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NAME

       Math::Symbolic::Compiler - Compile Math::Symbolic trees to Perl code

SYNOPSIS

         use Math::Symbolic::Compiler;

         # A tree to compile
         my $tree = Math::Symbolic->parse_from_string('a^2 + b * c * 2');

         # The Math::Symbolic::Variable 'a' will be evaluated to $_[1], etc.
         my $vars = [qw(b a c)];

         my ($closure, $code, $trees) =
           Math::Symbolic::Compiler->compile($tree, $vars);

         print $closure->(2, 3, 5); # (b, a, c)
         # prints 29 (= 3^2 + 2 * 5 * 2)

         # or:
         ($closure, $trees) =
           Math::Symbolic::Compiler->compile_to_sub($tree, $vars);

         ($code, $trees) = Math::Symbolic::Compiler->compile_to_code($tree, $vars);

DESCRIPTION

       This module allows one to compile Math::Symbolic trees to Perl code
       and/or anonymous subroutines whose arguments will be positionally
       mapped to the variables of the compiled Math::Symbolic tree.

       The reason you'd want to do this is that evaluating a Math::Symbolic
       tree to its numeric value is extremely slow. So is compiling, but once
       you've done all necessary symbolic calculations, you can take advantage
       of the speed gain of invoking a closure instead of evaluating a tree.

   UNCOMPILED LEFTOVER TREES
       Not all, however, is well in the land of compiled Math::Symbolic trees.
       There may occasionally be trees that cannot be compiled (such as a
       derivative) which need to be included into the code as trees. These
       trees will be returned in a referenced array by the compile*() methods.
       The closures will have access to the required trees as a special
       variable '@_TREES inside the closure's scope, so you need not worry
       about them in that case. But if you plan to use the generated code
       itself, you need to supply an array named @_TREES that contains the
       trees as returned by the compile*() methods in the scope of the eval()
       you evaluate the code with.

       Note that you give away all performance benefits compiling the tree
       might have if the closure contains uncompiled trees. You can tell there
       are any by checking the length of the referenced array that contains
       the trees. If it's 0, then there are no trees left to worry about.

   AVOIDING LEFTOVER TREES
       In most cases, this is pretty simple. Just apply all derivatives in the
       tree to make sure that there are none left in the tree. As of version
       0.130, there is no operator except derivatives that cannot be compiled.
       There may, however, be some operators you cannot get rid of this easily
       some time in the future.  If you have problems getting a tree to
       compile, try using the means of simplification provided by
       Math::Symbolic::* to get a simpler tree for compilation.

   EXPORT
       None by default, but you may choose to import the compile(),
       compile_to_sub(), and compile_to_code() subroutines to your namespace
       using the standard Exporter semantics including the ':all' tag.

SUBROUTINES

   ($code, $trees) = compile_to_code($tree, $vars)
       The compile_to_code() class method takes one mandatory argument which
       is the Math::Symbolic tree to be compiled. Second argument is optional
       and an array reference to an array of variable mappings.  See "VARIABLE
       PASSING STYLES" for details on how this works.

       compile_to_code() returns a string and an array reference. The string
       contains the compiled Perl code that uses the values stored in @_ as
       described in the section on positional variable passing. It also
       accesses a special variable @_TREES if there were any sub-trees (inside
       the tree that has been compiled) that were impossible to compile. The
       array reference returned by this method contains any of the
       aforementioned trees that failed to compile.

       If there are any such trees that did not compile, you may put them into
       the @_TREES variable in scope of the eval() that evaluates the compiled
       code in the same order that they were returned by this method. If you
       do that, the code will run and determine the value of the tree at run-
       time. Needless to say, that is slow.

   ($sub, $trees) = compile_to_sub($tree, $vars)
       The compile_to_sub() class method takes one mandatory argument which is
       the Math::Symbolic tree to be compiled. Second argument is optional and
       an array reference to an array of variable mappings.  See "VARIABLE
       PASSING STYLES" for details on how this works.

       compile_to_sub() returns a list of two elements, the first being the
       compiled anonymous subroutine. For details on the second element,
       please refer to the docs on the compile_to_code() subroutine.

   ($sub, $code, $trees) = compile($tree, $vars)
       The compile() class method takes one mandatory argument which is the
       Math::Symbolic tree to be compiled. Second argument is optional and an
       array reference to an array of variable mappings.  See "POSITIONAL
       VARIABLE PASSING" for details on how this works.

       compile() returns a list of three elements, the first being the
       compiled anonymous subroutine, the second being the compiled code. For
       details on the second and third elements, please refer to the docs on
       the compile_to_code() subroutine.

   VARIABLE PASSING STYLES
       Currently, the Math::Symbolic compiler only supports compiling to subs
       with positional variable passing. At some point, the user should be
       able to choose between positional- and named variable passing styles.
       The difference is best explained by an example:

         # positional:
         $sub->(4, 5, 1);

         # named: (NOT IMPLEMENTED!)
         $sub->(a => 5, b => 4, x => 1);

       With positional variable passing, the subroutine statically maps its
       arguments to its internal variables. The way the subroutine does that
       has been fixed at compile-time. It is determined by the second argument
       to the various compile_* functions found in this package. This second
       argument is expected to be a reference to an array of variable names.
       The order of the variable names determines which parameter of the
       compiled sub will be assigned to the variable. Example:

         my ($sub) =
           Math::Symbolic::Compiler->compile_to_sub($tree, [qw/c a b/]);

         # First argument will be mapped to c, second to a, and third to b
         # All others will be ignored.
         $sub->(4, 5, 6, 7);

         # Variable mapping: a = 5, b = 6, c = 4

       One important note remains: if any (or all) variables in the tree are
       unaccounted for, they will be lexicographically sorted and appended to
       the variable mapping in that order. That means if you don't map
       variables yourself, they will be sorted lexicographically.

       Thanks to Henrik Edlund's input, it's possible to pass a hash reference
       as second argument to the compile* functions instead of an array
       reference.  The order of the mapped variables is then determined by
       their associated value, which should be an integer starting with 0.
       Example:

         Math::Symbolic::Compiler->compile_to_sub($tree, {b => 2, a => 1, c => 0});

       Would result in the order c, a, b.

AUTHOR

       Please send feedback, bug reports, and support requests to the
       Math::Symbolic support mailing list: math-symbolic-support at lists dot
       sourceforge dot net. Please consider letting us know how you use
       Math::Symbolic. Thank you.

       If you're interested in helping with the development or extending the
       module's functionality, please contact the developers' mailing list:
       math-symbolic-develop at lists dot sourceforge dot net.

       List of contributors:

         Steffen MXller, symbolic-module at steffen-mueller dot net
         Stray Toaster, mwk at users dot sourceforge dot net
         Oliver EbenhXh

SEE ALSO

       New versions of this module can be found on http://steffen-mueller.net
       or CPAN. The module development takes place on Sourceforge at
       http://sourceforge.net/projects/math-symbolic/

       Math::Symbolic



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