<?php if ( ! defined( 'ABSPATH' ) ) exit;
* 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
* - 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
* - 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
//The following are defines for thrown exceptions
* No matching Open/Close pair
define('EQEOS_E_NO_SET', 5500);
define('EQEOS_E_DIV_ZERO', 5501);
define('EQEOS_E_NO_EQ', 5502);
* No variable replacement available
define('EQEOS_E_NO_VAR', 5503);
//We use a stack class so we don't have to keep track of indices for an array
// May eventually update to use `array_pop()` `end()` and `array_push()` instead
require_once "stack.class.php";
* 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
//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('+', '-');
protected $FNC = array('sin', 'cos', 'tan', 'csc', 'sec', 'cot');
* 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.
* @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
* @param String $infix Equation to check
* @throws Exception if malformed.
* @return Bool true if passes - throws an exception if not.
private function checkInfix($infix) {
throw new Exception("No Equation given", EQEOS_E_NO_EQ);
//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 '{$infix}'", EQEOS_E_NO_SET);
} elseif(substr_count($infix, '[') != substr_count($infix, ']')) {
throw new Exception("Mismatched brackets in '{$infix}'", EQEOS_E_NO_SET);
* Converts an infix (standard) equation to postfix (RPN) notation.
* Sets the internal variable $this->postFix for the eqEOS::solvePF()
* @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);
// remove all white-space
preg_replace("/\s/", "", $infix);
// Create postfix array index
//what was the last character? (useful for decerning between a sign for negation and subtraction)
//loop through all the characters and start doing stuff ^^
for($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 != "")) && (@$pf[$pfIndex]!="-"))
$pfIndex++; // increase the index so as not to overlap anything
// Add the number character to the array
// If the character opens a set e.g. '(' or '['
elseif(in_array($chr, $this->SEP['open'])) {
// if the last character was a number, place an assumed '*' on the stack
if(preg_match('/[0-9.]/i', $lChar))
// if the character closes a set e.g. ')' or ']'
elseif(in_array($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]) {
throw new Exception("Error while searching for '". $this->SEP['open'][$key] ."' in '{$infix}'.", EQEOS_E_NO_SET);
// If a special operator that has precedence over everything else
elseif(in_array($chr, $this->ST)) {
// Any other operator other than '+' and '-'
elseif(in_array($chr, $this->ST1)) {
while(in_array($ops->peek(), $this->ST1) || in_array($ops->peek(), $this->ST))
$pf[++$pfIndex] = $ops->pop();
elseif(in_array($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=="") && $chr=="-") {
// increase the index because there is no reason that it shouldn't..
// Otherwise it will function like a normal operator
while(in_array($ops->peek(), array_merge($this->ST1, $this->ST2, $this->ST)))
$pf[++$pfIndex] = $ops->pop();
// make sure we record this character to be refered to by the next one
// if there is anything on the stack after we are done...add it to the back of the RPN array
while(($tmp = $ops->pop()) !== false)
// re-index the array at 0
// set the private variable for later use if needed
// return the RPN array in case developer wants to use it fro some insane reason (bug testing ;]
* 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 : $pfArray;
// create our temporary function variables
// Loop through each number/operator
for($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
@$temp[$hold-2] = $temp[$hold-2] + $temp[$hold-1];
@$temp[$hold-2] = $temp[$hold-2] - $temp[$hold-1];
@$temp[$hold-2] = $temp[$hold-2] * $temp[$hold-1];
if($temp[$hold-1] == 0) {
throw new Exception("Division by 0 on: '{$temp[$hold-2]} / {$temp[$hold-1]}' in {$this->inFix}", EQEOS_E_DIV_ZERO);
@$temp[$hold-2] = $temp[$hold-2] / $temp[$hold-1];
@$temp[$hold-2] = pow($temp[$hold-2], $temp[$hold-1]);
if($temp[$hold-1] == 0) {
throw new Exception("Division by 0 on: '{$temp[$hold-2]} % {$temp[$hold-1]}' in {$this->inFix}", EQEOS_E_DIV_ZERO);
@$temp[$hold-2] = bcmod($temp[$hold-2], $temp[$hold-1]);
// Decrease the hold var to one above where the last number is
// return the last number in the array
* 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);
preg_replace("/\s/", "", $infix);
$hand=fopen("eq.txt","a");
//Find all the variables that were passed and replaces them
while((preg_match('/(.){0,1}[&$]([a-zA-Z]+)(.){0,1}/', $infix, $match)) != 0) {
//remove notices by defining if undefined.
fwrite($hand, "{$match[1]} || {$match[3]}\n");
// 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])) //$this->SEP['close'] removed
if((!in_array($match[3], array_merge($this->ST, $this->ST1, $this->ST2, $this->SEP['close'])) && $match[3] != "") || is_numeric($match[3])) //$this->SEP['open'] removed
//Make sure that the variable does have a replacement
if(!isset($vArray[$match[2]]) && (!is_array($vArray != "") && !is_numeric($vArray))) {
throw new Exception("Variable replacement does not exist for '". substr($match[0], 1, -1) ."' in {$this->inFix}", EQEOS_E_NO_VAR);
} elseif(!isset($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], $infix);
fwrite($hand, "$infix\n");
// 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]);
throw new Exception("Division by 0 on: 'sec({$func}) = 1/cos({$func})' in {$this->inFix}", EQEOS_E_DIV_ZERO);
throw new Exception("Division by 0 on: 'csc({$func}) = 1/sin({$func})' in {$this->inFix}", EQEOS_E_DIV_ZERO);
throw new Exception("Division by 0 on: 'cot({$func}) = 1/tan({$func})' in {$this->inFix}", EQEOS_E_DIV_ZERO);
$infix = str_replace($match[0], $ans, $infix);
return $this->solvePF($this->in2post($infix));
// fun class that requires the GD libraries to give visual output to the user
/* extends the eqEOS class so that it doesn't need to create it as a private var
- and it extends the functionality of that class */
* Fun class that requires the GD libraries to give visual output of an
* equation to the user. Extends the eqEOS class.
* @author Jon Lawrence <jlawrence11@gmail.com>
* @copyright Copyright �2005-2013 Jon Lawrence
* @license http://opensource.org/licenses/LGPL-2.1 LGPL 2.1 License
class eqGraph extends eqEOS {
* Sets up the Graph class with an image width and height defaults to
* @param Integer $width Image width
* @param Integer $height Image height
public function __construct($width=640, $height=480) {
// default width and height equal to that of a poor monitor (in early 2000s)
//initialize main class variables
* Creates a GD image based on the equation given with the parameters that are set
* @param String $eq Equation to use. Needs variable in equation to create graph, all variables are interpreted as 'x'
* @param Integer $xLow Lower x-bound for graph
* @param Integer $xHigh Upper x-bound for graph
* @param Float $xStep Stepping points while solving, the lower, the better precision. Slow if lower than .01
* @param Boolean $xyGrid Draw gridlines?
* @param Boolean $yGuess Guess the upper/lower yBounds?
* @param Integer $yLow Lower y-bound
* @param Integer $yHigh Upper y-bound
public function graph($eq, $xLow, $xHigh, $xStep, $xyGrid = false, $yGuess = true, $yLow=false, $yHigh=false) {
//create our image and allocate the two colors
$img = ImageCreate($this->width, $this->height);
$white = ImageColorAllocate($img, 255, 255, 255);
$black = ImageColorAllocate($img, 0, 0, 0);
$grey = ImageColorAllocate($img, 220, 220, 220);
//DEVELOPER, UNCOMMENT NEXT LINE IF WANTING TO PREVENT SLOW GRAPHS
//$xStep = ($xStep > .01) ? $xStep : 0.01;
list($xLow, $xHigh) = array($xHigh, $xLow); //swap function
It is recommended that you Edit text format, this type of Fix handles quite a lot in one request
