<?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 );
    
    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 );
  }
  
  /**
   * 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 );
  }
  
  /**
   * 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 );
  }
  
  /**
   * 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 );
  }
  
  /**
   * 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 );
    
    $parsedComplex = self::parseComplex ( $complexNumber );
    
    return sqrt ( ($parsedComplex ['real'] * $parsedComplex ['real']) + ($parsedComplex ['imaginary'] * $parsedComplex ['imaginary']) );
  }
  
  /**
   * 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'] ) );
    }
  }
  
  /**
   * 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'] ) );
    }
  }
  
  /**
   * 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'] ) );
    }
  }
  
  /**
   * 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'] );
    }
  }
  
  /**
   * 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'] );
    }
  }
  
  /**
   * 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'] );
    }
  }
  
  /**
   * 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 ) );
  }
  
  /**
   * 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 ) );
  }
  
  /**
   * 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'] );
    }
  }
  
  /**
   * 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'] );
    }
  }
  
  /**
   * 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;
    }
  }
  
  /**
   * 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'] );
  }
  
  /**
   * 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 );
  }
  
  /**
   * 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 );
  }
  
  /**
   * 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);
  }
  
  /**
   * 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);
  }
  
  //
  // Private method to calculate the erf value
  //
  private static $twoSqrtPi = 1.128379167095512574;
  public static function erfVal($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 / $sum ) > PRECISION );
    return self::$twoSqrtPi * $sum;
  }
  
  /**
   * 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 ();
  }
  
  //
  // Private method to calculate the erfc value
  //
  private static $oneSqrtPi = 0.564189583547756287;
  private static function erfcVal($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 ) / $q2) > PRECISION );
    return self::$oneSqrtPi * exp ( - $x * $x ) * $q2;
  }
  
  /**
   * 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 ();
  }
  
  /**
   * 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 ) );
  }
  
  /**
   * 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;
  }
  
  /**
   * 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;
  }
  
  /**
   * 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;
  }
  
  /**
   * 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;
  }
}
