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Calculation.php in Loft Data Grids 6.2

Same filename and directory in other branches
  1. 7.2 vendor/phpoffice/phpexcel/Classes/PHPExcel/Calculation.php

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vendor/phpoffice/phpexcel/Classes/PHPExcel/Calculation.php
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<?php

/**
 * PHPExcel
 *
 * Copyright (c) 2006 - 2014 PHPExcel
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 *
 * @category   PHPExcel
 * @package    PHPExcel_Calculation
 * @copyright  Copyright (c) 2006 - 2014 PHPExcel (http://www.codeplex.com/PHPExcel)
 * @license	http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt	LGPL
 * @version	##VERSION##, ##DATE##
 */

/** PHPExcel root directory */
if (!defined('PHPEXCEL_ROOT')) {

  /**
   * @ignore
   */
  define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../');
  require PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php';
}
if (!defined('CALCULATION_REGEXP_CELLREF')) {

  //	Test for support of \P (multibyte options) in PCRE
  if (defined('PREG_BAD_UTF8_ERROR')) {

    //	Cell reference (cell or range of cells, with or without a sheet reference)
    define('CALCULATION_REGEXP_CELLREF', '((([^\\s,!&%^\\/\\*\\+<>=-]*)|(\'[^\']*\')|(\\"[^\\"]*\\"))!)?\\$?([a-z]{1,3})\\$?(\\d{1,7})');

    //	Named Range of cells
    define('CALCULATION_REGEXP_NAMEDRANGE', '((([^\\s,!&%^\\/\\*\\+<>=-]*)|(\'[^\']*\')|(\\"[^\\"]*\\"))!)?([_A-Z][_A-Z0-9\\.]*)');
  }
  else {

    //	Cell reference (cell or range of cells, with or without a sheet reference)
    define('CALCULATION_REGEXP_CELLREF', '(((\\w*)|(\'[^\']*\')|(\\"[^\\"]*\\"))!)?\\$?([a-z]{1,3})\\$?(\\d+)');

    //	Named Range of cells
    define('CALCULATION_REGEXP_NAMEDRANGE', '(((\\w*)|(\'.*\')|(\\".*\\"))!)?([_A-Z][_A-Z0-9\\.]*)');
  }
}

/**
 * PHPExcel_Calculation (Multiton)
 *
 * @category	PHPExcel
 * @package		PHPExcel_Calculation
 * @copyright	Copyright (c) 2006 - 2014 PHPExcel (http://www.codeplex.com/PHPExcel)
 */
class PHPExcel_Calculation {

  /** Constants				*/

  /** Regular Expressions		*/

  //	Numeric operand
  const CALCULATION_REGEXP_NUMBER = '[-+]?\\d*\\.?\\d+(e[-+]?\\d+)?';

  //	String operand
  const CALCULATION_REGEXP_STRING = '"(?:[^"]|"")*"';

  //	Opening bracket
  const CALCULATION_REGEXP_OPENBRACE = '\\(';

  //	Function (allow for the old @ symbol that could be used to prefix a function, but we'll ignore it)
  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 = CALCULATION_REGEXP_CELLREF;

  //	Named Range of cells
  const CALCULATION_REGEXP_NAMEDRANGE = CALCULATION_REGEXP_NAMEDRANGE;

  //	Error
  const CALCULATION_REGEXP_ERROR = '\\#[A-Z][A-Z0_\\/]*[!\\?]?';

  /** constants */
  const RETURN_ARRAY_AS_ERROR = 'error';
  const RETURN_ARRAY_AS_VALUE = 'value';
  const RETURN_ARRAY_AS_ARRAY = 'array';
  private static $returnArrayAsType = self::RETURN_ARRAY_AS_VALUE;

  /**
   * Instance of this class
   *
   * @access	private
   * @var PHPExcel_Calculation
   */
  private static $_instance;

  /**
   * Instance of the workbook this Calculation Engine is using
   *
   * @access	private
   * @var PHPExcel
   */
  private $_workbook;

  /**
   * List of instances of the calculation engine that we've instantiated for individual workbooks
   *
   * @access	private
   * @var PHPExcel_Calculation[]
   */
  private static $_workbookSets;

  /**
   * Calculation cache
   *
   * @access	private
   * @var array
   */
  private $_calculationCache = array();

  /**
   * Calculation cache enabled
   *
   * @access	private
   * @var boolean
   */
  private $_calculationCacheEnabled = TRUE;

  /**
   * List of operators that can be used within formulae
   * The true/false value indicates whether it is a binary operator or a unary operator
   *
   * @access	private
   * @var array
   */
  private static $_operators = array(
    '+' => TRUE,
    '-' => TRUE,
    '*' => TRUE,
    '/' => TRUE,
    '^' => TRUE,
    '&' => TRUE,
    '%' => FALSE,
    '~' => FALSE,
    '>' => TRUE,
    '<' => TRUE,
    '=' => TRUE,
    '>=' => TRUE,
    '<=' => TRUE,
    '<>' => TRUE,
    '|' => TRUE,
    ':' => TRUE,
  );

  /**
   * List of binary operators (those that expect two operands)
   *
   * @access	private
   * @var array
   */
  private static $_binaryOperators = array(
    '+' => TRUE,
    '-' => TRUE,
    '*' => TRUE,
    '/' => TRUE,
    '^' => TRUE,
    '&' => TRUE,
    '>' => TRUE,
    '<' => TRUE,
    '=' => TRUE,
    '>=' => TRUE,
    '<=' => TRUE,
    '<>' => TRUE,
    '|' => TRUE,
    ':' => TRUE,
  );

  /**
   * The debug log generated by the calculation engine
   *
   * @access	private
   * @var PHPExcel_CalcEngine_Logger
   *
   */
  private $debugLog;

  /**
   * Flag to determine how formula errors should be handled
   *		If true, then a user error will be triggered
   *		If false, then an exception will be thrown
   *
   * @access	public
   * @var boolean
   *
   */
  public $suppressFormulaErrors = FALSE;

  /**
   * Error message for any error that was raised/thrown by the calculation engine
   *
   * @access	public
   * @var string
   *
   */
  public $formulaError = NULL;

  /**
   * An array of the nested cell references accessed by the calculation engine, used for the debug log
   *
   * @access	private
   * @var array of string
   *
   */
  private $_cyclicReferenceStack;
  private $_cellStack = array();

  /**
   * Current iteration counter for cyclic formulae
   * If the value is 0 (or less) then cyclic formulae will throw an exception,
   *    otherwise they will iterate to the limit defined here before returning a result
   *
   * @var integer
   *
   */
  private $_cyclicFormulaCount = 1;
  private $_cyclicFormulaCell = '';

  /**
   * Number of iterations for cyclic formulae
   *
   * @var integer
   *
   */
  public $cyclicFormulaCount = 1;

  /**
   * Precision used for calculations
   *
   * @var integer
   *
   */
  private $_savedPrecision = 14;

  /**
   * The current locale setting
   *
   * @var string
   *
   */
  private static $_localeLanguage = 'en_us';

  //	US English	(default locale)

  /**
   * List of available locale settings
   * Note that this is read for the locale subdirectory only when requested
   *
   * @var string[]
   *
   */
  private static $_validLocaleLanguages = array(
    'en',
  );

  /**
   * Locale-specific argument separator for function arguments
   *
   * @var string
   *
   */
  private static $_localeArgumentSeparator = ',';
  private static $_localeFunctions = array();

  /**
   * Locale-specific translations for Excel constants (True, False and Null)
   *
   * @var string[]
   *
   */
  public static $_localeBoolean = array(
    'TRUE' => 'TRUE',
    'FALSE' => 'FALSE',
    'NULL' => 'NULL',
  );

  /**
   * Excel constant string translations to their PHP equivalents
   * Constant conversion from text name/value to actual (datatyped) value
   *
   * @var string[]
   *
   */
  private static $_ExcelConstants = array(
    'TRUE' => TRUE,
    'FALSE' => FALSE,
    'NULL' => NULL,
  );

  //	PHPExcel functions
  private static $_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_Financial::ACCRINT',
      'argumentCount' => '4-7',
    ),
    'ACCRINTM' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::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_LookupRef::CELL_ADDRESS',
      'argumentCount' => '2-5',
    ),
    'AMORDEGRC' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::AMORDEGRC',
      'argumentCount' => '6,7',
    ),
    'AMORLINC' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::AMORLINC',
      'argumentCount' => '6,7',
    ),
    'AND' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
      'functionCall' => 'PHPExcel_Calculation_Logical::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_MathTrig::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_Statistical::AVEDEV',
      'argumentCount' => '1+',
    ),
    'AVERAGE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::AVERAGE',
      'argumentCount' => '1+',
    ),
    'AVERAGEA' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::AVERAGEA',
      'argumentCount' => '1+',
    ),
    'AVERAGEIF' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::AVERAGEIF',
      '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_Engineering::BESSELI',
      'argumentCount' => '2',
    ),
    'BESSELJ' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::BESSELJ',
      'argumentCount' => '2',
    ),
    'BESSELK' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::BESSELK',
      'argumentCount' => '2',
    ),
    'BESSELY' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::BESSELY',
      'argumentCount' => '2',
    ),
    'BETADIST' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::BETADIST',
      'argumentCount' => '3-5',
    ),
    'BETAINV' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::BETAINV',
      'argumentCount' => '3-5',
    ),
    'BIN2DEC' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::BINTODEC',
      'argumentCount' => '1',
    ),
    'BIN2HEX' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::BINTOHEX',
      'argumentCount' => '1,2',
    ),
    'BIN2OCT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::BINTOOCT',
      'argumentCount' => '1,2',
    ),
    'BINOMDIST' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::BINOMDIST',
      'argumentCount' => '4',
    ),
    'CEILING' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::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_TextData::CHARACTER',
      'argumentCount' => '1',
    ),
    'CHIDIST' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::CHIDIST',
      'argumentCount' => '2',
    ),
    'CHIINV' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::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_LookupRef::CHOOSE',
      'argumentCount' => '2+',
    ),
    'CLEAN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::TRIMNONPRINTABLE',
      'argumentCount' => '1',
    ),
    'CODE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::ASCIICODE',
      'argumentCount' => '1',
    ),
    'COLUMN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
      'functionCall' => 'PHPExcel_Calculation_LookupRef::COLUMN',
      'argumentCount' => '-1',
      'passByReference' => array(
        TRUE,
      ),
    ),
    'COLUMNS' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
      'functionCall' => 'PHPExcel_Calculation_LookupRef::COLUMNS',
      'argumentCount' => '1',
    ),
    'COMBIN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::COMBIN',
      'argumentCount' => '2',
    ),
    'COMPLEX' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::COMPLEX',
      'argumentCount' => '2,3',
    ),
    'CONCATENATE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::CONCATENATE',
      'argumentCount' => '1+',
    ),
    'CONFIDENCE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::CONFIDENCE',
      'argumentCount' => '3',
    ),
    'CONVERT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::CONVERTUOM',
      'argumentCount' => '3',
    ),
    'CORREL' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::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_Statistical::COUNT',
      'argumentCount' => '1+',
    ),
    'COUNTA' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::COUNTA',
      'argumentCount' => '1+',
    ),
    'COUNTBLANK' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::COUNTBLANK',
      'argumentCount' => '1',
    ),
    'COUNTIF' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::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_Financial::COUPDAYBS',
      'argumentCount' => '3,4',
    ),
    'COUPDAYS' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::COUPDAYS',
      'argumentCount' => '3,4',
    ),
    'COUPDAYSNC' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::COUPDAYSNC',
      'argumentCount' => '3,4',
    ),
    'COUPNCD' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::COUPNCD',
      'argumentCount' => '3,4',
    ),
    'COUPNUM' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::COUPNUM',
      'argumentCount' => '3,4',
    ),
    'COUPPCD' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::COUPPCD',
      'argumentCount' => '3,4',
    ),
    'COVAR' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::COVAR',
      'argumentCount' => '2',
    ),
    'CRITBINOM' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::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_Financial::CUMIPMT',
      'argumentCount' => '6',
    ),
    'CUMPRINC' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::CUMPRINC',
      'argumentCount' => '6',
    ),
    'DATE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::DATE',
      'argumentCount' => '3',
    ),
    'DATEDIF' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::DATEDIF',
      'argumentCount' => '2,3',
    ),
    'DATEVALUE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::DATEVALUE',
      'argumentCount' => '1',
    ),
    'DAVERAGE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
      'functionCall' => 'PHPExcel_Calculation_Database::DAVERAGE',
      'argumentCount' => '3',
    ),
    'DAY' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::DAYOFMONTH',
      'argumentCount' => '1',
    ),
    'DAYS360' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::DAYS360',
      'argumentCount' => '2,3',
    ),
    'DB' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::DB',
      'argumentCount' => '4,5',
    ),
    'DCOUNT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
      'functionCall' => 'PHPExcel_Calculation_Database::DCOUNT',
      'argumentCount' => '3',
    ),
    'DCOUNTA' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
      'functionCall' => 'PHPExcel_Calculation_Database::DCOUNTA',
      'argumentCount' => '3',
    ),
    'DDB' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::DDB',
      'argumentCount' => '4,5',
    ),
    'DEC2BIN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::DECTOBIN',
      'argumentCount' => '1,2',
    ),
    'DEC2HEX' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::DECTOHEX',
      'argumentCount' => '1,2',
    ),
    'DEC2OCT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::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_Engineering::DELTA',
      'argumentCount' => '1,2',
    ),
    'DEVSQ' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::DEVSQ',
      'argumentCount' => '1+',
    ),
    'DGET' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
      'functionCall' => 'PHPExcel_Calculation_Database::DGET',
      'argumentCount' => '3',
    ),
    'DISC' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::DISC',
      'argumentCount' => '4,5',
    ),
    'DMAX' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
      'functionCall' => 'PHPExcel_Calculation_Database::DMAX',
      'argumentCount' => '3',
    ),
    'DMIN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
      'functionCall' => 'PHPExcel_Calculation_Database::DMIN',
      'argumentCount' => '3',
    ),
    'DOLLAR' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::DOLLAR',
      'argumentCount' => '1,2',
    ),
    'DOLLARDE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::DOLLARDE',
      'argumentCount' => '2',
    ),
    'DOLLARFR' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::DOLLARFR',
      'argumentCount' => '2',
    ),
    'DPRODUCT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
      'functionCall' => 'PHPExcel_Calculation_Database::DPRODUCT',
      'argumentCount' => '3',
    ),
    'DSTDEV' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
      'functionCall' => 'PHPExcel_Calculation_Database::DSTDEV',
      'argumentCount' => '3',
    ),
    'DSTDEVP' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
      'functionCall' => 'PHPExcel_Calculation_Database::DSTDEVP',
      'argumentCount' => '3',
    ),
    'DSUM' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
      'functionCall' => 'PHPExcel_Calculation_Database::DSUM',
      'argumentCount' => '3',
    ),
    '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_Database::DVAR',
      'argumentCount' => '3',
    ),
    'DVARP' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
      'functionCall' => 'PHPExcel_Calculation_Database::DVARP',
      'argumentCount' => '3',
    ),
    'EDATE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::EDATE',
      'argumentCount' => '2',
    ),
    'EFFECT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::EFFECT',
      'argumentCount' => '2',
    ),
    'EOMONTH' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::EOMONTH',
      'argumentCount' => '2',
    ),
    'ERF' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::ERF',
      'argumentCount' => '1,2',
    ),
    'ERFC' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::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_MathTrig::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_Statistical::EXPONDIST',
      'argumentCount' => '3',
    ),
    'FACT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::FACT',
      'argumentCount' => '1',
    ),
    'FACTDOUBLE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::FACTDOUBLE',
      'argumentCount' => '1',
    ),
    'FALSE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
      'functionCall' => 'PHPExcel_Calculation_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_TextData::SEARCHSENSITIVE',
      'argumentCount' => '2,3',
    ),
    'FINDB' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::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_Statistical::FISHER',
      'argumentCount' => '1',
    ),
    'FISHERINV' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::FISHERINV',
      'argumentCount' => '1',
    ),
    'FIXED' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::FIXEDFORMAT',
      'argumentCount' => '1-3',
    ),
    'FLOOR' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::FLOOR',
      'argumentCount' => '2',
    ),
    'FORECAST' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::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_Financial::FV',
      'argumentCount' => '3-5',
    ),
    'FVSCHEDULE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::FVSCHEDULE',
      'argumentCount' => '2',
    ),
    'GAMMADIST' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::GAMMADIST',
      'argumentCount' => '4',
    ),
    'GAMMAINV' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::GAMMAINV',
      'argumentCount' => '3',
    ),
    'GAMMALN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::GAMMALN',
      'argumentCount' => '1',
    ),
    'GCD' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::GCD',
      'argumentCount' => '1+',
    ),
    'GEOMEAN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::GEOMEAN',
      'argumentCount' => '1+',
    ),
    'GESTEP' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::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_Statistical::GROWTH',
      'argumentCount' => '1-4',
    ),
    'HARMEAN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::HARMEAN',
      'argumentCount' => '1+',
    ),
    'HEX2BIN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::HEXTOBIN',
      'argumentCount' => '1,2',
    ),
    'HEX2DEC' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::HEXTODEC',
      'argumentCount' => '1',
    ),
    'HEX2OCT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::HEXTOOCT',
      'argumentCount' => '1,2',
    ),
    'HLOOKUP' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
      'functionCall' => 'PHPExcel_Calculation_LookupRef::HLOOKUP',
      'argumentCount' => '3,4',
    ),
    'HOUR' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::HOUROFDAY',
      'argumentCount' => '1',
    ),
    'HYPERLINK' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
      'functionCall' => 'PHPExcel_Calculation_LookupRef::HYPERLINK',
      'argumentCount' => '1,2',
      'passCellReference' => TRUE,
    ),
    'HYPGEOMDIST' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::HYPGEOMDIST',
      'argumentCount' => '4',
    ),
    'IF' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
      'functionCall' => 'PHPExcel_Calculation_Logical::STATEMENT_IF',
      'argumentCount' => '1-3',
    ),
    'IFERROR' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
      'functionCall' => 'PHPExcel_Calculation_Logical::IFERROR',
      'argumentCount' => '2',
    ),
    'IMABS' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMABS',
      'argumentCount' => '1',
    ),
    'IMAGINARY' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMAGINARY',
      'argumentCount' => '1',
    ),
    'IMARGUMENT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMARGUMENT',
      'argumentCount' => '1',
    ),
    'IMCONJUGATE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMCONJUGATE',
      'argumentCount' => '1',
    ),
    'IMCOS' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMCOS',
      'argumentCount' => '1',
    ),
    'IMDIV' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMDIV',
      'argumentCount' => '2',
    ),
    'IMEXP' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMEXP',
      'argumentCount' => '1',
    ),
    'IMLN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMLN',
      'argumentCount' => '1',
    ),
    'IMLOG10' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMLOG10',
      'argumentCount' => '1',
    ),
    'IMLOG2' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMLOG2',
      'argumentCount' => '1',
    ),
    'IMPOWER' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMPOWER',
      'argumentCount' => '2',
    ),
    'IMPRODUCT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMPRODUCT',
      'argumentCount' => '1+',
    ),
    'IMREAL' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMREAL',
      'argumentCount' => '1',
    ),
    'IMSIN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMSIN',
      'argumentCount' => '1',
    ),
    'IMSQRT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMSQRT',
      'argumentCount' => '1',
    ),
    'IMSUB' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMSUB',
      'argumentCount' => '2',
    ),
    'IMSUM' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::IMSUM',
      'argumentCount' => '1+',
    ),
    'INDEX' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
      'functionCall' => 'PHPExcel_Calculation_LookupRef::INDEX',
      'argumentCount' => '1-4',
    ),
    'INDIRECT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
      'functionCall' => 'PHPExcel_Calculation_LookupRef::INDIRECT',
      'argumentCount' => '1,2',
      'passCellReference' => TRUE,
    ),
    '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_MathTrig::INT',
      'argumentCount' => '1',
    ),
    'INTERCEPT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::INTERCEPT',
      'argumentCount' => '2',
    ),
    'INTRATE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::INTRATE',
      'argumentCount' => '4,5',
    ),
    'IPMT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::IPMT',
      'argumentCount' => '4-6',
    ),
    'IRR' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::IRR',
      '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_Financial::ISPMT',
      '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_Statistical::KURT',
      'argumentCount' => '1+',
    ),
    'LARGE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::LARGE',
      'argumentCount' => '2',
    ),
    'LCM' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::LCM',
      'argumentCount' => '1+',
    ),
    'LEFT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::LEFT',
      'argumentCount' => '1,2',
    ),
    'LEFTB' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::LEFT',
      'argumentCount' => '1,2',
    ),
    'LEN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::STRINGLENGTH',
      'argumentCount' => '1',
    ),
    'LENB' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::STRINGLENGTH',
      'argumentCount' => '1',
    ),
    'LINEST' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::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_MathTrig::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_Statistical::LOGEST',
      'argumentCount' => '1-4',
    ),
    'LOGINV' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::LOGINV',
      'argumentCount' => '3',
    ),
    'LOGNORMDIST' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::LOGNORMDIST',
      'argumentCount' => '3',
    ),
    'LOOKUP' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
      'functionCall' => 'PHPExcel_Calculation_LookupRef::LOOKUP',
      'argumentCount' => '2,3',
    ),
    'LOWER' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::LOWERCASE',
      'argumentCount' => '1',
    ),
    'MATCH' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
      'functionCall' => 'PHPExcel_Calculation_LookupRef::MATCH',
      'argumentCount' => '2,3',
    ),
    'MAX' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::MAX',
      'argumentCount' => '1+',
    ),
    'MAXA' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::MAXA',
      'argumentCount' => '1+',
    ),
    'MAXIF' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::MAXIF',
      'argumentCount' => '2+',
    ),
    'MDETERM' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::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_Statistical::MEDIAN',
      'argumentCount' => '1+',
    ),
    'MEDIANIF' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Functions::DUMMY',
      'argumentCount' => '2+',
    ),
    'MID' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::MID',
      'argumentCount' => '3',
    ),
    'MIDB' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::MID',
      'argumentCount' => '3',
    ),
    'MIN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::MIN',
      'argumentCount' => '1+',
    ),
    'MINA' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::MINA',
      'argumentCount' => '1+',
    ),
    'MINIF' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::MINIF',
      'argumentCount' => '2+',
    ),
    'MINUTE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::MINUTEOFHOUR',
      'argumentCount' => '1',
    ),
    'MINVERSE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::MINVERSE',
      'argumentCount' => '1',
    ),
    'MIRR' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::MIRR',
      'argumentCount' => '3',
    ),
    'MMULT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::MMULT',
      'argumentCount' => '2',
    ),
    'MOD' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::MOD',
      'argumentCount' => '2',
    ),
    'MODE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::MODE',
      'argumentCount' => '1+',
    ),
    'MONTH' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::MONTHOFYEAR',
      'argumentCount' => '1',
    ),
    'MROUND' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::MROUND',
      'argumentCount' => '2',
    ),
    'MULTINOMIAL' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::MULTINOMIAL',
      'argumentCount' => '1+',
    ),
    'N' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
      'functionCall' => 'PHPExcel_Calculation_Functions::N',
      '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_Statistical::NEGBINOMDIST',
      'argumentCount' => '3',
    ),
    'NETWORKDAYS' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::NETWORKDAYS',
      'argumentCount' => '2+',
    ),
    'NOMINAL' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::NOMINAL',
      'argumentCount' => '2',
    ),
    'NORMDIST' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::NORMDIST',
      'argumentCount' => '4',
    ),
    'NORMINV' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::NORMINV',
      'argumentCount' => '3',
    ),
    'NORMSDIST' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::NORMSDIST',
      'argumentCount' => '1',
    ),
    'NORMSINV' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::NORMSINV',
      'argumentCount' => '1',
    ),
    'NOT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
      'functionCall' => 'PHPExcel_Calculation_Logical::NOT',
      'argumentCount' => '1',
    ),
    'NOW' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::DATETIMENOW',
      'argumentCount' => '0',
    ),
    'NPER' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::NPER',
      'argumentCount' => '3-5',
    ),
    'NPV' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::NPV',
      'argumentCount' => '2+',
    ),
    'OCT2BIN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::OCTTOBIN',
      'argumentCount' => '1,2',
    ),
    'OCT2DEC' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::OCTTODEC',
      'argumentCount' => '1',
    ),
    'OCT2HEX' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
      'functionCall' => 'PHPExcel_Calculation_Engineering::OCTTOHEX',
      'argumentCount' => '1,2',
    ),
    'ODD' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::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_LookupRef::OFFSET',
      'argumentCount' => '3,5',
      'passCellReference' => TRUE,
      'passByReference' => array(
        TRUE,
      ),
    ),
    'OR' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
      'functionCall' => 'PHPExcel_Calculation_Logical::LOGICAL_OR',
      'argumentCount' => '1+',
    ),
    'PEARSON' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::CORREL',
      'argumentCount' => '2',
    ),
    'PERCENTILE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::PERCENTILE',
      'argumentCount' => '2',
    ),
    'PERCENTRANK' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::PERCENTRANK',
      'argumentCount' => '2,3',
    ),
    'PERMUT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::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_Financial::PMT',
      'argumentCount' => '3-5',
    ),
    'POISSON' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::POISSON',
      'argumentCount' => '3',
    ),
    'POWER' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::POWER',
      'argumentCount' => '2',
    ),
    'PPMT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::PPMT',
      'argumentCount' => '4-6',
    ),
    'PRICE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::PRICE',
      'argumentCount' => '6,7',
    ),
    'PRICEDISC' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::PRICEDISC',
      'argumentCount' => '4,5',
    ),
    'PRICEMAT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::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_MathTrig::PRODUCT',
      'argumentCount' => '1+',
    ),
    'PROPER' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::PROPERCASE',
      'argumentCount' => '1',
    ),
    'PV' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::PV',
      'argumentCount' => '3-5',
    ),
    'QUARTILE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::QUARTILE',
      'argumentCount' => '2',
    ),
    'QUOTIENT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::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_MathTrig::RAND',
      'argumentCount' => '0',
    ),
    'RANDBETWEEN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::RAND',
      'argumentCount' => '2',
    ),
    'RANK' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::RANK',
      'argumentCount' => '2,3',
    ),
    'RATE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::RATE',
      'argumentCount' => '3-6',
    ),
    'RECEIVED' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::RECEIVED',
      'argumentCount' => '4-5',
    ),
    'REPLACE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::REPLACE',
      'argumentCount' => '4',
    ),
    'REPLACEB' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::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_TextData::RIGHT',
      'argumentCount' => '1,2',
    ),
    'RIGHTB' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::RIGHT',
      'argumentCount' => '1,2',
    ),
    'ROMAN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::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_MathTrig::ROUNDDOWN',
      'argumentCount' => '2',
    ),
    'ROUNDUP' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::ROUNDUP',
      'argumentCount' => '2',
    ),
    'ROW' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
      'functionCall' => 'PHPExcel_Calculation_LookupRef::ROW',
      'argumentCount' => '-1',
      'passByReference' => array(
        TRUE,
      ),
    ),
    'ROWS' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
      'functionCall' => 'PHPExcel_Calculation_LookupRef::ROWS',
      'argumentCount' => '1',
    ),
    'RSQ' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::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_TextData::SEARCHINSENSITIVE',
      'argumentCount' => '2,3',
    ),
    'SEARCHB' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::SEARCHINSENSITIVE',
      'argumentCount' => '2,3',
    ),
    'SECOND' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::SECONDOFMINUTE',
      'argumentCount' => '1',
    ),
    'SERIESSUM' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::SERIESSUM',
      'argumentCount' => '4',
    ),
    'SIGN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::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_Statistical::SKEW',
      'argumentCount' => '1+',
    ),
    'SLN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::SLN',
      'argumentCount' => '3',
    ),
    'SLOPE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::SLOPE',
      'argumentCount' => '2',
    ),
    'SMALL' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::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_MathTrig::SQRTPI',
      'argumentCount' => '1',
    ),
    'STANDARDIZE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::STANDARDIZE',
      'argumentCount' => '3',
    ),
    'STDEV' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::STDEV',
      'argumentCount' => '1+',
    ),
    'STDEVA' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::STDEVA',
      'argumentCount' => '1+',
    ),
    'STDEVP' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::STDEVP',
      'argumentCount' => '1+',
    ),
    'STDEVPA' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::STDEVPA',
      'argumentCount' => '1+',
    ),
    'STEYX' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::STEYX',
      'argumentCount' => '2',
    ),
    'SUBSTITUTE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::SUBSTITUTE',
      'argumentCount' => '3,4',
    ),
    'SUBTOTAL' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::SUBTOTAL',
      'argumentCount' => '2+',
    ),
    'SUM' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::SUM',
      'argumentCount' => '1+',
    ),
    'SUMIF' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::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_MathTrig::SUMPRODUCT',
      'argumentCount' => '1+',
    ),
    'SUMSQ' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::SUMSQ',
      'argumentCount' => '1+',
    ),
    'SUMX2MY2' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::SUMX2MY2',
      'argumentCount' => '2',
    ),
    'SUMX2PY2' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::SUMX2PY2',
      'argumentCount' => '2',
    ),
    'SUMXMY2' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::SUMXMY2',
      'argumentCount' => '2',
    ),
    'SYD' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::SYD',
      'argumentCount' => '4',
    ),
    'T' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::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_Financial::TBILLEQ',
      'argumentCount' => '3',
    ),
    'TBILLPRICE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::TBILLPRICE',
      'argumentCount' => '3',
    ),
    'TBILLYIELD' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::TBILLYIELD',
      'argumentCount' => '3',
    ),
    'TDIST' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::TDIST',
      'argumentCount' => '3',
    ),
    'TEXT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::TEXTFORMAT',
      'argumentCount' => '2',
    ),
    'TIME' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::TIME',
      'argumentCount' => '3',
    ),
    'TIMEVALUE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::TIMEVALUE',
      'argumentCount' => '1',
    ),
    'TINV' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::TINV',
      'argumentCount' => '2',
    ),
    'TODAY' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::DATENOW',
      'argumentCount' => '0',
    ),
    'TRANSPOSE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
      'functionCall' => 'PHPExcel_Calculation_LookupRef::TRANSPOSE',
      'argumentCount' => '1',
    ),
    'TREND' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::TREND',
      'argumentCount' => '1-4',
    ),
    'TRIM' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::TRIMSPACES',
      'argumentCount' => '1',
    ),
    'TRIMMEAN' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::TRIMMEAN',
      'argumentCount' => '2',
    ),
    'TRUE' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
      'functionCall' => 'PHPExcel_Calculation_Logical::TRUE',
      'argumentCount' => '0',
    ),
    'TRUNC' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
      'functionCall' => 'PHPExcel_Calculation_MathTrig::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::TYPE',
      'argumentCount' => '1',
    ),
    'UPPER' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
      'functionCall' => 'PHPExcel_Calculation_TextData::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_TextData::VALUE',
      'argumentCount' => '1',
    ),
    'VAR' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::VARFunc',
      'argumentCount' => '1+',
    ),
    'VARA' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::VARA',
      'argumentCount' => '1+',
    ),
    'VARP' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::VARP',
      'argumentCount' => '1+',
    ),
    'VARPA' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::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_LookupRef::VLOOKUP',
      'argumentCount' => '3,4',
    ),
    'WEEKDAY' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::DAYOFWEEK',
      'argumentCount' => '1,2',
    ),
    'WEEKNUM' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::WEEKOFYEAR',
      'argumentCount' => '1,2',
    ),
    'WEIBULL' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::WEIBULL',
      'argumentCount' => '4',
    ),
    'WORKDAY' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::WORKDAY',
      'argumentCount' => '2+',
    ),
    'XIRR' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::XIRR',
      'argumentCount' => '2,3',
    ),
    'XNPV' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::XNPV',
      'argumentCount' => '3',
    ),
    'YEAR' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::YEAR',
      'argumentCount' => '1',
    ),
    'YEARFRAC' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
      'functionCall' => 'PHPExcel_Calculation_DateTime::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_Financial::YIELDDISC',
      'argumentCount' => '4,5',
    ),
    'YIELDMAT' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
      'functionCall' => 'PHPExcel_Calculation_Financial::YIELDMAT',
      'argumentCount' => '5,6',
    ),
    'ZTEST' => array(
      'category' => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
      'functionCall' => 'PHPExcel_Calculation_Statistical::ZTEST',
      'argumentCount' => '2-3',
    ),
  );

  //	Internal functions used for special control purposes
  private static $_controlFunctions = array(
    'MKMATRIX' => array(
      'argumentCount' => '*',
      'functionCall' => 'self::_mkMatrix',
    ),
  );
  private function __construct(PHPExcel $workbook = NULL) {
    $setPrecision = PHP_INT_SIZE == 4 ? 14 : 16;
    $this->_savedPrecision = ini_get('precision');
    if ($this->_savedPrecision < $setPrecision) {
      ini_set('precision', $setPrecision);
    }
    $this->delta = 1 * pow(10, -$setPrecision);
    if ($workbook !== NULL) {
      self::$_workbookSets[$workbook
        ->getID()] = $this;
    }
    $this->_workbook = $workbook;
    $this->_cyclicReferenceStack = new PHPExcel_CalcEngine_CyclicReferenceStack();
    $this->_debugLog = new PHPExcel_CalcEngine_Logger($this->_cyclicReferenceStack);
  }

  //	function __construct()
  public function __destruct() {
    if ($this->_savedPrecision != ini_get('precision')) {
      ini_set('precision', $this->_savedPrecision);
    }
  }
  private static function _loadLocales() {
    $localeFileDirectory = PHPEXCEL_ROOT . 'PHPExcel/locale/';
    foreach (glob($localeFileDirectory . '/*', GLOB_ONLYDIR) as $filename) {
      $filename = substr($filename, strlen($localeFileDirectory) + 1);
      if ($filename != 'en') {
        self::$_validLocaleLanguages[] = $filename;
      }
    }
  }

  /**
   * Get an instance of this class
   *
   * @access	public
   * @param   PHPExcel $workbook  Injected workbook for working with a PHPExcel object,
   *									or NULL to create a standalone claculation engine
   * @return PHPExcel_Calculation
   */
  public static function getInstance(PHPExcel $workbook = NULL) {
    if ($workbook !== NULL) {
      if (isset(self::$_workbookSets[$workbook
        ->getID()])) {
        return self::$_workbookSets[$workbook
          ->getID()];
      }
      return new PHPExcel_Calculation($workbook);
    }
    if (!isset(self::$_instance) || self::$_instance === NULL) {
      self::$_instance = new PHPExcel_Calculation();
    }
    return self::$_instance;
  }

  //	function getInstance()

  /**
   * Unset an instance of this class
   *
   * @access	public
   * @param   PHPExcel $workbook  Injected workbook identifying the instance to unset
   */
  public static function unsetInstance(PHPExcel $workbook = NULL) {
    if ($workbook !== NULL) {
      if (isset(self::$_workbookSets[$workbook
        ->getID()])) {
        unset(self::$_workbookSets[$workbook
          ->getID()]);
      }
    }
  }

  /**
   * Flush the calculation cache for any existing instance of this class
   *		but only if a PHPExcel_Calculation instance exists
   *
   * @access	public
   * @return null
   */
  public function flushInstance() {
    $this
      ->clearCalculationCache();
  }

  //	function flushInstance()

  /**
   * Get the debuglog for this claculation engine instance
   *
   * @access	public
   * @return PHPExcel_CalcEngine_Logger
   */
  public function getDebugLog() {
    return $this->_debugLog;
  }

  /**
   * __clone implementation. Cloning should not be allowed in a Singleton!
   *
   * @access	public
   * @throws	PHPExcel_Calculation_Exception
   */
  public final function __clone() {
    throw new PHPExcel_Calculation_Exception('Cloning the calculation engine is not allowed!');
  }

  //	function __clone()

  /**
   * Return the locale-specific translation of TRUE
   *
   * @access	public
   * @return	 string		locale-specific translation of TRUE
   */
  public static function getTRUE() {
    return self::$_localeBoolean['TRUE'];
  }

  /**
   * Return the locale-specific translation of FALSE
   *
   * @access	public
   * @return	 string		locale-specific translation of FALSE
   */
  public static function getFALSE() {
    return self::$_localeBoolean['FALSE'];
  }

  /**
   * Set the Array Return Type (Array or Value of first element in the array)
   *
   * @access	public
   * @param	 string	$returnType			Array return type
   * @return	 boolean					Success or failure
   */
  public static function setArrayReturnType($returnType) {
    if ($returnType == self::RETURN_ARRAY_AS_VALUE || $returnType == self::RETURN_ARRAY_AS_ERROR || $returnType == self::RETURN_ARRAY_AS_ARRAY) {
      self::$returnArrayAsType = $returnType;
      return TRUE;
    }
    return FALSE;
  }

  //	function setArrayReturnType()

  /**
   * Return the Array Return Type (Array or Value of first element in the array)
   *
   * @access	public
   * @return	 string		$returnType			Array return type
   */
  public static function getArrayReturnType() {
    return self::$returnArrayAsType;
  }

  //	function getArrayReturnType()

  /**
   * Is calculation caching enabled?
   *
   * @access	public
   * @return boolean
   */
  public function getCalculationCacheEnabled() {
    return $this->_calculationCacheEnabled;
  }

  //	function getCalculationCacheEnabled()

  /**
   * Enable/disable calculation cache
   *
   * @access	public
   * @param boolean $pValue
   */
  public function setCalculationCacheEnabled($pValue = TRUE) {
    $this->_calculationCacheEnabled = $pValue;
    $this
      ->clearCalculationCache();
  }

  //	function setCalculationCacheEnabled()

  /**
   * Enable calculation cache
   */
  public function enableCalculationCache() {
    $this
      ->setCalculationCacheEnabled(TRUE);
  }

  //	function enableCalculationCache()

  /**
   * Disable calculation cache
   */
  public function disableCalculationCache() {
    $this
      ->setCalculationCacheEnabled(FALSE);
  }

  //	function disableCalculationCache()

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

  //	function clearCalculationCache()

  /**
   * Clear calculation cache for a specified worksheet
   *
   * @param string $worksheetName
   */
  public function clearCalculationCacheForWorksheet($worksheetName) {
    if (isset($this->_calculationCache[$worksheetName])) {
      unset($this->_calculationCache[$worksheetName]);
    }
  }

  //	function clearCalculationCacheForWorksheet()

  /**
   * Rename calculation cache for a specified worksheet
   *
   * @param string $fromWorksheetName
   * @param string $toWorksheetName
   */
  public function renameCalculationCacheForWorksheet($fromWorksheetName, $toWorksheetName) {
    if (isset($this->_calculationCache[$fromWorksheetName])) {
      $this->_calculationCache[$toWorksheetName] =& $this->_calculationCache[$fromWorksheetName];
      unset($this->_calculationCache[$fromWorksheetName]);
    }
  }

  //	function renameCalculationCacheForWorksheet()

  /**
   * Get the currently defined locale code
   *
   * @return string
   */
  public function getLocale() {
    return self::$_localeLanguage;
  }

  //	function getLocale()

  /**
   * Set the locale code
   *
   * @param string $locale  The locale to use for formula translation
   * @return boolean
   */
  public function setLocale($locale = 'en_us') {

    //	Identify our locale and language
    $language = $locale = strtolower($locale);
    if (strpos($locale, '_') !== FALSE) {
      list($language) = explode('_', $locale);
    }
    if (count(self::$_validLocaleLanguages) == 1) {
      self::_loadLocales();
    }

    //	Test whether we have any language data for this language (any locale)
    if (in_array($language, self::$_validLocaleLanguages)) {

      //	initialise language/locale settings
      self::$_localeFunctions = array();
      self::$_localeArgumentSeparator = ',';
      self::$_localeBoolean = array(
        'TRUE' => 'TRUE',
        'FALSE' => 'FALSE',
        'NULL' => 'NULL',
      );

      //	Default is English, if user isn't requesting english, then read the necessary data from the locale files
      if ($locale != 'en_us') {

        //	Search for a file with a list of function names for locale
        $functionNamesFile = PHPEXCEL_ROOT . 'PHPExcel' . DIRECTORY_SEPARATOR . 'locale' . DIRECTORY_SEPARATOR . str_replace('_', DIRECTORY_SEPARATOR, $locale) . DIRECTORY_SEPARATOR . 'functions';
        if (!file_exists($functionNamesFile)) {

          //	If there isn't a locale specific function file, look for a language specific function file
          $functionNamesFile = PHPEXCEL_ROOT . 'PHPExcel' . DIRECTORY_SEPARATOR . 'locale' . DIRECTORY_SEPARATOR . $language . DIRECTORY_SEPARATOR . 'functions';
          if (!file_exists($functionNamesFile)) {
            return FALSE;
          }
        }

        //	Retrieve the list of locale or language specific function names
        $localeFunctions = file($functionNamesFile, FILE_IGNORE_NEW_LINES | FILE_SKIP_EMPTY_LINES);
        foreach ($localeFunctions as $localeFunction) {
          list($localeFunction) = explode('##', $localeFunction);

          //	Strip out comments
          if (strpos($localeFunction, '=') !== FALSE) {
            list($fName, $lfName) = explode('=', $localeFunction);
            $fName = trim($fName);
            $lfName = trim($lfName);
            if (isset(self::$_PHPExcelFunctions[$fName]) && $lfName != '' && $fName != $lfName) {
              self::$_localeFunctions[$fName] = $lfName;
            }
          }
        }

        //	Default the TRUE and FALSE constants to the locale names of the TRUE() and FALSE() functions
        if (isset(self::$_localeFunctions['TRUE'])) {
          self::$_localeBoolean['TRUE'] = self::$_localeFunctions['TRUE'];
        }
        if (isset(self::$_localeFunctions['FALSE'])) {
          self::$_localeBoolean['FALSE'] = self::$_localeFunctions['FALSE'];
        }
        $configFile = PHPEXCEL_ROOT . 'PHPExcel' . DIRECTORY_SEPARATOR . 'locale' . DIRECTORY_SEPARATOR . str_replace('_', DIRECTORY_SEPARATOR, $locale) . DIRECTORY_SEPARATOR . 'config';
        if (!file_exists($configFile)) {
          $configFile = PHPEXCEL_ROOT . 'PHPExcel' . DIRECTORY_SEPARATOR . 'locale' . DIRECTORY_SEPARATOR . $language . DIRECTORY_SEPARATOR . 'config';
        }
        if (file_exists($configFile)) {
          $localeSettings = file($configFile, FILE_IGNORE_NEW_LINES | FILE_SKIP_EMPTY_LINES);
          foreach ($localeSettings as $localeSetting) {
            list($localeSetting) = explode('##', $localeSetting);

            //	Strip out comments
            if (strpos($localeSetting, '=') !== FALSE) {
              list($settingName, $settingValue) = explode('=', $localeSetting);
              $settingName = strtoupper(trim($settingName));
              switch ($settingName) {
                case 'ARGUMENTSEPARATOR':
                  self::$_localeArgumentSeparator = trim($settingValue);
                  break;
              }
            }
          }
        }
      }
      self::$functionReplaceFromExcel = self::$functionReplaceToExcel = self::$functionReplaceFromLocale = self::$functionReplaceToLocale = NULL;
      self::$_localeLanguage = $locale;
      return TRUE;
    }
    return FALSE;
  }

  //	function setLocale()
  public static function _translateSeparator($fromSeparator, $toSeparator, $formula, &$inBraces) {
    $strlen = mb_strlen($formula);
    for ($i = 0; $i < $strlen; ++$i) {
      $chr = mb_substr($formula, $i, 1);
      switch ($chr) {
        case '{':
          $inBraces = TRUE;
          break;
        case '}':
          $inBraces = FALSE;
          break;
        case $fromSeparator:
          if (!$inBraces) {
            $formula = mb_substr($formula, 0, $i) . $toSeparator . mb_substr($formula, $i + 1);
          }
      }
    }
    return $formula;
  }
  private static function _translateFormula($from, $to, $formula, $fromSeparator, $toSeparator) {

    //	Convert any Excel function names to the required language
    if (self::$_localeLanguage !== 'en_us') {
      $inBraces = FALSE;

      //	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);
        $i = FALSE;
        foreach ($temp as &$value) {

          //	Only count/replace in alternating array entries
          if ($i = !$i) {
            $value = preg_replace($from, $to, $value);
            $value = self::_translateSeparator($fromSeparator, $toSeparator, $value, $inBraces);
          }
        }
        unset($value);

        //	Then rebuild the formula string
        $formula = implode('"', $temp);
      }
      else {

        //	If there's no quoted strings, then we do a simple count/replace
        $formula = preg_replace($from, $to, $formula);
        $formula = self::_translateSeparator($fromSeparator, $toSeparator, $formula, $inBraces);
      }
    }
    return $formula;
  }
  private static $functionReplaceFromExcel = NULL;
  private static $functionReplaceToLocale = NULL;
  public function _translateFormulaToLocale($formula) {
    if (self::$functionReplaceFromExcel === NULL) {
      self::$functionReplaceFromExcel = array();
      foreach (array_keys(self::$_localeFunctions) as $excelFunctionName) {
        self::$functionReplaceFromExcel[] = '/(@?[^\\w\\.])' . preg_quote($excelFunctionName) . '([\\s]*\\()/Ui';
      }
      foreach (array_keys(self::$_localeBoolean) as $excelBoolean) {
        self::$functionReplaceFromExcel[] = '/(@?[^\\w\\.])' . preg_quote($excelBoolean) . '([^\\w\\.])/Ui';
      }
    }
    if (self::$functionReplaceToLocale === NULL) {
      self::$functionReplaceToLocale = array();
      foreach (array_values(self::$_localeFunctions) as $localeFunctionName) {
        self::$functionReplaceToLocale[] = '$1' . trim($localeFunctionName) . '$2';
      }
      foreach (array_values(self::$_localeBoolean) as $localeBoolean) {
        self::$functionReplaceToLocale[] = '$1' . trim($localeBoolean) . '$2';
      }
    }
    return self::_translateFormula(self::$functionReplaceFromExcel, self::$functionReplaceToLocale, $formula, ',', self::$_localeArgumentSeparator);
  }

  //	function _translateFormulaToLocale()
  private static $functionReplaceFromLocale = NULL;
  private static $functionReplaceToExcel = NULL;
  public function _translateFormulaToEnglish($formula) {
    if (self::$functionReplaceFromLocale === NULL) {
      self::$functionReplaceFromLocale = array();
      foreach (array_values(self::$_localeFunctions) as $localeFunctionName) {
        self::$functionReplaceFromLocale[] = '/(@?[^\\w\\.])' . preg_quote($localeFunctionName) . '([\\s]*\\()/Ui';
      }
      foreach (array_values(self::$_localeBoolean) as $excelBoolean) {
        self::$functionReplaceFromLocale[] = '/(@?[^\\w\\.])' . preg_quote($excelBoolean) . '([^\\w\\.])/Ui';
      }
    }
    if (self::$functionReplaceToExcel === NULL) {
      self::$functionReplaceToExcel = array();
      foreach (array_keys(self::$_localeFunctions) as $excelFunctionName) {
        self::$functionReplaceToExcel[] = '$1' . trim($excelFunctionName) . '$2';
      }
      foreach (array_keys(self::$_localeBoolean) as $excelBoolean) {
        self::$functionReplaceToExcel[] = '$1' . trim($excelBoolean) . '$2';
      }
    }
    return self::_translateFormula(self::$functionReplaceFromLocale, self::$functionReplaceToExcel, $formula, self::$_localeArgumentSeparator, ',');
  }

  //	function _translateFormulaToEnglish()
  public static function _localeFunc($function) {
    if (self::$_localeLanguage !== 'en_us') {
      $functionName = trim($function, '(');
      if (isset(self::$_localeFunctions[$functionName])) {
        $brace = $functionName != $function;
        $function = self::$_localeFunctions[$functionName];
        if ($brace) {
          $function .= '(';
        }
      }
    }
    return $function;
  }

  /**
   * Wrap string values in quotes
   *
   * @param mixed $value
   * @return mixed
   */
  public static function _wrapResult($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()

  /**
   * Remove quotes used as a wrapper to identify string values
   *
   * @param mixed $value
   * @return mixed
   */
  public static function _unwrapResult($value) {
    if (is_string($value)) {
      if (isset($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()

  /**
   * Calculate cell value (using formula from a cell ID)
   * Retained for backward compatibility
   *
   * @access	public
   * @param	PHPExcel_Cell	$pCell	Cell to calculate
   * @return	mixed
   * @throws	PHPExcel_Calculation_Exception
   */
  public function calculate(PHPExcel_Cell $pCell = NULL) {
    try {
      return $this
        ->calculateCellValue($pCell);
    } catch (PHPExcel_Exception $e) {
      throw new PHPExcel_Calculation_Exception($e
        ->getMessage());
    }
  }

  //	function calculate()

  /**
   * Calculate the value of a cell formula
   *
   * @access	public
   * @param	PHPExcel_Cell	$pCell		Cell to calculate
   * @param	Boolean			$resetLog	Flag indicating whether the debug log should be reset or not
   * @return	mixed
   * @throws	PHPExcel_Calculation_Exception
   */
  public function calculateCellValue(PHPExcel_Cell $pCell = NULL, $resetLog = TRUE) {
    if ($pCell === NULL) {
      return NULL;
    }
    $returnArrayAsType = self::$returnArrayAsType;
    if ($resetLog) {

      //	Initialise the logging settings if requested
      $this->formulaError = null;
      $this->_debugLog
        ->clearLog();
      $this->_cyclicReferenceStack
        ->clear();
      $this->_cyclicFormulaCount = 1;
      self::$returnArrayAsType = self::RETURN_ARRAY_AS_ARRAY;
    }

    //	Execute the calculation for the cell formula
    $this->_cellStack[] = array(
      'sheet' => $pCell
        ->getWorksheet()
        ->getTitle(),
      'cell' => $pCell
        ->getCoordinate(),
    );
    try {
      $result = self::_unwrapResult($this
        ->_calculateFormulaValue($pCell
        ->getValue(), $pCell
        ->getCoordinate(), $pCell));
      $cellAddress = array_pop($this->_cellStack);
      $this->_workbook
        ->getSheetByName($cellAddress['sheet'])
        ->getCell($cellAddress['cell']);
    } catch (PHPExcel_Exception $e) {
      $cellAddress = array_pop($this->_cellStack);
      $this->_workbook
        ->getSheetByName($cellAddress['sheet'])
        ->getCell($cellAddress['cell']);
      throw new PHPExcel_Calculation_Exception($e
        ->getMessage());
    }
    if (is_array($result) && self::$returnArrayAsType != self::RETURN_ARRAY_AS_ARRAY) {
      self::$returnArrayAsType = $returnArrayAsType;
      $testResult = PHPExcel_Calculation_Functions::flattenArray($result);
      if (self::$returnArrayAsType == self::RETURN_ARRAY_AS_ERROR) {
        return PHPExcel_Calculation_Functions::VALUE();
      }

      //	If there's only a single cell in the array, then we allow it
      if (count($testResult) != 1) {

        //	If keys are numeric, then it's a matrix result rather than a cell range result, so we permit it
        $r = array_keys($result);
        $r = array_shift($r);
        if (!is_numeric($r)) {
          return PHPExcel_Calculation_Functions::VALUE();
        }
        if (is_array($result[$r])) {
          $c = array_keys($result[$r]);
          $c = array_shift($c);
          if (!is_numeric($c)) {
            return PHPExcel_Calculation_Functions::VALUE();
          }
        }
      }
      $result = array_shift($testResult);
    }
    self::$returnArrayAsType = $returnArrayAsType;
    if ($result === NULL) {
      return 0;
    }
    elseif (is_float($result) && (is_nan($result) || is_infinite($result))) {
      return PHPExcel_Calculation_Functions::NaN();
    }
    return $result;
  }

  //	function calculateCellValue(

  /**
   * Validate and parse a formula string
   *
   * @param	string		$formula		Formula to parse
   * @return	array
   * @throws	PHPExcel_Calculation_Exception
   */
  public function parseFormula($formula) {

    //	Basic validation that this is indeed a formula
    //	We return an empty array if not
    $formula = trim($formula);
    if (!isset($formula[0]) || $formula[0] != '=') {
      return array();
    }
    $formula = ltrim(substr($formula, 1));
    if (!isset($formula[0])) {
      return array();
    }

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

  //	function parseFormula()

  /**
   * Calculate the value of a formula
   *
   * @param	string			$formula	Formula to parse
   * @param	string			$cellID		Address of the cell to calculate
   * @param	PHPExcel_Cell	$pCell		Cell to calculate
   * @return	mixed
   * @throws	PHPExcel_Calculation_Exception
   */
  public function calculateFormula($formula, $cellID = NULL, PHPExcel_Cell $pCell = NULL) {

    //	Initialise the logging settings
    $this->formulaError = null;
    $this->_debugLog
      ->clearLog();
    $this->_cyclicReferenceStack
      ->clear();

    //	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
    try {
      $result = self::_unwrapResult($this
        ->_calculateFormulaValue($formula, $cellID, $pCell));
    } catch (PHPExcel_Exception $e) {
      throw new PHPExcel_Calculation_Exception($e
        ->getMessage());
    }

    //	Reset calculation cacheing to its previous state
    $this->_calculationCacheEnabled = $resetCache;
    return $result;
  }

  //	function calculateFormula()
  public function getValueFromCache($cellReference, &$cellValue) {

    // Is calculation cacheing enabled?
    // Is the value present in calculation cache?
    $this->_debugLog
      ->writeDebugLog('Testing cache value for cell ', $cellReference);
    if ($this->_calculationCacheEnabled && isset($this->_calculationCache[$cellReference])) {
      $this->_debugLog
        ->writeDebugLog('Retrieving value for cell ', $cellReference, ' from cache');

      // Return the cached result
      $cellValue = $this->_calculationCache[$cellReference];
      return TRUE;
    }
    return FALSE;
  }
  public function saveValueToCache($cellReference, $cellValue) {
    if ($this->_calculationCacheEnabled) {
      $this->_calculationCache[$cellReference] = $cellValue;
    }
  }

  /**
   * Parse a cell formula and calculate its value
   *
   * @param	string			$formula	The formula to parse and calculate
   * @param	string			$cellID		The ID (e.g. A3) of the cell that we are calculating
   * @param	PHPExcel_Cell	$pCell		Cell to calculate
   * @return	mixed
   * @throws	PHPExcel_Calculation_Exception
   */
  public function _calculateFormulaValue($formula, $cellID = null, PHPExcel_Cell $pCell = null) {
    $cellValue = null;

    //	Basic validation that this is indeed a formula
    //	We simply return the cell value if not
    $formula = trim($formula);
    if ($formula[0] != '=') {
      return self::_wrapResult($formula);
    }
    $formula = ltrim(substr($formula, 1));
    if (!isset($formula[0])) {
      return self::_wrapResult($formula);
    }
    $pCellParent = $pCell !== NULL ? $pCell
      ->getWorksheet() : NULL;
    $wsTitle = $pCellParent !== NULL ? $pCellParent
      ->getTitle() : "\0Wrk";
    $wsCellReference = $wsTitle . '!' . $cellID;
    if ($cellID !== NULL && $this
      ->getValueFromCache($wsCellReference, $cellValue)) {
      return $cellValue;
    }
    if ($wsTitle[0] !== "\0" && $this->_cyclicReferenceStack
      ->onStack($wsCellReference)) {
      if ($this->cyclicFormulaCount <= 0) {
        $this->_cyclicFormulaCell = '';
        return $this
          ->_raiseFormulaError('Cyclic Reference in Formula');
      }
      elseif ($this->_cyclicFormulaCell === $wsCellReference) {
        ++$this->_cyclicFormulaCount;
        if ($this->_cyclicFormulaCount >= $this->cyclicFormulaCount) {
          $this->_cyclicFormulaCell = '';
          return $cellValue;
        }
      }
      elseif ($this->_cyclicFormulaCell == '') {
        if ($this->_cyclicFormulaCount >= $this->cyclicFormulaCount) {
          return $cellValue;
        }
        $this->_cyclicFormulaCell = $wsCellReference;
      }
    }

    //	Parse the formula onto the token stack and calculate the value
    $this->_cyclicReferenceStack
      ->push($wsCellReference);
    $cellValue = $this
      ->_processTokenStack($this
      ->_parseFormula($formula, $pCell), $cellID, $pCell);
    $this->_cyclicReferenceStack
      ->pop();

    // Save to calculation cache
    if ($cellID !== NULL) {
      $this
        ->saveValueToCache($wsCellReference, $cellValue);
    }

    //	Return the calculated value
    return $cellValue;
  }

  //	function _calculateFormulaValue()

  /**
   * Ensure that paired matrix operands are both matrices and of the same size
   *
   * @param	mixed		&$operand1	First matrix operand
   * @param	mixed		&$operand2	Second matrix operand
   * @param	integer		$resize		Flag indicating whether the matrices should be resized to match
   *										and (if so), whether the smaller dimension should grow or the
   *										larger should shrink.
   *											0 = no resize
   *											1 = shrink to fit
   *											2 = extend to fit
   */
  private static function _checkMatrixOperands(&$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));
      $resize = 0;
    }
    list($matrix1Rows, $matrix1Columns) = self::_getMatrixDimensions($operand1);
    list($matrix2Rows, $matrix2Columns) = self::_getMatrixDimensions($operand2);
    if ($matrix1Rows == $matrix2Columns && $matrix2Rows == $matrix1Columns) {
      $resize = 1;
    }
    if ($resize == 2) {

      //	Given two matrices of (potentially) unequal size, convert the smaller in each dimension to match the larger
      self::_resizeMatricesExtend($operand1, $operand2, $matrix1Rows, $matrix1Columns, $matrix2Rows, $matrix2Columns);
    }
    elseif ($resize == 1) {

      //	Given two matrices of (potentially) unequal size, convert the larger in each dimension to match the smaller
      self::_resizeMatricesShrink($operand1, $operand2, $matrix1Rows, $matrix1Columns, $matrix2Rows, $matrix2Columns);
    }
    return array(
      $matrix1Rows,
      $matrix1Columns,
      $matrix2Rows,
      $matrix2Columns,
    );
  }

  //	function _checkMatrixOperands()

  /**
   * Read the dimensions of a matrix, and re-index it with straight numeric keys starting from row 0, column 0
   *
   * @param	mixed		&$matrix		matrix operand
   * @return	array		An array comprising the number of rows, and number of columns
   */
  public static function _getMatrixDimensions(&$matrix) {
    $matrixRows = count($matrix);
    $matrixColumns = 0;
    foreach ($matrix as $rowKey => $rowValue) {
      $matrixColumns = max(count($rowValue), $matrixColumns);
      if (!is_array($rowValue)) {
        $matrix[$rowKey] = array(
          $rowValue,
        );
      }
      else {
        $matrix[$rowKey] = array_values($rowValue);
      }
    }
    $matrix = array_values($matrix);
    return array(
      $matrixRows,
      $matrixColumns,
    );
  }

  //	function _getMatrixDimensions()

  /**
   * Ensure that paired matrix operands are both matrices of the same size
   *
   * @param	mixed		&$matrix1		First matrix operand
   * @param	mixed		&$matrix2		Second matrix operand
   * @param	integer		$matrix1Rows	Row size of first matrix operand
   * @param	integer		$matrix1Columns	Column size of first matrix operand
   * @param	integer		$matrix2Rows	Row size of second matrix operand
   * @param	integer		$matrix2Columns	Column size of second matrix operand
   */
  private static function _resizeMatricesShrink(&$matrix1, &$matrix2, $matrix1Rows, $matrix1Columns, $matrix2Rows, $matrix2Columns) {
    if ($matrix2Columns < $matrix1Columns || $matrix2Rows < $matrix1Rows) {
      if ($matrix2Rows < $matrix1Rows) {
        for ($i = $matrix2Rows; $i < $matrix1Rows; ++$i) {
          unset($matrix1[$i]);
        }
      }
      if ($matrix2Columns < $matrix1Columns) {
        for ($i = 0; $i < $matrix1Rows; ++$i) {
          for ($j = $matrix2Columns; $j < $matrix1Columns; ++$j) {
            unset($matrix1[$i][$j]);
          }
        }
      }
    }
    if ($matrix1Columns < $matrix2Columns || $matrix1Rows < $matrix2Rows) {
      if ($matrix1Rows < $matrix2Rows) {
        for ($i = $matrix1Rows; $i < $matrix2Rows; ++$i) {
          unset($matrix2[$i]);
        }
      }
      if ($matrix1Columns < $matrix2Columns) {
        for ($i = 0; $i < $matrix2Rows; ++$i) {
          for ($j = $matrix1Columns; $j < $matrix2Columns; ++$j) {
            unset($matrix2[$i][$j]);
          }
        }
      }
    }
  }

  //	function _resizeMatricesShrink()

  /**
   * Ensure that paired matrix operands are both matrices of the same size
   *
   * @param	mixed		&$matrix1	First matrix operand
   * @param	mixed		&$matrix2	Second matrix operand
   * @param	integer		$matrix1Rows	Row size of first matrix operand
   * @param	integer		$matrix1Columns	Column size of first matrix operand
   * @param	integer		$matrix2Rows	Row size of second matrix operand
   * @param	integer		$matrix2Columns	Column size of second matrix operand
   */
  private static function _resizeMatricesExtend(&$matrix1, &$matrix2, $matrix1Rows, $matrix1Columns, $matrix2Rows, $matrix2Columns) {
    if ($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()

  /**
   * Format details of an operand for display in the log (based on operand type)
   *
   * @param	mixed		$value	First matrix operand
   * @return	mixed
   */
  private function _showValue($value) {
    if ($this->_debugLog
      ->getWriteDebugLog()) {
      $testArray = PHPExcel_Calculation_Functions::flattenArray($value);
      if (count($testArray) == 1) {
        $value = array_pop($testArray);
      }
      if (is_array($value)) {
        $returnMatrix = array();
        $pad = $rpad = ', ';
        foreach ($value as $row) {
          if (is_array($row)) {
            $returnMatrix[] = implode($pad, array_map(array(
              $this,
              '_showValue',
            ), $row));
            $rpad = '; ';
          }
          else {
            $returnMatrix[] = $this
              ->_showValue($row);
          }
        }
        return '{ ' . implode($rpad, $returnMatrix) . ' }';
      }
      elseif (is_string($value) && trim($value, '"') == $value) {
        return '"' . $value . '"';
      }
      elseif (is_bool($value)) {
        return $value ? self::$_localeBoolean['TRUE'] : self::$_localeBoolean['FALSE'];
      }
    }
    return PHPExcel_Calculation_Functions::flattenSingleValue($value);
  }

  //	function _showValue()

  /**
   * Format type and details of an operand for display in the log (based on operand type)
   *
   * @param	mixed		$value	First matrix operand
   * @return	mixed
   */
  private function _showTypeDetails($value) {
    if ($this->_debugLog
      ->getWriteDebugLog()) {
      $testArray = PHPExcel_Calculation_Functions::flattenArray($value);
      if (count($testArray) == 1) {
        $value = array_pop($testArray);
      }
      if ($value === NULL) {
        return 'a NULL value';
      }
      elseif (is_float($value)) {
        $typeString = 'a floating point number';
      }
      elseif (is_int($value)) {
        $typeString = 'an integer number';
      }
      elseif (is_bool($value)) {
        $typeString = 'a boolean';
      }
      elseif (is_array($value)) {
        $typeString = 'a matrix';
      }
      else {
        if ($value == '') {
          return 'an empty string';
        }
        elseif ($value[0] == '#') {
          return 'a ' . $value . ' error';
        }
        else {
          $typeString = 'a string';
        }
      }
      return $typeString . ' with a value of ' . $this
        ->_showValue($value);
    }
  }

  //	function _showTypeDetails()
  private 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) {

      //	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);

        //	Open and Closed counts used for trapping mismatched braces in the formula
        $openCount = $closeCount = 0;
        $i = FALSE;
        foreach ($temp as &$value) {

          //	Only count/replace in alternating array entries
          if ($i = !$i) {
            $openCount += substr_count($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()
  //	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
  private static $_operatorAssociativity = array(
    '^' => 0,
    //	Exponentiation
    '*' => 0,
    '/' => 0,
    //	Multiplication and Division
    '+' => 0,
    '-' => 0,
    //	Addition and Subtraction
    '&' => 0,
    //	Concatenation
    '|' => 0,
    ':' => 0,
    //	Intersect and Range
    '>' => 0,
    '<' => 0,
    '=' => 0,
    '>=' => 0,
    '<=' => 0,
    '<>' => 0,
  );

  //	Comparison (Boolean) Operators
  //	These operators work on two values, but always return a boolean result
  private static $_comparisonOperators = array(
    '>' => TRUE,
    '<' => TRUE,
    '=' => TRUE,
    '>=' => TRUE,
    '<=' => TRUE,
    '<>' => TRUE,
  );

  //	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
  private static $_operatorPrecedence = array(
    ':' => 8,
    //	Range
    '|' => 7,
    //	Intersect
    '~' => 6,
    //	Negation
    '%' => 5,
    //	Percentage
    '^' => 4,
    //	Exponentiation
    '*' => 3,
    '/' => 3,
    //	Multiplication and Division
    '+' => 2,
    '-' => 2,
    //	Addition and Subtraction
    '&' => 1,
    //	Concatenation
    '>' => 0,
    '<' => 0,
    '=' => 0,
    '>=' => 0,
    '<=' => 0,
    '<>' => 0,
  );

  // Convert infix to postfix notation
  private function _parseFormula($formula, PHPExcel_Cell $pCell = NULL) {
    if (($formula = $this
      ->_convertMatrixReferences(trim($formula))) === FALSE) {
      return FALSE;
    }

    //	If we're using cell caching, then $pCell may well be flushed back to the cache (which detaches the parent worksheet),
    //		so we store the parent worksheet so that we can re-attach it when necessary
    $pCellParent = $pCell !== NULL ? $pCell
      ->getWorksheet() : NULL;
    $regexpMatchString = '/^(' . self::CALCULATION_REGEXP_FUNCTION . '|' . self::CALCULATION_REGEXP_CELLREF . '|' . self::CALCULATION_REGEXP_NUMBER . '|' . self::CALCULATION_REGEXP_STRING . '|' . self::CALCULATION_REGEXP_OPENBRACE . '|' . self::CALCULATION_REGEXP_NAMEDRANGE . '|' . self::CALCULATION_REGEXP_ERROR . ')/si';

    //	Start with initialisation
    $index = 0;
    $stack = new PHPExcel_Calculation_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 '.substr($formula, $index),PHP_EOL;
      $opCharacter = $formula[$index];

      //	Get the first character of the value at the current index position

      //echo 'Initial character of expression block is '.$opCharacter,PHP_EOL;
      if (isset(self::$_comparisonOperators[$opCharacter]) && strlen($formula) > $index && isset(self::$_comparisonOperators[$formula[$index + 1]])) {
        $opCharacter .= $formula[++$index];

        //echo 'Initial character of expression block is comparison operator '.$opCharacter.PHP_EOL;
      }

      //	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').PHP_EOL;

      //var_dump($match);
      if ($opCharacter == '-' && !$expectingOperator) {

        //	Is it a negation instead of a minus?

        //echo 'Element is a Negation operator',PHP_EOL;
        $stack
          ->push('Unary Operator', '~');

        //	Put a negation on the stack
        ++$index;

        //		and drop the negation symbol
      }
      elseif ($opCharacter == '%' && $expectingOperator) {

        //echo 'Element is a Percentage operator',PHP_EOL;
        $stack
          ->push('Unary Operator', '%');

        //	Put a percentage on the stack
        ++$index;
      }
      elseif ($opCharacter == '+' && !$expectingOperator) {

        //	Positive (unary plus rather than binary operator plus) can be discarded?

        //echo 'Element is a Positive number, not Plus operator',PHP_EOL;
        ++$index;

        //	Drop the redundant plus symbol
      }
      elseif (($opCharacter == '~' || $opCharacter == '|') && !$isOperandOrFunction) {

        //	We have to explicitly deny a tilde or pipe, because they are legal
        return $this
          ->_raiseFormulaError("Formula Error: Illegal character '~'");

        //		on the stack but not in the input expression
      }
      elseif ((isset(self::$_operators[$opCharacter]) or $isOperandOrFunction) && $expectingOperator) {

        //	Are we putting an operator on the stack?

        //echo 'Element with value '.$opCharacter.' is an Operator',PHP_EOL;
        while ($stack
          ->count() > 0 && ($o2 = $stack
          ->last()) && isset(self::$_operators[$o2['value']]) && @(self::$_operatorAssociativity[$opCharacter] ? self::$_operatorPrecedence[$opCharacter] < self::$_operatorPrecedence[$o2['value']] : self::$_operatorPrecedence[$opCharacter] <= self::$_operatorPrecedence[$o2['value']])) {
          $output[] = $stack
            ->pop();

          //	Swap operands and higher precedence operators from the stack to the output
        }
        $stack
          ->push('Binary Operator', $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',PHP_EOL;
        $expectingOperand = FALSE;
        while (($o2 = $stack
          ->pop()) && $o2['value'] != '(') {

          //	Pop off the stack back to the last (
          if ($o2 === NULL) {
            return $this
              ->_raiseFormulaError('Formula Error: Unexpected closing brace ")"');
          }
          else {
            $output[] = $o2;
          }
        }
        $d = $stack
          ->last(2);
        if (preg_match('/^' . self::CALCULATION_REGEXP_FUNCTION . '$/i', $d['value'], $matches)) {

          //	Did this parenthesis just close a function?
          $functionName = $matches[1];

          //	Get the function name

          //echo 'Closed Function is '.$functionName,PHP_EOL;
          $d = $stack
            ->pop();
          $argumentCount = $d['value'];

          //	See how many arguments there were (argument count is the next value stored on the stack)

          //if ($argumentCount == 0) {

          //	echo 'With no arguments',PHP_EOL;

          //} elseif ($argumentCount == 1) {

          //	echo 'With 1 argument',PHP_EOL;

          //} else {

          //	echo 'With '.$argumentCount.' arguments',PHP_EOL;

          //}
          $output[] = $d;

          //	Dump the argument count on the output
          $output[] = $stack
            ->pop();

          //	Pop the function and push onto the output
          if (isset(self::$_controlFunctions[$functionName])) {

            //echo 'Built-in function '.$functionName,PHP_EOL;
            $expectedArgumentCount = self::$_controlFunctions[$functionName]['argumentCount'];
            $functionCall = self::$_controlFunctions[$functionName]['functionCall'];
          }
          elseif (isset(self::$_PHPExcelFunctions[$functionName])) {

            //echo 'PHPExcel function '.$functionName,PHP_EOL;
            $expectedArgumentCount = self::$_PHPExcelFunctions[$functionName]['argumentCount'];
            $functionCall = self::$_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),PHP_EOL;
              if ($argumentCount > abs($expectedArgumentCount)) {
                $argumentCountError = TRUE;
                $expectedArgumentCountString = 'no more than ' . abs($expectedArgumentCount);
              }
            }
            else {

              //echo '$expectedArgumentCount is numeric '.$expectedArgumentCount,PHP_EOL;
              if ($argumentCount != $expectedArgumentCount) {
                $argumentCountError = TRUE;
                $expectedArgumentCountString = $expectedArgumentCount;
              }
            }
          }
          elseif ($expectedArgumentCount != '*') {
            $isOperandOrFunction = preg_match('/(\\d*)([-+,])(\\d*)/', $expectedArgumentCount, $argMatch);

            //print_r($argMatch);

            //echo PHP_EOL;
            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 separator for function arguments?

        //echo 'Element is a Function argument separator',PHP_EOL;
        while (($o2 = $stack
          ->pop()) && $o2['value'] != '(') {

          //	Pop off the stack back to the last (
          if ($o2 === NULL) {
            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) {
          $output[] = array(
            'type' => 'NULL Value',
            'value' => self::$_ExcelConstants['NULL'],
            'reference' => NULL,
          );
        }

        // make sure there was a function
        $d = $stack
          ->last(2);
        if (!preg_match('/^' . self::CALCULATION_REGEXP_FUNCTION . '$/i', $d['value'], $matches)) {
          return $this
            ->_raiseFormulaError("Formula Error: Unexpected ,");
        }
        $d = $stack
          ->pop();
        $stack
          ->push($d['type'], ++$d['value'], $d['reference']);

        // increment the argument count
        $stack
          ->push('Brace', '(');

        // 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 />';
        $stack
          ->push('Brace', '(');
        ++$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/u', '', $val);

          //					echo 'Element '.$val.' is a Function<br />';
          if (isset(self::$_PHPExcelFunctions[strtoupper($matches[1])]) || isset(self::$_controlFunctions[strtoupper($matches[1])])) {

            // it's a function
            $stack
              ->push('Function', strtoupper($val));
            $ax = preg_match('/^\\s*(\\s*\\))/ui', substr($formula, $index + $length), $amatch);
            if ($ax) {
              $stack
                ->push('Operand Count for Function ' . strtoupper($val) . ')', 0);
              $expectingOperator = TRUE;
            }
            else {
              $stack
                ->push('Operand Count for Function ' . strtoupper($val) . ')', 1);
              $expectingOperator = FALSE;
            }
            $stack
              ->push('Brace', '(');
          }
          else {

            // it's a var w/ implicit multiplication
            $output[] = array(
              'type' => 'Value',
              'value' => $matches[1],
              'reference' => NULL,
            );
          }
        }
        elseif (preg_match('/^' . self::CALCULATION_REGEXP_CELLREF . '$/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
          //	If the last entry on the stack was a : operator, then we have a cell range reference
          $testPrevOp = $stack
            ->last(1);
          if ($testPrevOp['value'] == ':') {

            //	If we have a worksheet reference, then we're playing with a 3D reference
            if ($matches[2] == '') {

              //	Otherwise, we 'inherit' the worksheet reference from the start cell reference
              //	The start of the cell range reference should be the last entry in $output
              $startCellRef = $output[count($output) - 1]['value'];
              preg_match('/^' . self::CALCULATION_REGEXP_CELLREF . '$/i', $startCellRef, $startMatches);
              if ($startMatches[2] > '') {
                $val = $startMatches[2] . '!' . $val;
              }
            }
            else {
              return $this
                ->_raiseFormulaError("3D Range references are not yet supported");
            }
          }
          $output[] = array(
            'type' => 'Cell Reference',
            'value' => $val,
            'reference' => $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 the last entry on the stack was a : operator, then we may have a row or column range reference
          $testPrevOp = $stack
            ->last(1);
          if ($testPrevOp['value'] == ':') {
            $startRowColRef = $output[count($output) - 1]['value'];
            $rangeWS1 = '';
            if (strpos('!', $startRowColRef) !== FALSE) {
              list($rangeWS1, $startRowColRef) = explode('!', $startRowColRef);
            }
            if ($rangeWS1 != '') {
              $rangeWS1 .= '!';
            }
            $rangeWS2 = $rangeWS1;
            if (strpos('!', $val) !== FALSE) {
              list($rangeWS2, $val) = explode('!', $val);
            }
            if ($rangeWS2 != '') {
              $rangeWS2 .= '!';
            }
            if (is_integer($startRowColRef) && ctype_digit($val) && $startRowColRef <= 1048576 && $val <= 1048576) {

              //	Row range
              $endRowColRef = $pCellParent !== NULL ? $pCellParent
                ->getHighestColumn() : 'XFD';

              //	Max 16,384 columns for Excel2007
              $output[count($output) - 1]['value'] = $rangeWS1 . 'A' . $startRowColRef;
              $val = $rangeWS2 . $endRowColRef . $val;
            }
            elseif (ctype_alpha($startRowColRef) && ctype_alpha($val) && strlen($startRowColRef) <= 3 && strlen($val) <= 3) {

              //	Column range
              $endRowColRef = $pCellParent !== NULL ? $pCellParent
                ->getHighestRow() : 1048576;

              //	Max 1,048,576 rows for Excel2007
              $output[count($output) - 1]['value'] = $rangeWS1 . strtoupper($startRowColRef) . '1';
              $val = $rangeWS2 . $val . $endRowColRef;
            }
          }
          $localeConstant = FALSE;
          if ($opCharacter == '"') {

            //						echo 'Element is a String<br />';
            //	UnEscape any quotes within the string
            $val = self::_wrapResult(str_replace('""', '"', self::_unwrapResult($val)));
          }
          elseif (is_numeric($val)) {

            //						echo 'Element is a Number<br />';
            if (strpos($val, '.') !== FALSE || stripos($val, 'e') !== FALSE || $val > PHP_INT_MAX || $val < -PHP_INT_MAX) {

              //							echo 'Casting '.$val.' to float<br />';
              $val = (double) $val;
            }
            else {

              //							echo 'Casting '.$val.' to integer<br />';
              $val = (int) $val;
            }
          }
          elseif (isset(self::$_ExcelConstants[trim(strtoupper($val))])) {
            $excelConstant = trim(strtoupper($val));

            //						echo 'Element '.$excelConstant.' is an Excel Constant<br />';
            $val = self::$_ExcelConstants[$excelConstant];
          }
          elseif (($localeConstant = array_search(trim(strtoupper($val)), self::$_localeBoolean)) !== FALSE) {

            //						echo 'Element '.$localeConstant.' is an Excel Constant<br />';
            $val = self::$_ExcelConstants[$localeConstant];
          }
          $details = array(
            'type' => 'Value',
            'value' => $val,
            'reference' => NULL,
          );
          if ($localeConstant) {
            $details['localeValue'] = $localeConstant;
          }
          $output[] = $details;
        }
        $index += $length;
      }
      elseif ($opCharacter == '$') {

        // absolute row or column range
        ++$index;
      }
      elseif ($opCharacter == ')') {

        // miscellaneous error checking
        if ($expectingOperand) {
          $output[] = array(
            'type' => 'NULL Value',
            'value' => self::$_ExcelConstants['NULL'],
            'reference' => NULL,
          );
          $expectingOperand = FALSE;
          $expectingOperator = TRUE;
        }
        else {
          return $this
            ->_raiseFormulaError("Formula Error: Unexpected ')'");
        }
      }
      elseif (isset(self::$_operators[$opCharacter]) && !$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 (isset(self::$_operators[$opCharacter]) && $opCharacter != '%') {
          return $this
            ->_raiseFormulaError("Formula Error: Operator '{$opCharacter}' has no operands");
        }
        else {
          break;
        }
      }

      //	Ignore white space
      while ($formula[$index] == "\n" || $formula[$index] == "\r") {
        ++$index;
      }
      if ($formula[$index] == ' ') {
        while ($formula[$index] == ' ') {
          ++$index;
        }

        //	If we're expecting an operator, but only have a space between the previous and next operands (and both are
        //		Cell References) then we have an INTERSECTION operator
        //				echo 'Possible Intersect Operator<br />';
        if ($expectingOperator && preg_match('/^' . self::CALCULATION_REGEXP_CELLREF . '.*/Ui', substr($formula, $index), $match) && $output[count($output) - 1]['type'] == 'Cell Reference') {

          //					echo 'Element is an Intersect Operator<br />';
          while ($stack
            ->count() > 0 && ($o2 = $stack
            ->last()) && isset(self::$_operators[$o2['value']]) && @(self::$_operatorAssociativity[$opCharacter] ? self::$_operatorPrecedence[$opCharacter] < self::$_operatorPrecedence[$o2['value']] : self::$_operatorPrecedence[$opCharacter] <= self::$_operatorPrecedence[$o2['value']])) {
            $output[] = $stack
              ->pop();

            //	Swap operands and higher precedence operators from the stack to the output
          }
          $stack
            ->push('Binary Operator', '|');

          //	Put an Intersect Operator on the stack
          $expectingOperator = FALSE;
        }
      }
    }
    while (($op = $stack
      ->pop()) !== NULL) {

      // pop everything off the stack and push onto output
      if (is_array($op) && $op['value'] == '(' || $op === '(') {
        return $this
          ->_raiseFormulaError("Formula Error: Expecting ')'");
      }

      // if there are any opening braces on the stack, then braces were unbalanced
      $output[] = $op;
    }
    return $output;
  }

  //	function _parseFormula()
  private static function _dataTestReference(&$operandData) {
    $operand = $operandData['value'];
    if ($operandData['reference'] === NULL && is_array($operand)) {
      $rKeys = array_keys($operand);
      $rowKey = array_shift($rKeys);
      $cKeys = array_keys(array_keys($operand[$rowKey]));
      $colKey = array_shift($cKeys);
      if (ctype_upper($colKey)) {
        $operandData['reference'] = $colKey . $rowKey;
      }
    }
    return $operand;
  }

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

    //	If we're using cell caching, then $pCell may well be flushed back to the cache (which detaches the parent cell collection),
    //		so we store the parent cell collection so that we can re-attach it when necessary
    $pCellWorksheet = $pCell !== NULL ? $pCell
      ->getWorksheet() : NULL;
    $pCellParent = $pCell !== NULL ? $pCell
      ->getParent() : null;
    $stack = new PHPExcel_Calculation_Token_Stack();

    //	Loop through each token in turn
    foreach ($tokens as $tokenData) {

      //			print_r($tokenData);
      //			echo '<br />';
      $token = $tokenData['value'];

      //			echo '<b>Token is '.$token.'</b><br />';
      // if the token is a binary operator, pop the top two values off the stack, do the operation, and push the result back on the stack
      if (isset(self::$_binaryOperators[$token])) {

        //				echo 'Token is a binary operator<br />';
        //	We must have two operands, error if we don't
        if (($operand2Data = $stack
          ->pop()) === NULL) {
          return $this
            ->_raiseFormulaError('Internal error - Operand value missing from stack');
        }
        if (($operand1Data = $stack
          ->pop()) === NULL) {
          return $this
            ->_raiseFormulaError('Internal error - Operand value missing from stack');
        }
        $operand1 = self::_dataTestReference($operand1Data);
        $operand2 = self::_dataTestReference($operand2Data);

        //	Log what we're doing
        if ($token == ':') {
          $this->_debugLog
            ->writeDebugLog('Evaluating Range ', $this
            ->_showValue($operand1Data['reference']), ' ', $token, ' ', $this
            ->_showValue($operand2Data['reference']));
        }
        else {
          $this->_debugLog
            ->writeDebugLog('Evaluating ', $this
            ->_showValue($operand1), ' ', $token, ' ', $this
            ->_showValue($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 ':':

            //	Range
            $sheet1 = $sheet2 = '';
            if (strpos($operand1Data['reference'], '!') !== FALSE) {
              list($sheet1, $operand1Data['reference']) = explode('!', $operand1Data['reference']);
            }
            else {
              $sheet1 = $pCellParent !== NULL ? $pCellWorksheet
                ->getTitle() : '';
            }
            if (strpos($operand2Data['reference'], '!') !== FALSE) {
              list($sheet2, $operand2Data['reference']) = explode('!', $operand2Data['reference']);
            }
            else {
              $sheet2 = $sheet1;
            }
            if ($sheet1 == $sheet2) {
              if ($operand1Data['reference'] === NULL) {
                if (trim($operand1Data['value']) != '' && is_numeric($operand1Data['value'])) {
                  $operand1Data['reference'] = $pCell
                    ->getColumn() . $operand1Data['value'];
                }
                elseif (trim($operand1Data['reference']) == '') {
                  $operand1Data['reference'] = $pCell
                    ->getCoordinate();
                }
                else {
                  $operand1Data['reference'] = $operand1Data['value'] . $pCell
                    ->getRow();
                }
              }
              if ($operand2Data['reference'] === NULL) {
                if (trim($operand2Data['value']) != '' && is_numeric($operand2Data['value'])) {
                  $operand2Data['reference'] = $pCell
                    ->getColumn() . $operand2Data['value'];
                }
                elseif (trim($operand2Data['reference']) == '') {
                  $operand2Data['reference'] = $pCell
                    ->getCoordinate();
                }
                else {
                  $operand2Data['reference'] = $operand2Data['value'] . $pCell
                    ->getRow();
                }
              }
              $oData = array_merge(explode(':', $operand1Data['reference']), explode(':', $operand2Data['reference']));
              $oCol = $oRow = array();
              foreach ($oData as $oDatum) {
                $oCR = PHPExcel_Cell::coordinateFromString($oDatum);
                $oCol[] = PHPExcel_Cell::columnIndexFromString($oCR[0]) - 1;
                $oRow[] = $oCR[1];
              }
              $cellRef = PHPExcel_Cell::stringFromColumnIndex(min($oCol)) . min($oRow) . ':' . PHPExcel_Cell::stringFromColumnIndex(max($oCol)) . max($oRow);
              if ($pCellParent !== NULL) {
                $cellValue = $this
                  ->extractCellRange($cellRef, $this->_workbook
                  ->getSheetByName($sheet1), FALSE);
              }
              else {
                return $this
                  ->_raiseFormulaError('Unable to access Cell Reference');
              }
              $stack
                ->push('Cell Reference', $cellValue, $cellRef);
            }
            else {
              $stack
                ->push('Error', PHPExcel_Calculation_Functions::REF(), NULL);
            }
            break;
          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_bool($operand1)) {
              $operand1 = $operand1 ? self::$_localeBoolean['TRUE'] : self::$_localeBoolean['FALSE'];
            }
            if (is_bool($operand2)) {
              $operand2 = $operand2 ? self::$_localeBoolean['TRUE'] : self::$_localeBoolean['FALSE'];
            }
            if (is_array($operand1) || is_array($operand2)) {

              //	Ensure that both operands are arrays/matrices
              self::_checkMatrixOperands($operand1, $operand2, 2);
              try {

                //	Convert operand 1 from a PHP array to a matrix
                $matrix = new PHPExcel_Shared_JAMA_Matrix($operand1);

                //	Perform the required operation against the operand 1 matrix, passing in operand 2
                $matrixResult = $matrix
                  ->concat($operand2);
                $result = $matrixResult
                  ->getArray();
              } catch (PHPExcel_Exception $ex) {
                $this->_debugLog
                  ->writeDebugLog('JAMA Matrix Exception: ', $ex
                  ->getMessage());
                $result = '#VALUE!';
              }
            }
            else {
              $result = '"' . str_replace('""', '"', self::_unwrapResult($operand1, '"') . self::_unwrapResult($operand2, '"')) . '"';
            }
            $this->_debugLog
              ->writeDebugLog('Evaluation Result is ', $this
              ->_showTypeDetails($result));
            $stack
              ->push('Value', $result);
            break;
          case '|':

            //	Intersect
            $rowIntersect = array_intersect_key($operand1, $operand2);
            $cellIntersect = $oCol = $oRow = array();
            foreach (array_keys($rowIntersect) as $row) {
              $oRow[] = $row;
              foreach ($rowIntersect[$row] as $col => $data) {
                $oCol[] = PHPExcel_Cell::columnIndexFromString($col) - 1;
                $cellIntersect[$row] = array_intersect_key($operand1[$row], $operand2[$row]);
              }
            }
            $cellRef = PHPExcel_Cell::stringFromColumnIndex(min($oCol)) . min($oRow) . ':' . PHPExcel_Cell::stringFromColumnIndex(max($oCol)) . max($oRow);
            $this->_debugLog
              ->writeDebugLog('Evaluation Result is ', $this
              ->_showTypeDetails($cellIntersect));
            $stack
              ->push('Value', $cellIntersect, $cellRef);
            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 (($arg = $stack
          ->pop()) === NULL) {
          return $this
            ->_raiseFormulaError('Internal error - Operand value missing from stack');
        }
        $arg = $arg['value'];
        if ($token === '~') {

          //					echo 'Token is a negation operator<br />';
          $this->_debugLog
            ->writeDebugLog('Evaluating Negation of ', $this
            ->_showValue($arg));
          $multiplier = -1;
        }
        else {

          //					echo 'Token is a percentile operator<br />';
          $this->_debugLog
            ->writeDebugLog('Evaluating Percentile of ', $this
            ->_showValue($arg));
          $multiplier = 0.01;
        }
        if (is_array($arg)) {
          self::_checkMatrixOperands($arg, $multiplier, 2);
          try {
            $matrix1 = new PHPExcel_Shared_JAMA_Matrix($arg);
            $matrixResult = $matrix1
              ->arrayTimesEquals($multiplier);
            $result = $matrixResult
              ->getArray();
          } catch (PHPExcel_Exception $ex) {
            $this->_debugLog
              ->writeDebugLog('JAMA Matrix Exception: ', $ex
              ->getMessage());
            $result = '#VALUE!';
          }
          $this->_debugLog
            ->writeDebugLog('Evaluation Result is ', $this
            ->_showTypeDetails($result));
          $stack
            ->push('Value', $result);
        }
        else {
          $this
            ->_executeNumericBinaryOperation($cellID, $multiplier, $arg, '*', 'arrayTimesEquals', $stack);
        }
      }
      elseif (preg_match('/^' . self::CALCULATION_REGEXP_CELLREF . '$/i', $token, $matches)) {
        $cellRef = NULL;

        //				echo 'Element '.$token.' is a Cell reference<br />';
        if (isset($matches[8])) {

          //					echo 'Reference is a Range of cells<br />';
          if ($pCell === NULL) {

            //						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] > '') {
              $matches[2] = trim($matches[2], "\"'");
              if (strpos($matches[2], '[') !== FALSE || strpos($matches[2], ']') !== FALSE) {

                //	It's a Reference to an external workbook (not currently supported)
                return $this
                  ->_raiseFormulaError('Unable to access External Workbook');
              }
              $matches[2] = trim($matches[2], "\"'");

              //							echo '$cellRef='.$cellRef.' in worksheet '.$matches[2].'<br />';
              $this->_debugLog
                ->writeDebugLog('Evaluating Cell Range ', $cellRef, ' in worksheet ', $matches[2]);
              if ($pCellParent !== NULL) {
                $cellValue = $this
                  ->extractCellRange($cellRef, $this->_workbook
                  ->getSheetByName($matches[2]), FALSE);
              }
              else {
                return $this
                  ->_raiseFormulaError('Unable to access Cell Reference');
              }
              $this->_debugLog
                ->writeDebugLog('Evaluation Result for cells ', $cellRef, ' in worksheet ', $matches[2], ' is ', $this
                ->_showTypeDetails($cellValue));

              //							$cellRef = $matches[2].'!'.$cellRef;
            }
            else {

              //							echo '$cellRef='.$cellRef.' in current worksheet<br />';
              $this->_debugLog
                ->writeDebugLog('Evaluating Cell Range ', $cellRef, ' in current worksheet');
              if ($pCellParent !== NULL) {
                $cellValue = $this
                  ->extractCellRange($cellRef, $pCellWorksheet, FALSE);
              }
              else {
                return $this
                  ->_raiseFormulaError('Unable to access Cell Reference');
              }
              $this->_debugLog
                ->writeDebugLog('Evaluation Result for cells ', $cellRef, ' is ', $this
                ->_showTypeDetails($cellValue));
            }
          }
        }
        else {

          //					echo 'Reference is a single Cell<br />';
          if ($pCell === NULL) {

            //						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] > '') {
              $matches[2] = trim($matches[2], "\"'");
              if (strpos($matches[2], '[') !== FALSE || strpos($matches[2], ']') !== FALSE) {

                //	It's a Reference to an external workbook (not currently supported)
                return $this
                  ->_raiseFormulaError('Unable to access External Workbook');
              }

              //							echo '$cellRef='.$cellRef.' in worksheet '.$matches[2].'<br />';
              $this->_debugLog
                ->writeDebugLog('Evaluating Cell ', $cellRef, ' in worksheet ', $matches[2]);
              if ($pCellParent !== NULL) {
                $cellSheet = $this->_workbook
                  ->getSheetByName($matches[2]);
                if ($cellSheet && $cellSheet
                  ->cellExists($cellRef)) {
                  $cellValue = $this
                    ->extractCellRange($cellRef, $this->_workbook
                    ->getSheetByName($matches[2]), FALSE);
                  $pCell
                    ->attach($pCellParent);
                }
                else {
                  $cellValue = NULL;
                }
              }
              else {
                return $this
                  ->_raiseFormulaError('Unable to access Cell Reference');
              }
              $this->_debugLog
                ->writeDebugLog('Evaluation Result for cell ', $cellRef, ' in worksheet ', $matches[2], ' is ', $this
                ->_showTypeDetails($cellValue));

              //							$cellRef = $matches[2].'!'.$cellRef;
            }
            else {

              //							echo '$cellRef='.$cellRef.' in current worksheet<br />';
              $this->_debugLog
                ->writeDebugLog('Evaluating Cell ', $cellRef, ' in current worksheet');
              if ($pCellParent
                ->isDataSet($cellRef)) {
                $cellValue = $this
                  ->extractCellRange($cellRef, $pCellWorksheet, FALSE);
                $pCell
                  ->attach($pCellParent);
              }
              else {
                $cellValue = NULL;
              }
              $this->_debugLog
                ->writeDebugLog('Evaluation Result for cell ', $cellRef, ' is ', $this
                ->_showTypeDetails($cellValue));
            }
          }
        }
        $stack
          ->push('Value', $cellValue, $cellRef);

        // 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();
        $argCount = $argCount['value'];
        if ($functionName != 'MKMATRIX') {
          $this->_debugLog
            ->writeDebugLog('Evaluating Function ', self::_localeFunc($functionName), '() with ', $argCount == 0 ? 'no' : $argCount, ' argument', $argCount == 1 ? '' : 's');
        }
        if (isset(self::$_PHPExcelFunctions[$functionName]) || isset(self::$_controlFunctions[$functionName])) {

          // function
          if (isset(self::$_PHPExcelFunctions[$functionName])) {
            $functionCall = self::$_PHPExcelFunctions[$functionName]['functionCall'];
            $passByReference = isset(self::$_PHPExcelFunctions[$functionName]['passByReference']);
            $passCellReference = isset(self::$_PHPExcelFunctions[$functionName]['passCellReference']);
          }
          elseif (isset(self::$_controlFunctions[$functionName])) {
            $functionCall = self::$_controlFunctions[$functionName]['functionCall'];
            $passByReference = isset(self::$_controlFunctions[$functionName]['passByReference']);
            $passCellReference = isset(self::$_controlFunctions[$functionName]['passCellReference']);
          }

          // get the arguments for this function
          //					echo 'Function '.$functionName.' expects '.$argCount.' arguments<br />';
          $args = $argArrayVals = array();
          for ($i = 0; $i < $argCount; ++$i) {
            $arg = $stack
              ->pop();
            $a = $argCount - $i - 1;
            if ($passByReference && isset(self::$_PHPExcelFunctions[$functionName]['passByReference'][$a]) && self::$_PHPExcelFunctions[$functionName]['passByReference'][$a]) {
              if ($arg['reference'] === NULL) {
                $args[] = $cellID;
                if ($functionName != 'MKMATRIX') {
                  $argArrayVals[] = $this
                    ->_showValue($cellID);
                }
              }
              else {
                $args[] = $arg['reference'];
                if ($functionName != 'MKMATRIX') {
                  $argArrayVals[] = $this
                    ->_showValue($arg['reference']);
                }
              }
            }
            else {
              $args[] = self::_unwrapResult($arg['value']);
              if ($functionName != 'MKMATRIX') {
                $argArrayVals[] = $this
                  ->_showValue($arg['value']);
              }
            }
          }

          //	Reverse the order of the arguments
          krsort($args);
          if ($passByReference && $argCount == 0) {
            $args[] = $cellID;
            $argArrayVals[] = $this
              ->_showValue($cellID);
          }

          //					echo 'Arguments are: ';
          //					print_r($args);
          //					echo '<br />';
          if ($functionName != 'MKMATRIX') {
            if ($this->_debugLog
              ->getWriteDebugLog()) {
              krsort($argArrayVals);
              $this->_debugLog
                ->writeDebugLog('Evaluating ', self::_localeFunc($functionName), '( ', implode(self::$_localeArgumentSeparator . ' ', PHPExcel_Calculation_Functions::flattenArray($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->_debugLog->writeDebugLog('Argument is a matrix: ', $this->_showValue($operand1));
          //						$result = array();
          //						$row = 0;
          //						foreach($operand1 as $args) {
          //							if (is_array($args)) {
          //								foreach($args as $arg) {
          //									$this->_debugLog->writeDebugLog('Evaluating ', self::_localeFunc($functionName), '( ', $this->_showValue($arg), ' )');
          //									$r = call_user_func_array($functionCall,$arg);
          //									$this->_debugLog->writeDebugLog('Evaluation Result for ', self::_localeFunc($functionName), '() function call is ', $this->_showTypeDetails($r));
          //									$result[$row][] = $r;
          //								}
          //								++$row;
          //							} else {
          //								$this->_debugLog->writeDebugLog('Evaluating ', self::_localeFunc($functionName), '( ', $this->_showValue($args), ' )');
          //								$r = call_user_func_array($functionCall,$args);
          //								$this->_debugLog->writeDebugLog('Evaluation Result for ', self::_localeFunc($functionName), '() function call is ', $this->_showTypeDetails($r));
          //								$result[] = $r;
          //							}
          //						}
          //					} else {
          //	Process the argument with the appropriate function call
          if ($passCellReference) {
            $args[] = $pCell;
          }
          if (strpos($functionCall, '::') !== FALSE) {
            $result = call_user_func_array(explode('::', $functionCall), $args);
          }
          else {
            foreach ($args as &$arg) {
              $arg = PHPExcel_Calculation_Functions::flattenSingleValue($arg);
            }
            unset($arg);
            $result = call_user_func_array($functionCall, $args);
          }

          //					}
          if ($functionName != 'MKMATRIX') {
            $this->_debugLog
              ->writeDebugLog('Evaluation Result for ', self::_localeFunc($functionName), '() function call is ', $this
              ->_showTypeDetails($result));
          }
          $stack
            ->push('Value', self::_wrapResult($result));
        }
      }
      else {

        // if the token is a number, boolean, string or an Excel error, push it onto the stack
        if (isset(self::$_ExcelConstants[strtoupper($token)])) {
          $excelConstant = strtoupper($token);

          //					echo 'Token is a PHPExcel constant: '.$excelConstant.'<br />';
          $stack
            ->push('Constant Value', self::$_ExcelConstants[$excelConstant]);
          $this->_debugLog
            ->writeDebugLog('Evaluating Constant ', $excelConstant, ' as ', $this
            ->_showTypeDetails(self::$_ExcelConstants[$excelConstant]));
        }
        elseif (is_numeric($token) || $token === NULL || is_bool($token) || $token == '' || $token[0] == '"' || $token[0] == '#') {

          //					echo 'Token is a number, boolean, string, null or an Excel error<br />';
          $stack
            ->push('Value', $token);

          // if the token is a named range, push the named range name onto 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->_debugLog
            ->writeDebugLog('Evaluating Named Range ', $namedRange);
          $cellValue = $this
            ->extractNamedRange($namedRange, NULL !== $pCell ? $pCellWorksheet : NULL, FALSE);
          $pCell
            ->attach($pCellParent);
          $this->_debugLog
            ->writeDebugLog('Evaluation Result for named range ', $namedRange, ' is ', $this
            ->_showTypeDetails($cellValue));
          $stack
            ->push('Named Range', $cellValue, $namedRange);
        }
        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();
    $output = $output['value'];

    //		if ((is_array($output)) && (self::$returnArrayAsType != self::RETURN_ARRAY_AS_ARRAY)) {
    //			return array_shift(PHPExcel_Calculation_Functions::flattenArray($output));
    //		}
    return $output;
  }

  //	function _processTokenStack()
  private function _validateBinaryOperand($cellID, &$operand, &$stack) {
    if (is_array($operand)) {
      if (count($operand, COUNT_RECURSIVE) - count($operand) == 1) {
        do {
          $operand = array_pop($operand);
        } while (is_array($operand));
      }
    }

    //	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('Value', $operand);
          $this->_debugLog
            ->writeDebugLog('Evaluation Result is ', $this
            ->_showTypeDetails($operand));
          return FALSE;
        }
        elseif (!PHPExcel_Shared_String::convertToNumberIfFraction($operand)) {

          //	If not a numeric or a fraction, then it's a text string, and so can't be used in mathematical binary operations
          $stack
            ->push('Value', '#VALUE!');
          $this->_debugLog
            ->writeDebugLog('Evaluation Result is a ', $this
            ->_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, $recursingArrays = FALSE) {

    //	If we're dealing with matrix operations, we want a matrix result
    if (is_array($operand1) || is_array($operand2)) {
      $result = array();
      if (is_array($operand1) && !is_array($operand2)) {
        foreach ($operand1 as $x => $operandData) {
          $this->_debugLog
            ->writeDebugLog('Evaluating Comparison ', $this
            ->_showValue($operandData), ' ', $operation, ' ', $this
            ->_showValue($operand2));
          $this
            ->_executeBinaryComparisonOperation($cellID, $operandData, $operand2, $operation, $stack);
          $r = $stack
            ->pop();
          $result[$x] = $r['value'];
        }
      }
      elseif (!is_array($operand1) && is_array($operand2)) {
        foreach ($operand2 as $x => $operandData) {
          $this->_debugLog
            ->writeDebugLog('Evaluating Comparison ', $this
            ->_showValue($operand1), ' ', $operation, ' ', $this
            ->_showValue($operandData));
          $this
            ->_executeBinaryComparisonOperation($cellID, $operand1, $operandData, $operation, $stack);
          $r = $stack
            ->pop();
          $result[$x] = $r['value'];
        }
      }
      else {
        if (!$recursingArrays) {
          self::_checkMatrixOperands($operand1, $operand2, 2);
        }
        foreach ($operand1 as $x => $operandData) {
          $this->_debugLog
            ->writeDebugLog('Evaluating Comparison ', $this
            ->_showValue($operandData), ' ', $operation, ' ', $this
            ->_showValue($operand2[$x]));
          $this
            ->_executeBinaryComparisonOperation($cellID, $operandData, $operand2[$x], $operation, $stack, TRUE);
          $r = $stack
            ->pop();
          $result[$x] = $r['value'];
        }
      }

      //	Log the result details
      $this->_debugLog
        ->writeDebugLog('Comparison Evaluation Result is ', $this
        ->_showTypeDetails($result));

      //	And push the result onto the stack
      $stack
        ->push('Array', $result);
      return TRUE;
    }

    //	Simple validate the two operands if they are string values
    if (is_string($operand1) && $operand1 > '' && $operand1[0] == '"') {
      $operand1 = self::_unwrapResult($operand1);
    }
    if (is_string($operand2) && $operand2 > '' && $operand2[0] == '"') {
      $operand2 = self::_unwrapResult($operand2);
    }

    // Use case insensitive comparaison if not OpenOffice mode
    if (PHPExcel_Calculation_Functions::getCompatibilityMode() != PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
      if (is_string($operand1)) {
        $operand1 = strtoupper($operand1);
      }
      if (is_string($operand2)) {
        $operand2 = strtoupper($operand2);
      }
    }
    $useLowercaseFirstComparison = is_string($operand1) && is_string($operand2) && PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE;

    //	execute the necessary operation
    switch ($operation) {

      //	Greater than
      case '>':
        if ($useLowercaseFirstComparison) {
          $result = $this
            ->strcmpLowercaseFirst($operand1, $operand2) > 0;
        }
        else {
          $result = $operand1 > $operand2;
        }
        break;

      //	Less than
      case '<':
        if ($useLowercaseFirstComparison) {
          $result = $this
            ->strcmpLowercaseFirst($operand1, $operand2) < 0;
        }
        else {
          $result = $operand1 < $operand2;
        }
        break;

      //	Equality
      case '=':
        if (is_numeric($operand1) && is_numeric($operand2)) {
          $result = abs($operand1 - $operand2) < $this->delta;
        }
        else {
          $result = strcmp($operand1, $operand2) == 0;
        }
        break;

      //	Greater than or equal
      case '>=':
        if (is_numeric($operand1) && is_numeric($operand2)) {
          $result = abs($operand1 - $operand2) < $this->delta || $operand1 > $operand2;
        }
        elseif ($useLowercaseFirstComparison) {
          $result = $this
            ->strcmpLowercaseFirst($operand1, $operand2) >= 0;
        }
        else {
          $result = strcmp($operand1, $operand2) >= 0;
        }
        break;

      //	Less than or equal
      case '<=':
        if (is_numeric($operand1) && is_numeric($operand2)) {
          $result = abs($operand1 - $operand2) < $this->delta || $operand1 < $operand2;
        }
        elseif ($useLowercaseFirstComparison) {
          $result = $this
            ->strcmpLowercaseFirst($operand1, $operand2) <= 0;
        }
        else {
          $result = strcmp($operand1, $operand2) <= 0;
        }
        break;

      //	Inequality
      case '<>':
        if (is_numeric($operand1) && is_numeric($operand2)) {
          $result = abs($operand1 - $operand2) > 1.0E-14;
        }
        else {
          $result = strcmp($operand1, $operand2) != 0;
        }
        break;
    }

    //	Log the result details
    $this->_debugLog
      ->writeDebugLog('Evaluation Result is ', $this
      ->_showTypeDetails($result));

    //	And push the result onto the stack
    $stack
      ->push('Value', $result);
    return true;
  }

  /**
   * Compare two strings in the same way as strcmp() except that lowercase come before uppercase letters
   * @param    string    $str1    First string value for the comparison
   * @param    string    $str2    Second string value for the comparison
   * @return   integer
   */
  private function strcmpLowercaseFirst($str1, $str2) {
    $inversedStr1 = PHPExcel_Shared_String::StrCaseReverse($str1);
    $inversedStr2 = PHPExcel_Shared_String::StrCaseReverse($str2);
    return strcmp($inversedStr1, $inversedStr2);
  }
  private function _executeNumericBinaryOperation($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 of the same size
      self::_checkMatrixOperands($operand1, $operand2, 2);
      try {

        //	Convert operand 1 from a PHP array to a matrix
        $matrix = new PHPExcel_Shared_JAMA_Matrix($operand1);

        //	Perform the required operation against the operand 1 matrix, passing in operand 2
        $matrixResult = $matrix
          ->{$matrixFunction}($operand2);
        $result = $matrixResult
          ->getArray();
      } catch (PHPExcel_Exception $ex) {
        $this->_debugLog
          ->writeDebugLog('JAMA Matrix Exception: ', $ex
          ->getMessage());
        $result = '#VALUE!';
      }
    }
    else {
      if (PHPExcel_Calculation_Functions::getCompatibilityMode() != PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE && (is_string($operand1) && !is_numeric($operand1) && strlen($operand1) > 0 || is_string($operand2) && !is_numeric($operand2) && strlen($operand2) > 0)) {
        $result = PHPExcel_Calculation_Functions::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('Value', '#DIV/0!');
              $this->_debugLog
                ->writeDebugLog('Evaluation Result is ', $this
                ->_showTypeDetails('#DIV/0!'));
              return FALSE;
            }
            else {
              $result = $operand1 / $operand2;
            }
            break;

          //	Power
          case '^':
            $result = pow($operand1, $operand2);
            break;
        }
      }
    }

    //	Log the result details
    $this->_debugLog
      ->writeDebugLog('Evaluation Result is ', $this
      ->_showTypeDetails($result));

    //	And push the result onto the stack
    $stack
      ->push('Value', $result);
    return TRUE;
  }

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

  //	function _raiseFormulaError()

  /**
   * Extract range values
   *
   * @param	string				&$pRange	String based range representation
   * @param	PHPExcel_Worksheet	$pSheet		Worksheet
   * @param	boolean				$resetLog	Flag indicating whether calculation log should be reset or not
   * @return  mixed				Array of values in range if range contains more than one element. Otherwise, a single value is returned.
   * @throws	PHPExcel_Calculation_Exception
   */
  public function extractCellRange(&$pRange = 'A1', PHPExcel_Worksheet $pSheet = NULL, $resetLog = TRUE) {

    // Return value
    $returnValue = array();

    //		echo 'extractCellRange('.$pRange.')',PHP_EOL;
    if ($pSheet !== NULL) {
      $pSheetName = $pSheet
        ->getTitle();

      //			echo 'Passed sheet name is '.$pSheetName.PHP_EOL;
      //			echo 'Range reference is '.$pRange.PHP_EOL;
      if (strpos($pRange, '!') !== false) {

        //				echo '$pRange reference includes sheet reference',PHP_EOL;
        list($pSheetName, $pRange) = PHPExcel_Worksheet::extractSheetTitle($pRange, true);

        //				echo 'New sheet name is '.$pSheetName,PHP_EOL;
        //				echo 'Adjusted Range reference is '.$pRange,PHP_EOL;
        $pSheet = $this->_workbook
          ->getSheetByName($pSheetName);
      }

      // Extract range
      $aReferences = PHPExcel_Cell::extractAllCellReferencesInRange($pRange);
      $pRange = $pSheetName . '!' . $pRange;
      if (!isset($aReferences[1])) {

        //	Single cell in range
        sscanf($aReferences[0], '%[A-Z]%d', $currentCol, $currentRow);
        $cellValue = NULL;
        if ($pSheet
          ->cellExists($aReferences[0])) {
          $returnValue[$currentRow][$currentCol] = $pSheet
            ->getCell($aReferences[0])
            ->getCalculatedValue($resetLog);
        }
        else {
          $returnValue[$currentRow][$currentCol] = NULL;
        }
      }
      else {

        // Extract cell data for all cells in the range
        foreach ($aReferences as $reference) {

          // Extract range
          sscanf($reference, '%[A-Z]%d', $currentCol, $currentRow);
          $cellValue = NULL;
          if ($pSheet
            ->cellExists($reference)) {
            $returnValue[$currentRow][$currentCol] = $pSheet
              ->getCell($reference)
              ->getCalculatedValue($resetLog);
          }
          else {
            $returnValue[$currentRow][$currentCol] = NULL;
          }
        }
      }
    }

    // Return
    return $returnValue;
  }

  //	function extractCellRange()

  /**
   * Extract range values
   *
   * @param	string				&$pRange	String based range representation
   * @param	PHPExcel_Worksheet	$pSheet		Worksheet
   * @return  mixed				Array of values in range if range contains more than one element. Otherwise, a single value is returned.
   * @param	boolean				$resetLog	Flag indicating whether calculation log should be reset or not
   * @throws	PHPExcel_Calculation_Exception
   */
  public function extractNamedRange(&$pRange = 'A1', PHPExcel_Worksheet $pSheet = NULL, $resetLog = TRUE) {

    // Return value
    $returnValue = array();

    //		echo 'extractNamedRange('.$pRange.')<br />';
    if ($pSheet !== NULL) {
      $pSheetName = $pSheet
        ->getTitle();

      //			echo 'Current sheet name is '.$pSheetName.'<br />';
      //			echo 'Range reference is '.$pRange.'<br />';
      if (strpos($pRange, '!') !== false) {

        //				echo '$pRange reference includes sheet reference',PHP_EOL;
        list($pSheetName, $pRange) = PHPExcel_Worksheet::extractSheetTitle($pRange, true);

        //				echo 'New sheet name is '.$pSheetName,PHP_EOL;
        //				echo 'Adjusted Range reference is '.$pRange,PHP_EOL;
        $pSheet = $this->_workbook
          ->getSheetByName($pSheetName);
      }

      // Named range?
      $namedRange = PHPExcel_NamedRange::resolveRange($pRange, $pSheet);
      if ($namedRange !== NULL) {
        $pSheet = $namedRange
          ->getWorksheet();

        //				echo 'Named Range '.$pRange.' (';
        $pRange = $namedRange
          ->getRange();
        $splitRange = PHPExcel_Cell::splitRange($pRange);

        //	Convert row and column references
        if (ctype_alpha($splitRange[0][0])) {
          $pRange = $splitRange[0][0] . '1:' . $splitRange[0][1] . $namedRange
            ->getWorksheet()
            ->getHighestRow();
        }
        elseif (ctype_digit($splitRange[0][0])) {
          $pRange = 'A' . $splitRange[0][0] . ':' . $namedRange
            ->getWorksheet()
            ->getHighestColumn() . $splitRange[0][1];
        }

        //				echo $pRange.') is in sheet '.$namedRange->getWorksheet()->getTitle().'<br />';
        //				if ($pSheet->getTitle() != $namedRange->getWorksheet()->getTitle()) {
        //					if (!$namedRange->getLocalOnly()) {
        //						$pSheet = $namedRange->getWorksheet();
        //					} else {
        //						return $returnValue;
        //					}
        //				}
      }
      else {
        return PHPExcel_Calculation_Functions::REF();
      }

      // Extract range
      $aReferences = PHPExcel_Cell::extractAllCellReferencesInRange($pRange);

      //			var_dump($aReferences);
      if (!isset($aReferences[1])) {

        //	Single cell (or single column or row) in range
        list($currentCol, $currentRow) = PHPExcel_Cell::coordinateFromString($aReferences[0]);
        $cellValue = NULL;
        if ($pSheet
          ->cellExists($aReferences[0])) {
          $returnValue[$currentRow][$currentCol] = $pSheet
            ->getCell($aReferences[0])
            ->getCalculatedValue($resetLog);
        }
        else {
          $returnValue[$currentRow][$currentCol] = NULL;
        }
      }
      else {

        // Extract cell data for all cells in the range
        foreach ($aReferences as $reference) {

          // Extract range
          list($currentCol, $currentRow) = PHPExcel_Cell::coordinateFromString($reference);

          //					echo 'NAMED RANGE: $currentCol='.$currentCol.' $currentRow='.$currentRow.'<br />';
          $cellValue = NULL;
          if ($pSheet
            ->cellExists($reference)) {
            $returnValue[$currentRow][$currentCol] = $pSheet
              ->getCell($reference)
              ->getCalculatedValue($resetLog);
          }
          else {
            $returnValue[$currentRow][$currentCol] = NULL;
          }
        }
      }

      //				print_r($returnValue);
      //			echo '<br />';
    }

    // Return
    return $returnValue;
  }

  //	function extractNamedRange()

  /**
   * Is a specific function implemented?
   *
   * @param	string	$pFunction	Function Name
   * @return	boolean
   */
  public function isImplemented($pFunction = '') {
    $pFunction = strtoupper($pFunction);
    if (isset(self::$_PHPExcelFunctions[$pFunction])) {
      return self::$_PHPExcelFunctions[$pFunction]['functionCall'] != 'PHPExcel_Calculation_Functions::DUMMY';
    }
    else {
      return FALSE;
    }
  }

  //	function isImplemented()

  /**
   * Get a list of all implemented functions as an array of function objects
   *
   * @return	array of PHPExcel_Calculation_Function
   */
  public function listFunctions() {

    // Return value
    $returnValue = array();

    // Loop functions
    foreach (self::$_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()

  /**
   * Get a list of all Excel function names
   *
   * @return	array
   */
  public function listAllFunctionNames() {
    return array_keys(self::$_PHPExcelFunctions);
  }

  //	function listAllFunctionNames()

  /**
   * Get a list of implemented Excel function names
   *
   * @return	array
   */
  public function listFunctionNames() {

    // Return value
    $returnValue = array();

    // Loop functions
    foreach (self::$_PHPExcelFunctions as $functionName => $function) {
      if ($function['functionCall'] != 'PHPExcel_Calculation_Functions::DUMMY') {
        $returnValue[] = $functionName;
      }
    }

    // Return
    return $returnValue;
  }

}

//	class PHPExcel_Calculation

Classes

Namesort descending Description
PHPExcel_Calculation PHPExcel_Calculation (Multiton)