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authorAnton Luka Šijanec <anton@sijanec.eu>2022-01-11 12:35:47 +0100
committerAnton Luka Šijanec <anton@sijanec.eu>2022-01-11 12:35:47 +0100
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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 1.7.8, 2012-10-12
+ */
+
+
+/** 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
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-10 13:01:40 +0100