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=encoding utf8
=head1 NAME
Math::Symbolic::Compiler - Compile Math::Symbolic trees to Perl code
=head1 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);
=head1 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.
=head2 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.
=head2 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.
=head2 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.
=head1 SUBROUTINES
=cut
package Math::Symbolic::Compiler;
use 5.006;
use strict;
use warnings;
use Math::Symbolic::ExportConstants qw/:all/;
our @ISA = qw(Exporter);
our %EXPORT_TAGS = (
    'all' => [
        qw(
          compile
          compile_to_sub
          compile_to_code
          )
    ]
);
our @EXPORT_OK = ( @{ $EXPORT_TAGS{'all'} } );
our @EXPORT = qw();
our $VERSION = '0.613';
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=head2 ($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 L<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.
=cut
sub compile_to_code {
    my $tree = shift;
    $tree = shift if not ref $tree and $tree eq __PACKAGE__;
    my $order = shift || [];
    my %order;
    if (ref($order) eq 'HASH') {
        %order = %$order;
    }
    elsif (ref($order) eq 'ARRAY') {
        my $count = 0;
        %order = map { ( $_, $count++ ) } @$order;
    }
    no warnings 'recursion';
    my $vars = [ $tree->explicit_signature() ];
    my %vars;
    my @not_placed;
    foreach (@$vars) {
        my $pos = $order{$_};
        if ( defined $pos ) {
            $vars{$_} = $pos;
        }
        else {
            push @not_placed, $_;
        }
    }
    my $count = 0;
    foreach ( sort @not_placed ) {
        $vars{$_} = @$vars - @not_placed + $count++;
    }
    # The user is to do that himself. Left in to show that it would be
    # a sensible (if slow) thing to do.
    # $tree = $tree->simplify();
    # $tree = $tree->apply_derivatives();
    # $tree = $tree->simplify();
    my @trees;
    my $code = _rec_ms_to_sub( $tree, \%vars, \@trees );
    return ( $code, \@trees );
}
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=head2 ($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 L<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.
=cut
sub compile_to_sub {
    my ( $code, $trees ) = Math::Symbolic::Compiler::compile_to_code(@_);
    my $sub = _compile_sub( 'sub {' . $code . '}', @$trees );
    return ( $sub, $trees );
}
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=head2 ($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 L<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.
=cut
sub compile {
    my ( $code, $trees ) = Math::Symbolic::Compiler::compile_to_code(@_);
    my $sub = _compile_sub( 'sub {' . $code . '}', @$trees );
    return ( $sub, $code, $trees );
}
sub _compile_sub {
    my @_TREES;
    @_TREES = @_[ 1 .. $#_ ] if @_ > 1;
    my $sub = eval $_[0];
    die "$@" if $@;
    return $sub;
}
sub _rec_ms_to_sub {
    my $tree  = shift;
    my $vars  = shift;
    my $trees = shift;
    my $code  = '';
    my $ttype = $tree->term_type();
    if ( $ttype == T_CONSTANT ) {
        $code .= $tree->value();
    }
    elsif ( $ttype == T_VARIABLE ) {
        $code .= '$_[' . $vars->{ $tree->name() } . ']';
    }
    else {
        my $type  = $tree->type();
        my $otype = $Math::Symbolic::Operator::Op_Types[$type];
        my $app   = $otype->{application};
        if ( ref($app) eq 'CODE' ) {
            push @$trees, $tree->new();
            my $arg_str = join( ', ',
                map { "'$_' => \$_[" . $vars->{$_} . ']' } keys %$vars );
            my $index = $#$trees;
            $code .= <<HERE
(\$_TREES[$index]->value($arg_str))
HERE
        }
        else {
            my @app = split /\$_\[(\d+)\]/, $app;
            if ( @app > 1 ) {
                for ( my $i = 1 ; $i < @app ; $i += 2 ) {
                    $app[$i] = '('
                      . _rec_ms_to_sub( $tree->{operands}[ $app[$i] ],
                        $vars, $trees )
                      . ')';
                }
            }
            $code .= join '', @app;
        }
    }
    return $code;
}
1;
__END__
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=head2 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.
=head1 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 Müller, symbolic-module at steffen-mueller dot net
  Stray Toaster, mwk at users dot sourceforge dot net
  Oliver Ebenhöh
=head1 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/
L<Math::Symbolic>
=cut