Abnormal memory consumption during compilation of models with inline integration and symbolic differentiation

[Francesco Casella]

Please consider the SmoothSat model in the attached Save Total file. The inline smoothSat function

function smoothSat "Smooth saturation function"
  input Real x;
  input Real xmin "Lower bound of range where y = x";
  input Real xmax "Upper bound of range where y = x";
  input Real dxmin "Width of lower smoothing range";
  input Real dxmax=dxmin "Width of upper smoothing range";
  output Real y;
algorithm
   y := if x < xmin + dxmin then xmin + dxmin - dxmin*(xmin + dxmin - x)/(dxmin^4 + (xmin + dxmin - x)^4)^0.25 else if x > xmax - dxmax then xmax - dxmax + dxmax*(x - xmax + dxmax)/(dxmax^4 + (x - xmax + dxmax)^4)^0.25 else x;
  annotation (smoothOrder=4, InLine=true);
end smoothSat;

gets differentiated 5 times in the test model:

}}}. 

The Cryogenics_Test_SmoothSat.c file defines about 10000 temporary expressions. Most of them are repeated a lot of times: for example, (1.0 + (0.1 - time)) is repeated 5021 times, (time + -1.7) is repeated 4520 times.

When compiling the C code under MinGW with the default settings, cc1.exe allocates over 3 GB of memory (!). Removing the 5th differentiation brings down memory allocation to 300 MB.

Differentiating an expression 5 times is probably a bit extreme (the idea was to check that the first 4 derivatives are continuous, and only the 5th is discontinuous), however there is something going badly wrong with common subexpressions in the differentiated functions, and I guess this is worth having a look at.

[Francesco Casella]

C file generated by omc