Calculation.php

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<?php
if (!defined('PHPEXCEL_ROOT')) {
        define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../');
}

require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/Matrix.php';

require_once PHPEXCEL_ROOT . 'PHPExcel/Calculation/Function.php';

require_once PHPEXCEL_ROOT . 'PHPExcel/Calculation/Functions.php';


class PHPExcel_Calculation {

        //      Numeric operand
        const CALCULATION_REGEXP_NUMBER         = '[-+]?\d*\.?\d+(e[-+]?\d+)?';
        //      String operand
        const CALCULATION_REGEXP_STRING         = '"(?:[^"]|"")*"';
        //      Opening bracket
        const CALCULATION_REGEXP_OPENBRACE      = '\(';
        //      Function
        const CALCULATION_REGEXP_FUNCTION       = '([A-Z][A-Z0-9\.]*)[\s]*\(';
        //      Cell reference (cell or range of cells, with or without a sheet reference)
        const CALCULATION_REGEXP_CELLREF        = '(((\w*)|(\'.*\')|(\".*\"))!)?\$?([a-z]+)\$?(\d+)(:\$?([a-z]+)\$?(\d+))?';
        //      Named Range of cells
        const CALCULATION_REGEXP_NAMEDRANGE     = '(((\w*)|(\'.*\')|(\".*\"))!)?([_A-Z][_A-Z0-9]*)';
        //      Error
        const CALCULATION_REGEXP_ERROR          = '\#[^!]+!';


        const RETURN_ARRAY_AS_VALUE = 'value';
        const RETURN_ARRAY_AS_ARRAY = 'array';

        private static $returnArrayAsType       = self::RETURN_ARRAY_AS_ARRAY;

        private static $_instance;


        private $_calculationCache = array ();


        private $_calculationCacheEnabled = true;


        private $_calculationCacheExpirationTime = 0.01;


        private $_operators                     = array('+', '-', '*', '/', '^', '&', '%', '_', '>', '<', '=', '>=', '<=', '<>');


        private $_binaryOperators       = array('+', '-', '*', '/', '^', '&', '>', '<', '=', '>=', '<=', '<>');

        public $suppressFormulaErrors = false;
        public $formulaError = null;
        public $writeDebugLog = false;
        private $debugLogStack = array();
        public $debugLog = array();


        //      Constant conversion from text name/value to actual (datatyped) value
        private $_ExcelConstants = array('TRUE'         => True,
                                                                         'FALSE'        => False,
                                                                         'NULL'         => Null
                                                                        );

        //      PHPExcel functions
        private $_PHPExcelFunctions = array(    // PHPExcel functions
                                'ABS'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'abs',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ACCRINT'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::ACCRINT',
                                                                                                 'argumentCount'        =>      '4-7'
                                                                                                ),
                                'ACCRINTM'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::ACCRINTM',
                                                                                                 'argumentCount'        =>      '3-5'
                                                                                                ),
                                'ACOS'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'acos',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ACOSH'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'acosh',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ADDRESS'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::CELL_ADDRESS',
                                                                                                 'argumentCount'        =>      '2-5'
                                                                                                ),
                                'AMORDEGRC'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '6,7'
                                                                                                ),
                                'AMORLINC'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '6,7'
                                                                                                ),
                                'AND'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LOGICAL_AND',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'AREAS'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ASC'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ASIN'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'asin',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ASINH'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'asinh',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ATAN'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'atan',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ATAN2'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::REVERSE_ATAN2',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'ATANH'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'atanh',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'AVEDEV'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::AVEDEV',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'AVERAGE'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::AVERAGE',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'AVERAGEA'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::AVERAGEA',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'AVERAGEIF'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '2,3'
                                                                                                ),
                                'AVERAGEIFS'                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3+'
                                                                                                ),
                                'BAHTTEXT'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'BESSELI'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::BESSELI',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'BESSELJ'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::BESSELJ',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'BESSELK'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::BESSELK',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'BESSELY'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::BESSELY',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'BETADIST'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::BETADIST',
                                                                                                 'argumentCount'        =>      '3-5'
                                                                                                ),
                                'BETAINV'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::BETAINV',
                                                                                                 'argumentCount'        =>      '3-5'
                                                                                                ),
                                'BIN2DEC'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::BINTODEC',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'BIN2HEX'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::BINTOHEX',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'BIN2OCT'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::BINTOOCT',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'BINOMDIST'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::BINOMDIST',
                                                                                                 'argumentCount'        =>      '4'
                                                                                                ),
                                'CEILING'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::CEILING',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'CELL'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'CHAR'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::CHARACTER',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'CHIDIST'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::CHIDIST',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'CHIINV'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::CHIINV',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'CHITEST'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'CHOOSE'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::CHOOSE',
                                                                                                 'argumentCount'        =>      '2+'
                                                                                                ),
                                'CLEAN'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::TRIMNONPRINTABLE',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'CODE'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::ASCIICODE',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'COLUMN'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::COLUMN',
                                                                                                 'argumentCount'        =>      '-1'
                                                                                                ),
                                'COLUMNS'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'COMBIN'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::COMBIN',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'COMPLEX'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::COMPLEX',
                                                                                                 'argumentCount'        =>      '2,3'
                                                                                                ),
                                'CONCATENATE'                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::CONCATENATE',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'CONFIDENCE'                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::CONFIDENCE',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'CONVERT'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::CONVERTUOM',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'CORREL'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::CORREL',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'COS'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'cos',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'COSH'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'cosh',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'COUNT'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::COUNT',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'COUNTA'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::COUNTA',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'COUNTBLANK'                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::COUNTBLANK',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'COUNTIF'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::COUNTIF',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'COUNTIFS'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'COUPDAYBS'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3,4'
                                                                                                ),
                                'COUPDAYS'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3,4'
                                                                                                ),
                                'COUPDAYSNC'                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3,4'
                                                                                                ),
                                'COUPNCD'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3,4'
                                                                                                ),
                                'COUPNUM'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3,4'
                                                                                                ),
                                'COUPPCD'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3,4'
                                                                                                ),
                                'COVAR'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::COVAR',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'CRITBINOM'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::CRITBINOM',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'CUBEKPIMEMBER'                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_CUBE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'CUBEMEMBER'                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_CUBE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'CUBEMEMBERPROPERTY'    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_CUBE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'CUBERANKEDMEMBER'              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_CUBE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'CUBESET'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_CUBE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'CUBESETCOUNT'                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_CUBE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'CUBEVALUE'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_CUBE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'CUMIPMT'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::CUMIPMT',
                                                                                                 'argumentCount'        =>      '6'
                                                                                                ),
                                'CUMPRINC'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::CUMPRINC',
                                                                                                 'argumentCount'        =>      '6'
                                                                                                ),
                                'DATE'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DATE',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'DATEDIF'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DATEDIF',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'DATEVALUE'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DATEVALUE',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'DAVERAGE'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'DAY'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DAYOFMONTH',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'DAYS360'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DAYS360',
                                                                                                 'argumentCount'        =>      '2,3'
                                                                                                ),
                                'DB'                                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DB',
                                                                                                 'argumentCount'        =>      '4,5'
                                                                                                ),
                                'DCOUNT'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'DCOUNTA'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'DDB'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DDB',
                                                                                                 'argumentCount'        =>      '4,5'
                                                                                                ),
                                'DEC2BIN'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DECTOBIN',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'DEC2HEX'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DECTOHEX',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'DEC2OCT'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DECTOOCT',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'DEGREES'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'rad2deg',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'DELTA'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DELTA',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'DEVSQ'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DEVSQ',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'DGET'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'DISC'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DISC',
                                                                                                 'argumentCount'        =>      '4,5'
                                                                                                ),
                                'DMAX'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'DMIN'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'DOLLAR'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DOLLAR',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'DOLLARDE'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DOLLARDE',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'DOLLARFR'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DOLLARFR',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'DPRODUCT'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'DSTDEV'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'DSTDEVP'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'DSUM'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'DURATION'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '5,6'
                                                                                                ),
                                'DVAR'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'DVARP'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'EDATE'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::EDATE',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'EFFECT'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::EFFECT',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'EOMONTH'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::EOMONTH',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'ERF'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::ERF',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'ERFC'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::ERFC',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ERROR.TYPE'                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::ERROR_TYPE',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'EVEN'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::EVEN',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'EXACT'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'EXP'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'exp',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'EXPONDIST'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::EXPONDIST',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'FACT'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::FACT',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'FACTDOUBLE'                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::FACTDOUBLE',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'FALSE'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LOGICAL_FALSE',
                                                                                                 'argumentCount'        =>      '0'
                                                                                                ),
                                'FDIST'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'FIND'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SEARCHSENSITIVE',
                                                                                                 'argumentCount'        =>      '2,3'
                                                                                                ),
                                'FINDB'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SEARCHSENSITIVE',
                                                                                                 'argumentCount'        =>      '2,3'
                                                                                                ),
                                'FINV'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'FISHER'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::FISHER',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'FISHERINV'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::FISHERINV',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'FIXED'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::FIXEDFORMAT',
                                                                                                 'argumentCount'        =>      '1-3'
                                                                                                ),
                                'FLOOR'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::FLOOR',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'FORECAST'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::FORECAST',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'FREQUENCY'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'FTEST'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'FV'                                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::FV',
                                                                                                 'argumentCount'        =>      '3-5'
                                                                                                ),
                                'FVSCHEDULE'                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'GAMMADIST'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::GAMMADIST',
                                                                                                 'argumentCount'        =>      '4'
                                                                                                ),
                                'GAMMAINV'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::GAMMAINV',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'GAMMALN'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::GAMMALN',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'GCD'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::GCD',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'GEOMEAN'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::GEOMEAN',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'GESTEP'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::GESTEP',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'GETPIVOTDATA'                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '2+'
                                                                                                ),
                                'GROWTH'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::GROWTH',
                                                                                                 'argumentCount'        =>      '1-4'
                                                                                                ),
                                'HARMEAN'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::HARMEAN',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'HEX2BIN'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::HEXTOBIN',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'HEX2DEC'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::HEXTODEC',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'HEX2OCT'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::HEXTOOCT',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'HLOOKUP'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3,4'
                                                                                                ),
                                'HOUR'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::HOUROFDAY',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'HYPERLINK'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'HYPGEOMDIST'                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::HYPGEOMDIST',
                                                                                                 'argumentCount'        =>      '4'
                                                                                                ),
                                'IF'                                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::STATEMENT_IF',
                                                                                                 'argumentCount'        =>      '1-3'
                                                                                                ),
                                'IFERROR'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::STATEMENT_IFERROR',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'IMABS'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMABS',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'IMAGINARY'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMAGINARY',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'IMARGUMENT'                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMARGUMENT',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'IMCONJUGATE'                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMCONJUGATE',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'IMCOS'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMCOS',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'IMDIV'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMDIV',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'IMEXP'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMEXP',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'IMLN'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMLN',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'IMLOG10'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMLOG10',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'IMLOG2'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMLOG2',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'IMPOWER'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMPOWER',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'IMPRODUCT'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMPRODUCT',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'IMREAL'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMREAL',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'IMSIN'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMSIN',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'IMSQRT'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMSQRT',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'IMSUB'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMSUB',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'IMSUM'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IMSUM',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'INDEX'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::INDEX',
                                                                                                 'argumentCount'        =>      '1-4'
                                                                                                ),
                                'INDIRECT'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'INFO'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'INT'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::INTVALUE',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'INTERCEPT'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::INTERCEPT',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'INTRATE'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::INTRATE',
                                                                                                 'argumentCount'        =>      '4,5'
                                                                                                ),
                                'IPMT'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IPMT',
                                                                                                 'argumentCount'        =>      '4-6'
                                                                                                ),
                                'IRR'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'ISBLANK'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IS_BLANK',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ISERR'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IS_ERR',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ISERROR'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IS_ERROR',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ISEVEN'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IS_EVEN',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ISLOGICAL'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IS_LOGICAL',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ISNA'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IS_NA',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ISNONTEXT'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IS_NONTEXT',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ISNUMBER'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IS_NUMBER',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ISODD'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IS_ODD',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ISPMT'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '4'
                                                                                                ),
                                'ISREF'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ISTEXT'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::IS_TEXT',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'JIS'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'KURT'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::KURT',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'LARGE'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LARGE',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'LCM'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LCM',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'LEFT'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LEFT',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'LEFTB'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LEFT',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'LEN'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::STRINGLENGTH',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'LENB'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::STRINGLENGTH',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'LINEST'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LINEST',
                                                                                                 'argumentCount'        =>      '1-4'
                                                                                                ),
                                'LN'                                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'log',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'LOG'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LOG_BASE',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'LOG10'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'log10',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'LOGEST'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LOGEST',
                                                                                                 'argumentCount'        =>      '1-4'
                                                                                                ),
                                'LOGINV'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LOGINV',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'LOGNORMDIST'                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LOGNORMDIST',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'LOOKUP'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LOOKUP',
                                                                                                 'argumentCount'        =>      '2,3'
                                                                                                ),
                                'LOWER'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LOWERCASE',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'MATCH'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MATCH',
                                                                                                 'argumentCount'        =>      '2,3'
                                                                                                ),
                                'MAX'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MAX',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'MAXA'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MAXA',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'MDETERM'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MDETERM',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'MDURATION'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '5,6'
                                                                                                ),
                                'MEDIAN'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MEDIAN',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'MID'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MID',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'MIDB'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MID',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'MIN'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MIN',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'MINA'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MINA',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'MINUTE'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MINUTEOFHOUR',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'MINVERSE'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MINVERSE',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'MIRR'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'MMULT'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MMULT',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'MOD'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MOD',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'MODE'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MODE',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'MONTH'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MONTHOFYEAR',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'MROUND'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MROUND',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'MULTINOMIAL'                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::MULTINOMIAL',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'N'                                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'NA'                                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::NA',
                                                                                                 'argumentCount'        =>      '0'
                                                                                                ),
                                'NEGBINOMDIST'                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::NEGBINOMDIST',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'NETWORKDAYS'                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::NETWORKDAYS',
                                                                                                 'argumentCount'        =>      '2+'
                                                                                                ),
                                'NOMINAL'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::NOMINAL',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'NORMDIST'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::NORMDIST',
                                                                                                 'argumentCount'        =>      '4'
                                                                                                ),
                                'NORMINV'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::NORMINV',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'NORMSDIST'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::NORMSDIST',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'NORMSINV'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::NORMSINV',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'NOT'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LOGICAL_NOT',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'NOW'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DATETIMENOW',
                                                                                                 'argumentCount'        =>      '0'
                                                                                                ),
                                'NPER'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::NPER',
                                                                                                 'argumentCount'        =>      '3-5'
                                                                                                ),
                                'NPV'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::NPV',
                                                                                                 'argumentCount'        =>      '2+'
                                                                                                ),
                                'OCT2BIN'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::OCTTOBIN',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'OCT2DEC'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::OCTTODEC',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'OCT2HEX'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::OCTTOHEX',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'ODD'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::ODD',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'ODDFPRICE'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '8,9'
                                                                                                ),
                                'ODDFYIELD'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '8,9'
                                                                                                ),
                                'ODDLPRICE'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '7,8'
                                                                                                ),
                                'ODDLYIELD'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '7,8'
                                                                                                ),
                                'OFFSET'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::OFFSET',
                                                                                                 'argumentCount'        =>      '3,5'
                                                                                                ),
                                'OR'                                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LOGICAL_OR',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'PEARSON'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::CORREL',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'PERCENTILE'                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::PERCENTILE',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'PERCENTRANK'                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::PERCENTRANK',
                                                                                                 'argumentCount'        =>      '2,3'
                                                                                                ),
                                'PERMUT'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::PERMUT',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'PHONETIC'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'PI'                                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'pi',
                                                                                                 'argumentCount'        =>      '0'
                                                                                                ),
                                'PMT'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::PMT',
                                                                                                 'argumentCount'        =>      '3-5'
                                                                                                ),
                                'POISSON'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::POISSON',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'POWER'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::POWER',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'PPMT'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::PPMT',
                                                                                                 'argumentCount'        =>      '4-6'
                                                                                                ),
                                'PRICE'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '6,7'
                                                                                                ),
                                'PRICEDISC'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::PRICEDISC',
                                                                                                 'argumentCount'        =>      '4,5'
                                                                                                ),
                                'PRICEMAT'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::PRICEMAT',
                                                                                                 'argumentCount'        =>      '5,6'
                                                                                                ),
                                'PROB'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3,4'
                                                                                                ),
                                'PRODUCT'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::PRODUCT',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'PROPER'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::PROPERCASE',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'PV'                                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::PV',
                                                                                                 'argumentCount'        =>      '3-5'
                                                                                                ),
                                'QUARTILE'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::QUARTILE',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'QUOTIENT'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::QUOTIENT',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'RADIANS'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'deg2rad',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'RAND'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::RAND',
                                                                                                 'argumentCount'        =>      '0'
                                                                                                ),
                                'RANDBETWEEN'                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::RAND',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'RANK'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::RANK',
                                                                                                 'argumentCount'        =>      '2,3'
                                                                                                ),
                                'RATE'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3-6'
                                                                                                ),
                                'RECEIVED'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::RECEIVED',
                                                                                                 'argumentCount'        =>      '4-5'
                                                                                                ),
                                'REPLACE'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::REPLACE',
                                                                                                 'argumentCount'        =>      '4'
                                                                                                ),
                                'REPLACEB'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::REPLACE',
                                                                                                 'argumentCount'        =>      '4'
                                                                                                ),
                                'REPT'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'str_repeat',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'RIGHT'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::RIGHT',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'RIGHTB'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::RIGHT',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'ROMAN'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::ROMAN',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'ROUND'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'round',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'ROUNDDOWN'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::ROUNDDOWN',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'ROUNDUP'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::ROUNDUP',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'ROW'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::ROW',
                                                                                                 'argumentCount'        =>      '-1'
                                                                                                ),
                                'ROWS'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'RSQ'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::RSQ',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'RTD'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'SEARCH'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SEARCHINSENSITIVE',
                                                                                                 'argumentCount'        =>      '2,3'
                                                                                                ),
                                'SEARCHB'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SEARCHINSENSITIVE',
                                                                                                 'argumentCount'        =>      '2,3'
                                                                                                ),
                                'SECOND'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SECONDOFMINUTE',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'SERIESSUM'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SERIESSUM',
                                                                                                 'argumentCount'        =>      '4'
                                                                                                ),
                                'SIGN'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SIGN',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'SIN'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'sin',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'SINH'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'sinh',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'SKEW'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SKEW',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'SLN'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SLN',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'SLOPE'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SLOPE',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'SMALL'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SMALL',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'SQRT'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'sqrt',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'SQRTPI'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SQRTPI',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'STANDARDIZE'                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::STANDARDIZE',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'STDEV'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::STDEV',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'STDEVA'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::STDEVA',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'STDEVP'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::STDEVP',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'STDEVPA'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::STDEVPA',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'STEYX'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::STEYX',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'SUBSTITUTE'                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3,4'
                                                                                                ),
                                'SUBTOTAL'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SUBTOTAL',
                                                                                                 'argumentCount'        =>      '2+'
                                                                                                ),
                                'SUM'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SUM',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'SUMIF'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SUMIF',
                                                                                                 'argumentCount'        =>      '2,3'
                                                                                                ),
                                'SUMIFS'                                => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                ),
                                'SUMPRODUCT'                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'SUMSQ'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SUMSQ',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'SUMX2MY2'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SUMX2MY2',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'SUMX2PY2'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SUMX2PY2',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'SUMXMY2'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SUMXMY2',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'SYD'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::SYD',
                                                                                                 'argumentCount'        =>      '4'
                                                                                                ),
                                'T'                                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::RETURNSTRING',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'TAN'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'tan',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'TANH'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'tanh',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'TBILLEQ'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::TBILLEQ',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'TBILLPRICE'                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::TBILLPRICE',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'TBILLYIELD'                    => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::TBILLYIELD',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'TDIST'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::TDIST',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'TEXT'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::TEXTFORMAT',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'TIME'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::TIME',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'TIMEVALUE'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::TIMEVALUE',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'TINV'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::TINV',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'TODAY'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DATENOW',
                                                                                                 'argumentCount'        =>      '0'
                                                                                                ),
                                'TRANSPOSE'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::TRANSPOSE',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'TREND'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::TREND',
                                                                                                 'argumentCount'        =>      '1-4'
                                                                                                ),
                                'TRIM'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::TRIMSPACES',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'TRIMMEAN'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::TRIMMEAN',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'TRUE'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::LOGICAL_TRUE',
                                                                                                 'argumentCount'        =>      '0'
                                                                                                ),
                                'TRUNC'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::TRUNC',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'TTEST'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '4'
                                                                                                ),
                                'TYPE'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'UPPER'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::UPPERCASE',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'USDOLLAR'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '2'
                                                                                                ),
                                'VALUE'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'VAR'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::VARFunc',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'VARA'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::VARA',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'VARP'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::VARP',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'VARPA'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::VARPA',
                                                                                                 'argumentCount'        =>      '1+'
                                                                                                ),
                                'VDB'                                   => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '5-7'
                                                                                                ),
                                'VERSION'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::VERSION',
                                                                                                 'argumentCount'        =>      '0'
                                                                                                ),
                                'VLOOKUP'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::VLOOKUP',
                                                                                                 'argumentCount'        =>      '3,4'
                                                                                                ),
                                'WEEKDAY'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DAYOFWEEK',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'WEEKNUM'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::WEEKOFYEAR',
                                                                                                 'argumentCount'        =>      '1,2'
                                                                                                ),
                                'WEIBULL'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::WEIBULL',
                                                                                                 'argumentCount'        =>      '4'
                                                                                                ),
                                'WORKDAY'                               => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::WORKDAY',
                                                                                                 'argumentCount'        =>      '2+'
                                                                                                ),
                                'XIRR'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '2,3'
                                                                                                ),
                                'XNPV'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '3'
                                                                                                ),
                                'YEAR'                                  => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::YEAR',
                                                                                                 'argumentCount'        =>      '1'
                                                                                                ),
                                'YEARFRAC'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::YEARFRAC',
                                                                                                 'argumentCount'        =>      '2,3'
                                                                                                ),
                                'YIELD'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '6,7'
                                                                                                ),
                                'YIELDDISC'                             => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::YIELDDISC',
                                                                                                 'argumentCount'        =>      '4,5'
                                                                                                ),
                                'YIELDMAT'                              => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::YIELDMAT',
                                                                                                 'argumentCount'        =>      '5,6'
                                                                                                ),
                                'ZTEST'                                 => array('category'                     =>      PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                                                                                                 'functionCall'         =>      'PHPExcel_Calculation_Functions::DUMMY',
                                                                                                 'argumentCount'        =>      '?'
                                                                                                )
                        );


        //      Internal functions used for special control purposes
        private $_controlFunctions = array(
                                'MKMATRIX'      => array('argumentCount'        =>      '*',
                                                                         'functionCall'         =>      array('self','_mkMatrix')
                                                                        )
                        );




        public static function getInstance() {
                if (!isset(self::$_instance) || is_null(self::$_instance)) {
                        self::$_instance = new PHPExcel_Calculation();
                }

                return self::$_instance;
        }       //      function getInstance()


        public final function __clone() {
                throw new Exception ( 'Cloning a Singleton is not allowed!' );
        }       //      function __clone()


        public static function setArrayReturnType($returnType) {
                if (($returnType == self::RETURN_ARRAY_AS_VALUE) ||
                        ($returnType == self::RETURN_ARRAY_AS_ARRAY)) {
                        self::$returnArrayAsType = $returnType;
                        return True;
                }
                return False;
        }       //      function setExcelCalendar()


        public static function getArrayReturnType() {
                return self::$returnArrayAsType;
        }       //      function getExcelCalendar()


        public function getCalculationCacheEnabled() {
                return $this->_calculationCacheEnabled;
        }       //      function getCalculationCacheEnabled()


        public function setCalculationCacheEnabled($pValue = true) {
                $this->_calculationCacheEnabled = $pValue;
                $this->clearCalculationCache();
        }       //      function setCalculationCacheEnabled()


        public function enableCalculationCache() {
                $this->setCalculationCacheEnabled(true);
        }       //      function enableCalculationCache()


        public function disableCalculationCache() {
                $this->setCalculationCacheEnabled(false);
        }       //      function disableCalculationCache()


        public function clearCalculationCache() {
                $this->_calculationCache = array();
        }       //      function clearCalculationCache()


        public function getCalculationCacheExpirationTime() {
                return $this->_calculationCacheExpirationTime;
        }       //      getCalculationCacheExpirationTime()


        public function setCalculationCacheExpirationTime($pValue = 0.01) {
                $this->_calculationCacheExpirationTime = $pValue;
        }       //      function setCalculationCacheExpirationTime()




        public static function _wrapResult($value) {
                if (is_string($value)) {
                        //      Error values cannot be "wrapped"
                        if (preg_match('/^'.self::CALCULATION_REGEXP_ERROR.'$/i', $value, $match)) {
                                //      Return Excel errors "as is"
                                return $value;
                        }
                        //      Return strings wrapped in quotes
                        return '"'.$value.'"';
                //      Convert numeric errors to NaN error
                } else if((is_float($value)) && ((is_nan($value)) || (is_infinite($value)))) {
                        return PHPExcel_Calculation_Functions::NaN();
                }

                return $value;
        }       //      function _wrapResult()


        public static function _unwrapResult($value) {
                if (is_string($value)) {
                        if ((strlen($value) > 0) && ($value{0} == '"') && (substr($value,-1) == '"')) {
                                return substr($value,1,-1);
                        }
                //      Convert numeric errors to NaN error
                } else if((is_float($value)) && ((is_nan($value)) || (is_infinite($value)))) {
                        return PHPExcel_Calculation_Functions::NaN();
                }
                return $value;
        }       //      function _unwrapResult()




        public function calculate(PHPExcel_Cell $pCell = null) {
                return $this->calculateCellValue($pCell);
        }       //      function calculate()


        public function calculateCellValue(PHPExcel_Cell $pCell = null, $resetLog = true) {
                if ($resetLog) {
                        //      Initialise the logging settings if requested
                        $this->formulaError = null;
                        $this->debugLog = array();
                        $this->debugLogStack = array();
                }

                //      Read the formula from the cell
                if (is_null($pCell)) {
                        return null;
                }
                $formula = $pCell->getValue();
                $cellID = $pCell->getCoordinate();

                //      Execute the calculation for the cell formula
                return self::_unwrapResult($this->_calculateFormulaValue($formula, $cellID, $pCell));
        }       //      function calculateCellValue(


        public function parseFormula($formula) {
                //      Basic validation that this is indeed a formula
                //      We return an empty array if not
                $formula = trim($formula);
                if ($formula{0} != '=') return array();
                $formula = trim(substr($formula,1));
                $formulaLength = strlen($formula);
                if ($formulaLength < 1) return array();

                //      Parse the formula and return the token stack
                return $this->_parseFormula($formula);
        }       //      function parseFormula()


        public function calculateFormula($formula, $cellID=null, PHPExcel_Cell $pCell = null) {
                //      Initialise the logging settings
                $this->formulaError = null;
                $this->debugLog = array();
                $this->debugLogStack = array();

                //      Disable calculation cacheing because it only applies to cell calculations, not straight formulae
                //      But don't actually flush any cache
                $resetCache = $this->getCalculationCacheEnabled();
                $this->_calculationCacheEnabled = false;
                //      Execute the calculation
                $result = self::_unwrapResult($this->_calculateFormulaValue($formula, $cellID, $pCell));
                //      Reset calculation cacheing to its previous state
                $this->_calculationCacheEnabled = $resetCache;

                return $result;
        }       //      function calculateFormula()


        public function _calculateFormulaValue($formula, $cellID=null, PHPExcel_Cell $pCell = null) {
//              echo '<b>'.$cellID.'</b><br />';
                $cellValue = '';

                //      Basic validation that this is indeed a formula
                //      We simply return the "cell value" (formula) if not
                $formula = trim($formula);
                if ($formula{0} != '=') return self::_wrapResult($formula);
                $formula = trim(substr($formula,1));
                $formulaLength = strlen($formula);
                if ($formulaLength < 1) return self::_wrapResult($formula);

                // Is calculation cacheing enabled?
                if (!is_null($cellID)) {
                        if ($this->_calculationCacheEnabled) {
                                // Is the value present in calculation cache?
//                              echo 'Testing cache value<br />';
                                if (isset($this->_calculationCache[$pCell->getParent()->getTitle()][$pCell->getCoordinate()])) {
//                                      echo 'Value is in cache<br />';
                                        $this->_writeDebug($cellID,'Testing cache value');
                                        //      Is cache still valid?
                                        if ((time() + microtime()) - $this->_calculationCache[$pCell->getParent()->getTitle()][$pCell->getCoordinate()]['time'] < $this->_calculationCacheExpirationTime) {
//                                              echo 'Cache time is still valid<br />';
                                                $this->_writeDebug($cellID,'Retrieving value from cache');
                                                // Return the cached result
                                                $returnValue = $this->_calculationCache[$pCell->getParent()->getTitle()][$pCell->getCoordinate()]['data'];
//                                              echo 'Retrieving data value of '.$returnValue.' for '.$pCell->getCoordinate().' from cache<br />';
                                                if (is_array($returnValue)) {
                                                        return array_shift(PHPExcel_Calculation_Functions::flattenArray($returnValue));
                                                }
                                                return $returnValue;
                                        } else {
//                                              echo 'Cache has expired<br />';
                                                $this->_writeDebug($cellID,'Cache value has expired');
                                                //      Clear the cache if it's no longer valid
                                                unset($this->_calculationCache[$pCell->getParent()->getTitle()][$pCell->getCoordinate()]);
                                        }
                                }
                        }
                }

                $this->debugLogStack[] = $cellID;
                //      Parse the formula onto the token stack and calculate the value
                $cellValue = $this->_processTokenStack($this->_parseFormula($formula), $cellID, $pCell);
                array_pop($this->debugLogStack);

                // Save to calculation cache
                if (!is_null($cellID)) {
                        if ($this->_calculationCacheEnabled) {
                                $this->_calculationCache[$pCell->getParent()->getTitle()][$pCell->getCoordinate()]['time'] = (time() + microtime());
                                $this->_calculationCache[$pCell->getParent()->getTitle()][$pCell->getCoordinate()]['data'] = $cellValue;
                        }
                }

                //      Return the calculated value
                if (is_array($cellValue)) {
                        $cellValue = array_shift(PHPExcel_Calculation_Functions::flattenArray($cellValue));
                }

                return $cellValue;
        }       //      function _calculateFormulaValue()


        private static function _checkMatrixOperands(&$operand1,&$operand2,$resize = 1) {
                //      Examine each of the two operands, and turn them into an array if they aren't one already
                //      Note that this function should only be called if one or both of the operand is already an array
                if (!is_array($operand1)) {
                        list($matrixRows,$matrixColumns) = self::_getMatrixDimensions($operand2);
                        $operand1 = array_fill(0,$matrixRows,array_fill(0,$matrixColumns,$operand1));
                        $resize = 0;
                } elseif (!is_array($operand2)) {
                        list($matrixRows,$matrixColumns) = self::_getMatrixDimensions($operand1);
                        $operand2 = array_fill(0,$matrixRows,array_fill(0,$matrixColumns,$operand2));
                        $resize = 0;
                }

                //      Given two matrices of (potentially) unequal size, convert the smaller in each dimension to match the larger
                if ($resize == 2) {
                        self::_resizeMatricesExtend($operand1,$operand2);
                } elseif ($resize == 1) {
                        self::_resizeMatricesShrink($operand1,$operand2);
                }
        }       //      function _checkMatrixOperands()


        private static function _reindexMatrixDimensions($matrix) {
                foreach($matrix as $rowKey => $rowValue) {
                        $matrix[$rowKey] = array_values($rowValue);
                }
                return array_values($matrix);
        }       //      function _getMatrixDimensions()


        private static function _getMatrixDimensions(&$matrix) {
                $matrixRows = count($matrix);
                $matrixColumns = 0;
                foreach($matrix as $rowKey => $rowValue) {
                        $colCount = count($rowValue);
                        if ($colCount > $matrixColumns) {
                                $matrixColumns = $colCount;
                        }
                        $matrix[$rowKey] = array_values($rowValue);
                }
                $matrix = array_values($matrix);
                return array($matrixRows,$matrixColumns);
        }       //      function _getMatrixDimensions()


        private static function _resizeMatricesShrink(&$matrix1,&$matrix2) {
                list($matrix1Rows,$matrix1Columns) = self::_getMatrixDimensions($matrix1);
                list($matrix2Rows,$matrix2Columns) = self::_getMatrixDimensions($matrix2);

                if (($matrix2Columns < $matrix1Columns) || ($matrix2Rows < $matrix1Rows)) {
                        if ($matrix2Columns < $matrix1Columns) {
                                for ($i = 0; $i < $matrix1Rows; ++$i) {
                                        for ($j = $matrix2Columns; $j < $matrix1Columns; ++$j) {
                                                unset($matrix1[$i][$j]);
                                        }
                                }
                        }
                        if ($matrix2Rows < $matrix1Rows) {
                                for ($i = $matrix2Rows; $i < $matrix1Rows; ++$i) {
                                        unset($matrix1[$i]);
                                }
                        }
                }

                if (($matrix1Columns < $matrix2Columns) || ($matrix1Rows < $matrix2Rows)) {
                        if ($matrix1Columns < $matrix2Columns) {
                                for ($i = 0; $i < $matrix2Rows; ++$i) {
                                        for ($j = $matrix1Columns; $j < $matrix2Columns; ++$j) {
                                                unset($matrix2[$i][$j]);
                                        }
                                }
                        }
                        if ($matrix1Rows < $matrix2Rows) {
                                for ($i = $matrix1Rows; $i < $matrix2Rows; ++$i) {
                                        unset($matrix2[$i]);
                                }
                        }
                }
        }       //      function _resizeMatricesShrink()


        private static function _resizeMatricesExtend(&$matrix1,&$matrix2) {
                list($matrix1Rows,$matrix1Columns) = self::_getMatrixDimensions($matrix1);
                list($matrix2Rows,$matrix2Columns) = self::_getMatrixDimensions($matrix2);

                if (($matrix2Columns < $matrix1Columns) || ($matrix2Rows < $matrix1Rows)) {
                        if ($matrix2Columns < $matrix1Columns) {
                                for ($i = 0; $i < $matrix2Rows; ++$i) {
                                        $x = $matrix2[$i][$matrix2Columns-1];
                                        for ($j = $matrix2Columns; $j < $matrix1Columns; ++$j) {
                                                $matrix2[$i][$j] = $x;
                                        }
                                }
                        }
                        if ($matrix2Rows < $matrix1Rows) {
                                $x = $matrix2[$matrix2Rows-1];
                                for ($i = 0; $i < $matrix1Rows; ++$i) {
                                        $matrix2[$i] = $x;
                                }
                        }
                }

                if (($matrix1Columns < $matrix2Columns) || ($matrix1Rows < $matrix2Rows)) {
                        if ($matrix1Columns < $matrix2Columns) {
                                for ($i = 0; $i < $matrix1Rows; ++$i) {
                                        $x = $matrix1[$i][$matrix1Columns-1];
                                        for ($j = $matrix1Columns; $j < $matrix2Columns; ++$j) {
                                                $matrix1[$i][$j] = $x;
                                        }
                                }
                        }
                        if ($matrix1Rows < $matrix2Rows) {
                                $x = $matrix1[$matrix1Rows-1];
                                for ($i = 0; $i < $matrix2Rows; ++$i) {
                                        $matrix1[$i] = $x;
                                }
                        }
                }
        }       //      function _resizeMatricesExtend()


        private static function _showValue($value) {
                if (is_array($value)) {
                        $retVal = '';
                        $i = 0;
                        foreach($value as $row) {
                                if (is_array($row)) {
                                        if ($i > 0) { $retVal .= '; '; }
                                        $j = 0;
                                        foreach($row as $column) {
                                                if ($j > 0) { $retVal .= ', '; }
                                                $retVal .= $column;
                                                ++$j;
                                        }
                                } else {
                                        if ($i > 0) { $retVal .= ', '; }
                                        $retVal .= $row;
                                }
                                ++$i;
                        }
                        return '{ '.$retVal.' }';
                } elseif(is_bool($value)) {
                        return ($value) ? 'TRUE' : 'FALSE';
                }

                return $value;
        }       //      function _showValue()


        private static function _showTypeDetails($value) {
                switch (gettype($value)) {
                        case 'double'   :
                        case 'float'    :
                                $typeString = 'a floating point number';
                                break;
                        case 'integer'  :
                                $typeString = 'an integer number';
                                break;
                        case 'boolean'  :
                                $typeString = 'a boolean';
                                break;
                        case 'array'    :
                                $typeString = 'a matrix';
                                break;
                        case 'string'   :
                                if ($value == '') {
                                        return 'an empty string';
                                } elseif ($value{0} == '#') {
                                        return 'a '.$value.' error';
                                } else {
                                        $typeString = 'a string';
                                }
                                break;
                        case 'NULL'     :
                                return 'a null value';
                }
                return $typeString.' with a value of '.self::_showValue($value);
        }       //      function _showTypeDetails()


        private static function _convertMatrixReferences($formula) {
                static $matrixReplaceFrom = array('{',';','}');
                static $matrixReplaceTo = array('MKMATRIX(MKMATRIX(','),MKMATRIX(','))');

                //      Convert any Excel matrix references to the MKMATRIX() function
                if (strpos($formula,'{') !== false) {
                        //      Open and Closed counts used for trapping mismatched braces in the formula
                        $openCount = $closeCount = 0;
                        //      If there is the possibility of braces within a quoted string, then we don't treat those as matrix indicators
                        if (strpos($formula,'"') !== false) {
                                //      So instead we skip replacing in any quoted strings by only replacing in every other array element after we've exploded
                                //              the formula
                                $temp = explode('"',$formula);
                                $i = 0;
                                foreach($temp as &$value) {
                                        //      Only count/replace in alternate array entries
                                        if (($i++ % 2) == 0) {
                                                $openCount += substr_count($value,'{');
                                                $closeCount += substr_count($value,'}');
                                                $value = str_replace($matrixReplaceFrom,$matrixReplaceTo,$value);
                                        }
                                }
                                unset($value);
                                //      Then rebuild the formula string
                                $formula = implode('"',$temp);
                        } else {
                                //      If there's no quoted strings, then we do a simple count/replace
                                $openCount += substr_count($formula,'{');
                                $closeCount += substr_count($formula,'}');
                                $formula = str_replace($matrixReplaceFrom,$matrixReplaceTo,$formula);
                        }
                        //      Trap for mismatched braces and trigger an appropriate error
                        if ($openCount < $closeCount) {
                                if ($openCount > 0) {
                                        return $this->_raiseFormulaError("Formula Error: Mismatched matrix braces '}'");
                                } else {
                                        return $this->_raiseFormulaError("Formula Error: Unexpected '}' encountered");
                                }
                        } elseif ($openCount > $closeCount) {
                                if ($closeCount > 0) {
                                        return $this->_raiseFormulaError("Formula Error: Mismatched matrix braces '{'");
                                } else {
                                        return $this->_raiseFormulaError("Formula Error: Unexpected '{' encountered");
                                }
                        }
                }

                return $formula;
        }       //      function _convertMatrixReferences()


        private static function _mkMatrix() {
                return func_get_args();
        }       //      function _mkMatrix()


        // Convert infix to postfix notation
        private function _parseFormula($formula) {
                if (($formula = self::_convertMatrixReferences(trim($formula))) === false) {
                        return false;
                }

                //      Binary Operators
                //      These operators always work on two values
                //      Array key is the operator, the value indicates whether this is a left or right associative operator
                $operatorAssociativity  = array('^' => 0,                                                                                                                       //      Exponentiation
                                                                                '*' => 0, '/' => 0,                                                                                             //      Multiplication and Division
                                                                                '+' => 0, '-' => 0,                                                                                                     //      Addition and Subtraction
                                                                                '&' => 1,                                                                                                                       //      Concatenation
                                                                                '>' => 0, '<' => 0, '=' => 0, '>=' => 0, '<=' => 0, '<>' => 0           //      Comparison
                                                                          );
                //      Comparison (Boolean) Operators
                //      These operators work on two values, but always return a boolean result
                $comparisonOperators    = array('>', '<', '=', '>=', '<=', '<>');

                //      Operator Precedence
                //      This list includes all valid operators, whether binary (including boolean) or unary (such as %)
                //      Array key is the operator, the value is its precedence
                $operatorPrecedence     = array('_' => 6,                                                                                                                               //      Negation
                                                                        '%' => 5,                                                                                                                               //      Percentage
                                                                        '^' => 4,                                                                                                                               //      Exponentiation
                                                                        '*' => 3, '/' => 3,                                                                                                     //      Multiplication and Division
                                                                        '+' => 2, '-' => 2,                                                                                                             //      Addition and Subtraction
                                                                        '&' => 1,                                                                                                                               //      Concatenation
                                                                        '>' => 0, '<' => 0, '=' => 0, '>=' => 0, '<=' => 0, '<>' => 0                   //      Comparison
                                                                   );

                $regexpMatchString = '/^('.self::CALCULATION_REGEXP_FUNCTION.
                                                           '|'.self::CALCULATION_REGEXP_NUMBER.
                                                           '|'.self::CALCULATION_REGEXP_STRING.
                                                           '|'.self::CALCULATION_REGEXP_OPENBRACE.
                                                           '|'.self::CALCULATION_REGEXP_CELLREF.
                                                           '|'.self::CALCULATION_REGEXP_NAMEDRANGE.
                                                         ')/i';

                //      Start with initialisation
                $index = 0;
                $stack = new PHPExcel_Token_Stack;
                $output = array();
                $expectingOperator = false;                                     //      We use this test in syntax-checking the expression to determine when a
                                                                                                        //              - is a negation or + is a positive operator rather than an operation
                $expectingOperand = false;                                      //      We use this test in syntax-checking the expression to determine whether an operand
                                                                                                        //              should be null in a function call
                //      The guts of the lexical parser
                //      Loop through the formula extracting each operator and operand in turn
                while(True) {
//                      echo 'Assessing Expression <b>'.substr($formula, $index).'</b><br />';
                        $opCharacter = $formula{$index};        //      Get the first character of the value at the current index position
//                      echo 'Initial character of expression block is '.$opCharacter.'<br />';
                        if ((in_array($opCharacter, $comparisonOperators)) && (strlen($formula) > $index) && (in_array($formula{$index+1}, $comparisonOperators))) {
                                $opCharacter .= $formula{++$index};
//                              echo 'Initial character of expression block is comparison operator '.$opCharacter.'<br />';
                        }

                        //      Find out if we're currently at the beginning of a number, variable, cell reference, function, parenthesis or operand
                        $isOperandOrFunction = preg_match($regexpMatchString, substr($formula, $index), $match);
//                      echo '$isOperandOrFunction is '.(($isOperandOrFunction)?'True':'False').'<br />';

                        if ($opCharacter == '-' && !$expectingOperator) {                               //      Is it a negation instead of a minus?
//                              echo 'Element is a Negation operator<br />';
                                $stack->push('_');                                                                                      //      Put a negation on the stack
                                ++$index;                                                                                                       //              and drop the negation symbol
                        } elseif ($opCharacter == '%' && $expectingOperator) {
//                              echo 'Element is a Percentage operator<br />';
                                $stack->push('%');                                                                                      //      Put a percentage on the stack
                                ++$index;
                        } elseif ($opCharacter == '+' && !$expectingOperator) {                 //      Positive (rather than plus) can be discarded?
//                              echo 'Element is a Positive number, not Plus operator<br />';
                                ++$index;                                                                                                       //      Drop the redundant plus symbol
                        } elseif (($opCharacter == '_') && (!$isOperandOrFunction)) {   //      We have to explicitly deny an underscore, because it's legal on
                                return $this->_raiseFormulaError("Formula Error: Illegal character '_'");       //              the stack but not in the input expression
                                                                                                                                                        //      Note that _ is a valid first character in named ranges
                                                                                                                                                        //              and this will need modifying soon when we start integrating
                                                                                                                                                        //              with PHPExcel proper

                        } elseif ((in_array($opCharacter, $this->_operators) or $isOperandOrFunction) && $expectingOperator) {  //      Are we putting an operator on the stack?
//                              echo 'Element with value '.$opCharacter.' is an Operator<br />';
                                while($stack->count() > 0 &&
                                        ($o2 = $stack->last()) &&
                                        in_array($o2, $this->_operators) &&
                                        ($operatorAssociativity[$opCharacter] ? $operatorPrecedence[$opCharacter] < $operatorPrecedence[$o2] : $operatorPrecedence[$opCharacter] <= $operatorPrecedence[$o2])) {
                                        $output[] = $stack->pop();                                                              //      Swap operands and higher precedence operators from the stack to the output
                                }
                                $stack->push($opCharacter);     //      Finally put our current operator onto the stack
                                ++$index;
                                $expectingOperator = false;

                        } elseif ($opCharacter == ')' && $expectingOperator) {                  //      Are we expecting to close a parenthesis?
//                              echo 'Element is a Closing bracket<br />';
                                $expectingOperand = false;
                                while (($o2 = $stack->pop()) != '(') {                                          //      Pop off the stack back to the last (
                                        if (is_null($o2)) return $this->_raiseFormulaError('Formula Error: Unexpected closing brace ")"');
                                        else $output[] = $o2;
                                }
                                if (preg_match('/^'.self::CALCULATION_REGEXP_FUNCTION.'$/i', $stack->last(2), $matches)) {      //      Did this parenthesis just close a function?
                                        $functionName = $matches[1];                                                                            //      Get the function name
//                                      echo 'Closed Function is '.$functionName.'<br />';
                                        $argumentCount = $stack->pop();         //      See how many arguments there were (argument count is the next value stored on the stack)
//                                      if ($argumentCount == 0) {
//                                              echo 'With no arguments<br />';
//                                      } elseif ($argumentCount == 1) {
//                                              echo 'With 1 argument<br />';
//                                      } else {
//                                              echo 'With '.$argumentCount.' arguments<br />';
//                                      }
                                        $output[] = $argumentCount;                     //      Dump the argument count on the output
                                        $output[] = $stack->pop();                      //      Pop the function and push onto the output
                                        if (array_key_exists($functionName, $this->_controlFunctions)) {
//                                              echo 'Built-in function '.$functionName.'<br />';
                                                $expectedArgumentCount = $this->_controlFunctions[$functionName]['argumentCount'];
                                                $functionCall = $this->_controlFunctions[$functionName]['functionCall'];
                                        } elseif (array_key_exists($functionName, $this->_PHPExcelFunctions)) {
//                                              echo 'PHPExcel function '.$functionName.'<br />';
                                                $expectedArgumentCount = $this->_PHPExcelFunctions[$functionName]['argumentCount'];
                                                $functionCall = $this->_PHPExcelFunctions[$functionName]['functionCall'];
                                        } else {        // did we somehow push a non-function on the stack? this should never happen
                                                return $this->_raiseFormulaError("Formula Error: Internal error, non-function on stack");
                                        }
                                        //      Check the argument count
                                        $argumentCountError = False;
                                        if (is_numeric($expectedArgumentCount)) {
                                                if ($expectedArgumentCount < 0) {
//                                                      echo '$expectedArgumentCount is between 0 and '.abs($expectedArgumentCount).'<br />';
                                                        if ($argumentCount > abs($expectedArgumentCount)) {
                                                                $argumentCountError = True;
                                                                $expectedArgumentCountString = 'no more than '.abs($expectedArgumentCount);
                                                        }
                                                } else {
//                                                      echo '$expectedArgumentCount is numeric '.$expectedArgumentCount.'<br />';
                                                        if ($argumentCount != $expectedArgumentCount) {
                                                                $argumentCountError = True;
                                                                $expectedArgumentCountString = $expectedArgumentCount;
                                                        }
                                                }
                                        } elseif ($expectedArgumentCount != '*') {
                                                $isOperandOrFunction = preg_match('/(\d*)([-+,])(\d*)/',$expectedArgumentCount,$argMatch);
//                                              print_r($argMatch);
//                                              echo '<br />';
                                                switch ($argMatch[2]) {
                                                        case '+' :
                                                                if ($argumentCount < $argMatch[1]) {
                                                                        $argumentCountError = True;
                                                                        $expectedArgumentCountString = $argMatch[1].' or more ';
                                                                }
                                                                break;
                                                        case '-' :
                                                                if (($argumentCount < $argMatch[1]) || ($argumentCount > $argMatch[3])) {
                                                                        $argumentCountError = True;
                                                                        $expectedArgumentCountString = 'between '.$argMatch[1].' and '.$argMatch[3];
                                                                }
                                                                break;
                                                        case ',' :
                                                                if (($argumentCount != $argMatch[1]) && ($argumentCount != $argMatch[3])) {
                                                                        $argumentCountError = True;
                                                                        $expectedArgumentCountString = 'either '.$argMatch[1].' or '.$argMatch[3];
                                                                }
                                                                break;
                                                }
                                        }
                                        if ($argumentCountError) {
                                                return $this->_raiseFormulaError("Formula Error: Wrong number of arguments for $functionName() function: $argumentCount given, ".$expectedArgumentCountString." expected");
                                        }
                                }
                                ++$index;

                        } elseif ($opCharacter == ',') {                        //      Is this the comma separator for function arguments?
//                              echo 'Element is a Function argument separator<br />';
                                while (($o2 = $stack->pop()) != '(') {
                                        if (is_null($o2)) return $this->_raiseFormulaError("Formula Error: Unexpected ','");
                                        else $output[] = $o2;   // pop the argument expression stuff and push onto the output
                                }
                                //      If we've a comma when we're expecting an operand, then what we actually have is a null operand;
                                //              so push a null onto the stack
                                if (($expectingOperand) || (!$expectingOperator)) {
                                        $output[] = $this->_ExcelConstants['NULL'];
                                }
                                // make sure there was a function
                                if (!preg_match('/^'.self::CALCULATION_REGEXP_FUNCTION.'$/i', $stack->last(2), $matches))
                                        return $this->_raiseFormulaError("Formula Error: Unexpected ','");
                                $stack->push($stack->pop()+1);  // increment the argument count
                                $stack->push('(');      // put the ( back on, we'll need to pop back to it again
                                $expectingOperator = false;
                                $expectingOperand = true;
                                ++$index;

                        } elseif ($opCharacter == '(' && !$expectingOperator) {
//                              echo 'Element is an Opening Bracket<br />';
                                $stack->push('(');
                                ++$index;

                        } elseif ($isOperandOrFunction && !$expectingOperator) {        // do we now have a function/variable/number?
                                $expectingOperator = true;
                                $expectingOperand = false;
                                $val = $match[1];
                                $length = strlen($val);
//                              echo 'Element with value '.$val.' is an Operand, Variable, Constant, String, Number, Cell Reference or Function<br />';

                                if (preg_match('/^'.self::CALCULATION_REGEXP_FUNCTION.'$/i', $val, $matches)) {
                                        $val = preg_replace('/\s/','',$val);
//                                      echo 'Element '.$val.' is a Function<br />';
                                        if (array_key_exists(strtoupper($matches[1]), $this->_controlFunctions) || array_key_exists(strtoupper($matches[1]), $this->_PHPExcelFunctions)) {      // it's a func
                                                $stack->push(strtoupper($val));
                                                $ax = preg_match('/^\s*(\s*\))/i', substr($formula, $index+$length), $amatch);
                                                if ($ax) {
                                                        $stack->push(0);
                                                        $expectingOperator = true;
                                                } else {
                                                        $stack->push(1);
                                                        $expectingOperator = false;
                                                }
                                                $stack->push('(');
                                        } else {        // it's a var w/ implicit multiplication
                                                $val = $matches[1];
                                                $output[] = $val;
                                        }
                                } elseif (preg_match('/^'.self::CALCULATION_REGEXP_CELLREF.'$/i', $val, $matches)) {
//                                      echo 'Element '.$val.' is a Cell reference<br />';
//                                      Watch for this case-change when modifying to allow cell references in different worksheets...
//                                              Should only be applied to the actual cell column, not the worksheet name
//                                      $cellRef = strtoupper($val);
//                                      $output[] = $cellRef;
                                        $output[] = $val;
//                                      $expectingOperator = false;
                                } else {        // it's a variable, constant, string, number or boolean
//                                      echo 'Element is a Variable, Constant, String, Number or Boolean<br />';
                                        if ($opCharacter == '"') {
//                                              echo 'Element is a String<br />';
                                                $val = str_replace('""','"',$val);
                                        } elseif (is_numeric($val)) {
//                                              echo 'Element is a Number<br />';
                                                if ((strpos($val,'.') !== False) || (stripos($val,'e') !== False)) {
//                                                      echo 'Casting '.$val.' to float<br />';
                                                        $val = (float) $val;
                                                } else {
//                                                      echo 'Casting '.$val.' to integer<br />';
                                                        $val = (integer) $val;
                                                }
//                                      } elseif (array_key_exists(trim(strtoupper($val)), $this->_ExcelConstants)) {
//                                              $excelConstant = trim(strtoupper($val));
//                                              echo 'Element '.$val.' is an Excel Constant<br />';
//                                              $val = $this->_ExcelConstants[$excelConstant];
                                        }
                                        $output[] = $val;
                                }
                                $index += $length;

                        } elseif ($opCharacter == ')') {        // miscellaneous error checking
                                if ($expectingOperand) {
                                        $output[] = $this->_ExcelConstants['NULL'];
                                        $expectingOperand = false;
                                        $expectingOperator = True;
                                } else {
                                        return $this->_raiseFormulaError("Formula Error: Unexpected ')'");
                                }
                        } elseif (in_array($opCharacter, $this->_operators) && !$expectingOperator) {
                                return $this->_raiseFormulaError("Formula Error: Unexpected operator '$opCharacter'");
                        } else {        // I don't even want to know what you did to get here
                                return $this->_raiseFormulaError("Formula Error: An unexpected error occured");
                        }
                        //      Test for end of formula string
                        if ($index == strlen($formula)) {
                                //      Did we end with an operator?.
                                //      Only valid for the % unary operator
                                if ((in_array($opCharacter, $this->_operators)) && ($opCharacter != '%')) {
                                        return $this->_raiseFormulaError("Formula Error: Operator '$opCharacter' has no operands");
                                } else {
                                        break;
                                }
                        }
                        //      Ignore white space
                        while (substr($formula, $index, 1) == ' ') {
                                ++$index;
                        }
                }

                while (!is_null($opCharacter = $stack->pop())) {        // pop everything off the stack and push onto output
                        if ($opCharacter == '(') return $this->_raiseFormulaError("Formula Error: Expecting ')'");      // if there are any opening braces on the stack, then braces were unbalanced
                        $output[] = $opCharacter;
                }
                return $output;
        }       //      function _parseFormula()


        // evaluate postfix notation
        private function _processTokenStack($tokens, $cellID=null, PHPExcel_Cell $pCell = null) {
                if ($tokens == false) return false;

                $stack = new PHPExcel_Token_Stack;

                //      Loop through each token in turn
                foreach ($tokens as $token) {
//                      echo '<b>Token is '.$token.'</b><br />';
                        // if the token is a binary operator, pop the top two values off the stack, do the operation, and push the result back on the stack
                        if (in_array($token, $this->_binaryOperators, true)) {
//                              echo 'Token is a binary operator<br />';
                                //      We must have two operands, error if we don't
                                if (is_null($operand2 = $stack->pop())) return $this->_raiseFormulaError('Internal error - Operand value missing from stack');
                                if (is_null($operand1 = $stack->pop())) return $this->_raiseFormulaError('Internal error - Operand value missing from stack');
                                //      Log what we're doing
                                $this->_writeDebug($cellID,'Evaluating '.self::_showValue($operand1).' '.$token.' '.self::_showValue($operand2));
                                //      Process the operation in the appropriate manner
                                switch ($token) {
                                        //      Comparison (Boolean) Operators
                                        case '>'        :                       //      Greater than
                                        case '<'        :                       //      Less than
                                        case '>='       :                       //      Greater than or Equal to
                                        case '<='       :                       //      Less than or Equal to
                                        case '='        :                       //      Equality
                                        case '<>'       :                       //      Inequality
                                                $this->_executeBinaryComparisonOperation($cellID,$operand1,$operand2,$token,$stack);
                                                break;
                                        //      Binary Operators
                                        case '+'        :                       //      Addition
                                                $this->_executeNumericBinaryOperation($cellID,$operand1,$operand2,$token,'plusEquals',$stack);
                                                break;
                                        case '-'        :                       //      Subtraction
                                                $this->_executeNumericBinaryOperation($cellID,$operand1,$operand2,$token,'minusEquals',$stack);
                                                break;
                                        case '*'        :                       //      Multiplication
                                                $this->_executeNumericBinaryOperation($cellID,$operand1,$operand2,$token,'arrayTimesEquals',$stack);
                                                break;
                                        case '/'        :                       //      Division
                                                $this->_executeNumericBinaryOperation($cellID,$operand1,$operand2,$token,'arrayRightDivide',$stack);
                                                break;
                                        case '^'        :                       //      Exponential
                                                $this->_executeNumericBinaryOperation($cellID,$operand1,$operand2,$token,'power',$stack);
                                                break;
                                        case '&'        :                       //      Concatenation
                                                //      If either of the operands is a matrix, we need to treat them both as matrices
                                                //              (converting the other operand to a matrix if need be); then perform the required
                                                //              matrix operation
                                                if ((is_array($operand1)) || (is_array($operand2))) {
                                                        //      Ensure that both operands are arrays/matrices
                                                        self::_checkMatrixOperands($operand1,$operand2);
                                                        try {
                                                                //      Convert operand 1 from a PHP array to a matrix
                                                                $matrix = new Matrix($operand1);
                                                                //      Perform the required operation against the operand 1 matrix, passing in operand 2
                                                                $matrixResult = $matrix->concat($operand2);
                                                                $result = $matrixResult->getArray();
                                                        } catch (Exception $ex) {
                                                                $this->_writeDebug($cellID,'JAMA Matrix Exception: '.$ex->getMessage());
                                                                $result = '#VALUE!';
                                                        }
                                                } else {
                                                        $result = '"'.str_replace('""','"',self::_unwrapResult($operand1,'"').self::_unwrapResult($operand2,'"')).'"';
                                                }
                                                $this->_writeDebug($cellID,'Evaluation Result is '.self::_showTypeDetails($result));
                                                $stack->push($result);
                                                break;
                                }

                        // if the token is a unary operator, pop one value off the stack, do the operation, and push it back on
                        } elseif (($token === "_") || ($token === "%")) {
//                              echo 'Token is a unary operator<br />';
                                if (is_null($arg = $stack->pop())) return $this->_raiseFormulaError('Internal error - Operand value missing from stack');
                                if ($token === "_") {
//                                      echo 'Token is a negation operator<br />';
                                        $this->_writeDebug($cellID,'Evaluating Negation of '.self::_showValue($arg));
                                        $multiplier = -1;
                                } else {
//                                      echo 'Token is a percentile operator<br />';
                                        $this->_writeDebug($cellID,'Evaluating Percentile of '.self::_showValue($arg));
                                        $multiplier = 0.01;
                                }
                                if (is_array($arg)) {
                                        self::_checkMatrixOperands($arg,$multiplier);
                                        try {
                                                $matrix1 = new Matrix($arg);
                                                $matrixResult = $matrix1->arrayTimesEquals($multiplier);
                                                $result = $matrixResult->getArray();
                                        } catch (Exception $ex) {
                                                $this->_writeDebug($cellID,'JAMA Matrix Exception: '.$ex->getMessage());
                                                $result = '#VALUE!';
                                        }

                                } else {
                                        $result = $multiplier * $arg;
                                }
                                $this->_writeDebug($cellID,'Evaluation Result is '.self::_showTypeDetails($result));
                                $stack->push($result);

                        } elseif (preg_match('/^'.self::CALCULATION_REGEXP_CELLREF.'$/i', $token, $matches)) {
//                              echo 'Element '.$token.' is a Cell reference<br />';
                                if (isset($matches[8])) {
//                                      echo 'Reference is a Range of cells<br />';
                                        if (is_null($pCell)) {
//                                              We can't access the range, so return a REF error
                                                $cellValue = PHPExcel_Calculation_Functions::REF();
                                        } else {
                                                $cellRef = $matches[6].$matches[7].':'.$matches[9].$matches[10];
                                                if ($matches[2] > '') {
//                                                      echo '$cellRef='.$cellRef.' in worksheet '.$matches[2].'<br />';
                                                        $this->_writeDebug($cellID,'Evaluating Cell Range '.$cellRef.' in worksheet '.$matches[2]);
                                                        $cellValue = $this->extractCellRange($cellRef, $pCell->getParent()->getParent()->getSheetByName($matches[2]), false);
                                                        $this->_writeDebug($cellID,'Evaluation Result for cells '.$cellRef.' in worksheet '.$matches[2].' is '.self::_showTypeDetails($cellValue));
                                                } else {
//                                                      echo '$cellRef='.$cellRef.' in current worksheet<br />';
                                                        $this->_writeDebug($cellID,'Evaluating Cell Range '.$cellRef.' in current worksheet');
                                                        $cellValue = $this->extractCellRange($cellRef, $pCell->getParent(), false);
                                                        $this->_writeDebug($cellID,'Evaluation Result for cells '.$cellRef.' is '.self::_showTypeDetails($cellValue));
                                                }
                                        }
                                } else {
//                                      echo 'Reference is a single Cell<br />';
                                        if (is_null($pCell)) {
//                                              We can't access the cell, so return a REF error
                                                $cellValue = PHPExcel_Calculation_Functions::REF();
                                        } else {
                                                $cellRef = $matches[6].$matches[7];
                                                if ($matches[2] > '') {
//                                                      echo '$cellRef='.$cellRef.' in worksheet '.$matches[2].'<br />';
                                                        $this->_writeDebug($cellID,'Evaluating Cell '.$cellRef.' in worksheet '.$matches[2]);
                                                        if ($pCell->getParent()->cellExists($cellRef)) {
                                                                $cellValue = $this->extractCellRange($cellRef, $pCell->getParent()->getParent()->getSheetByName($matches[2]), false);
                                                        } else {
                                                                $cellValue = null;
                                                        }
                                                        $this->_writeDebug($cellID,'Evaluation Result for cell '.$cellRef.' in worksheet '.$matches[2].' is '.self::_showTypeDetails($cellValue));
                                                } else {
//                                                      echo '$cellRef='.$cellRef.' in current worksheet<br />';
                                                        $this->_writeDebug($cellID,'Evaluating Cell '.$cellRef.' in current worksheet');
                                                        if ($pCell->getParent()->cellExists($cellRef)) {
                                                                $cellValue = $pCell->getParent()->getCell($cellRef)->getCalculatedValue(false);
                                                        } else {
                                                                $cellValue = '';
                                                        }
                                                        $this->_writeDebug($cellID,'Evaluation Result for cell '.$cellRef.' is '.self::_showTypeDetails($cellValue));
                                                }
                                        }
                                }
                                $stack->push($cellValue);

                        // if the token is a function, pop arguments off the stack, hand them to the function, and push the result back on
                        } elseif (preg_match('/^'.self::CALCULATION_REGEXP_FUNCTION.'$/i', $token, $matches)) {
//                              echo 'Token is a function<br />';
                                $functionName = $matches[1];
                                $argCount = $stack->pop();
                                if ($functionName != 'MKMATRIX') {
                                        $this->_writeDebug($cellID,'Evaluating Function '.$functionName.'() with '.(($argCount == 0) ? 'no' : $argCount).' argument'.(($argCount == 1) ? '' : 's'));
                                }
                                if ((array_key_exists($functionName, $this->_controlFunctions)) || (array_key_exists($functionName, $this->_PHPExcelFunctions))) {      // function
                                        if (array_key_exists($functionName, $this->_controlFunctions)) {
                                                $functionCall = $this->_controlFunctions[$functionName]['functionCall'];
                                        } elseif (array_key_exists($functionName, $this->_PHPExcelFunctions)) {
                                                $functionCall = $this->_PHPExcelFunctions[$functionName]['functionCall'];
                                        }
                                        // get the arguments for this function
//                                      echo 'Function '.$functionName.' expects '.$argCount.' arguments<br />';
                                        $args = array();
                                        for ($i = $argCount; $i > 0; --$i) {
                                                $arg = $stack->pop();
//                                              if (is_null($arg)) return $this->_raiseFormulaError("internal error");
                                                $args[$i] = $arg;
                                        }
                                        //      Reverse the order of the arguments
                                        ksort($args);
//                                      echo 'Arguments are: ';
//                                      print_r($args);
//                                      echo '<br />';
                                        if ($functionName != 'MKMATRIX') {
                                                $argArrayVals = array();
                                                foreach($args as &$arg) {
                                                        $argArrayVals[] = self::_showValue($arg);
                                                        $arg = self::_unwrapResult($arg);
                                                }
                                                unset($arg);
                                                $this->_writeDebug($cellID,'Evaluating '. $functionName.'( '.implode(', ',$argArrayVals).' )');
                                        }
                                        //      Process each argument in turn, building the return value as an array
//                                      if (($argCount == 1) && (is_array($args[1])) && ($functionName != 'MKMATRIX')) {
//                                              $operand1 = $args[1];
//                                              $this->_writeDebug($cellID,'Argument is a matrix: '.self::_showValue($operand1));
//                                              $result = array();
//                                              $row = 0;
//                                              foreach($operand1 as $args) {
//                                                      if (is_array($args)) {
//                                                              foreach($args as $arg) {
//                                                                      $this->_writeDebug($cellID,'Evaluating '. $functionName.'( '.self::_showValue($arg).' )');
//                                                                      $r = call_user_func_array($functionCall,$arg);
//                                                                      $this->_writeDebug($cellID,'Evaluation Result is '.self::_showTypeDetails($r));
//                                                                      $result[$row][] = $r;
//                                                              }
//                                                              ++$row;
//                                                      } else {
//                                                              $this->_writeDebug($cellID,'Evaluating '. $functionName.'( '.self::_showValue($args).' )');
//                                                              $r = call_user_func_array($functionCall,$args);
//                                                              $this->_writeDebug($cellID,'Evaluation Result is '.self::_showTypeDetails($r));
//                                                              $result[] = $r;
//                                                      }
//                                              }
//                                      } else {
                                        //      Process the argument with the appropriate function call
                                                $result = call_user_func_array($functionCall,$args);
//                                      }
                                        if ($functionName != 'MKMATRIX') {
                                                $this->_writeDebug($cellID,'Evaluation Result is '.self::_showTypeDetails($result));
                                        }
                                        $stack->push(self::_wrapResult($result));
                                }

                        } else {
                                // if the token is a number, boolean, string or an Excel error, push it onto the stack
                                if (array_key_exists(strtoupper($token), $this->_ExcelConstants)) {
                                        $excelConstant = strtoupper($token);
//                                      echo 'Token is a PHPExcel constant: '.$excelConstant.'<br />';
                                        $stack->push($this->_ExcelConstants[$excelConstant]);
                                        $this->_writeDebug($cellID,'Evaluating Constant '.$excelConstant.' as '.self::_showTypeDetails($this->_ExcelConstants[$excelConstant]));
                                } elseif ((is_null($token)) || ($token == '') || (is_bool($token)) || (is_numeric($token)) || ($token{0} == '"') || ($token{0} == '#')) {
//                                      echo 'Token is a number, boolean, string or an Excel error<br />';
                                        $stack->push($token);
                                // if the token is a constant, push the constant value on the stack
                                } elseif (preg_match('/^'.self::CALCULATION_REGEXP_NAMEDRANGE.'$/i', $token, $matches)) {
//                                      echo 'Token is a named range<br />';
                                        $namedRange = $matches[6];
//                                      echo 'Named Range is '.$namedRange.'<br />';
                                        $this->_writeDebug($cellID,'Evaluating Named Range '.$namedRange);
                                        $cellValue = $this->extractNamedRange($namedRange, $pCell->getParent(), false);
                                        $this->_writeDebug($cellID,'Evaluation Result for named range '.$namedRange.' is '.self::_showTypeDetails($cellValue));
                                        $stack->push($cellValue);
                                } else {
                                        return $this->_raiseFormulaError("undefined variable '$token'");
                                }
                        }
                }
                // when we're out of tokens, the stack should have a single element, the final result
                if ($stack->count() != 1) return $this->_raiseFormulaError("internal error");
                $output = $stack->pop();
                if ((is_array($output)) && (self::$returnArrayAsType != self::RETURN_ARRAY_AS_ARRAY)) {
                        return array_unshift(array_unshift($output));
                }
                return $output;
        }       //      function _processTokenStack()


        private function _validateBinaryOperand($cellID,&$operand,&$stack) {
                //      Numbers, matrices and booleans can pass straight through, as they're already valid
                if (is_string($operand)) {
                        //      We only need special validations for the operand if it is a string
                        //      Start by stripping off the quotation marks we use to identify true excel string values internally
                        if ($operand > '' && $operand{0} == '"') { $operand = self::_unwrapResult($operand,'"'); }
                        //      If the string is a numeric value, we treat it as a numeric, so no further testing
                        if (!is_numeric($operand)) {
                                //      If not a numeric, test to see if the value is an Excel error, and so can't be used in normal binary operations
                                if ($operand > '' && $operand{0} == '#') {
                                        $stack->push($operand);
                                        $this->_writeDebug($cellID,'Evaluation Result is '.self::_showTypeDetails($operand));
                                        return false;
                                } else {
                                //      If not a numeric, then it's a text string, and so can't be used in mathematical binary operations
                                        $stack->push('#VALUE!');
                                        $this->_writeDebug($cellID,'Evaluation Result is a '.self::_showTypeDetails('#VALUE!'));
                                        return false;
                                }
                        }
                }

                //      return a true if the value of the operand is one that we can use in normal binary operations
                return true;
        }       //      function _validateBinaryOperand()


        private function _executeBinaryComparisonOperation($cellID,$operand1,$operand2,$operation,&$stack) {
                //      Validate the two operands

                //      If we're dealing with non-matrix operations, execute the necessary operation
                switch ($operation) {
                        //      Greater than
                        case '>':
                                $result = ($operand1 > $operand2);
                                break;
                        //      Less than
                        case '<':
                                $result = ($operand1 < $operand2);
                                break;
                        //      Equality
                        case '=':
                                $result = ($operand1 == $operand2);
                                break;
                        //      Greater than or equal
                        case '>=':
                                $result = ($operand1 >= $operand2);
                                break;
                        //      Less than or equal
                        case '<=':
                                $result = ($operand1 <= $operand2);
                                break;
                        //      Inequality
                        case '<>':
                                $result = ($operand1 != $operand2);
                                break;
                }

                //      Log the result details
                $this->_writeDebug($cellID,'Evaluation Result is '.self::_showTypeDetails($result));
                //      And push the result onto the stack
                $stack->push($result);
                return true;
        }       //      function _executeBinaryComparisonOperation()

        private function _executeNumericBinaryOperation($cellID,$operand1,$operand2,$operation,$matrixFunction,&$stack) {
                //      Validate the two operands
                if (!$this->_validateBinaryOperand($cellID,$operand1,$stack)) return false;
                if (!$this->_validateBinaryOperand($cellID,$operand2,$stack)) return false;

                //      If either of the operands is a matrix, we need to treat them both as matrices
                //              (converting the other operand to a matrix if need be); then perform the required
                //              matrix operation
                if ((is_array($operand1)) || (is_array($operand2))) {
                        //      Ensure that both operands are arrays/matrices
                        self::_checkMatrixOperands($operand1,$operand2);
                        try {
                                //      Convert operand 1 from a PHP array to a matrix
                                $matrix = new Matrix($operand1);
                                //      Perform the required operation against the operand 1 matrix, passing in operand 2
                                $matrixResult = $matrix->$matrixFunction($operand2);
                                $result = $matrixResult->getArray();
                        } catch (Exception $ex) {
                                $this->_writeDebug($cellID,'JAMA Matrix Exception: '.$ex->getMessage());
                                $result = '#VALUE!';
                        }
                } else {
                        //      If we're dealing with non-matrix operations, execute the necessary operation
                        switch ($operation) {
                                //      Addition
                                case '+':
                                        $result = $operand1+$operand2;
                                        break;
                                //      Subtraction
                                case '-':
                                        $result = $operand1-$operand2;
                                        break;
                                //      Multiplication
                                case '*':
                                        $result = $operand1*$operand2;
                                        break;
                                //      Division
                                case '/':
                                        if ($operand2 == 0) {
                                                //      Trap for Divide by Zero error
                                                $stack->push('#DIV/0!');
                                                $this->_writeDebug($cellID,'Evaluation Result is '.self::_showTypeDetails('#DIV/0!'));
                                                return false;
                                        } else {
                                                $result = $operand1/$operand2;
                                        }
                                        break;
                                //      Power
                                case '^':
                                        $result = pow($operand1,$operand2);
                                        break;
                        }
                }

                //      Log the result details
                $this->_writeDebug($cellID,'Evaluation Result is '.self::_showTypeDetails($result));
                //      And push the result onto the stack
                $stack->push($result);
                return true;
        }       //      function _executeNumericBinaryOperation()


        private function _writeDebug($cellID,$message) {
                //      Only write the debug log if logging is enabled
                if ($this->writeDebugLog) {
//                      $prefix = substr(implode(' -> ',$this->debugLogStack).' -> ',4+strlen($this->debugLogStack[0]));
                        $prefix = implode(' -> ',$this->debugLogStack).' -> ';
                        $this->debugLog[] = $prefix.$message;
                }
        }       //      function _writeDebug()


        // trigger an error, but nicely, if need be
        private function _raiseFormulaError($errorMessage) {
                $this->formulaError = $errorMessage;
                if (!$this->suppressFormulaErrors) throw new Exception($errorMessage);
                trigger_error($errorMessage, E_USER_ERROR);
        }       //      function _raiseFormulaError()


        public function extractCellRange($pRange = 'A1', PHPExcel_Worksheet $pSheet = null, $resetLog=true) {
                // Return value
                $returnValue = array ( );

//              echo 'extractCellRange('.$pRange.')<br />';
                // Worksheet given?
                if (!is_null($pSheet)) {
                        // Worksheet reference?
//                      echo 'Current sheet name is '.$pSheet->getTitle().'<br />';
//                      echo 'Range reference is '.$pRange.'<br />';
                        if (strpos ($pRange, '!') !== false) {
//                              echo '$pRange reference includes sheet reference<br />';
                                $worksheetReference = PHPExcel_Worksheet::extractSheetTitle($pRange, true);
                                $pSheet = $pSheet->getParent()->getSheetByName($worksheetReference[0]);
//                              echo 'New sheet name is '.$pSheet->getTitle().'<br />';
                                $pRange = $worksheetReference[1];
//                              echo 'Adjusted Range reference is '.$pRange.'<br />';
                        }

                        // Extract range
                        $aReferences = PHPExcel_Cell::extractAllCellReferencesInRange($pRange);
                        if (count($aReferences) == 1) {
                                return $pSheet->getCell($aReferences[0])->getCalculatedValue($resetLog);
                        }

                        // Extract cell data
                        foreach ($aReferences as $reference) {
                                // Extract range
                                list($currentCol,$currentRow) = PHPExcel_Cell::coordinateFromString($reference);

                                $returnValue[$currentCol][$currentRow] = $pSheet->getCell($reference)->getCalculatedValue($resetLog);
                        }
                }

                // Return
                return $returnValue;
        }       //      function extractCellRange()


        public function extractNamedRange($pRange = 'A1', PHPExcel_Worksheet $pSheet = null, $resetLog=true) {
                // Return value
                $returnValue = array ( );

//              echo 'extractNamedRange('.$pRange.')<br />';
                // Worksheet given?
                if (!is_null($pSheet)) {
                        // Worksheet reference?
//                      echo 'Current sheet name is '.$pSheet->getTitle().'<br />';
//                      echo 'Range reference is '.$pRange.'<br />';
                        if (strpos ($pRange, '!') !== false) {
//                              echo '$pRange reference includes sheet reference<br />';
                                $worksheetReference = PHPExcel_Worksheet::extractSheetTitle($pRange, true);
                                $pSheet = $pSheet->getParent()->getSheetByName($worksheetReference[0]);
//                              echo 'New sheet name is '.$pSheet->getTitle().'<br />';
                                $pRange = $worksheetReference[1];
//                              echo 'Adjusted Range reference is '.$pRange.'<br />';
                        }

                        // Named range?
                        $namedRange = PHPExcel_NamedRange::resolveRange($pRange, $pSheet);
                        if (!is_null($namedRange)) {
//                              echo 'Named Range '.$pRange.' (';
                                $pRange = $namedRange->getRange();
//                              echo $pRange.') is in sheet '.$namedRange->getWorksheet()->getTitle().'<br />';
                                if ($pSheet->getTitle() != $namedRange->getWorksheet()->getTitle()) {
                                        if (!$namedRange->getLocalOnly()) {
                                                $pSheet = $namedRange->getWorksheet();
                                        } else {
                                                return $returnValue;
                                        }
                                }
                        }

                        // Extract range
                        $aReferences = PHPExcel_Cell::extractAllCellReferencesInRange($pRange);
                        if (count($aReferences) == 1) {
                                return $pSheet->getCell($aReferences[0])->getCalculatedValue($resetLog);
                        }

                        // Extract cell data
                        foreach ($aReferences as $reference) {
                                // Extract range
                                list($currentCol,$currentRow) = PHPExcel_Cell::coordinateFromString($reference);
//                              echo 'NAMED RANGE: $currentCol='.$currentCol.' $currentRow='.$currentRow.'<br />';
                                $returnValue[$currentRow][$currentCol] = $pSheet->getCell($reference)->getCalculatedValue($resetLog);
                        }
//                      print_r($returnValue);
//                      echo '<br />';
                        $returnValue = array_values($returnValue);
                        foreach($returnValue as &$rr) {
                                $rr = array_values($rr);
                        }
                        unset($rr);
//                      print_r($returnValue);
//                      echo '<br />';
                }

                // Return
                return $returnValue;
        }       //      function extractNamedRange()


        public function isImplemented($pFunction = '') {
                $pFunction = strtoupper ($pFunction);
                if (isset ($this->_PHPExcelFunctions[$pFunction])) {
                        return ($this->_PHPExcelFunctions[$pFunction]['functionCall'] != 'PHPExcel_Calculation_Functions::DUMMY');
                } else {
                        return false;
                }
        }       //      function isImplemented()


        public function listFunctions() {
                // Return value
                $returnValue = array();
                // Loop functions
                foreach($this->_PHPExcelFunctions as $functionName => $function) {
                        if ($function['functionCall'] != 'PHPExcel_Calculation_Functions::DUMMY') {
                                $returnValue[$functionName] = new PHPExcel_Calculation_Function($function['category'],
                                                                                                                                                                $functionName,
                                                                                                                                                                $function['functionCall']
                                                                                                                                                           );
                        }
                }

                // Return
                return $returnValue;
        }       //      function listFunctions()


        public function listFunctionNames() {
                // Return value
                $returnValue = array();
                // Loop functions
                foreach ($this->_PHPExcelFunctions as $functionName => $function) {
                        $returnValue[] = $functionName;
                }

                // Return
                return $returnValue;
        }       //      function listFunctionNames()

}       //      class PHPExcel_Calculation




// for internal use
class PHPExcel_Token_Stack {

        private $_stack = array();
        private $_count = 0;

        public function count() {
                return $this->_count;
        }

        public function push($value) {
                $this->_stack[$this->_count++] = $value;
        }

        public function pop() {
                if ($this->_count > 0) {
                        return $this->_stack[--$this->_count];
                }
                return null;
        }

        public function last($n=1) {
                if ($this->_count-$n < 0) {
                        return null;
                }
                return $this->_stack[$this->_count-$n];
        }

        function __construct() {
        }

}       //      class PHPExcel_Token_Stack