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<?php
namespace PhpOffice\PhpSpreadsheet\Calculation;
use Complex\Complex;
use Complex\Exception as ComplexException;
class Engineering
{
/**
* EULER.
*/
const EULER = 2.71828182845904523536;
/**
* Details of the Units of measure that can be used in CONVERTUOM().
*
* @var mixed[]
*/
private static $conversionUnits = [
'g' => ['Group' => 'Mass', 'Unit Name' => 'Gram', 'AllowPrefix' => true],
'sg' => ['Group' => 'Mass', 'Unit Name' => 'Slug', 'AllowPrefix' => false],
'lbm' => ['Group' => 'Mass', 'Unit Name' => 'Pound mass (avoirdupois)', 'AllowPrefix' => false],
'u' => ['Group' => 'Mass', 'Unit Name' => 'U (atomic mass unit)', 'AllowPrefix' => true],
'ozm' => ['Group' => 'Mass', 'Unit Name' => 'Ounce mass (avoirdupois)', 'AllowPrefix' => false],
'm' => ['Group' => 'Distance', 'Unit Name' => 'Meter', 'AllowPrefix' => true],
'mi' => ['Group' => 'Distance', 'Unit Name' => 'Statute mile', 'AllowPrefix' => false],
'Nmi' => ['Group' => 'Distance', 'Unit Name' => 'Nautical mile', 'AllowPrefix' => false],
'in' => ['Group' => 'Distance', 'Unit Name' => 'Inch', 'AllowPrefix' => false],
'ft' => ['Group' => 'Distance', 'Unit Name' => 'Foot', 'AllowPrefix' => false],
'yd' => ['Group' => 'Distance', 'Unit Name' => 'Yard', 'AllowPrefix' => false],
'ang' => ['Group' => 'Distance', 'Unit Name' => 'Angstrom', 'AllowPrefix' => true],
'Pica' => ['Group' => 'Distance', 'Unit Name' => 'Pica (1/72 in)', 'AllowPrefix' => false],
'yr' => ['Group' => 'Time', 'Unit Name' => 'Year', 'AllowPrefix' => false],
'day' => ['Group' => 'Time', 'Unit Name' => 'Day', 'AllowPrefix' => false],
'hr' => ['Group' => 'Time', 'Unit Name' => 'Hour', 'AllowPrefix' => false],
'mn' => ['Group' => 'Time', 'Unit Name' => 'Minute', 'AllowPrefix' => false],
'sec' => ['Group' => 'Time', 'Unit Name' => 'Second', 'AllowPrefix' => true],
'Pa' => ['Group' => 'Pressure', 'Unit Name' => 'Pascal', 'AllowPrefix' => true],
'p' => ['Group' => 'Pressure', 'Unit Name' => 'Pascal', 'AllowPrefix' => true],
'atm' => ['Group' => 'Pressure', 'Unit Name' => 'Atmosphere', 'AllowPrefix' => true],
'at' => ['Group' => 'Pressure', 'Unit Name' => 'Atmosphere', 'AllowPrefix' => true],
'mmHg' => ['Group' => 'Pressure', 'Unit Name' => 'mm of Mercury', 'AllowPrefix' => true],
'N' => ['Group' => 'Force', 'Unit Name' => 'Newton', 'AllowPrefix' => true],
'dyn' => ['Group' => 'Force', 'Unit Name' => 'Dyne', 'AllowPrefix' => true],
'dy' => ['Group' => 'Force', 'Unit Name' => 'Dyne', 'AllowPrefix' => true],
'lbf' => ['Group' => 'Force', 'Unit Name' => 'Pound force', 'AllowPrefix' => false],
'J' => ['Group' => 'Energy', 'Unit Name' => 'Joule', 'AllowPrefix' => true],
'e' => ['Group' => 'Energy', 'Unit Name' => 'Erg', 'AllowPrefix' => true],
'c' => ['Group' => 'Energy', 'Unit Name' => 'Thermodynamic calorie', 'AllowPrefix' => true],
'cal' => ['Group' => 'Energy', 'Unit Name' => 'IT calorie', 'AllowPrefix' => true],
'eV' => ['Group' => 'Energy', 'Unit Name' => 'Electron volt', 'AllowPrefix' => true],
'ev' => ['Group' => 'Energy', 'Unit Name' => 'Electron volt', 'AllowPrefix' => true],
'HPh' => ['Group' => 'Energy', 'Unit Name' => 'Horsepower-hour', 'AllowPrefix' => false],
'hh' => ['Group' => 'Energy', 'Unit Name' => 'Horsepower-hour', 'AllowPrefix' => false],
'Wh' => ['Group' => 'Energy', 'Unit Name' => 'Watt-hour', 'AllowPrefix' => true],
'wh' => ['Group' => 'Energy', 'Unit Name' => 'Watt-hour', 'AllowPrefix' => true],
'flb' => ['Group' => 'Energy', 'Unit Name' => 'Foot-pound', 'AllowPrefix' => false],
'BTU' => ['Group' => 'Energy', 'Unit Name' => 'BTU', 'AllowPrefix' => false],
'btu' => ['Group' => 'Energy', 'Unit Name' => 'BTU', 'AllowPrefix' => false],
'HP' => ['Group' => 'Power', 'Unit Name' => 'Horsepower', 'AllowPrefix' => false],
'h' => ['Group' => 'Power', 'Unit Name' => 'Horsepower', 'AllowPrefix' => false],
'W' => ['Group' => 'Power', 'Unit Name' => 'Watt', 'AllowPrefix' => true],
'w' => ['Group' => 'Power', 'Unit Name' => 'Watt', 'AllowPrefix' => true],
'T' => ['Group' => 'Magnetism', 'Unit Name' => 'Tesla', 'AllowPrefix' => true],
'ga' => ['Group' => 'Magnetism', 'Unit Name' => 'Gauss', 'AllowPrefix' => true],
'C' => ['Group' => 'Temperature', 'Unit Name' => 'Celsius', 'AllowPrefix' => false],
'cel' => ['Group' => 'Temperature', 'Unit Name' => 'Celsius', 'AllowPrefix' => false],
'F' => ['Group' => 'Temperature', 'Unit Name' => 'Fahrenheit', 'AllowPrefix' => false],
'fah' => ['Group' => 'Temperature', 'Unit Name' => 'Fahrenheit', 'AllowPrefix' => false],
'K' => ['Group' => 'Temperature', 'Unit Name' => 'Kelvin', 'AllowPrefix' => false],
'kel' => ['Group' => 'Temperature', 'Unit Name' => 'Kelvin', 'AllowPrefix' => false],
'tsp' => ['Group' => 'Liquid', 'Unit Name' => 'Teaspoon', 'AllowPrefix' => false],
'tbs' => ['Group' => 'Liquid', 'Unit Name' => 'Tablespoon', 'AllowPrefix' => false],
'oz' => ['Group' => 'Liquid', 'Unit Name' => 'Fluid Ounce', 'AllowPrefix' => false],
'cup' => ['Group' => 'Liquid', 'Unit Name' => 'Cup', 'AllowPrefix' => false],
'pt' => ['Group' => 'Liquid', 'Unit Name' => 'U.S. Pint', 'AllowPrefix' => false],
'us_pt' => ['Group' => 'Liquid', 'Unit Name' => 'U.S. Pint', 'AllowPrefix' => false],
'uk_pt' => ['Group' => 'Liquid', 'Unit Name' => 'U.K. Pint', 'AllowPrefix' => false],
'qt' => ['Group' => 'Liquid', 'Unit Name' => 'Quart', 'AllowPrefix' => false],
'gal' => ['Group' => 'Liquid', 'Unit Name' => 'Gallon', 'AllowPrefix' => false],
'l' => ['Group' => 'Liquid', 'Unit Name' => 'Litre', 'AllowPrefix' => true],
'lt' => ['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 = [
'Y' => ['multiplier' => 1E24, 'name' => 'yotta'],
'Z' => ['multiplier' => 1E21, 'name' => 'zetta'],
'E' => ['multiplier' => 1E18, 'name' => 'exa'],
'P' => ['multiplier' => 1E15, 'name' => 'peta'],
'T' => ['multiplier' => 1E12, 'name' => 'tera'],
'G' => ['multiplier' => 1E9, 'name' => 'giga'],
'M' => ['multiplier' => 1E6, 'name' => 'mega'],
'k' => ['multiplier' => 1E3, 'name' => 'kilo'],
'h' => ['multiplier' => 1E2, 'name' => 'hecto'],
'e' => ['multiplier' => 1E1, 'name' => 'deka'],
'd' => ['multiplier' => 1E-1, 'name' => 'deci'],
'c' => ['multiplier' => 1E-2, 'name' => 'centi'],
'm' => ['multiplier' => 1E-3, 'name' => 'milli'],
'u' => ['multiplier' => 1E-6, 'name' => 'micro'],
'n' => ['multiplier' => 1E-9, 'name' => 'nano'],
'p' => ['multiplier' => 1E-12, 'name' => 'pico'],
'f' => ['multiplier' => 1E-15, 'name' => 'femto'],
'a' => ['multiplier' => 1E-18, 'name' => 'atto'],
'z' => ['multiplier' => 1E-21, 'name' => 'zepto'],
'y' => ['multiplier' => 1E-24, 'name' => 'yocto'],
];
/**
* Details of the Units of measure conversion factors, organised by group.
*
* @var mixed[]
*/
private static $unitConversions = [
'Mass' => [
'g' => [
'g' => 1.0,
'sg' => 6.85220500053478E-05,
'lbm' => 2.20462291469134E-03,
'u' => 6.02217000000000E+23,
'ozm' => 3.52739718003627E-02,
],
'sg' => [
'g' => 1.45938424189287E+04,
'sg' => 1.0,
'lbm' => 3.21739194101647E+01,
'u' => 8.78866000000000E+27,
'ozm' => 5.14782785944229E+02,
],
'lbm' => [
'g' => 4.5359230974881148E+02,
'sg' => 3.10810749306493E-02,
'lbm' => 1.0,
'u' => 2.73161000000000E+26,
'ozm' => 1.60000023429410E+01,
],
'u' => [
'g' => 1.66053100460465E-24,
'sg' => 1.13782988532950E-28,
'lbm' => 3.66084470330684E-27,
'u' => 1.0,
'ozm' => 5.85735238300524E-26,
],
'ozm' => [
'g' => 2.83495152079732E+01,
'sg' => 1.94256689870811E-03,
'lbm' => 6.24999908478882E-02,
'u' => 1.70725600000000E+25,
'ozm' => 1.0,
],
],
'Distance' => [
'm' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'yr' => [
'yr' => 1.0,
'day' => 365.25,
'hr' => 8766.0,
'mn' => 525960.0,
'sec' => 31557600.0,
],
'day' => [
'yr' => 2.73785078713210E-03,
'day' => 1.0,
'hr' => 24.0,
'mn' => 1440.0,
'sec' => 86400.0,
],
'hr' => [
'yr' => 1.14077116130504E-04,
'day' => 4.16666666666667E-02,
'hr' => 1.0,
'mn' => 60.0,
'sec' => 3600.0,
],
'mn' => [
'yr' => 1.90128526884174E-06,
'day' => 6.94444444444444E-04,
'hr' => 1.66666666666667E-02,
'mn' => 1.0,
'sec' => 60.0,
],
'sec' => [
'yr' => 3.16880878140289E-08,
'day' => 1.15740740740741E-05,
'hr' => 2.77777777777778E-04,
'mn' => 1.66666666666667E-02,
'sec' => 1.0,
],
],
'Pressure' => [
'Pa' => [
'Pa' => 1.0,
'p' => 1.0,
'atm' => 9.86923299998193E-06,
'at' => 9.86923299998193E-06,
'mmHg' => 7.50061707998627E-03,
],
'p' => [
'Pa' => 1.0,
'p' => 1.0,
'atm' => 9.86923299998193E-06,
'at' => 9.86923299998193E-06,
'mmHg' => 7.50061707998627E-03,
],
'atm' => [
'Pa' => 1.01324996583000E+05,
'p' => 1.01324996583000E+05,
'atm' => 1.0,
'at' => 1.0,
'mmHg' => 760.0,
],
'at' => [
'Pa' => 1.01324996583000E+05,
'p' => 1.01324996583000E+05,
'atm' => 1.0,
'at' => 1.0,
'mmHg' => 760.0,
],
'mmHg' => [
'Pa' => 1.33322363925000E+02,
'p' => 1.33322363925000E+02,
'atm' => 1.31578947368421E-03,
'at' => 1.31578947368421E-03,
'mmHg' => 1.0,
],
],
'Force' => [
'N' => [
'N' => 1.0,
'dyn' => 1.0E+5,
'dy' => 1.0E+5,
'lbf' => 2.24808923655339E-01,
],
'dyn' => [
'N' => 1.0E-5,
'dyn' => 1.0,
'dy' => 1.0,
'lbf' => 2.24808923655339E-06,
],
'dy' => [
'N' => 1.0E-5,
'dyn' => 1.0,
'dy' => 1.0,
'lbf' => 2.24808923655339E-06,
],
'lbf' => [
'N' => 4.448222,
'dyn' => 4.448222E+5,
'dy' => 4.448222E+5,
'lbf' => 1.0,
],
],
'Energy' => [
'J' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'HP' => [
'HP' => 1.0,
'h' => 1.0,
'W' => 7.45701000000000E+02,
'w' => 7.45701000000000E+02,
],
'h' => [
'HP' => 1.0,
'h' => 1.0,
'W' => 7.45701000000000E+02,
'w' => 7.45701000000000E+02,
],
'W' => [
'HP' => 1.34102006031908E-03,
'h' => 1.34102006031908E-03,
'W' => 1.0,
'w' => 1.0,
],
'w' => [
'HP' => 1.34102006031908E-03,
'h' => 1.34102006031908E-03,
'W' => 1.0,
'w' => 1.0,
],
],
'Magnetism' => [
'T' => [
'T' => 1.0,
'ga' => 10000.0,
],
'ga' => [
'T' => 0.0001,
'ga' => 1.0,
],
],
'Liquid' => [
'tsp' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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' => [
'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
*
* @deprecated 2.0.0 No longer used by internal code. Please use the Complex\Complex class instead
*
* @param string $complexNumber The complex number
*
* @return mixed[] Indexed on "real", "imaginary" and "suffix"
*/
public static function parseComplex($complexNumber)
{
$complex = new Complex($complexNumber);
return [
'real' => $complex->getReal(),
'imaginary' => $complex->getImaginary(),
'suffix' => $complex->getSuffix(),
];
}
/**
* Formats a number base string value with leading zeroes.
*
* @param string $xVal The "number" to pad
* @param int $places The length that we want to pad this value
*
* @return string The padded "number"
*/
private static function nbrConversionFormat($xVal, $places)
{
if ($places !== null) {
if (is_numeric($places)) {
$places = (int) $places;
} else {
return Functions::VALUE();
}
if ($places < 0) {
return Functions::NAN();
}
if (strlen($xVal) <= $places) {
return substr(str_pad($xVal, $places, '0', STR_PAD_LEFT), -10);
}
return Functions::NAN();
}
return substr($xVal, -10);
}
/**
* BESSELI.
*
* Returns the modified Bessel function In(x), which is equivalent to the Bessel function evaluated
* for purely imaginary arguments
*
* Excel Function:
* BESSELI(x,ord)
*
* @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 int $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)
{
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
if ((is_numeric($x)) && (is_numeric($ord))) {
$ord = floor($ord);
if ($ord < 0) {
return Functions::NAN();
}
if (abs($x) <= 30) {
$fResult = $fTerm = pow($x / 2, $ord) / MathTrig::FACT($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)) ? Functions::NAN() : $fResult;
}
return Functions::VALUE();
}
/**
* BESSELJ.
*
* Returns the Bessel function
*
* Excel Function:
* BESSELJ(x,ord)
*
* @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 int $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)
{
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
if ((is_numeric($x)) && (is_numeric($ord))) {
$ord = floor($ord);
if ($ord < 0) {
return Functions::NAN();
}
$fResult = 0;
if (abs($x) <= 30) {
$fResult = $fTerm = pow($x / 2, $ord) / MathTrig::FACT($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(Functions::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)) ? Functions::NAN() : $fResult;
}
return Functions::VALUE();
}
private static function besselK0($fNum)
{
if ($fNum <= 2) {
$fNum2 = $fNum * 0.5;
$y = ($fNum2 * $fNum2);
$fRet = -log($fNum2) * self::BESSELI($fNum, 0) +
(-0.57721566 + $y * (0.42278420 + $y * (0.23069756 + $y * (0.3488590e-1 + $y * (0.262698e-2 + $y *
(0.10750e-3 + $y * 0.74e-5))))));
} else {
$y = 2 / $fNum;
$fRet = exp(-$fNum) / sqrt($fNum) *
(1.25331414 + $y * (-0.7832358e-1 + $y * (0.2189568e-1 + $y * (-0.1062446e-1 + $y *
(0.587872e-2 + $y * (-0.251540e-2 + $y * 0.53208e-3))))));
}
return $fRet;
}
private static function besselK1($fNum)
{
if ($fNum <= 2) {
$fNum2 = $fNum * 0.5;
$y = ($fNum2 * $fNum2);
$fRet = log($fNum2) * self::BESSELI($fNum, 1) +
(1 + $y * (0.15443144 + $y * (-0.67278579 + $y * (-0.18156897 + $y * (-0.1919402e-1 + $y *
(-0.110404e-2 + $y * (-0.4686e-4))))))) / $fNum;
} else {
$y = 2 / $fNum;
$fRet = exp(-$fNum) / sqrt($fNum) *
(1.25331414 + $y * (0.23498619 + $y * (-0.3655620e-1 + $y * (0.1504268e-1 + $y * (-0.780353e-2 + $y *
(0.325614e-2 + $y * (-0.68245e-3)))))));
}
return $fRet;
}
/**
* BESSELK.
*
* Returns the modified Bessel function Kn(x), which is equivalent to the Bessel functions evaluated
* for purely imaginary arguments.
*
* Excel Function:
* BESSELK(x,ord)
*
* @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 int $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)
{
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
if ((is_numeric($x)) && (is_numeric($ord))) {
if (($ord < 0) || ($x == 0.0)) {
return Functions::NAN();
}
switch (floor($ord)) {
case 0:
$fBk = self::besselK0($x);
break;
case 1:
$fBk = self::besselK1($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)) ? Functions::NAN() : $fBk;
}
return Functions::VALUE();
}
private static function besselY0($fNum)
{
if ($fNum < 8.0) {
$y = ($fNum * $fNum);
$f1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y * (-86327.92757 + $y * 228.4622733))));
$f2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y * (47447.26470 + $y * (226.1030244 + $y))));
$fRet = $f1 / $f2 + 0.636619772 * self::BESSELJ($fNum, 0) * log($fNum);
} else {
$z = 8.0 / $fNum;
$y = ($z * $z);
$xx = $fNum - 0.785398164;
$f1 = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
$f2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y * (-0.934945152e-7))));
$fRet = sqrt(0.636619772 / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
}
return $fRet;
}
private static function besselY1($fNum)
{
if ($fNum < 8.0) {
$y = ($fNum * $fNum);
$f1 = $fNum * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y * (0.7349264551e9 + $y *
(-0.4237922726e7 + $y * 0.8511937935e4)))));
$f2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y *
(0.1020426050e6 + $y * (0.3549632885e3 + $y)))));
$fRet = $f1 / $f2 + 0.636619772 * (self::BESSELJ($fNum, 1) * log($fNum) - 1 / $fNum);
} else {
$fRet = sqrt(0.636619772 / $fNum) * sin($fNum - 2.356194491);
}
return $fRet;
}
/**
* BESSELY.
*
* Returns the Bessel function, which is also called the Weber function or the Neumann function.
*
* Excel Function:
* BESSELY(x,ord)
*
* @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 int $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)
{
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
if ((is_numeric($x)) && (is_numeric($ord))) {
if (($ord < 0) || ($x == 0.0)) {
return Functions::NAN();
}
switch (floor($ord)) {
case 0:
$fBy = self::besselY0($x);
break;
case 1:
$fBy = self::besselY1($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)) ? Functions::NAN() : $fBy;
}
return Functions::VALUE();
}
/**
* BINTODEC.
*
* Return a binary value as decimal.
*
* Excel Function:
* BIN2DEC(x)
*
* @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)
{
$x = Functions::flattenSingleValue($x);
if (is_bool($x)) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return Functions::VALUE();
}
}
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
$x = floor($x);
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
return Functions::NAN();
}
if (strlen($x) > 10) {
return Functions::NAN();
} elseif (strlen($x) == 10) {
// Two's Complement
$x = substr($x, -9);
return '-' . (512 - bindec($x));
}
return bindec($x);
}
/**
* BINTOHEX.
*
* Return a binary value as hex.
*
* Excel Function:
* BIN2HEX(x[,places])
*
* @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 int $places The number of characters to use. If places is omitted, BIN2HEX uses the
* minimum number of characters necessary. Places is useful for padding the
* return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, BIN2HEX returns the #VALUE! error value.
* If places is negative, BIN2HEX returns the #NUM! error value.
*
* @return string
*/
public static function BINTOHEX($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
// Argument X
if (is_bool($x)) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return Functions::VALUE();
}
}
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
$x = floor($x);
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
return Functions::NAN();
}
if (strlen($x) > 10) {
return Functions::NAN();
} elseif (strlen($x) == 10) {
// Two's Complement
return str_repeat('F', 8) . substr(strtoupper(dechex(bindec(substr($x, -9)))), -2);
}
$hexVal = (string) strtoupper(dechex(bindec($x)));
return self::nbrConversionFormat($hexVal, $places);
}
/**
* BINTOOCT.
*
* Return a binary value as octal.
*
* Excel Function:
* BIN2OCT(x[,places])
*
* @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 int $places The number of characters to use. If places is omitted, BIN2OCT uses the
* minimum number of characters necessary. Places is useful for padding the
* return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, BIN2OCT returns the #VALUE! error value.
* If places is negative, BIN2OCT returns the #NUM! error value.
*
* @return string
*/
public static function BINTOOCT($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return Functions::VALUE();
}
}
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
$x = floor($x);
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
return Functions::NAN();
}
if (strlen($x) > 10) {
return Functions::NAN();
} elseif (strlen($x) == 10) {
// Two's Complement
return str_repeat('7', 7) . substr(strtoupper(decoct(bindec(substr($x, -9)))), -3);
}
$octVal = (string) decoct(bindec($x));
return self::nbrConversionFormat($octVal, $places);
}
/**
* DECTOBIN.
*
* Return a decimal value as binary.
*
* Excel Function:
* DEC2BIN(x[,places])
*
* @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 int $places The number of characters to use. If places is omitted, DEC2BIN uses
* the minimum number of characters necessary. Places is useful for
* padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, DEC2BIN returns the #VALUE! error value.
* If places is zero or negative, DEC2BIN returns the #NUM! error value.
*
* @return string
*/
public static function DECTOBIN($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return Functions::VALUE();
}
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
return Functions::VALUE();
}
$x = (string) floor($x);
if ($x < -512 || $x > 511) {
return Functions::NAN();
}
$r = decbin($x);
// Two's Complement
$r = substr($r, -10);
if (strlen($r) >= 11) {
return Functions::NAN();
}
return self::nbrConversionFormat($r, $places);
}
/**
* DECTOHEX.
*
* Return a decimal value as hex.
*
* Excel Function:
* DEC2HEX(x[,places])
*
* @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 int $places The number of characters to use. If places is omitted, DEC2HEX uses
* the minimum number of characters necessary. Places is useful for
* padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, DEC2HEX returns the #VALUE! error value.
* If places is zero or negative, DEC2HEX returns the #NUM! error value.
*
* @return string
*/
public static function DECTOHEX($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return Functions::VALUE();
}
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
return Functions::VALUE();
}
$x = (string) floor($x);
$r = strtoupper(dechex($x));
if (strlen($r) == 8) {
// Two's Complement
$r = 'FF' . $r;
}
return self::nbrConversionFormat($r, $places);
}
/**
* DECTOOCT.
*
* Return an decimal value as octal.
*
* Excel Function:
* DEC2OCT(x[,places])
*
* @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 int $places The number of characters to use. If places is omitted, DEC2OCT uses
* the minimum number of characters necessary. Places is useful for
* padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, DEC2OCT returns the #VALUE! error value.
* If places is zero or negative, DEC2OCT returns the #NUM! error value.
*
* @return string
*/
public static function DECTOOCT($x, $places = null)
{
$xorig = $x;
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return Functions::VALUE();
}
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
return Functions::VALUE();
}
$x = (string) floor($x);
$r = decoct($x);
if (strlen($r) == 11) {
// Two's Complement
$r = substr($r, -10);
}
return self::nbrConversionFormat($r, $places);
}
/**
* HEXTOBIN.
*
* Return a hex value as binary.
*
* Excel Function:
* HEX2BIN(x[,places])
*
* @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 int $places The number of characters to use. If places is omitted,
* HEX2BIN uses the minimum number of characters necessary. Places
* is useful for padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, HEX2BIN returns the #VALUE! error value.
* If places is negative, HEX2BIN returns the #NUM! error value.
*
* @return string
*/
public static function HEXTOBIN($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
return Functions::VALUE();
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
return Functions::NAN();
}
return self::DECTOBIN(self::HEXTODEC($x), $places);
}
/**
* HEXTODEC.
*
* Return a hex value as decimal.
*
* Excel Function:
* HEX2DEC(x)
*
* @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)
{
$x = Functions::flattenSingleValue($x);
if (is_bool($x)) {
return Functions::VALUE();
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
return Functions::NAN();
}
if (strlen($x) > 10) {
return Functions::NAN();
}
$binX = '';
foreach (str_split($x) as $char) {
$binX .= str_pad(base_convert($char, 16, 2), 4, '0', STR_PAD_LEFT);
}
if (strlen($binX) == 40 && $binX[0] == '1') {
for ($i = 0; $i < 40; ++$i) {
$binX[$i] = ($binX[$i] == '1' ? '0' : '1');
}
return (bindec($binX) + 1) * -1;
}
return bindec($binX);
}
/**
* HEXTOOCT.
*
* Return a hex value as octal.
*
* Excel Function:
* HEX2OCT(x[,places])
*
* @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 int $places The number of characters to use. If places is omitted, HEX2OCT
* uses the minimum number of characters necessary. Places is
* useful for padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, HEX2OCT returns the #VALUE! error
* value.
* If places is negative, HEX2OCT returns the #NUM! error value.
*
* @return string
*/
public static function HEXTOOCT($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
return Functions::VALUE();
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
return Functions::NAN();
}
$decimal = self::HEXTODEC($x);
if ($decimal < -536870912 || $decimal > 536870911) {
return Functions::NAN();
}
return self::DECTOOCT($decimal, $places);
}
/**
* OCTTOBIN.
*
* Return an octal value as binary.
*
* Excel Function:
* OCT2BIN(x[,places])
*
* @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 int $places The number of characters to use. If places is omitted,
* OCT2BIN uses the minimum number of characters necessary.
* Places is useful for padding the return value with
* leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, OCT2BIN returns the #VALUE!
* error value.
* If places is negative, OCT2BIN returns the #NUM! error
* value.
*
* @return string
*/
public static function OCTTOBIN($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
return Functions::VALUE();
}
$x = (string) $x;
if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
return Functions::NAN();
}
return self::DECTOBIN(self::OCTTODEC($x), $places);
}
/**
* OCTTODEC.
*
* Return an octal value as decimal.
*
* Excel Function:
* OCT2DEC(x)
*
* @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)
{
$x = Functions::flattenSingleValue($x);
if (is_bool($x)) {
return Functions::VALUE();
}
$x = (string) $x;
if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
return Functions::NAN();
}
$binX = '';
foreach (str_split($x) as $char) {
$binX .= str_pad(decbin((int) $char), 3, '0', STR_PAD_LEFT);
}
if (strlen($binX) == 30 && $binX[0] == '1') {
for ($i = 0; $i < 30; ++$i) {
$binX[$i] = ($binX[$i] == '1' ? '0' : '1');
}
return (bindec($binX) + 1) * -1;
}
return bindec($binX);
}
/**
* OCTTOHEX.
*
* Return an octal value as hex.
*
* Excel Function:
* OCT2HEX(x[,places])
*
* @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 int $places The number of characters to use. If places is omitted, OCT2HEX
* uses the minimum number of characters necessary. Places is useful
* for padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, OCT2HEX returns the #VALUE! error value.
* If places is negative, OCT2HEX returns the #NUM! error value.
*
* @return string
*/
public static function OCTTOHEX($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
return Functions::VALUE();
}
$x = (string) $x;
if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
return Functions::NAN();
}
$hexVal = strtoupper(dechex(self::OCTTODEC($x)));
return self::nbrConversionFormat($hexVal, $places);
}
/**
* COMPLEX.
*
* Converts real and imaginary coefficients into a complex number of the form x +/- yi or x +/- yj.
*
* Excel Function:
* COMPLEX(realNumber,imaginary[,suffix])
*
* @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')
{
$realNumber = ($realNumber === null) ? 0.0 : Functions::flattenSingleValue($realNumber);
$imaginary = ($imaginary === null) ? 0.0 : Functions::flattenSingleValue($imaginary);
$suffix = ($suffix === null) ? 'i' : Functions::flattenSingleValue($suffix);
if (((is_numeric($realNumber)) && (is_numeric($imaginary))) &&
(($suffix == 'i') || ($suffix == 'j') || ($suffix == ''))
) {
$complex = new Complex($realNumber, $imaginary, $suffix);
return (string) $complex;
}
return Functions::VALUE();
}
/**
* IMAGINARY.
*
* Returns the imaginary coefficient of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMAGINARY(complexNumber)
*
* @category Engineering Functions
*
* @param string $complexNumber the complex number for which you want the imaginary
* coefficient
*
* @return float
*/
public static function IMAGINARY($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (new Complex($complexNumber))->getImaginary();
}
/**
* IMREAL.
*
* Returns the real coefficient of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMREAL(complexNumber)
*
* @category Engineering Functions
*
* @param string $complexNumber the complex number for which you want the real coefficient
*
* @return float
*/
public static function IMREAL($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (new Complex($complexNumber))->getReal();
}
/**
* 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)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (new Complex($complexNumber))->abs();
}
/**
* 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 $complexNumber the complex number for which you want the argument theta
*
* @return float|string
*/
public static function IMARGUMENT($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
$complex = new Complex($complexNumber);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return Functions::DIV0();
}
return $complex->argument();
}
/**
* 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)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->conjugate();
}
/**
* IMCOS.
*
* Returns the cosine of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMCOS(complexNumber)
*
* @param string $complexNumber the complex number for which you want the cosine
*
* @return float|string
*/
public static function IMCOS($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->cos();
}
/**
* IMCOSH.
*
* Returns the hyperbolic cosine of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMCOSH(complexNumber)
*
* @param string $complexNumber the complex number for which you want the hyperbolic cosine
*
* @return float|string
*/
public static function IMCOSH($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->cosh();
}
/**
* IMCOT.
*
* Returns the cotangent of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMCOT(complexNumber)
*
* @param string $complexNumber the complex number for which you want the cotangent
*
* @return float|string
*/
public static function IMCOT($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->cot();
}
/**
* IMCSC.
*
* Returns the cosecant of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMCSC(complexNumber)
*
* @param string $complexNumber the complex number for which you want the cosecant
*
* @return float|string
*/
public static function IMCSC($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->csc();
}
/**
* IMCSCH.
*
* Returns the hyperbolic cosecant of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMCSCH(complexNumber)
*
* @param string $complexNumber the complex number for which you want the hyperbolic cosecant
*
* @return float|string
*/
public static function IMCSCH($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->csch();
}
/**
* IMSIN.
*
* Returns the sine of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMSIN(complexNumber)
*
* @param string $complexNumber the complex number for which you want the sine
*
* @return float|string
*/
public static function IMSIN($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->sin();
}
/**
* IMSINH.
*
* Returns the hyperbolic sine of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMSINH(complexNumber)
*
* @param string $complexNumber the complex number for which you want the hyperbolic sine
*
* @return float|string
*/
public static function IMSINH($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->sinh();
}
/**
* IMSEC.
*
* Returns the secant of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMSEC(complexNumber)
*
* @param string $complexNumber the complex number for which you want the secant
*
* @return float|string
*/
public static function IMSEC($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->sec();
}
/**
* IMSECH.
*
* Returns the hyperbolic secant of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMSECH(complexNumber)
*
* @param string $complexNumber the complex number for which you want the hyperbolic secant
*
* @return float|string
*/
public static function IMSECH($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->sech();
}
/**
* IMTAN.
*
* Returns the tangent of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMTAN(complexNumber)
*
* @param string $complexNumber the complex number for which you want the tangent
*
* @return float|string
*/
public static function IMTAN($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->tan();
}
/**
* 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)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
$theta = self::IMARGUMENT($complexNumber);
if ($theta === Functions::DIV0()) {
return '0';
}
return (string) (new Complex($complexNumber))->sqrt();
}
/**
* 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)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
$complex = new Complex($complexNumber);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return Functions::NAN();
}
return (string) (new Complex($complexNumber))->ln();
}
/**
* 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)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
$complex = new Complex($complexNumber);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return Functions::NAN();
}
return (string) (new Complex($complexNumber))->log10();
}
/**
* IMLOG2.
*
* Returns the base-2 logarithm of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMLOG2(complexNumber)
*
* @param string $complexNumber the complex number for which you want the base-2 logarithm
*
* @return string
*/
public static function IMLOG2($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
$complex = new Complex($complexNumber);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return Functions::NAN();
}
return (string) (new Complex($complexNumber))->log2();
}
/**
* 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)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->exp();
}
/**
* 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)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
$realNumber = Functions::flattenSingleValue($realNumber);
if (!is_numeric($realNumber)) {
return Functions::VALUE();
}
return (string) (new Complex($complexNumber))->pow($realNumber);
}
/**
* 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)
{
$complexDividend = Functions::flattenSingleValue($complexDividend);
$complexDivisor = Functions::flattenSingleValue($complexDivisor);
try {
return (string) (new Complex($complexDividend))->divideby(new Complex($complexDivisor));
} catch (ComplexException $e) {
return Functions::NAN();
}
}
/**
* 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)
{
$complexNumber1 = Functions::flattenSingleValue($complexNumber1);
$complexNumber2 = Functions::flattenSingleValue($complexNumber2);
try {
return (string) (new Complex($complexNumber1))->subtract(new Complex($complexNumber2));
} catch (ComplexException $e) {
return Functions::NAN();
}
}
/**
* IMSUM.
*
* Returns the sum of two or more complex numbers in x + yi or x + yj text format.
*
* Excel Function:
* IMSUM(complexNumber[,complexNumber[,...]])
*
* @param string ...$complexNumbers Series of complex numbers to add
*
* @return string
*/
public static function IMSUM(...$complexNumbers)
{
// Return value
$returnValue = new Complex(0.0);
$aArgs = Functions::flattenArray($complexNumbers);
try {
// Loop through the arguments
foreach ($aArgs as $complex) {
$returnValue = $returnValue->add(new Complex($complex));
}
} catch (ComplexException $e) {
return Functions::NAN();
}
return (string) $returnValue;
}
/**
* IMPRODUCT.
*
* Returns the product of two or more complex numbers in x + yi or x + yj text format.
*
* Excel Function:
* IMPRODUCT(complexNumber[,complexNumber[,...]])
*
* @param string ...$complexNumbers Series of complex numbers to multiply
*
* @return string
*/
public static function IMPRODUCT(...$complexNumbers)
{
// Return value
$returnValue = new Complex(1.0);
$aArgs = Functions::flattenArray($complexNumbers);
try {
// Loop through the arguments
foreach ($aArgs as $complex) {
$returnValue = $returnValue->multiply(new Complex($complex));
}
} catch (ComplexException $e) {
return Functions::NAN();
}
return (string) $returnValue;
}
/**
* 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)
{
$a = Functions::flattenSingleValue($a);
$b = Functions::flattenSingleValue($b);
return (int) ($a == $b);
}
/**
* GESTEP.
*
* Excel Function:
* GESTEP(number[,step])
*
* Returns 1 if number >= step; returns 0 (zero) otherwise
* Use this function to filter a set of values. For example, by summing several GESTEP
* functions you calculate the count of values that exceed a threshold.
*
* @param float $number the value to test against step
* @param float $step The threshold value.
* If you omit a value for step, GESTEP uses zero.
*
* @return int
*/
public static function GESTEP($number, $step = 0)
{
$number = Functions::flattenSingleValue($number);
$step = Functions::flattenSingleValue($step);
return (int) ($number >= $step);
}
//
// Private method to calculate the erf value
//
private static $twoSqrtPi = 1.128379167095512574;
public static function erfVal($x)
{
if (abs($x) > 2.2) {
return 1 - self::erfcVal($x);
}
$sum = $term = $x;
$xsqr = ($x * $x);
$j = 1;
do {
$term *= $xsqr / $j;
$sum -= $term / (2 * $j + 1);
++$j;
$term *= $xsqr / $j;
$sum += $term / (2 * $j + 1);
++$j;
if ($sum == 0.0) {
break;
}
} while (abs($term / $sum) > Functions::PRECISION);
return self::$twoSqrtPi * $sum;
}
/**
* Validate arguments passed to the bitwise functions.
*
* @param mixed $value
*
* @throws Exception
*
* @return int
*/
private static function validateBitwiseArgument($value)
{
$value = Functions::flattenSingleValue($value);
if (is_int($value)) {
return $value;
} elseif (is_numeric($value)) {
if ($value == (int) ($value)) {
$value = (int) ($value);
if (($value > pow(2, 48) - 1) || ($value < 0)) {
throw new Exception(Functions::NAN());
}
return $value;
}
throw new Exception(Functions::NAN());
}
throw new Exception(Functions::VALUE());
}
/**
* BITAND.
*
* Returns the bitwise AND of two integer values.
*
* Excel Function:
* BITAND(number1, number2)
*
* @category Engineering Functions
*
* @param int $number1
* @param int $number2
*
* @return int|string
*/
public static function BITAND($number1, $number2)
{
try {
$number1 = self::validateBitwiseArgument($number1);
$number2 = self::validateBitwiseArgument($number2);
} catch (Exception $e) {
return $e->getMessage();
}
return $number1 & $number2;
}
/**
* BITOR.
*
* Returns the bitwise OR of two integer values.
*
* Excel Function:
* BITOR(number1, number2)
*
* @category Engineering Functions
*
* @param int $number1
* @param int $number2
*
* @return int|string
*/
public static function BITOR($number1, $number2)
{
try {
$number1 = self::validateBitwiseArgument($number1);
$number2 = self::validateBitwiseArgument($number2);
} catch (Exception $e) {
return $e->getMessage();
}
return $number1 | $number2;
}
/**
* BITXOR.
*
* Returns the bitwise XOR of two integer values.
*
* Excel Function:
* BITXOR(number1, number2)
*
* @category Engineering Functions
*
* @param int $number1
* @param int $number2
*
* @return int|string
*/
public static function BITXOR($number1, $number2)
{
try {
$number1 = self::validateBitwiseArgument($number1);
$number2 = self::validateBitwiseArgument($number2);
} catch (Exception $e) {
return $e->getMessage();
}
return $number1 ^ $number2;
}
/**
* BITLSHIFT.
*
* Returns the number value shifted left by shift_amount bits.
*
* Excel Function:
* BITLSHIFT(number, shift_amount)
*
* @category Engineering Functions
*
* @param int $number
* @param int $shiftAmount
*
* @return int|string
*/
public static function BITLSHIFT($number, $shiftAmount)
{
try {
$number = self::validateBitwiseArgument($number);
} catch (Exception $e) {
return $e->getMessage();
}
$shiftAmount = Functions::flattenSingleValue($shiftAmount);
$result = $number << $shiftAmount;
if ($result > pow(2, 48) - 1) {
return Functions::NAN();
}
return $result;
}
/**
* BITRSHIFT.
*
* Returns the number value shifted right by shift_amount bits.
*
* Excel Function:
* BITRSHIFT(number, shift_amount)
*
* @category Engineering Functions
*
* @param int $number
* @param int $shiftAmount
*
* @return int|string
*/
public static function BITRSHIFT($number, $shiftAmount)
{
try {
$number = self::validateBitwiseArgument($number);
} catch (Exception $e) {
return $e->getMessage();
}
$shiftAmount = Functions::flattenSingleValue($shiftAmount);
return $number >> $shiftAmount;
}
/**
* 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.
* PhpSpreadsheet follows Excel 2010 behaviour, and accepts negative arguments.
*
* Excel Function:
* ERF(lower[,upper])
*
* @param float $lower lower bound for integrating ERF
* @param float $upper upper bound for integrating ERF.
* If omitted, ERF integrates between zero and lower_limit
*
* @return float|string
*/
public static function ERF($lower, $upper = null)
{
$lower = Functions::flattenSingleValue($lower);
$upper = Functions::flattenSingleValue($upper);
if (is_numeric($lower)) {
if ($upper === null) {
return self::erfVal($lower);
}
if (is_numeric($upper)) {
return self::erfVal($upper) - self::erfVal($lower);
}
}
return Functions::VALUE();
}
/**
* ERFPRECISE.
*
* Returns the error function integrated between the lower and upper bound arguments.
*
* Excel Function:
* ERF.PRECISE(limit)
*
* @param float $limit bound for integrating ERF
*
* @return float|string
*/
public static function ERFPRECISE($limit)
{
$limit = Functions::flattenSingleValue($limit);
return self::ERF($limit);
}
//
// Private method to calculate the erfc value
//
private static $oneSqrtPi = 0.564189583547756287;
private static function erfcVal($x)
{
if (abs($x) < 2.2) {
return 1 - self::erfVal($x);
}
if ($x < 0) {
return 2 - self::ERFC(-$x);
}
$a = $n = 1;
$b = $c = $x;
$d = ($x * $x) + 0.5;
$q1 = $q2 = $b / $d;
$t = 0;
do {
$t = $a * $n + $b * $x;
$a = $b;
$b = $t;
$t = $c * $n + $d * $x;
$c = $d;
$d = $t;
$n += 0.5;
$q1 = $q2;
$q2 = $b / $d;
} while ((abs($q1 - $q2) / $q2) > Functions::PRECISION);
return self::$oneSqrtPi * exp(-$x * $x) * $q2;
}
/**
* ERFC.
*
* Returns the complementary ERF function integrated between x and infinity
*
* Note: In Excel 2007 or earlier, if you input a negative value for the lower bound argument,
* the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
* improved, so that it can now calculate the function for both positive and negative x values.
* PhpSpreadsheet follows Excel 2010 behaviour, and accepts nagative arguments.
*
* Excel Function:
* ERFC(x)
*
* @param float $x The lower bound for integrating ERFC
*
* @return float|string
*/
public static function ERFC($x)
{
$x = Functions::flattenSingleValue($x);
if (is_numeric($x)) {
return self::erfcVal($x);
}
return Functions::VALUE();
}
/**
* getConversionGroups
* Returns a list of the different conversion groups for UOM conversions.
*
* @return array
*/
public static function getConversionGroups()
{
$conversionGroups = [];
foreach (self::$conversionUnits as $conversionUnit) {
$conversionGroups[] = $conversionUnit['Group'];
}
return array_merge(array_unique($conversionGroups));
}
/**
* getConversionGroupUnits
* Returns an array of units of measure, for a specified conversion group, or for all groups.
*
* @param string $group The group whose units of measure you want to retrieve
*
* @return array
*/
public static function getConversionGroupUnits($group = null)
{
$conversionGroups = [];
foreach (self::$conversionUnits as $conversionUnit => $conversionGroup) {
if (($group === null) || ($conversionGroup['Group'] == $group)) {
$conversionGroups[$conversionGroup['Group']][] = $conversionUnit;
}
}
return $conversionGroups;
}
/**
* getConversionGroupUnitDetails.
*
* @param string $group The group whose units of measure you want to retrieve
*
* @return array
*/
public static function getConversionGroupUnitDetails($group = null)
{
$conversionGroups = [];
foreach (self::$conversionUnits as $conversionUnit => $conversionGroup) {
if (($group === null) || ($conversionGroup['Group'] == $group)) {
$conversionGroups[$conversionGroup['Group']][] = [
'unit' => $conversionUnit,
'description' => $conversionGroup['Unit Name'],
];
}
}
return $conversionGroups;
}
/**
* getConversionMultipliers
* Returns an array of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM().
*
* @return array of mixed
*/
public static function getConversionMultipliers()
{
return self::$conversionMultipliers;
}
/**
* CONVERTUOM.
*
* Converts a number from one measurement system to another.
* For example, CONVERT can translate a table of distances in miles to a table of distances
* in kilometers.
*
* Excel Function:
* CONVERT(value,fromUOM,toUOM)
*
* @param float $value the value in fromUOM to convert
* @param string $fromUOM the units for value
* @param string $toUOM the units for the result
*
* @return float
*/
public static function CONVERTUOM($value, $fromUOM, $toUOM)
{
$value = Functions::flattenSingleValue($value);
$fromUOM = Functions::flattenSingleValue($fromUOM);
$toUOM = Functions::flattenSingleValue($toUOM);
if (!is_numeric($value)) {
return 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[$fromMultiplier]['multiplier'];
} else {
return Functions::NA();
}
if ((isset(self::$conversionUnits[$fromUOM])) && (self::$conversionUnits[$fromUOM]['AllowPrefix'])) {
$unitGroup1 = self::$conversionUnits[$fromUOM]['Group'];
} else {
return 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[$toMultiplier]['multiplier'];
} else {
return Functions::NA();
}
if ((isset(self::$conversionUnits[$toUOM])) && (self::$conversionUnits[$toUOM]['AllowPrefix'])) {
$unitGroup2 = self::$conversionUnits[$toUOM]['Group'];
} else {
return Functions::NA();
}
}
if ($unitGroup1 != $unitGroup2) {
return Functions::NA();
}
if (($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;
}
$value = (($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;
}
}