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<?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
* the system at risk.
*
* 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);
//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
// of this class.
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
* @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($infix) == "") {
throw new Exception("No Equation given", EQEOS_E_NO_EQ);
return false;
}
//Make sure we have the same number of '(' as we do ')'
// and the same # of '[' as we do ']'
if(substr_count($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 != "")) && (@$pf[$pfIndex]!="-"))
$pfIndex++; // increase the index so as not to overlap anything
// Add the number character to the array
@$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) {
throw new Exception("Division by 0 on: '{$temp[$hold-2]} / {$temp[$hold-1]}' in {$this->inFix}", EQEOS_E_DIV_ZERO);
return false;
}
@$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) {
throw new Exception("Division by 0 on: '{$temp[$hold-2]} % {$temp[$hold-1]}' in {$this->inFix}", EQEOS_E_DIV_ZERO);
return false;
}
@$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);
if(DEBUG)
$hand=fopen("eq.txt","a");
//Find all the variables that were passed and replaces them
while((preg_match('/(.){0,1}[&$]([a-zA-Z]+)(.){0,1}/', $infix, $match)) != 0) {
//remove notices by defining if undefined.
if(!isset($match[3])) {
$match[3] = "";
}
if(DEBUG)
fwrite($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
$back = "";
//Make sure that the variable does have a replacement
if(!isset($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], $infix);
}
}
if(DEBUG)
fwrite($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]);
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}", EQEOS_E_DIV_ZERO);
return false;
}
$ans = 1/$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}", EQEOS_E_DIV_ZERO);
return false;
}
$ans = 1/$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}", EQEOS_E_DIV_ZERO);
return false;
}
$ans = 1/$tmp;
break;
default:
break;
}
$infix = str_replace($match[0], $ans, $infix);
}
if(DEBUG)
fclose($hand);
return $this->solvePF($this->in2post($infix));
} //end function solveIF
} //end class 'eqEOS'
// 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 */
/**
* Equation Graph
*
* 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
* @package Math
* @subpackage EOS
* @version 2.0
*/
class eqGraph extends eqEOS {
private $width;
private $height;
//GD Image reference
private $image;
/**
* Constructor
*
* Sets up the Graph class with an image width and height defaults to
* 640x480
*
* @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)
$this->width = $width;
$this->height = $height;
//initialize main class variables
parent::__construct();
} //end function eqGraph
/**
* Create GD Graph Image
*
* 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 $yHigh Upper y-bound
* @return Null
*/
public function graph($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);
$xStep = abs($xStep);
//DEVELOPER, UNCOMMENT NEXT LINE IF WANTING TO PREVENT SLOW GRAPHS
//$xStep = ($xStep > .01) ? $xStep : 0.01;
if($xLow > $xHigh)
list($xLow, $xHigh) = array($xHigh, $xLow); //swap function
$xScale = $this->width/($xHigh-$xLow);
$counter = 0;
if(DEBUG) {
$hand=fopen("eqgraph.txt","w");
fwrite($hand, "$eq\n");
}
for($i=$xLow;$i<=$xHigh;$i+=$xStep) {
$tester = sprintf("%10.3f",$i);
if($tester == "-0.000") $i = 0;
$y = $this->solveIF($eq, $i);
//eval('$y='. str_replace('&x', $i, $eq).";"); /* used to debug my eqEOS class results */
if(DEBUG) {
$tmp1 = sprintf("y(%5.3f) = %10.3f\n", $i, $y);
fwrite($hand, $tmp1);
}
// If developer asked us to find the upper and lower bounds for y...
if($yGuess==true) {
$yLow = ($yLow===false || ($y<$yLow)) ? $y : $yLow;
$yHigh = ($yHigh===false || $y>$yHigh) ? $y : $yHigh;
}
$xVars[$counter] = $y;
$counter++;
}
if(DEBUG)
fclose($hand);
// add 0.01 to each side so that if y is from 1 to 5, the lines at 1 and 5 are seen
$yLow-=0.01;$yHigh+=0.01;
//Now that we have all the variables stored...find the yScale
$yScale = $this->height/(($yHigh)-($yLow));
// if developer wanted a grid on the graph, add it now
if($xyGrid==true) {
for($i=ceil($yLow);$i<=floor($yHigh);$i++) {
$i0 = abs($yHigh-$i);
ImageLine($img, 0, $i0*$yScale, $this->width, $i0*$yScale, $grey);
}
for($i=ceil($xLow);$i<=floor($xHigh);$i++) {
$i0 = abs($xLow-$i);
ImageLine($img, $i0*$xScale, 0, $i0*$xScale, $this->height, $grey);
}
}
//Now that we have the scales, let's see if we can draw an x/y-axis
if($xLow <= 0 && $xHigh >= 0) {
//the y-axis is within our range - draw it.
$x0 = abs($xLow)*$xScale;
ImageLine($img, $x0, 0, $x0, $this->height, $black);
for($i=ceil($yLow);$i<=floor($yHigh);$i++) {
$i0 = abs($yHigh-$i);
ImageLine($img, $x0-3, $i0*$yScale, $x0+3, $i0*$yScale, $black);
}
}
if($yLow <= 0 && $yHigh >= 0) {
//the x-axis is within our range - draw it.
$y0 = abs($yHigh)*$yScale;
ImageLine($img, 0, $y0, $this->width, $y0, $black);
for($i=ceil($xLow);$i<=floor($xHigh);$i++) {
$i0 = abs($xLow-$i);
ImageLine($img, $i0*$xScale, $y0-3, $i0*$xScale, $y0+3, $black);
}
}
$counter=2;
//now graph it all ;]
for($i=$xLow+$xStep;$i<=$xHigh;$i+=$xStep) {
$x1 = (abs($xLow - ($i - $xStep)))*$xScale;
$y1 = (($xVars[$counter-1]<$yLow) || ($xVars[$counter-1] > $yHigh)) ? -1 : (abs($yHigh - $xVars[$counter-1]))*$yScale;
$x2 = (abs($xLow - $i))*$xScale;
$y2 = (($xVars[$counter]<$yLow) || ($xVars[$counter] > $yHigh)) ? -1 : (abs($yHigh - $xVars[$counter]))*$yScale;
// if any of the y values were found to be off of the y-bounds, don't graph those connecting lines
if($y1!=-1 && $y2!=-1)
ImageLine($img, $x1, $y1, $x2, $y2, $black);
$counter++;
}
$this->image = $img;
} //end function 'graph'
/**
* Sends JPG to browser
*
* Sends a JPG image with proper header to output
*/
public function outJPG() {
header("Content-type: image/jpeg");
ImageJpeg($this->image);
}
/**
* Sends PNG to browser
*
* Sends a PNG image with proper header to output
*/
function outPNG() {
header("Content-type: image/png");
ImagePng($this->image);
}
/**
* Output GD Image
*
* Will give the developer the GD resource for the graph that
* can be used to store the graph to the FS or other media
*
* @return Resource GD Image Resource
*/
public function getImage() {
return $this->image;
}
/**
* Output GD Image
*
* Alias for eqGraph::getImage()
*
* @return Resource GD Image resource
*/
public function outGD() {
return $this->getImage();
}
} //end class 'eqGraph'
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