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