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PhpSpreadsheet/Classes/PHPExcel/Calculation/Engineering.php
Mark Baker 59932b0cac Bugfix: Work item 18370 - Error loading xlsx file with column breaks 
Deprecated the getCalculatedValue(), setCalculatedValue(), setFormulaAttributes() and getFormulaAttributes() methods in PHPExcel_Cell.
Documentation changes and unit tests.
2012-07-18 12:29:33 +01:00

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<?php
/**
* PHPExcel
*
* Copyright (c) 2006 - 2012 PHPExcel
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*
* @category PHPExcel
* @package PHPExcel_Calculation
* @copyright Copyright (c) 2006 - 2012 PHPExcel (http://www.codeplex.com/PHPExcel)
* @license http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt LGPL
* @version ##VERSION##, ##DATE##
*/
/** PHPExcel root directory */
if (!defined('PHPEXCEL_ROOT')) {
/**
* @ignore
*/
define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../');
require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
}
/** EULER */
define('EULER', 2.71828182845904523536);
/**
* PHPExcel_Calculation_Engineering
*
* @category PHPExcel
* @package PHPExcel_Calculation
* @copyright Copyright (c) 2006 - 2012 PHPExcel (http://www.codeplex.com/PHPExcel)
*/
class PHPExcel_Calculation_Engineering {
/**
* Details of the Units of measure that can be used in CONVERTUOM()
*
* @var mixed[]
*/
private static $_conversionUnits = array( 'g' => array( 'Group' => 'Mass', 'Unit Name' => 'Gram', 'AllowPrefix' => True ),
'sg' => array( 'Group' => 'Mass', 'Unit Name' => 'Slug', 'AllowPrefix' => False ),
'lbm' => array( 'Group' => 'Mass', 'Unit Name' => 'Pound mass (avoirdupois)', 'AllowPrefix' => False ),
'u' => array( 'Group' => 'Mass', 'Unit Name' => 'U (atomic mass unit)', 'AllowPrefix' => True ),
'ozm' => array( 'Group' => 'Mass', 'Unit Name' => 'Ounce mass (avoirdupois)', 'AllowPrefix' => False ),
'm' => array( 'Group' => 'Distance', 'Unit Name' => 'Meter', 'AllowPrefix' => True ),
'mi' => array( 'Group' => 'Distance', 'Unit Name' => 'Statute mile', 'AllowPrefix' => False ),
'Nmi' => array( 'Group' => 'Distance', 'Unit Name' => 'Nautical mile', 'AllowPrefix' => False ),
'in' => array( 'Group' => 'Distance', 'Unit Name' => 'Inch', 'AllowPrefix' => False ),
'ft' => array( 'Group' => 'Distance', 'Unit Name' => 'Foot', 'AllowPrefix' => False ),
'yd' => array( 'Group' => 'Distance', 'Unit Name' => 'Yard', 'AllowPrefix' => False ),
'ang' => array( 'Group' => 'Distance', 'Unit Name' => 'Angstrom', 'AllowPrefix' => True ),
'Pica' => array( 'Group' => 'Distance', 'Unit Name' => 'Pica (1/72 in)', 'AllowPrefix' => False ),
'yr' => array( 'Group' => 'Time', 'Unit Name' => 'Year', 'AllowPrefix' => False ),
'day' => array( 'Group' => 'Time', 'Unit Name' => 'Day', 'AllowPrefix' => False ),
'hr' => array( 'Group' => 'Time', 'Unit Name' => 'Hour', 'AllowPrefix' => False ),
'mn' => array( 'Group' => 'Time', 'Unit Name' => 'Minute', 'AllowPrefix' => False ),
'sec' => array( 'Group' => 'Time', 'Unit Name' => 'Second', 'AllowPrefix' => True ),
'Pa' => array( 'Group' => 'Pressure', 'Unit Name' => 'Pascal', 'AllowPrefix' => True ),
'p' => array( 'Group' => 'Pressure', 'Unit Name' => 'Pascal', 'AllowPrefix' => True ),
'atm' => array( 'Group' => 'Pressure', 'Unit Name' => 'Atmosphere', 'AllowPrefix' => True ),
'at' => array( 'Group' => 'Pressure', 'Unit Name' => 'Atmosphere', 'AllowPrefix' => True ),
'mmHg' => array( 'Group' => 'Pressure', 'Unit Name' => 'mm of Mercury', 'AllowPrefix' => True ),
'N' => array( 'Group' => 'Force', 'Unit Name' => 'Newton', 'AllowPrefix' => True ),
'dyn' => array( 'Group' => 'Force', 'Unit Name' => 'Dyne', 'AllowPrefix' => True ),
'dy' => array( 'Group' => 'Force', 'Unit Name' => 'Dyne', 'AllowPrefix' => True ),
'lbf' => array( 'Group' => 'Force', 'Unit Name' => 'Pound force', 'AllowPrefix' => False ),
'J' => array( 'Group' => 'Energy', 'Unit Name' => 'Joule', 'AllowPrefix' => True ),
'e' => array( 'Group' => 'Energy', 'Unit Name' => 'Erg', 'AllowPrefix' => True ),
'c' => array( 'Group' => 'Energy', 'Unit Name' => 'Thermodynamic calorie', 'AllowPrefix' => True ),
'cal' => array( 'Group' => 'Energy', 'Unit Name' => 'IT calorie', 'AllowPrefix' => True ),
'eV' => array( 'Group' => 'Energy', 'Unit Name' => 'Electron volt', 'AllowPrefix' => True ),
'ev' => array( 'Group' => 'Energy', 'Unit Name' => 'Electron volt', 'AllowPrefix' => True ),
'HPh' => array( 'Group' => 'Energy', 'Unit Name' => 'Horsepower-hour', 'AllowPrefix' => False ),
'hh' => array( 'Group' => 'Energy', 'Unit Name' => 'Horsepower-hour', 'AllowPrefix' => False ),
'Wh' => array( 'Group' => 'Energy', 'Unit Name' => 'Watt-hour', 'AllowPrefix' => True ),
'wh' => array( 'Group' => 'Energy', 'Unit Name' => 'Watt-hour', 'AllowPrefix' => True ),
'flb' => array( 'Group' => 'Energy', 'Unit Name' => 'Foot-pound', 'AllowPrefix' => False ),
'BTU' => array( 'Group' => 'Energy', 'Unit Name' => 'BTU', 'AllowPrefix' => False ),
'btu' => array( 'Group' => 'Energy', 'Unit Name' => 'BTU', 'AllowPrefix' => False ),
'HP' => array( 'Group' => 'Power', 'Unit Name' => 'Horsepower', 'AllowPrefix' => False ),
'h' => array( 'Group' => 'Power', 'Unit Name' => 'Horsepower', 'AllowPrefix' => False ),
'W' => array( 'Group' => 'Power', 'Unit Name' => 'Watt', 'AllowPrefix' => True ),
'w' => array( 'Group' => 'Power', 'Unit Name' => 'Watt', 'AllowPrefix' => True ),
'T' => array( 'Group' => 'Magnetism', 'Unit Name' => 'Tesla', 'AllowPrefix' => True ),
'ga' => array( 'Group' => 'Magnetism', 'Unit Name' => 'Gauss', 'AllowPrefix' => True ),
'C' => array( 'Group' => 'Temperature', 'Unit Name' => 'Celsius', 'AllowPrefix' => False ),
'cel' => array( 'Group' => 'Temperature', 'Unit Name' => 'Celsius', 'AllowPrefix' => False ),
'F' => array( 'Group' => 'Temperature', 'Unit Name' => 'Fahrenheit', 'AllowPrefix' => False ),
'fah' => array( 'Group' => 'Temperature', 'Unit Name' => 'Fahrenheit', 'AllowPrefix' => False ),
'K' => array( 'Group' => 'Temperature', 'Unit Name' => 'Kelvin', 'AllowPrefix' => False ),
'kel' => array( 'Group' => 'Temperature', 'Unit Name' => 'Kelvin', 'AllowPrefix' => False ),
'tsp' => array( 'Group' => 'Liquid', 'Unit Name' => 'Teaspoon', 'AllowPrefix' => False ),
'tbs' => array( 'Group' => 'Liquid', 'Unit Name' => 'Tablespoon', 'AllowPrefix' => False ),
'oz' => array( 'Group' => 'Liquid', 'Unit Name' => 'Fluid Ounce', 'AllowPrefix' => False ),
'cup' => array( 'Group' => 'Liquid', 'Unit Name' => 'Cup', 'AllowPrefix' => False ),
'pt' => array( 'Group' => 'Liquid', 'Unit Name' => 'U.S. Pint', 'AllowPrefix' => False ),
'us_pt' => array( 'Group' => 'Liquid', 'Unit Name' => 'U.S. Pint', 'AllowPrefix' => False ),
'uk_pt' => array( 'Group' => 'Liquid', 'Unit Name' => 'U.K. Pint', 'AllowPrefix' => False ),
'qt' => array( 'Group' => 'Liquid', 'Unit Name' => 'Quart', 'AllowPrefix' => False ),
'gal' => array( 'Group' => 'Liquid', 'Unit Name' => 'Gallon', 'AllowPrefix' => False ),
'l' => array( 'Group' => 'Liquid', 'Unit Name' => 'Litre', 'AllowPrefix' => True ),
'lt' => array( 'Group' => 'Liquid', 'Unit Name' => 'Litre', 'AllowPrefix' => True )
);
/**
* Details of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM()
*
* @var mixed[]
*/
private static $_conversionMultipliers = array( 'Y' => array( 'multiplier' => 1E24, 'name' => 'yotta' ),
'Z' => array( 'multiplier' => 1E21, 'name' => 'zetta' ),
'E' => array( 'multiplier' => 1E18, 'name' => 'exa' ),
'P' => array( 'multiplier' => 1E15, 'name' => 'peta' ),
'T' => array( 'multiplier' => 1E12, 'name' => 'tera' ),
'G' => array( 'multiplier' => 1E9, 'name' => 'giga' ),
'M' => array( 'multiplier' => 1E6, 'name' => 'mega' ),
'k' => array( 'multiplier' => 1E3, 'name' => 'kilo' ),
'h' => array( 'multiplier' => 1E2, 'name' => 'hecto' ),
'e' => array( 'multiplier' => 1E1, 'name' => 'deka' ),
'd' => array( 'multiplier' => 1E-1, 'name' => 'deci' ),
'c' => array( 'multiplier' => 1E-2, 'name' => 'centi' ),
'm' => array( 'multiplier' => 1E-3, 'name' => 'milli' ),
'u' => array( 'multiplier' => 1E-6, 'name' => 'micro' ),
'n' => array( 'multiplier' => 1E-9, 'name' => 'nano' ),
'p' => array( 'multiplier' => 1E-12, 'name' => 'pico' ),
'f' => array( 'multiplier' => 1E-15, 'name' => 'femto' ),
'a' => array( 'multiplier' => 1E-18, 'name' => 'atto' ),
'z' => array( 'multiplier' => 1E-21, 'name' => 'zepto' ),
'y' => array( 'multiplier' => 1E-24, 'name' => 'yocto' )
);
/**
* Details of the Units of measure conversion factors, organised by group
*
* @var mixed[]
*/
private static $_unitConversions = array( 'Mass' => array( 'g' => array( 'g' => 1.0,
'sg' => 6.85220500053478E-05,
'lbm' => 2.20462291469134E-03,
'u' => 6.02217000000000E+23,
'ozm' => 3.52739718003627E-02
),
'sg' => array( 'g' => 1.45938424189287E+04,
'sg' => 1.0,
'lbm' => 3.21739194101647E+01,
'u' => 8.78866000000000E+27,
'ozm' => 5.14782785944229E+02
),
'lbm' => array( 'g' => 4.5359230974881148E+02,
'sg' => 3.10810749306493E-02,
'lbm' => 1.0,
'u' => 2.73161000000000E+26,
'ozm' => 1.60000023429410E+01
),
'u' => array( 'g' => 1.66053100460465E-24,
'sg' => 1.13782988532950E-28,
'lbm' => 3.66084470330684E-27,
'u' => 1.0,
'ozm' => 5.85735238300524E-26
),
'ozm' => array( 'g' => 2.83495152079732E+01,
'sg' => 1.94256689870811E-03,
'lbm' => 6.24999908478882E-02,
'u' => 1.70725600000000E+25,
'ozm' => 1.0
)
),
'Distance' => array( 'm' => array( 'm' => 1.0,
'mi' => 6.21371192237334E-04,
'Nmi' => 5.39956803455724E-04,
'in' => 3.93700787401575E+01,
'ft' => 3.28083989501312E+00,
'yd' => 1.09361329797891E+00,
'ang' => 1.00000000000000E+10,
'Pica' => 2.83464566929116E+03
),
'mi' => array( 'm' => 1.60934400000000E+03,
'mi' => 1.0,
'Nmi' => 8.68976241900648E-01,
'in' => 6.33600000000000E+04,
'ft' => 5.28000000000000E+03,
'yd' => 1.76000000000000E+03,
'ang' => 1.60934400000000E+13,
'Pica' => 4.56191999999971E+06
),
'Nmi' => array( 'm' => 1.85200000000000E+03,
'mi' => 1.15077944802354E+00,
'Nmi' => 1.0,
'in' => 7.29133858267717E+04,
'ft' => 6.07611548556430E+03,
'yd' => 2.02537182785694E+03,
'ang' => 1.85200000000000E+13,
'Pica' => 5.24976377952723E+06
),
'in' => array( 'm' => 2.54000000000000E-02,
'mi' => 1.57828282828283E-05,
'Nmi' => 1.37149028077754E-05,
'in' => 1.0,
'ft' => 8.33333333333333E-02,
'yd' => 2.77777777686643E-02,
'ang' => 2.54000000000000E+08,
'Pica' => 7.19999999999955E+01
),
'ft' => array( 'm' => 3.04800000000000E-01,
'mi' => 1.89393939393939E-04,
'Nmi' => 1.64578833693305E-04,
'in' => 1.20000000000000E+01,
'ft' => 1.0,
'yd' => 3.33333333223972E-01,
'ang' => 3.04800000000000E+09,
'Pica' => 8.63999999999946E+02
),
'yd' => array( 'm' => 9.14400000300000E-01,
'mi' => 5.68181818368230E-04,
'Nmi' => 4.93736501241901E-04,
'in' => 3.60000000118110E+01,
'ft' => 3.00000000000000E+00,
'yd' => 1.0,
'ang' => 9.14400000300000E+09,
'Pica' => 2.59200000085023E+03
),
'ang' => array( 'm' => 1.00000000000000E-10,
'mi' => 6.21371192237334E-14,
'Nmi' => 5.39956803455724E-14,
'in' => 3.93700787401575E-09,
'ft' => 3.28083989501312E-10,
'yd' => 1.09361329797891E-10,
'ang' => 1.0,
'Pica' => 2.83464566929116E-07
),
'Pica' => array( 'm' => 3.52777777777800E-04,
'mi' => 2.19205948372629E-07,
'Nmi' => 1.90484761219114E-07,
'in' => 1.38888888888898E-02,
'ft' => 1.15740740740748E-03,
'yd' => 3.85802469009251E-04,
'ang' => 3.52777777777800E+06,
'Pica' => 1.0
)
),
'Time' => array( 'yr' => array( 'yr' => 1.0,
'day' => 365.25,
'hr' => 8766.0,
'mn' => 525960.0,
'sec' => 31557600.0
),
'day' => array( 'yr' => 2.73785078713210E-03,
'day' => 1.0,
'hr' => 24.0,
'mn' => 1440.0,
'sec' => 86400.0
),
'hr' => array( 'yr' => 1.14077116130504E-04,
'day' => 4.16666666666667E-02,
'hr' => 1.0,
'mn' => 60.0,
'sec' => 3600.0
),
'mn' => array( 'yr' => 1.90128526884174E-06,
'day' => 6.94444444444444E-04,
'hr' => 1.66666666666667E-02,
'mn' => 1.0,
'sec' => 60.0
),
'sec' => array( 'yr' => 3.16880878140289E-08,
'day' => 1.15740740740741E-05,
'hr' => 2.77777777777778E-04,
'mn' => 1.66666666666667E-02,
'sec' => 1.0
)
),
'Pressure' => array( 'Pa' => array( 'Pa' => 1.0,
'p' => 1.0,
'atm' => 9.86923299998193E-06,
'at' => 9.86923299998193E-06,
'mmHg' => 7.50061707998627E-03
),
'p' => array( 'Pa' => 1.0,
'p' => 1.0,
'atm' => 9.86923299998193E-06,
'at' => 9.86923299998193E-06,
'mmHg' => 7.50061707998627E-03
),
'atm' => array( 'Pa' => 1.01324996583000E+05,
'p' => 1.01324996583000E+05,
'atm' => 1.0,
'at' => 1.0,
'mmHg' => 760.0
),
'at' => array( 'Pa' => 1.01324996583000E+05,
'p' => 1.01324996583000E+05,
'atm' => 1.0,
'at' => 1.0,
'mmHg' => 760.0
),
'mmHg' => array( 'Pa' => 1.33322363925000E+02,
'p' => 1.33322363925000E+02,
'atm' => 1.31578947368421E-03,
'at' => 1.31578947368421E-03,
'mmHg' => 1.0
)
),
'Force' => array( 'N' => array( 'N' => 1.0,
'dyn' => 1.0E+5,
'dy' => 1.0E+5,
'lbf' => 2.24808923655339E-01
),
'dyn' => array( 'N' => 1.0E-5,
'dyn' => 1.0,
'dy' => 1.0,
'lbf' => 2.24808923655339E-06
),
'dy' => array( 'N' => 1.0E-5,
'dyn' => 1.0,
'dy' => 1.0,
'lbf' => 2.24808923655339E-06
),
'lbf' => array( 'N' => 4.448222,
'dyn' => 4.448222E+5,
'dy' => 4.448222E+5,
'lbf' => 1.0
)
),
'Energy' => array( 'J' => array( 'J' => 1.0,
'e' => 9.99999519343231E+06,
'c' => 2.39006249473467E-01,
'cal' => 2.38846190642017E-01,
'eV' => 6.24145700000000E+18,
'ev' => 6.24145700000000E+18,
'HPh' => 3.72506430801000E-07,
'hh' => 3.72506430801000E-07,
'Wh' => 2.77777916238711E-04,
'wh' => 2.77777916238711E-04,
'flb' => 2.37304222192651E+01,
'BTU' => 9.47815067349015E-04,
'btu' => 9.47815067349015E-04
),
'e' => array( 'J' => 1.00000048065700E-07,
'e' => 1.0,
'c' => 2.39006364353494E-08,
'cal' => 2.38846305445111E-08,
'eV' => 6.24146000000000E+11,
'ev' => 6.24146000000000E+11,
'HPh' => 3.72506609848824E-14,
'hh' => 3.72506609848824E-14,
'Wh' => 2.77778049754611E-11,
'wh' => 2.77778049754611E-11,
'flb' => 2.37304336254586E-06,
'BTU' => 9.47815522922962E-11,
'btu' => 9.47815522922962E-11
),
'c' => array( 'J' => 4.18399101363672E+00,
'e' => 4.18398900257312E+07,
'c' => 1.0,
'cal' => 9.99330315287563E-01,
'eV' => 2.61142000000000E+19,
'ev' => 2.61142000000000E+19,
'HPh' => 1.55856355899327E-06,
'hh' => 1.55856355899327E-06,
'Wh' => 1.16222030532950E-03,
'wh' => 1.16222030532950E-03,
'flb' => 9.92878733152102E+01,
'BTU' => 3.96564972437776E-03,
'btu' => 3.96564972437776E-03
),
'cal' => array( 'J' => 4.18679484613929E+00,
'e' => 4.18679283372801E+07,
'c' => 1.00067013349059E+00,
'cal' => 1.0,
'eV' => 2.61317000000000E+19,
'ev' => 2.61317000000000E+19,
'HPh' => 1.55960800463137E-06,
'hh' => 1.55960800463137E-06,
'Wh' => 1.16299914807955E-03,
'wh' => 1.16299914807955E-03,
'flb' => 9.93544094443283E+01,
'BTU' => 3.96830723907002E-03,
'btu' => 3.96830723907002E-03
),
'eV' => array( 'J' => 1.60219000146921E-19,
'e' => 1.60218923136574E-12,
'c' => 3.82933423195043E-20,
'cal' => 3.82676978535648E-20,
'eV' => 1.0,
'ev' => 1.0,
'HPh' => 5.96826078912344E-26,
'hh' => 5.96826078912344E-26,
'Wh' => 4.45053000026614E-23,
'wh' => 4.45053000026614E-23,
'flb' => 3.80206452103492E-18,
'BTU' => 1.51857982414846E-22,
'btu' => 1.51857982414846E-22
),
'ev' => array( 'J' => 1.60219000146921E-19,
'e' => 1.60218923136574E-12,
'c' => 3.82933423195043E-20,
'cal' => 3.82676978535648E-20,
'eV' => 1.0,
'ev' => 1.0,
'HPh' => 5.96826078912344E-26,
'hh' => 5.96826078912344E-26,
'Wh' => 4.45053000026614E-23,
'wh' => 4.45053000026614E-23,
'flb' => 3.80206452103492E-18,
'BTU' => 1.51857982414846E-22,
'btu' => 1.51857982414846E-22
),
'HPh' => array( 'J' => 2.68451741316170E+06,
'e' => 2.68451612283024E+13,
'c' => 6.41616438565991E+05,
'cal' => 6.41186757845835E+05,
'eV' => 1.67553000000000E+25,
'ev' => 1.67553000000000E+25,
'HPh' => 1.0,
'hh' => 1.0,
'Wh' => 7.45699653134593E+02,
'wh' => 7.45699653134593E+02,
'flb' => 6.37047316692964E+07,
'BTU' => 2.54442605275546E+03,
'btu' => 2.54442605275546E+03
),
'hh' => array( 'J' => 2.68451741316170E+06,
'e' => 2.68451612283024E+13,
'c' => 6.41616438565991E+05,
'cal' => 6.41186757845835E+05,
'eV' => 1.67553000000000E+25,
'ev' => 1.67553000000000E+25,
'HPh' => 1.0,
'hh' => 1.0,
'Wh' => 7.45699653134593E+02,
'wh' => 7.45699653134593E+02,
'flb' => 6.37047316692964E+07,
'BTU' => 2.54442605275546E+03,
'btu' => 2.54442605275546E+03
),
'Wh' => array( 'J' => 3.59999820554720E+03,
'e' => 3.59999647518369E+10,
'c' => 8.60422069219046E+02,
'cal' => 8.59845857713046E+02,
'eV' => 2.24692340000000E+22,
'ev' => 2.24692340000000E+22,
'HPh' => 1.34102248243839E-03,
'hh' => 1.34102248243839E-03,
'Wh' => 1.0,
'wh' => 1.0,
'flb' => 8.54294774062316E+04,
'BTU' => 3.41213254164705E+00,
'btu' => 3.41213254164705E+00
),
'wh' => array( 'J' => 3.59999820554720E+03,
'e' => 3.59999647518369E+10,
'c' => 8.60422069219046E+02,
'cal' => 8.59845857713046E+02,
'eV' => 2.24692340000000E+22,
'ev' => 2.24692340000000E+22,
'HPh' => 1.34102248243839E-03,
'hh' => 1.34102248243839E-03,
'Wh' => 1.0,
'wh' => 1.0,
'flb' => 8.54294774062316E+04,
'BTU' => 3.41213254164705E+00,
'btu' => 3.41213254164705E+00
),
'flb' => array( 'J' => 4.21400003236424E-02,
'e' => 4.21399800687660E+05,
'c' => 1.00717234301644E-02,
'cal' => 1.00649785509554E-02,
'eV' => 2.63015000000000E+17,
'ev' => 2.63015000000000E+17,
'HPh' => 1.56974211145130E-08,
'hh' => 1.56974211145130E-08,
'Wh' => 1.17055614802000E-05,
'wh' => 1.17055614802000E-05,
'flb' => 1.0,
'BTU' => 3.99409272448406E-05,
'btu' => 3.99409272448406E-05
),
'BTU' => array( 'J' => 1.05505813786749E+03,
'e' => 1.05505763074665E+10,
'c' => 2.52165488508168E+02,
'cal' => 2.51996617135510E+02,
'eV' => 6.58510000000000E+21,
'ev' => 6.58510000000000E+21,
'HPh' => 3.93015941224568E-04,
'hh' => 3.93015941224568E-04,
'Wh' => 2.93071851047526E-01,
'wh' => 2.93071851047526E-01,
'flb' => 2.50369750774671E+04,
'BTU' => 1.0,
'btu' => 1.0,
),
'btu' => array( 'J' => 1.05505813786749E+03,
'e' => 1.05505763074665E+10,
'c' => 2.52165488508168E+02,
'cal' => 2.51996617135510E+02,
'eV' => 6.58510000000000E+21,
'ev' => 6.58510000000000E+21,
'HPh' => 3.93015941224568E-04,
'hh' => 3.93015941224568E-04,
'Wh' => 2.93071851047526E-01,
'wh' => 2.93071851047526E-01,
'flb' => 2.50369750774671E+04,
'BTU' => 1.0,
'btu' => 1.0,
)
),
'Power' => array( 'HP' => array( 'HP' => 1.0,
'h' => 1.0,
'W' => 7.45701000000000E+02,
'w' => 7.45701000000000E+02
),
'h' => array( 'HP' => 1.0,
'h' => 1.0,
'W' => 7.45701000000000E+02,
'w' => 7.45701000000000E+02
),
'W' => array( 'HP' => 1.34102006031908E-03,
'h' => 1.34102006031908E-03,
'W' => 1.0,
'w' => 1.0
),
'w' => array( 'HP' => 1.34102006031908E-03,
'h' => 1.34102006031908E-03,
'W' => 1.0,
'w' => 1.0
)
),
'Magnetism' => array( 'T' => array( 'T' => 1.0,
'ga' => 10000.0
),
'ga' => array( 'T' => 0.0001,
'ga' => 1.0
)
),
'Liquid' => array( 'tsp' => array( 'tsp' => 1.0,
'tbs' => 3.33333333333333E-01,
'oz' => 1.66666666666667E-01,
'cup' => 2.08333333333333E-02,
'pt' => 1.04166666666667E-02,
'us_pt' => 1.04166666666667E-02,
'uk_pt' => 8.67558516821960E-03,
'qt' => 5.20833333333333E-03,
'gal' => 1.30208333333333E-03,
'l' => 4.92999408400710E-03,
'lt' => 4.92999408400710E-03
),
'tbs' => array( 'tsp' => 3.00000000000000E+00,
'tbs' => 1.0,
'oz' => 5.00000000000000E-01,
'cup' => 6.25000000000000E-02,
'pt' => 3.12500000000000E-02,
'us_pt' => 3.12500000000000E-02,
'uk_pt' => 2.60267555046588E-02,
'qt' => 1.56250000000000E-02,
'gal' => 3.90625000000000E-03,
'l' => 1.47899822520213E-02,
'lt' => 1.47899822520213E-02
),
'oz' => array( 'tsp' => 6.00000000000000E+00,
'tbs' => 2.00000000000000E+00,
'oz' => 1.0,
'cup' => 1.25000000000000E-01,
'pt' => 6.25000000000000E-02,
'us_pt' => 6.25000000000000E-02,
'uk_pt' => 5.20535110093176E-02,
'qt' => 3.12500000000000E-02,
'gal' => 7.81250000000000E-03,
'l' => 2.95799645040426E-02,
'lt' => 2.95799645040426E-02
),
'cup' => array( 'tsp' => 4.80000000000000E+01,
'tbs' => 1.60000000000000E+01,
'oz' => 8.00000000000000E+00,
'cup' => 1.0,
'pt' => 5.00000000000000E-01,
'us_pt' => 5.00000000000000E-01,
'uk_pt' => 4.16428088074541E-01,
'qt' => 2.50000000000000E-01,
'gal' => 6.25000000000000E-02,
'l' => 2.36639716032341E-01,
'lt' => 2.36639716032341E-01
),
'pt' => array( 'tsp' => 9.60000000000000E+01,
'tbs' => 3.20000000000000E+01,
'oz' => 1.60000000000000E+01,
'cup' => 2.00000000000000E+00,
'pt' => 1.0,
'us_pt' => 1.0,
'uk_pt' => 8.32856176149081E-01,
'qt' => 5.00000000000000E-01,
'gal' => 1.25000000000000E-01,
'l' => 4.73279432064682E-01,
'lt' => 4.73279432064682E-01
),
'us_pt' => array( 'tsp' => 9.60000000000000E+01,
'tbs' => 3.20000000000000E+01,
'oz' => 1.60000000000000E+01,
'cup' => 2.00000000000000E+00,
'pt' => 1.0,
'us_pt' => 1.0,
'uk_pt' => 8.32856176149081E-01,
'qt' => 5.00000000000000E-01,
'gal' => 1.25000000000000E-01,
'l' => 4.73279432064682E-01,
'lt' => 4.73279432064682E-01
),
'uk_pt' => array( 'tsp' => 1.15266000000000E+02,
'tbs' => 3.84220000000000E+01,
'oz' => 1.92110000000000E+01,
'cup' => 2.40137500000000E+00,
'pt' => 1.20068750000000E+00,
'us_pt' => 1.20068750000000E+00,
'uk_pt' => 1.0,
'qt' => 6.00343750000000E-01,
'gal' => 1.50085937500000E-01,
'l' => 5.68260698087162E-01,
'lt' => 5.68260698087162E-01
),
'qt' => array( 'tsp' => 1.92000000000000E+02,
'tbs' => 6.40000000000000E+01,
'oz' => 3.20000000000000E+01,
'cup' => 4.00000000000000E+00,
'pt' => 2.00000000000000E+00,
'us_pt' => 2.00000000000000E+00,
'uk_pt' => 1.66571235229816E+00,
'qt' => 1.0,
'gal' => 2.50000000000000E-01,
'l' => 9.46558864129363E-01,
'lt' => 9.46558864129363E-01
),
'gal' => array( 'tsp' => 7.68000000000000E+02,
'tbs' => 2.56000000000000E+02,
'oz' => 1.28000000000000E+02,
'cup' => 1.60000000000000E+01,
'pt' => 8.00000000000000E+00,
'us_pt' => 8.00000000000000E+00,
'uk_pt' => 6.66284940919265E+00,
'qt' => 4.00000000000000E+00,
'gal' => 1.0,
'l' => 3.78623545651745E+00,
'lt' => 3.78623545651745E+00
),
'l' => array( 'tsp' => 2.02840000000000E+02,
'tbs' => 6.76133333333333E+01,
'oz' => 3.38066666666667E+01,
'cup' => 4.22583333333333E+00,
'pt' => 2.11291666666667E+00,
'us_pt' => 2.11291666666667E+00,
'uk_pt' => 1.75975569552166E+00,
'qt' => 1.05645833333333E+00,
'gal' => 2.64114583333333E-01,
'l' => 1.0,
'lt' => 1.0
),
'lt' => array( 'tsp' => 2.02840000000000E+02,
'tbs' => 6.76133333333333E+01,
'oz' => 3.38066666666667E+01,
'cup' => 4.22583333333333E+00,
'pt' => 2.11291666666667E+00,
'us_pt' => 2.11291666666667E+00,
'uk_pt' => 1.75975569552166E+00,
'qt' => 1.05645833333333E+00,
'gal' => 2.64114583333333E-01,
'l' => 1.0,
'lt' => 1.0
)
)
);
/**
* _parseComplex
*
* Parses a complex number into its real and imaginary parts, and an I or J suffix
*
* @param string $complexNumber The complex number
* @return string[] Indexed on "real", "imaginary" and "suffix"
*/
public static function _parseComplex($complexNumber) {
$workString = (string) $complexNumber;
$realNumber = $imaginary = 0;
// Extract the suffix, if there is one
$suffix = substr($workString,-1);
if (!is_numeric($suffix)) {
$workString = substr($workString,0,-1);
} else {
$suffix = '';
}
// Split the input into its Real and Imaginary components
$leadingSign = 0;
if (strlen($workString) > 0) {
$leadingSign = (($workString{0} == '+') || ($workString{0} == '-')) ? 1 : 0;
}
$power = '';
$realNumber = strtok($workString, '+-');
if (strtoupper(substr($realNumber,-1)) == 'E') {
$power = strtok('+-');
++$leadingSign;
}
$realNumber = substr($workString,0,strlen($realNumber)+strlen($power)+$leadingSign);
if ($suffix != '') {
$imaginary = substr($workString,strlen($realNumber));
if (($imaginary == '') && (($realNumber == '') || ($realNumber == '+') || ($realNumber == '-'))) {
$imaginary = $realNumber.'1';
$realNumber = '0';
} else if ($imaginary == '') {
$imaginary = $realNumber;
$realNumber = '0';
} elseif (($imaginary == '+') || ($imaginary == '-')) {
$imaginary .= '1';
}
}
return array( 'real' => $realNumber,
'imaginary' => $imaginary,
'suffix' => $suffix
);
} // function _parseComplex()
/**
* _cleanComplex
*
* Cleans the leading characters in a complex number string
*
* @param string $complexNumber The complex number to clean
* @return string The "cleaned" complex number
*/
private static function _cleanComplex($complexNumber) {
if ($complexNumber{0} == '+') $complexNumber = substr($complexNumber,1);
if ($complexNumber{0} == '0') $complexNumber = substr($complexNumber,1);
if ($complexNumber{0} == '.') $complexNumber = '0'.$complexNumber;
if ($complexNumber{0} == '+') $complexNumber = substr($complexNumber,1);
return $complexNumber;
}
private static function _nbrConversionFormat($xVal,$places) {
if (!is_null($places)) {
if (strlen($xVal) <= $places) {
return substr(str_pad($xVal,$places,'0',STR_PAD_LEFT),-10);
} else {
return PHPExcel_Calculation_Functions::NaN();
}
}
return substr($xVal,-10);
} // function _nbrConversionFormat()
/**
* BESSELI
*
* Returns the modified Bessel function In(x), which is equivalent to the Bessel function evaluated
* for purely imaginary arguments
*
* Excel Function:
* BESSELI(x,ord)
*
* @access public
* @category Engineering Functions
* @param float $x The value at which to evaluate the function.
* If x is nonnumeric, BESSELI returns the #VALUE! error value.
* @param integer $ord The order of the Bessel function.
* If ord is not an integer, it is truncated.
* If $ord is nonnumeric, BESSELI returns the #VALUE! error value.
* If $ord < 0, BESSELI returns the #NUM! error value.
* @return float
*
*/
public static function BESSELI($x, $ord) {
$x = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
$ord = (is_null($ord)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);
if ((is_numeric($x)) && (is_numeric($ord))) {
$ord = floor($ord);
if ($ord < 0) {
return PHPExcel_Calculation_Functions::NaN();
}
if (abs($x) <= 30) {
$fResult = $fTerm = pow($x / 2, $ord) / PHPExcel_Calculation_MathTrig::FACT($ord);
$ordK = 1;
$fSqrX = ($x * $x) / 4;
do {
$fTerm *= $fSqrX;
$fTerm /= ($ordK * ($ordK + $ord));
$fResult += $fTerm;
} while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
} else {
$f_2_PI = 2 * M_PI;
$fXAbs = abs($x);
$fResult = exp($fXAbs) / sqrt($f_2_PI * $fXAbs);
if (($ord & 1) && ($x < 0)) {
$fResult = -$fResult;
}
}
return (is_nan($fResult)) ? PHPExcel_Calculation_Functions::NaN() : $fResult;
}
return PHPExcel_Calculation_Functions::VALUE();
} // function BESSELI()
/**
* BESSELJ
*
* Returns the Bessel function
*
* Excel Function:
* BESSELJ(x,ord)
*
* @access public
* @category Engineering Functions
* @param float $x The value at which to evaluate the function.
* If x is nonnumeric, BESSELJ returns the #VALUE! error value.
* @param integer $ord The order of the Bessel function. If n is not an integer, it is truncated.
* If $ord is nonnumeric, BESSELJ returns the #VALUE! error value.
* If $ord < 0, BESSELJ returns the #NUM! error value.
* @return float
*
*/
public static function BESSELJ($x, $ord) {
$x = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
$ord = (is_null($ord)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);
if ((is_numeric($x)) && (is_numeric($ord))) {
$ord = floor($ord);
if ($ord < 0) {
return PHPExcel_Calculation_Functions::NaN();
}
$fResult = 0;
if (abs($x) <= 30) {
$fResult = $fTerm = pow($x / 2, $ord) / PHPExcel_Calculation_MathTrig::FACT($ord);
$ordK = 1;
$fSqrX = ($x * $x) / -4;
do {
$fTerm *= $fSqrX;
$fTerm /= ($ordK * ($ordK + $ord));
$fResult += $fTerm;
} while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
} else {
$f_PI_DIV_2 = M_PI / 2;
$f_PI_DIV_4 = M_PI / 4;
$fXAbs = abs($x);
$fResult = sqrt(M_2DIVPI / $fXAbs) * cos($fXAbs - $ord * $f_PI_DIV_2 - $f_PI_DIV_4);
if (($ord & 1) && ($x < 0)) {
$fResult = -$fResult;
}
}
return (is_nan($fResult)) ? PHPExcel_Calculation_Functions::NaN() : $fResult;
}
return PHPExcel_Calculation_Functions::VALUE();
} // function BESSELJ()
private static function _Besselk0($fNum) {
if ($fNum <= 2) {
$fNum2 = $fNum * 0.5;
$y = ($fNum2 * $fNum2);
$fRet = -log($fNum2) * self::BESSELI($fNum, 0) +
(-0.57721566 + $y * (0.42278420 + $y * (0.23069756 + $y * (0.3488590e-1 + $y * (0.262698e-2 + $y *
(0.10750e-3 + $y * 0.74e-5))))));
} else {
$y = 2 / $fNum;
$fRet = exp(-$fNum) / sqrt($fNum) *
(1.25331414 + $y * (-0.7832358e-1 + $y * (0.2189568e-1 + $y * (-0.1062446e-1 + $y *
(0.587872e-2 + $y * (-0.251540e-2 + $y * 0.53208e-3))))));
}
return $fRet;
} // function _Besselk0()
private static function _Besselk1($fNum) {
if ($fNum <= 2) {
$fNum2 = $fNum * 0.5;
$y = ($fNum2 * $fNum2);
$fRet = log($fNum2) * self::BESSELI($fNum, 1) +
(1 + $y * (0.15443144 + $y * (-0.67278579 + $y * (-0.18156897 + $y * (-0.1919402e-1 + $y *
(-0.110404e-2 + $y * (-0.4686e-4))))))) / $fNum;
} else {
$y = 2 / $fNum;
$fRet = exp(-$fNum) / sqrt($fNum) *
(1.25331414 + $y * (0.23498619 + $y * (-0.3655620e-1 + $y * (0.1504268e-1 + $y * (-0.780353e-2 + $y *
(0.325614e-2 + $y * (-0.68245e-3)))))));
}
return $fRet;
} // function _Besselk1()
/**
* BESSELK
*
* Returns the modified Bessel function Kn(x), which is equivalent to the Bessel functions evaluated
* for purely imaginary arguments.
*
* Excel Function:
* BESSELK(x,ord)
*
* @access public
* @category Engineering Functions
* @param float $x The value at which to evaluate the function.
* If x is nonnumeric, BESSELK returns the #VALUE! error value.
* @param integer $ord The order of the Bessel function. If n is not an integer, it is truncated.
* If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
* If $ord < 0, BESSELK returns the #NUM! error value.
* @return float
*
*/
public static function BESSELK($x, $ord) {
$x = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
$ord = (is_null($ord)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);
if ((is_numeric($x)) && (is_numeric($ord))) {
if (($ord < 0) || ($x == 0.0)) {
return PHPExcel_Calculation_Functions::NaN();
}
switch(floor($ord)) {
case 0 : return self::_Besselk0($x);
break;
case 1 : return self::_Besselk1($x);
break;
default : $fTox = 2 / $x;
$fBkm = self::_Besselk0($x);
$fBk = self::_Besselk1($x);
for ($n = 1; $n < $ord; ++$n) {
$fBkp = $fBkm + $n * $fTox * $fBk;
$fBkm = $fBk;
$fBk = $fBkp;
}
}
return (is_nan($fBk)) ? PHPExcel_Calculation_Functions::NaN() : $fBk;
}
return PHPExcel_Calculation_Functions::VALUE();
} // function BESSELK()
private static function _Bessely0($fNum) {
if ($fNum < 8.0) {
$y = ($fNum * $fNum);
$f1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y * (-86327.92757 + $y * 228.4622733))));
$f2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y * (47447.26470 + $y * (226.1030244 + $y))));
$fRet = $f1 / $f2 + 0.636619772 * self::BESSELJ($fNum, 0) * log($fNum);
} else {
$z = 8.0 / $fNum;
$y = ($z * $z);
$xx = $fNum - 0.785398164;
$f1 = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
$f2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y * (-0.934945152e-7))));
$fRet = sqrt(0.636619772 / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
}
return $fRet;
} // function _Bessely0()
private static function _Bessely1($fNum) {
if ($fNum < 8.0) {
$y = ($fNum * $fNum);
$f1 = $fNum * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y * (0.7349264551e9 + $y *
(-0.4237922726e7 + $y * 0.8511937935e4)))));
$f2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y *
(0.1020426050e6 + $y * (0.3549632885e3 + $y)))));
$fRet = $f1 / $f2 + 0.636619772 * ( self::BESSELJ($fNum, 1) * log($fNum) - 1 / $fNum);
} else {
$fRet = sqrt(0.636619772 / $fNum) * sin($fNum - 2.356194491);
}
return $fRet;
} // function _Bessely1()
/**
* BESSELY
*
* Returns the Bessel function, which is also called the Weber function or the Neumann function.
*
* Excel Function:
* BESSELY(x,ord)
*
* @access public
* @category Engineering Functions
* @param float $x The value at which to evaluate the function.
* If x is nonnumeric, BESSELK returns the #VALUE! error value.
* @param integer $ord The order of the Bessel function. If n is not an integer, it is truncated.
* If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
* If $ord < 0, BESSELK returns the #NUM! error value.
*
* @return float
*/
public static function BESSELY($x, $ord) {
$x = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
$ord = (is_null($ord)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);
if ((is_numeric($x)) && (is_numeric($ord))) {
if (($ord < 0) || ($x == 0.0)) {
return PHPExcel_Calculation_Functions::NaN();
}
switch(floor($ord)) {
case 0 : return self::_Bessely0($x);
break;
case 1 : return self::_Bessely1($x);
break;
default: $fTox = 2 / $x;
$fBym = self::_Bessely0($x);
$fBy = self::_Bessely1($x);
for ($n = 1; $n < $ord; ++$n) {
$fByp = $n * $fTox * $fBy - $fBym;
$fBym = $fBy;
$fBy = $fByp;
}
}
return (is_nan($fBy)) ? PHPExcel_Calculation_Functions::NaN() : $fBy;
}
return PHPExcel_Calculation_Functions::VALUE();
} // function BESSELY()
/**
* BINTODEC
*
* Return a binary value as decimal.
*
* Excel Function:
* BIN2DEC(x)
*
* @access public
* @category Engineering Functions
* @param string $x The binary number (as a string) that you want to convert. The number
* cannot contain more than 10 characters (10 bits). The most significant
* bit of number is the sign bit. The remaining 9 bits are magnitude bits.
* Negative numbers are represented using two's-complement notation.
* If number is not a valid binary number, or if number contains more than
* 10 characters (10 bits), BIN2DEC returns the #NUM! error value.
* @return string
*/
public static function BINTODEC($x) {
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
if (is_bool($x)) {
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return PHPExcel_Calculation_Functions::VALUE();
}
}
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
$x = floor($x);
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
return PHPExcel_Calculation_Functions::NaN();
}
if (strlen($x) > 10) {
return PHPExcel_Calculation_Functions::NaN();
} elseif (strlen($x) == 10) {
// Two's Complement
$x = substr($x,-9);
return '-'.(512-bindec($x));
}
return bindec($x);
} // function BINTODEC()
/**
* BINTOHEX
*
* Return a binary value as hex.
*
* Excel Function:
* BIN2HEX(x[,places])
*
* @access public
* @category Engineering Functions
* @param string $x The binary number (as a string) that you want to convert. The number
* cannot contain more than 10 characters (10 bits). The most significant
* bit of number is the sign bit. The remaining 9 bits are magnitude bits.
* Negative numbers are represented using two's-complement notation.
* If number is not a valid binary number, or if number contains more than
* 10 characters (10 bits), BIN2HEX returns the #NUM! error value.
* @param integer $places The number of characters to use. If places is omitted, BIN2HEX uses the
* minimum number of characters necessary. Places is useful for padding the
* return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, BIN2HEX returns the #VALUE! error value.
* If places is negative, BIN2HEX returns the #NUM! error value.
* @return string
*/
public static function BINTOHEX($x, $places=NULL) {
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
if (is_bool($x)) {
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return PHPExcel_Calculation_Functions::VALUE();
}
}
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
$x = floor($x);
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
return PHPExcel_Calculation_Functions::NaN();
}
if (strlen($x) > 10) {
return PHPExcel_Calculation_Functions::NaN();
} elseif (strlen($x) == 10) {
// Two's Complement
return str_repeat('F',8).substr(strtoupper(dechex(bindec(substr($x,-9)))),-2);
}
$hexVal = (string) strtoupper(dechex(bindec($x)));
return self::_nbrConversionFormat($hexVal,$places);
} // function BINTOHEX()
/**
* BINTOOCT
*
* Return a binary value as octal.
*
* Excel Function:
* BIN2OCT(x[,places])
*
* @access public
* @category Engineering Functions
* @param string $x The binary number (as a string) that you want to convert. The number
* cannot contain more than 10 characters (10 bits). The most significant
* bit of number is the sign bit. The remaining 9 bits are magnitude bits.
* Negative numbers are represented using two's-complement notation.
* If number is not a valid binary number, or if number contains more than
* 10 characters (10 bits), BIN2OCT returns the #NUM! error value.
* @param integer $places The number of characters to use. If places is omitted, BIN2OCT uses the
* minimum number of characters necessary. Places is useful for padding the
* return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, BIN2OCT returns the #VALUE! error value.
* If places is negative, BIN2OCT returns the #NUM! error value.
* @return string
*/
public static function BINTOOCT($x, $places=NULL) {
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
if (is_bool($x)) {
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return PHPExcel_Calculation_Functions::VALUE();
}
}
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
$x = floor($x);
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
return PHPExcel_Calculation_Functions::NaN();
}
if (strlen($x) > 10) {
return PHPExcel_Calculation_Functions::NaN();
} elseif (strlen($x) == 10) {
// Two's Complement
return str_repeat('7',7).substr(strtoupper(decoct(bindec(substr($x,-9)))),-3);
}
$octVal = (string) decoct(bindec($x));
return self::_nbrConversionFormat($octVal,$places);
} // function BINTOOCT()
/**
* DECTOBIN
*
* Return a decimal value as binary.
*
* Excel Function:
* DEC2BIN(x[,places])
*
* @access public
* @category Engineering Functions
* @param string $x The decimal integer you want to convert. If number is negative,
* valid place values are ignored and DEC2BIN returns a 10-character
* (10-bit) binary number in which the most significant bit is the sign
* bit. The remaining 9 bits are magnitude bits. Negative numbers are
* represented using two's-complement notation.
* If number < -512 or if number > 511, DEC2BIN returns the #NUM! error
* value.
* If number is nonnumeric, DEC2BIN returns the #VALUE! error value.
* If DEC2BIN requires more than places characters, it returns the #NUM!
* error value.
* @param integer $places The number of characters to use. If places is omitted, DEC2BIN uses
* the minimum number of characters necessary. Places is useful for
* padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, DEC2BIN returns the #VALUE! error value.
* If places is zero or negative, DEC2BIN returns the #NUM! error value.
* @return string
*/
public static function DECTOBIN($x, $places=NULL) {
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
if (is_bool($x)) {
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return PHPExcel_Calculation_Functions::VALUE();
}
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
return PHPExcel_Calculation_Functions::VALUE();
}
$x = (string) floor($x);
$r = decbin($x);
if (strlen($r) == 32) {
// Two's Complement
$r = substr($r,-10);
} elseif (strlen($r) > 11) {
return PHPExcel_Calculation_Functions::NaN();
}
return self::_nbrConversionFormat($r,$places);
} // function DECTOBIN()
/**
* DECTOHEX
*
* Return a decimal value as hex.
*
* Excel Function:
* DEC2HEX(x[,places])
*
* @access public
* @category Engineering Functions
* @param string $x The decimal integer you want to convert. If number is negative,
* places is ignored and DEC2HEX returns a 10-character (40-bit)
* hexadecimal number in which the most significant bit is the sign
* bit. The remaining 39 bits are magnitude bits. Negative numbers
* are represented using two's-complement notation.
* If number < -549,755,813,888 or if number > 549,755,813,887,
* DEC2HEX returns the #NUM! error value.
* If number is nonnumeric, DEC2HEX returns the #VALUE! error value.
* If DEC2HEX requires more than places characters, it returns the
* #NUM! error value.
* @param integer $places The number of characters to use. If places is omitted, DEC2HEX uses
* the minimum number of characters necessary. Places is useful for
* padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, DEC2HEX returns the #VALUE! error value.
* If places is zero or negative, DEC2HEX returns the #NUM! error value.
* @return string
*/
public static function DECTOHEX($x, $places=null) {
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
if (is_bool($x)) {
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return PHPExcel_Calculation_Functions::VALUE();
}
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
return PHPExcel_Calculation_Functions::VALUE();
}
$x = (string) floor($x);
$r = strtoupper(dechex($x));
if (strlen($r) == 8) {
// Two's Complement
$r = 'FF'.$r;
}
return self::_nbrConversionFormat($r,$places);
} // function DECTOHEX()
/**
* DECTOOCT
*
* Return an decimal value as octal.
*
* Excel Function:
* DEC2OCT(x[,places])
*
* @access public
* @category Engineering Functions
* @param string $x The decimal integer you want to convert. If number is negative,
* places is ignored and DEC2OCT returns a 10-character (30-bit)
* octal number in which the most significant bit is the sign bit.
* The remaining 29 bits are magnitude bits. Negative numbers are
* represented using two's-complement notation.
* If number < -536,870,912 or if number > 536,870,911, DEC2OCT
* returns the #NUM! error value.
* If number is nonnumeric, DEC2OCT returns the #VALUE! error value.
* If DEC2OCT requires more than places characters, it returns the
* #NUM! error value.
* @param integer $places The number of characters to use. If places is omitted, DEC2OCT uses
* the minimum number of characters necessary. Places is useful for
* padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, DEC2OCT returns the #VALUE! error value.
* If places is zero or negative, DEC2OCT returns the #NUM! error value.
* @return string
*/
public static function DECTOOCT($x, $places=null) {
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
if (is_bool($x)) {
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return PHPExcel_Calculation_Functions::VALUE();
}
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
return PHPExcel_Calculation_Functions::VALUE();
}
$x = (string) floor($x);
$r = decoct($x);
if (strlen($r) == 11) {
// Two's Complement
$r = substr($r,-10);
}
return self::_nbrConversionFormat($r,$places);
} // function DECTOOCT()
/**
* HEXTOBIN
*
* Return a hex value as binary.
*
* Excel Function:
* HEX2BIN(x[,places])
*
* @access public
* @category Engineering Functions
* @param string $x the hexadecimal number you want to convert. Number cannot
* contain more than 10 characters. The most significant bit of
* number is the sign bit (40th bit from the right). The remaining
* 9 bits are magnitude bits. Negative numbers are represented
* using two's-complement notation.
* If number is negative, HEX2BIN ignores places and returns a
* 10-character binary number.
* If number is negative, it cannot be less than FFFFFFFE00, and
* if number is positive, it cannot be greater than 1FF.
* If number is not a valid hexadecimal number, HEX2BIN returns
* the #NUM! error value.
* If HEX2BIN requires more than places characters, it returns
* the #NUM! error value.
* @param integer $places The number of characters to use. If places is omitted,
* HEX2BIN uses the minimum number of characters necessary. Places
* is useful for padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, HEX2BIN returns the #VALUE! error value.
* If places is negative, HEX2BIN returns the #NUM! error value.
* @return string
*/
public static function HEXTOBIN($x, $places=null) {
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
if (is_bool($x)) {
return PHPExcel_Calculation_Functions::VALUE();
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
return PHPExcel_Calculation_Functions::NaN();
}
$binVal = decbin(hexdec($x));
return substr(self::_nbrConversionFormat($binVal,$places),-10);
} // function HEXTOBIN()
/**
* HEXTODEC
*
* Return a hex value as decimal.
*
* Excel Function:
* HEX2DEC(x)
*
* @access public
* @category Engineering Functions
* @param string $x The hexadecimal number you want to convert. This number cannot
* contain more than 10 characters (40 bits). The most significant
* bit of number is the sign bit. The remaining 39 bits are magnitude
* bits. Negative numbers are represented using two's-complement
* notation.
* If number is not a valid hexadecimal number, HEX2DEC returns the
* #NUM! error value.
* @return string
*/
public static function HEXTODEC($x) {
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
if (is_bool($x)) {
return PHPExcel_Calculation_Functions::VALUE();
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
return PHPExcel_Calculation_Functions::NaN();
}
return hexdec($x);
} // function HEXTODEC()
/**
* HEXTOOCT
*
* Return a hex value as octal.
*
* Excel Function:
* HEX2OCT(x[,places])
*
* @access public
* @category Engineering Functions
* @param string $x The hexadecimal number you want to convert. Number cannot
* contain more than 10 characters. The most significant bit of
* number is the sign bit. The remaining 39 bits are magnitude
* bits. Negative numbers are represented using two's-complement
* notation.
* If number is negative, HEX2OCT ignores places and returns a
* 10-character octal number.
* If number is negative, it cannot be less than FFE0000000, and
* if number is positive, it cannot be greater than 1FFFFFFF.
* If number is not a valid hexadecimal number, HEX2OCT returns
* the #NUM! error value.
* If HEX2OCT requires more than places characters, it returns
* the #NUM! error value.
* @param integer $places The number of characters to use. If places is omitted, HEX2OCT
* uses the minimum number of characters necessary. Places is
* useful for padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, HEX2OCT returns the #VALUE! error
* value.
* If places is negative, HEX2OCT returns the #NUM! error value.
* @return string
*/
public static function HEXTOOCT($x, $places=null) {
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
if (is_bool($x)) {
return PHPExcel_Calculation_Functions::VALUE();
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
return PHPExcel_Calculation_Functions::NaN();
}
$octVal = decoct(hexdec($x));
return self::_nbrConversionFormat($octVal,$places);
} // function HEXTOOCT()
/**
* OCTTOBIN
*
* Return an octal value as binary.
*
* Excel Function:
* OCT2BIN(x[,places])
*
* @access public
* @category Engineering Functions
* @param string $x The octal number you want to convert. Number may not
* contain more than 10 characters. The most significant
* bit of number is the sign bit. The remaining 29 bits
* are magnitude bits. Negative numbers are represented
* using two's-complement notation.
* If number is negative, OCT2BIN ignores places and returns
* a 10-character binary number.
* If number is negative, it cannot be less than 7777777000,
* and if number is positive, it cannot be greater than 777.
* If number is not a valid octal number, OCT2BIN returns
* the #NUM! error value.
* If OCT2BIN requires more than places characters, it
* returns the #NUM! error value.
* @param integer $places The number of characters to use. If places is omitted,
* OCT2BIN uses the minimum number of characters necessary.
* Places is useful for padding the return value with
* leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, OCT2BIN returns the #VALUE!
* error value.
* If places is negative, OCT2BIN returns the #NUM! error
* value.
* @return string
*/
public static function OCTTOBIN($x, $places=null) {
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
if (is_bool($x)) {
return PHPExcel_Calculation_Functions::VALUE();
}
$x = (string) $x;
if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
return PHPExcel_Calculation_Functions::NaN();
}
$r = decbin(octdec($x));
return self::_nbrConversionFormat($r,$places);
} // function OCTTOBIN()
/**
* OCTTODEC
*
* Return an octal value as decimal.
*
* Excel Function:
* OCT2DEC(x)
*
* @access public
* @category Engineering Functions
* @param string $x The octal number you want to convert. Number may not contain
* more than 10 octal characters (30 bits). The most significant
* bit of number is the sign bit. The remaining 29 bits are
* magnitude bits. Negative numbers are represented using
* two's-complement notation.
* If number is not a valid octal number, OCT2DEC returns the
* #NUM! error value.
* @return string
*/
public static function OCTTODEC($x) {
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
if (is_bool($x)) {
return PHPExcel_Calculation_Functions::VALUE();
}
$x = (string) $x;
if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
return PHPExcel_Calculation_Functions::NaN();
}
return octdec($x);
} // function OCTTODEC()
/**
* OCTTOHEX
*
* Return an octal value as hex.
*
* Excel Function:
* OCT2HEX(x[,places])
*
* @access public
* @category Engineering Functions
* @param string $x The octal number you want to convert. Number may not contain
* more than 10 octal characters (30 bits). The most significant
* bit of number is the sign bit. The remaining 29 bits are
* magnitude bits. Negative numbers are represented using
* two's-complement notation.
* If number is negative, OCT2HEX ignores places and returns a
* 10-character hexadecimal number.
* If number is not a valid octal number, OCT2HEX returns the
* #NUM! error value.
* If OCT2HEX requires more than places characters, it returns
* the #NUM! error value.
* @param integer $places The number of characters to use. If places is omitted, OCT2HEX
* uses the minimum number of characters necessary. Places is useful
* for padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, OCT2HEX returns the #VALUE! error value.
* If places is negative, OCT2HEX returns the #NUM! error value.
* @return string
*/
public static function OCTTOHEX($x, $places=null) {
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
$places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
if (is_bool($x)) {
return PHPExcel_Calculation_Functions::VALUE();
}
$x = (string) $x;
if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
return PHPExcel_Calculation_Functions::NaN();
}
$hexVal = strtoupper(dechex(octdec($x)));
return self::_nbrConversionFormat($hexVal,$places);
} // function OCTTOHEX()
/**
* COMPLEX
*
* Converts real and imaginary coefficients into a complex number of the form x + yi or x + yj.
*
* Excel Function:
* COMPLEX(realNumber,imaginary[,places])
*
* @access public
* @category Engineering Functions
* @param float $realNumber The real coefficient of the complex number.
* @param float $imaginary The imaginary coefficient of the complex number.
* @param string $suffix The suffix for the imaginary component of the complex number.
* If omitted, the suffix is assumed to be "i".
* @return string
*/
public static function COMPLEX($realNumber=0.0, $imaginary=0.0, $suffix='i') {
$realNumber = (is_null($realNumber)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);
$imaginary = (is_null($imaginary)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($imaginary);
$suffix = (is_null($suffix)) ? 'i' : PHPExcel_Calculation_Functions::flattenSingleValue($suffix);
if (((is_numeric($realNumber)) && (is_numeric($imaginary))) &&
(($suffix == 'i') || ($suffix == 'j') || ($suffix == ''))) {
$realNumber = (float) $realNumber;
$imaginary = (float) $imaginary;
if ($suffix == '') $suffix = 'i';
if ($realNumber == 0.0) {
if ($imaginary == 0.0) {
return (string) '0';
} elseif ($imaginary == 1.0) {
return (string) $suffix;
} elseif ($imaginary == -1.0) {
return (string) '-'.$suffix;
}
return (string) $imaginary.$suffix;
} elseif ($imaginary == 0.0) {
return (string) $realNumber;
} elseif ($imaginary == 1.0) {
return (string) $realNumber.'+'.$suffix;
} elseif ($imaginary == -1.0) {
return (string) $realNumber.'-'.$suffix;
}
if ($imaginary > 0) { $imaginary = (string) '+'.$imaginary; }
return (string) $realNumber.$imaginary.$suffix;
}
return PHPExcel_Calculation_Functions::VALUE();
} // function COMPLEX()
/**
* IMAGINARY
*
* Returns the imaginary coefficient of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMAGINARY(complexNumber)
*
* @access public
* @category Engineering Functions
* @param string $complexNumber The complex number for which you want the imaginary
* coefficient.
* @return float
*/
public static function IMAGINARY($complexNumber) {
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
$parsedComplex = self::_parseComplex($complexNumber);
return $parsedComplex['imaginary'];
} // function IMAGINARY()
/**
* IMREAL
*
* Returns the real coefficient of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMREAL(complexNumber)
*
* @access public
* @category Engineering Functions
* @param string $complexNumber The complex number for which you want the real coefficient.
* @return float
*/
public static function IMREAL($complexNumber) {
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
$parsedComplex = self::_parseComplex($complexNumber);
return $parsedComplex['real'];
} // function IMREAL()
/**
* IMABS
*
* Returns the absolute value (modulus) of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMABS(complexNumber)
*
* @param string $complexNumber The complex number for which you want the absolute value.
* @return float
*/
public static function IMABS($complexNumber) {
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
$parsedComplex = self::_parseComplex($complexNumber);
return sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
} // function IMABS()
/**
* IMARGUMENT
*
* Returns the argument theta of a complex number, i.e. the angle in radians from the real
* axis to the representation of the number in polar coordinates.
*
* Excel Function:
* IMARGUMENT(complexNumber)
*
* @param string $complexNumber The complex number for which you want the argument theta.
* @return float
*/
public static function IMARGUMENT($complexNumber) {
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
$parsedComplex = self::_parseComplex($complexNumber);
if ($parsedComplex['real'] == 0.0) {
if ($parsedComplex['imaginary'] == 0.0) {
return 0.0;
} elseif($parsedComplex['imaginary'] < 0.0) {
return M_PI / -2;
} else {
return M_PI / 2;
}
} elseif ($parsedComplex['real'] > 0.0) {
return atan($parsedComplex['imaginary'] / $parsedComplex['real']);
} elseif ($parsedComplex['imaginary'] < 0.0) {
return 0 - (M_PI - atan(abs($parsedComplex['imaginary']) / abs($parsedComplex['real'])));
} else {
return M_PI - atan($parsedComplex['imaginary'] / abs($parsedComplex['real']));
}
} // function IMARGUMENT()
/**
* IMCONJUGATE
*
* Returns the complex conjugate of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMCONJUGATE(complexNumber)
*
* @param string $complexNumber The complex number for which you want the conjugate.
* @return string
*/
public static function IMCONJUGATE($complexNumber) {
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
$parsedComplex = self::_parseComplex($complexNumber);
if ($parsedComplex['imaginary'] == 0.0) {
return $parsedComplex['real'];
} else {
return self::_cleanComplex( self::COMPLEX( $parsedComplex['real'],
0 - $parsedComplex['imaginary'],
$parsedComplex['suffix']
)
);
}
} // function IMCONJUGATE()
/**
* IMCOS
*
* Returns the cosine of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMCOS(complexNumber)
*
* @param string $complexNumber The complex number for which you want the cosine.
* @return string|float
*/
public static function IMCOS($complexNumber) {
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
$parsedComplex = self::_parseComplex($complexNumber);
if ($parsedComplex['imaginary'] == 0.0) {
return cos($parsedComplex['real']);
} else {
return self::IMCONJUGATE(self::COMPLEX(cos($parsedComplex['real']) * cosh($parsedComplex['imaginary']),sin($parsedComplex['real']) * sinh($parsedComplex['imaginary']),$parsedComplex['suffix']));
}
} // function IMCOS()
/**
* IMSIN
*
* Returns the sine of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMSIN(complexNumber)
*
* @param string $complexNumber The complex number for which you want the sine.
* @return string|float
*/
public static function IMSIN($complexNumber) {
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
$parsedComplex = self::_parseComplex($complexNumber);
if ($parsedComplex['imaginary'] == 0.0) {
return sin($parsedComplex['real']);
} else {
return self::COMPLEX(sin($parsedComplex['real']) * cosh($parsedComplex['imaginary']),cos($parsedComplex['real']) * sinh($parsedComplex['imaginary']),$parsedComplex['suffix']);
}
} // function IMSIN()
/**
* IMSQRT
*
* Returns the square root of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMSQRT(complexNumber)
*
* @param string $complexNumber The complex number for which you want the square root.
* @return string
*/
public static function IMSQRT($complexNumber) {
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
$parsedComplex = self::_parseComplex($complexNumber);
$theta = self::IMARGUMENT($complexNumber);
$d1 = cos($theta / 2);
$d2 = sin($theta / 2);
$r = sqrt(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));
if ($parsedComplex['suffix'] == '') {
return self::COMPLEX($d1 * $r,$d2 * $r);
} else {
return self::COMPLEX($d1 * $r,$d2 * $r,$parsedComplex['suffix']);
}
} // function IMSQRT()
/**
* IMLN
*
* Returns the natural logarithm of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMLN(complexNumber)
*
* @param string $complexNumber The complex number for which you want the natural logarithm.
* @return string
*/
public static function IMLN($complexNumber) {
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
$parsedComplex = self::_parseComplex($complexNumber);
if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
return PHPExcel_Calculation_Functions::NaN();
}
$logR = log(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));
$t = self::IMARGUMENT($complexNumber);
if ($parsedComplex['suffix'] == '') {
return self::COMPLEX($logR,$t);
} else {
return self::COMPLEX($logR,$t,$parsedComplex['suffix']);
}
} // function IMLN()
/**
* IMLOG10
*
* Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMLOG10(complexNumber)
*
* @param string $complexNumber The complex number for which you want the common logarithm.
* @return string
*/
public static function IMLOG10($complexNumber) {
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
$parsedComplex = self::_parseComplex($complexNumber);
if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
return PHPExcel_Calculation_Functions::NaN();
} elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
return log10($parsedComplex['real']);
}
return self::IMPRODUCT(log10(EULER),self::IMLN($complexNumber));
} // function IMLOG10()
/**
* IMLOG2
*
* Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMLOG2(complexNumber)
*
* @param string $complexNumber The complex number for which you want the base-2 logarithm.
* @return string
*/
public static function IMLOG2($complexNumber) {
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
$parsedComplex = self::_parseComplex($complexNumber);
if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
return PHPExcel_Calculation_Functions::NaN();
} elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
return log($parsedComplex['real'],2);
}
return self::IMPRODUCT(log(EULER,2),self::IMLN($complexNumber));
} // function IMLOG2()
/**
* IMEXP
*
* Returns the exponential of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMEXP(complexNumber)
*
* @param string $complexNumber The complex number for which you want the exponential.
* @return string
*/
public static function IMEXP($complexNumber) {
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
$parsedComplex = self::_parseComplex($complexNumber);
if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
return '1';
}
$e = exp($parsedComplex['real']);
$eX = $e * cos($parsedComplex['imaginary']);
$eY = $e * sin($parsedComplex['imaginary']);
if ($parsedComplex['suffix'] == '') {
return self::COMPLEX($eX,$eY);
} else {
return self::COMPLEX($eX,$eY,$parsedComplex['suffix']);
}
} // function IMEXP()
/**
* IMPOWER
*
* Returns a complex number in x + yi or x + yj text format raised to a power.
*
* Excel Function:
* IMPOWER(complexNumber,realNumber)
*
* @param string $complexNumber The complex number you want to raise to a power.
* @param float $realNumber The power to which you want to raise the complex number.
* @return string
*/
public static function IMPOWER($complexNumber,$realNumber) {
$complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
$realNumber = PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);
if (!is_numeric($realNumber)) {
return PHPExcel_Calculation_Functions::VALUE();
}
$parsedComplex = self::_parseComplex($complexNumber);
$r = sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
$rPower = pow($r,$realNumber);
$theta = self::IMARGUMENT($complexNumber) * $realNumber;
if ($theta == 0) {
return 1;
} elseif ($parsedComplex['imaginary'] == 0.0) {
return self::COMPLEX($rPower * cos($theta),$rPower * sin($theta),$parsedComplex['suffix']);
} else {
return self::COMPLEX($rPower * cos($theta),$rPower * sin($theta),$parsedComplex['suffix']);
}
} // function IMPOWER()
/**
* IMDIV
*
* Returns the quotient of two complex numbers in x + yi or x + yj text format.
*
* Excel Function:
* IMDIV(complexDividend,complexDivisor)
*
* @param string $complexDividend The complex numerator or dividend.
* @param string $complexDivisor The complex denominator or divisor.
* @return string
*/
public static function IMDIV($complexDividend,$complexDivisor) {
$complexDividend = PHPExcel_Calculation_Functions::flattenSingleValue($complexDividend);
$complexDivisor = PHPExcel_Calculation_Functions::flattenSingleValue($complexDivisor);
$parsedComplexDividend = self::_parseComplex($complexDividend);
$parsedComplexDivisor = self::_parseComplex($complexDivisor);
if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] != '') &&
($parsedComplexDividend['suffix'] != $parsedComplexDivisor['suffix'])) {
return PHPExcel_Calculation_Functions::NaN();
}
if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] == '')) {
$parsedComplexDivisor['suffix'] = $parsedComplexDividend['suffix'];
}
$d1 = ($parsedComplexDividend['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['imaginary']);
$d2 = ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['real']) - ($parsedComplexDividend['real'] * $parsedComplexDivisor['imaginary']);
$d3 = ($parsedComplexDivisor['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDivisor['imaginary'] * $parsedComplexDivisor['imaginary']);
$r = $d1/$d3;
$i = $d2/$d3;
if ($i > 0.0) {
return self::_cleanComplex($r.'+'.$i.$parsedComplexDivisor['suffix']);
} elseif ($i < 0.0) {
return self::_cleanComplex($r.$i.$parsedComplexDivisor['suffix']);
} else {
return $r;
}
} // function IMDIV()
/**
* IMSUB
*
* Returns the difference of two complex numbers in x + yi or x + yj text format.
*
* Excel Function:
* IMSUB(complexNumber1,complexNumber2)
*
* @param string $complexNumber1 The complex number from which to subtract complexNumber2.
* @param string $complexNumber2 The complex number to subtract from complexNumber1.
* @return string
*/
public static function IMSUB($complexNumber1,$complexNumber2) {
$complexNumber1 = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber1);
$complexNumber2 = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber2);
$parsedComplex1 = self::_parseComplex($complexNumber1);
$parsedComplex2 = self::_parseComplex($complexNumber2);
if ((($parsedComplex1['suffix'] != '') && ($parsedComplex2['suffix'] != '')) &&
($parsedComplex1['suffix'] != $parsedComplex2['suffix'])) {
return PHPExcel_Calculation_Functions::NaN();
} elseif (($parsedComplex1['suffix'] == '') && ($parsedComplex2['suffix'] != '')) {
$parsedComplex1['suffix'] = $parsedComplex2['suffix'];
}
$d1 = $parsedComplex1['real'] - $parsedComplex2['real'];
$d2 = $parsedComplex1['imaginary'] - $parsedComplex2['imaginary'];
return self::COMPLEX($d1,$d2,$parsedComplex1['suffix']);
} // function IMSUB()
/**
* IMSUM
*
* Returns the sum of two or more complex numbers in x + yi or x + yj text format.
*
* Excel Function:
* IMSUM(complexNumber[,complexNumber[,...]])
*
* @param string $complexNumber,... Series of complex numbers to add
* @return string
*/
public static function IMSUM() {
// Return value
$returnValue = self::_parseComplex('0');
$activeSuffix = '';
// Loop through the arguments
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
foreach ($aArgs as $arg) {
$parsedComplex = self::_parseComplex($arg);
if ($activeSuffix == '') {
$activeSuffix = $parsedComplex['suffix'];
} elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
return PHPExcel_Calculation_Functions::VALUE();
}
$returnValue['real'] += $parsedComplex['real'];
$returnValue['imaginary'] += $parsedComplex['imaginary'];
}
if ($returnValue['imaginary'] == 0.0) { $activeSuffix = ''; }
return self::COMPLEX($returnValue['real'],$returnValue['imaginary'],$activeSuffix);
} // function IMSUM()
/**
* IMPRODUCT
*
* Returns the product of two or more complex numbers in x + yi or x + yj text format.
*
* Excel Function:
* IMPRODUCT(complexNumber[,complexNumber[,...]])
*
* @param string $complexNumber,... Series of complex numbers to multiply
* @return string
*/
public static function IMPRODUCT() {
// Return value
$returnValue = self::_parseComplex('1');
$activeSuffix = '';
// Loop through the arguments
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
foreach ($aArgs as $arg) {
$parsedComplex = self::_parseComplex($arg);
$workValue = $returnValue;
if (($parsedComplex['suffix'] != '') && ($activeSuffix == '')) {
$activeSuffix = $parsedComplex['suffix'];
} elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
return PHPExcel_Calculation_Functions::NaN();
}
$returnValue['real'] = ($workValue['real'] * $parsedComplex['real']) - ($workValue['imaginary'] * $parsedComplex['imaginary']);
$returnValue['imaginary'] = ($workValue['real'] * $parsedComplex['imaginary']) + ($workValue['imaginary'] * $parsedComplex['real']);
}
if ($returnValue['imaginary'] == 0.0) { $activeSuffix = ''; }
return self::COMPLEX($returnValue['real'],$returnValue['imaginary'],$activeSuffix);
} // function IMPRODUCT()
/**
* DELTA
*
* Tests whether two values are equal. Returns 1 if number1 = number2; returns 0 otherwise.
* Use this function to filter a set of values. For example, by summing several DELTA
* functions you calculate the count of equal pairs. This function is also known as the
* Kronecker Delta function.
*
* Excel Function:
* DELTA(a[,b])
*
* @param float $a The first number.
* @param float $b The second number. If omitted, b is assumed to be zero.
* @return int
*/
public static function DELTA($a, $b=0) {
$a = PHPExcel_Calculation_Functions::flattenSingleValue($a);
$b = PHPExcel_Calculation_Functions::flattenSingleValue($b);
return (int) ($a == $b);
} // function DELTA()
/**
* GESTEP
*
* Excel Function:
* GESTEP(number[,step])
*
* Returns 1 if number >= step; returns 0 (zero) otherwise
* Use this function to filter a set of values. For example, by summing several GESTEP
* functions you calculate the count of values that exceed a threshold.
*
* @param float $number The value to test against step.
* @param float $step The threshold value.
* If you omit a value for step, GESTEP uses zero.
* @return int
*/
public static function GESTEP($number, $step=0) {
$number = PHPExcel_Calculation_Functions::flattenSingleValue($number);
$step = PHPExcel_Calculation_Functions::flattenSingleValue($step);
return (int) ($number >= $step);
} // function GESTEP()
//
// Private method to calculate the erf value
//
private static $_two_sqrtpi = 1.128379167095512574;
public static function _erfVal($x) {
if (abs($x) > 2.2) {
return 1 - self::_erfcVal($x);
}
$sum = $term = $x;
$xsqr = ($x * $x);
$j = 1;
do {
$term *= $xsqr / $j;
$sum -= $term / (2 * $j + 1);
++$j;
$term *= $xsqr / $j;
$sum += $term / (2 * $j + 1);
++$j;
if ($sum == 0.0) {
break;
}
} while (abs($term / $sum) > PRECISION);
return self::$_two_sqrtpi * $sum;
} // function _erfVal()
/**
* ERF
*
* Returns the error function integrated between the lower and upper bound arguments.
*
* Note: In Excel 2007 or earlier, if you input a negative value for the upper or lower bound arguments,
* the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
* improved, so that it can now calculate the function for both positive and negative ranges.
* PHPExcel follows Excel 2010 behaviour, and accepts nagative arguments.
*
* Excel Function:
* ERF(lower[,upper])
*
* @param float $lower lower bound for integrating ERF
* @param float $upper upper bound for integrating ERF.
* If omitted, ERF integrates between zero and lower_limit
* @return float
*/
public static function ERF($lower, $upper = NULL) {
$lower = PHPExcel_Calculation_Functions::flattenSingleValue($lower);
$upper = PHPExcel_Calculation_Functions::flattenSingleValue($upper);
if (is_numeric($lower)) {
if (is_null($upper)) {
return self::_erfVal($lower);
}
if (is_numeric($upper)) {
return self::_erfVal($upper) - self::_erfVal($lower);
}
}
return PHPExcel_Calculation_Functions::VALUE();
} // function ERF()
//
// Private method to calculate the erfc value
//
private static $_one_sqrtpi = 0.564189583547756287;
private static function _erfcVal($x) {
if (abs($x) < 2.2) {
return 1 - self::_erfVal($x);
}
if ($x < 0) {
return 2 - self::ERFC(-$x);
}
$a = $n = 1;
$b = $c = $x;
$d = ($x * $x) + 0.5;
$q1 = $q2 = $b / $d;
$t = 0;
do {
$t = $a * $n + $b * $x;
$a = $b;
$b = $t;
$t = $c * $n + $d * $x;
$c = $d;
$d = $t;
$n += 0.5;
$q1 = $q2;
$q2 = $b / $d;
} while ((abs($q1 - $q2) / $q2) > PRECISION);
return self::$_one_sqrtpi * exp(-$x * $x) * $q2;
} // function _erfcVal()
/**
* ERFC
*
* Returns the complementary ERF function integrated between x and infinity
*
* Note: In Excel 2007 or earlier, if you input a negative value for the lower bound argument,
* the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
* improved, so that it can now calculate the function for both positive and negative x values.
* PHPExcel follows Excel 2010 behaviour, and accepts nagative arguments.
*
* Excel Function:
* ERFC(x)
*
* @param float $x The lower bound for integrating ERFC
* @return float
*/
public static function ERFC($x) {
$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
if (is_numeric($x)) {
return self::_erfcVal($x);
}
return PHPExcel_Calculation_Functions::VALUE();
} // function ERFC()
/**
* getConversionGroups
* Returns a list of the different conversion groups for UOM conversions
*
* @return array
*/
public static function getConversionGroups() {
$conversionGroups = array();
foreach(self::$_conversionUnits as $conversionUnit) {
$conversionGroups[] = $conversionUnit['Group'];
}
return array_merge(array_unique($conversionGroups));
} // function getConversionGroups()
/**
* getConversionGroupUnits
* Returns an array of units of measure, for a specified conversion group, or for all groups
*
* @param string $group The group whose units of measure you want to retrieve
*
* @return array
*/
public static function getConversionGroupUnits($group = NULL) {
$conversionGroups = array();
foreach(self::$_conversionUnits as $conversionUnit => $conversionGroup) {
if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
$conversionGroups[$conversionGroup['Group']][] = $conversionUnit;
}
}
return $conversionGroups;
} // function getConversionGroupUnits()
/**
* getConversionGroupUnitDetails
*
* @return array
*/
public static function getConversionGroupUnitDetails($group = NULL) {
$conversionGroups = array();
foreach(self::$_conversionUnits as $conversionUnit => $conversionGroup) {
if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
$conversionGroups[$conversionGroup['Group']][] = array( 'unit' => $conversionUnit,
'description' => $conversionGroup['Unit Name']
);
}
}
return $conversionGroups;
} // function getConversionGroupUnitDetails()
/**
* getConversionMultipliers
* Returns an array of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM()
*
* @return array of mixed
*/
public static function getConversionMultipliers() {
return self::$_conversionMultipliers;
} // function getConversionGroups()
/**
* CONVERTUOM
*
* Converts a number from one measurement system to another.
* For example, CONVERT can translate a table of distances in miles to a table of distances
* in kilometers.
*
* Excel Function:
* CONVERT(value,fromUOM,toUOM)
*
* @param float $value The value in fromUOM to convert.
* @param string $fromUOM The units for value.
* @param string $toUOM The units for the result.
*
* @return float
*/
public static function CONVERTUOM($value, $fromUOM, $toUOM) {
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
$fromUOM = PHPExcel_Calculation_Functions::flattenSingleValue($fromUOM);
$toUOM = PHPExcel_Calculation_Functions::flattenSingleValue($toUOM);
if (!is_numeric($value)) {
return PHPExcel_Calculation_Functions::VALUE();
}
$fromMultiplier = 1.0;
if (isset(self::$_conversionUnits[$fromUOM])) {
$unitGroup1 = self::$_conversionUnits[$fromUOM]['Group'];
} else {
$fromMultiplier = substr($fromUOM,0,1);
$fromUOM = substr($fromUOM,1);
if (isset(self::$_conversionMultipliers[$fromMultiplier])) {
$fromMultiplier = self::$_conversionMultipliers[$fromMultiplier]['multiplier'];
} else {
return PHPExcel_Calculation_Functions::NA();
}
if ((isset(self::$_conversionUnits[$fromUOM])) && (self::$_conversionUnits[$fromUOM]['AllowPrefix'])) {
$unitGroup1 = self::$_conversionUnits[$fromUOM]['Group'];
} else {
return PHPExcel_Calculation_Functions::NA();
}
}
$value *= $fromMultiplier;
$toMultiplier = 1.0;
if (isset(self::$_conversionUnits[$toUOM])) {
$unitGroup2 = self::$_conversionUnits[$toUOM]['Group'];
} else {
$toMultiplier = substr($toUOM,0,1);
$toUOM = substr($toUOM,1);
if (isset(self::$_conversionMultipliers[$toMultiplier])) {
$toMultiplier = self::$_conversionMultipliers[$toMultiplier]['multiplier'];
} else {
return PHPExcel_Calculation_Functions::NA();
}
if ((isset(self::$_conversionUnits[$toUOM])) && (self::$_conversionUnits[$toUOM]['AllowPrefix'])) {
$unitGroup2 = self::$_conversionUnits[$toUOM]['Group'];
} else {
return PHPExcel_Calculation_Functions::NA();
}
}
if ($unitGroup1 != $unitGroup2) {
return PHPExcel_Calculation_Functions::NA();
}
if (($fromUOM == $toUOM) && ($fromMultiplier == $toMultiplier)) {
// We've already factored $fromMultiplier into the value, so we need
// to reverse it again
return $value / $fromMultiplier;
} elseif ($unitGroup1 == 'Temperature') {
if (($fromUOM == 'F') || ($fromUOM == 'fah')) {
if (($toUOM == 'F') || ($toUOM == 'fah')) {
return $value;
} else {
$value = (($value - 32) / 1.8);
if (($toUOM == 'K') || ($toUOM == 'kel')) {
$value += 273.15;
}
return $value;
}
} elseif ((($fromUOM == 'K') || ($fromUOM == 'kel')) &&
(($toUOM == 'K') || ($toUOM == 'kel'))) {
return $value;
} elseif ((($fromUOM == 'C') || ($fromUOM == 'cel')) &&
(($toUOM == 'C') || ($toUOM == 'cel'))) {
return $value;
}
if (($toUOM == 'F') || ($toUOM == 'fah')) {
if (($fromUOM == 'K') || ($fromUOM == 'kel')) {
$value -= 273.15;
}
return ($value * 1.8) + 32;
}
if (($toUOM == 'C') || ($toUOM == 'cel')) {
return $value - 273.15;
}
return $value + 273.15;
}
return ($value * self::$_unitConversions[$unitGroup1][$fromUOM][$toUOM]) / $toMultiplier;
} // function CONVERTUOM()
} // class PHPExcel_Calculation_Engineering
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