# moritz/math-expression-evaluator

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Perl module for evaluating mathemtical expressions in a secure way
Perl

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

SYNOPSIS
use Math::Expression::Evaluator;
my \$m = Math::Expression::Evaluator->new;

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

You can call "parse" on an existing Math::Expression::Evaluator object
to re-use it, in which case previously set variables and callbacks
persist between calls.

This (perhaps contrived) example explains this:

my \$m = Math::Expression::Evaluator->new('a = 3; a');
\$m->val();
\$m->parse('a + 5');
print \$m->val(), "\n"   # prints 8, because a = 3 was re-used

If that's not what you want, create a new object instead - the
constructor is rather cheap.

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 = MathExpr->new;
\$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.

set_var_callback
Allows you to set a callback which the Match::Expression::Evaluator
object calls when it can't find a variable. The name of the variable
is passed in as the first argument. If the callback function can't
handle that variable either, it should die, just like the default one
does.

my \$m = Math::Expression::Evaluator->new();
\$m->parse('1 + a');
my \$callback = sub { ord(\$_[0]) };
\$m->set_var_callback(\$callback);
print \$m->val();    # calls \$callback, which returns 97
# so \$m->val() return 98

The callback will be called every time the variable is accessed, so if
it requires expensive calculations, you are encouraged to cache it
either yourself our automatically with Memoize.

set_function
Allows to add a user-defined function, or to override a built-in
function.

my \$m = Math::Expression::Evaluator->new();
\$m->set_function('abs', sub { abs(\$_[0]) });
\$m->parse('abs(10.6)');
print \$m->val();

If you first compile the expression to a perl closure and then call
"<\$m-"set_function>> again, the compiled function stays unaffected, so

\$m->set_function('f', sub { 42 });
my \$compiled = \$m->parse('f')->compiled;
\$m->set_function('f', sub { -23 });
print \$compiled->();

print out 42, not -23.

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

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). Note that the exact form of the AST is
considered to be an implementation detail, and subject to change.

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

If you want to do symbolic (aka algebraic) transformations,

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

Copyright (C) 2007 - 2009 Moritz Lenz, <http://perlgeek.de/>,
moritz@faui2k3.org

DEVELOPMENT
You can obtain the latest development version from github
<http://github.com/moritz/math-expression-evaluator>.

git clone git://github.com/moritz/math-expression-evaluator.git

If you want to contribute something to this module, please ask me for a
commit bit to the github repository, I'm giving them out freely.

ACKNOWLEDGEMENTS
The following people have contributed to this module, in no particular
order:

Leonardo Herrera
Initial patch for "set_function"

Tina Müller