Compilation: Avoiding inlining

*To*: mathgroup at smc.vnet.net*Subject*: [mg121448] Compilation: Avoiding inlining*From*: DmitryG <einschlag at gmail.com>*Date*: Thu, 15 Sep 2011 04:41:19 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

This message refers to the extensive exchange here: http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_thread/thread/4ea9938ad1d523c6/735f864eab188778?lnk=gst&q=dmitryg#735f864eab188778 The problem is to solve a system of N ordinary differential equations (ODE) with Runge-Kutta-4 method with compilation. Here is an example of working program *************************************************************************** (* Runge-Kutta-4 routine *) makeCompRK[fIn_] := With[{f = fIn}, Compile[{{x0, _Real, 1}, {t0, _Real}, {tMax, _Real}, {n, _Integer}}, Module[{h, K1, K2, K3, K4, SolList, x = x0, t}, h = (tMax - t0)/n; SolList = Table[x0, {n + 1}]; Do[t = t0 + k h; K1 = h f[t, x]; K2 = h f[t + (1/2) h, x + (1/2) K1]; K3 = h f[t + (1/2) h, x + (1/2) K2]; K4 = h f[t + h, x + K3]; x = x + (1/6) K1 + (1/3) K2 + (1/3) K3 + (1/6) K4; SolList[[k + 1]] = x , {k, 1, n}]; SolList],(*CompilationTarget->"C"*)]]; (* Definition of the equations *) NN = 100; Timing[ RHS = Quiet[ Table[-x[[i]] Sin[ 0.3 t]^2/(1 + 300 Sum[x[[j]], {j, 1, NN}]^2/NN^2), {i, 1, NN}]];] (* Quiet to suppress complaints *) F = Function[{t, x}, Evaluate[RHS]]; (* Evaluate to use actual form of RHS *) Print[] (* Compilation *) tt0 = AbsoluteTime[]; Timing[RK4Comp = makeCompRK[F];] AbsoluteTime[] - tt0 Print[]; (* Setting parameters and Calculation *) x0 = Table[ RandomReal[{0, 1}], {i, 1, NN}]; t0 = 0; tMax = 100; n = 500; tt0 = AbsoluteTime[]; Sol = RK4Comp[x0, t0, tMax, n]; AbsoluteTime[] - tt0 Print["Compilation: ", Developer`PackedArrayQ@Sol] (* Plotting time dependences *) x1List = Table[{1. t0 + (tMax - t0) k/n, Sol[[k + 1, 1]]}, {k, 0, n}]; x2List = Table[{1. t0 + (tMax - t0) k/n, Sol[[k + 1, 2]]}, {k, 0, n}]; x3List = Table[{1. t0 + (tMax - t0) k/n, Sol[[k + 1, 3]]}, {k, 0, n}]; ListLinePlot[{x1List, x2List, x3List}, PlotMarkers -> Automatic, PlotStyle -> {Blue, Green, Red}, PlotRange -> {0, 1}] ********************************************************************************** The drawback of this solution is what Oliver Ruebenkoenig called "inlining". For large NN the RHS of the equations is a lot the explicit code generated by Mathematica. This code then gets compiled and the size of the compiled code strongly increases with NN (it can be seen by the CompilePrint[RK4Comp] command). That is, we write a lot of code inline instead of letting it be generated in the course of the execution, with the compiled code being small. Mathematica's own compiler tolerates inlining, although the large code eats up the memory. If we uncomment the option "CompilationTarget- >"C"", we will see that for large NN compilation goes for ages. That is, inlining has to be avoided. Daniel Lichtblau has rewritten my similar program in the vectorized form that avoided inlining and could be compiled to C, and was fast. But vectorization is not always possible or easy. Oliver wrote that inlining can also be avoided by defining a function and then calling it, but there were no examples at that time. Now I am interested in the cases such as the program above where vectorization is unwanted. How to avoid inlining by defining a function in this case? I have tried to replace RHS = Quiet[Table[-x[[i]] Sin[0.3 t]^2/(1 + 300 Sum[x[[j]], {j, 1, NN}]^2/NN^2), {i, 1, NN}]]; by FRHS[i_][x_List, t_] = -x[[i]] Sin[0.3 t]^2/(1 + 100 Sum[x[[i + j]], {j, 1, Min[3, NN - i]}]^2); RHS = Quiet[Table[FRHS[i][x, t], {i, 1, NN}]]; This works correctly but does not compile, and the execution time is longer. Something is wrong here. Oliver, Daniel, and others, please, help! Thank you, Dmitry

**Follow-Ups**:**Re: Compilation: Avoiding inlining***From:*Oliver Ruebenkoenig <ruebenko@wolfram.com>