2175 lines
78 KiB
PHP
2175 lines
78 KiB
PHP
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<?php
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/**
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* PHPExcel
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*
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* Copyright (c) 2006 - 2010 PHPExcel
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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*
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* @category PHPExcel
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* @package PHPExcel_Calculation
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* @copyright Copyright (c) 2006 - 2010 PHPExcel (http://www.codeplex.com/PHPExcel)
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* @license http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt LGPL
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* @version ##VERSION##, ##DATE##
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*/
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/** PHPExcel root directory */
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if (!defined('PHPEXCEL_ROOT')) {
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/**
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* @ignore
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*/
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define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../');
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require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
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}
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/** EULER */
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define('EULER', 2.71828182845904523536);
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/**
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* PHPExcel_Calculation_Engineering
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*
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* @category PHPExcel
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* @package PHPExcel_Calculation
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* @copyright Copyright (c) 2006 - 2010 PHPExcel (http://www.codeplex.com/PHPExcel)
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*/
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class PHPExcel_Calculation_Engineering {
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private static $_conversionUnits = array( 'g' => array( 'Group' => 'Mass', 'Unit Name' => 'Gram', 'AllowPrefix' => True ),
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'sg' => array( 'Group' => 'Mass', 'Unit Name' => 'Slug', 'AllowPrefix' => False ),
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'lbm' => array( 'Group' => 'Mass', 'Unit Name' => 'Pound mass (avoirdupois)', 'AllowPrefix' => False ),
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'u' => array( 'Group' => 'Mass', 'Unit Name' => 'U (atomic mass unit)', 'AllowPrefix' => True ),
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'ozm' => array( 'Group' => 'Mass', 'Unit Name' => 'Ounce mass (avoirdupois)', 'AllowPrefix' => False ),
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'm' => array( 'Group' => 'Distance', 'Unit Name' => 'Meter', 'AllowPrefix' => True ),
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'mi' => array( 'Group' => 'Distance', 'Unit Name' => 'Statute mile', 'AllowPrefix' => False ),
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'Nmi' => array( 'Group' => 'Distance', 'Unit Name' => 'Nautical mile', 'AllowPrefix' => False ),
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'in' => array( 'Group' => 'Distance', 'Unit Name' => 'Inch', 'AllowPrefix' => False ),
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'ft' => array( 'Group' => 'Distance', 'Unit Name' => 'Foot', 'AllowPrefix' => False ),
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'yd' => array( 'Group' => 'Distance', 'Unit Name' => 'Yard', 'AllowPrefix' => False ),
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'ang' => array( 'Group' => 'Distance', 'Unit Name' => 'Angstrom', 'AllowPrefix' => True ),
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'Pica' => array( 'Group' => 'Distance', 'Unit Name' => 'Pica (1/72 in)', 'AllowPrefix' => False ),
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'yr' => array( 'Group' => 'Time', 'Unit Name' => 'Year', 'AllowPrefix' => False ),
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'day' => array( 'Group' => 'Time', 'Unit Name' => 'Day', 'AllowPrefix' => False ),
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'hr' => array( 'Group' => 'Time', 'Unit Name' => 'Hour', 'AllowPrefix' => False ),
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'mn' => array( 'Group' => 'Time', 'Unit Name' => 'Minute', 'AllowPrefix' => False ),
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'sec' => array( 'Group' => 'Time', 'Unit Name' => 'Second', 'AllowPrefix' => True ),
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'Pa' => array( 'Group' => 'Pressure', 'Unit Name' => 'Pascal', 'AllowPrefix' => True ),
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'p' => array( 'Group' => 'Pressure', 'Unit Name' => 'Pascal', 'AllowPrefix' => True ),
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'atm' => array( 'Group' => 'Pressure', 'Unit Name' => 'Atmosphere', 'AllowPrefix' => True ),
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'at' => array( 'Group' => 'Pressure', 'Unit Name' => 'Atmosphere', 'AllowPrefix' => True ),
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'mmHg' => array( 'Group' => 'Pressure', 'Unit Name' => 'mm of Mercury', 'AllowPrefix' => True ),
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'N' => array( 'Group' => 'Force', 'Unit Name' => 'Newton', 'AllowPrefix' => True ),
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'dyn' => array( 'Group' => 'Force', 'Unit Name' => 'Dyne', 'AllowPrefix' => True ),
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'dy' => array( 'Group' => 'Force', 'Unit Name' => 'Dyne', 'AllowPrefix' => True ),
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'lbf' => array( 'Group' => 'Force', 'Unit Name' => 'Pound force', 'AllowPrefix' => False ),
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'J' => array( 'Group' => 'Energy', 'Unit Name' => 'Joule', 'AllowPrefix' => True ),
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'e' => array( 'Group' => 'Energy', 'Unit Name' => 'Erg', 'AllowPrefix' => True ),
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'c' => array( 'Group' => 'Energy', 'Unit Name' => 'Thermodynamic calorie', 'AllowPrefix' => True ),
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'cal' => array( 'Group' => 'Energy', 'Unit Name' => 'IT calorie', 'AllowPrefix' => True ),
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'eV' => array( 'Group' => 'Energy', 'Unit Name' => 'Electron volt', 'AllowPrefix' => True ),
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'ev' => array( 'Group' => 'Energy', 'Unit Name' => 'Electron volt', 'AllowPrefix' => True ),
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'HPh' => array( 'Group' => 'Energy', 'Unit Name' => 'Horsepower-hour', 'AllowPrefix' => False ),
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'hh' => array( 'Group' => 'Energy', 'Unit Name' => 'Horsepower-hour', 'AllowPrefix' => False ),
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'Wh' => array( 'Group' => 'Energy', 'Unit Name' => 'Watt-hour', 'AllowPrefix' => True ),
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'wh' => array( 'Group' => 'Energy', 'Unit Name' => 'Watt-hour', 'AllowPrefix' => True ),
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'flb' => array( 'Group' => 'Energy', 'Unit Name' => 'Foot-pound', 'AllowPrefix' => False ),
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'BTU' => array( 'Group' => 'Energy', 'Unit Name' => 'BTU', 'AllowPrefix' => False ),
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'btu' => array( 'Group' => 'Energy', 'Unit Name' => 'BTU', 'AllowPrefix' => False ),
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'HP' => array( 'Group' => 'Power', 'Unit Name' => 'Horsepower', 'AllowPrefix' => False ),
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'h' => array( 'Group' => 'Power', 'Unit Name' => 'Horsepower', 'AllowPrefix' => False ),
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'W' => array( 'Group' => 'Power', 'Unit Name' => 'Watt', 'AllowPrefix' => True ),
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'w' => array( 'Group' => 'Power', 'Unit Name' => 'Watt', 'AllowPrefix' => True ),
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'T' => array( 'Group' => 'Magnetism', 'Unit Name' => 'Tesla', 'AllowPrefix' => True ),
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'ga' => array( 'Group' => 'Magnetism', 'Unit Name' => 'Gauss', 'AllowPrefix' => True ),
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'C' => array( 'Group' => 'Temperature', 'Unit Name' => 'Celsius', 'AllowPrefix' => False ),
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'cel' => array( 'Group' => 'Temperature', 'Unit Name' => 'Celsius', 'AllowPrefix' => False ),
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'F' => array( 'Group' => 'Temperature', 'Unit Name' => 'Fahrenheit', 'AllowPrefix' => False ),
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'fah' => array( 'Group' => 'Temperature', 'Unit Name' => 'Fahrenheit', 'AllowPrefix' => False ),
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'K' => array( 'Group' => 'Temperature', 'Unit Name' => 'Kelvin', 'AllowPrefix' => False ),
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'kel' => array( 'Group' => 'Temperature', 'Unit Name' => 'Kelvin', 'AllowPrefix' => False ),
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'tsp' => array( 'Group' => 'Liquid', 'Unit Name' => 'Teaspoon', 'AllowPrefix' => False ),
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'tbs' => array( 'Group' => 'Liquid', 'Unit Name' => 'Tablespoon', 'AllowPrefix' => False ),
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'oz' => array( 'Group' => 'Liquid', 'Unit Name' => 'Fluid Ounce', 'AllowPrefix' => False ),
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'cup' => array( 'Group' => 'Liquid', 'Unit Name' => 'Cup', 'AllowPrefix' => False ),
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'pt' => array( 'Group' => 'Liquid', 'Unit Name' => 'U.S. Pint', 'AllowPrefix' => False ),
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'us_pt' => array( 'Group' => 'Liquid', 'Unit Name' => 'U.S. Pint', 'AllowPrefix' => False ),
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'uk_pt' => array( 'Group' => 'Liquid', 'Unit Name' => 'U.K. Pint', 'AllowPrefix' => False ),
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'qt' => array( 'Group' => 'Liquid', 'Unit Name' => 'Quart', 'AllowPrefix' => False ),
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'gal' => array( 'Group' => 'Liquid', 'Unit Name' => 'Gallon', 'AllowPrefix' => False ),
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'l' => array( 'Group' => 'Liquid', 'Unit Name' => 'Litre', 'AllowPrefix' => True ),
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'lt' => array( 'Group' => 'Liquid', 'Unit Name' => 'Litre', 'AllowPrefix' => True )
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);
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private static $_conversionMultipliers = array( 'Y' => array( 'multiplier' => 1E24, 'name' => 'yotta' ),
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'Z' => array( 'multiplier' => 1E21, 'name' => 'zetta' ),
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'E' => array( 'multiplier' => 1E18, 'name' => 'exa' ),
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'P' => array( 'multiplier' => 1E15, 'name' => 'peta' ),
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'T' => array( 'multiplier' => 1E12, 'name' => 'tera' ),
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'G' => array( 'multiplier' => 1E9, 'name' => 'giga' ),
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'M' => array( 'multiplier' => 1E6, 'name' => 'mega' ),
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'k' => array( 'multiplier' => 1E3, 'name' => 'kilo' ),
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'h' => array( 'multiplier' => 1E2, 'name' => 'hecto' ),
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'e' => array( 'multiplier' => 1E1, 'name' => 'deka' ),
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'd' => array( 'multiplier' => 1E-1, 'name' => 'deci' ),
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'c' => array( 'multiplier' => 1E-2, 'name' => 'centi' ),
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'm' => array( 'multiplier' => 1E-3, 'name' => 'milli' ),
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'u' => array( 'multiplier' => 1E-6, 'name' => 'micro' ),
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'n' => array( 'multiplier' => 1E-9, 'name' => 'nano' ),
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'p' => array( 'multiplier' => 1E-12, 'name' => 'pico' ),
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'f' => array( 'multiplier' => 1E-15, 'name' => 'femto' ),
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'a' => array( 'multiplier' => 1E-18, 'name' => 'atto' ),
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'z' => array( 'multiplier' => 1E-21, 'name' => 'zepto' ),
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'y' => array( 'multiplier' => 1E-24, 'name' => 'yocto' )
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);
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private static $_unitConversions = array( 'Mass' => array( 'g' => array( 'g' => 1.0,
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'sg' => 6.85220500053478E-05,
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'lbm' => 2.20462291469134E-03,
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'u' => 6.02217000000000E+23,
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'ozm' => 3.52739718003627E-02
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),
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'sg' => array( 'g' => 1.45938424189287E+04,
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'sg' => 1.0,
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'lbm' => 3.21739194101647E+01,
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'u' => 8.78866000000000E+27,
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'ozm' => 5.14782785944229E+02
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),
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'lbm' => array( 'g' => 4.5359230974881148E+02,
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'sg' => 3.10810749306493E-02,
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'lbm' => 1.0,
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'u' => 2.73161000000000E+26,
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'ozm' => 1.60000023429410E+01
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),
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'u' => array( 'g' => 1.66053100460465E-24,
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'sg' => 1.13782988532950E-28,
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'lbm' => 3.66084470330684E-27,
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'u' => 1.0,
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'ozm' => 5.85735238300524E-26
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),
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'ozm' => array( 'g' => 2.83495152079732E+01,
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'sg' => 1.94256689870811E-03,
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'lbm' => 6.24999908478882E-02,
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'u' => 1.70725600000000E+25,
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'ozm' => 1.0
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)
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),
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'Distance' => array( 'm' => array( 'm' => 1.0,
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'mi' => 6.21371192237334E-04,
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'Nmi' => 5.39956803455724E-04,
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'in' => 3.93700787401575E+01,
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'ft' => 3.28083989501312E+00,
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'yd' => 1.09361329797891E+00,
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'ang' => 1.00000000000000E+10,
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'Pica' => 2.83464566929116E+03
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),
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'mi' => array( 'm' => 1.60934400000000E+03,
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'mi' => 1.0,
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'Nmi' => 8.68976241900648E-01,
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'in' => 6.33600000000000E+04,
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'ft' => 5.28000000000000E+03,
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'yd' => 1.76000000000000E+03,
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'ang' => 1.60934400000000E+13,
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'Pica' => 4.56191999999971E+06
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),
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'Nmi' => array( 'm' => 1.85200000000000E+03,
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'mi' => 1.15077944802354E+00,
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'Nmi' => 1.0,
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'in' => 7.29133858267717E+04,
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'ft' => 6.07611548556430E+03,
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'yd' => 2.02537182785694E+03,
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'ang' => 1.85200000000000E+13,
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'Pica' => 5.24976377952723E+06
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),
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'in' => array( 'm' => 2.54000000000000E-02,
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'mi' => 1.57828282828283E-05,
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'Nmi' => 1.37149028077754E-05,
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'in' => 1.0,
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'ft' => 8.33333333333333E-02,
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'yd' => 2.77777777686643E-02,
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'ang' => 2.54000000000000E+08,
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'Pica' => 7.19999999999955E+01
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),
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'ft' => array( 'm' => 3.04800000000000E-01,
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'mi' => 1.89393939393939E-04,
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'Nmi' => 1.64578833693305E-04,
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'in' => 1.20000000000000E+01,
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'ft' => 1.0,
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'yd' => 3.33333333223972E-01,
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'ang' => 3.04800000000000E+09,
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'Pica' => 8.63999999999946E+02
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),
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'yd' => array( 'm' => 9.14400000300000E-01,
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'mi' => 5.68181818368230E-04,
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'Nmi' => 4.93736501241901E-04,
|
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'in' => 3.60000000118110E+01,
|
||
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'ft' => 3.00000000000000E+00,
|
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'yd' => 1.0,
|
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'ang' => 9.14400000300000E+09,
|
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'Pica' => 2.59200000085023E+03
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),
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'ang' => array( 'm' => 1.00000000000000E-10,
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'mi' => 6.21371192237334E-14,
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'Nmi' => 5.39956803455724E-14,
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'in' => 3.93700787401575E-09,
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'ft' => 3.28083989501312E-10,
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'yd' => 1.09361329797891E-10,
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'ang' => 1.0,
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'Pica' => 2.83464566929116E-07
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),
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'Pica' => array( 'm' => 3.52777777777800E-04,
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'mi' => 2.19205948372629E-07,
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'Nmi' => 1.90484761219114E-07,
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'in' => 1.38888888888898E-02,
|
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'ft' => 1.15740740740748E-03,
|
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'yd' => 3.85802469009251E-04,
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'ang' => 3.52777777777800E+06,
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'Pica' => 1.0
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)
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),
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'Time' => array( 'yr' => array( 'yr' => 1.0,
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'day' => 365.25,
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'hr' => 8766.0,
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'mn' => 525960.0,
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'sec' => 31557600.0
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),
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'day' => array( 'yr' => 2.73785078713210E-03,
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'day' => 1.0,
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'hr' => 24.0,
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'mn' => 1440.0,
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'sec' => 86400.0
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),
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'hr' => array( 'yr' => 1.14077116130504E-04,
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'day' => 4.16666666666667E-02,
|
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'hr' => 1.0,
|
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'mn' => 60.0,
|
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'sec' => 3600.0
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||
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),
|
||
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'mn' => array( 'yr' => 1.90128526884174E-06,
|
||
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'day' => 6.94444444444444E-04,
|
||
|
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'hr' => 1.66666666666667E-02,
|
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|
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'mn' => 1.0,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'mn' => 1.66666666666667E-02,
|
||
|
|
'sec' => 1.0
|
||
|
|
)
|
||
|
|
),
|
||
|
|
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|
||
|
|
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|
||
|
|
'atm' => 9.86923299998193E-06,
|
||
|
|
'at' => 9.86923299998193E-06,
|
||
|
|
'mmHg' => 7.50061707998627E-03
|
||
|
|
),
|
||
|
|
'p' => array( 'Pa' => 1.0,
|
||
|
|
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|
||
|
|
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|
||
|
|
'at' => 9.86923299998193E-06,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'atm' => 1.0,
|
||
|
|
'at' => 1.0,
|
||
|
|
'mmHg' => 760.0
|
||
|
|
),
|
||
|
|
'at' => array( 'Pa' => 1.01324996583000E+05,
|
||
|
|
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|
||
|
|
'atm' => 1.0,
|
||
|
|
'at' => 1.0,
|
||
|
|
'mmHg' => 760.0
|
||
|
|
),
|
||
|
|
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|
||
|
|
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|
||
|
|
'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
|
||
|
|
),
|
||
|
|
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|
||
|
|
'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,
|
||
|
|
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|
||
|
|
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|
||
|
|
'btu' => 9.47815067349015E-04
|
||
|
|
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|
||
|
|
'e' => array( 'J' => 1.00000048065700E-07,
|
||
|
|
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|
||
|
|
'c' => 2.39006364353494E-08,
|
||
|
|
'cal' => 2.38846305445111E-08,
|
||
|
|
'eV' => 6.24146000000000E+11,
|
||
|
|
'ev' => 6.24146000000000E+11,
|
||
|
|
'HPh' => 3.72506609848824E-14,
|
||
|
|
'hh' => 3.72506609848824E-14,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'btu' => 9.47815522922962E-11
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'c' => 1.0,
|
||
|
|
'cal' => 9.99330315287563E-01,
|
||
|
|
'eV' => 2.61142000000000E+19,
|
||
|
|
'ev' => 2.61142000000000E+19,
|
||
|
|
'HPh' => 1.55856355899327E-06,
|
||
|
|
'hh' => 1.55856355899327E-06,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'c' => 1.00067013349059E+00,
|
||
|
|
'cal' => 1.0,
|
||
|
|
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|
||
|
|
'ev' => 2.61317000000000E+19,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'wh' => 1.16299914807955E-03,
|
||
|
|
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|
||
|
|
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|
||
|
|
'btu' => 3.96830723907002E-03
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'c' => 3.82933423195043E-20,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'hh' => 5.96826078912344E-26,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'c' => 6.41616438565991E+05,
|
||
|
|
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|
||
|
|
'eV' => 1.67553000000000E+25,
|
||
|
|
'ev' => 1.67553000000000E+25,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'wh' => 7.45699653134593E+02,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'cal' => 6.41186757845835E+05,
|
||
|
|
'eV' => 1.67553000000000E+25,
|
||
|
|
'ev' => 1.67553000000000E+25,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'wh' => 7.45699653134593E+02,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'c' => 8.60422069219046E+02,
|
||
|
|
'cal' => 8.59845857713046E+02,
|
||
|
|
'eV' => 2.24692340000000E+22,
|
||
|
|
'ev' => 2.24692340000000E+22,
|
||
|
|
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|
||
|
|
'hh' => 1.34102248243839E-03,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
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|
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||
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|
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||
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|
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|
||
|
|
'cal' => 8.59845857713046E+02,
|
||
|
|
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|
||
|
|
'ev' => 2.24692340000000E+22,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
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|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
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|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'ev' => 2.63015000000000E+17,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'wh' => 1.17055614802000E-05,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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||
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|
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|
||
|
|
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|
||
|
|
'c' => 2.52165488508168E+02,
|
||
|
|
'cal' => 2.51996617135510E+02,
|
||
|
|
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|
||
|
|
'ev' => 6.58510000000000E+21,
|
||
|
|
'HPh' => 3.93015941224568E-04,
|
||
|
|
'hh' => 3.93015941224568E-04,
|
||
|
|
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|
||
|
|
'wh' => 2.93071851047526E-01,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
'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,
|
||
|
|
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|
||
|
|
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|
||
|
|
'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
|
||
|
|
)
|
||
|
|
)
|
||
|
|
);
|
||
|
|
|
||
|
|
|
||
|
|
public static function _parseComplex($complexNumber) {
|
||
|
|
$workString = (string) $complexNumber;
|
||
|
|
|
||
|
|
$realNumber = $imaginary = 0;
|
||
|
|
// Extract the suffix, if there is one
|
||
|
|
$suffix = substr($workString,-1);
|
||
|
|
if (!is_numeric($suffix)) {
|
||
|
|
$workString = substr($workString,0,-1);
|
||
|
|
} else {
|
||
|
|
$suffix = '';
|
||
|
|
}
|
||
|
|
|
||
|
|
// Split the input into its Real and Imaginary components
|
||
|
|
$leadingSign = 0;
|
||
|
|
if (strlen($workString) > 0) {
|
||
|
|
$leadingSign = (($workString{0} == '+') || ($workString{0} == '-')) ? 1 : 0;
|
||
|
|
}
|
||
|
|
$power = '';
|
||
|
|
$realNumber = strtok($workString, '+-');
|
||
|
|
if (strtoupper(substr($realNumber,-1)) == 'E') {
|
||
|
|
$power = strtok('+-');
|
||
|
|
++$leadingSign;
|
||
|
|
}
|
||
|
|
|
||
|
|
$realNumber = substr($workString,0,strlen($realNumber)+strlen($power)+$leadingSign);
|
||
|
|
|
||
|
|
if ($suffix != '') {
|
||
|
|
$imaginary = substr($workString,strlen($realNumber));
|
||
|
|
|
||
|
|
if (($imaginary == '') && (($realNumber == '') || ($realNumber == '+') || ($realNumber == '-'))) {
|
||
|
|
$imaginary = $realNumber.'1';
|
||
|
|
$realNumber = '0';
|
||
|
|
} else if ($imaginary == '') {
|
||
|
|
$imaginary = $realNumber;
|
||
|
|
$realNumber = '0';
|
||
|
|
} elseif (($imaginary == '+') || ($imaginary == '-')) {
|
||
|
|
$imaginary .= '1';
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return array( 'real' => $realNumber,
|
||
|
|
'imaginary' => $imaginary,
|
||
|
|
'suffix' => $suffix
|
||
|
|
);
|
||
|
|
} // function _parseComplex()
|
||
|
|
|
||
|
|
|
||
|
|
private static function _cleanComplex($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 $complexNumber;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
private static function _nbrConversionFormat($xVal,$places) {
|
||
|
|
if (!is_null($places)) {
|
||
|
|
if (strlen($xVal) <= $places) {
|
||
|
|
return substr(str_pad($xVal,$places,'0',STR_PAD_LEFT),-10);
|
||
|
|
} else {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return substr($xVal,-10);
|
||
|
|
} // function _nbrConversionFormat()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* BESSELI
|
||
|
|
*
|
||
|
|
* Returns the modified Bessel function, which is equivalent to the Bessel function evaluated for purely imaginary arguments
|
||
|
|
*
|
||
|
|
* @param float $x
|
||
|
|
* @param float $n
|
||
|
|
* @return int
|
||
|
|
*/
|
||
|
|
public static function BESSELI($x, $n) {
|
||
|
|
$x = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
|
||
|
|
$n = (is_null($n)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($n);
|
||
|
|
|
||
|
|
if ((is_numeric($x)) && (is_numeric($n))) {
|
||
|
|
$n = floor($n);
|
||
|
|
if ($n < 0) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
$f_2_PI = 2 * M_PI;
|
||
|
|
|
||
|
|
if (abs($x) <= 30) {
|
||
|
|
$fTerm = pow($x / 2, $n) / PHPExcel_Calculation_MathTrig::FACT($n);
|
||
|
|
$nK = 1;
|
||
|
|
$fResult = $fTerm;
|
||
|
|
$fSqrX = ($x * $x) / 4;
|
||
|
|
do {
|
||
|
|
$fTerm *= $fSqrX;
|
||
|
|
$fTerm /= ($nK * ($nK + $n));
|
||
|
|
$fResult += $fTerm;
|
||
|
|
} while ((abs($fTerm) > 1e-10) && (++$nK < 100));
|
||
|
|
} else {
|
||
|
|
$fXAbs = abs($x);
|
||
|
|
$fResult = exp($fXAbs) / sqrt($f_2_PI * $fXAbs);
|
||
|
|
if (($n && 1) && ($x < 0)) {
|
||
|
|
$fResult = -$fResult;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return $fResult;
|
||
|
|
}
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
} // function BESSELI()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* BESSELJ
|
||
|
|
*
|
||
|
|
* Returns the Bessel function
|
||
|
|
*
|
||
|
|
* @param float $x
|
||
|
|
* @param float $n
|
||
|
|
* @return int
|
||
|
|
*/
|
||
|
|
public static function BESSELJ($x, $n) {
|
||
|
|
$x = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
|
||
|
|
$n = (is_null($n)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($n);
|
||
|
|
|
||
|
|
if ((is_numeric($x)) && (is_numeric($n))) {
|
||
|
|
$n = floor($n);
|
||
|
|
if ($n < 0) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
$f_PI_DIV_2 = M_PI / 2;
|
||
|
|
$f_PI_DIV_4 = M_PI / 4;
|
||
|
|
|
||
|
|
$fResult = 0;
|
||
|
|
if (abs($x) <= 30) {
|
||
|
|
$fTerm = pow($x / 2, $n) / PHPExcel_Calculation_MathTrig::FACT($n);
|
||
|
|
$nK = 1;
|
||
|
|
$fResult = $fTerm;
|
||
|
|
$fSqrX = ($x * $x) / -4;
|
||
|
|
do {
|
||
|
|
$fTerm *= $fSqrX;
|
||
|
|
$fTerm /= ($nK * ($nK + $n));
|
||
|
|
$fResult += $fTerm;
|
||
|
|
} while ((abs($fTerm) > 1e-10) && (++$nK < 100));
|
||
|
|
} else {
|
||
|
|
$fXAbs = abs($x);
|
||
|
|
$fResult = sqrt(M_2DIVPI / $fXAbs) * cos($fXAbs - $n * $f_PI_DIV_2 - $f_PI_DIV_4);
|
||
|
|
if (($n && 1) && ($x < 0)) {
|
||
|
|
$fResult = -$fResult;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return $fResult;
|
||
|
|
}
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
} // function BESSELJ()
|
||
|
|
|
||
|
|
|
||
|
|
private static function _Besselk0($fNum) {
|
||
|
|
if ($fNum <= 2) {
|
||
|
|
$fNum2 = $fNum * 0.5;
|
||
|
|
$y = ($fNum2 * $fNum2);
|
||
|
|
$fRet = -log($fNum2) * self::BESSELI($fNum, 0) +
|
||
|
|
(-0.57721566 + $y * (0.42278420 + $y * (0.23069756 + $y * (0.3488590e-1 + $y * (0.262698e-2 + $y *
|
||
|
|
(0.10750e-3 + $y * 0.74e-5))))));
|
||
|
|
} else {
|
||
|
|
$y = 2 / $fNum;
|
||
|
|
$fRet = exp(-$fNum) / sqrt($fNum) *
|
||
|
|
(1.25331414 + $y * (-0.7832358e-1 + $y * (0.2189568e-1 + $y * (-0.1062446e-1 + $y *
|
||
|
|
(0.587872e-2 + $y * (-0.251540e-2 + $y * 0.53208e-3))))));
|
||
|
|
}
|
||
|
|
return $fRet;
|
||
|
|
} // function _Besselk0()
|
||
|
|
|
||
|
|
|
||
|
|
private static function _Besselk1($fNum) {
|
||
|
|
if ($fNum <= 2) {
|
||
|
|
$fNum2 = $fNum * 0.5;
|
||
|
|
$y = ($fNum2 * $fNum2);
|
||
|
|
$fRet = log($fNum2) * self::BESSELI($fNum, 1) +
|
||
|
|
(1 + $y * (0.15443144 + $y * (-0.67278579 + $y * (-0.18156897 + $y * (-0.1919402e-1 + $y *
|
||
|
|
(-0.110404e-2 + $y * (-0.4686e-4))))))) / $fNum;
|
||
|
|
} else {
|
||
|
|
$y = 2 / $fNum;
|
||
|
|
$fRet = exp(-$fNum) / sqrt($fNum) *
|
||
|
|
(1.25331414 + $y * (0.23498619 + $y * (-0.3655620e-1 + $y * (0.1504268e-1 + $y * (-0.780353e-2 + $y *
|
||
|
|
(0.325614e-2 + $y * (-0.68245e-3)))))));
|
||
|
|
}
|
||
|
|
return $fRet;
|
||
|
|
} // function _Besselk1()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* BESSELK
|
||
|
|
*
|
||
|
|
* Returns the modified Bessel function, which is equivalent to the Bessel functions evaluated for purely imaginary arguments.
|
||
|
|
*
|
||
|
|
* @param float $x
|
||
|
|
* @param float $ord
|
||
|
|
* @return float
|
||
|
|
*/
|
||
|
|
public static function BESSELK($x, $ord) {
|
||
|
|
$x = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
|
||
|
|
$ord = (is_null($ord)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);
|
||
|
|
|
||
|
|
if ((is_numeric($x)) && (is_numeric($ord))) {
|
||
|
|
if (($ord < 0) || ($x == 0.0)) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
|
||
|
|
switch(floor($ord)) {
|
||
|
|
case 0 : return self::_Besselk0($x);
|
||
|
|
break;
|
||
|
|
case 1 : return self::_Besselk1($x);
|
||
|
|
break;
|
||
|
|
default : $fTox = 2 / $x;
|
||
|
|
$fBkm = self::_Besselk0($x);
|
||
|
|
$fBk = self::_Besselk1($x);
|
||
|
|
for ($n = 1; $n < $ord; ++$n) {
|
||
|
|
$fBkp = $fBkm + $n * $fTox * $fBk;
|
||
|
|
$fBkm = $fBk;
|
||
|
|
$fBk = $fBkp;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return $fBk;
|
||
|
|
}
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
} // function BESSELK()
|
||
|
|
|
||
|
|
|
||
|
|
private static function _Bessely0($fNum) {
|
||
|
|
if ($fNum < 8.0) {
|
||
|
|
$y = ($fNum * $fNum);
|
||
|
|
$f1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y * (-86327.92757 + $y * 228.4622733))));
|
||
|
|
$f2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y * (47447.26470 + $y * (226.1030244 + $y))));
|
||
|
|
$fRet = $f1 / $f2 + M_2DIVPI * self::BESSELJ($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(M_2DIVPI / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
|
||
|
|
}
|
||
|
|
return $fRet;
|
||
|
|
} // function _Bessely0()
|
||
|
|
|
||
|
|
|
||
|
|
private static function _Bessely1($fNum) {
|
||
|
|
if ($fNum < 8.0) {
|
||
|
|
$y = ($fNum * $fNum);
|
||
|
|
$f1 = $fNum * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y * (0.7349264551e9 + $y *
|
||
|
|
(-0.4237922726e7 + $y * 0.8511937935e4)))));
|
||
|
|
$f2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y *
|
||
|
|
(0.1020426050e6 + $y * (0.3549632885e3 + $y)))));
|
||
|
|
$fRet = $f1 / $f2 + M_2DIVPI * ( self::BESSELJ($fNum, 1) * log($fNum) - 1 / $fNum);
|
||
|
|
} else {
|
||
|
|
$z = 8.0 / $fNum;
|
||
|
|
$y = ($z * $z);
|
||
|
|
$xx = $fNum - 2.356194491;
|
||
|
|
$f1 = 1 + $y * (0.183105e-2 + $y * (-0.3516396496e-4 + $y * (0.2457520174e-5 + $y * (-0.240337019e6))));
|
||
|
|
$f2 = 0.04687499995 + $y * (-0.2002690873e-3 + $y * (0.8449199096e-5 + $y * (-0.88228987e-6 + $y * 0.105787412e-6)));
|
||
|
|
$fRet = sqrt(M_2DIVPI / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
|
||
|
|
#i12430# ...but this seems to work much better.
|
||
|
|
// $fRet = sqrt(M_2DIVPI / $fNum) * sin($fNum - 2.356194491);
|
||
|
|
}
|
||
|
|
return $fRet;
|
||
|
|
} // function _Bessely1()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* BESSELY
|
||
|
|
*
|
||
|
|
* Returns the Bessel function, which is also called the Weber function or the Neumann function.
|
||
|
|
*
|
||
|
|
* @param float $x
|
||
|
|
* @param float $n
|
||
|
|
* @return int
|
||
|
|
*/
|
||
|
|
public static function BESSELY($x, $ord) {
|
||
|
|
$x = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
|
||
|
|
$ord = (is_null($ord)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);
|
||
|
|
|
||
|
|
if ((is_numeric($x)) && (is_numeric($ord))) {
|
||
|
|
if (($ord < 0) || ($x == 0.0)) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
|
||
|
|
switch(floor($ord)) {
|
||
|
|
case 0 : return self::_Bessely0($x);
|
||
|
|
break;
|
||
|
|
case 1 : return self::_Bessely1($x);
|
||
|
|
break;
|
||
|
|
default: $fTox = 2 / $x;
|
||
|
|
$fBym = self::_Bessely0($x);
|
||
|
|
$fBy = self::_Bessely1($x);
|
||
|
|
for ($n = 1; $n < $ord; ++$n) {
|
||
|
|
$fByp = $n * $fTox * $fBy - $fBym;
|
||
|
|
$fBym = $fBy;
|
||
|
|
$fBy = $fByp;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return $fBy;
|
||
|
|
}
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
} // function BESSELY()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* BINTODEC
|
||
|
|
*
|
||
|
|
* Return a binary value as Decimal.
|
||
|
|
*
|
||
|
|
* @param string $x
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function BINTODEC($x) {
|
||
|
|
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
|
||
|
|
|
||
|
|
if (is_bool($x)) {
|
||
|
|
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
|
||
|
|
$x = (int) $x;
|
||
|
|
} else {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
|
||
|
|
$x = floor($x);
|
||
|
|
}
|
||
|
|
$x = (string) $x;
|
||
|
|
if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
if (strlen($x) > 10) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
} elseif (strlen($x) == 10) {
|
||
|
|
// Two's Complement
|
||
|
|
$x = substr($x,-9);
|
||
|
|
return '-'.(512-bindec($x));
|
||
|
|
}
|
||
|
|
return bindec($x);
|
||
|
|
} // function BINTODEC()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* BINTOHEX
|
||
|
|
*
|
||
|
|
* Return a binary value as Hex.
|
||
|
|
*
|
||
|
|
* @param string $x
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function BINTOHEX($x, $places=null) {
|
||
|
|
$x = floor(PHPExcel_Calculation_Functions::flattenSingleValue($x));
|
||
|
|
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
|
||
|
|
|
||
|
|
if (is_bool($x)) {
|
||
|
|
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
|
||
|
|
$x = (int) $x;
|
||
|
|
} else {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
|
||
|
|
$x = floor($x);
|
||
|
|
}
|
||
|
|
$x = (string) $x;
|
||
|
|
if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
if (strlen($x) > 10) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
} elseif (strlen($x) == 10) {
|
||
|
|
// Two's Complement
|
||
|
|
return str_repeat('F',8).substr(strtoupper(dechex(bindec(substr($x,-9)))),-2);
|
||
|
|
}
|
||
|
|
$hexVal = (string) strtoupper(dechex(bindec($x)));
|
||
|
|
|
||
|
|
return self::_nbrConversionFormat($hexVal,$places);
|
||
|
|
} // function BINTOHEX()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* BINTOOCT
|
||
|
|
*
|
||
|
|
* Return a binary value as Octal.
|
||
|
|
*
|
||
|
|
* @param string $x
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function BINTOOCT($x, $places=null) {
|
||
|
|
$x = floor(PHPExcel_Calculation_Functions::flattenSingleValue($x));
|
||
|
|
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
|
||
|
|
|
||
|
|
if (is_bool($x)) {
|
||
|
|
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
|
||
|
|
$x = (int) $x;
|
||
|
|
} else {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
|
||
|
|
$x = floor($x);
|
||
|
|
}
|
||
|
|
$x = (string) $x;
|
||
|
|
if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
if (strlen($x) > 10) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
} elseif (strlen($x) == 10) {
|
||
|
|
// Two's Complement
|
||
|
|
return str_repeat('7',7).substr(strtoupper(decoct(bindec(substr($x,-9)))),-3);
|
||
|
|
}
|
||
|
|
$octVal = (string) decoct(bindec($x));
|
||
|
|
|
||
|
|
return self::_nbrConversionFormat($octVal,$places);
|
||
|
|
} // function BINTOOCT()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* DECTOBIN
|
||
|
|
*
|
||
|
|
* Return an octal value as binary.
|
||
|
|
*
|
||
|
|
* @param string $x
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function DECTOBIN($x, $places=null) {
|
||
|
|
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
|
||
|
|
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
|
||
|
|
|
||
|
|
if (is_bool($x)) {
|
||
|
|
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
|
||
|
|
$x = (int) $x;
|
||
|
|
} else {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
$x = (string) $x;
|
||
|
|
if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
$x = (string) floor($x);
|
||
|
|
$r = decbin($x);
|
||
|
|
if (strlen($r) == 32) {
|
||
|
|
// Two's Complement
|
||
|
|
$r = substr($r,-10);
|
||
|
|
} elseif (strlen($r) > 11) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
|
||
|
|
return self::_nbrConversionFormat($r,$places);
|
||
|
|
} // function DECTOBIN()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* DECTOHEX
|
||
|
|
*
|
||
|
|
* Return an octal value as binary.
|
||
|
|
*
|
||
|
|
* @param string $x
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function DECTOHEX($x, $places=null) {
|
||
|
|
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
|
||
|
|
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
|
||
|
|
|
||
|
|
if (is_bool($x)) {
|
||
|
|
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
|
||
|
|
$x = (int) $x;
|
||
|
|
} else {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
$x = (string) $x;
|
||
|
|
if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
$x = (string) floor($x);
|
||
|
|
$r = strtoupper(dechex($x));
|
||
|
|
if (strlen($r) == 8) {
|
||
|
|
// Two's Complement
|
||
|
|
$r = 'FF'.$r;
|
||
|
|
}
|
||
|
|
|
||
|
|
return self::_nbrConversionFormat($r,$places);
|
||
|
|
} // function DECTOHEX()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* DECTOOCT
|
||
|
|
*
|
||
|
|
* Return an octal value as binary.
|
||
|
|
*
|
||
|
|
* @param string $x
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function DECTOOCT($x, $places=null) {
|
||
|
|
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
|
||
|
|
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
|
||
|
|
|
||
|
|
if (is_bool($x)) {
|
||
|
|
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
|
||
|
|
$x = (int) $x;
|
||
|
|
} else {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
$x = (string) $x;
|
||
|
|
if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
$x = (string) floor($x);
|
||
|
|
$r = decoct($x);
|
||
|
|
if (strlen($r) == 11) {
|
||
|
|
// Two's Complement
|
||
|
|
$r = substr($r,-10);
|
||
|
|
}
|
||
|
|
|
||
|
|
return self::_nbrConversionFormat($r,$places);
|
||
|
|
} // function DECTOOCT()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* HEXTOBIN
|
||
|
|
*
|
||
|
|
* Return a hex value as binary.
|
||
|
|
*
|
||
|
|
* @param string $x
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function HEXTOBIN($x, $places=null) {
|
||
|
|
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
|
||
|
|
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
|
||
|
|
|
||
|
|
if (is_bool($x)) {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
$x = (string) $x;
|
||
|
|
if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
$binVal = decbin(hexdec($x));
|
||
|
|
|
||
|
|
return substr(self::_nbrConversionFormat($binVal,$places),-10);
|
||
|
|
} // function HEXTOBIN()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* HEXTODEC
|
||
|
|
*
|
||
|
|
* Return a hex value as octal.
|
||
|
|
*
|
||
|
|
* @param string $x
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function HEXTODEC($x) {
|
||
|
|
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
|
||
|
|
|
||
|
|
if (is_bool($x)) {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
$x = (string) $x;
|
||
|
|
if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
return hexdec($x);
|
||
|
|
} // function HEXTODEC()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* HEXTOOCT
|
||
|
|
*
|
||
|
|
* Return a hex value as octal.
|
||
|
|
*
|
||
|
|
* @param string $x
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function HEXTOOCT($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.
|
||
|
|
*
|
||
|
|
* @param string $x
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function OCTTOBIN($x, $places=null) {
|
||
|
|
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
|
||
|
|
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
|
||
|
|
|
||
|
|
if (is_bool($x)) {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
$x = (string) $x;
|
||
|
|
if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
$r = decbin(octdec($x));
|
||
|
|
|
||
|
|
return self::_nbrConversionFormat($r,$places);
|
||
|
|
} // function OCTTOBIN()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* OCTTODEC
|
||
|
|
*
|
||
|
|
* Return an octal value as binary.
|
||
|
|
*
|
||
|
|
* @param string $x
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function OCTTODEC($x) {
|
||
|
|
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
|
||
|
|
|
||
|
|
if (is_bool($x)) {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
$x = (string) $x;
|
||
|
|
if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
return octdec($x);
|
||
|
|
} // function OCTTODEC()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* OCTTOHEX
|
||
|
|
*
|
||
|
|
* Return an octal value as hex.
|
||
|
|
*
|
||
|
|
* @param string $x
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function OCTTOHEX($x, $places=null) {
|
||
|
|
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
|
||
|
|
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
|
||
|
|
|
||
|
|
if (is_bool($x)) {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
$x = (string) $x;
|
||
|
|
if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
$hexVal = strtoupper(dechex(octdec($x)));
|
||
|
|
|
||
|
|
return self::_nbrConversionFormat($hexVal,$places);
|
||
|
|
} // function OCTTOHEX()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* COMPLEX
|
||
|
|
*
|
||
|
|
* returns a complex number of the form x + yi or x + yj.
|
||
|
|
*
|
||
|
|
* @param float $realNumber
|
||
|
|
* @param float $imaginary
|
||
|
|
* @param string $suffix
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function COMPLEX($realNumber=0.0, $imaginary=0.0, $suffix='i') {
|
||
|
|
$realNumber = (is_null($realNumber)) ? 0.0 : (float) PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);
|
||
|
|
$imaginary = (is_null($imaginary)) ? 0.0 : (float) 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 == ''))) {
|
||
|
|
if ($suffix == '') $suffix = 'i';
|
||
|
|
if ($realNumber == 0.0) {
|
||
|
|
if ($imaginary == 0.0) {
|
||
|
|
return (string) '0';
|
||
|
|
} elseif ($imaginary == 1.0) {
|
||
|
|
return (string) $suffix;
|
||
|
|
} elseif ($imaginary == -1.0) {
|
||
|
|
return (string) '-'.$suffix;
|
||
|
|
}
|
||
|
|
return (string) $imaginary.$suffix;
|
||
|
|
} elseif ($imaginary == 0.0) {
|
||
|
|
return (string) $realNumber;
|
||
|
|
} elseif ($imaginary == 1.0) {
|
||
|
|
return (string) $realNumber.'+'.$suffix;
|
||
|
|
} elseif ($imaginary == -1.0) {
|
||
|
|
return (string) $realNumber.'-'.$suffix;
|
||
|
|
}
|
||
|
|
if ($imaginary > 0) { $imaginary = (string) '+'.$imaginary; }
|
||
|
|
return (string) $realNumber.$imaginary.$suffix;
|
||
|
|
}
|
||
|
|
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
} // function COMPLEX()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMAGINARY
|
||
|
|
*
|
||
|
|
* Returns the imaginary coefficient of a complex number in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param string $complexNumber
|
||
|
|
* @return real
|
||
|
|
*/
|
||
|
|
public static function IMAGINARY($complexNumber) {
|
||
|
|
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
|
||
|
|
|
||
|
|
$parsedComplex = self::_parseComplex($complexNumber);
|
||
|
|
if (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
return $parsedComplex['imaginary'];
|
||
|
|
} // function IMAGINARY()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMREAL
|
||
|
|
*
|
||
|
|
* Returns the real coefficient of a complex number in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param string $complexNumber
|
||
|
|
* @return real
|
||
|
|
*/
|
||
|
|
public static function IMREAL($complexNumber) {
|
||
|
|
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
|
||
|
|
|
||
|
|
$parsedComplex = self::_parseComplex($complexNumber);
|
||
|
|
if (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
return $parsedComplex['real'];
|
||
|
|
} // function IMREAL()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMABS
|
||
|
|
*
|
||
|
|
* Returns the absolute value (modulus) of a complex number in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param string $complexNumber
|
||
|
|
* @return real
|
||
|
|
*/
|
||
|
|
public static function IMABS($complexNumber) {
|
||
|
|
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
|
||
|
|
|
||
|
|
$parsedComplex = self::_parseComplex($complexNumber);
|
||
|
|
if (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
return sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
|
||
|
|
} // function IMABS()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMARGUMENT
|
||
|
|
*
|
||
|
|
* Returns the argument theta of a complex number, i.e. the angle in radians from the real axis to the representation of the number in polar coordinates.
|
||
|
|
*
|
||
|
|
* @param string $complexNumber
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function IMARGUMENT($complexNumber) {
|
||
|
|
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
|
||
|
|
|
||
|
|
$parsedComplex = self::_parseComplex($complexNumber);
|
||
|
|
if (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
|
||
|
|
if ($parsedComplex['real'] == 0.0) {
|
||
|
|
if ($parsedComplex['imaginary'] == 0.0) {
|
||
|
|
return 0.0;
|
||
|
|
} elseif($parsedComplex['imaginary'] < 0.0) {
|
||
|
|
return M_PI / -2;
|
||
|
|
} else {
|
||
|
|
return M_PI / 2;
|
||
|
|
}
|
||
|
|
} elseif ($parsedComplex['real'] > 0.0) {
|
||
|
|
return atan($parsedComplex['imaginary'] / $parsedComplex['real']);
|
||
|
|
} elseif ($parsedComplex['imaginary'] < 0.0) {
|
||
|
|
return 0 - (M_PI - atan(abs($parsedComplex['imaginary']) / abs($parsedComplex['real'])));
|
||
|
|
} else {
|
||
|
|
return M_PI - atan($parsedComplex['imaginary'] / abs($parsedComplex['real']));
|
||
|
|
}
|
||
|
|
} // function IMARGUMENT()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMCONJUGATE
|
||
|
|
*
|
||
|
|
* Returns the complex conjugate of a complex number in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param string $complexNumber
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function IMCONJUGATE($complexNumber) {
|
||
|
|
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
|
||
|
|
|
||
|
|
$parsedComplex = self::_parseComplex($complexNumber);
|
||
|
|
|
||
|
|
if (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
|
||
|
|
if ($parsedComplex['imaginary'] == 0.0) {
|
||
|
|
return $parsedComplex['real'];
|
||
|
|
} else {
|
||
|
|
return self::_cleanComplex(self::COMPLEX($parsedComplex['real'], 0 - $parsedComplex['imaginary'], $parsedComplex['suffix']));
|
||
|
|
}
|
||
|
|
} // function IMCONJUGATE()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMCOS
|
||
|
|
*
|
||
|
|
* Returns the cosine of a complex number in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param string $complexNumber
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function IMCOS($complexNumber) {
|
||
|
|
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
|
||
|
|
|
||
|
|
$parsedComplex = self::_parseComplex($complexNumber);
|
||
|
|
if (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
|
||
|
|
if ($parsedComplex['imaginary'] == 0.0) {
|
||
|
|
return cos($parsedComplex['real']);
|
||
|
|
} else {
|
||
|
|
return self::IMCONJUGATE(self::COMPLEX(cos($parsedComplex['real']) * cosh($parsedComplex['imaginary']),sin($parsedComplex['real']) * sinh($parsedComplex['imaginary']),$parsedComplex['suffix']));
|
||
|
|
}
|
||
|
|
} // function IMCOS()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMSIN
|
||
|
|
*
|
||
|
|
* Returns the sine of a complex number in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param string $complexNumber
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function IMSIN($complexNumber) {
|
||
|
|
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
|
||
|
|
|
||
|
|
$parsedComplex = self::_parseComplex($complexNumber);
|
||
|
|
if (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
|
||
|
|
if ($parsedComplex['imaginary'] == 0.0) {
|
||
|
|
return sin($parsedComplex['real']);
|
||
|
|
} else {
|
||
|
|
return self::COMPLEX(sin($parsedComplex['real']) * cosh($parsedComplex['imaginary']),cos($parsedComplex['real']) * sinh($parsedComplex['imaginary']),$parsedComplex['suffix']);
|
||
|
|
}
|
||
|
|
} // function IMSIN()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMSQRT
|
||
|
|
*
|
||
|
|
* Returns the square root of a complex number in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param string $complexNumber
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function IMSQRT($complexNumber) {
|
||
|
|
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
|
||
|
|
|
||
|
|
$parsedComplex = self::_parseComplex($complexNumber);
|
||
|
|
if (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
|
||
|
|
$theta = self::IMARGUMENT($complexNumber);
|
||
|
|
$d1 = cos($theta / 2);
|
||
|
|
$d2 = sin($theta / 2);
|
||
|
|
$r = sqrt(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));
|
||
|
|
|
||
|
|
if ($parsedComplex['suffix'] == '') {
|
||
|
|
return self::COMPLEX($d1 * $r,$d2 * $r);
|
||
|
|
} else {
|
||
|
|
return self::COMPLEX($d1 * $r,$d2 * $r,$parsedComplex['suffix']);
|
||
|
|
}
|
||
|
|
} // function IMSQRT()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMLN
|
||
|
|
*
|
||
|
|
* Returns the natural logarithm of a complex number in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param string $complexNumber
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function IMLN($complexNumber) {
|
||
|
|
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
|
||
|
|
|
||
|
|
$parsedComplex = self::_parseComplex($complexNumber);
|
||
|
|
if (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
|
||
|
|
$logR = log(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));
|
||
|
|
$t = self::IMARGUMENT($complexNumber);
|
||
|
|
|
||
|
|
if ($parsedComplex['suffix'] == '') {
|
||
|
|
return self::COMPLEX($logR,$t);
|
||
|
|
} else {
|
||
|
|
return self::COMPLEX($logR,$t,$parsedComplex['suffix']);
|
||
|
|
}
|
||
|
|
} // function IMLN()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMLOG10
|
||
|
|
*
|
||
|
|
* Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param string $complexNumber
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function IMLOG10($complexNumber) {
|
||
|
|
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
|
||
|
|
|
||
|
|
$parsedComplex = self::_parseComplex($complexNumber);
|
||
|
|
if (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
} elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
|
||
|
|
return log10($parsedComplex['real']);
|
||
|
|
}
|
||
|
|
|
||
|
|
return self::IMPRODUCT(log10(EULER),self::IMLN($complexNumber));
|
||
|
|
} // function IMLOG10()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMLOG2
|
||
|
|
*
|
||
|
|
* Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param string $complexNumber
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function IMLOG2($complexNumber) {
|
||
|
|
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
|
||
|
|
|
||
|
|
$parsedComplex = self::_parseComplex($complexNumber);
|
||
|
|
if (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
} elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
|
||
|
|
return log($parsedComplex['real'],2);
|
||
|
|
}
|
||
|
|
|
||
|
|
return self::IMPRODUCT(log(EULER,2),self::IMLN($complexNumber));
|
||
|
|
} // function IMLOG2()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMEXP
|
||
|
|
*
|
||
|
|
* Returns the exponential of a complex number in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param string $complexNumber
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function IMEXP($complexNumber) {
|
||
|
|
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
|
||
|
|
|
||
|
|
$parsedComplex = self::_parseComplex($complexNumber);
|
||
|
|
if (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
|
||
|
|
return '1';
|
||
|
|
}
|
||
|
|
|
||
|
|
$e = exp($parsedComplex['real']);
|
||
|
|
$eX = $e * cos($parsedComplex['imaginary']);
|
||
|
|
$eY = $e * sin($parsedComplex['imaginary']);
|
||
|
|
|
||
|
|
if ($parsedComplex['suffix'] == '') {
|
||
|
|
return self::COMPLEX($eX,$eY);
|
||
|
|
} else {
|
||
|
|
return self::COMPLEX($eX,$eY,$parsedComplex['suffix']);
|
||
|
|
}
|
||
|
|
} // function IMEXP()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMPOWER
|
||
|
|
*
|
||
|
|
* Returns a complex number in x + yi or x + yj text format raised to a power.
|
||
|
|
*
|
||
|
|
* @param string $complexNumber
|
||
|
|
* @return string
|
||
|
|
*/
|
||
|
|
public static function IMPOWER($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);
|
||
|
|
if (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
|
||
|
|
$r = sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
|
||
|
|
$rPower = pow($r,$realNumber);
|
||
|
|
$theta = self::IMARGUMENT($complexNumber) * $realNumber;
|
||
|
|
if ($theta == 0) {
|
||
|
|
return 1;
|
||
|
|
} elseif ($parsedComplex['imaginary'] == 0.0) {
|
||
|
|
return self::COMPLEX($rPower * cos($theta),$rPower * sin($theta),$parsedComplex['suffix']);
|
||
|
|
} else {
|
||
|
|
return self::COMPLEX($rPower * cos($theta),$rPower * sin($theta),$parsedComplex['suffix']);
|
||
|
|
}
|
||
|
|
} // function IMPOWER()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMDIV
|
||
|
|
*
|
||
|
|
* Returns the quotient of two complex numbers in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param string $complexDividend
|
||
|
|
* @param string $complexDivisor
|
||
|
|
* @return real
|
||
|
|
*/
|
||
|
|
public static function IMDIV($complexDividend,$complexDivisor) {
|
||
|
|
$complexDividend = PHPExcel_Calculation_Functions::flattenSingleValue($complexDividend);
|
||
|
|
$complexDivisor = PHPExcel_Calculation_Functions::flattenSingleValue($complexDivisor);
|
||
|
|
|
||
|
|
$parsedComplexDividend = self::_parseComplex($complexDividend);
|
||
|
|
if (!is_array($parsedComplexDividend)) {
|
||
|
|
return $parsedComplexDividend;
|
||
|
|
}
|
||
|
|
|
||
|
|
$parsedComplexDivisor = self::_parseComplex($complexDivisor);
|
||
|
|
if (!is_array($parsedComplexDivisor)) {
|
||
|
|
return $parsedComplexDividend;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] != '') &&
|
||
|
|
($parsedComplexDividend['suffix'] != $parsedComplexDivisor['suffix'])) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] == '')) {
|
||
|
|
$parsedComplexDivisor['suffix'] = $parsedComplexDividend['suffix'];
|
||
|
|
}
|
||
|
|
|
||
|
|
$d1 = ($parsedComplexDividend['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['imaginary']);
|
||
|
|
$d2 = ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['real']) - ($parsedComplexDividend['real'] * $parsedComplexDivisor['imaginary']);
|
||
|
|
$d3 = ($parsedComplexDivisor['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDivisor['imaginary'] * $parsedComplexDivisor['imaginary']);
|
||
|
|
|
||
|
|
$r = $d1/$d3;
|
||
|
|
$i = $d2/$d3;
|
||
|
|
|
||
|
|
if ($i > 0.0) {
|
||
|
|
return self::_cleanComplex($r.'+'.$i.$parsedComplexDivisor['suffix']);
|
||
|
|
} elseif ($i < 0.0) {
|
||
|
|
return self::_cleanComplex($r.$i.$parsedComplexDivisor['suffix']);
|
||
|
|
} else {
|
||
|
|
return $r;
|
||
|
|
}
|
||
|
|
} // function IMDIV()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMSUB
|
||
|
|
*
|
||
|
|
* Returns the difference of two complex numbers in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param string $complexNumber1
|
||
|
|
* @param string $complexNumber2
|
||
|
|
* @return real
|
||
|
|
*/
|
||
|
|
public static function IMSUB($complexNumber1,$complexNumber2) {
|
||
|
|
$complexNumber1 = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber1);
|
||
|
|
$complexNumber2 = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber2);
|
||
|
|
|
||
|
|
$parsedComplex1 = self::_parseComplex($complexNumber1);
|
||
|
|
if (!is_array($parsedComplex1)) {
|
||
|
|
return $parsedComplex1;
|
||
|
|
}
|
||
|
|
|
||
|
|
$parsedComplex2 = self::_parseComplex($complexNumber2);
|
||
|
|
if (!is_array($parsedComplex2)) {
|
||
|
|
return $parsedComplex2;
|
||
|
|
}
|
||
|
|
|
||
|
|
if ((($parsedComplex1['suffix'] != '') && ($parsedComplex2['suffix'] != '')) &&
|
||
|
|
($parsedComplex1['suffix'] != $parsedComplex2['suffix'])) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
} elseif (($parsedComplex1['suffix'] == '') && ($parsedComplex2['suffix'] != '')) {
|
||
|
|
$parsedComplex1['suffix'] = $parsedComplex2['suffix'];
|
||
|
|
}
|
||
|
|
|
||
|
|
$d1 = $parsedComplex1['real'] - $parsedComplex2['real'];
|
||
|
|
$d2 = $parsedComplex1['imaginary'] - $parsedComplex2['imaginary'];
|
||
|
|
|
||
|
|
return self::COMPLEX($d1,$d2,$parsedComplex1['suffix']);
|
||
|
|
} // function IMSUB()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMSUM
|
||
|
|
*
|
||
|
|
* Returns the sum of two or more complex numbers in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param array of mixed Data Series
|
||
|
|
* @return real
|
||
|
|
*/
|
||
|
|
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 (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
|
||
|
|
if ($activeSuffix == '') {
|
||
|
|
$activeSuffix = $parsedComplex['suffix'];
|
||
|
|
} elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
}
|
||
|
|
|
||
|
|
$returnValue['real'] += $parsedComplex['real'];
|
||
|
|
$returnValue['imaginary'] += $parsedComplex['imaginary'];
|
||
|
|
}
|
||
|
|
|
||
|
|
if ($returnValue['imaginary'] == 0.0) { $activeSuffix = ''; }
|
||
|
|
return self::COMPLEX($returnValue['real'],$returnValue['imaginary'],$activeSuffix);
|
||
|
|
} // function IMSUM()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* IMPRODUCT
|
||
|
|
*
|
||
|
|
* Returns the product of two or more complex numbers in x + yi or x + yj text format.
|
||
|
|
*
|
||
|
|
* @param array of mixed Data Series
|
||
|
|
* @return real
|
||
|
|
*/
|
||
|
|
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);
|
||
|
|
if (!is_array($parsedComplex)) {
|
||
|
|
return $parsedComplex;
|
||
|
|
}
|
||
|
|
$workValue = $returnValue;
|
||
|
|
if (($parsedComplex['suffix'] != '') && ($activeSuffix == '')) {
|
||
|
|
$activeSuffix = $parsedComplex['suffix'];
|
||
|
|
} elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
$returnValue['real'] = ($workValue['real'] * $parsedComplex['real']) - ($workValue['imaginary'] * $parsedComplex['imaginary']);
|
||
|
|
$returnValue['imaginary'] = ($workValue['real'] * $parsedComplex['imaginary']) + ($workValue['imaginary'] * $parsedComplex['real']);
|
||
|
|
}
|
||
|
|
|
||
|
|
if ($returnValue['imaginary'] == 0.0) { $activeSuffix = ''; }
|
||
|
|
return self::COMPLEX($returnValue['real'],$returnValue['imaginary'],$activeSuffix);
|
||
|
|
} // function IMPRODUCT()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* DELTA
|
||
|
|
*
|
||
|
|
* Tests whether two values are equal. Returns 1 if number1 = number2; returns 0 otherwise.
|
||
|
|
*
|
||
|
|
* @param float $a
|
||
|
|
* @param float $b
|
||
|
|
* @return int
|
||
|
|
*/
|
||
|
|
public static function DELTA($a, $b=0) {
|
||
|
|
$a = PHPExcel_Calculation_Functions::flattenSingleValue($a);
|
||
|
|
$b = PHPExcel_Calculation_Functions::flattenSingleValue($b);
|
||
|
|
|
||
|
|
return (int) ($a == $b);
|
||
|
|
} // function DELTA()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* GESTEP
|
||
|
|
*
|
||
|
|
* Returns 1 if number = step; returns 0 (zero) otherwise
|
||
|
|
*
|
||
|
|
* @param float $number
|
||
|
|
* @param float $step
|
||
|
|
* @return int
|
||
|
|
*/
|
||
|
|
public static function GESTEP($number, $step=0) {
|
||
|
|
$number = PHPExcel_Calculation_Functions::flattenSingleValue($number);
|
||
|
|
$step = PHPExcel_Calculation_Functions::flattenSingleValue($step);
|
||
|
|
|
||
|
|
return (int) ($number >= $step);
|
||
|
|
} // function GESTEP()
|
||
|
|
|
||
|
|
|
||
|
|
//
|
||
|
|
// Private method to calculate the erf value
|
||
|
|
//
|
||
|
|
private static $_two_sqrtpi = 1.128379167095512574;
|
||
|
|
|
||
|
|
public static function _erfVal($x) {
|
||
|
|
if (abs($x) > 2.2) {
|
||
|
|
return 1 - self::_erfcVal($x);
|
||
|
|
}
|
||
|
|
$sum = $term = $x;
|
||
|
|
$xsqr = ($x * $x);
|
||
|
|
$j = 1;
|
||
|
|
do {
|
||
|
|
$term *= $xsqr / $j;
|
||
|
|
$sum -= $term / (2 * $j + 1);
|
||
|
|
++$j;
|
||
|
|
$term *= $xsqr / $j;
|
||
|
|
$sum += $term / (2 * $j + 1);
|
||
|
|
++$j;
|
||
|
|
if ($sum == 0.0) {
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
} while (abs($term / $sum) > PRECISION);
|
||
|
|
return self::$_two_sqrtpi * $sum;
|
||
|
|
} // function _erfVal()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* ERF
|
||
|
|
*
|
||
|
|
* Returns the error function integrated between lower_limit and upper_limit
|
||
|
|
*
|
||
|
|
* @param float $lower lower bound for integrating ERF
|
||
|
|
* @param float $upper upper bound for integrating ERF.
|
||
|
|
* If omitted, ERF integrates between zero and lower_limit
|
||
|
|
* @return int
|
||
|
|
*/
|
||
|
|
public static function ERF($lower, $upper = null) {
|
||
|
|
$lower = PHPExcel_Calculation_Functions::flattenSingleValue($lower);
|
||
|
|
$upper = PHPExcel_Calculation_Functions::flattenSingleValue($upper);
|
||
|
|
|
||
|
|
if (is_numeric($lower)) {
|
||
|
|
if ($lower < 0) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
if (is_null($upper)) {
|
||
|
|
return self::_erfVal($lower);
|
||
|
|
}
|
||
|
|
if (is_numeric($upper)) {
|
||
|
|
if ($upper < 0) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
return self::_erfVal($upper) - self::_erfVal($lower);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
} // function ERF()
|
||
|
|
|
||
|
|
|
||
|
|
//
|
||
|
|
// Private method to calculate the erfc value
|
||
|
|
//
|
||
|
|
private static $_one_sqrtpi = 0.564189583547756287;
|
||
|
|
|
||
|
|
private static function _erfcVal($x) {
|
||
|
|
if (abs($x) < 2.2) {
|
||
|
|
return 1 - self::_erfVal($x);
|
||
|
|
}
|
||
|
|
if ($x < 0) {
|
||
|
|
return 2 - self::ERFC(-$x);
|
||
|
|
}
|
||
|
|
$a = $n = 1;
|
||
|
|
$b = $c = $x;
|
||
|
|
$d = ($x * $x) + 0.5;
|
||
|
|
$q1 = $q2 = $b / $d;
|
||
|
|
$t = 0;
|
||
|
|
do {
|
||
|
|
$t = $a * $n + $b * $x;
|
||
|
|
$a = $b;
|
||
|
|
$b = $t;
|
||
|
|
$t = $c * $n + $d * $x;
|
||
|
|
$c = $d;
|
||
|
|
$d = $t;
|
||
|
|
$n += 0.5;
|
||
|
|
$q1 = $q2;
|
||
|
|
$q2 = $b / $d;
|
||
|
|
} while ((abs($q1 - $q2) / $q2) > PRECISION);
|
||
|
|
return self::$_one_sqrtpi * exp(-$x * $x) * $q2;
|
||
|
|
} // function _erfcVal()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* ERFC
|
||
|
|
*
|
||
|
|
* Returns the complementary ERF function integrated between x and infinity
|
||
|
|
*
|
||
|
|
* @param float $x The lower bound for integrating ERF
|
||
|
|
* @return int
|
||
|
|
*/
|
||
|
|
public static function ERFC($x) {
|
||
|
|
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
|
||
|
|
|
||
|
|
if (is_numeric($x)) {
|
||
|
|
if ($x < 0) {
|
||
|
|
return PHPExcel_Calculation_Functions::NaN();
|
||
|
|
}
|
||
|
|
return self::_erfcVal($x);
|
||
|
|
}
|
||
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
||
|
|
} // function ERFC()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* getConversionGroups
|
||
|
|
*
|
||
|
|
* @return array
|
||
|
|
*/
|
||
|
|
public static function getConversionGroups() {
|
||
|
|
$conversionGroups = array();
|
||
|
|
foreach(self::$_conversionUnits as $conversionUnit) {
|
||
|
|
$conversionGroups[] = $conversionUnit['Group'];
|
||
|
|
}
|
||
|
|
return array_merge(array_unique($conversionGroups));
|
||
|
|
} // function getConversionGroups()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* getConversionGroupUnits
|
||
|
|
*
|
||
|
|
* @return array
|
||
|
|
*/
|
||
|
|
public static function getConversionGroupUnits($group = NULL) {
|
||
|
|
$conversionGroups = array();
|
||
|
|
foreach(self::$_conversionUnits as $conversionUnit => $conversionGroup) {
|
||
|
|
if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
|
||
|
|
$conversionGroups[$conversionGroup['Group']][] = $conversionUnit;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return $conversionGroups;
|
||
|
|
} // function getConversionGroupUnits()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* getConversionGroupUnitDetails
|
||
|
|
*
|
||
|
|
* @return array
|
||
|
|
*/
|
||
|
|
public static function getConversionGroupUnitDetails($group = NULL) {
|
||
|
|
$conversionGroups = array();
|
||
|
|
foreach(self::$_conversionUnits as $conversionUnit => $conversionGroup) {
|
||
|
|
if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
|
||
|
|
$conversionGroups[$conversionGroup['Group']][] = array( 'unit' => $conversionUnit,
|
||
|
|
'description' => $conversionGroup['Unit Name']
|
||
|
|
);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return $conversionGroups;
|
||
|
|
} // function getConversionGroupUnitDetails()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* getConversionGroups
|
||
|
|
*
|
||
|
|
* @return array
|
||
|
|
*/
|
||
|
|
public static function getConversionMultipliers() {
|
||
|
|
return self::$_conversionMultipliers;
|
||
|
|
} // function getConversionGroups()
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* CONVERTUOM
|
||
|
|
*
|
||
|
|
* @param float $value
|
||
|
|
* @param string $fromUOM
|
||
|
|
* @param string $toUOM
|
||
|
|
* @return float
|
||
|
|
*/
|
||
|
|
public static function CONVERTUOM($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();
|
||
|
|
}
|
||
|
|
$fromMultiplier = 1;
|
||
|
|
if (isset(self::$_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;
|
||
|
|
|
||
|
|
$toMultiplier = 1;
|
||
|
|
if (isset(self::$_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 == $toUOM) {
|
||
|
|
return 1.0;
|
||
|
|
} elseif ($unitGroup1 == 'Temperature') {
|
||
|
|
if (($fromUOM == 'F') || ($fromUOM == 'fah')) {
|
||
|
|
if (($toUOM == 'F') || ($toUOM == 'fah')) {
|
||
|
|
return 1.0;
|
||
|
|
} else {
|
||
|
|
$value = (($value - 32) / 1.8);
|
||
|
|
if (($toUOM == 'K') || ($toUOM == 'kel')) {
|
||
|
|
$value += 273.15;
|
||
|
|
}
|
||
|
|
return $value;
|
||
|
|
}
|
||
|
|
} elseif ((($fromUOM == 'K') || ($fromUOM == 'kel')) &&
|
||
|
|
(($toUOM == 'K') || ($toUOM == 'kel'))) {
|
||
|
|
return 1.0;
|
||
|
|
} elseif ((($fromUOM == 'C') || ($fromUOM == 'cel')) &&
|
||
|
|
(($toUOM == 'C') || ($toUOM == 'cel'))) {
|
||
|
|
return 1.0;
|
||
|
|
}
|
||
|
|
if (($toUOM == 'F') || ($toUOM == 'fah')) {
|
||
|
|
if (($fromUOM == 'K') || ($fromUOM == 'kel')) {
|
||
|
|
$value -= 273.15;
|
||
|
|
}
|
||
|
|
return ($value * 1.8) + 32;
|
||
|
|
}
|
||
|
|
if (($toUOM == 'C') || ($toUOM == 'cel')) {
|
||
|
|
return $value - 273.15;
|
||
|
|
}
|
||
|
|
return $value + 273.15;
|
||
|
|
}
|
||
|
|
return ($value * self::$_unitConversions[$unitGroup1][$fromUOM][$toUOM]) / $toMultiplier;
|
||
|
|
} // function CONVERTUOM()
|
||
|
|
|
||
|
|
} // class PHPExcel_Calculation_Engineering
|