['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 * * @param string $complexNumber The complex number * * @return string[] Indexed on "real", "imaginary" and "suffix" */ public static function parseComplex($complexNumber) { $workString = (string) $complexNumber; $realNumber = $imaginary = 0; // Extract the suffix, if there is one $suffix = substr($workString, -1); if (!is_numeric($suffix)) { $workString = substr($workString, 0, -1); } else { $suffix = ''; } // Split the input into its Real and Imaginary components $leadingSign = 0; if (strlen($workString) > 0) { $leadingSign = (($workString[0] == '+') || ($workString[0] == '-')) ? 1 : 0; } $power = ''; $realNumber = strtok($workString, '+-'); if (strtoupper(substr($realNumber, -1)) == 'E') { $power = strtok('+-'); ++$leadingSign; } $realNumber = substr($workString, 0, strlen($realNumber) + strlen($power) + $leadingSign); if ($suffix != '') { $imaginary = substr($workString, strlen($realNumber)); if (($imaginary == '') && (($realNumber == '') || ($realNumber == '+') || ($realNumber == '-'))) { $imaginary = $realNumber . '1'; $realNumber = '0'; } elseif ($imaginary == '') { $imaginary = $realNumber; $realNumber = '0'; } elseif (($imaginary == '+') || ($imaginary == '-')) { $imaginary .= '1'; } } return [ 'real' => $realNumber, 'imaginary' => $imaginary, 'suffix' => $suffix, ]; } /** * Cleans the leading characters in a complex number string. * * @param string $complexNumber The complex number to clean * * @return string The "cleaned" complex number */ private static function cleanComplex($complexNumber) { if ($complexNumber[0] == '+') { $complexNumber = substr($complexNumber, 1); } if ($complexNumber[0] == '0') { $complexNumber = substr($complexNumber, 1); } if ($complexNumber[0] == '.') { $complexNumber = '0' . $complexNumber; } if ($complexNumber[0] == '+') { $complexNumber = substr($complexNumber, 1); } return $complexNumber; } /** * Formats a number base string value with leading zeroes. * * @param string $xVal The "number" to pad * @param int $places The length that we want to pad this value * * @return string The padded "number" */ private static function nbrConversionFormat($xVal, $places) { if (!is_null($places)) { if (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) { $x = (is_null($x)) ? 0.0 : Functions::flattenSingleValue($x); $ord = (is_null($ord)) ? 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) { $x = (is_null($x)) ? 0.0 : Functions::flattenSingleValue($x); $ord = (is_null($ord)) ? 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(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) { $x = (is_null($x)) ? 0.0 : Functions::flattenSingleValue($x); $ord = (is_null($ord)) ? 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) { $x = (is_null($x)) ? 0.0 : Functions::flattenSingleValue($x); $ord = (is_null($ord)) ? 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[,places]) * * @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 : Functions::flattenSingleValue($realNumber); $imaginary = (is_null($imaginary)) ? 0.0 : Functions::flattenSingleValue($imaginary); $suffix = (is_null($suffix)) ? 'i' : 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 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); $parsedComplex = self::parseComplex($complexNumber); return $parsedComplex['imaginary']; } /** * IMREAL. * * Returns the real coefficient of a complex number in x + yi or x + yj text format. * * Excel Function: * IMREAL(complexNumber) * * @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); $parsedComplex = self::parseComplex($complexNumber); return $parsedComplex['real']; } /** * IMABS. * * Returns the absolute value (modulus) of a complex number in x + yi or x + yj text format. * * Excel Function: * IMABS(complexNumber) * * @param string $complexNumber the complex number for which you want the absolute value * * @return float */ public static function IMABS($complexNumber) { $complexNumber = Functions::flattenSingleValue($complexNumber); $parsedComplex = self::parseComplex($complexNumber); return sqrt( ($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']) ); } /** * IMARGUMENT. * * Returns the argument theta of a complex number, i.e. the angle in radians from the real * axis to the representation of the number in polar coordinates. * * Excel Function: * IMARGUMENT(complexNumber) * * @param string $complexNumber the complex number for which you want the argument theta * * @return float */ public static function IMARGUMENT($complexNumber) { $complexNumber = Functions::flattenSingleValue($complexNumber); $parsedComplex = self::parseComplex($complexNumber); if ($parsedComplex['real'] == 0.0) { if ($parsedComplex['imaginary'] == 0.0) { return Functions::DIV0(); } elseif ($parsedComplex['imaginary'] < 0.0) { return M_PI / -2; } return M_PI / 2; } elseif ($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']))); } return M_PI - atan($parsedComplex['imaginary'] / abs($parsedComplex['real'])); } /** * IMCONJUGATE. * * Returns the complex conjugate of a complex number in x + yi or x + yj text format. * * Excel Function: * IMCONJUGATE(complexNumber) * * @param string $complexNumber the complex number for which you want the conjugate * * @return string */ public static function IMCONJUGATE($complexNumber) { $complexNumber = Functions::flattenSingleValue($complexNumber); $parsedComplex = self::parseComplex($complexNumber); if ($parsedComplex['imaginary'] == 0.0) { return $parsedComplex['real']; } return self::cleanComplex( self::COMPLEX( $parsedComplex['real'], 0 - $parsedComplex['imaginary'], $parsedComplex['suffix'] ) ); } /** * IMCOS. * * Returns the cosine of a complex number in x + yi or x + yj text format. * * Excel Function: * IMCOS(complexNumber) * * @param string $complexNumber the complex number for which you want the cosine * * @return string|float */ public static function IMCOS($complexNumber) { $complexNumber = Functions::flattenSingleValue($complexNumber); $parsedComplex = self::parseComplex($complexNumber); if ($parsedComplex['imaginary'] == 0.0) { return cos($parsedComplex['real']); } return self::IMCONJUGATE( self::COMPLEX( cos($parsedComplex['real']) * cosh($parsedComplex['imaginary']), sin($parsedComplex['real']) * sinh($parsedComplex['imaginary']), $parsedComplex['suffix'] ) ); } /** * IMSIN. * * Returns the sine of a complex number in x + yi or x + yj text format. * * Excel Function: * IMSIN(complexNumber) * * @param string $complexNumber the complex number for which you want the sine * * @return string|float */ public static function IMSIN($complexNumber) { $complexNumber = Functions::flattenSingleValue($complexNumber); $parsedComplex = self::parseComplex($complexNumber); if ($parsedComplex['imaginary'] == 0.0) { return sin($parsedComplex['real']); } return self::COMPLEX( sin($parsedComplex['real']) * cosh($parsedComplex['imaginary']), cos($parsedComplex['real']) * sinh($parsedComplex['imaginary']), $parsedComplex['suffix'] ); } /** * IMSQRT. * * Returns the square root of a complex number in x + yi or x + yj text format. * * Excel Function: * IMSQRT(complexNumber) * * @param string $complexNumber the complex number for which you want the square root * * @return string */ public static function IMSQRT($complexNumber) { $complexNumber = Functions::flattenSingleValue($complexNumber); $parsedComplex = self::parseComplex($complexNumber); $theta = self::IMARGUMENT($complexNumber); if ($theta === functions::DIV0()) { return '0'; } $d1 = cos($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 * $r); } return self::COMPLEX($d1 * $r, $d2 * $r, $parsedComplex['suffix']); } /** * IMLN. * * Returns the natural logarithm of a complex number in x + yi or x + yj text format. * * Excel Function: * IMLN(complexNumber) * * @param string $complexNumber the complex number for which you want the natural logarithm * * @return string */ public static function IMLN($complexNumber) { $complexNumber = Functions::flattenSingleValue($complexNumber); $parsedComplex = self::parseComplex($complexNumber); if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) { return Functions::NAN(); } $logR = log(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']))); $t = self::IMARGUMENT($complexNumber); if ($parsedComplex['suffix'] == '') { return self::COMPLEX($logR, $t); } return self::COMPLEX($logR, $t, $parsedComplex['suffix']); } /** * IMLOG10. * * Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format. * * Excel Function: * IMLOG10(complexNumber) * * @param string $complexNumber the complex number for which you want the common logarithm * * @return string */ public static function IMLOG10($complexNumber) { $complexNumber = Functions::flattenSingleValue($complexNumber); $parsedComplex = self::parseComplex($complexNumber); if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) { return Functions::NAN(); } elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) { return log10($parsedComplex['real']); } return self::IMPRODUCT(log10(EULER), self::IMLN($complexNumber)); } /** * IMLOG2. * * Returns the base-2 logarithm of a complex number in x + yi or x + yj text format. * * Excel Function: * IMLOG2(complexNumber) * * @param string $complexNumber the complex number for which you want the base-2 logarithm * * @return string */ public static function IMLOG2($complexNumber) { $complexNumber = Functions::flattenSingleValue($complexNumber); $parsedComplex = self::parseComplex($complexNumber); if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) { return Functions::NAN(); } elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) { return log($parsedComplex['real'], 2); } return self::IMPRODUCT(log(EULER, 2), self::IMLN($complexNumber)); } /** * IMEXP. * * Returns the exponential of a complex number in x + yi or x + yj text format. * * Excel Function: * IMEXP(complexNumber) * * @param string $complexNumber the complex number for which you want the exponential * * @return string */ public static function IMEXP($complexNumber) { $complexNumber = Functions::flattenSingleValue($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, $eY); } return self::COMPLEX($eX, $eY, $parsedComplex['suffix']); } /** * IMPOWER. * * Returns a complex number in x + yi or x + yj text format raised to a power. * * Excel Function: * IMPOWER(complexNumber,realNumber) * * @param string $complexNumber the complex number you want to raise to a power * @param float $realNumber the power to which you want to raise the complex number * * @return string */ public static function IMPOWER($complexNumber, $realNumber) { $complexNumber = Functions::flattenSingleValue($complexNumber); $realNumber = Functions::flattenSingleValue($realNumber); if (!is_numeric($realNumber)) { return 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), $parsedComplex['suffix']); } return self::COMPLEX($rPower * cos($theta), $rPower * sin($theta), $parsedComplex['suffix']); } /** * IMDIV. * * Returns the quotient of two complex numbers in x + yi or x + yj text format. * * Excel Function: * IMDIV(complexDividend,complexDivisor) * * @param string $complexDividend the complex numerator or dividend * @param string $complexDivisor the complex denominator or divisor * * @return string */ public static function IMDIV($complexDividend, $complexDivisor) { $complexDividend = Functions::flattenSingleValue($complexDividend); $complexDivisor = Functions::flattenSingleValue($complexDivisor); $parsedComplexDividend = self::parseComplex($complexDividend); $parsedComplexDivisor = self::parseComplex($complexDivisor); if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] != '') && ($parsedComplexDividend['suffix'] != $parsedComplexDivisor['suffix']) ) { return Functions::NAN(); } if (($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']); } return $r; } /** * IMSUB. * * Returns the difference of two complex numbers in x + yi or x + yj text format. * * Excel Function: * IMSUB(complexNumber1,complexNumber2) * * @param string $complexNumber1 the complex number from which to subtract complexNumber2 * @param string $complexNumber2 the complex number to subtract from complexNumber1 * * @return string */ public static function IMSUB($complexNumber1, $complexNumber2) { $complexNumber1 = Functions::flattenSingleValue($complexNumber1); $complexNumber2 = Functions::flattenSingleValue($complexNumber2); $parsedComplex1 = self::parseComplex($complexNumber1); $parsedComplex2 = self::parseComplex($complexNumber2); if ((($parsedComplex1['suffix'] != '') && ($parsedComplex2['suffix'] != '')) && ($parsedComplex1['suffix'] != $parsedComplex2['suffix']) ) { return Functions::NAN(); } elseif (($parsedComplex1['suffix'] == '') && ($parsedComplex2['suffix'] != '')) { $parsedComplex1['suffix'] = $parsedComplex2['suffix']; } $d1 = $parsedComplex1['real'] - $parsedComplex2['real']; $d2 = $parsedComplex1['imaginary'] - $parsedComplex2['imaginary']; return self::COMPLEX($d1, $d2, $parsedComplex1['suffix']); } /** * IMSUM. * * Returns the sum of two or more complex numbers in x + yi or x + yj text format. * * Excel Function: * IMSUM(complexNumber[,complexNumber[,...]]) * * @param string $complexNumbers Series of complex numbers to add * * @return string */ public static function IMSUM(...$complexNumbers) { // Return value $returnValue = self::parseComplex('0'); $activeSuffix = ''; // Loop through the arguments $aArgs = Functions::flattenArray($complexNumbers); foreach ($aArgs as $arg) { $parsedComplex = self::parseComplex($arg); if ($activeSuffix == '') { $activeSuffix = $parsedComplex['suffix']; } elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) { return Functions::NAN(); } $returnValue['real'] += $parsedComplex['real']; $returnValue['imaginary'] += $parsedComplex['imaginary']; } if ($returnValue['imaginary'] == 0.0) { $activeSuffix = ''; } return self::COMPLEX($returnValue['real'], $returnValue['imaginary'], $activeSuffix); } /** * IMPRODUCT. * * Returns the product of two or more complex numbers in x + yi or x + yj text format. * * Excel Function: * IMPRODUCT(complexNumber[,complexNumber[,...]]) * * @param string $complexNumbers Series of complex numbers to multiply * * @return string */ public static function IMPRODUCT(...$complexNumbers) { // Return value $returnValue = self::parseComplex('1'); $activeSuffix = ''; // Loop through the arguments $aArgs = Functions::flattenArray($complexNumbers); foreach ($aArgs as $arg) { $parsedComplex = self::parseComplex($arg); $workValue = $returnValue; if (($parsedComplex['suffix'] != '') && ($activeSuffix == '')) { $activeSuffix = $parsedComplex['suffix']; } elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) { return Functions::NAN(); } $returnValue['real'] = ($workValue['real'] * $parsedComplex['real']) - ($workValue['imaginary'] * $parsedComplex['imaginary']); $returnValue['imaginary'] = ($workValue['real'] * $parsedComplex['imaginary']) + ($workValue['imaginary'] * $parsedComplex['real']); } if ($returnValue['imaginary'] == 0.0) { $activeSuffix = ''; } return self::COMPLEX($returnValue['real'], $returnValue['imaginary'], $activeSuffix); } /** * DELTA. * * Tests whether two values are equal. Returns 1 if number1 = number2; returns 0 otherwise. * Use this function to filter a set of values. For example, by summing several DELTA * functions you calculate the count of equal pairs. This function is also known as the * Kronecker Delta function. * * Excel Function: * DELTA(a[,b]) * * @param float $a the first number * @param float $b The second number. If omitted, b is assumed to be zero. * * @return int */ public static function DELTA($a, $b = 0) { $a = Functions::flattenSingleValue($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 / $sum) > PRECISION); return self::$twoSqrtPi * $sum; } /** * ERF. * * Returns the error function integrated between the lower and upper bound arguments. * * Note: In Excel 2007 or earlier, if you input a negative value for the upper or lower bound arguments, * the function would return a #NUM! error. However, in Excel 2010, the function algorithm was * improved, so that it can now calculate the function for both positive and negative ranges. * PhpSpreadsheet 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) { $lower = Functions::flattenSingleValue($lower); $upper = Functions::flattenSingleValue($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 Functions::VALUE(); } // // Private method to calculate the erfc value // private static $oneSqrtPi = 0.564189583547756287; private static function erfcVal($x) { if (abs($x) < 2.2) { return 1 - self::erfVal($x); } if ($x < 0) { return 2 - self::ERFC(-$x); } $a = $n = 1; $b = $c = $x; $d = ($x * $x) + 0.5; $q1 = $q2 = $b / $d; $t = 0; do { $t = $a * $n + $b * $x; $a = $b; $b = $t; $t = $c * $n + $d * $x; $c = $d; $d = $t; $n += 0.5; $q1 = $q2; $q2 = $b / $d; } while ((abs($q1 - $q2) / $q2) > PRECISION); return self::$oneSqrtPi * exp(-$x * $x) * $q2; } /** * ERFC. * * Returns the complementary ERF function integrated between x and infinity * * Note: In Excel 2007 or earlier, if you input a negative value for the lower bound argument, * the function would return a #NUM! error. However, in Excel 2010, the function algorithm was * improved, so that it can now calculate the function for both positive and negative x values. * PhpSpreadsheet 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) { $x = Functions::flattenSingleValue($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 => $conversionGroup) { if ((is_null($group)) || ($conversionGroup['Group'] == $group)) { $conversionGroups[$conversionGroup['Group']][] = $conversionUnit; } } return $conversionGroups; } /** * getConversionGroupUnitDetails. * * @param string $group The group whose units of measure you want to retrieve * * @return array */ public static function getConversionGroupUnitDetails($group = null) { $conversionGroups = []; foreach (self::$conversionUnits as $conversionUnit => $conversionGroup) { if ((is_null($group)) || ($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; } }