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<?php
/*
* MODIFICATIONS
* - 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
* the system at risk.
*
* 2015/07
* - Added all real number factorial support
* - Added gamma function to class
*
* 2014/08
* - Added scientific notation support
* - Added basic factorial support
*
* 2013/06 UPDATE:
* - Added 'abs' (absolute value) support per tjbaron's update.
*
* 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
*
* @author Jon Lawrence <jlawrence11@gmail.com>
* @copyright Copyright 2005-2015, Jon Lawrence
* @license http://opensource.org/licenses/LGPL-2.1 LGPL 2.1 License
* @package EOS
* @version 2.2.1
*/
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
* @package Math
* @subpackage EOS
* @version 2.2.1
*/
class NF_EOS_Parser {
/**
* No matching Open/Close pair
*/
const E_NO_SET = 5500;
/**
* Division by 0
*/
const E_DIV_ZERO = 5501;
/**
* No Equation
*/
const E_NO_EQ = 5502;
/**
* No variable replacement available
*/
const E_NO_VAR = 5503;
/**
* Not a number
*/
const E_NAN = 5504;
/**
* @var bool Activate Debug output.
* @see __construct()
* @see solveIF()
*/
public static $debug = FALSE;
/**#@+
*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', 'abs', 'log', 'log10', 'sqrt');
/**#@-*/
/**
* 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 Parser::solveIF()
* @param String $inFix Standard format equation
*/
public function __construct($inFix = null) {
if(defined('DEBUG') && DEBUG) {
self::$debug = true;
}
$this->inFix = (isset($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($infix) == "") {
throw new Exception("No Equation given", NF_EOS_Parser::E_NO_EQ);
}
//Make sure we have the same number of '(' as we do ')'
// and the same # of '[' as we do ']'
if(substr_count($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);
}
$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 Parser::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 $infix A standard notation equation
* @throws Exception When parenthesis are mismatched.
* @return Array Fully formed RPN Stack
*/
public function in2post($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);
$pf = array();
$ops = new NF_EOS_Stack();
//$vars = new Stack();
// remove all white-space
$infix = 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 != "")) && (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])) {
$pf[$pfIndex] .= $chr;
} else {
$pf[$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}'.", NF_EOS_Parser::E_NO_SET);
}
}
$ops->pop();
}
// If a special operator that has precedence over everything else
elseif(in_array($chr, $this->ST)) {
while(in_array($ops->peek(), $this->ST))
$pf[++$pfIndex] = $ops->pop();
$ops->push($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 referred 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 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
$temp = array();
//$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) {
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];
break;
case '^':
$temp[$hold-2] = pow($temp[$hold-2], $temp[$hold-1]);
break;
case '!':
$temp[$hold-1] = $this->factorial($temp[$hold-1]);
$hold++;
break;
case '%':
if($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]);
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
public function solve($equation, $values = null) {
if(is_array($equation)) {
return $this->solvePF($equation);
} else {
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);
//$ops = new Stack();
//$vars = new Stack();
$hand = null;
//remove all white-space
$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], $vArray);
switch($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($tmp == 0) {
throw new Exception("Division by 0 on: 'sec({$func}) = 1/cos({$func})' in {$this->inFix}", NF_EOS_Parser::E_DIV_ZERO);
}
$ans = 1/$tmp;
break;
case "csc":
$tmp = sin($func);
if($tmp == 0) {
throw new Exception("Division by 0 on: 'csc({$func}) = 1/sin({$func})' in {$this->inFix}", NF_EOS_Parser::E_DIV_ZERO);
}
$ans = 1/$tmp;
break;
case "cot":
$tmp = tan($func);
if($tmp == 0) {
throw new Exception("Division by 0 on: 'cot({$func}) = 1/tan({$func})' in {$this->inFix}", NF_EOS_Parser::E_DIV_ZERO);
}
$ans = 1/$tmp;
break;
case "abs":
$ans = abs($func);
break;
case "log":
$ans = log($func);
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);
}
break;
case "log10":
$ans = log10($func);
if(is_nan($ans) || is_infinite($ans)) {
throw new Exception("Result of 'log10({$func}) = {$ans}' is either infinite or a non-number in {$this->inFix}", NF_EOS_Parser::E_NAN);
}
break;
case "sqrt":
if($func < 0) {
throw new Exception("Result of 'sqrt({$func}) = i. We can't handle imaginary numbers", NF_EOS_Parser::E_NAN);
}
$ans = sqrt($func);
break;
default:
$ans = 0;
break;
}
$infix = str_replace($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, $match)) != 0) {
//remove notices by defining if undefined.
if(!isset($match[3])) {
$match[3] = "";
}
if(NF_EOS_Parser::$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
$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
$back = "";
//Make sure that the variable does have a replacement
//First check for pi and e variables that wll automagically be replaced
if(in_array(strtolower($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)
fclose($hand);
return $this->solvePF($this->in2post($infix));
} //end function solveIF
/**
* Solve factorial (!)
*
* Will take any real positive number and solve for it's factorial. Eg.
* `5!` will become `1*2*3*4*5` = `120` For integers
* and
* 5.2! will become gamma(6.2) for non-integers
* DONE:
* Solve for non-integer factorials 2015/07/02
*
* @param Float $num Non-negative real number to get factorial of
* @throws Exception if number is at or less than 0
* @return Float Solved factorial
*/
protected function factorial($num) {
if($num < 0) {
throw new Exception("Factorial Error: Factorials don't exist for numbers < 0", NF_EOS_Parser::E_NAN);
}
//A non-integer! Gamma that sucker up!
if(intval($num) != $num) {
return $this->gamma($num + 1);
}
$tot = 1;
for($i=1;$i<=$num;$i++) {
$tot *= $i;
}
return $tot;
} //end function factorial
/**
* Gamma Function
*
* Because we can. This function exists as a catch-all for different
* numerical approx. of gamma if I decide to add any past Lanczos'.
* This method is public because a function doesn't currently exist
* within this parser to use it. That will change in the future.
*
* @param $z Number to compute gamma from
* @return Float The gamma (hopefully, I'll test it after writing the code)
*/
public function gamma($z)
{
return $this->laGamma($z);
}
/**
* Lanczos Approximation
*
* The Lanczos Approximation method of finding gamma values
*
* @link http://www.rskey.org/CMS/index.php/the-library/11
* @link http://algolist.manual.ru/maths/count_fast/gamma_function.php
* @link https://en.wikipedia.org/wiki/Lanczos_approximation
* @param float $z Number to obtain the gamma of
* @return float Gamma of inputted number
* @throws Exception if Number is less than or equal to 0
*/
protected function laGamma($z)
{
//check validity of $z, throw error if not a valid number to be used with gamma
if($z <= 0) {
throw new Exception("Gamma cannot be calculated on numbers less than or equal to 0", NF_EOS_Parser::E_NAN);
}
// Set up coefficients
$p = array(
0 => 1.000000000190015,
1 => 76.18009172947146,
2 => -86.50532032941677,
3 => 24.01409824083091,
4 => -1.231739572450155,
5 => 1.208650973866179E-3,
6 => -5.395239384953E-6
);
//formula:
// ((sqrt(2pi)/z)(p[0]+sum(p[n]/(z+n), 1, 6)))(z+5.5)^(z+0.5)*e^(-(z+5.5))
// Break it down now...
$g1 = sqrt(2*pi())/$z;
//Next comes our summation
$g2 =0;
for($n=1;$n<=6;$n++) {
$g2 += $p[$n]/($z+$n);
}
// Don't forget to add p[0] to it...
$g2 += $p[0];
$g3 = pow($z+5.5, $z + .5);
$g4 = exp(-($z+5.5));
//now just multiply them all together
$gamma = $g1 * $g2 * $g3 * $g4;
return $gamma;
}
} //end class 'Parser'