: str_replace(): Passing null to parameter #2 ($replace) of type array|string is deprecated in
* - Removed `\` for php5.2 support (does not support namespaces).
* - Renamed with prefix to avoid naming collisions.
* - Updated references to the EOS Stack class to reflect name changes.
* Equation Operating System Classes.
* This class was created for the safe parsing of mathematical equations
* in PHP. There is a need for a way to successfully parse equations
* in PHP that do NOT require the use of `eval`. `eval` at its core
* opens the system using it to so many security vulnerabilities it is oft
* suggested /never/ to use it, and for good reason. This class set will
* successfully take an equation, parse it, and provide solutions to the
* developer. It is a safe way to evaluate expressions without putting
* - Added all real number factorial support
* - Added gamma function to class
* - Added scientific notation support
* - Added basic factorial support
* - Added 'abs' (absolute value) support per tjbaron's update.
* - Moved to native class functions for PHP5
* - Removed deprecated `eregi` calls to `preg_match`
* - Updated to PHPDoc comment syntax
* - Added Exception throwing instead of silent exits
* - Added additional variable prefix of '$', '&' is still allowed as well
* - Fixed small implied multiplication problem
* @author Jon Lawrence <jlawrence11@gmail.com>
* @copyright Copyright 2005-2015, Jon Lawrence
* @license http://opensource.org/licenses/LGPL-2.1 LGPL 2.1 License
require_once 'Stack.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
* No matching Open/Close pair
* No variable replacement available
* @var bool Activate Debug output.
public static $debug = FALSE;
//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', 'abs', 'log', 'log10', 'sqrt');
* 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) {
if(defined('DEBUG') && DEBUG) {
$this->inFix = (isset($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", NF_EOS_Parser::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 '{$infix}'", NF_EOS_Parser::E_NO_SET);
} elseif(substr_count($infix, '[') != substr_count($infix, ']')) {
throw new Exception("Mismatched brackets in '{$infix}'", NF_EOS_Parser::E_NO_SET);
* Converts an infix (standard) equation to postfix (RPN) notation.
* Sets the internal variable $this->postFix for the Parser::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 $infix A standard notation equation
* @throws Exception When parenthesis are mismatched.
* @return Array Fully formed RPN Stack
public function in2post($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);
$ops = new NF_EOS_Stack();
// remove all white-space
$infix = 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 != "")) && (isset($pf[$pfIndex]) && ($pf[$pfIndex]!="-")))
$pfIndex++; // increase the index so as not to overlap anything
// Add the number character to the array
if(isset($pf[$pfIndex])) {
// If the character opens a set e.g. '(' or '['
elseif(in_array($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 '{$infix}'.", NF_EOS_Parser::E_NO_SET);
// If a special operator that has precedence over everything else
elseif(in_array($chr, $this->ST)) {
while(in_array($ops->peek(), $this->ST))
$pf[++$pfIndex] = $ops->pop();
// Any other operator other than '+' and '-'
elseif(in_array($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] = $ops->pop();
// make sure we record this character to be referred to by the next one
// if there is anything on the stack after we are done...add it to the back of the RPN array
while(($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 Parser::in2post(), can take
* an array input to solve as well, though default action is preferred.
* @link http://en.wikipedia.org/wiki/Reverse_Polish_notation Postix Notation
* @param Array $pfArray RPN formatted array. Optional.
* @throws Exception On division by zero.
* @return Float Result of the operation.
public function solvePF($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}", NF_EOS_Parser::E_DIV_ZERO);
$temp[$hold-2] = $temp[$hold-2] / $temp[$hold-1];
$temp[$hold-2] = pow($temp[$hold-2], $temp[$hold-1]);
$temp[$hold-1] = $this->factorial($temp[$hold-1]);
if($temp[$hold-1] == 0) {
throw new Exception("Division by 0 on: '{$temp[$hold-2]} % {$temp[$hold-1]}' in {$this->inFix}", NF_EOS_Parser::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
public function solve($equation, $values = null) {
if(is_array($equation)) {
return $this->solvePF($equation);
return $this->solveIF($equation, $values);
* Solve Infix (Standard) Notation Equation
* Will take a standard equation with optional variables and solve it. Variables
* must begin with '&' or '$'
* 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 $vArray Variable replacement
* @throws Exception On division by zero and on NaN and lack of variable replacement.
* @return Float Solved equation
function solveIF($infix, $vArray = null) {
$infix = ($infix != "") ? $infix : $this->inFix;
//Check to make sure a 'valid' expression
$this->checkInfix($infix);
$infix = preg_replace("/\s/", "", $infix);
if(NF_EOS_Parser::$debug) {
$hand=fopen("eq.txt","a");
//replace scientific notation with normal notation (2e-9 to 2*10^-9)
$infix = preg_replace('/([\d])([eE])(-?\d)/', '$1*10^$3', $infix);
if(NF_EOS_Parser::$debug) {
fwrite($hand, "$infix\n");
// Finds all the 'functions' within the equation and calculates them
// NOTE - when using function, only 1 set of parenthesis will be found, instead use brackets for sets within functions!!
//while((preg_match("/(". implode("|", $this->FNC) . ")\(([^\)\(]*(\([^\)]*\)[^\(\)]*)*[^\)\(]*)\)/", $infix, $match)) != 0) {
//Nested parenthesis are now a go!
while((preg_match("/(". implode("|", $this->FNC) . ")\(((?:[^()]|\((?2)\))*+)\)/", $infix, $match)) != 0) {
$func = $this->solveIF($match[2], $vArray);
throw new Exception("Division by 0 on: 'sec({$func}) = 1/cos({$func})' in {$this->inFix}", NF_EOS_Parser::E_DIV_ZERO);
throw new Exception("Division by 0 on: 'csc({$func}) = 1/sin({$func})' in {$this->inFix}", NF_EOS_Parser::E_DIV_ZERO);
throw new Exception("Division by 0 on: 'cot({$func}) = 1/tan({$func})' in {$this->inFix}", NF_EOS_Parser::E_DIV_ZERO);
if(is_nan($ans) || is_infinite($ans)) {
throw new Exception("Result of 'log({$func}) = {$ans}' is either infinite or a non-number in {$this->inFix}", NF_EOS_Parser::E_NAN);
if(is_nan($ans) || is_infinite($ans)) {
throw new Exception("Result of 'log10({$func}) = {$ans}' is either infinite or a non-number in {$this->inFix}", NF_EOS_Parser::E_NAN);
throw new Exception("Result of 'sqrt({$func}) = i. We can't handle imaginary numbers", NF_EOS_Parser::E_NAN);
$infix = str_replace($match[0], "({$ans})", $infix);
$infix = preg_replace('/[$&]/', "", $infix);
//Find all the variables that were passed and replaces them
while((preg_match('/([^a-zA-Z]){0,1}([a-zA-Z]+)([^a-zA-Z]){0,1}/', $infix, $match)) != 0) {
//remove notices by defining if undefined.
if(NF_EOS_Parser::$debug)
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])) //$this->SEP['open'] removed
//Make sure that the variable does have a replacement
//First check for pi and e variables that wll automagically be replaced
if(in_array(strtolower($match[2]), array('pi', 'e'))) {
$t = (strtolower($match[2])=='pi') ? pi() : exp(1);
$infix = str_replace($match[0], $match[1] . $front. $t. $back . $match[3], $infix);
} elseif(!isset($vArray[$match[2]]) && (!is_array($vArray != "") && !is_numeric($vArray) && 0 !== $vArray)) {
throw new Exception("Variable replacement does not exist for '". substr($match[0], 1, 1). $match[2] ."' in {$this->inFix}", NF_EOS_Parser::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], $infix);
if(NF_EOS_Parser::$debug)
return $this->solvePF($this->in2post($infix));
It is recommended that you Edit text format, this type of Fix handles quite a lot in one request
