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<?php
/**
* EOS v2.0
* https://github.com/jlawrence11/Classes
*
* Equation Operating System Classes
*
* Copyright 2005-2013, Jon Lawrence <jlawrence11@gmail.com>
* Licensed under LGPL 2.1 License
*/
/**
* Equation Operating System Classes.
*
* This class was created for the safe parsing of mathematical equations
* in PHP. There is a need for a way to successfully parse equations
* in PHP that do NOT require the use of `eval`. `eval` at its core
* opens the system using it to so many security vulnerabilities it is oft
* suggested /never/ to use it, and for good reason. This class set will
* successfully take an equation, parse it, and provide solutions to the
* developer. It is a safe way to evaluate expressions without putting
* the system at risk.
*
* Modified as per https://github.com/jlawrence11/eos/issues/2
*
* 2013/04 UPDATE:
* - Moved to native class functions for PHP5
* - Removed deprecated `eregi` calls to `preg_match`
* - Updated to PHPDoc comment syntax
* - Added Exception throwing instead of silent exits
* - Added additional variable prefix of '$', '&' is still allowed as well
* - Fixed small implied multiplication problem
*
* TODO:
* - Add factorial support. (ie 5! = 120)
*
* @author Jon Lawrence <jlawrence11@gmail.com>
* @copyright Copyright ©2005-2013, Jon Lawrence
* @license http://opensource.org/licenses/LGPL-2.1 LGPL 2.1 License
* @package EOS
* @version 2.0
*/
// The following are defines for thrown exceptions
/**
* No matching Open/Close pair
*/
define( 'EQEOS_E_NO_SET', 5500 );
/**
* Division by 0
*/
define( 'EQEOS_E_DIV_ZERO', 5501 );
/**
* No Equation
*/
define( 'EQEOS_E_NO_EQ', 5502 );
/**
* No variable replacement available
*/
define( 'EQEOS_E_NO_VAR', 5503 );
if ( ! defined( 'DEBUG' ) ) {
define( 'DEBUG', false );
}
/**
* Equation Operating System (EOS) Parser
*
* An EOS that can safely parse equations from unknown sources returning
* the calculated value of it. Can also handle solving equations with
* variables, if the variables are defined (useful for the Graph creation
* that the second and extended class in this file provides. {@see eqGraph})
* This class was created for PHP4 in 2005, updated to fully PHP5 in 2013.
*
* @author Jon Lawrence <jlawrence11@gmail.com>
* @copyright Copyright ©2005-2013, Jon Lawrence
* @license http://opensource.org/licenses/LGPL-2.1 LGPL 2.1 License
* @package Math
* @subpackage EOS
* @version 2.0
*/
class eqEOS {
/**#@+
* Private variables
*/
private $postFix;
private $inFix;
/**#@-*/
/**#@+
* Protected variables
*/
// What are opening and closing selectors
protected $SEP = array(
'open' => array( '(', '[' ),
'close' => array( ')', ']' ),
);
// Top presedence following operator - not in use
protected $SGL = array( '!' );
// Order of operations arrays follow
protected $ST = array( '^' );
protected $ST1 = array( '/', '*', '%' );
protected $ST2 = array( '+', '-' );
// Allowed functions
protected $FNC = array( 'sin', 'cos', 'tan', 'csc', 'sec', 'cot' );
/**#@-*/
/**
* Construct method
*
* Will initiate the class. If variable given, will assign to
* internal variable to solve with this::solveIF() without needing
* additional input. Initializing with a variable is not suggested.
*
* @see eqEOS::solveIF()
* @param String $inFix Standard format equation
*/
public function __construct( $inFix = null ) {
$this->inFix = ( isset( $inFix ) ) ? $inFix : null;
$this->postFix = array();
}
/**
* Check Infix for opening closing pair matches.
*
* This function is meant to solely check to make sure every opening
* statement has a matching closing one, and throws an exception if
* it doesn't.
*
* @param String $infix Equation to check
* @throws Exception if malformed.
* @return Bool true if passes - throws an exception if not.
*/
private function checkInfix( $infix ) {
if ( trim( $infix ) == '' ) {
return 0;
}
// Make sure we have the same number of '(' as we do ')'
// and the same # of '[' as we do ']'
if ( substr_count( $infix, '(' ) != substr_count( $infix, ')' ) ) {
throw new Exception( "Mismatched parenthesis in '{$infix}'", EQEOS_E_NO_SET );
return false;
} elseif ( substr_count( $infix, '[' ) != substr_count( $infix, ']' ) ) {
throw new Exception( "Mismatched brackets in '{$infix}'", EQEOS_E_NO_SET );
return false;
}
$this->inFix = $infix;
return true;
}
/**
* Infix to Postfix
*
* Converts an infix (standard) equation to postfix (RPN) notation.
* Sets the internal variable $this->postFix for the eqEOS::solvePF()
* function to use.
*
* @link http://en.wikipedia.org/wiki/Infix_notation Infix Notation
* @link http://en.wikipedia.org/wiki/Reverse_Polish_notation Reverse Polish Notation
* @param String $infix A standard notation equation
* @return Array Fully formed RPN Stack
*/
public function in2post( $infix = null ) {
// if an equation was not passed, use the one that was passed in the constructor
$infix = ( isset( $infix ) ) ? $infix : $this->inFix;
// check to make sure 'valid' equation
$this->checkInfix( $infix );
$pf = array();
$ops = new phpStack();
$vars = new phpStack();
// remove all white-space
preg_replace( '/\s/', '', $infix );
// Create postfix array index
$pfIndex = 0;
// what was the last character? (useful for decerning between a sign for negation and subtraction)
$lChar = '';
// loop through all the characters and start doing stuff ^^
for ( $i = 0;$i < strlen( $infix );$i++ ) {
// pull out 1 character from the string
$chr = substr( $infix, $i, 1 );
// if the character is numerical
if ( preg_match( '/[0-9.]/i', $chr ) ) {
// if the previous character was not a '-' or a number
if ( ( ! preg_match( '/[0-9.]/i', $lChar ) && ( $lChar != '' ) ) && ( array_key_exists( $pfIndex, @$pf ) && @$pf[ $pfIndex ] != '-' ) ) {
$pfIndex++; // increase the index so as not to overlap anything
}
// if the array key doesn't exist
if ( ! array_key_exists( $pfIndex, @$pf ) ) {
@$pf[ $pfIndex ] = null; // add index to the array
}
// Add the number character to the array
@$pf[ $pfIndex ] .= $chr;
}
// If the character opens a set e.g. '(' or '['
elseif ( in_array( $chr, $this->SEP['open'] ) ) {
// if the last character was a number, place an assumed '*' on the stack
if ( preg_match( '/[0-9.]/i', $lChar ) ) {
$ops->push( '*' );
}
$ops->push( $chr );
}
// if the character closes a set e.g. ')' or ']'
elseif ( in_array( $chr, $this->SEP['close'] ) ) {
// find what set it was i.e. matches ')' with '(' or ']' with '['
$key = array_search( $chr, $this->SEP['close'] );
// while the operator on the stack isn't the matching pair...pop it off
while ( $ops->peek() != $this->SEP['open'][ $key ] ) {
$nchr = $ops->pop();
if ( $nchr ) {
$pf[ ++$pfIndex ] = $nchr;
} else {
throw new Exception( "Error while searching for '" . $this->SEP['open'][ $key ] . "' in '{$infix}'.", EQEOS_E_NO_SET );
return false;
}
}
$ops->pop();
}
// If a special operator that has precedence over everything else
elseif ( in_array( $chr, $this->ST ) ) {
$ops->push( $chr );
$pfIndex++;
}
// Any other operator other than '+' and '-'
elseif ( in_array( $chr, $this->ST1 ) ) {
while ( in_array( $ops->peek(), $this->ST1 ) || in_array( $ops->peek(), $this->ST ) ) {
$pf[ ++$pfIndex ] = $ops->pop();
}
$ops->push( $chr );
$pfIndex++;
}
// if a '+' or '-'
elseif ( in_array( $chr, $this->ST2 ) ) {
// if it is a '-' and the character before it was an operator or nothingness (e.g. it negates a number)
if ( ( in_array( $lChar, array_merge( $this->ST1, $this->ST2, $this->ST, $this->SEP['open'] ) ) || $lChar == '' ) && $chr == '-' ) {
// increase the index because there is no reason that it shouldn't..
$pfIndex++;
$pf[ $pfIndex ] = $chr;
}
// Otherwise it will function like a normal operator
else {
while ( in_array( $ops->peek(), array_merge( $this->ST1, $this->ST2, $this->ST ) ) ) {
$pf[ ++$pfIndex ] = $ops->pop();
}
$ops->push( $chr );
$pfIndex++;
}
}
// make sure we record this character to be refered to by the next one
$lChar = $chr;
}
// if there is anything on the stack after we are done...add it to the back of the RPN array
while ( ( $tmp = $ops->pop() ) !== false ) {
$pf[ ++$pfIndex ] = $tmp;
}
// re-index the array at 0
$pf = array_values( $pf );
// set the private variable for later use if needed
$this->postFix = $pf;
// return the RPN array in case developer wants to use it fro some insane reason (bug testing ;]
return $pf;
} //end function in2post
/**
* Solve Postfix (RPN)
*
* This function will solve a RPN array. Default action is to solve
* the RPN array stored in the class from eqEOS::in2post(), can take
* an array input to solve as well, though default action is prefered.
*
* @link http://en.wikipedia.org/wiki/Reverse_Polish_notation Postix Notation
* @param Array $pfArray RPN formatted array. Optional.
* @return Float Result of the operation.
*/
public function solvePF( $pfArray = null ) {
// if no RPN array is passed - use the one stored in the private var
$pf = ( ! is_array( $pfArray ) ) ? $this->postFix : $pfArray;
// create our temporary function variables
$temp = array();
$tot = 0;
$hold = 0;
// Loop through each number/operator
for ( $i = 0;$i < count( $pf ); $i++ ) {
// If the string isn't an operator, add it to the temp var as a holding place
if ( ! in_array( $pf[ $i ], array_merge( $this->ST, $this->ST1, $this->ST2 ) ) ) {
$temp[ $hold++ ] = $pf[ $i ];
}
// ...Otherwise perform the operator on the last two numbers
else {
switch ( $pf[ $i ] ) {
case '+':
$temp[ $hold - 2 ] = $temp[ $hold - 2 ] + $temp[ $hold - 1 ];
break;
case '-':
$temp[ $hold - 2 ] = $temp[ $hold - 2 ] - $temp[ $hold - 1 ];
break;
case '*':
$temp[ $hold - 2 ] = $temp[ $hold - 2 ] * $temp[ $hold - 1 ];
break;
case '/':
if ( $temp[ $hold - 1 ] == 0 ) {
return 0;
}
$temp[ $hold - 2 ] = $temp[ $hold - 2 ] / $temp[ $hold - 1 ];
break;
case '^':
$temp[ $hold - 2 ] = pow( $temp[ $hold - 2 ], $temp[ $hold - 1 ] );
break;
case '%':
if ( $temp[ $hold - 1 ] == 0 ) {
return 0;
}
$temp[ $hold - 2 ] = bcmod( $temp[ $hold - 2 ], $temp[ $hold - 1 ] );
break;
}
// Decrease the hold var to one above where the last number is
$hold = $hold - 1;
}
}
// return the last number in the array
return $temp[ $hold - 1 ];
} //end function solvePF
/**
* Solve Infix (Standard) Notation Equation
*
* Will take a standard equation with optional variables and solve it. Variables
* must begin with '&' will expand to allow variables to begin with '$' (TODO)
* The variable array must be in the format of 'variable' => value. If
* variable array is scalar (ie 5), all variables will be replaced with it.
*
* @param String $infix Standard Equation to solve
* @param String|Array $vArray Variable replacement
* @return Float Solved equation
*/
function solveIF( $infix, $vArray = null ) {
$infix = ( $infix != '' ) ? $infix : $this->inFix;
// Check to make sure a 'valid' expression
$this->checkInfix( $infix );
$ops = new phpStack();
$vars = new phpStack();
// remove all white-space
preg_replace( '/\s/', '', $infix );
// Find all the variables that were passed and replaces them
while ( ( preg_match( '/(.){0,1}[&$]([a-zA-Z0-9_]+)(.){0,1}/', $infix, $match ) ) != 0 ) {
// remove notices by defining if undefined.
if ( ! isset( $match[3] ) ) {
$match[3] = '';
}
// Ensure that the variable has an operator or something of that sort in front and back - if it doesn't, add an implied '*'
if ( ( ! in_array( $match[1], array_merge( $this->ST, $this->ST1, $this->ST2, $this->SEP['open'] ) ) && $match[1] != '' ) || is_numeric( $match[1] ) ) { // $this->SEP['close'] removed
$front = '*';
} else {
$front = '';
}
if ( ( ! in_array( $match[3], array_merge( $this->ST, $this->ST1, $this->ST2, $this->SEP['close'] ) ) && $match[3] != '' ) || is_numeric( $match[3] ) ) { // $this->SEP['open'] removed
$back = '*';
} else {
$back = '';
}
// Make sure that the variable does have a replacement
if ( ! isset( $vArray[ $match[2] ] ) && ( ! is_array( $vArray != '' ) && ! is_numeric( $vArray ) ) ) {
throw new Exception( "Variable replacement does not exist for '" . substr( $match[0], 1, -1 ) . "' in {$this->inFix}", EQEOS_E_NO_VAR );
return false;
} elseif ( ! isset( $vArray[ $match[2] ] ) && ( ! is_array( $vArray != '' ) && is_numeric( $vArray ) ) ) {
$infix = str_replace( $match[0], $match[1] . $front . $vArray . $back . $match[3], $infix );
} elseif ( isset( $vArray[ $match[2] ] ) ) {
$infix = str_replace( $match[0], $match[1] . $front . $vArray[ $match[2] ] . $back . $match[3], $infix );
}
}
// Finds all the 'functions' within the equation and calculates them
// NOTE - when using function, only 1 set of paranthesis will be found, instead use brackets for sets within functions!!
while ( ( preg_match( '/(' . implode( '|', $this->FNC ) . ')\(([^\)\(]*(\([^\)]*\)[^\(\)]*)*[^\)\(]*)\)/', $infix, $match ) ) != 0 ) {
$func = $this->solveIF( $match[2] );
switch ( $match[1] ) {
case 'cos':
$ans = cos( $func );
break;
case 'sin':
$ans = sin( $func );
break;
case 'tan':
$ans = tan( $func );
break;
case 'sec':
$tmp = cos( $func );
if ( $tmp == 0 ) {
return 0;
}
$ans = 1 / $tmp;
break;
case 'csc':
$tmp = sin( $func );
if ( $tmp == 0 ) {
return 0;
}
$ans = 1 / $tmp;
break;
case 'cot':
$tmp = tan( $func );
if ( $tmp == 0 ) {
return 0;
}
$ans = 1 / $tmp;
break;
default:
break;
}
$infix = str_replace( $match[0], $ans, $infix );
}
return $this->solvePF( $this->in2post( $infix ) );
} //end function solveIF
} //end class 'eqEOS'