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✏️ Editing: Engineering.php

<?php

/** 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
 *
 * Copyright (c) 2006 - 2015 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 - 2015 PHPExcel (http://www.codeplex.com/PHPExcel)
 * @license        http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
 * @version        ##VERSION##, ##DATE##
 */
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,
                'lbf' => 2.24808923655339E-01,
            ),
            'dyn' => array(
                'N'   => 1.0E-5,
                'dyn' => 1.0,
                'dy'  => 1.0,
                'lbf' => 2.24808923655339E-06,
            ),
            'dy' => array(
                'N'   => 1.0E-5,
                'dyn' => 1.0,
                'dy'  => 1.0,
                'lbf' => 2.24808923655339E-06,
            ),
            'lbf' => array(
                'N'   => 4.448222,
                'dyn' => 4.448222E+5,
                'dy'  => 4.448222E+5,
                'lbf' => 1.0,
            ),
        ),
        'Energy' => array(
            'J' => array(
                'J'   => 1.0,
                'e'   => 9.99999519343231E+06,
                'c'   => 2.39006249473467E-01,
                'cal' => 2.38846190642017E-01,
                'eV'  => 6.24145700000000E+18,
                'ev'  => 6.24145700000000E+18,
                'HPh' => 3.72506430801000E-07,
                'hh'  => 3.72506430801000E-07,
                'Wh'  => 2.77777916238711E-04,
                'wh'  => 2.77777916238711E-04,
                'flb' => 2.37304222192651E+01,
                'BTU' => 9.47815067349015E-04,
                'btu' => 9.47815067349015E-04,
            ),
            'e' => array(
                'J'   => 1.00000048065700E-07,
                'e'   => 1.0,
                'c'   => 2.39006364353494E-08,
                'cal' => 2.38846305445111E-08,
                'eV'  => 6.24146000000000E+11,
                'ev'  => 6.24146000000000E+11,
                'HPh' => 3.72506609848824E-14,
                'hh'  => 3.72506609848824E-14,
                'Wh'  => 2.77778049754611E-11,
                'wh'  => 2.77778049754611E-11,
                'flb' => 2.37304336254586E-06,
                'BTU' => 9.47815522922962E-11,
                'btu' => 9.47815522922962E-11,
            ),
            'c' => array(
                'J'   => 4.18399101363672E+00,
                'e'   => 4.18398900257312E+07,
                'c'   => 1.0,
                'cal' => 9.99330315287563E-01,
                'eV'  => 2.61142000000000E+19,
                'ev'  => 2.61142000000000E+19,
                'HPh' => 1.55856355899327E-06,
                'hh'  => 1.55856355899327E-06,
                'Wh'  => 1.16222030532950E-03,
                'wh'  => 1.16222030532950E-03,
                'flb' => 9.92878733152102E+01,
                'BTU' => 3.96564972437776E-03,
                'btu' => 3.96564972437776E-03,
            ),
            'cal' => array(
                'J'   => 4.18679484613929E+00,
                'e'   => 4.18679283372801E+07,
                'c'   => 1.00067013349059E+00,
                'cal' => 1.0,
                'eV'  => 2.61317000000000E+19,
                'ev'  => 2.61317000000000E+19,
                'HPh' => 1.55960800463137E-06,
                'hh'  => 1.55960800463137E-06,
                'Wh'  => 1.16299914807955E-03,
                'wh'  => 1.16299914807955E-03,
                'flb' => 9.93544094443283E+01,
                'BTU' => 3.96830723907002E-03,
                'btu' => 3.96830723907002E-03,
            ),
            'eV' => array(
                'J'   => 1.60219000146921E-19,
                'e'   => 1.60218923136574E-12,
                'c'   => 3.82933423195043E-20,
                'cal' => 3.82676978535648E-20,
                'eV'  => 1.0,
                'ev'  => 1.0,
                'HPh' => 5.96826078912344E-26,
                'hh'  => 5.96826078912344E-26,
                'Wh'  => 4.45053000026614E-23,
                'wh'  => 4.45053000026614E-23,
                'flb' => 3.80206452103492E-18,
                'BTU' => 1.51857982414846E-22,
                'btu' => 1.51857982414846E-22,
            ),
            'ev' => array(
                'J'   => 1.60219000146921E-19,
                'e'   => 1.60218923136574E-12,
                'c'   => 3.82933423195043E-20,
                'cal' => 3.82676978535648E-20,
                'eV'  => 1.0,
                'ev'  => 1.0,
                'HPh' => 5.96826078912344E-26,
                'hh'  => 5.96826078912344E-26,
                'Wh'  => 4.45053000026614E-23,
                'wh'  => 4.45053000026614E-23,
                'flb' => 3.80206452103492E-18,
                'BTU' => 1.51857982414846E-22,
                'btu' => 1.51857982414846E-22,
            ),
            'HPh' => array(
                'J'   => 2.68451741316170E+06,
                'e'   => 2.68451612283024E+13,
                'c'   => 6.41616438565991E+05,
                'cal' => 6.41186757845835E+05,
                'eV'  => 1.67553000000000E+25,
                'ev'  => 1.67553000000000E+25,
                'HPh' => 1.0,
                'hh'  => 1.0,
                'Wh'  => 7.45699653134593E+02,
                'wh'  => 7.45699653134593E+02,
                'flb' => 6.37047316692964E+07,
                'BTU' => 2.54442605275546E+03,
                'btu' => 2.54442605275546E+03,
            ),
            'hh' => array(
                'J'   => 2.68451741316170E+06,
                'e'   => 2.68451612283024E+13,
                'c'   => 6.41616438565991E+05,
                'cal' => 6.41186757845835E+05,
                'eV'  => 1.67553000000000E+25,
                'ev'  => 1.67553000000000E+25,
                'HPh' => 1.0,
                'hh'  => 1.0,
                'Wh'  => 7.45699653134593E+02,
                'wh'  => 7.45699653134593E+02,
                'flb' => 6.37047316692964E+07,
                'BTU' => 2.54442605275546E+03,
                'btu' => 2.54442605275546E+03,
            ),
            'Wh' => array(
                'J'   => 3.59999820554720E+03,
                'e'   => 3.59999647518369E+10,
                'c'   => 8.60422069219046E+02,
                'cal' => 8.59845857713046E+02,
                'eV'  => 2.24692340000000E+22,
                'ev'  => 2.24692340000000E+22,
                'HPh' => 1.34102248243839E-03,
                'hh'  => 1.34102248243839E-03,
                'Wh'  => 1.0,
                'wh'  => 1.0,
                'flb' => 8.54294774062316E+04,
                'BTU' => 3.41213254164705E+00,
                'btu' => 3.41213254164705E+00,
            ),
            'wh' => array(
                'J'   => 3.59999820554720E+03,
                'e'   => 3.59999647518369E+10,
                'c'   => 8.60422069219046E+02,
                'cal' => 8.59845857713046E+02,
                'eV'  => 2.24692340000000E+22,
                'ev'  => 2.24692340000000E+22,
                'HPh' => 1.34102248243839E-03,
                'hh'  => 1.34102248243839E-03,
                'Wh'  => 1.0,
                'wh'  => 1.0,
                'flb' => 8.54294774062316E+04,
                'BTU' => 3.41213254164705E+00,
                'btu' => 3.41213254164705E+00,
            ),
            'flb' => array(
                'J'   => 4.21400003236424E-02,
                'e'   => 4.21399800687660E+05,
                'c'   => 1.00717234301644E-02,
                'cal' => 1.00649785509554E-02,
                'eV'  => 2.63015000000000E+17,
                'ev'  => 2.63015000000000E+17,
                'HPh' => 1.56974211145130E-08,
                'hh'  => 1.56974211145130E-08,
                'Wh'  => 1.17055614802000E-05,
                'wh'  => 1.17055614802000E-05,
                'flb' => 1.0,
                'BTU' => 3.99409272448406E-05,
                'btu' => 3.99409272448406E-05,
            ),
            'BTU' => array(
                'J'   => 1.05505813786749E+03,
                'e'   => 1.05505763074665E+10,
                'c'   => 2.52165488508168E+02,
                'cal' => 2.51996617135510E+02,
                'eV'  => 6.58510000000000E+21,
                'ev'  => 6.58510000000000E+21,
                'HPh' => 3.93015941224568E-04,
                'hh'  => 3.93015941224568E-04,
                'Wh'  => 2.93071851047526E-01,
                'wh'  => 2.93071851047526E-01,
                'flb' => 2.50369750774671E+04,
                'BTU' => 1.0,
                'btu' => 1.0,
            ),
            'btu' => array(
                'J'   => 1.05505813786749E+03,
                'e'   => 1.05505763074665E+10,
                'c'   => 2.52165488508168E+02,
                'cal' => 2.51996617135510E+02,
                'eV'  => 6.58510000000000E+21,
                'ev'  => 6.58510000000000E+21,
                'HPh' => 3.93015941224568E-04,
                'hh'  => 3.93015941224568E-04,
                'Wh'  => 2.93071851047526E-01,
                'wh'  => 2.93071851047526E-01,
                'flb' => 2.50369750774671E+04,
                'BTU' => 1.0,
                'btu' => 1.0,
            ),
        ),
        'Power' => array(
            'HP' => array(
                'HP' => 1.0,
                'h'  => 1.0,
                'W'  => 7.45701000000000E+02,
                'w'  => 7.45701000000000E+02,
            ),
            'h' => array(
                'HP' => 1.0,
                'h'  => 1.0,
                'W'  => 7.45701000000000E+02,
                'w'  => 7.45701000000000E+02,
            ),
            'W' => array(
                'HP' => 1.34102006031908E-03,
                'h'  => 1.34102006031908E-03,
                'W'  => 1.0,
                'w'  => 1.0,
            ),
            'w' => array(
                'HP' => 1.34102006031908E-03,
                'h'  => 1.34102006031908E-03,
                'W'  => 1.0,
                'w'  => 1.0,
            ),
        ),
        'Magnetism' => array(
            'T' => array(
                'T'  => 1.0,
                'ga' => 10000.0,
            ),
            'ga' => array(
                'T'  => 0.0001,
                'ga' => 1.0,
            ),
        ),
        'Liquid' => array(
            'tsp' => array(
                'tsp'   => 1.0,
                'tbs'   => 3.33333333333333E-01,
                'oz'    => 1.66666666666667E-01,
                'cup'   => 2.08333333333333E-02,
                'pt'    => 1.04166666666667E-02,
                'us_pt' => 1.04166666666667E-02,
                'uk_pt' => 8.67558516821960E-03,
                'qt'    => 5.20833333333333E-03,
                'gal'   => 1.30208333333333E-03,
                'l'     => 4.92999408400710E-03,
                'lt'    => 4.92999408400710E-03,
            ),
            'tbs' => array(
                'tsp'   => 3.00000000000000E+00,
                'tbs'   => 1.0,
                'oz'    => 5.00000000000000E-01,
                'cup'   => 6.25000000000000E-02,
                'pt'    => 3.12500000000000E-02,
                'us_pt' => 3.12500000000000E-02,
                'uk_pt' => 2.60267555046588E-02,
                'qt'    => 1.56250000000000E-02,
                'gal'   => 3.90625000000000E-03,
                'l'     => 1.47899822520213E-02,
                'lt'    => 1.47899822520213E-02,
            ),
            'oz' => array(
                'tsp'   => 6.00000000000000E+00,
                'tbs'   => 2.00000000000000E+00,
                'oz'    => 1.0,
                'cup'   => 1.25000000000000E-01,
                'pt'    => 6.25000000000000E-02,
                'us_pt' => 6.25000000000000E-02,
                'uk_pt' => 5.20535110093176E-02,
                'qt'    => 3.12500000000000E-02,
                'gal'   => 7.81250000000000E-03,
                'l'     => 2.95799645040426E-02,
                'lt'    => 2.95799645040426E-02,
            ),
            'cup' => array(
                'tsp'   => 4.80000000000000E+01,
                'tbs'   => 1.60000000000000E+01,
                'oz'    => 8.00000000000000E+00,
                'cup'   => 1.0,
                'pt'    => 5.00000000000000E-01,
                'us_pt' => 5.00000000000000E-01,
                'uk_pt' => 4.16428088074541E-01,
                'qt'    => 2.50000000000000E-01,
                'gal'   => 6.25000000000000E-02,
                'l'     => 2.36639716032341E-01,
                'lt'    => 2.36639716032341E-01,
            ),
            'pt' => array(
                'tsp'   => 9.60000000000000E+01,
                'tbs'   => 3.20000000000000E+01,
                'oz'    => 1.60000000000000E+01,
                'cup'   => 2.00000000000000E+00,
                'pt'    => 1.0,
                'us_pt' => 1.0,
                'uk_pt' => 8.32856176149081E-01,
                'qt'    => 5.00000000000000E-01,
                'gal'   => 1.25000000000000E-01,
                'l'     => 4.73279432064682E-01,
                'lt'    => 4.73279432064682E-01,
            ),
            'us_pt' => array(
                'tsp'   => 9.60000000000000E+01,
                'tbs'   => 3.20000000000000E+01,
                'oz'    => 1.60000000000000E+01,
                'cup'   => 2.00000000000000E+00,
                'pt'    => 1.0,
                'us_pt' => 1.0,
                'uk_pt' => 8.32856176149081E-01,
                'qt'    => 5.00000000000000E-01,
                'gal'   => 1.25000000000000E-01,
                'l'     => 4.73279432064682E-01,
                'lt'    => 4.73279432064682E-01,
            ),
            'uk_pt' => array(
                'tsp'   => 1.15266000000000E+02,
                'tbs'   => 3.84220000000000E+01,
                'oz'    => 1.92110000000000E+01,
                'cup'   => 2.40137500000000E+00,
                'pt'    => 1.20068750000000E+00,
                'us_pt' => 1.20068750000000E+00,
                'uk_pt' => 1.0,
                'qt'    => 6.00343750000000E-01,
                'gal'   => 1.50085937500000E-01,
                'l'     => 5.68260698087162E-01,
                'lt'    => 5.68260698087162E-01,
            ),
            'qt' => array(
                'tsp'   => 1.92000000000000E+02,
                'tbs'   => 6.40000000000000E+01,
                'oz'    => 3.20000000000000E+01,
                'cup'   => 4.00000000000000E+00,
                'pt'    => 2.00000000000000E+00,
                'us_pt' => 2.00000000000000E+00,
                'uk_pt' => 1.66571235229816E+00,
                'qt'    => 1.0,
                'gal'   => 2.50000000000000E-01,
                'l'     => 9.46558864129363E-01,
                'lt'    => 9.46558864129363E-01,
            ),
            'gal' => array(
                'tsp'   => 7.68000000000000E+02,
                'tbs'   => 2.56000000000000E+02,
                'oz'    => 1.28000000000000E+02,
                'cup'   => 1.60000000000000E+01,
                'pt'    => 8.00000000000000E+00,
                'us_pt' => 8.00000000000000E+00,
                'uk_pt' => 6.66284940919265E+00,
                'qt'    => 4.00000000000000E+00,
                'gal'   => 1.0,
                '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';
                $realNumber = '0';
            } elseif ($imaginary == '') {
                $imaginary = $realNumber;
                $realNumber = '0';
            } elseif (($imaginary == '+') || ($imaginary == '-')) {
                $imaginary .= '1';
            }
        }

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

/**
     * 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);
    }

/**
     *    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();
    }

/**
     *    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();
    }

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;
    }

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;
    }

/**
     *    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);
                case 1:
                    return self::besselK1($x);
                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();
    }

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;
    }

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;
    }

/**
     *    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);
                case 1:
                    return self::besselY1($x);
                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();
    }

/**
     * 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);
    }

/**
     * 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);
    }

/**
     * 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);
    }

/**
     * 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);
    }

/**
     * 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);
    }

/**
     * 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);
    }

/**
     * 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);
    }

/**
     * 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);

/**
     * 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);

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);
    }

/**
     * 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);

/**
     * 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);

return self::nbrConversionFormat($hexVal, $places);
    }

/**
     * 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();
    }

/**
     * 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'];
    }

/**
     * 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'];
    }

/**
     * 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);