NAME

Math::Expression::Evaluator - parses, compiles and evaluates mathematic expressions

SYNOPSIS

use Math::Expression::Evaluator;
my $m = new Math::Expression::Evaluator;

print $m->parse("a = 12; a*3")->val(), "\n";
# prints 36
print $m->parse("2^(a/3)")->val(), "\n";
# prints 8 (ie 2**3)
print $m->parse("a / b")->val({ b => 6 }), "\n";
# prints 36
print $m->parse("log2(16)")->val(), "\n";
# prints 4

# if you care about speed
my $func = $m->parse('2 + (4 * b)')->compiled;
for (0 .. 100){
    print $func->({b => $_}), "\n";
}

DESCRIPTION

Math::Expression::Evaluator is a parser, compiler and interpreter for mathematical expressions. It can handle normal arithmetics (includings powers ^), builtin functions like sin() and variables.

Multiplication *, division / and modulo % have the same precedence, and are evaluated left to right. The modulo operation follows the standard perl semantics, that is is the arguments are castet to integer before preforming the modulo operation.

Multiple exressions can be seperated by whitespaces or by semicolons ';'. In case of multiple expressions the value of the last expression is returned.

Variables can be assigned with a single '=' sign, their name has to start with a alphabetic character or underscore [a-zA-Z_], and may contain alphabetic characters, digits and underscores.

Values for variables can also be provided as a hash ref as a parameter to val(). In case of collision the explicitly provided value is used:

$m->parse("a = 2; a")->val({a => 1}); 

will return 1, not 2.

The following builtin functions are supported atm:

• trignometric functions: sin, cos, tan

• inverse trigonomic functions: asin, acos, atan

• Square root: sqrt

• exponentials: exp, sinh, cosh

• logarithms: log, log2, log10

• constants: pi() (you need the parenthesis to distinguish it from the variable pi)

• rounding: ceil(), floor()

• other: theta (theta(x) = 1 for x > 0, theta(x) = 0 for x < 0)

METHODS

new

generates a new MathExpr object. accepts an optional argument, a hash ref that contains configurations. If this hash sets force_semicolon to true, expressions have to be separated by a semicolon ';'.

parse

Takes a string as argument, and generates an Abstract Syntax Tree(AST) that is stored internally.

Returns a reference to the object, so that method calls can be chained:

print MathExpr->new->parse("1+2")->val;

Parse failures cause this method to die with a stack trace.

compiled

Returns an anonymous function that is a compiled version of the current expression. It is much faster to execute than the other methods, but its error messages aren't as informative (instead of complaining about a non-existing variable it dies with Use of uninitialized value in...).

Note that variables are not persistent between calls to compiled functions (and it wouldn't make sense anyway, because such a function corresponds always to exactly one expression, not many as a MEE object).

Variables that were stored at the time when compiled() is called are availble in the compiled function, though.

val

Executes the AST generated by parse(), and returns the number that the expression is evaluated to. It accepts an optional hash reference that contain values for variables:

my $m = new MathExpr;
$m->parse("(x - 1) / (x + 1)");
foreach (0 .. 10) {
    print $_, "\t", $m->val({x => $_}), "\n";
}

optimize

Optimizes the internal AST, so that subsequent calls to val() will be a bit faster. See Math::Expression::Evaluator::Optimizer for performance considerations and informations on the implemented optimizations.

But note that a call to optimize() only pays off if you call val() multiple times.

variables

variables() returns a list of variables that are used in the expression.

ast_size

ast_size returns an integer which gives a crude measure of the logical size of the expression. Note that this value isn't guarantueed to be stable across multiple versions of this module. It is mainly intended for testing.

SPEED

MEE isn't as fast as perl, because it is built on top of perl.

If you execute an expression multiple times, it pays off to either optimize it first, or (even better) compile it to a pure perl function.

               Rate  no_optimize     optimize opt_compiled     compiled
no_optimize  83.9/s           --         -44%         -82%         -83%
optimize      150/s          78%           --         -68%         -69%
opt_compiled  472/s         463%         215%           --          -4%
compiled      490/s         485%         227%           4%           --

This shows the time for 200 evaluations of 2+a+5+(3+4) (with MEE 0.0.5). As you can see, the non-optimized version is painfully slow, optimization nearly doubles the execution speed. The compiled and the optimized-and-then-compiled versions are both much faster.

With this example expression the optimization prior to compilation pays off if you evaluate it more than 1000 times. But even if you call it 10**5 times the optimized and compiled version is only 3% faster than the directly compiled one (mostly due to perl's overhead for method calls).

So to summarize you should compile your expresions, and if you have really many iterations it might pay off to optimize it first (or to write your program in C instead ;-).

BUGS AND LIMITATIONS

• Modulo operator produces an unnecessary big AST, making it relatively slow

INTERNALS

The AST can be accessed as $obj-{ast}>. Its structure is described in Math::Expression::Evaluator::Parser (or you can use Data::Dumper to figure it out for yourself).

SEE ALSO

Math::Expression also evaluates mathematical expressions, but also handles string operations.

If you want to do symbolic (aka algebraic) transformations, Math::Symbolic will fit your needs.

LICENSE

This module is free software. You may use, redistribute and modify it under the same terms as perl itself.

AUTHOR

Moritz Lenz, http://moritz.faui2k3.org/, moritz@faui2k3.org

DEVELOPMENT

You can obtain the latest development version via subversion:

svn co https://faui2k3.org/svn/moritz/cpan/Math-Expression-Evaluator/