Compile

Compile[{x1,x2,},expr]

creates a compiled function that evaluates expr assuming numerical values of the xi.

Compile[{{x1,t1},},expr]

assumes that xi is of a type that matches ti.

Compile[{{x1,t1,n1},},expr]

assumes that xi is a rank ni array of objects, each of a type that matches ti.

Compile[vars,expr,{{p1,pt1},}]

assumes that subexpressions in expr that match pi are of types that match pti.

Details and Options

  • The types handled by Compile are:
  • _Integermachinesize integer
    _Realmachineprecision approximate real number (default)
    _Complexmachineprecision 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.
  • Compile generates a CompiledFunction object.
  • Compiled code does not handle numerical precision and local variables in the same way as ordinary Wolfram Language code.
  • If a compiled function cannot be evaluated with particular arguments using compiled code, ordinary Wolfram Language code is used instead.
  • Ordinary Wolfram Language code can be called from within compiled code. Results obtained from the Wolfram Language 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 Wolfram Language 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

Examples

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Basic Examples  (1)

Compile the function Sin[x]+x^2-1/(1-x) for machine real x:

The CompiledFunction evaluates with machine numbers:

Plot the compiled function:

Scope  (1)

Compile the function to take Newton iterations for and identify the nearest root:

Plot the basins of attraction for the three roots:

Options  (9)

CompilationOptions  (1)

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:

CompilationTarget  (2)

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:

Parallelization  (2)

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:

RuntimeAttributes  (3)

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 :

RuntimeOptions  (1)

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:

Possible Issues  (1)

With the default setting for RuntimeOptions intermediate overflow may be missed:

With the "Quality" setting, intermediate terms are tested for overflow:

Neat Examples  (1)

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:

Introduced in 1991
 (2.0)
 |
Updated in 1996
 (3.0)
2010
 (8.0)