# NAME

Math::SymbolicX::FastEvaluator - Fast, XS, stack-based formula evaluator

# SYNOPSIS

```
use Math::Symbolic qw/:all/;
use Math::Symbolic::Custom::DumpToFastEval;
my $formula = parse_from_string("a+b^2");
print "Normal evaluation: " . $formula->value(a => 3.1, b => 2.5), "\n";
my $expression = $formula->to_fasteval;
print "Much faster: " . $formula->Evaluate([3.1, 2.5]);
```

# DESCRIPTION

*WARNING*: Highly experimental! Wrong usage results in segmentation faults and pain.

There are two was to evaluate a Math::Symbolic formula that come with the main distribution: Calling the `value()`

method on it or using the Math::Symbolic::Compiler to produce a Perl subroutine that can calculate the value much quicker.

However, sometimes that's not quite fast enough. Then, you can use the Math::Symbolic::Custom::CCompiler module with Inline::C to compile your formula to C code, compile it, and link it at run-time. Unfortunately, that requires compiling C code at run-time and caching the resulting files, etc. Not very user-friendly.

This module is a fourth alternative: Translate it to a stream of C-level structs in *Reverse Polish Notation*, then execute it in a fast RPN evaluator (implemented in C/XS).

The basic usage of this module is to generate the RPN data with a call to `my $expr = $formula->to_fasteval()`

which returns a `Math::SymbolicX::FastEvaluator::Expression`

object. You can now get its value by calling `$expr->Evaluate(\@variable_values)`

. This will internally construct a `Math::SymbolicX::FastEvaluator`

object, use it to evaluate the expression and destroy it when it's done. This is a tiny overhead, but you can avoid it by constructing a `FastEvaluator`

object yourself and calling `$fasteval->Evaluate($expr, \@variable_values)`

.

## WHY?

Two reasons: Experimentation and the distant hope of passing the expressions to numeric optimization routines, which are naturally implemented in C, C++, or even FORTRAN.

## PERFORMANCE

Using all this combersome indirection, the evaluation of `FastEvaluator`

expressions proceeded at a pace of over 200 million tokens per second on my 1.8GHz Core2 laptop which was busy with various desktop tasks at the same time. A token is a number, variable or operator. Since I was testing with a string of multiplications, this translates to roughly 100 MFLOPS. You can consider this fast or slow, but compared to Perl evaluation, this is at least a factor of ten faster. When variables are added into the picture, the improvement should be even larger. Since the overhead of this method is still large compared to the actual computation time, sums, differences, products and divisions are approximately equally fast.

## PORTABILITY

The code was developed on Linux and compiled with the GNU compiler collection. Currently, the C++ compiler is hardwired to `g++`

in the `Makefile.PL`

. Improvements welcome.

# EXAMPLE

The *SYNOPSIS* above covers typical usage.

## EXPLICIT CONSTRUCTION

This is the explicit low-level interface. It's tedious and error prone. If you construct bad RPN and try to evaluate it, you may crash your perl interpreter. The RPN evaluator does not check the input as it tries to be as fast as possible.

This is here for completeness sake. Consider using the Math::Symbolic::Custom::DumpToFastEval interface (see SYNOPSIS) instead!

```
use Math::SymbolicX::FastEvaluator;
use Math::Symbolic qw/:all/;
my $eval = Math::SymbolicX::FastEvaluator->new();
my $expr = Math::SymbolicX::FastEvaluator::Expression->new();
my $op = Math::SymbolicX::FastEvaluator::Op->new();
# This is RPN based: Essentially, compute "a+b^2"
$op->SetVariable();
$op->SetValue(1.0); # first variable (aka a)
$expr->AddOp($op);
$op->SetVariable();
$op->SetValue(2.0); # second variable (aka b)
$expr->AddOp($op);
$op->SetNumber();
$op->SetValue(2.0); # the exponent
$expr->AddOp($op);
$op->SetOpType(B_EXP); # see Math::Symbolic for this constant
$expr->AddOp($op); # I.e. b^2
$op->SetOpType(U_SUM); # see Math::Symbolic for this constant
$expr->AddOp($op); # I.e. a + (b^2)
# Insert variables 1 and 2 (a and b) and evaluate:
print "The value is: " . $eval->Evaluate($expr, [3.1, 2.5]);
# should be 3.1+2.5**2 == 9.35
```

# AUTHOR

Steffen Mueller, <smueller@cpan.org>

# COPYRIGHT AND LICENSE

Copyright (C) 2008 by Steffen Mueller

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.8 or, at your option, any later version of Perl 5 you may have available.