This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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creates a compiled function that evaluates expr assuming numerical values of the .
assumes that is of a type that matches .
assumes that is a rank array of objects, each of a type that matches .
assumes that subexpressions in expr that match are of types that match .
_Integermachine-size integer
_Realmachine-precision approximate real number (default)
_Complexmachine-precision approximate complex number
True | Falselogical variable
  • Nested lists given as input to a compiled function must be full arrays of numbers.
  • Compile handles numerical functions, matrix operations, procedural programming constructs, list manipulation functions, and functional programming constructs, etc.
  • Compiled code does not handle numerical precision and local variables in the same way as ordinary Mathematica code.
  • If a compiled function cannot be evaluated with particular arguments using compiled code, ordinary Mathematica code is used instead.
  • Ordinary Mathematica code can be called from within compiled code. Results obtained from the Mathematica code are assumed to be approximate real numbers, unless specified otherwise by the third argument of Compile.
  • The number of times and the order in which objects are evaluated by Compile may be different from ordinary Mathematica code.
  • Compile has attribute HoldAll, and does not by default do any evaluation before compilation.
  • You can use Compile[..., Evaluate[expr]] to specify that expr should be evaluated symbolically before compilation.
  • The following options can be given:
CompilationOptionsAutomaticoptions for the compilation process
CompilationTarget$CompilationTargetthe target runtime for code generation
ParallelizationAutomaticparallel controls for compiled function execution
RuntimeAttributes{}evaluation attributes for the compiled function
RuntimeOptionsAutomaticruntime options for the compiled function
Compile the function Sin[x]+x^2-1/(1-x) for machine real x:
The CompiledFunction evaluates with machine numbers:
Plot the compiled function:
Compile the function Sin[x]+x^2-1/(1-x) for machine real x:
Click for copyable input
The CompiledFunction evaluates with machine numbers:
Click for copyable input
Plot the compiled function:
Click for copyable input
Compile the function to take Newton iterations for and identify the nearest root:
Plot the basins of attraction for the three roots:
The default setting of Automatic generates more efficient code by avoiding computing the same result more than once:
When the optimization level is reduced, less efficient code is generated:
This generates C code and links it back in for execution:
This is a larger example that demonstrates the speed advantages of C code generation:
The default operation runs more slowly:
Listable compiled functions can execute in parallel using threads:
This shows the operation running sequentially:
Typically, $ProcessorCount is used to determine how many threads to be used:
You can combine parallel operations with C code generation to get even faster operation:
This creates a listable compiled function:
It operates on a single input in normal fashion:
When the arguments include a list that does not match the input specification, it threads over that argument:
If there is a branch, listability needs a function to be defined, as shown below using Function:
A listable compiled function is equivalent but executes faster:
A listable compiled function can run in parallel, giving an acceleration on multicore machines:
Using the listable attribute is typically faster than invoking CompiledFunction many times:
Using parallelization can give an even greater speedup:
The results are identical:
A detailed plot of the basins of attraction for Newton's method for :
Typically, integer arithmetic overflow is caught and the computation switches to use bignums:
Turning off overflow checking makes for faster execution, but the result can be incorrect:
Perlin noise is a common algorithm used to generate procedural textures:
This defines the parameters to the Perlin noise function and uses the Perlin function to generate a landscape procedural texture:
The same noise function, with different parameters and color set, can simulate wood grain:
You can apply textures to 3D objects:
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