calculatie-parser

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index.php

Code (php)
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<?php

error_reporting(E_ALL | E_STRICT);
ini_set('display_errors', 'on');

include 'lib.php';

$str = $_SERVER['QUERY_STRING'];

$parser = new Parser();

$fac = function($v){
    $n = round($v[0]);
    if($n > 0) {
        $return = $n;
        while(--$n > 0) {
            $return *= $n;
        }

        return $return;
    }
elseif($n == 0) {
        return 1;
    }
else {
        throw new Exception('Faculty using neg. number');
        return false;
    }
};

            
$parser ->addOperator('Multiply', '*', 2, function($v){return $v[0]*$v[1];})
        ->
addOperator('Division', '/', 2, function($v){if($v[1] == 0) {throw new Exception('Division by 0');} return $v[0]/$v[1];})
        ->
addOperator('Plus', '+', 1, function($v){return $v[0]+$v[1];})
        ->
addOperator('Minus', '-', 1, function($v){return $v[0]-$v[1];})
        ->
addOperator('Power', '^', 3, function($v){return pow($v[0],$v[1]);})
        ->
addOperator('Faculty', '!', 4, $fac, OperatorRule::VAR_BEFORE)
        ->
addOperator('SquareRoot', 'W', 3, function($v){if($v[0] < 0) {throw new Exception('Irreal result');} return sqrt($v[0]);}, OperatorRule::VAR_AFTER)
        ->
addOperator('Logarithm', 'log', 4, function($v){if($v[0] < 0 || $v[1] < 0) {throw new Exception('Irreal result');} return log($v[0],$v[1]);})
        ->
addOperator('Pi', 'pi', null, function($v){return M_PI;}, OperatorRule::VAR_NONE)
        ->
addOperator('E', 'e', null, function($v){return M_E;}, OperatorRule::VAR_NONE)
        ->
addOperator('Equation', '=', 0, function($v){return ($v[0]==$v[1])?1:0;});
try {
    $res =  $parser->parse($str);
    echo $str.'&nbsp;&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;'.$res;
}
catch(Exception $e) {
    echo $e->getMessage();
}

?>

index_old.ph
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<?php

error_reporting(E_ALL | E_STRICT);
ini_set('display_errors', 'on');

include 'lib.php';

$str = $_SERVER['QUERY_STRING'];

$parser = new Parser();

function
calcMultiply($v) {
    return $v[0]*$v[1];
}

function
calcDivision($v) {
    if($v[1] == 0) {
        throw new Exception('Division by 0');
    }

    return $v[0]/$v[1];
}

function
calcPlus($v) {
    return $v[0]+$v[1];
}

function
calcMinus($v) {
    return $v[0]-$v[1];
}

function
calcPower($v) {
    return pow($v[0], $v[1]);
}

function
calcFaculty($v){
    $n = round($v[0]);
    if($n > 0) {
        $return = $n;
        while(--$n > 0) {
            $return *= $n;
        }

        return $return;
    }
elseif($n == 0) {
        return 1;
    }
else {
        throw new Exception('Faculty using neg. number');
        return false;
    }
};
            
function
calcSquareRoot($v) {
    if($v[0] < 0) {
        throw new Exception('Irreal result');
    }

    return sqrt($v[0]);
}

function
calcLogarithm($v) {
    if($v[0] < 0 || $v[1] < 0) {
        throw new Exception('Irreal result');
    }

    return log($v[0], $v[1]);
}

function
calcE($v) {
    return M_E;
}

function
calcEquation($v) {
    return ($v[0]==$v[1])?1:0;
}


$parser ->addOperator('Multiply', '*', 2, 'calcMultiply')
        ->
addOperator('Division', '/', 2, 'calcDivision')
        ->
addOperator('Plus', '+', 1, 'calcPlus')
        ->
addOperator('Minus', '-', 1, 'calcMinus')
        ->
addOperator('Power', '^', 3, 'calcPower')
        ->
addOperator('Faculty', '!', 4, 'calcFaculty', OperatorRule::VAR_BEFORE)
        ->
addOperator('SquareRoot', 'W', 3, 'calcSquareRoot', OperatorRule::VAR_AFTER)
        ->
addOperator('Logarithm', 'log', 4, 'calcLogarithm')
        ->
addOperator('Pi', 'pi', null, 'pi', OperatorRule::VAR_NONE)
        ->
addOperator('E', 'e', null, 'calcE', OperatorRule::VAR_NONE)
        ->
addOperator('Equation', '=', 0, 'calcEquation');
try {
    $res =  $parser->parse($str);
    echo $str.'&nbsp;&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;'.$res;
}
catch(Exception $e) {
    echo $e->getMessage();
}

?>

lib.php
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<?php
/**
 * CalculationParser
 *
 * @autor Pim de Haan <[email protected]>
 * @version 1.0
 * @package CalculationParser
 *
 * @todo Support for argumented operators, e.g. x(a, b)
 * @todo Improving error messages
 * @todo Seperate Lexer and part handler
 */
/**
 * The Parser class
 * @package CalculationParser
 */

class Parser {
    
    /**
     * Storing the lexer
     * @var Lexer
     */

    private $_lex;
    
    /**
     * List of added {@link OperatorRule}
     * @var array
     */

    private $_operators = array();                                
    
    /**
     * Constructor sets up the {@link $_lex}
     */

    public function __construct() {
        $this->_lex = new Lexer;
    }

    
    /**
     * Adds an {@link OperatorRule} to {@link $_operators}
     * Return itself for chained calls
     *
     * @param string $name Name
     * @param string $symbol Symbol
     * @param int $hierarchy Hierarchy level
     * @param Closure $function The anonymous function which provides the actual operation
     * @param int $varPos Providing where the operators elements are located
     * @return Parser
     */

    public function addOperator($name, $symbol, $hierarchy, $function, $varPos = null) {
        $this->_operators[$symbol] = new OperatorRule($name, $symbol, $hierarchy, $function, $varPos);
        return $this;
    }

    
    /**
     * Return the array of operator symbols
     * @return array
     */

    private function _operatorArray() {
        $return = array();
        foreach($this->_operators as $op) {
            $return[] = $op->getSymbol();
        }
    }

    
    /**
     * The actual parsing.
     * At first, splits the input string by the {@link Lexer}
     * Then loops following code until only a single float remains:
     * <ul>
     *
     *     <li>All tokens, {@link Token}, are retrieved one by one.
     *     <ul>
     *         <li>If the token is a operator, {@link OperatorToken}, a new {@link Operator} is added to the operators array along with its hierarchy and part offset.</li>
     *         <li>If it is a parentesis, {@link OpenToken} or {@link CloseToken}, the parenthesesOpen variable is modified, which alters the next operators hierarchy.</li>
     *     </ul></li>
     *
     *     <li>Then the operator with the higherst hierarchy is selected.</li>
     *
     *     <li>If the operator has a variable in front of it, the next actions are exectued
     *     <ul>
     *         <li>The number in front of it is retrieved</li>
     *         <li>It is tested wether it's a number</li>
     *         <li>It is deleted from the {@link Lexer}s parts list</li>
     *         <li>It is added as a variable to the operator</li>
     *     </ul>
     *     This is also executed if it has a variable after it</li>
     *
     *     <li>The operators result is calculated</li>
     *     <li>The result replaces the operator in the {@link Lexer}s parts list</li>
     *     <li>The parenteses behind and after it are deleted from the {@link Lexer}s parts list</li>
     *
     * </ul>
     *
     * @return int
     */

    public function parse($text) {
        
        $this->_lex->lex($text, array_keys($this->_operators));
        
        while(false === $res = $this->_lex->done()) {
            
            $parenthesesOpen = 0;
            
            $operators = array();
            
            $this->_lex->reset();
            
            while(false !== $token = $this->_lex->getToken()) {
                if($token instanceof OperatorToken) {
    
                    $hierarchy = $this->_operators[$token->getOperation()]->getHierarchy() + 20*$parenthesesOpen;
                    $operators[] = new Operator($this->_operators[$token->getOperation()], $hierarchy, $token->getOffset());
                    
                }
elseif($token instanceof OpenToken) {
                    $parenthesesOpen++;
                }
elseif($token instanceof CloseToken) {
                    if($parenthesesOpen-- == 0) {
                        throw new Exception('Syntax Error');
                    }
                }
            }

            
            if(empty($operators)) {
                throw new Exception('Syntax Error');
            }

            
            $highestOperator = null;
            $highestHierarchy = -10;
            
            foreach($operators as $operator) {
                if($operator->getHierarchy() > $highestHierarchy) {
                    $highestOperator = $operator;
                    $highestHierarchy = $operator->getHierarchy();
                }
            }

            
            $operator = $highestOperator;
            $operatorOffset = $operator->getOffset();
            
            $varPositions = $operator->getRule()->getVarPositions();
            
            $parenthesisBeforeOffset = 1;
            $parenthesisAfterOffset = 1;
            
            // If operator has a variable before it
            if($varPositions & OperatorRule::VAR_BEFORE) {
                $num = $this->_lex->getToken($operatorOffset-1);
                if(!is_float($num)) {
                    throw new Exception('Syntax error');
                }

                $this->_lex->delete($operatorOffset-1);
                $operator->addVar($num);
                
                $parenthesisBeforeOffset = 2;
            }

            
            // If operator has a variable after it
            if($varPositions & OperatorRule::VAR_AFTER) {
                $num = $this->_lex->getToken($operatorOffset+1);
                if(!is_float($num)) {
                    throw new Exception('Syntax error');
                }

                $this->_lex->delete($operatorOffset+1);
                $operator->addVar($num);
                
                $parenthesisAfterOffset = 2;
            }

            
            $res = $operator->calc();
            
            $this->_lex->replace($operatorOffset, $res);
            
            
            // Delete Haakjes
            if($this->_lex->getToken($operatorOffset-$parenthesisBeforeOffset) instanceof OpenToken &&
                    $this->_lex->getToken($operatorOffset+$parenthesisAfterOffset) instanceof CloseToken) {
                $this->_lex->delete($operatorOffset-$parenthesisBeforeOffset)->delete($operatorOffset+$parenthesisAfterOffset);
            }

            
            $this->_lex->update();
        }

        
        return $res;
    }
}


/**
 * The lexer wich splits the input text into parts and provides and modifies these parts
 * @package CalculationParser
 */


class Lexer {
    
    /**
     * The list of parts
     * @var array
     */

    private $_parts;
    
    /**
     * The amount of parts
     * @var int
     */

    private $_partsCount;
    
    /**
     * The internal pointer
     * @var int
     */

    private $_pointer = -1;
    
    /**
     * The list of operator symbols
     * @var array
     */

    private $_operators;
    
    /**
     * The lexer function, which:
     * <ul>
     *     <li>Removes spaces</li>
     *     <li>Modefies the shorthand writing, 4(5+2) to 4*(5+2)</li>
     *     <li>Prepares the operator list using {@link $_operators} to be used in the regex</li>
     *     <li>Splits using preg_match_all</li>
     *     <li>Checks wether parts are remaining and if so, throw an excpetion</li>
     *     <li>Fills {@link $_parts} and {@link $_partsCount}</li>
     * </ul>
     *
     * @param string $text The input text
     * @param array $operators The array of operator symbols {@link $_operators}
     */

    public function lex($text, $operators) {
        $text = str_replace(' ', '', $text);
        $text = preg_replace('/([0-9|\)])\(/', '$1*(', $text);
        
        $this->_operators = $operators;
        
        $tokenList = implode('|', array_map('preg_quote', $operators));
        
        /**
         * Explanation regex:
         * Define part if string:
         * - is a Operator
         * - is a Parentesis
         * - is a number may or may not be followed by a dot and another number
         *                                    following a minus sign, which is not following by a number
         *
         *                                     followed by a E and a positive or negative number
         * - is a dot follewed by a number may or may not be following a minus sign, which is not following a number
         */

        
        $reg = '#((?<!\d)\-)?((\d+(\.?\d+)?)|(\.\d+))(E[\+\-]?\d+?)?|'.$tokenList.'|\(|\)#';

        preg_match_all($reg, $text, $matches);
        
        // Checks for remaining parts
        $total = 0;
        foreach($matches[0] as $match) {
            $total += strlen($match);
        }

        if($total != strlen($text)) {
            throw new Exception('Syntax error');
        }

        
        $this->_parts = $matches[0];
        
        $this->_partsCount = count($this->_parts);
        
        if($this->_partsCount == 0) {
            throw new Exception('No input given');
        }
    }

    
    /**
     * Detemines wether only one float is left and if so, returns its value
     *
     * @return int|false
     */

    public function done() {
        if($this->_partsCount == 1 && is_numeric($this->_parts[0])) {
            return ((float)$this->_parts[0]);
        }
else {
            return false;
        }
    }

    
    /**
     * Analyzes {@link _analyze()} and returns next {@link Token} or the token at the specified offset
     *
     * @param int $offset The optional offset
     * @return Token
     */

    public function getToken($offset = null) {
        if(is_null($offset)) {
            $offset = ++$this->_pointer;
        }

        
        if(isset($this->_parts[$offset])) {
            return $this->_analyze($this->_parts[$offset], $offset);
        }
else {
            return false;
        }
    }

    
    /**
     * Analyses the given string and returns a {@link Token} or float
     *
     * @param string $token The input string
     * @param int $offset The strings offset
     * @return float|OpenToken|CloseToken|OperatorToken
     */

    private function _analyze($token, $offset) {
        
        if(is_numeric($token)) {
            return (float) $token;
        }
elseif($token == '(') {
            return new OpenToken;
        }
elseif($token == ')') {
            return new CloseToken;
        }
else {
            if(!in_array($token, $this->_operators)) {
                throw new Exception('Foute operator: "'.$token.'"');
                return;
            }
else {
                return new OperatorToken($token, $offset);
            }
        }    
    }

    
    /**
     * Updates {@link $_parts} by removing empty parts
     *
     * @return Lexer
     */
    
    public function update() {
        $new = array();
        foreach($this->_parts as $part) {
            $new[] = $part;
        }

        $this->_parts = $new;
        $this->_partsCount = count($this->_parts);
        
        return $this;
    }

    
    /**
     * Deletes part from {@link $_parts} at given offset
     *
     * @param int $offset Offset
     * @return Lexer
     */

    public function delete($offset) {
        if(isset($this->_parts[$offset])) {
            unset($this->_parts[$offset]);
        }

        return $this;
    }

    
    /**
     * Resets internal {@link $_pointer}
     *
     * @return Lexer
     */

    public function reset() {
        $this->_pointer = -1;
        return $this;
    }

    
    /**
     * Replaces part at given offset with given part
     *
     * @param int $offset Offset
     * @param float|string $part Replacement value
     */

    public function replace($offset, $part) {
        $this->_parts[$offset] = $part;
        return $this;
    }
}


/**
 * Currently empty abstract class which is extends by specified Token classes
 *
 * Tokens are parts returned by {@link Lexer::_getToken()} which contain a certain part of the input string
 * @package CalculationParser
 */

abstract class Token {}

/**
 * Token for an opening parentesis
 * @package CalculationParser
 */

class OpenToken extends Token {}

/**
 * Token for an closing parentesis
 * @package CalculationParser
 */

class CloseToken extends Token {}

/**
 * Token for an operator
 * @package CalculationParser
 */

class OperatorToken extends Token {
    
    /**
     * The operation symbol
     * @var string
     */

    private $_operation;
    
    /**
     * The offset in the {@link Lexer::$_parts}
     * @var string
     */

    private $_offset;
    
    /**
     * The constructor, sets {@link $_operation} and {@link $_offset}
     *
     * @param string $operation The operation symbol
     * @param int $offset The offset
     */

    public function __construct($operation, $offset) {
        $this->_operation = $operation;
        $this->_offset = $offset;
    }

    
    /**
     * Returns {@link $_operation}
     * @return string
     */

    public function getOperation() {
        return $this->_operation;
    }

    
    /**
     * Returns {@link $_offset}
     * @return int
     */

    public function getOffset() {
        return $this->_offset;
    }
}


/**
 * The operator in {@link Parser::parse()}
 * @package CalculationParser
 */

class Operator {
    
    /**
     * The {@link OperatorRule}
     * @var OperatorRule
     */

    private $_rule;
    
    /**
     * The hierarchy
     * @var int
     */

    private $_hierarchy;
    
    /**
     * The offset in the {@link Lexer::$_parts}
     * @var int
     */

    private $_offset;
    
    /**
     * The variables
     * @var array
     */

    private $_vars = array();
    
    /**
     * The constructor, sets {@link $_rule}, {@link $_hierarchy} and {@link $_offset}
     *
     * @param OperatorRule $rule The OperatorRule
     * @param int $hierarchy The hierarchy
     * @param int $offset The offset
     */

    public function __construct(OperatorRule $rule, $hierarchy, $offset) {
        $this->_rule = $rule;
        $this->_hierarchy = $hierarchy;
        $this->_offset = $offset;
    }

    
    /**
     * Returns {@link $_rule}
     * @return OperatorRule
     */

    public function getRule() {
        return $this->_rule;
    }

    
    /**
     * Returns {@link $_hierarchy}
     * @return int
     */

    public function getHierarchy() {
        return $this->_hierarchy;
    }

    
    /**
     * Returns {@link $_offset}
     * @return int
     */

    public function getOffset() {
        return $this->_offset;
    }

    
    /**
     * Adds a variable to {@link $_vars}
     *
     * @param float $var The variable
     * @return Operator
     */

    public function addVar($var) {
        $this->_vars[] = $var;
        return $this;
    }

    
    /**
     * Do the calculation based on {@link $_vars} by calling the anonymous funtion in the {@link $_rule}
     */

    public function calc() {
        return $this->_rule->calc($this->_vars);
    }
}


/**
 * Class for defining operations
 * @package CalculationParser
 */

class OperatorRule {
    
    /**
     * The name
     * @var string
     */

    private $_name;
    
    /**
     * The symbol
     * @var string
     */

    private $_symbol;
    
    /**
     * The base hierarchy
     * @var int
     */

    private $_hierarchy;
    
    /**
     * The anonymous function
     * @var Closure
     */

    private $_function;
    
    /**
     * The positions of the variables, bitwise
     * @var int
     */

    private $_varPositions;
    
    
    /**
     * The constant for the variable position 'before'
     * @see $_varPositions
     *
     * @var int
     */

    const VAR_BEFORE = 1;
    
    /**
     * The constant for the variable position 'after'
     * @see $_varPositions
     *
     * @var int
     */

    const VAR_AFTER = 2;
    
    /**
     * The constant for the variable position 'after' and 'before'
     * @see $_varPositions
     *
     * @var int
     */

    const VAR_BOTH = 3;
    
    /**
     * The constant for no variable positions, meaning the operator is a constant
     * @see $_varPositions
     *
     * @var int
     */

    const VAR_NONE = 0;
    
    /**
     * The constructor, sets {@link $_name}, {@link $_symbol}, {@link $_hierarchy}, {@link $_function}, and optionally {@link $_varPositions}
     * If the operator is a constant, the hierarchy is very high
     *
     * @param string $name The name
     * @param string $symbol The symbol
     * @param int $hierarchy The hierarchy
     * @param Closure $function The anonymous function
     * @param int $varPositions The optional variable positions
     */

    public function __construct($name, $symbol, $hierarchy, $function, $varPositions = null) {
        $this->_name = $name;
        $this->_symbol = $symbol;
        $this->_hierarchy = ($varPositions === self::VAR_NONE)?1000:$hierarchy;
        $this->_function = $function;
        $this->_varPositions = (!is_null($varPositions) ? $varPositions : self::VAR_BOTH);
    }

    
    /**
     * Returns {@link $_name}
     * @return string
     */

    public function getName() {
        return $this->_name;
    }

    
    /**
     * Returns {@link $_symbol}
     * @return string
     */

    public function getSymbol() {
        return $this->_symbol;
    }

    
    /**
     * Returns {@link $_hierarchy}
     * @return int
     */

    public function getHierarchy() {
        return $this->_hierarchy;
    }

    
    /**
     * Returns {@link $_varPositions}
     * @return int
     */

    public function getVarPositions() {
        return $this->_varPositions;
    }

    
    /**
     * Do the calculation by executing the {@link $_function} and give the arguments to this method as arguments to the anonymous function
     * @param float $v,... The variables
     * @return float The result
     */

    public function calc() {
        $args = func_get_args();
        return (float) call_user_func_array($this->_function, $args);
    }
    
}

?>

 
 

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