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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_Writer_Excel5
 * @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    1.8.0, 2014-03-02
 */
// Original file header of PEAR::Spreadsheet_Excel_Writer_Parser (used as the base for this class):
// -----------------------------------------------------------------------------------------
// *  Class for parsing Excel formulas
// *
// *  License Information:
// *
// *    Spreadsheet_Excel_Writer:  A library for generating Excel Spreadsheets
// *    Copyright (c) 2002-2003 Xavier Noguer xnoguer@rezebra.com
// *
// *    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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
// */

/**
 * PHPExcel_Writer_Excel5_Parser
 *
 * @category   PHPExcel
 * @package    PHPExcel_Writer_Excel5
 * @copyright  Copyright (c) 2006 - 2014 PHPExcel (http://www.codeplex.com/PHPExcel)
 */
class PHPExcel_Writer_Excel5_Parser {

    /** 	Constants				 */
    // Sheet title in unquoted form
    // Invalid sheet title characters cannot occur in the sheet title:
    // 		*:/\?[]
    // Moreover, there are valid sheet title characters that cannot occur in unquoted form (there may be more?)
    // +-% '^&<>=,;#()"{}
    const REGEX_SHEET_TITLE_UNQUOTED = '[^\*\:\/\\\\\?\[\]\+\-\% \\\'\^\&\<\>\=\,\;\#\(\)\"\{\}]+';
    // Sheet title in quoted form (without surrounding quotes)
    // Invalid sheet title characters cannot occur in the sheet title:
    // *:/\?[]					(usual invalid sheet title characters)
    // Single quote is represented as a pair ''
    const REGEX_SHEET_TITLE_QUOTED = '(([^\*\:\/\\\\\?\[\]\\\'])+|(\\\'\\\')+)+';

    /**
     * The index of the character we are currently looking at
     * @var integer
     */
    public $_current_char;

    /**
     * The token we are working on.
     * @var string
     */
    public $_current_token;

    /**
     * The formula to parse
     * @var string
     */
    public $_formula;

    /**
     * The character ahead of the current char
     * @var string
     */
    public $_lookahead;

    /**
     * The parse tree to be generated
     * @var string
     */
    public $_parse_tree;

    /**
     * Array of external sheets
     * @var array
     */
    public $_ext_sheets;

    /**
     * Array of sheet references in the form of REF structures
     * @var array
     */
    public $_references;

    /**
     * The class constructor
     *
     */
    public function __construct() {
        $this->_current_char = 0;
        $this->_current_token = '';       // The token we are working on.
        $this->_formula = '';       // The formula to parse.
        $this->_lookahead = '';       // The character ahead of the current char.
        $this->_parse_tree = '';       // The parse tree to be generated.
        $this->_initializeHashes();      // Initialize the hashes: ptg's and function's ptg's
        $this->_ext_sheets = array();
        $this->_references = array();
    }

    /**
     * Initialize the ptg and function hashes.
     *
     * @access private
     */
    function _initializeHashes() {
        // The Excel ptg indices
        $this->ptg = array(
            'ptgExp' => 0x01,
            'ptgTbl' => 0x02,
            'ptgAdd' => 0x03,
            'ptgSub' => 0x04,
            'ptgMul' => 0x05,
            'ptgDiv' => 0x06,
            'ptgPower' => 0x07,
            'ptgConcat' => 0x08,
            'ptgLT' => 0x09,
            'ptgLE' => 0x0A,
            'ptgEQ' => 0x0B,
            'ptgGE' => 0x0C,
            'ptgGT' => 0x0D,
            'ptgNE' => 0x0E,
            'ptgIsect' => 0x0F,
            'ptgUnion' => 0x10,
            'ptgRange' => 0x11,
            'ptgUplus' => 0x12,
            'ptgUminus' => 0x13,
            'ptgPercent' => 0x14,
            'ptgParen' => 0x15,
            'ptgMissArg' => 0x16,
            'ptgStr' => 0x17,
            'ptgAttr' => 0x19,
            'ptgSheet' => 0x1A,
            'ptgEndSheet' => 0x1B,
            'ptgErr' => 0x1C,
            'ptgBool' => 0x1D,
            'ptgInt' => 0x1E,
            'ptgNum' => 0x1F,
            'ptgArray' => 0x20,
            'ptgFunc' => 0x21,
            'ptgFuncVar' => 0x22,
            'ptgName' => 0x23,
            'ptgRef' => 0x24,
            'ptgArea' => 0x25,
            'ptgMemArea' => 0x26,
            'ptgMemErr' => 0x27,
            'ptgMemNoMem' => 0x28,
            'ptgMemFunc' => 0x29,
            'ptgRefErr' => 0x2A,
            'ptgAreaErr' => 0x2B,
            'ptgRefN' => 0x2C,
            'ptgAreaN' => 0x2D,
            'ptgMemAreaN' => 0x2E,
            'ptgMemNoMemN' => 0x2F,
            'ptgNameX' => 0x39,
            'ptgRef3d' => 0x3A,
            'ptgArea3d' => 0x3B,
            'ptgRefErr3d' => 0x3C,
            'ptgAreaErr3d' => 0x3D,
            'ptgArrayV' => 0x40,
            'ptgFuncV' => 0x41,
            'ptgFuncVarV' => 0x42,
            'ptgNameV' => 0x43,
            'ptgRefV' => 0x44,
            'ptgAreaV' => 0x45,
            'ptgMemAreaV' => 0x46,
            'ptgMemErrV' => 0x47,
            'ptgMemNoMemV' => 0x48,
            'ptgMemFuncV' => 0x49,
            'ptgRefErrV' => 0x4A,
            'ptgAreaErrV' => 0x4B,
            'ptgRefNV' => 0x4C,
            'ptgAreaNV' => 0x4D,
            'ptgMemAreaNV' => 0x4E,
            'ptgMemNoMemN' => 0x4F,
            'ptgFuncCEV' => 0x58,
            'ptgNameXV' => 0x59,
            'ptgRef3dV' => 0x5A,
            'ptgArea3dV' => 0x5B,
            'ptgRefErr3dV' => 0x5C,
            'ptgAreaErr3d' => 0x5D,
            'ptgArrayA' => 0x60,
            'ptgFuncA' => 0x61,
            'ptgFuncVarA' => 0x62,
            'ptgNameA' => 0x63,
            'ptgRefA' => 0x64,
            'ptgAreaA' => 0x65,
            'ptgMemAreaA' => 0x66,
            'ptgMemErrA' => 0x67,
            'ptgMemNoMemA' => 0x68,
            'ptgMemFuncA' => 0x69,
            'ptgRefErrA' => 0x6A,
            'ptgAreaErrA' => 0x6B,
            'ptgRefNA' => 0x6C,
            'ptgAreaNA' => 0x6D,
            'ptgMemAreaNA' => 0x6E,
            'ptgMemNoMemN' => 0x6F,
            'ptgFuncCEA' => 0x78,
            'ptgNameXA' => 0x79,
            'ptgRef3dA' => 0x7A,
            'ptgArea3dA' => 0x7B,
            'ptgRefErr3dA' => 0x7C,
            'ptgAreaErr3d' => 0x7D
        );

        // Thanks to Michael Meeks and Gnumeric for the initial arg values.
        //
		// The following hash was generated by "function_locale.pl" in the distro.
        // Refer to function_locale.pl for non-English function names.
        //
		// The array elements are as follow:
        // ptg:   The Excel function ptg code.
        // args:  The number of arguments that the function takes:
        //           >=0 is a fixed number of arguments.
        //           -1  is a variable  number of arguments.
        // class: The reference, value or array class of the function args.
        // vol:   The function is volatile.
        //
		$this->_functions = array(
            // function                  ptg  args  class  vol
            'COUNT' => array(0, -1, 0, 0),
            'IF' => array(1, -1, 1, 0),
            'ISNA' => array(2, 1, 1, 0),
            'ISERROR' => array(3, 1, 1, 0),
            'SUM' => array(4, -1, 0, 0),
            'AVERAGE' => array(5, -1, 0, 0),
            'MIN' => array(6, -1, 0, 0),
            'MAX' => array(7, -1, 0, 0),
            'ROW' => array(8, -1, 0, 0),
            'COLUMN' => array(9, -1, 0, 0),
            'NA' => array(10, 0, 0, 0),
            'NPV' => array(11, -1, 1, 0),
            'STDEV' => array(12, -1, 0, 0),
            'DOLLAR' => array(13, -1, 1, 0),
            'FIXED' => array(14, -1, 1, 0),
            'SIN' => array(15, 1, 1, 0),
            'COS' => array(16, 1, 1, 0),
            'TAN' => array(17, 1, 1, 0),
            'ATAN' => array(18, 1, 1, 0),
            'PI' => array(19, 0, 1, 0),
            'SQRT' => array(20, 1, 1, 0),
            'EXP' => array(21, 1, 1, 0),
            'LN' => array(22, 1, 1, 0),
            'LOG10' => array(23, 1, 1, 0),
            'ABS' => array(24, 1, 1, 0),
            'INT' => array(25, 1, 1, 0),
            'SIGN' => array(26, 1, 1, 0),
            'ROUND' => array(27, 2, 1, 0),
            'LOOKUP' => array(28, -1, 0, 0),
            'INDEX' => array(29, -1, 0, 1),
            'REPT' => array(30, 2, 1, 0),
            'MID' => array(31, 3, 1, 0),
            'LEN' => array(32, 1, 1, 0),
            'VALUE' => array(33, 1, 1, 0),
            'TRUE' => array(34, 0, 1, 0),
            'FALSE' => array(35, 0, 1, 0),
            'AND' => array(36, -1, 0, 0),
            'OR' => array(37, -1, 0, 0),
            'NOT' => array(38, 1, 1, 0),
            'MOD' => array(39, 2, 1, 0),
            'DCOUNT' => array(40, 3, 0, 0),
            'DSUM' => array(41, 3, 0, 0),
            'DAVERAGE' => array(42, 3, 0, 0),
            'DMIN' => array(43, 3, 0, 0),
            'DMAX' => array(44, 3, 0, 0),
            'DSTDEV' => array(45, 3, 0, 0),
            'VAR' => array(46, -1, 0, 0),
            'DVAR' => array(47, 3, 0, 0),
            'TEXT' => array(48, 2, 1, 0),
            'LINEST' => array(49, -1, 0, 0),
            'TREND' => array(50, -1, 0, 0),
            'LOGEST' => array(51, -1, 0, 0),
            'GROWTH' => array(52, -1, 0, 0),
            'PV' => array(56, -1, 1, 0),
            'FV' => array(57, -1, 1, 0),
            'NPER' => array(58, -1, 1, 0),
            'PMT' => array(59, -1, 1, 0),
            'RATE' => array(60, -1, 1, 0),
            'MIRR' => array(61, 3, 0, 0),
            'IRR' => array(62, -1, 0, 0),
            'RAND' => array(63, 0, 1, 1),
            'MATCH' => array(64, -1, 0, 0),
            'DATE' => array(65, 3, 1, 0),
            'TIME' => array(66, 3, 1, 0),
            'DAY' => array(67, 1, 1, 0),
            'MONTH' => array(68, 1, 1, 0),
            'YEAR' => array(69, 1, 1, 0),
            'WEEKDAY' => array(70, -1, 1, 0),
            'HOUR' => array(71, 1, 1, 0),
            'MINUTE' => array(72, 1, 1, 0),
            'SECOND' => array(73, 1, 1, 0),
            'NOW' => array(74, 0, 1, 1),
            'AREAS' => array(75, 1, 0, 1),
            'ROWS' => array(76, 1, 0, 1),
            'COLUMNS' => array(77, 1, 0, 1),
            'OFFSET' => array(78, -1, 0, 1),
            'SEARCH' => array(82, -1, 1, 0),
            'TRANSPOSE' => array(83, 1, 1, 0),
            'TYPE' => array(86, 1, 1, 0),
            'ATAN2' => array(97, 2, 1, 0),
            'ASIN' => array(98, 1, 1, 0),
            'ACOS' => array(99, 1, 1, 0),
            'CHOOSE' => array(100, -1, 1, 0),
            'HLOOKUP' => array(101, -1, 0, 0),
            'VLOOKUP' => array(102, -1, 0, 0),
            'ISREF' => array(105, 1, 0, 0),
            'LOG' => array(109, -1, 1, 0),
            'CHAR' => array(111, 1, 1, 0),
            'LOWER' => array(112, 1, 1, 0),
            'UPPER' => array(113, 1, 1, 0),
            'PROPER' => array(114, 1, 1, 0),
            'LEFT' => array(115, -1, 1, 0),
            'RIGHT' => array(116, -1, 1, 0),
            'EXACT' => array(117, 2, 1, 0),
            'TRIM' => array(118, 1, 1, 0),
            'REPLACE' => array(119, 4, 1, 0),
            'SUBSTITUTE' => array(120, -1, 1, 0),
            'CODE' => array(121, 1, 1, 0),
            'FIND' => array(124, -1, 1, 0),
            'CELL' => array(125, -1, 0, 1),
            'ISERR' => array(126, 1, 1, 0),
            'ISTEXT' => array(127, 1, 1, 0),
            'ISNUMBER' => array(128, 1, 1, 0),
            'ISBLANK' => array(129, 1, 1, 0),
            'T' => array(130, 1, 0, 0),
            'N' => array(131, 1, 0, 0),
            'DATEVALUE' => array(140, 1, 1, 0),
            'TIMEVALUE' => array(141, 1, 1, 0),
            'SLN' => array(142, 3, 1, 0),
            'SYD' => array(143, 4, 1, 0),
            'DDB' => array(144, -1, 1, 0),
            'INDIRECT' => array(148, -1, 1, 1),
            'CALL' => array(150, -1, 1, 0),
            'CLEAN' => array(162, 1, 1, 0),
            'MDETERM' => array(163, 1, 2, 0),
            'MINVERSE' => array(164, 1, 2, 0),
            'MMULT' => array(165, 2, 2, 0),
            'IPMT' => array(167, -1, 1, 0),
            'PPMT' => array(168, -1, 1, 0),
            'COUNTA' => array(169, -1, 0, 0),
            'PRODUCT' => array(183, -1, 0, 0),
            'FACT' => array(184, 1, 1, 0),
            'DPRODUCT' => array(189, 3, 0, 0),
            'ISNONTEXT' => array(190, 1, 1, 0),
            'STDEVP' => array(193, -1, 0, 0),
            'VARP' => array(194, -1, 0, 0),
            'DSTDEVP' => array(195, 3, 0, 0),
            'DVARP' => array(196, 3, 0, 0),
            'TRUNC' => array(197, -1, 1, 0),
            'ISLOGICAL' => array(198, 1, 1, 0),
            'DCOUNTA' => array(199, 3, 0, 0),
            'USDOLLAR' => array(204, -1, 1, 0),
            'FINDB' => array(205, -1, 1, 0),
            'SEARCHB' => array(206, -1, 1, 0),
            'REPLACEB' => array(207, 4, 1, 0),
            'LEFTB' => array(208, -1, 1, 0),
            'RIGHTB' => array(209, -1, 1, 0),
            'MIDB' => array(210, 3, 1, 0),
            'LENB' => array(211, 1, 1, 0),
            'ROUNDUP' => array(212, 2, 1, 0),
            'ROUNDDOWN' => array(213, 2, 1, 0),
            'ASC' => array(214, 1, 1, 0),
            'DBCS' => array(215, 1, 1, 0),
            'RANK' => array(216, -1, 0, 0),
            'ADDRESS' => array(219, -1, 1, 0),
            'DAYS360' => array(220, -1, 1, 0),
            'TODAY' => array(221, 0, 1, 1),
            'VDB' => array(222, -1, 1, 0),
            'MEDIAN' => array(227, -1, 0, 0),
            'SUMPRODUCT' => array(228, -1, 2, 0),
            'SINH' => array(229, 1, 1, 0),
            'COSH' => array(230, 1, 1, 0),
            'TANH' => array(231, 1, 1, 0),
            'ASINH' => array(232, 1, 1, 0),
            'ACOSH' => array(233, 1, 1, 0),
            'ATANH' => array(234, 1, 1, 0),
            'DGET' => array(235, 3, 0, 0),
            'INFO' => array(244, 1, 1, 1),
            'DB' => array(247, -1, 1, 0),
            'FREQUENCY' => array(252, 2, 0, 0),
            'ERROR.TYPE' => array(261, 1, 1, 0),
            'REGISTER.ID' => array(267, -1, 1, 0),
            'AVEDEV' => array(269, -1, 0, 0),
            'BETADIST' => array(270, -1, 1, 0),
            'GAMMALN' => array(271, 1, 1, 0),
            'BETAINV' => array(272, -1, 1, 0),
            'BINOMDIST' => array(273, 4, 1, 0),
            'CHIDIST' => array(274, 2, 1, 0),
            'CHIINV' => array(275, 2, 1, 0),
            'COMBIN' => array(276, 2, 1, 0),
            'CONFIDENCE' => array(277, 3, 1, 0),
            'CRITBINOM' => array(278, 3, 1, 0),
            'EVEN' => array(279, 1, 1, 0),
            'EXPONDIST' => array(280, 3, 1, 0),
            'FDIST' => array(281, 3, 1, 0),
            'FINV' => array(282, 3, 1, 0),
            'FISHER' => array(283, 1, 1, 0),
            'FISHERINV' => array(284, 1, 1, 0),
            'FLOOR' => array(285, 2, 1, 0),
            'GAMMADIST' => array(286, 4, 1, 0),
            'GAMMAINV' => array(287, 3, 1, 0),
            'CEILING' => array(288, 2, 1, 0),
            'HYPGEOMDIST' => array(289, 4, 1, 0),
            'LOGNORMDIST' => array(290, 3, 1, 0),
            'LOGINV' => array(291, 3, 1, 0),
            'NEGBINOMDIST' => array(292, 3, 1, 0),
            'NORMDIST' => array(293, 4, 1, 0),
            'NORMSDIST' => array(294, 1, 1, 0),
            'NORMINV' => array(295, 3, 1, 0),
            'NORMSINV' => array(296, 1, 1, 0),
            'STANDARDIZE' => array(297, 3, 1, 0),
            'ODD' => array(298, 1, 1, 0),
            'PERMUT' => array(299, 2, 1, 0),
            'POISSON' => array(300, 3, 1, 0),
            'TDIST' => array(301, 3, 1, 0),
            'WEIBULL' => array(302, 4, 1, 0),
            'SUMXMY2' => array(303, 2, 2, 0),
            'SUMX2MY2' => array(304, 2, 2, 0),
            'SUMX2PY2' => array(305, 2, 2, 0),
            'CHITEST' => array(306, 2, 2, 0),
            'CORREL' => array(307, 2, 2, 0),
            'COVAR' => array(308, 2, 2, 0),
            'FORECAST' => array(309, 3, 2, 0),
            'FTEST' => array(310, 2, 2, 0),
            'INTERCEPT' => array(311, 2, 2, 0),
            'PEARSON' => array(312, 2, 2, 0),
            'RSQ' => array(313, 2, 2, 0),
            'STEYX' => array(314, 2, 2, 0),
            'SLOPE' => array(315, 2, 2, 0),
            'TTEST' => array(316, 4, 2, 0),
            'PROB' => array(317, -1, 2, 0),
            'DEVSQ' => array(318, -1, 0, 0),
            'GEOMEAN' => array(319, -1, 0, 0),
            'HARMEAN' => array(320, -1, 0, 0),
            'SUMSQ' => array(321, -1, 0, 0),
            'KURT' => array(322, -1, 0, 0),
            'SKEW' => array(323, -1, 0, 0),
            'ZTEST' => array(324, -1, 0, 0),
            'LARGE' => array(325, 2, 0, 0),
            'SMALL' => array(326, 2, 0, 0),
            'QUARTILE' => array(327, 2, 0, 0),
            'PERCENTILE' => array(328, 2, 0, 0),
            'PERCENTRANK' => array(329, -1, 0, 0),
            'MODE' => array(330, -1, 2, 0),
            'TRIMMEAN' => array(331, 2, 0, 0),
            'TINV' => array(332, 2, 1, 0),
            'CONCATENATE' => array(336, -1, 1, 0),
            'POWER' => array(337, 2, 1, 0),
            'RADIANS' => array(342, 1, 1, 0),
            'DEGREES' => array(343, 1, 1, 0),
            'SUBTOTAL' => array(344, -1, 0, 0),
            'SUMIF' => array(345, -1, 0, 0),
            'COUNTIF' => array(346, 2, 0, 0),
            'COUNTBLANK' => array(347, 1, 0, 0),
            'ISPMT' => array(350, 4, 1, 0),
            'DATEDIF' => array(351, 3, 1, 0),
            'DATESTRING' => array(352, 1, 1, 0),
            'NUMBERSTRING' => array(353, 2, 1, 0),
            'ROMAN' => array(354, -1, 1, 0),
            'GETPIVOTDATA' => array(358, -1, 0, 0),
            'HYPERLINK' => array(359, -1, 1, 0),
            'PHONETIC' => array(360, 1, 0, 0),
            'AVERAGEA' => array(361, -1, 0, 0),
            'MAXA' => array(362, -1, 0, 0),
            'MINA' => array(363, -1, 0, 0),
            'STDEVPA' => array(364, -1, 0, 0),
            'VARPA' => array(365, -1, 0, 0),
            'STDEVA' => array(366, -1, 0, 0),
            'VARA' => array(367, -1, 0, 0),
            'BAHTTEXT' => array(368, 1, 0, 0),
        );
    }

    /**
     * Convert a token to the proper ptg value.
     *
     * @access private
     * @param mixed $token The token to convert.
     * @return mixed the converted token on success
     */
    function _convert($token) {
        if (preg_match("/\"([^\"]|\"\"){0,255}\"/", $token)) {
            return $this->_convertString($token);
        } elseif (is_numeric($token)) {
            return $this->_convertNumber($token);

            // match references like A1 or $A$1
        } elseif (preg_match('/^\$?([A-Ia-i]?[A-Za-z])\$?(\d+)$/', $token)) {
            return $this->_convertRef2d($token);

            // match external references like Sheet1!A1 or Sheet1:Sheet2!A1 or Sheet1!$A$1 or Sheet1:Sheet2!$A$1
        } elseif (preg_match("/^" . self::REGEX_SHEET_TITLE_UNQUOTED . "(\:" . self::REGEX_SHEET_TITLE_UNQUOTED . ")?\!\\$?[A-Ia-i]?[A-Za-z]\\$?(\d+)$/u", $token)) {
            return $this->_convertRef3d($token);

            // match external references like 'Sheet1'!A1 or 'Sheet1:Sheet2'!A1 or 'Sheet1'!$A$1 or 'Sheet1:Sheet2'!$A$1
        } elseif (preg_match("/^'" . self::REGEX_SHEET_TITLE_QUOTED . "(\:" . self::REGEX_SHEET_TITLE_QUOTED . ")?'\!\\$?[A-Ia-i]?[A-Za-z]\\$?(\d+)$/u", $token)) {
            return $this->_convertRef3d($token);

            // match ranges like A1:B2 or $A$1:$B$2
        } elseif (preg_match('/^(\$)?[A-Ia-i]?[A-Za-z](\$)?(\d+)\:(\$)?[A-Ia-i]?[A-Za-z](\$)?(\d+)$/', $token)) {
            return $this->_convertRange2d($token);

            // match external ranges like Sheet1!A1:B2 or Sheet1:Sheet2!A1:B2 or Sheet1!$A$1:$B$2 or Sheet1:Sheet2!$A$1:$B$2
        } elseif (preg_match("/^" . self::REGEX_SHEET_TITLE_UNQUOTED . "(\:" . self::REGEX_SHEET_TITLE_UNQUOTED . ")?\!\\$?([A-Ia-i]?[A-Za-z])?\\$?(\d+)\:\\$?([A-Ia-i]?[A-Za-z])?\\$?(\d+)$/u", $token)) {
            return $this->_convertRange3d($token);

            // match external ranges like 'Sheet1'!A1:B2 or 'Sheet1:Sheet2'!A1:B2 or 'Sheet1'!$A$1:$B$2 or 'Sheet1:Sheet2'!$A$1:$B$2
        } elseif (preg_match("/^'" . self::REGEX_SHEET_TITLE_QUOTED . "(\:" . self::REGEX_SHEET_TITLE_QUOTED . ")?'\!\\$?([A-Ia-i]?[A-Za-z])?\\$?(\d+)\:\\$?([A-Ia-i]?[A-Za-z])?\\$?(\d+)$/u", $token)) {
            return $this->_convertRange3d($token);

            // operators (including parentheses)
        } elseif (isset($this->ptg[$token])) {
            return pack("C", $this->ptg[$token]);

            // match error codes
        } elseif (preg_match("/^#[A-Z0\/]{3,5}[!?]{1}$/", $token) or $token == '#N/A') {
            return $this->_convertError($token);

            // commented so argument number can be processed correctly. See toReversePolish().
            /* elseif (preg_match("/[A-Z0-9\xc0-\xdc\.]+/",$token))
              {
              return($this->_convertFunction($token,$this->_func_args));
              } */

            // if it's an argument, ignore the token (the argument remains)
        } elseif ($token == 'arg') {
            return '';
        }

        // TODO: use real error codes
        throw new PHPExcel_Writer_Exception("Unknown token $token");
    }

    /**
     * Convert a number token to ptgInt or ptgNum
     *
     * @access private
     * @param mixed $num an integer or double for conversion to its ptg value
     */
    function _convertNumber($num) {
        // Integer in the range 0..2**16-1
        if ((preg_match("/^\d+$/", $num)) and ( $num <= 65535)) {
            return pack("Cv", $this->ptg['ptgInt'], $num);
        } else { // A float
            if (PHPExcel_Writer_Excel5_BIFFwriter::getByteOrder()) { // if it's Big Endian
                $num = strrev($num);
            }
            return pack("Cd", $this->ptg['ptgNum'], $num);
        }
    }

    /**
     * Convert a string token to ptgStr
     *
     * @access private
     * @param string $string A string for conversion to its ptg value.
     * @return mixed the converted token on success
     */
    function _convertString($string) {
        // chop away beggining and ending quotes
        $string = substr($string, 1, strlen($string) - 2);
        if (strlen($string) > 255) {
            throw new PHPExcel_Writer_Exception("String is too long");
        }

        return pack('C', $this->ptg['ptgStr']) . PHPExcel_Shared_String::UTF8toBIFF8UnicodeShort($string);
    }

    /**
     * Convert a function to a ptgFunc or ptgFuncVarV depending on the number of
     * args that it takes.
     *
     * @access private
     * @param string  $token    The name of the function for convertion to ptg value.
     * @param integer $num_args The number of arguments the function receives.
     * @return string The packed ptg for the function
     */
    function _convertFunction($token, $num_args) {
        $args = $this->_functions[$token][1];
//		$volatile = $this->_functions[$token][3];
        // Fixed number of args eg. TIME($i,$j,$k).
        if ($args >= 0) {
            return pack("Cv", $this->ptg['ptgFuncV'], $this->_functions[$token][0]);
        }
        // Variable number of args eg. SUM($i,$j,$k, ..).
        if ($args == -1) {
            return pack("CCv", $this->ptg['ptgFuncVarV'], $num_args, $this->_functions[$token][0]);
        }
    }

    /**
     * Convert an Excel range such as A1:D4 to a ptgRefV.
     *
     * @access private
     * @param string	$range	An Excel range in the A1:A2
     * @param int		$class
     */
    function _convertRange2d($range, $class = 0) {

        // TODO: possible class value 0,1,2 check Formula.pm
        // Split the range into 2 cell refs
        if (preg_match('/^(\$)?([A-Ia-i]?[A-Za-z])(\$)?(\d+)\:(\$)?([A-Ia-i]?[A-Za-z])(\$)?(\d+)$/', $range)) {
            list($cell1, $cell2) = explode(':', $range);
        } else {
            // TODO: use real error codes
            throw new PHPExcel_Writer_Exception("Unknown range separator");
        }

        // Convert the cell references
        list($row1, $col1) = $this->_cellToPackedRowcol($cell1);
        list($row2, $col2) = $this->_cellToPackedRowcol($cell2);

        // The ptg value depends on the class of the ptg.
        if ($class == 0) {
            $ptgArea = pack("C", $this->ptg['ptgArea']);
        } elseif ($class == 1) {
            $ptgArea = pack("C", $this->ptg['ptgAreaV']);
        } elseif ($class == 2) {
            $ptgArea = pack("C", $this->ptg['ptgAreaA']);
        } else {
            // TODO: use real error codes
            throw new PHPExcel_Writer_Exception("Unknown class $class");
        }
        return $ptgArea . $row1 . $row2 . $col1 . $col2;
    }

    /**
     * Convert an Excel 3d range such as "Sheet1!A1:D4" or "Sheet1:Sheet2!A1:D4" to
     * a ptgArea3d.
     *
     * @access private
     * @param string $token An Excel range in the Sheet1!A1:A2 format.
     * @return mixed The packed ptgArea3d token on success.
     */
    function _convertRange3d($token) {
//		$class = 0; // formulas like Sheet1!$A$1:$A$2 in list type data validation need this class (0x3B)
        // Split the ref at the ! symbol
        list($ext_ref, $range) = explode('!', $token);

        // Convert the external reference part (different for BIFF8)
        $ext_ref = $this->_getRefIndex($ext_ref);

        // Split the range into 2 cell refs
        list($cell1, $cell2) = explode(':', $range);

        // Convert the cell references
        if (preg_match("/^(\\$)?[A-Ia-i]?[A-Za-z](\\$)?(\d+)$/", $cell1)) {
            list($row1, $col1) = $this->_cellToPackedRowcol($cell1);
            list($row2, $col2) = $this->_cellToPackedRowcol($cell2);
        } else { // It's a rows range (like 26:27)
            list($row1, $col1, $row2, $col2) = $this->_rangeToPackedRange($cell1 . ':' . $cell2);
        }

        // The ptg value depends on the class of the ptg.
//		if ($class == 0) {
        $ptgArea = pack("C", $this->ptg['ptgArea3d']);
//		} elseif ($class == 1) {
//			$ptgArea = pack("C", $this->ptg['ptgArea3dV']);
//		} elseif ($class == 2) {
//			$ptgArea = pack("C", $this->ptg['ptgArea3dA']);
//		} else {
//			throw new PHPExcel_Writer_Exception("Unknown class $class");
//		}

        return $ptgArea . $ext_ref . $row1 . $row2 . $col1 . $col2;
    }

    /**
     * Convert an Excel reference such as A1, $B2, C$3 or $D$4 to a ptgRefV.
     *
     * @access private
     * @param string $cell An Excel cell reference
     * @return string The cell in packed() format with the corresponding ptg
     */
    function _convertRef2d($cell) {
//		$class = 2; // as far as I know, this is magick.
        // Convert the cell reference
        $cell_array = $this->_cellToPackedRowcol($cell);
        list($row, $col) = $cell_array;

        // The ptg value depends on the class of the ptg.
//		if ($class == 0) {
//			$ptgRef = pack("C", $this->ptg['ptgRef']);
//		} elseif ($class == 1) {
//			$ptgRef = pack("C", $this->ptg['ptgRefV']);
//		} elseif ($class == 2) {
        $ptgRef = pack("C", $this->ptg['ptgRefA']);
//		} else {
//			// TODO: use real error codes
//			throw new PHPExcel_Writer_Exception("Unknown class $class");
//		}
        return $ptgRef . $row . $col;
    }

    /**
     * Convert an Excel 3d reference such as "Sheet1!A1" or "Sheet1:Sheet2!A1" to a
     * ptgRef3d.
     *
     * @access private
     * @param string $cell An Excel cell reference
     * @return mixed The packed ptgRef3d token on success.
     */
    function _convertRef3d($cell) {
//		$class = 2; // as far as I know, this is magick.
        // Split the ref at the ! symbol
        list($ext_ref, $cell) = explode('!', $cell);

        // Convert the external reference part (different for BIFF8)
        $ext_ref = $this->_getRefIndex($ext_ref);

        // Convert the cell reference part
        list($row, $col) = $this->_cellToPackedRowcol($cell);

        // The ptg value depends on the class of the ptg.
//		if ($class == 0) {
//			$ptgRef = pack("C", $this->ptg['ptgRef3d']);
//		} elseif ($class == 1) {
//			$ptgRef = pack("C", $this->ptg['ptgRef3dV']);
//		} elseif ($class == 2) {
        $ptgRef = pack("C", $this->ptg['ptgRef3dA']);
//		} else {
//			throw new PHPExcel_Writer_Exception("Unknown class $class");
//		}

        return $ptgRef . $ext_ref . $row . $col;
    }

    /**
     * Convert an error code to a ptgErr
     *
     * @access	private
     * @param	string	$errorCode	The error code for conversion to its ptg value
     * @return	string				The error code ptgErr
     */
    function _convertError($errorCode) {
        switch ($errorCode) {
            case '#NULL!': return pack("C", 0x00);
            case '#DIV/0!': return pack("C", 0x07);
            case '#VALUE!': return pack("C", 0x0F);
            case '#REF!': return pack("C", 0x17);
            case '#NAME?': return pack("C", 0x1D);
            case '#NUM!': return pack("C", 0x24);
            case '#N/A': return pack("C", 0x2A);
        }
        return pack("C", 0xFF);
    }

    /**
     * Convert the sheet name part of an external reference, for example "Sheet1" or
     * "Sheet1:Sheet2", to a packed structure.
     *
     * @access	private
     * @param	string	$ext_ref	The name of the external reference
     * @return	string				The reference index in packed() format
     */
    function _packExtRef($ext_ref) {
        $ext_ref = preg_replace("/^'/", '', $ext_ref); // Remove leading  ' if any.
        $ext_ref = preg_replace("/'$/", '', $ext_ref); // Remove trailing ' if any.
        // Check if there is a sheet range eg., Sheet1:Sheet2.
        if (preg_match("/:/", $ext_ref)) {
            list($sheet_name1, $sheet_name2) = explode(':', $ext_ref);

            $sheet1 = $this->_getSheetIndex($sheet_name1);
            if ($sheet1 == -1) {
                throw new PHPExcel_Writer_Exception("Unknown sheet name $sheet_name1 in formula");
            }
            $sheet2 = $this->_getSheetIndex($sheet_name2);
            if ($sheet2 == -1) {
                throw new PHPExcel_Writer_Exception("Unknown sheet name $sheet_name2 in formula");
            }

            // Reverse max and min sheet numbers if necessary
            if ($sheet1 > $sheet2) {
                list($sheet1, $sheet2) = array($sheet2, $sheet1);
            }
        } else { // Single sheet name only.
            $sheet1 = $this->_getSheetIndex($ext_ref);
            if ($sheet1 == -1) {
                throw new PHPExcel_Writer_Exception("Unknown sheet name $ext_ref in formula");
            }
            $sheet2 = $sheet1;
        }

        // References are stored relative to 0xFFFF.
        $offset = -1 - $sheet1;

        return pack('vdvv', $offset, 0x00, $sheet1, $sheet2);
    }

    /**
     * Look up the REF index that corresponds to an external sheet name
     * (or range). If it doesn't exist yet add it to the workbook's references
     * array. It assumes all sheet names given must exist.
     *
     * @access private
     * @param string $ext_ref The name of the external reference
     * @return mixed The reference index in packed() format on success
     */
    function _getRefIndex($ext_ref) {
        $ext_ref = preg_replace("/^'/", '', $ext_ref); // Remove leading  ' if any.
        $ext_ref = preg_replace("/'$/", '', $ext_ref); // Remove trailing ' if any.
        $ext_ref = str_replace('\'\'', '\'', $ext_ref); // Replace escaped '' with '
        // Check if there is a sheet range eg., Sheet1:Sheet2.
        if (preg_match("/:/", $ext_ref)) {
            list($sheet_name1, $sheet_name2) = explode(':', $ext_ref);

            $sheet1 = $this->_getSheetIndex($sheet_name1);
            if ($sheet1 == -1) {
                throw new PHPExcel_Writer_Exception("Unknown sheet name $sheet_name1 in formula");
            }
            $sheet2 = $this->_getSheetIndex($sheet_name2);
            if ($sheet2 == -1) {
                throw new PHPExcel_Writer_Exception("Unknown sheet name $sheet_name2 in formula");
            }

            // Reverse max and min sheet numbers if necessary
            if ($sheet1 > $sheet2) {
                list($sheet1, $sheet2) = array($sheet2, $sheet1);
            }
        } else { // Single sheet name only.
            $sheet1 = $this->_getSheetIndex($ext_ref);
            if ($sheet1 == -1) {
                throw new PHPExcel_Writer_Exception("Unknown sheet name $ext_ref in formula");
            }
            $sheet2 = $sheet1;
        }

        // assume all references belong to this document
        $supbook_index = 0x00;
        $ref = pack('vvv', $supbook_index, $sheet1, $sheet2);
        $total_references = count($this->_references);
        $index = -1;
        for ($i = 0; $i < $total_references; ++$i) {
            if ($ref == $this->_references[$i]) {
                $index = $i;
                break;
            }
        }
        // if REF was not found add it to references array
        if ($index == -1) {
            $this->_references[$total_references] = $ref;
            $index = $total_references;
        }

        return pack('v', $index);
    }

    /**
     * Look up the index that corresponds to an external sheet name. The hash of
     * sheet names is updated by the addworksheet() method of the
     * PHPExcel_Writer_Excel5_Workbook class.
     *
     * @access	private
     * @param	string	$sheet_name		Sheet name
     * @return	integer					The sheet index, -1 if the sheet was not found
     */
    function _getSheetIndex($sheet_name) {
        if (!isset($this->_ext_sheets[$sheet_name])) {
            return -1;
        } else {
            return $this->_ext_sheets[$sheet_name];
        }
    }

    /**
     * This method is used to update the array of sheet names. It is
     * called by the addWorksheet() method of the
     * PHPExcel_Writer_Excel5_Workbook class.
     *
     * @access public
     * @see PHPExcel_Writer_Excel5_Workbook::addWorksheet()
     * @param string  $name  The name of the worksheet being added
     * @param integer $index The index of the worksheet being added
     */
    function setExtSheet($name, $index) {
        $this->_ext_sheets[$name] = $index;
    }

    /**
     * pack() row and column into the required 3 or 4 byte format.
     *
     * @access private
     * @param string $cell The Excel cell reference to be packed
     * @return array Array containing the row and column in packed() format
     */
    function _cellToPackedRowcol($cell) {
        $cell = strtoupper($cell);
        list($row, $col, $row_rel, $col_rel) = $this->_cellToRowcol($cell);
        if ($col >= 256) {
            throw new PHPExcel_Writer_Exception("Column in: $cell greater than 255");
        }
        if ($row >= 65536) {
            throw new PHPExcel_Writer_Exception("Row in: $cell greater than 65536 ");
        }

        // Set the high bits to indicate if row or col are relative.
        $col |= $col_rel << 14;
        $col |= $row_rel << 15;
        $col = pack('v', $col);

        $row = pack('v', $row);

        return array($row, $col);
    }

    /**
     * pack() row range into the required 3 or 4 byte format.
     * Just using maximum col/rows, which is probably not the correct solution
     *
     * @access private
     * @param string $range The Excel range to be packed
     * @return array Array containing (row1,col1,row2,col2) in packed() format
     */
    function _rangeToPackedRange($range) {
        preg_match('/(\$)?(\d+)\:(\$)?(\d+)/', $range, $match);
        // return absolute rows if there is a $ in the ref
        $row1_rel = empty($match[1]) ? 1 : 0;
        $row1 = $match[2];
        $row2_rel = empty($match[3]) ? 1 : 0;
        $row2 = $match[4];
        // Convert 1-index to zero-index
        --$row1;
        --$row2;
        // Trick poor inocent Excel
        $col1 = 0;
        $col2 = 65535; // FIXME: maximum possible value for Excel 5 (change this!!!)
        // FIXME: this changes for BIFF8
        if (($row1 >= 65536) or ( $row2 >= 65536)) {
            throw new PHPExcel_Writer_Exception("Row in: $range greater than 65536 ");
        }

        // Set the high bits to indicate if rows are relative.
        $col1 |= $row1_rel << 15;
        $col2 |= $row2_rel << 15;
        $col1 = pack('v', $col1);
        $col2 = pack('v', $col2);

        $row1 = pack('v', $row1);
        $row2 = pack('v', $row2);

        return array($row1, $col1, $row2, $col2);
    }

    /**
     * Convert an Excel cell reference such as A1 or $B2 or C$3 or $D$4 to a zero
     * indexed row and column number. Also returns two (0,1) values to indicate
     * whether the row or column are relative references.
     *
     * @access private
     * @param string $cell The Excel cell reference in A1 format.
     * @return array
     */
    function _cellToRowcol($cell) {
        preg_match('/(\$)?([A-I]?[A-Z])(\$)?(\d+)/', $cell, $match);
        // return absolute column if there is a $ in the ref
        $col_rel = empty($match[1]) ? 1 : 0;
        $col_ref = $match[2];
        $row_rel = empty($match[3]) ? 1 : 0;
        $row = $match[4];

        // Convert base26 column string to a number.
        $expn = strlen($col_ref) - 1;
        $col = 0;
        $col_ref_length = strlen($col_ref);
        for ($i = 0; $i < $col_ref_length; ++$i) {
            $col += (ord($col_ref{$i}) - 64) * pow(26, $expn);
            --$expn;
        }

        // Convert 1-index to zero-index
        --$row;
        --$col;

        return array($row, $col, $row_rel, $col_rel);
    }

    /**
     * Advance to the next valid token.
     *
     * @access private
     */
    function _advance() {
        $i = $this->_current_char;
        $formula_length = strlen($this->_formula);
        // eat up white spaces
        if ($i < $formula_length) {
            while ($this->_formula{$i} == " ") {
                ++$i;
            }

            if ($i < ($formula_length - 1)) {
                $this->_lookahead = $this->_formula{$i + 1};
            }
            $token = '';
        }

        while ($i < $formula_length) {
            $token .= $this->_formula{$i};

            if ($i < ($formula_length - 1)) {
                $this->_lookahead = $this->_formula{$i + 1};
            } else {
                $this->_lookahead = '';
            }

            if ($this->_match($token) != '') {
                //if ($i < strlen($this->_formula) - 1) {
                //    $this->_lookahead = $this->_formula{$i+1};
                //}
                $this->_current_char = $i + 1;
                $this->_current_token = $token;
                return 1;
            }

            if ($i < ($formula_length - 2)) {
                $this->_lookahead = $this->_formula{$i + 2};
            } else { // if we run out of characters _lookahead becomes empty
                $this->_lookahead = '';
            }
            ++$i;
        }
        //die("Lexical error ".$this->_current_char);
    }

    /**
     * Checks if it's a valid token.
     *
     * @access private
     * @param mixed $token The token to check.
     * @return mixed       The checked token or false on failure
     */
    function _match($token) {
        switch ($token) {
            case "+":
            case "-":
            case "*":
            case "/":
            case "(":
            case ")":
            case ",":
            case ";":
            case ">=":
            case "<=":
            case "=":
            case "<>":
            case "^":
            case "&":
            case "%":
                return $token;
                break;
            case ">":
                if ($this->_lookahead == '=') { // it's a GE token
                    break;
                }
                return $token;
                break;
            case "<":
                // it's a LE or a NE token
                if (($this->_lookahead == '=') or ( $this->_lookahead == '>')) {
                    break;
                }
                return $token;
                break;
            default:
                // if it's a reference A1 or $A$1 or $A1 or A$1
                if (preg_match('/^\$?[A-Ia-i]?[A-Za-z]\$?[0-9]+$/', $token) and ! preg_match("/[0-9]/", $this->_lookahead) and ( $this->_lookahead != ':') and ( $this->_lookahead != '.') and ( $this->_lookahead != '!')) {
                    return $token;
                }
                // If it's an external reference (Sheet1!A1 or Sheet1:Sheet2!A1 or Sheet1!$A$1 or Sheet1:Sheet2!$A$1)
                elseif (preg_match("/^" . self::REGEX_SHEET_TITLE_UNQUOTED . "(\:" . self::REGEX_SHEET_TITLE_UNQUOTED . ")?\!\\$?[A-Ia-i]?[A-Za-z]\\$?[0-9]+$/u", $token) and ! preg_match("/[0-9]/", $this->_lookahead) and ( $this->_lookahead != ':') and ( $this->_lookahead != '.')) {
                    return $token;
                }
                // If it's an external reference ('Sheet1'!A1 or 'Sheet1:Sheet2'!A1 or 'Sheet1'!$A$1 or 'Sheet1:Sheet2'!$A$1)
                elseif (preg_match("/^'" . self::REGEX_SHEET_TITLE_QUOTED . "(\:" . self::REGEX_SHEET_TITLE_QUOTED . ")?'\!\\$?[A-Ia-i]?[A-Za-z]\\$?[0-9]+$/u", $token) and ! preg_match("/[0-9]/", $this->_lookahead) and ( $this->_lookahead != ':') and ( $this->_lookahead != '.')) {
                    return $token;
                }
                // if it's a range A1:A2 or $A$1:$A$2
                elseif (preg_match('/^(\$)?[A-Ia-i]?[A-Za-z](\$)?[0-9]+:(\$)?[A-Ia-i]?[A-Za-z](\$)?[0-9]+$/', $token) and ! preg_match("/[0-9]/", $this->_lookahead)) {
                    return $token;
                }
                // If it's an external range like Sheet1!A1:B2 or Sheet1:Sheet2!A1:B2 or Sheet1!$A$1:$B$2 or Sheet1:Sheet2!$A$1:$B$2
                elseif (preg_match("/^" . self::REGEX_SHEET_TITLE_UNQUOTED . "(\:" . self::REGEX_SHEET_TITLE_UNQUOTED . ")?\!\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+:\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+$/u", $token) and ! preg_match("/[0-9]/", $this->_lookahead)) {
                    return $token;
                }
                // If it's an external range like 'Sheet1'!A1:B2 or 'Sheet1:Sheet2'!A1:B2 or 'Sheet1'!$A$1:$B$2 or 'Sheet1:Sheet2'!$A$1:$B$2
                elseif (preg_match("/^'" . self::REGEX_SHEET_TITLE_QUOTED . "(\:" . self::REGEX_SHEET_TITLE_QUOTED . ")?'\!\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+:\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+$/u", $token) and ! preg_match("/[0-9]/", $this->_lookahead)) {
                    return $token;
                }
                // If it's a number (check that it's not a sheet name or range)
                elseif (is_numeric($token) and ( !is_numeric($token . $this->_lookahead) or ( $this->_lookahead == '')) and ( $this->_lookahead != '!') and ( $this->_lookahead != ':')) {
                    return $token;
                }
                // If it's a string (of maximum 255 characters)
                elseif (preg_match("/\"([^\"]|\"\"){0,255}\"/", $token) and $this->_lookahead != '"' and ( substr_count($token, '"') % 2 == 0)) {
                    return $token;
                }
                // If it's an error code
                elseif (preg_match("/^#[A-Z0\/]{3,5}[!?]{1}$/", $token) or $token == '#N/A') {
                    return $token;
                }
                // if it's a function call
                elseif (preg_match("/^[A-Z0-9\xc0-\xdc\.]+$/i", $token) and ( $this->_lookahead == "(")) {
                    return $token;
                }
                //	It's an argument of some description (e.g. a named range),
                //		precise nature yet to be determined
                elseif (substr($token, -1) == ')') {
                    return $token;
                }
                return '';
        }
    }

    /**
     * The parsing method. It parses a formula.
     *
     * @access public
     * @param string $formula The formula to parse, without the initial equal
     *                        sign (=).
     * @return mixed true on success
     */
    function parse($formula) {
        $this->_current_char = 0;
        $this->_formula = $formula;
        $this->_lookahead = isset($formula{1}) ? $formula{1} : '';
        $this->_advance();
        $this->_parse_tree = $this->_condition();
        return true;
    }

    /**
     * It parses a condition. It assumes the following rule:
     * Cond -> Expr [(">" | "<") Expr]
     *
     * @access private
     * @return mixed The parsed ptg'd tree on success
     */
    function _condition() {
        $result = $this->_expression();
        if ($this->_current_token == "<") {
            $this->_advance();
            $result2 = $this->_expression();
            $result = $this->_createTree('ptgLT', $result, $result2);
        } elseif ($this->_current_token == ">") {
            $this->_advance();
            $result2 = $this->_expression();
            $result = $this->_createTree('ptgGT', $result, $result2);
        } elseif ($this->_current_token == "<=") {
            $this->_advance();
            $result2 = $this->_expression();
            $result = $this->_createTree('ptgLE', $result, $result2);
        } elseif ($this->_current_token == ">=") {
            $this->_advance();
            $result2 = $this->_expression();
            $result = $this->_createTree('ptgGE', $result, $result2);
        } elseif ($this->_current_token == "=") {
            $this->_advance();
            $result2 = $this->_expression();
            $result = $this->_createTree('ptgEQ', $result, $result2);
        } elseif ($this->_current_token == "<>") {
            $this->_advance();
            $result2 = $this->_expression();
            $result = $this->_createTree('ptgNE', $result, $result2);
        } elseif ($this->_current_token == "&") {
            $this->_advance();
            $result2 = $this->_expression();
            $result = $this->_createTree('ptgConcat', $result, $result2);
        }
        return $result;
    }

    /**
     * It parses a expression. It assumes the following rule:
     * Expr -> Term [("+" | "-") Term]
     *      -> "string"
     *      -> "-" Term : Negative value
     *      -> "+" Term : Positive value
     *      -> Error code
     *
     * @access private
     * @return mixed The parsed ptg'd tree on success
     */
    function _expression() {
        // If it's a string return a string node
        if (preg_match("/\"([^\"]|\"\"){0,255}\"/", $this->_current_token)) {
            $tmp = str_replace('""', '"', $this->_current_token);
            if (($tmp == '"') || ($tmp == ''))
                $tmp = '""'; //	Trap for "" that has been used for an empty string
            $result = $this->_createTree($tmp, '', '');
            $this->_advance();
            return $result;
            // If it's an error code
        } elseif (preg_match("/^#[A-Z0\/]{3,5}[!?]{1}$/", $this->_current_token) or $this->_current_token == '#N/A') {
            $result = $this->_createTree($this->_current_token, 'ptgErr', '');
            $this->_advance();
            return $result;
            // If it's a negative value
        } elseif ($this->_current_token == "-") {
            // catch "-" Term
            $this->_advance();
            $result2 = $this->_expression();
            $result = $this->_createTree('ptgUminus', $result2, '');
            return $result;
            // If it's a positive value
        } elseif ($this->_current_token == "+") {
            // catch "+" Term
            $this->_advance();
            $result2 = $this->_expression();
            $result = $this->_createTree('ptgUplus', $result2, '');
            return $result;
        }
        $result = $this->_term();
        while (($this->_current_token == "+") or ( $this->_current_token == "-") or ( $this->_current_token == "^")) {
            /**/
            if ($this->_current_token == "+") {
                $this->_advance();
                $result2 = $this->_term();
                $result = $this->_createTree('ptgAdd', $result, $result2);
            } elseif ($this->_current_token == "-") {
                $this->_advance();
                $result2 = $this->_term();
                $result = $this->_createTree('ptgSub', $result, $result2);
            } else {
                $this->_advance();
                $result2 = $this->_term();
                $result = $this->_createTree('ptgPower', $result, $result2);
            }
        }
        return $result;
    }

    /**
     * This function just introduces a ptgParen element in the tree, so that Excel
     * doesn't get confused when working with a parenthesized formula afterwards.
     *
     * @access private
     * @see _fact()
     * @return array The parsed ptg'd tree
     */
    function _parenthesizedExpression() {
        $result = $this->_createTree('ptgParen', $this->_expression(), '');
        return $result;
    }

    /**
     * It parses a term. It assumes the following rule:
     * Term -> Fact [("*" | "/") Fact]
     *
     * @access private
     * @return mixed The parsed ptg'd tree on success
     */
    function _term() {
        $result = $this->_fact();
        while (($this->_current_token == "*") or ( $this->_current_token == "/")) {
            /**/
            if ($this->_current_token == "*") {
                $this->_advance();
                $result2 = $this->_fact();
                $result = $this->_createTree('ptgMul', $result, $result2);
            } else {
                $this->_advance();
                $result2 = $this->_fact();
                $result = $this->_createTree('ptgDiv', $result, $result2);
            }
        }
        return $result;
    }

    /**
     * It parses a factor. It assumes the following rule:
     * Fact -> ( Expr )
     *       | CellRef
     *       | CellRange
     *       | Number
     *       | Function
     *
     * @access private
     * @return mixed The parsed ptg'd tree on success
     */
    function _fact() {
        if ($this->_current_token == "(") {
            $this->_advance();         // eat the "("
            $result = $this->_parenthesizedExpression();
            if ($this->_current_token != ")") {
                throw new PHPExcel_Writer_Exception("')' token expected.");
            }
            $this->_advance();         // eat the ")"
            return $result;
        }
        // if it's a reference
        if (preg_match('/^\$?[A-Ia-i]?[A-Za-z]\$?[0-9]+$/', $this->_current_token)) {
            $result = $this->_createTree($this->_current_token, '', '');
            $this->_advance();
            return $result;
        }
        // If it's an external reference (Sheet1!A1 or Sheet1:Sheet2!A1 or Sheet1!$A$1 or Sheet1:Sheet2!$A$1)
        elseif (preg_match("/^" . self::REGEX_SHEET_TITLE_UNQUOTED . "(\:" . self::REGEX_SHEET_TITLE_UNQUOTED . ")?\!\\$?[A-Ia-i]?[A-Za-z]\\$?[0-9]+$/u", $this->_current_token)) {
            $result = $this->_createTree($this->_current_token, '', '');
            $this->_advance();
            return $result;
        }
        // If it's an external reference ('Sheet1'!A1 or 'Sheet1:Sheet2'!A1 or 'Sheet1'!$A$1 or 'Sheet1:Sheet2'!$A$1)
        elseif (preg_match("/^'" . self::REGEX_SHEET_TITLE_QUOTED . "(\:" . self::REGEX_SHEET_TITLE_QUOTED . ")?'\!\\$?[A-Ia-i]?[A-Za-z]\\$?[0-9]+$/u", $this->_current_token)) {
            $result = $this->_createTree($this->_current_token, '', '');
            $this->_advance();
            return $result;
        }
        // if it's a range A1:B2 or $A$1:$B$2
        elseif (preg_match('/^(\$)?[A-Ia-i]?[A-Za-z](\$)?[0-9]+:(\$)?[A-Ia-i]?[A-Za-z](\$)?[0-9]+$/', $this->_current_token) or
                preg_match('/^(\$)?[A-Ia-i]?[A-Za-z](\$)?[0-9]+\.\.(\$)?[A-Ia-i]?[A-Za-z](\$)?[0-9]+$/', $this->_current_token)) {
            // must be an error?
            $result = $this->_createTree($this->_current_token, '', '');
            $this->_advance();
            return $result;
        }
        // If it's an external range (Sheet1!A1:B2 or Sheet1:Sheet2!A1:B2 or Sheet1!$A$1:$B$2 or Sheet1:Sheet2!$A$1:$B$2)
        elseif (preg_match("/^" . self::REGEX_SHEET_TITLE_UNQUOTED . "(\:" . self::REGEX_SHEET_TITLE_UNQUOTED . ")?\!\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+:\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+$/u", $this->_current_token)) {
            // must be an error?
            //$result = $this->_current_token;
            $result = $this->_createTree($this->_current_token, '', '');
            $this->_advance();
            return $result;
        }
        // If it's an external range ('Sheet1'!A1:B2 or 'Sheet1'!A1:B2 or 'Sheet1'!$A$1:$B$2 or 'Sheet1'!$A$1:$B$2)
        elseif (preg_match("/^'" . self::REGEX_SHEET_TITLE_QUOTED . "(\:" . self::REGEX_SHEET_TITLE_QUOTED . ")?'\!\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+:\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+$/u", $this->_current_token)) {
            // must be an error?
            //$result = $this->_current_token;
            $result = $this->_createTree($this->_current_token, '', '');
            $this->_advance();
            return $result;
        }
        // If it's a number or a percent
        elseif (is_numeric($this->_current_token)) {
            if ($this->_lookahead == '%') {
                $result = $this->_createTree('ptgPercent', $this->_current_token, '');
            } else {
                $result = $this->_createTree($this->_current_token, '', '');
            }
            $this->_advance();
            return $result;
        }
        // if it's a function call
        elseif (preg_match("/^[A-Z0-9\xc0-\xdc\.]+$/i", $this->_current_token)) {
            $result = $this->_func();
            return $result;
        }
        throw new PHPExcel_Writer_Exception("Syntax error: " . $this->_current_token .
        ", lookahead: " . $this->_lookahead .
        ", current char: " . $this->_current_char);
    }

    /**
     * It parses a function call. It assumes the following rule:
     * Func -> ( Expr [,Expr]* )
     *
     * @access private
     * @return mixed The parsed ptg'd tree on success
     */
    function _func() {
        $num_args = 0; // number of arguments received
        $function = strtoupper($this->_current_token);
        $result = ''; // initialize result
        $this->_advance();
        $this->_advance();         // eat the "("
        while ($this->_current_token != ')') {
            /**/
            if ($num_args > 0) {
                if ($this->_current_token == "," or
                        $this->_current_token == ";") {
                    $this->_advance();  // eat the "," or ";"
                } else {
                    throw new PHPExcel_Writer_Exception("Syntax error: comma expected in " .
                    "function $function, arg #{$num_args}");
                }
                $result2 = $this->_condition();
                $result = $this->_createTree('arg', $result, $result2);
            } else { // first argument
                $result2 = $this->_condition();
                $result = $this->_createTree('arg', '', $result2);
            }
            ++$num_args;
        }
        if (!isset($this->_functions[$function])) {
            throw new PHPExcel_Writer_Exception("Function $function() doesn't exist");
        }
        $args = $this->_functions[$function][1];
        // If fixed number of args eg. TIME($i,$j,$k). Check that the number of args is valid.
        if (($args >= 0) and ( $args != $num_args)) {
            throw new PHPExcel_Writer_Exception("Incorrect number of arguments in function $function() ");
        }

        $result = $this->_createTree($function, $result, $num_args);
        $this->_advance();         // eat the ")"
        return $result;
    }

    /**
     * Creates a tree. In fact an array which may have one or two arrays (sub-trees)
     * as elements.
     *
     * @access private
     * @param mixed $value The value of this node.
     * @param mixed $left  The left array (sub-tree) or a final node.
     * @param mixed $right The right array (sub-tree) or a final node.
     * @return array A tree
     */
    function _createTree($value, $left, $right) {
        return array('value' => $value, 'left' => $left, 'right' => $right);
    }

    /**
     * Builds a string containing the tree in reverse polish notation (What you
     * would use in a HP calculator stack).
     * The following tree:
     *
     *    +
     *   / \
     *  2   3
     *
     * produces: "23+"
     *
     * The following tree:
     *
     *    +
     *   / \
     *  3   *
     *     / \
     *    6   A1
     *
     * produces: "36A1*+"
     *
     * In fact all operands, functions, references, etc... are written as ptg's
     *
     * @access public
     * @param array $tree The optional tree to convert.
     * @return string The tree in reverse polish notation
     */
    function toReversePolish($tree = array()) {
        $polish = ""; // the string we are going to return
        if (empty($tree)) { // If it's the first call use _parse_tree
            $tree = $this->_parse_tree;
        }

        if (is_array($tree['left'])) {
            $converted_tree = $this->toReversePolish($tree['left']);
            $polish .= $converted_tree;
        } elseif ($tree['left'] != '') { // It's a final node
            $converted_tree = $this->_convert($tree['left']);
            $polish .= $converted_tree;
        }
        if (is_array($tree['right'])) {
            $converted_tree = $this->toReversePolish($tree['right']);
            $polish .= $converted_tree;
        } elseif ($tree['right'] != '') { // It's a final node
            $converted_tree = $this->_convert($tree['right']);
            $polish .= $converted_tree;
        }
        // if it's a function convert it here (so we can set it's arguments)
        if (preg_match("/^[A-Z0-9\xc0-\xdc\.]+$/", $tree['value']) and ! preg_match('/^([A-Ia-i]?[A-Za-z])(\d+)$/', $tree['value']) and ! preg_match("/^[A-Ia-i]?[A-Za-z](\d+)\.\.[A-Ia-i]?[A-Za-z](\d+)$/", $tree['value']) and ! is_numeric($tree['value']) and ! isset($this->ptg[$tree['value']])) {
            // left subtree for a function is always an array.
            if ($tree['left'] != '') {
                $left_tree = $this->toReversePolish($tree['left']);
            } else {
                $left_tree = '';
            }
            // add it's left subtree and return.
            return $left_tree . $this->_convertFunction($tree['value'], $tree['right']);
        } else {
            $converted_tree = $this->_convert($tree['value']);
        }
        $polish .= $converted_tree;
        return $polish;
    }

}