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<?php
/**
 * PHPExcel
 *
 * Copyright (c) 2006 - 2013 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 - 2013 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');
}


/** EULER */
define('EULER', 2.71828182845904523536);


/**
 * PHPExcel_Calculation_Engineering
 *
 * @category    PHPExcel
 * @package             PHPExcel_Calculation
 * @copyright   Copyright (c) 2006 - 2013 PHPExcel (http://www.codeplex.com/PHPExcel)
 */
class PHPExcel_Calculation_Engineering {

        /**
         * Details of the Units of measure that can be used in CONVERTUOM()
         *
         * @var mixed[]
         */
        private static $_conversionUnits = array( 'g'           => array(       'Group' => 'Mass',                      'Unit Name'     => 'Gram',                                              'AllowPrefix'   => True         ),
                                                                                          'sg'          => array(       'Group' => 'Mass',                      'Unit Name'     => 'Slug',                                              'AllowPrefix'   => False        ),
                                                                                          'lbm'         => array(       'Group' => 'Mass',                      'Unit Name'     => 'Pound mass (avoirdupois)',  'AllowPrefix'   => False        ),
                                                                                          'u'           => array(       'Group' => 'Mass',                      'Unit Name'     => 'U (atomic mass unit)',              'AllowPrefix'   => True         ),
                                                                                          'ozm'         => array(       'Group' => 'Mass',                      'Unit Name'     => 'Ounce mass (avoirdupois)',  'AllowPrefix'   => False        ),
                                                                                          'm'           => array(       'Group' => 'Distance',          'Unit Name'     => 'Meter',                                             'AllowPrefix'   => True         ),
                                                                                          'mi'          => array(       'Group' => 'Distance',          'Unit Name'     => 'Statute mile',                              'AllowPrefix'   => False        ),
                                                                                          'Nmi'         => array(       'Group' => 'Distance',          'Unit Name'     => 'Nautical mile',                             'AllowPrefix'   => False        ),
                                                                                          'in'          => array(       'Group' => 'Distance',          'Unit Name'     => 'Inch',                                              'AllowPrefix'   => False        ),
                                                                                          'ft'          => array(       'Group' => 'Distance',          'Unit Name'     => 'Foot',                                              'AllowPrefix'   => False        ),
                                                                                          'yd'          => array(       'Group' => 'Distance',          'Unit Name'     => 'Yard',                                              'AllowPrefix'   => False        ),
                                                                                          'ang'         => array(       'Group' => 'Distance',          'Unit Name'     => 'Angstrom',                                  'AllowPrefix'   => True         ),
                                                                                          'Pica'        => array(       'Group' => 'Distance',          'Unit Name'     => 'Pica (1/72 in)',                    'AllowPrefix'   => False        ),
                                                                                          'yr'          => array(       'Group' => 'Time',                      'Unit Name'     => 'Year',                                              'AllowPrefix'   => False        ),
                                                                                          'day'         => array(       'Group' => 'Time',                      'Unit Name'     => 'Day',                                               'AllowPrefix'   => False        ),
                                                                                          'hr'          => array(       'Group' => 'Time',                      'Unit Name'     => 'Hour',                                              'AllowPrefix'   => False        ),
                                                                                          'mn'          => array(       'Group' => 'Time',                      'Unit Name'     => 'Minute',                                    'AllowPrefix'   => False        ),
                                                                                          'sec'         => array(       'Group' => 'Time',                      'Unit Name'     => 'Second',                                    'AllowPrefix'   => True         ),
                                                                                          'Pa'          => array(       'Group' => 'Pressure',          'Unit Name'     => 'Pascal',                                    'AllowPrefix'   => True         ),
                                                                                          'p'           => array(       'Group' => 'Pressure',          'Unit Name'     => 'Pascal',                                    'AllowPrefix'   => True         ),
                                                                                          'atm'         => array(       'Group' => 'Pressure',          'Unit Name'     => 'Atmosphere',                                'AllowPrefix'   => True         ),
                                                                                          'at'          => array(       'Group' => 'Pressure',          'Unit Name'     => 'Atmosphere',                                'AllowPrefix'   => True         ),
                                                                                          'mmHg'        => array(       'Group' => 'Pressure',          'Unit Name'     => 'mm of Mercury',                             'AllowPrefix'   => True         ),
                                                                                          'N'           => array(       'Group' => 'Force',                     'Unit Name'     => 'Newton',                                    'AllowPrefix'   => True         ),
                                                                                          'dyn'         => array(       'Group' => 'Force',                     'Unit Name'     => 'Dyne',                                              'AllowPrefix'   => True         ),
                                                                                          'dy'          => array(       'Group' => 'Force',                     'Unit Name'     => 'Dyne',                                              'AllowPrefix'   => True         ),
                                                                                          'lbf'         => array(       'Group' => 'Force',                     'Unit Name'     => 'Pound force',                               'AllowPrefix'   => False        ),
                                                                                          'J'           => array(       'Group' => 'Energy',            'Unit Name'     => 'Joule',                                             'AllowPrefix'   => True         ),
                                                                                          'e'           => array(       'Group' => 'Energy',            'Unit Name'     => 'Erg',                                               'AllowPrefix'   => True         ),
                                                                                          'c'           => array(       'Group' => 'Energy',            'Unit Name'     => 'Thermodynamic calorie',             'AllowPrefix'   => True         ),
                                                                                          'cal'         => array(       'Group' => 'Energy',            'Unit Name'     => 'IT calorie',                                'AllowPrefix'   => True         ),
                                                                                          'eV'          => array(       'Group' => 'Energy',            'Unit Name'     => 'Electron volt',                             'AllowPrefix'   => True         ),
                                                                                          'ev'          => array(       'Group' => 'Energy',            'Unit Name'     => 'Electron volt',                             'AllowPrefix'   => True         ),
                                                                                          'HPh'         => array(       'Group' => 'Energy',            'Unit Name'     => 'Horsepower-hour',                   'AllowPrefix'   => False        ),
                                                                                          'hh'          => array(       'Group' => 'Energy',            'Unit Name'     => 'Horsepower-hour',                   'AllowPrefix'   => False        ),
                                                                                          'Wh'          => array(       'Group' => 'Energy',            'Unit Name'     => 'Watt-hour',                                 'AllowPrefix'   => True         ),
                                                                                          'wh'          => array(       'Group' => 'Energy',            'Unit Name'     => 'Watt-hour',                                 'AllowPrefix'   => True         ),
                                                                                          'flb'         => array(       'Group' => 'Energy',            'Unit Name'     => 'Foot-pound',                                'AllowPrefix'   => False        ),
                                                                                          'BTU'         => array(       'Group' => 'Energy',            'Unit Name'     => 'BTU',                                               'AllowPrefix'   => False        ),
                                                                                          'btu'         => array(       'Group' => 'Energy',            'Unit Name'     => 'BTU',                                               'AllowPrefix'   => False        ),
                                                                                          'HP'          => array(       'Group' => 'Power',                     'Unit Name'     => 'Horsepower',                                'AllowPrefix'   => False        ),
                                                                                          'h'           => array(       'Group' => 'Power',                     'Unit Name'     => 'Horsepower',                                'AllowPrefix'   => False        ),
                                                                                          'W'           => array(       'Group' => 'Power',                     'Unit Name'     => 'Watt',                                              'AllowPrefix'   => True         ),
                                                                                          'w'           => array(       'Group' => 'Power',                     'Unit Name'     => 'Watt',                                              'AllowPrefix'   => True         ),
                                                                                          'T'           => array(       'Group' => 'Magnetism',         'Unit Name'     => 'Tesla',                                             'AllowPrefix'   => True         ),
                                                                                          'ga'          => array(       'Group' => 'Magnetism',         'Unit Name'     => 'Gauss',                                             'AllowPrefix'   => True         ),
                                                                                          'C'           => array(       'Group' => 'Temperature',       'Unit Name'     => 'Celsius',                                   'AllowPrefix'   => False        ),
                                                                                          'cel'         => array(       'Group' => 'Temperature',       'Unit Name'     => 'Celsius',                                   'AllowPrefix'   => False        ),
                                                                                          'F'           => array(       'Group' => 'Temperature',       'Unit Name'     => 'Fahrenheit',                                'AllowPrefix'   => False        ),
                                                                                          'fah'         => array(       'Group' => 'Temperature',       'Unit Name'     => 'Fahrenheit',                                'AllowPrefix'   => False        ),
                                                                                          'K'           => array(       'Group' => 'Temperature',       'Unit Name'     => 'Kelvin',                                    'AllowPrefix'   => False        ),
                                                                                          'kel'         => array(       'Group' => 'Temperature',       'Unit Name'     => 'Kelvin',                                    'AllowPrefix'   => False        ),
                                                                                          'tsp'         => array(       'Group' => 'Liquid',            'Unit Name'     => 'Teaspoon',                                  'AllowPrefix'   => False        ),
                                                                                          'tbs'         => array(       'Group' => 'Liquid',            'Unit Name'     => 'Tablespoon',                                'AllowPrefix'   => False        ),
                                                                                          'oz'          => array(       'Group' => 'Liquid',            'Unit Name'     => 'Fluid Ounce',                               'AllowPrefix'   => False        ),
                                                                                          'cup'         => array(       'Group' => 'Liquid',            'Unit Name'     => 'Cup',                                               'AllowPrefix'   => False        ),
                                                                                          'pt'          => array(       'Group' => 'Liquid',            'Unit Name'     => 'U.S. Pint',                                 'AllowPrefix'   => False        ),
                                                                                          'us_pt'       => array(       'Group' => 'Liquid',            'Unit Name'     => 'U.S. Pint',                                 'AllowPrefix'   => False        ),
                                                                                          'uk_pt'       => array(       'Group' => 'Liquid',            'Unit Name'     => 'U.K. Pint',                                 'AllowPrefix'   => False        ),
                                                                                          'qt'          => array(       'Group' => 'Liquid',            'Unit Name'     => 'Quart',                                             'AllowPrefix'   => False        ),
                                                                                          'gal'         => array(       'Group' => 'Liquid',            'Unit Name'     => 'Gallon',                                    'AllowPrefix'   => False        ),
                                                                                          'l'           => array(       'Group' => 'Liquid',            'Unit Name'     => 'Litre',                                             'AllowPrefix'   => True         ),
                                                                                          'lt'          => array(       'Group' => 'Liquid',            'Unit Name'     => 'Litre',                                             'AllowPrefix'   => True         )
                                                                                        );

        /**
         * Details of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM()
         *
         * @var mixed[]
         */
        private static $_conversionMultipliers = array( 'Y'     => array(       'multiplier'    => 1E24,        'name'  => 'yotta'      ),
                                                                                                        'Z'     => array(       'multiplier'    => 1E21,        'name'  => 'zetta'      ),
                                                                                                        'E'     => array(       'multiplier'    => 1E18,        'name'  => 'exa'        ),
                                                                                                        'P'     => array(       'multiplier'    => 1E15,        'name'  => 'peta'       ),
                                                                                                        'T'     => array(       'multiplier'    => 1E12,        'name'  => 'tera'       ),
                                                                                                        'G'     => array(       'multiplier'    => 1E9,         'name'  => 'giga'       ),
                                                                                                        'M'     => array(       'multiplier'    => 1E6,         'name'  => 'mega'       ),
                                                                                                        'k'     => array(       'multiplier'    => 1E3,         'name'  => 'kilo'       ),
                                                                                                        'h'     => array(       'multiplier'    => 1E2,         'name'  => 'hecto'      ),
                                                                                                        'e'     => array(       'multiplier'    => 1E1,         'name'  => 'deka'       ),
                                                                                                        'd'     => array(       'multiplier'    => 1E-1,        'name'  => 'deci'       ),
                                                                                                        'c'     => array(       'multiplier'    => 1E-2,        'name'  => 'centi'      ),
                                                                                                        'm'     => array(       'multiplier'    => 1E-3,        'name'  => 'milli'      ),
                                                                                                        'u'     => array(       'multiplier'    => 1E-6,        'name'  => 'micro'      ),
                                                                                                        'n'     => array(       'multiplier'    => 1E-9,        'name'  => 'nano'       ),
                                                                                                        'p'     => array(       'multiplier'    => 1E-12,       'name'  => 'pico'       ),
                                                                                                        'f'     => array(       'multiplier'    => 1E-15,       'name'  => 'femto'      ),
                                                                                                        'a'     => array(       'multiplier'    => 1E-18,       'name'  => 'atto'       ),
                                                                                                        'z'     => array(       'multiplier'    => 1E-21,       'name'  => 'zepto'      ),
                                                                                                        'y'     => array(       'multiplier'    => 1E-24,       'name'  => 'yocto'      )
                                                                                                 );

        /**
         * Details of the Units of measure conversion factors, organised by group
         *
         * @var mixed[]
         */
        private static $_unitConversions = array(       'Mass'          => array(       'g'             => array(       'g'             => 1.0,
                                                                                                                                                                                        'sg'    => 6.85220500053478E-05,
                                                                                                                                                                                        'lbm'   => 2.20462291469134E-03,
                                                                                                                                                                                        'u'             => 6.02217000000000E+23,
                                                                                                                                                                                        'ozm'   => 3.52739718003627E-02
                                                                                                                                                                                ),
                                                                                                                                                'sg'    => array(       'g'             => 1.45938424189287E+04,
                                                                                                                                                                                        'sg'    => 1.0,
                                                                                                                                                                                        'lbm'   => 3.21739194101647E+01,
                                                                                                                                                                                        'u'             => 8.78866000000000E+27,
                                                                                                                                                                                        'ozm'   => 5.14782785944229E+02
                                                                                                                                                                                ),
                                                                                                                                                'lbm'   => array(       'g'             => 4.5359230974881148E+02,
                                                                                                                                                                                        'sg'    => 3.10810749306493E-02,
                                                                                                                                                                                        'lbm'   => 1.0,
                                                                                                                                                                                        'u'             => 2.73161000000000E+26,
                                                                                                                                                                                        'ozm'   => 1.60000023429410E+01
                                                                                                                                                                                ),
                                                                                                                                                'u'             => array(       'g'             => 1.66053100460465E-24,
                                                                                                                                                                                        'sg'    => 1.13782988532950E-28,
                                                                                                                                                                                        'lbm'   => 3.66084470330684E-27,
                                                                                                                                                                                        'u'             => 1.0,
                                                                                                                                                                                        'ozm'   => 5.85735238300524E-26
                                                                                                                                                                                ),
                                                                                                                                                'ozm'   => array(       'g'             => 2.83495152079732E+01,
                                                                                                                                                                                        'sg'    => 1.94256689870811E-03,
                                                                                                                                                                                        'lbm'   => 6.24999908478882E-02,
                                                                                                                                                                                        'u'             => 1.70725600000000E+25,
                                                                                                                                                                                        'ozm'   => 1.0
                                                                                                                                                                                )
                                                                                                                                        ),
                                                                                                'Distance'      => array(       'm'             => array(       'm'             => 1.0,
                                                                                                                                                                                        'mi'    => 6.21371192237334E-04,
                                                                                                                                                                                        'Nmi'   => 5.39956803455724E-04,
                                                                                                                                                                                        'in'    => 3.93700787401575E+01,
                                                                                                                                                                                        'ft'    => 3.28083989501312E+00,
                                                                                                                                                                                        'yd'    => 1.09361329797891E+00,
                                                                                                                                                                                        'ang'   => 1.00000000000000E+10,
                                                                                                                                                                                        'Pica'  => 2.83464566929116E+03
                                                                                                                                                                                ),
                                                                                                                                                'mi'    => array(       'm'             => 1.60934400000000E+03,
                                                                                                                                                                                        'mi'    => 1.0,
                                                                                                                                                                                        'Nmi'   => 8.68976241900648E-01,
                                                                                                                                                                                        'in'    => 6.33600000000000E+04,
                                                                                                                                                                                        'ft'    => 5.28000000000000E+03,
                                                                                                                                                                                        'yd'    => 1.76000000000000E+03,
                                                                                                                                                                                        'ang'   => 1.60934400000000E+13,
                                                                                                                                                                                        'Pica'  => 4.56191999999971E+06
                                                                                                                                                                                ),
                                                                                                                                                'Nmi'   => array(       'm'             => 1.85200000000000E+03,
                                                                                                                                                                                        'mi'    => 1.15077944802354E+00,
                                                                                                                                                                                        'Nmi'   => 1.0,
                                                                                                                                                                                        'in'    => 7.29133858267717E+04,
                                                                                                                                                                                        'ft'    => 6.07611548556430E+03,
                                                                                                                                                                                        'yd'    => 2.02537182785694E+03,
                                                                                                                                                                                        'ang'   => 1.85200000000000E+13,
                                                                                                                                                                                        'Pica'  => 5.24976377952723E+06
                                                                                                                                                                                ),
                                                                                                                                                'in'    => array(       'm'             => 2.54000000000000E-02,
                                                                                                                                                                                        'mi'    => 1.57828282828283E-05,
                                                                                                                                                                                        'Nmi'   => 1.37149028077754E-05,
                                                                                                                                                                                        'in'    => 1.0,
                                                                                                                                                                                        'ft'    => 8.33333333333333E-02,
                                                                                                                                                                                        'yd'    => 2.77777777686643E-02,
                                                                                                                                                                                        'ang'   => 2.54000000000000E+08,
                                                                                                                                                                                        'Pica'  => 7.19999999999955E+01
                                                                                                                                                                                ),
                                                                                                                                                'ft'    => array(       'm'             => 3.04800000000000E-01,
                                                                                                                                                                                        'mi'    => 1.89393939393939E-04,
                                                                                                                                                                                        'Nmi'   => 1.64578833693305E-04,
                                                                                                                                                                                        'in'    => 1.20000000000000E+01,
                                                                                                                                                                                        'ft'    => 1.0,
                                                                                                                                                                                        'yd'    => 3.33333333223972E-01,
                                                                                                                                                                                        'ang'   => 3.04800000000000E+09,
                                                                                                                                                                                        'Pica'  => 8.63999999999946E+02
                                                                                                                                                                                ),
                                                                                                                                                'yd'    => array(       'm'             => 9.14400000300000E-01,
                                                                                                                                                                                        'mi'    => 5.68181818368230E-04,
                                                                                                                                                                                        'Nmi'   => 4.93736501241901E-04,
                                                                                                                                                                                        'in'    => 3.60000000118110E+01,
                                                                                                                                                                                        'ft'    => 3.00000000000000E+00,
                                                                                                                                                                                        'yd'    => 1.0,
                                                                                                                                                                                        'ang'   => 9.14400000300000E+09,
                                                                                                                                                                                        'Pica'  => 2.59200000085023E+03
                                                                                                                                                                                ),
                                                                                                                                                'ang'   => array(       'm'             => 1.00000000000000E-10,
                                                                                                                                                                                        'mi'    => 6.21371192237334E-14,
                                                                                                                                                                                        'Nmi'   => 5.39956803455724E-14,
                                                                                                                                                                                        'in'    => 3.93700787401575E-09,
                                                                                                                                                                                        'ft'    => 3.28083989501312E-10,
                                                                                                                                                                                        'yd'    => 1.09361329797891E-10,
                                                                                                                                                                                        'ang'   => 1.0,
                                                                                                                                                                                        'Pica'  => 2.83464566929116E-07
                                                                                                                                                                                ),
                                                                                                                                                'Pica'  => array(       'm'             => 3.52777777777800E-04,
                                                                                                                                                                                        'mi'    => 2.19205948372629E-07,
                                                                                                                                                                                        'Nmi'   => 1.90484761219114E-07,
                                                                                                                                                                                        'in'    => 1.38888888888898E-02,
                                                                                                                                                                                        'ft'    => 1.15740740740748E-03,
                                                                                                                                                                                        'yd'    => 3.85802469009251E-04,
                                                                                                                                                                                        'ang'   => 3.52777777777800E+06,
                                                                                                                                                                                        'Pica'  => 1.0
                                                                                                                                                                                )
                                                                                                                                        ),
                                                                                                'Time'          => array(       'yr'    => array(       'yr'            => 1.0,
                                                                                                                                                                                        'day'           => 365.25,
                                                                                                                                                                                        'hr'            => 8766.0,
                                                                                                                                                                                        'mn'            => 525960.0,
                                                                                                                                                                                        'sec'           => 31557600.0
                                                                                                                                                                                ),
                                                                                                                                                'day'   => array(       'yr'            => 2.73785078713210E-03,
                                                                                                                                                                                        'day'           => 1.0,
                                                                                                                                                                                        'hr'            => 24.0,
                                                                                                                                                                                        'mn'            => 1440.0,
                                                                                                                                                                                        'sec'           => 86400.0
                                                                                                                                                                                ),
                                                                                                                                                'hr'    => array(       'yr'            => 1.14077116130504E-04,
                                                                                                                                                                                        'day'           => 4.16666666666667E-02,
                                                                                                                                                                                        'hr'            => 1.0,
                                                                                                                                                                                        'mn'            => 60.0,
                                                                                                                                                                                        'sec'           => 3600.0
                                                                                                                                                                                ),
                                                                                                                                                'mn'    => array(       'yr'            => 1.90128526884174E-06,
                                                                                                                                                                                        'day'           => 6.94444444444444E-04,
                                                                                                                                                                                        'hr'            => 1.66666666666667E-02,
                                                                                                                                                                                        'mn'            => 1.0,
                                                                                                                                                                                        'sec'           => 60.0
                                                                                                                                                                                ),
                                                                                                                                                'sec'   => array(       'yr'            => 3.16880878140289E-08,
                                                                                                                                                                                        'day'           => 1.15740740740741E-05,
                                                                                                                                                                                        'hr'            => 2.77777777777778E-04,
                                                                                                                                                                                        'mn'            => 1.66666666666667E-02,
                                                                                                                                                                                        'sec'           => 1.0
                                                                                                                                                                                )
                                                                                                                                        ),
                                                                                                'Pressure'      => array(       'Pa'    => array(       'Pa'            => 1.0,
                                                                                                                                                                                        'p'                     => 1.0,
                                                                                                                                                                                        'atm'           => 9.86923299998193E-06,
                                                                                                                                                                                        'at'            => 9.86923299998193E-06,
                                                                                                                                                                                        'mmHg'          => 7.50061707998627E-03
                                                                                                                                                                                ),
                                                                                                                                                'p'             => array(       'Pa'            => 1.0,
                                                                                                                                                                                        'p'                     => 1.0,
                                                                                                                                                                                        'atm'           => 9.86923299998193E-06,
                                                                                                                                                                                        'at'            => 9.86923299998193E-06,
                                                                                                                                                                                        'mmHg'          => 7.50061707998627E-03
                                                                                                                                                                                ),
                                                                                                                                                'atm'   => array(       'Pa'            => 1.01324996583000E+05,
                                                                                                                                                                                        'p'                     => 1.01324996583000E+05,
                                                                                                                                                                                        'atm'           => 1.0,
                                                                                                                                                                                        'at'            => 1.0,
                                                                                                                                                                                        'mmHg'          => 760.0
                                                                                                                                                                                ),
                                                                                                                                                'at'    => array(       'Pa'            => 1.01324996583000E+05,
                                                                                                                                                                                        'p'                     => 1.01324996583000E+05,
                                                                                                                                                                                        'atm'           => 1.0,
                                                                                                                                                                                        'at'            => 1.0,
                                                                                                                                                                                        'mmHg'          => 760.0
                                                                                                                                                                                ),
                                                                                                                                                'mmHg'  => array(       'Pa'            => 1.33322363925000E+02,
                                                                                                                                                                                        'p'                     => 1.33322363925000E+02,
                                                                                                                                                                                        'atm'           => 1.31578947368421E-03,
                                                                                                                                                                                        'at'            => 1.31578947368421E-03,
                                                                                                                                                                                        'mmHg'          => 1.0
                                                                                                                                                                                )
                                                                                                                                        ),
                                                                                                'Force'         => array(       'N'             => array(       'N'                     => 1.0,
                                                                                                                                                                                        'dyn'           => 1.0E+5,
                                                                                                                                                                                        'dy'            => 1.0E+5,
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                                                                                                                                                                                        'c'                     => 2.39006249473467E-01,
                                                                                                                                                                                        'cal'           => 2.38846190642017E-01,
                                                                                                                                                                                        'eV'            => 6.24145700000000E+18,
                                                                                                                                                                                        'ev'            => 6.24145700000000E+18,
                                                                                                                                                                                        'HPh'           => 3.72506430801000E-07,
                                                                                                                                                                                        'hh'            => 3.72506430801000E-07,
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                                                                                                                                                                                        'wh'            => 2.77777916238711E-04,
                                                                                                                                                                                        'flb'           => 2.37304222192651E+01,
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                                                                                                                                                                                        'btu'           => 9.47815067349015E-04
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                                                                                                                                                                                        'cal'           => 2.38846305445111E-08,
                                                                                                                                                                                        'eV'            => 6.24146000000000E+11,
                                                                                                                                                                                        'ev'            => 6.24146000000000E+11,
                                                                                                                                                                                        'HPh'           => 3.72506609848824E-14,
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                                                                                                                                                                                        'wh'            => 2.77778049754611E-11,
                                                                                                                                                                                        'flb'           => 2.37304336254586E-06,
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                                                                                                                                                                                        'eV'            => 2.61142000000000E+19,
                                                                                                                                                                                        'ev'            => 2.61142000000000E+19,
                                                                                                                                                                                        'HPh'           => 1.55856355899327E-06,
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                                                                                                                                                                                        'wh'            => 1.16222030532950E-03,
                                                                                                                                                                                        'flb'           => 9.92878733152102E+01,
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                                                                                                                                                                                        'cal'           => 1.0,
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                                                                                                                                                                                        'ev'            => 2.61317000000000E+19,
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                                                                                                                                                                                        'flb'           => 9.93544094443283E+01,
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                                                                                                                                                                                        'c'                     => 3.82933423195043E-20,
                                                                                                                                                                                        'cal'           => 3.82676978535648E-20,
                                                                                                                                                                                        'eV'            => 1.0,
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                                                                                                                                                                                        'HPh'           => 5.96826078912344E-26,
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                                                                                                                                                                                        'wh'            => 4.45053000026614E-23,
                                                                                                                                                                                        'flb'           => 3.80206452103492E-18,
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                                                                                                                                                                                        'wh'            => 4.45053000026614E-23,
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                                                                                                                                                                                        'cal'           => 6.41186757845835E+05,
                                                                                                                                                                                        'eV'            => 1.67553000000000E+25,
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                                                                                                                                                                                        'c'                     => 8.60422069219046E+02,
                                                                                                                                                                                        'cal'           => 8.59845857713046E+02,
                                                                                                                                                                                        'eV'            => 2.24692340000000E+22,
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                                                                                                                                                                                        'cal'           => 8.59845857713046E+02,
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                                                                                                                                                                                        'cal'           => 1.00649785509554E-02,
                                                                                                                                                                                        'eV'            => 2.63015000000000E+17,
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                                                                                                                                                                                        'HPh'           => 1.56974211145130E-08,
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                                                                                                                                                                                        'cal'           => 2.51996617135510E+02,
                                                                                                                                                                                        'eV'            => 6.58510000000000E+21,
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                                                                                                                                                                                        'HPh'           => 3.93015941224568E-04,
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                                                                                                                                                                                        'cal'           => 2.51996617135510E+02,
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                                                                                                                                                                                        'HPh'           => 3.93015941224568E-04,
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                                                                                                                                                                                        'l'                     => 3.78623545651745E+00,
                                                                                                                                                                                        'lt'            => 3.78623545651745E+00
                                                                                                                                                                                ),
                                                                                                                                                'l'             => array(       'tsp'           => 2.02840000000000E+02,
                                                                                                                                                                                        'tbs'           => 6.76133333333333E+01,
                                                                                                                                                                                        'oz'            => 3.38066666666667E+01,
                                                                                                                                                                                        'cup'           => 4.22583333333333E+00,
                                                                                                                                                                                        'pt'            => 2.11291666666667E+00,
                                                                                                                                                                                        'us_pt'         => 2.11291666666667E+00,
                                                                                                                                                                                        'uk_pt'         => 1.75975569552166E+00,
                                                                                                                                                                                        'qt'            => 1.05645833333333E+00,
                                                                                                                                                                                        'gal'           => 2.64114583333333E-01,
                                                                                                                                                                                        'l'                     => 1.0,
                                                                                                                                                                                        'lt'            => 1.0
                                                                                                                                                                                ),
                                                                                                                                                'lt'    => array(       'tsp'           => 2.02840000000000E+02,
                                                                                                                                                                                        'tbs'           => 6.76133333333333E+01,
                                                                                                                                                                                        'oz'            => 3.38066666666667E+01,
                                                                                                                                                                                        'cup'           => 4.22583333333333E+00,
                                                                                                                                                                                        'pt'            => 2.11291666666667E+00,
                                                                                                                                                                                        'us_pt'         => 2.11291666666667E+00,
                                                                                                                                                                                        'uk_pt'         => 1.75975569552166E+00,
                                                                                                                                                                                        'qt'            => 1.05645833333333E+00,
                                                                                                                                                                                        'gal'           => 2.64114583333333E-01,
                                                                                                                                                                                        'l'                     => 1.0,
                                                                                                                                                                                        'lt'            => 1.0
                                                                                                                                                                                )
                                                                                                                                        )
                                                                                        );


        /**
         * _parseComplex
         *
         * Parses a complex number into its real and imaginary parts, and an I or J suffix
         *
         * @param       string          $complexNumber  The complex number
         * @return      string[]        Indexed on "real", "imaginary" and "suffix"
         */
        public static function _parseComplex($complexNumber) {
                $workString = (string) $complexNumber;

                $realNumber = $imaginary = 0;
                //      Extract the suffix, if there is one
                $suffix = substr($workString,-1);
                if (!is_numeric($suffix)) {
                        $workString = substr($workString,0,-1);
                } else {
                        $suffix = '';
                }

                //      Split the input into its Real and Imaginary components
                $leadingSign = 0;
                if (strlen($workString) > 0) {
                        $leadingSign = (($workString{0} == '+') || ($workString{0} == '-')) ? 1 : 0;
                }
                $power = '';
                $realNumber = strtok($workString, '+-');
                if (strtoupper(substr($realNumber,-1)) == 'E') {
                        $power = strtok('+-');
                        ++$leadingSign;
                }

                $realNumber = substr($workString,0,strlen($realNumber)+strlen($power)+$leadingSign);

                if ($suffix != '') {
                        $imaginary = substr($workString,strlen($realNumber));

                        if (($imaginary == '') && (($realNumber == '') || ($realNumber == '+') || ($realNumber == '-'))) {
                                $imaginary = $realNumber.'1';
                                $realNumber = '0';
                        } else if ($imaginary == '') {
                                $imaginary = $realNumber;
                                $realNumber = '0';
                        } elseif (($imaginary == '+') || ($imaginary == '-')) {
                                $imaginary .= '1';
                        }
                }

                return array( 'real'            => $realNumber,
                                          'imaginary'   => $imaginary,
                                          'suffix'              => $suffix
                                        );
        }       //      function _parseComplex()


        /**
         * Cleans the leading characters in a complex number string
         *
         * @param       string          $complexNumber  The complex number to clean
         * @return      string          The "cleaned" complex number
         */
        private static function _cleanComplex($complexNumber) {
                if ($complexNumber{0} == '+') $complexNumber = substr($complexNumber,1);
                if ($complexNumber{0} == '0') $complexNumber = substr($complexNumber,1);
                if ($complexNumber{0} == '.') $complexNumber = '0'.$complexNumber;
                if ($complexNumber{0} == '+') $complexNumber = substr($complexNumber,1);
                return $complexNumber;
        }

        /**
         * Formats a number base string value with leading zeroes
         *
         * @param       string          $xVal           The "number" to pad
         * @param       integer         $places         The length that we want to pad this value
         * @return      string          The padded "number"
         */
        private static function _nbrConversionFormat($xVal, $places) {
                if (!is_null($places)) {
                        if (strlen($xVal) <= $places) {
                                return substr(str_pad($xVal, $places, '0', STR_PAD_LEFT), -10);
                        } else {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                }

                return substr($xVal, -10);
        }       //      function _nbrConversionFormat()

        /**
         *      BESSELI
         *
         *      Returns the modified Bessel function In(x), which is equivalent to the Bessel function evaluated
         *              for purely imaginary arguments
         *
         *      Excel Function:
         *              BESSELI(x,ord)
         *
         *      @access public
         *      @category Engineering Functions
         *      @param  float           $x              The value at which to evaluate the function.
         *                                                              If x is nonnumeric, BESSELI returns the #VALUE! error value.
         *      @param  integer         $ord    The order of the Bessel function.
         *                                                              If ord is not an integer, it is truncated.
         *                                                              If $ord is nonnumeric, BESSELI returns the #VALUE! error value.
         *                                                              If $ord < 0, BESSELI returns the #NUM! error value.
         *      @return float
         *
         */
        public static function BESSELI($x, $ord) {
                $x      = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
                $ord    = (is_null($ord))       ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);

                if ((is_numeric($x)) && (is_numeric($ord))) {
                        $ord    = floor($ord);
                        if ($ord < 0) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }

                        if (abs($x) <= 30) {
                                $fResult = $fTerm = pow($x / 2, $ord) / PHPExcel_Calculation_MathTrig::FACT($ord);
                                $ordK = 1;
                                $fSqrX = ($x * $x) / 4;
                                do {
                                        $fTerm *= $fSqrX;
                                        $fTerm /= ($ordK * ($ordK + $ord));
                                        $fResult += $fTerm;
                                } while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
                        } else {
                                $f_2_PI = 2 * M_PI;

                                $fXAbs = abs($x);
                                $fResult = exp($fXAbs) / sqrt($f_2_PI * $fXAbs);
                                if (($ord & 1) && ($x < 0)) {
                                        $fResult = -$fResult;
                                }
                        }
                        return (is_nan($fResult)) ? PHPExcel_Calculation_Functions::NaN() : $fResult;
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function BESSELI()


        /**
         *      BESSELJ
         *
         *      Returns the Bessel function
         *
         *      Excel Function:
         *              BESSELJ(x,ord)
         *
         *      @access public
         *      @category Engineering Functions
         *      @param  float           $x              The value at which to evaluate the function.
         *                                                              If x is nonnumeric, BESSELJ returns the #VALUE! error value.
         *      @param  integer         $ord    The order of the Bessel function. If n is not an integer, it is truncated.
         *                                                              If $ord is nonnumeric, BESSELJ returns the #VALUE! error value.
         *                                                              If $ord < 0, BESSELJ returns the #NUM! error value.
         *      @return float
         *
         */
        public static function BESSELJ($x, $ord) {
                $x      = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
                $ord    = (is_null($ord))       ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);

                if ((is_numeric($x)) && (is_numeric($ord))) {
                        $ord    = floor($ord);
                        if ($ord < 0) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }

                        $fResult = 0;
                        if (abs($x) <= 30) {
                                $fResult = $fTerm = pow($x / 2, $ord) / PHPExcel_Calculation_MathTrig::FACT($ord);
                                $ordK = 1;
                                $fSqrX = ($x * $x) / -4;
                                do {
                                        $fTerm *= $fSqrX;
                                        $fTerm /= ($ordK * ($ordK + $ord));
                                        $fResult += $fTerm;
                                } while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
                        } else {
                                $f_PI_DIV_2 = M_PI / 2;
                                $f_PI_DIV_4 = M_PI / 4;

                                $fXAbs = abs($x);
                                $fResult = sqrt(M_2DIVPI / $fXAbs) * cos($fXAbs - $ord * $f_PI_DIV_2 - $f_PI_DIV_4);
                                if (($ord & 1) && ($x < 0)) {
                                        $fResult = -$fResult;
                                }
                        }
                        return (is_nan($fResult)) ? PHPExcel_Calculation_Functions::NaN() : $fResult;
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function BESSELJ()


        private static function _Besselk0($fNum) {
                if ($fNum <= 2) {
                        $fNum2 = $fNum * 0.5;
                        $y = ($fNum2 * $fNum2);
                        $fRet = -log($fNum2) * self::BESSELI($fNum, 0) +
                                        (-0.57721566 + $y * (0.42278420 + $y * (0.23069756 + $y * (0.3488590e-1 + $y * (0.262698e-2 + $y *
                                        (0.10750e-3 + $y * 0.74e-5))))));
                } else {
                        $y = 2 / $fNum;
                        $fRet = exp(-$fNum) / sqrt($fNum) *
                                        (1.25331414 + $y * (-0.7832358e-1 + $y * (0.2189568e-1 + $y * (-0.1062446e-1 + $y *
                                        (0.587872e-2 + $y * (-0.251540e-2 + $y * 0.53208e-3))))));
                }
                return $fRet;
        }       //      function _Besselk0()


        private static function _Besselk1($fNum) {
                if ($fNum <= 2) {
                        $fNum2 = $fNum * 0.5;
                        $y = ($fNum2 * $fNum2);
                        $fRet = log($fNum2) * self::BESSELI($fNum, 1) +
                                        (1 + $y * (0.15443144 + $y * (-0.67278579 + $y * (-0.18156897 + $y * (-0.1919402e-1 + $y *
                                        (-0.110404e-2 + $y * (-0.4686e-4))))))) / $fNum;
                } else {
                        $y = 2 / $fNum;
                        $fRet = exp(-$fNum) / sqrt($fNum) *
                                        (1.25331414 + $y * (0.23498619 + $y * (-0.3655620e-1 + $y * (0.1504268e-1 + $y * (-0.780353e-2 + $y *
                                        (0.325614e-2 + $y * (-0.68245e-3)))))));
                }
                return $fRet;
        }       //      function _Besselk1()


        /**
         *      BESSELK
         *
         *      Returns the modified Bessel function Kn(x), which is equivalent to the Bessel functions evaluated
         *              for purely imaginary arguments.
         *
         *      Excel Function:
         *              BESSELK(x,ord)
         *
         *      @access public
         *      @category Engineering Functions
         *      @param  float           $x              The value at which to evaluate the function.
         *                                                              If x is nonnumeric, BESSELK returns the #VALUE! error value.
         *      @param  integer         $ord    The order of the Bessel function. If n is not an integer, it is truncated.
         *                                                              If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
         *                                                              If $ord < 0, BESSELK returns the #NUM! error value.
         *      @return float
         *
         */
        public static function BESSELK($x, $ord) {
                $x              = (is_null($x))         ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
                $ord    = (is_null($ord))       ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);

                if ((is_numeric($x)) && (is_numeric($ord))) {
                        if (($ord < 0) || ($x == 0.0)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }

                        switch(floor($ord)) {
                                case 0 :        return self::_Besselk0($x);
                                                        break;
                                case 1 :        return self::_Besselk1($x);
                                                        break;
                                default :       $fTox   = 2 / $x;
                                                        $fBkm   = self::_Besselk0($x);
                                                        $fBk    = self::_Besselk1($x);
                                                        for ($n = 1; $n < $ord; ++$n) {
                                                                $fBkp   = $fBkm + $n * $fTox * $fBk;
                                                                $fBkm   = $fBk;
                                                                $fBk    = $fBkp;
                                                        }
                        }
                        return (is_nan($fBk)) ? PHPExcel_Calculation_Functions::NaN() : $fBk;
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function BESSELK()


        private static function _Bessely0($fNum) {
                if ($fNum < 8.0) {
                        $y = ($fNum * $fNum);
                        $f1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y * (-86327.92757 + $y * 228.4622733))));
                        $f2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y * (47447.26470 + $y * (226.1030244 + $y))));
                        $fRet = $f1 / $f2 + 0.636619772 * self::BESSELJ($fNum, 0) * log($fNum);
                } else {
                        $z = 8.0 / $fNum;
                        $y = ($z * $z);
                        $xx = $fNum - 0.785398164;
                        $f1 = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
                        $f2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y * (-0.934945152e-7))));
                        $fRet = sqrt(0.636619772 / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
                }
                return $fRet;
        }       //      function _Bessely0()


        private static function _Bessely1($fNum) {
                if ($fNum < 8.0) {
                        $y = ($fNum * $fNum);
                        $f1 = $fNum * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y * (0.7349264551e9 + $y *
                                (-0.4237922726e7 + $y * 0.8511937935e4)))));
                        $f2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y *
                                (0.1020426050e6 + $y * (0.3549632885e3 + $y)))));
                        $fRet = $f1 / $f2 + 0.636619772 * ( self::BESSELJ($fNum, 1) * log($fNum) - 1 / $fNum);
                } else {
                        $fRet = sqrt(0.636619772 / $fNum) * sin($fNum - 2.356194491);
                }
                return $fRet;
        }       //      function _Bessely1()


        /**
         *      BESSELY
         *
         *      Returns the Bessel function, which is also called the Weber function or the Neumann function.
         *
         *      Excel Function:
         *              BESSELY(x,ord)
         *
         *      @access public
         *      @category Engineering Functions
         *      @param  float           $x              The value at which to evaluate the function.
         *                                                              If x is nonnumeric, BESSELK returns the #VALUE! error value.
         *      @param  integer         $ord    The order of the Bessel function. If n is not an integer, it is truncated.
         *                                                              If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
         *                                                              If $ord < 0, BESSELK returns the #NUM! error value.
         *
         *      @return float
         */
        public static function BESSELY($x, $ord) {
                $x              = (is_null($x))         ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
                $ord    = (is_null($ord))       ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);

                if ((is_numeric($x)) && (is_numeric($ord))) {
                        if (($ord < 0) || ($x == 0.0)) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }

                        switch(floor($ord)) {
                                case 0 :        return self::_Bessely0($x);
                                                        break;
                                case 1 :        return self::_Bessely1($x);
                                                        break;
                                default:        $fTox   = 2 / $x;
                                                        $fBym   = self::_Bessely0($x);
                                                        $fBy    = self::_Bessely1($x);
                                                        for ($n = 1; $n < $ord; ++$n) {
                                                                $fByp   = $n * $fTox * $fBy - $fBym;
                                                                $fBym   = $fBy;
                                                                $fBy    = $fByp;
                                                        }
                        }
                        return (is_nan($fBy)) ? PHPExcel_Calculation_Functions::NaN() : $fBy;
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function BESSELY()


        /**
         * BINTODEC
         *
         * Return a binary value as decimal.
         *
         * Excel Function:
         *              BIN2DEC(x)
         *
         * @access      public
         * @category Engineering Functions
         * @param       string          $x              The binary number (as a string) that you want to convert. The number
         *                                                              cannot contain more than 10 characters (10 bits). The most significant
         *                                                              bit of number is the sign bit. The remaining 9 bits are magnitude bits.
         *                                                              Negative numbers are represented using two's-complement notation.
         *                                                              If number is not a valid binary number, or if number contains more than
         *                                                              10 characters (10 bits), BIN2DEC returns the #NUM! error value.
         * @return      string
         */
        public static function BINTODEC($x) {
                $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);

                if (is_bool($x)) {
                        if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                                $x = (int) $x;
                        } else {
                                return PHPExcel_Calculation_Functions::VALUE();
                        }
                }
                if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
                        $x = floor($x);
                }
                $x = (string) $x;
                if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
                        return PHPExcel_Calculation_Functions::NaN();
                }
                if (strlen($x) > 10) {
                        return PHPExcel_Calculation_Functions::NaN();
                } elseif (strlen($x) == 10) {
                        //      Two's Complement
                        $x = substr($x,-9);
                        return '-'.(512-bindec($x));
                }
                return bindec($x);
        }       //      function BINTODEC()


        /**
         * BINTOHEX
         *
         * Return a binary value as hex.
         *
         * Excel Function:
         *              BIN2HEX(x[,places])
         *
         * @access      public
         * @category Engineering Functions
         * @param       string          $x              The binary number (as a string) that you want to convert. The number
         *                                                              cannot contain more than 10 characters (10 bits). The most significant
         *                                                              bit of number is the sign bit. The remaining 9 bits are magnitude bits.
         *                                                              Negative numbers are represented using two's-complement notation.
         *                                                              If number is not a valid binary number, or if number contains more than
         *                                                              10 characters (10 bits), BIN2HEX returns the #NUM! error value.
         * @param       integer         $places The number of characters to use. If places is omitted, BIN2HEX uses the
         *                                                              minimum number of characters necessary. Places is useful for padding the
         *                                                              return value with leading 0s (zeros).
         *                                                              If places is not an integer, it is truncated.
         *                                                              If places is nonnumeric, BIN2HEX returns the #VALUE! error value.
         *                                                              If places is negative, BIN2HEX returns the #NUM! error value.
         * @return      string
         */
        public static function BINTOHEX($x, $places=NULL) {
                $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
                $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);

                if (is_bool($x)) {
                        if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                                $x = (int) $x;
                        } else {
                                return PHPExcel_Calculation_Functions::VALUE();
                        }
                }
                if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
                        $x = floor($x);
                }
                $x = (string) $x;
                if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
                        return PHPExcel_Calculation_Functions::NaN();
                }
                if (strlen($x) > 10) {
                        return PHPExcel_Calculation_Functions::NaN();
                } elseif (strlen($x) == 10) {
                        //      Two's Complement
                        return str_repeat('F',8).substr(strtoupper(dechex(bindec(substr($x,-9)))),-2);
                }
                $hexVal = (string) strtoupper(dechex(bindec($x)));

                return self::_nbrConversionFormat($hexVal,$places);
        }       //      function BINTOHEX()


        /**
         * BINTOOCT
         *
         * Return a binary value as octal.
         *
         * Excel Function:
         *              BIN2OCT(x[,places])
         *
         * @access      public
         * @category Engineering Functions
         * @param       string          $x              The binary number (as a string) that you want to convert. The number
         *                                                              cannot contain more than 10 characters (10 bits). The most significant
         *                                                              bit of number is the sign bit. The remaining 9 bits are magnitude bits.
         *                                                              Negative numbers are represented using two's-complement notation.
         *                                                              If number is not a valid binary number, or if number contains more than
         *                                                              10 characters (10 bits), BIN2OCT returns the #NUM! error value.
         * @param       integer         $places The number of characters to use. If places is omitted, BIN2OCT uses the
         *                                                              minimum number of characters necessary. Places is useful for padding the
         *                                                              return value with leading 0s (zeros).
         *                                                              If places is not an integer, it is truncated.
         *                                                              If places is nonnumeric, BIN2OCT returns the #VALUE! error value.
         *                                                              If places is negative, BIN2OCT returns the #NUM! error value.
         * @return      string
         */
        public static function BINTOOCT($x, $places=NULL) {
                $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
                $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);

                if (is_bool($x)) {
                        if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                                $x = (int) $x;
                        } else {
                                return PHPExcel_Calculation_Functions::VALUE();
                        }
                }
                if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
                        $x = floor($x);
                }
                $x = (string) $x;
                if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
                        return PHPExcel_Calculation_Functions::NaN();
                }
                if (strlen($x) > 10) {
                        return PHPExcel_Calculation_Functions::NaN();
                } elseif (strlen($x) == 10) {
                        //      Two's Complement
                        return str_repeat('7',7).substr(strtoupper(decoct(bindec(substr($x,-9)))),-3);
                }
                $octVal = (string) decoct(bindec($x));

                return self::_nbrConversionFormat($octVal,$places);
        }       //      function BINTOOCT()


        /**
         * DECTOBIN
         *
         * Return a decimal value as binary.
         *
         * Excel Function:
         *              DEC2BIN(x[,places])
         *
         * @access      public
         * @category Engineering Functions
         * @param       string          $x              The decimal integer you want to convert. If number is negative,
         *                                                              valid place values are ignored and DEC2BIN returns a 10-character
         *                                                              (10-bit) binary number in which the most significant bit is the sign
         *                                                              bit. The remaining 9 bits are magnitude bits. Negative numbers are
         *                                                              represented using two's-complement notation.
         *                                                              If number < -512 or if number > 511, DEC2BIN returns the #NUM! error
         *                                                              value.
         *                                                              If number is nonnumeric, DEC2BIN returns the #VALUE! error value.
         *                                                              If DEC2BIN requires more than places characters, it returns the #NUM!
         *                                                              error value.
         * @param       integer         $places The number of characters to use. If places is omitted, DEC2BIN uses
         *                                                              the minimum number of characters necessary. Places is useful for
         *                                                              padding the return value with leading 0s (zeros).
         *                                                              If places is not an integer, it is truncated.
         *                                                              If places is nonnumeric, DEC2BIN returns the #VALUE! error value.
         *                                                              If places is zero or negative, DEC2BIN returns the #NUM! error value.
         * @return      string
         */
        public static function DECTOBIN($x, $places=NULL) {
                $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
                $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);

                if (is_bool($x)) {
                        if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                                $x = (int) $x;
                        } else {
                                return PHPExcel_Calculation_Functions::VALUE();
                        }
                }
                $x = (string) $x;
                if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $x = (string) floor($x);
                $r = decbin($x);
                if (strlen($r) == 32) {
                        //      Two's Complement
                        $r = substr($r,-10);
                } elseif (strlen($r) > 11) {
                        return PHPExcel_Calculation_Functions::NaN();
                }

                return self::_nbrConversionFormat($r,$places);
        }       //      function DECTOBIN()


        /**
         * DECTOHEX
         *
         * Return a decimal value as hex.
         *
         * Excel Function:
         *              DEC2HEX(x[,places])
         *
         * @access      public
         * @category Engineering Functions
         * @param       string          $x              The decimal integer you want to convert. If number is negative,
         *                                                              places is ignored and DEC2HEX returns a 10-character (40-bit)
         *                                                              hexadecimal number in which the most significant bit is the sign
         *                                                              bit. The remaining 39 bits are magnitude bits. Negative numbers
         *                                                              are represented using two's-complement notation.
         *                                                              If number < -549,755,813,888 or if number > 549,755,813,887,
         *                                                              DEC2HEX returns the #NUM! error value.
         *                                                              If number is nonnumeric, DEC2HEX returns the #VALUE! error value.
         *                                                              If DEC2HEX requires more than places characters, it returns the
         *                                                              #NUM! error value.
         * @param       integer         $places The number of characters to use. If places is omitted, DEC2HEX uses
         *                                                              the minimum number of characters necessary. Places is useful for
         *                                                              padding the return value with leading 0s (zeros).
         *                                                              If places is not an integer, it is truncated.
         *                                                              If places is nonnumeric, DEC2HEX returns the #VALUE! error value.
         *                                                              If places is zero or negative, DEC2HEX returns the #NUM! error value.
         * @return      string
         */
        public static function DECTOHEX($x, $places=null) {
                $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
                $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);

                if (is_bool($x)) {
                        if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                                $x = (int) $x;
                        } else {
                                return PHPExcel_Calculation_Functions::VALUE();
                        }
                }
                $x = (string) $x;
                if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $x = (string) floor($x);
                $r = strtoupper(dechex($x));
                if (strlen($r) == 8) {
                        //      Two's Complement
                        $r = 'FF'.$r;
                }

                return self::_nbrConversionFormat($r,$places);
        }       //      function DECTOHEX()


        /**
         * DECTOOCT
         *
         * Return an decimal value as octal.
         *
         * Excel Function:
         *              DEC2OCT(x[,places])
         *
         * @access      public
         * @category Engineering Functions
         * @param       string          $x              The decimal integer you want to convert. If number is negative,
         *                                                              places is ignored and DEC2OCT returns a 10-character (30-bit)
         *                                                              octal number in which the most significant bit is the sign bit.
         *                                                              The remaining 29 bits are magnitude bits. Negative numbers are
         *                                                              represented using two's-complement notation.
         *                                                              If number < -536,870,912 or if number > 536,870,911, DEC2OCT
         *                                                              returns the #NUM! error value.
         *                                                              If number is nonnumeric, DEC2OCT returns the #VALUE! error value.
         *                                                              If DEC2OCT requires more than places characters, it returns the
         *                                                              #NUM! error value.
         * @param       integer         $places The number of characters to use. If places is omitted, DEC2OCT uses
         *                                                              the minimum number of characters necessary. Places is useful for
         *                                                              padding the return value with leading 0s (zeros).
         *                                                              If places is not an integer, it is truncated.
         *                                                              If places is nonnumeric, DEC2OCT returns the #VALUE! error value.
         *                                                              If places is zero or negative, DEC2OCT returns the #NUM! error value.
         * @return      string
         */
        public static function DECTOOCT($x, $places=null) {
                $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
                $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);

                if (is_bool($x)) {
                        if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                                $x = (int) $x;
                        } else {
                                return PHPExcel_Calculation_Functions::VALUE();
                        }
                }
                $x = (string) $x;
                if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $x = (string) floor($x);
                $r = decoct($x);
                if (strlen($r) == 11) {
                        //      Two's Complement
                        $r = substr($r,-10);
                }

                return self::_nbrConversionFormat($r,$places);
        }       //      function DECTOOCT()


        /**
         * HEXTOBIN
         *
         * Return a hex value as binary.
         *
         * Excel Function:
         *              HEX2BIN(x[,places])
         *
         * @access      public
         * @category Engineering Functions
         * @param       string          $x                      the hexadecimal number you want to convert. Number cannot
         *                                                                      contain more than 10 characters. The most significant bit of
         *                                                                      number is the sign bit (40th bit from the right). The remaining
         *                                                                      9 bits are magnitude bits. Negative numbers are represented
         *                                                                      using two's-complement notation.
         *                                                                      If number is negative, HEX2BIN ignores places and returns a
         *                                                                      10-character binary number.
         *                                                                      If number is negative, it cannot be less than FFFFFFFE00, and
         *                                                                      if number is positive, it cannot be greater than 1FF.
         *                                                                      If number is not a valid hexadecimal number, HEX2BIN returns
         *                                                                      the #NUM! error value.
         *                                                                      If HEX2BIN requires more than places characters, it returns
         *                                                                      the #NUM! error value.
         * @param       integer         $places         The number of characters to use. If places is omitted,
         *                                                                      HEX2BIN uses the minimum number of characters necessary. Places
         *                                                                      is useful for padding the return value with leading 0s (zeros).
         *                                                                      If places is not an integer, it is truncated.
         *                                                                      If places is nonnumeric, HEX2BIN returns the #VALUE! error value.
         *                                                                      If places is negative, HEX2BIN returns the #NUM! error value.
         * @return      string
         */
        public static function HEXTOBIN($x, $places=null) {
                $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
                $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);

                if (is_bool($x)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $x = (string) $x;
                if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
                        return PHPExcel_Calculation_Functions::NaN();
                }
                $binVal = decbin(hexdec($x));

                return substr(self::_nbrConversionFormat($binVal,$places),-10);
        }       //      function HEXTOBIN()


        /**
         * HEXTODEC
         *
         * Return a hex value as decimal.
         *
         * Excel Function:
         *              HEX2DEC(x)
         *
         * @access      public
         * @category Engineering Functions
         * @param       string          $x              The hexadecimal number you want to convert. This number cannot
         *                                                              contain more than 10 characters (40 bits). The most significant
         *                                                              bit of number is the sign bit. The remaining 39 bits are magnitude
         *                                                              bits. Negative numbers are represented using two's-complement
         *                                                              notation.
         *                                                              If number is not a valid hexadecimal number, HEX2DEC returns the
         *                                                              #NUM! error value.
         * @return      string
         */
        public static function HEXTODEC($x) {
                $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);

                if (is_bool($x)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $x = (string) $x;
                if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
                        return PHPExcel_Calculation_Functions::NaN();
                }
                return hexdec($x);
        }       //      function HEXTODEC()


        /**
         * HEXTOOCT
         *
         * Return a hex value as octal.
         *
         * Excel Function:
         *              HEX2OCT(x[,places])
         *
         * @access      public
         * @category Engineering Functions
         * @param       string          $x                      The hexadecimal number you want to convert. Number cannot
         *                                                                      contain more than 10 characters. The most significant bit of
         *                                                                      number is the sign bit. The remaining 39 bits are magnitude
         *                                                                      bits. Negative numbers are represented using two's-complement
         *                                                                      notation.
         *                                                                      If number is negative, HEX2OCT ignores places and returns a
         *                                                                      10-character octal number.
         *                                                                      If number is negative, it cannot be less than FFE0000000, and
         *                                                                      if number is positive, it cannot be greater than 1FFFFFFF.
         *                                                                      If number is not a valid hexadecimal number, HEX2OCT returns
         *                                                                      the #NUM! error value.
         *                                                                      If HEX2OCT requires more than places characters, it returns
         *                                                                      the #NUM! error value.
         * @param       integer         $places         The number of characters to use. If places is omitted, HEX2OCT
         *                                                                      uses the minimum number of characters necessary. Places is
         *                                                                      useful for padding the return value with leading 0s (zeros).
         *                                                                      If places is not an integer, it is truncated.
         *                                                                      If places is nonnumeric, HEX2OCT returns the #VALUE! error
         *                                                                      value.
         *                                                                      If places is negative, HEX2OCT returns the #NUM! error value.
         * @return      string
         */
        public static function HEXTOOCT($x, $places=null) {
                $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
                $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);

                if (is_bool($x)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $x = (string) $x;
                if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
                        return PHPExcel_Calculation_Functions::NaN();
                }
                $octVal = decoct(hexdec($x));

                return self::_nbrConversionFormat($octVal,$places);
        }       //      function HEXTOOCT()


        /**
         * OCTTOBIN
         *
         * Return an octal value as binary.
         *
         * Excel Function:
         *              OCT2BIN(x[,places])
         *
         * @access      public
         * @category Engineering Functions
         * @param       string          $x                      The octal number you want to convert. Number may not
         *                                                                      contain more than 10 characters. The most significant
         *                                                                      bit of number is the sign bit. The remaining 29 bits
         *                                                                      are magnitude bits. Negative numbers are represented
         *                                                                      using two's-complement notation.
         *                                                                      If number is negative, OCT2BIN ignores places and returns
         *                                                                      a 10-character binary number.
         *                                                                      If number is negative, it cannot be less than 7777777000,
         *                                                                      and if number is positive, it cannot be greater than 777.
         *                                                                      If number is not a valid octal number, OCT2BIN returns
         *                                                                      the #NUM! error value.
         *                                                                      If OCT2BIN requires more than places characters, it
         *                                                                      returns the #NUM! error value.
         * @param       integer         $places         The number of characters to use. If places is omitted,
         *                                                                      OCT2BIN uses the minimum number of characters necessary.
         *                                                                      Places is useful for padding the return value with
         *                                                                      leading 0s (zeros).
         *                                                                      If places is not an integer, it is truncated.
         *                                                                      If places is nonnumeric, OCT2BIN returns the #VALUE!
         *                                                                      error value.
         *                                                                      If places is negative, OCT2BIN returns the #NUM! error
         *                                                                      value.
         * @return      string
         */
        public static function OCTTOBIN($x, $places=null) {
                $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
                $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);

                if (is_bool($x)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $x = (string) $x;
                if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
                        return PHPExcel_Calculation_Functions::NaN();
                }
                $r = decbin(octdec($x));

                return self::_nbrConversionFormat($r,$places);
        }       //      function OCTTOBIN()


        /**
         * OCTTODEC
         *
         * Return an octal value as decimal.
         *
         * Excel Function:
         *              OCT2DEC(x)
         *
         * @access      public
         * @category Engineering Functions
         * @param       string          $x              The octal number you want to convert. Number may not contain
         *                                                              more than 10 octal characters (30 bits). The most significant
         *                                                              bit of number is the sign bit. The remaining 29 bits are
         *                                                              magnitude bits. Negative numbers are represented using
         *                                                              two's-complement notation.
         *                                                              If number is not a valid octal number, OCT2DEC returns the
         *                                                              #NUM! error value.
         * @return      string
         */
        public static function OCTTODEC($x) {
                $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);

                if (is_bool($x)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $x = (string) $x;
                if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
                        return PHPExcel_Calculation_Functions::NaN();
                }
                return octdec($x);
        }       //      function OCTTODEC()


        /**
         * OCTTOHEX
         *
         * Return an octal value as hex.
         *
         * Excel Function:
         *              OCT2HEX(x[,places])
         *
         * @access      public
         * @category Engineering Functions
         * @param       string          $x                      The octal number you want to convert. Number may not contain
         *                                                                      more than 10 octal characters (30 bits). The most significant
         *                                                                      bit of number is the sign bit. The remaining 29 bits are
         *                                                                      magnitude bits. Negative numbers are represented using
         *                                                                      two's-complement notation.
         *                                                                      If number is negative, OCT2HEX ignores places and returns a
         *                                                                      10-character hexadecimal number.
         *                                                                      If number is not a valid octal number, OCT2HEX returns the
         *                                                                      #NUM! error value.
         *                                                                      If OCT2HEX requires more than places characters, it returns
         *                                                                      the #NUM! error value.
         * @param       integer         $places         The number of characters to use. If places is omitted, OCT2HEX
         *                                                                      uses the minimum number of characters necessary. Places is useful
         *                                                                      for padding the return value with leading 0s (zeros).
         *                                                                      If places is not an integer, it is truncated.
         *                                                                      If places is nonnumeric, OCT2HEX returns the #VALUE! error value.
         *                                                                      If places is negative, OCT2HEX returns the #NUM! error value.
         * @return      string
         */
        public static function OCTTOHEX($x, $places=null) {
                $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
                $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);

                if (is_bool($x)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $x = (string) $x;
                if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
                        return PHPExcel_Calculation_Functions::NaN();
                }
                $hexVal = strtoupper(dechex(octdec($x)));

                return self::_nbrConversionFormat($hexVal,$places);
        }       //      function OCTTOHEX()


        /**
         * COMPLEX
         *
         * Converts real and imaginary coefficients into a complex number of the form x + yi or x + yj.
         *
         * Excel Function:
         *              COMPLEX(realNumber,imaginary[,places])
         *
         * @access      public
         * @category Engineering Functions
         * @param       float           $realNumber             The real coefficient of the complex number.
         * @param       float           $imaginary              The imaginary coefficient of the complex number.
         * @param       string          $suffix                 The suffix for the imaginary component of the complex number.
         *                                                                              If omitted, the suffix is assumed to be "i".
         * @return      string
         */
        public static function COMPLEX($realNumber=0.0, $imaginary=0.0, $suffix='i') {
                $realNumber     = (is_null($realNumber))        ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);
                $imaginary      = (is_null($imaginary))         ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($imaginary);
                $suffix         = (is_null($suffix))            ? 'i' : PHPExcel_Calculation_Functions::flattenSingleValue($suffix);

                if (((is_numeric($realNumber)) && (is_numeric($imaginary))) &&
                        (($suffix == 'i') || ($suffix == 'j') || ($suffix == ''))) {
                        $realNumber     = (float) $realNumber;
                        $imaginary      = (float) $imaginary;

                        if ($suffix == '') $suffix = 'i';
                        if ($realNumber == 0.0) {
                                if ($imaginary == 0.0) {
                                        return (string) '0';
                                } elseif ($imaginary == 1.0) {
                                        return (string) $suffix;
                                } elseif ($imaginary == -1.0) {
                                        return (string) '-'.$suffix;
                                }
                                return (string) $imaginary.$suffix;
                        } elseif ($imaginary == 0.0) {
                                return (string) $realNumber;
                        } elseif ($imaginary == 1.0) {
                                return (string) $realNumber.'+'.$suffix;
                        } elseif ($imaginary == -1.0) {
                                return (string) $realNumber.'-'.$suffix;
                        }
                        if ($imaginary > 0) { $imaginary = (string) '+'.$imaginary; }
                        return (string) $realNumber.$imaginary.$suffix;
                }

                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function COMPLEX()


        /**
         * IMAGINARY
         *
         * Returns the imaginary coefficient of a complex number in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMAGINARY(complexNumber)
         *
         * @access      public
         * @category Engineering Functions
         * @param       string          $complexNumber  The complex number for which you want the imaginary
         *                                                                              coefficient.
         * @return      float
         */
        public static function IMAGINARY($complexNumber) {
                $complexNumber  = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

                $parsedComplex = self::_parseComplex($complexNumber);
                return $parsedComplex['imaginary'];
        }       //      function IMAGINARY()


        /**
         * IMREAL
         *
         * Returns the real coefficient of a complex number in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMREAL(complexNumber)
         *
         * @access      public
         * @category Engineering Functions
         * @param       string          $complexNumber  The complex number for which you want the real coefficient.
         * @return      float
         */
        public static function IMREAL($complexNumber) {
                $complexNumber  = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

                $parsedComplex = self::_parseComplex($complexNumber);
                return $parsedComplex['real'];
        }       //      function IMREAL()


        /**
         * IMABS
         *
         * Returns the absolute value (modulus) of a complex number in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMABS(complexNumber)
         *
         * @param       string          $complexNumber  The complex number for which you want the absolute value.
         * @return      float
         */
        public static function IMABS($complexNumber) {
                $complexNumber  = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

                $parsedComplex = self::_parseComplex($complexNumber);

                return sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
        }       //      function IMABS()


        /**
         * IMARGUMENT
         *
         * Returns the argument theta of a complex number, i.e. the angle in radians from the real
         * axis to the representation of the number in polar coordinates.
         *
         * Excel Function:
         *              IMARGUMENT(complexNumber)
         *
         * @param       string          $complexNumber  The complex number for which you want the argument theta.
         * @return      float
         */
        public static function IMARGUMENT($complexNumber) {
                $complexNumber  = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

                $parsedComplex = self::_parseComplex($complexNumber);

                if ($parsedComplex['real'] == 0.0) {
                        if ($parsedComplex['imaginary'] == 0.0) {
                                return 0.0;
                        } elseif($parsedComplex['imaginary'] < 0.0) {
                                return M_PI / -2;
                        } else {
                                return M_PI / 2;
                        }
                } elseif ($parsedComplex['real'] > 0.0) {
                        return atan($parsedComplex['imaginary'] / $parsedComplex['real']);
                } elseif ($parsedComplex['imaginary'] < 0.0) {
                        return 0 - (M_PI - atan(abs($parsedComplex['imaginary']) / abs($parsedComplex['real'])));
                } else {
                        return M_PI - atan($parsedComplex['imaginary'] / abs($parsedComplex['real']));
                }
        }       //      function IMARGUMENT()


        /**
         * IMCONJUGATE
         *
         * Returns the complex conjugate of a complex number in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMCONJUGATE(complexNumber)
         *
         * @param       string          $complexNumber  The complex number for which you want the conjugate.
         * @return      string
         */
        public static function IMCONJUGATE($complexNumber) {
                $complexNumber  = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

                $parsedComplex = self::_parseComplex($complexNumber);

                if ($parsedComplex['imaginary'] == 0.0) {
                        return $parsedComplex['real'];
                } else {
                        return self::_cleanComplex( self::COMPLEX( $parsedComplex['real'],
                                                                                                           0 - $parsedComplex['imaginary'],
                                                                                                           $parsedComplex['suffix']
                                                                                                         )
                                                                          );
                }
        }       //      function IMCONJUGATE()


        /**
         * IMCOS
         *
         * Returns the cosine of a complex number in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMCOS(complexNumber)
         *
         * @param       string          $complexNumber  The complex number for which you want the cosine.
         * @return      string|float
         */
        public static function IMCOS($complexNumber) {
                $complexNumber  = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

                $parsedComplex = self::_parseComplex($complexNumber);

                if ($parsedComplex['imaginary'] == 0.0) {
                        return cos($parsedComplex['real']);
                } else {
                        return self::IMCONJUGATE(self::COMPLEX(cos($parsedComplex['real']) * cosh($parsedComplex['imaginary']),sin($parsedComplex['real']) * sinh($parsedComplex['imaginary']),$parsedComplex['suffix']));
                }
        }       //      function IMCOS()


        /**
         * IMSIN
         *
         * Returns the sine of a complex number in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMSIN(complexNumber)
         *
         * @param       string          $complexNumber  The complex number for which you want the sine.
         * @return      string|float
         */
        public static function IMSIN($complexNumber) {
                $complexNumber  = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

                $parsedComplex = self::_parseComplex($complexNumber);

                if ($parsedComplex['imaginary'] == 0.0) {
                        return sin($parsedComplex['real']);
                } else {
                        return self::COMPLEX(sin($parsedComplex['real']) * cosh($parsedComplex['imaginary']),cos($parsedComplex['real']) * sinh($parsedComplex['imaginary']),$parsedComplex['suffix']);
                }
        }       //      function IMSIN()


        /**
         * IMSQRT
         *
         * Returns the square root of a complex number in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMSQRT(complexNumber)
         *
         * @param       string          $complexNumber  The complex number for which you want the square root.
         * @return      string
         */
        public static function IMSQRT($complexNumber) {
                $complexNumber  = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

                $parsedComplex = self::_parseComplex($complexNumber);

                $theta = self::IMARGUMENT($complexNumber);
                $d1 = cos($theta / 2);
                $d2 = sin($theta / 2);
                $r = sqrt(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));

                if ($parsedComplex['suffix'] == '') {
                        return self::COMPLEX($d1 * $r,$d2 * $r);
                } else {
                        return self::COMPLEX($d1 * $r,$d2 * $r,$parsedComplex['suffix']);
                }
        }       //      function IMSQRT()


        /**
         * IMLN
         *
         * Returns the natural logarithm of a complex number in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMLN(complexNumber)
         *
         * @param       string          $complexNumber  The complex number for which you want the natural logarithm.
         * @return      string
         */
        public static function IMLN($complexNumber) {
                $complexNumber  = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

                $parsedComplex = self::_parseComplex($complexNumber);

                if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
                        return PHPExcel_Calculation_Functions::NaN();
                }

                $logR = log(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));
                $t = self::IMARGUMENT($complexNumber);

                if ($parsedComplex['suffix'] == '') {
                        return self::COMPLEX($logR,$t);
                } else {
                        return self::COMPLEX($logR,$t,$parsedComplex['suffix']);
                }
        }       //      function IMLN()


        /**
         * IMLOG10
         *
         * Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMLOG10(complexNumber)
         *
         * @param       string          $complexNumber  The complex number for which you want the common logarithm.
         * @return      string
         */
        public static function IMLOG10($complexNumber) {
                $complexNumber  = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

                $parsedComplex = self::_parseComplex($complexNumber);

                if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
                        return PHPExcel_Calculation_Functions::NaN();
                } elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
                        return log10($parsedComplex['real']);
                }

                return self::IMPRODUCT(log10(EULER),self::IMLN($complexNumber));
        }       //      function IMLOG10()


        /**
         * IMLOG2
         *
         * Returns the base-2 logarithm of a complex number in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMLOG2(complexNumber)
         *
         * @param       string          $complexNumber  The complex number for which you want the base-2 logarithm.
         * @return      string
         */
        public static function IMLOG2($complexNumber) {
                $complexNumber  = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

                $parsedComplex = self::_parseComplex($complexNumber);

                if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
                        return PHPExcel_Calculation_Functions::NaN();
                } elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
                        return log($parsedComplex['real'],2);
                }

                return self::IMPRODUCT(log(EULER,2),self::IMLN($complexNumber));
        }       //      function IMLOG2()


        /**
         * IMEXP
         *
         * Returns the exponential of a complex number in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMEXP(complexNumber)
         *
         * @param       string          $complexNumber  The complex number for which you want the exponential.
         * @return      string
         */
        public static function IMEXP($complexNumber) {
                $complexNumber  = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

                $parsedComplex = self::_parseComplex($complexNumber);

                if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
                        return '1';
                }

                $e = exp($parsedComplex['real']);
                $eX = $e * cos($parsedComplex['imaginary']);
                $eY = $e * sin($parsedComplex['imaginary']);

                if ($parsedComplex['suffix'] == '') {
                        return self::COMPLEX($eX,$eY);
                } else {
                        return self::COMPLEX($eX,$eY,$parsedComplex['suffix']);
                }
        }       //      function IMEXP()


        /**
         * IMPOWER
         *
         * Returns a complex number in x + yi or x + yj text format raised to a power.
         *
         * Excel Function:
         *              IMPOWER(complexNumber,realNumber)
         *
         * @param       string          $complexNumber  The complex number you want to raise to a power.
         * @param       float           $realNumber             The power to which you want to raise the complex number.
         * @return      string
         */
        public static function IMPOWER($complexNumber,$realNumber) {
                $complexNumber  = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
                $realNumber             = PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);

                if (!is_numeric($realNumber)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }

                $parsedComplex = self::_parseComplex($complexNumber);

                $r = sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
                $rPower = pow($r,$realNumber);
                $theta = self::IMARGUMENT($complexNumber) * $realNumber;
                if ($theta == 0) {
                        return 1;
                } elseif ($parsedComplex['imaginary'] == 0.0) {
                        return self::COMPLEX($rPower * cos($theta),$rPower * sin($theta),$parsedComplex['suffix']);
                } else {
                        return self::COMPLEX($rPower * cos($theta),$rPower * sin($theta),$parsedComplex['suffix']);
                }
        }       //      function IMPOWER()


        /**
         * IMDIV
         *
         * Returns the quotient of two complex numbers in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMDIV(complexDividend,complexDivisor)
         *
         * @param       string          $complexDividend        The complex numerator or dividend.
         * @param       string          $complexDivisor         The complex denominator or divisor.
         * @return      string
         */
        public static function IMDIV($complexDividend,$complexDivisor) {
                $complexDividend        = PHPExcel_Calculation_Functions::flattenSingleValue($complexDividend);
                $complexDivisor = PHPExcel_Calculation_Functions::flattenSingleValue($complexDivisor);

                $parsedComplexDividend = self::_parseComplex($complexDividend);
                $parsedComplexDivisor = self::_parseComplex($complexDivisor);

                if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] != '') &&
                        ($parsedComplexDividend['suffix'] != $parsedComplexDivisor['suffix'])) {
                        return PHPExcel_Calculation_Functions::NaN();
                }
                if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] == '')) {
                        $parsedComplexDivisor['suffix'] = $parsedComplexDividend['suffix'];
                }

                $d1 = ($parsedComplexDividend['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['imaginary']);
                $d2 = ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['real']) - ($parsedComplexDividend['real'] * $parsedComplexDivisor['imaginary']);
                $d3 = ($parsedComplexDivisor['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDivisor['imaginary'] * $parsedComplexDivisor['imaginary']);

                $r = $d1/$d3;
                $i = $d2/$d3;

                if ($i > 0.0) {
                        return self::_cleanComplex($r.'+'.$i.$parsedComplexDivisor['suffix']);
                } elseif ($i < 0.0) {
                        return self::_cleanComplex($r.$i.$parsedComplexDivisor['suffix']);
                } else {
                        return $r;
                }
        }       //      function IMDIV()


        /**
         * IMSUB
         *
         * Returns the difference of two complex numbers in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMSUB(complexNumber1,complexNumber2)
         *
         * @param       string          $complexNumber1         The complex number from which to subtract complexNumber2.
         * @param       string          $complexNumber2         The complex number to subtract from complexNumber1.
         * @return      string
         */
        public static function IMSUB($complexNumber1,$complexNumber2) {
                $complexNumber1 = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber1);
                $complexNumber2 = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber2);

                $parsedComplex1 = self::_parseComplex($complexNumber1);
                $parsedComplex2 = self::_parseComplex($complexNumber2);

                if ((($parsedComplex1['suffix'] != '') && ($parsedComplex2['suffix'] != '')) &&
                        ($parsedComplex1['suffix'] != $parsedComplex2['suffix'])) {
                        return PHPExcel_Calculation_Functions::NaN();
                } elseif (($parsedComplex1['suffix'] == '') && ($parsedComplex2['suffix'] != '')) {
                        $parsedComplex1['suffix'] = $parsedComplex2['suffix'];
                }

                $d1 = $parsedComplex1['real'] - $parsedComplex2['real'];
                $d2 = $parsedComplex1['imaginary'] - $parsedComplex2['imaginary'];

                return self::COMPLEX($d1,$d2,$parsedComplex1['suffix']);
        }       //      function IMSUB()


        /**
         * IMSUM
         *
         * Returns the sum of two or more complex numbers in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMSUM(complexNumber[,complexNumber[,...]])
         *
         * @param       string          $complexNumber,...      Series of complex numbers to add
         * @return      string
         */
        public static function IMSUM() {
                // Return value
                $returnValue = self::_parseComplex('0');
                $activeSuffix = '';

                // Loop through the arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
                foreach ($aArgs as $arg) {
                        $parsedComplex = self::_parseComplex($arg);

                        if ($activeSuffix == '') {
                                $activeSuffix = $parsedComplex['suffix'];
                        } elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
                                return PHPExcel_Calculation_Functions::VALUE();
                        }

                        $returnValue['real'] += $parsedComplex['real'];
                        $returnValue['imaginary'] += $parsedComplex['imaginary'];
                }

                if ($returnValue['imaginary'] == 0.0) { $activeSuffix = ''; }
                return self::COMPLEX($returnValue['real'],$returnValue['imaginary'],$activeSuffix);
        }       //      function IMSUM()


        /**
         * IMPRODUCT
         *
         * Returns the product of two or more complex numbers in x + yi or x + yj text format.
         *
         * Excel Function:
         *              IMPRODUCT(complexNumber[,complexNumber[,...]])
         *
         * @param       string          $complexNumber,...      Series of complex numbers to multiply
         * @return      string
         */
        public static function IMPRODUCT() {
                // Return value
                $returnValue = self::_parseComplex('1');
                $activeSuffix = '';

                // Loop through the arguments
                $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
                foreach ($aArgs as $arg) {
                        $parsedComplex = self::_parseComplex($arg);

                        $workValue = $returnValue;
                        if (($parsedComplex['suffix'] != '') && ($activeSuffix == '')) {
                                $activeSuffix = $parsedComplex['suffix'];
                        } elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
                                return PHPExcel_Calculation_Functions::NaN();
                        }
                        $returnValue['real'] = ($workValue['real'] * $parsedComplex['real']) - ($workValue['imaginary'] * $parsedComplex['imaginary']);
                        $returnValue['imaginary'] = ($workValue['real'] * $parsedComplex['imaginary']) + ($workValue['imaginary'] * $parsedComplex['real']);
                }

                if ($returnValue['imaginary'] == 0.0) { $activeSuffix = ''; }
                return self::COMPLEX($returnValue['real'],$returnValue['imaginary'],$activeSuffix);
        }       //      function IMPRODUCT()


        /**
         *      DELTA
         *
         *      Tests whether two values are equal. Returns 1 if number1 = number2; returns 0 otherwise.
         *      Use this function to filter a set of values. For example, by summing several DELTA
         *      functions you calculate the count of equal pairs. This function is also known as the
         *      Kronecker Delta function.
         *
         *      Excel Function:
         *              DELTA(a[,b])
         *
         *      @param  float           $a      The first number.
         *      @param  float           $b      The second number. If omitted, b is assumed to be zero.
         *      @return int
         */
        public static function DELTA($a, $b=0) {
                $a      = PHPExcel_Calculation_Functions::flattenSingleValue($a);
                $b      = PHPExcel_Calculation_Functions::flattenSingleValue($b);

                return (int) ($a == $b);
        }       //      function DELTA()


        /**
         *      GESTEP
         *
         *      Excel Function:
         *              GESTEP(number[,step])
         *
         *      Returns 1 if number >= step; returns 0 (zero) otherwise
         *      Use this function to filter a set of values. For example, by summing several GESTEP
         *      functions you calculate the count of values that exceed a threshold.
         *
         *      @param  float           $number         The value to test against step.
         *      @param  float           $step           The threshold value.
         *                                                                      If you omit a value for step, GESTEP uses zero.
         *      @return int
         */
        public static function GESTEP($number, $step=0) {
                $number = PHPExcel_Calculation_Functions::flattenSingleValue($number);
                $step   = PHPExcel_Calculation_Functions::flattenSingleValue($step);

                return (int) ($number >= $step);
        }       //      function GESTEP()


        //
        //      Private method to calculate the erf value
        //
        private static $_two_sqrtpi = 1.128379167095512574;

        public static function _erfVal($x) {
                if (abs($x) > 2.2) {
                        return 1 - self::_erfcVal($x);
                }
                $sum = $term = $x;
                $xsqr = ($x * $x);
                $j = 1;
                do {
                        $term *= $xsqr / $j;
                        $sum -= $term / (2 * $j + 1);
                        ++$j;
                        $term *= $xsqr / $j;
                        $sum += $term / (2 * $j + 1);
                        ++$j;
                        if ($sum == 0.0) {
                                break;
                        }
                } while (abs($term / $sum) > PRECISION);
                return self::$_two_sqrtpi * $sum;
        }       //      function _erfVal()


        /**
         *      ERF
         *
         *      Returns the error function integrated between the lower and upper bound arguments.
         *
         *      Note: In Excel 2007 or earlier, if you input a negative value for the upper or lower bound arguments,
         *                      the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
         *                      improved, so that it can now calculate the function for both positive and negative ranges.
         *                      PHPExcel follows Excel 2010 behaviour, and accepts nagative arguments.
         *
         *      Excel Function:
         *              ERF(lower[,upper])
         *
         *      @param  float           $lower  lower bound for integrating ERF
         *      @param  float           $upper  upper bound for integrating ERF.
         *                                                              If omitted, ERF integrates between zero and lower_limit
         *      @return float
         */
        public static function ERF($lower, $upper = NULL) {
                $lower  = PHPExcel_Calculation_Functions::flattenSingleValue($lower);
                $upper  = PHPExcel_Calculation_Functions::flattenSingleValue($upper);

                if (is_numeric($lower)) {
                        if (is_null($upper)) {
                                return self::_erfVal($lower);
                        }
                        if (is_numeric($upper)) {
                                return self::_erfVal($upper) - self::_erfVal($lower);
                        }
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function ERF()


        //
        //      Private method to calculate the erfc value
        //
        private static $_one_sqrtpi = 0.564189583547756287;

        private static function _erfcVal($x) {
                if (abs($x) < 2.2) {
                        return 1 - self::_erfVal($x);
                }
                if ($x < 0) {
                        return 2 - self::ERFC(-$x);
                }
                $a = $n = 1;
                $b = $c = $x;
                $d = ($x * $x) + 0.5;
                $q1 = $q2 = $b / $d;
                $t = 0;
                do {
                        $t = $a * $n + $b * $x;
                        $a = $b;
                        $b = $t;
                        $t = $c * $n + $d * $x;
                        $c = $d;
                        $d = $t;
                        $n += 0.5;
                        $q1 = $q2;
                        $q2 = $b / $d;
                } while ((abs($q1 - $q2) / $q2) > PRECISION);
                return self::$_one_sqrtpi * exp(-$x * $x) * $q2;
        }       //      function _erfcVal()


        /**
         *      ERFC
         *
         *      Returns the complementary ERF function integrated between x and infinity
         *
         *      Note: In Excel 2007 or earlier, if you input a negative value for the lower bound argument,
         *              the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
         *              improved, so that it can now calculate the function for both positive and negative x values.
         *                      PHPExcel follows Excel 2010 behaviour, and accepts nagative arguments.
         *
         *      Excel Function:
         *              ERFC(x)
         *
         *      @param  float   $x      The lower bound for integrating ERFC
         *      @return float
         */
        public static function ERFC($x) {
                $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);

                if (is_numeric($x)) {
                        return self::_erfcVal($x);
                }
                return PHPExcel_Calculation_Functions::VALUE();
        }       //      function ERFC()


        /**
         *      getConversionGroups
         *      Returns a list of the different conversion groups for UOM conversions
         *
         *      @return array
         */
        public static function getConversionGroups() {
                $conversionGroups = array();
                foreach(self::$_conversionUnits as $conversionUnit) {
                        $conversionGroups[] = $conversionUnit['Group'];
                }
                return array_merge(array_unique($conversionGroups));
        }       //      function getConversionGroups()


        /**
         *      getConversionGroupUnits
         *      Returns an array of units of measure, for a specified conversion group, or for all groups
         *
         *      @param  string  $group  The group whose units of measure you want to retrieve
         *      @return array
         */
        public static function getConversionGroupUnits($group = NULL) {
                $conversionGroups = array();
                foreach(self::$_conversionUnits as $conversionUnit => $conversionGroup) {
                        if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
                                $conversionGroups[$conversionGroup['Group']][] = $conversionUnit;
                        }
                }
                return $conversionGroups;
        }       //      function getConversionGroupUnits()


        /**
         *      getConversionGroupUnitDetails
         *
         *      @param  string  $group  The group whose units of measure you want to retrieve
         *      @return array
         */
        public static function getConversionGroupUnitDetails($group = NULL) {
                $conversionGroups = array();
                foreach(self::$_conversionUnits as $conversionUnit => $conversionGroup) {
                        if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
                                $conversionGroups[$conversionGroup['Group']][] = array( 'unit'                  => $conversionUnit,
                                                                                                                                                'description'   => $conversionGroup['Unit Name']
                                                                                                                                          );
                        }
                }
                return $conversionGroups;
        }       //      function getConversionGroupUnitDetails()


        /**
         *      getConversionMultipliers
         *      Returns an array of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM()
         *
         *      @return array of mixed
         */
        public static function getConversionMultipliers() {
                return self::$_conversionMultipliers;
        }       //      function getConversionGroups()


        /**
         *      CONVERTUOM
         *
         *      Converts a number from one measurement system to another.
         *      For example, CONVERT can translate a table of distances in miles to a table of distances
         *      in kilometers.
         *
         *      Excel Function:
         *              CONVERT(value,fromUOM,toUOM)
         *
         *      @param  float           $value          The value in fromUOM to convert.
         *      @param  string          $fromUOM        The units for value.
         *      @param  string          $toUOM          The units for the result.
         *
         *      @return float
         */
        public static function CONVERTUOM($value, $fromUOM, $toUOM) {
                $value          = PHPExcel_Calculation_Functions::flattenSingleValue($value);
                $fromUOM        = PHPExcel_Calculation_Functions::flattenSingleValue($fromUOM);
                $toUOM          = PHPExcel_Calculation_Functions::flattenSingleValue($toUOM);

                if (!is_numeric($value)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                }
                $fromMultiplier = 1.0;
                if (isset(self::$_conversionUnits[$fromUOM])) {
                        $unitGroup1 = self::$_conversionUnits[$fromUOM]['Group'];
                } else {
                        $fromMultiplier = substr($fromUOM,0,1);
                        $fromUOM = substr($fromUOM,1);
                        if (isset(self::$_conversionMultipliers[$fromMultiplier])) {
                                $fromMultiplier = self::$_conversionMultipliers[$fromMultiplier]['multiplier'];
                        } else {
                                return PHPExcel_Calculation_Functions::NA();
                        }
                        if ((isset(self::$_conversionUnits[$fromUOM])) && (self::$_conversionUnits[$fromUOM]['AllowPrefix'])) {
                                $unitGroup1 = self::$_conversionUnits[$fromUOM]['Group'];
                        } else {
                                return PHPExcel_Calculation_Functions::NA();
                        }
                }
                $value *= $fromMultiplier;

                $toMultiplier = 1.0;
                if (isset(self::$_conversionUnits[$toUOM])) {
                        $unitGroup2 = self::$_conversionUnits[$toUOM]['Group'];
                } else {
                        $toMultiplier = substr($toUOM,0,1);
                        $toUOM = substr($toUOM,1);
                        if (isset(self::$_conversionMultipliers[$toMultiplier])) {
                                $toMultiplier = self::$_conversionMultipliers[$toMultiplier]['multiplier'];
                        } else {
                                return PHPExcel_Calculation_Functions::NA();
                        }
                        if ((isset(self::$_conversionUnits[$toUOM])) && (self::$_conversionUnits[$toUOM]['AllowPrefix'])) {
                                $unitGroup2 = self::$_conversionUnits[$toUOM]['Group'];
                        } else {
                                return PHPExcel_Calculation_Functions::NA();
                        }
                }
                if ($unitGroup1 != $unitGroup2) {
                        return PHPExcel_Calculation_Functions::NA();
                }

                if (($fromUOM == $toUOM) && ($fromMultiplier == $toMultiplier)) {
                        //      We've already factored $fromMultiplier into the value, so we need
                        //              to reverse it again
                        return $value / $fromMultiplier;
                } elseif ($unitGroup1 == 'Temperature') {
                        if (($fromUOM == 'F') || ($fromUOM == 'fah')) {
                                if (($toUOM == 'F') || ($toUOM == 'fah')) {
                                        return $value;
                                } else {
                                        $value = (($value - 32) / 1.8);
                                        if (($toUOM == 'K') || ($toUOM == 'kel')) {
                                                $value += 273.15;
                                        }
                                        return $value;
                                }
                        } elseif ((($fromUOM == 'K') || ($fromUOM == 'kel')) &&
                                          (($toUOM == 'K') || ($toUOM == 'kel'))) {
                                                return $value;
                        } elseif ((($fromUOM == 'C') || ($fromUOM == 'cel')) &&
                                          (($toUOM == 'C') || ($toUOM == 'cel'))) {
                                        return $value;
                        }
                        if (($toUOM == 'F') || ($toUOM == 'fah')) {
                                if (($fromUOM == 'K') || ($fromUOM == 'kel')) {
                                        $value -= 273.15;
                                }
                                return ($value * 1.8) + 32;
                        }
                        if (($toUOM == 'C') || ($toUOM == 'cel')) {
                                return $value - 273.15;
                        }
                        return $value + 273.15;
                }
                return ($value * self::$_unitConversions[$unitGroup1][$fromUOM][$toUOM]) / $toMultiplier;
        }       //      function CONVERTUOM()

}       //      class PHPExcel_Calculation_Engineering