > Elapsed time = 0:00:01 > Allocation = 164304 bytes standard / 113113 bytes conses > 0 Page faults > Calls to %EVAL 10035 CL-USER 1 > (pi/2-WH) 1.7724538509055174D0 CL-USER 2 > (time (dotimes (i 10000) (pi/2-WH))) Timing the evaluation of (DOTIMES (I 10000) (PI/2-WH)) .... Elapsed time = 0:00:12 .... CL-USER 4 > (pi/2-WH2) 1.7724538509055174D0 CL-USER 5 > (time (dotimes (i 10000) (pi/2-WH2))) Timing the evaluation of (DOTIMES (I 10000) (PI/2-WH2)) .... Elapsed time = 0:00:12 .... Thanks Wade! At 12s for the Lisp version (still with the same LW 4.4,6 PE compiler) I have no doubt that I now can successfully make my case! (Though, out of curiosity I'm going to try with SBCL and OpenMCL) Many thanks -- JFB
From: Raffael Cavallaro on 12 Aug 2006 18:07 On 2006-08-12 15:18:47 -0400, verec <verec(a)mac.com> said: > Are type-casts supposed to be implementation dependent? > > I thought (erroneously?) that (the float XYZ) would > just drop the imaginary part, precisely because that's > the purpose of a cast? Just to be clear, "the" is *not* a type cast - it is a special form that acts as a type declaration. (the float (foo ...)) is a special form telling the compiler/interpreter that you, the programmer, are certain that the expression beginning (foo ...) will definitely return a float so the compiler can treat the return of (foo ...) as a float. If you use this declaration with an expression that returns something other than a float you are in undefined territory: "The consequences are undefined if the values yielded by the form are not of the type specified by value-type." (from <http://www.lisp.org/HyperSpec/Body/speope_the.html#the>) The function cl:float takes a real number and an optional prototype for float format (e.g., 1.0d0) and returns a float of the same format as the prototype or a single float if no prototype is supplied: (float 1.0s0 1.0d0) => 1.0d0 (float 33/3 1.0d0) => 11.0d0 (float 2) => 2.0s0 If you want only the real part of a complex number use the function cl:realpart: (realpart #C(1.7724538 -7.747651E-8)) => 1.7724538
From: verec on 12 Aug 2006 18:19 On 2006-08-12 23:07:13 +0100, Raffael Cavallaro <raffaelcavallaro(a)pas-d'espam-s'il-vous-plait-mac.com> said: > "The consequences are undefined if the values yielded by the form are > not of the type specified by value-type." > (from <http://www.lisp.org/HyperSpec/Body/speope_the.html#the>) > [...] > If you want only the real part of a complex number use the function > cl:realpart: > > (realpart #C(1.7724538 -7.747651E-8)) > > => 1.7724538 Point taken. Many thanks. -- JFB
From: verec on 12 Aug 2006 18:20 On 2006-08-12 22:54:06 +0100, Barry Margolin <barmar(a)alum.mit.edu> said: > In article <44de2997$0$639$5a6aecb4(a)news.aaisp.net.uk>, > verec <verec(a)mac.com> wrote: > >> I thought (erroneously?) that (the float XYZ) would >> just drop the imaginary part, precisely because that's >> the purpose of a cast? Or should I use (coerce ... in >> addition? > > THE is not a type-cast, it is a declaration that the value of the > expression is known a priori to be of the specified type. It allows > the compiler to perform type dispatching at compile time rather than at > run time, but it doesn't perform any conversion to ensure that the > object is of that type. > > So you should write (the float (realpart xyz)). I knew that when with a hint of a doubt, I should head straight to the CLHS :-) Many Thanks -- JFB
From: Glenn.Ehrlich on 12 Aug 2006 18:28
Here are some good links on improving numerical computation speed in Common Lisp: "On using Common Lisp in scientific computing", by Nicolas Neuss. This has a pretty good tuturial-level introduction to how to do numerical optimization in Common Lisp. http://www.iwr.uni-heidelberg.de/organization/sfb359/PP/Preprint2002-40.ps.gz "Fast Floating-Point Processing in Common Lisp", by Richard Fateman. This is a more in-depth treatment. http://www.cs.berkeley.edu/~fateman/papers/lispfloat.ps Ken Anderson's Common Lisp Performance page: http://openmap.bbn.com/~kanderso/performance/ Additionally, here's a listing of math oriented libraries available for Common Lisp: http://www.cliki.net/mathematics Glenn |