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<?php |
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namespace PhpOffice\PhpSpreadsheet\Calculation; |
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class Engineering |
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{ |
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/** |
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* EULER. |
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*/ |
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const EULER = 2.71828182845904523536; |
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/** |
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* Details of the Units of measure that can be used in CONVERTUOM(). |
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* |
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* @var mixed[] |
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*/ |
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private static $conversionUnits = [ |
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'g' => ['Group' => 'Mass', 'Unit Name' => 'Gram', 'AllowPrefix' => true], |
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'sg' => ['Group' => 'Mass', 'Unit Name' => 'Slug', 'AllowPrefix' => false], |
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'lbm' => ['Group' => 'Mass', 'Unit Name' => 'Pound mass (avoirdupois)', 'AllowPrefix' => false], |
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'u' => ['Group' => 'Mass', 'Unit Name' => 'U (atomic mass unit)', 'AllowPrefix' => true], |
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'ozm' => ['Group' => 'Mass', 'Unit Name' => 'Ounce mass (avoirdupois)', 'AllowPrefix' => false], |
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'm' => ['Group' => 'Distance', 'Unit Name' => 'Meter', 'AllowPrefix' => true], |
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'mi' => ['Group' => 'Distance', 'Unit Name' => 'Statute mile', 'AllowPrefix' => false], |
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'Nmi' => ['Group' => 'Distance', 'Unit Name' => 'Nautical mile', 'AllowPrefix' => false], |
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'in' => ['Group' => 'Distance', 'Unit Name' => 'Inch', 'AllowPrefix' => false], |
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'ft' => ['Group' => 'Distance', 'Unit Name' => 'Foot', 'AllowPrefix' => false], |
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'yd' => ['Group' => 'Distance', 'Unit Name' => 'Yard', 'AllowPrefix' => false], |
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'ang' => ['Group' => 'Distance', 'Unit Name' => 'Angstrom', 'AllowPrefix' => true], |
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'Pica' => ['Group' => 'Distance', 'Unit Name' => 'Pica (1/72 in)', 'AllowPrefix' => false], |
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'yr' => ['Group' => 'Time', 'Unit Name' => 'Year', 'AllowPrefix' => false], |
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'day' => ['Group' => 'Time', 'Unit Name' => 'Day', 'AllowPrefix' => false], |
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'hr' => ['Group' => 'Time', 'Unit Name' => 'Hour', 'AllowPrefix' => false], |
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'mn' => ['Group' => 'Time', 'Unit Name' => 'Minute', 'AllowPrefix' => false], |
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'sec' => ['Group' => 'Time', 'Unit Name' => 'Second', 'AllowPrefix' => true], |
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'Pa' => ['Group' => 'Pressure', 'Unit Name' => 'Pascal', 'AllowPrefix' => true], |
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'p' => ['Group' => 'Pressure', 'Unit Name' => 'Pascal', 'AllowPrefix' => true], |
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'atm' => ['Group' => 'Pressure', 'Unit Name' => 'Atmosphere', 'AllowPrefix' => true], |
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'at' => ['Group' => 'Pressure', 'Unit Name' => 'Atmosphere', 'AllowPrefix' => true], |
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'mmHg' => ['Group' => 'Pressure', 'Unit Name' => 'mm of Mercury', 'AllowPrefix' => true], |
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'N' => ['Group' => 'Force', 'Unit Name' => 'Newton', 'AllowPrefix' => true], |
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'dyn' => ['Group' => 'Force', 'Unit Name' => 'Dyne', 'AllowPrefix' => true], |
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'dy' => ['Group' => 'Force', 'Unit Name' => 'Dyne', 'AllowPrefix' => true], |
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'lbf' => ['Group' => 'Force', 'Unit Name' => 'Pound force', 'AllowPrefix' => false], |
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'J' => ['Group' => 'Energy', 'Unit Name' => 'Joule', 'AllowPrefix' => true], |
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'e' => ['Group' => 'Energy', 'Unit Name' => 'Erg', 'AllowPrefix' => true], |
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'c' => ['Group' => 'Energy', 'Unit Name' => 'Thermodynamic calorie', 'AllowPrefix' => true], |
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'cal' => ['Group' => 'Energy', 'Unit Name' => 'IT calorie', 'AllowPrefix' => true], |
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'eV' => ['Group' => 'Energy', 'Unit Name' => 'Electron volt', 'AllowPrefix' => true], |
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'ev' => ['Group' => 'Energy', 'Unit Name' => 'Electron volt', 'AllowPrefix' => true], |
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'HPh' => ['Group' => 'Energy', 'Unit Name' => 'Horsepower-hour', 'AllowPrefix' => false], |
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'hh' => ['Group' => 'Energy', 'Unit Name' => 'Horsepower-hour', 'AllowPrefix' => false], |
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'Wh' => ['Group' => 'Energy', 'Unit Name' => 'Watt-hour', 'AllowPrefix' => true], |
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'wh' => ['Group' => 'Energy', 'Unit Name' => 'Watt-hour', 'AllowPrefix' => true], |
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'flb' => ['Group' => 'Energy', 'Unit Name' => 'Foot-pound', 'AllowPrefix' => false], |
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'BTU' => ['Group' => 'Energy', 'Unit Name' => 'BTU', 'AllowPrefix' => false], |
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'btu' => ['Group' => 'Energy', 'Unit Name' => 'BTU', 'AllowPrefix' => false], |
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'HP' => ['Group' => 'Power', 'Unit Name' => 'Horsepower', 'AllowPrefix' => false], |
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'h' => ['Group' => 'Power', 'Unit Name' => 'Horsepower', 'AllowPrefix' => false], |
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'W' => ['Group' => 'Power', 'Unit Name' => 'Watt', 'AllowPrefix' => true], |
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'w' => ['Group' => 'Power', 'Unit Name' => 'Watt', 'AllowPrefix' => true], |
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'T' => ['Group' => 'Magnetism', 'Unit Name' => 'Tesla', 'AllowPrefix' => true], |
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'ga' => ['Group' => 'Magnetism', 'Unit Name' => 'Gauss', 'AllowPrefix' => true], |
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'C' => ['Group' => 'Temperature', 'Unit Name' => 'Celsius', 'AllowPrefix' => false], |
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'cel' => ['Group' => 'Temperature', 'Unit Name' => 'Celsius', 'AllowPrefix' => false], |
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'F' => ['Group' => 'Temperature', 'Unit Name' => 'Fahrenheit', 'AllowPrefix' => false], |
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'fah' => ['Group' => 'Temperature', 'Unit Name' => 'Fahrenheit', 'AllowPrefix' => false], |
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'K' => ['Group' => 'Temperature', 'Unit Name' => 'Kelvin', 'AllowPrefix' => false], |
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'kel' => ['Group' => 'Temperature', 'Unit Name' => 'Kelvin', 'AllowPrefix' => false], |
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'tsp' => ['Group' => 'Liquid', 'Unit Name' => 'Teaspoon', 'AllowPrefix' => false], |
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'tbs' => ['Group' => 'Liquid', 'Unit Name' => 'Tablespoon', 'AllowPrefix' => false], |
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'oz' => ['Group' => 'Liquid', 'Unit Name' => 'Fluid Ounce', 'AllowPrefix' => false], |
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'cup' => ['Group' => 'Liquid', 'Unit Name' => 'Cup', 'AllowPrefix' => false], |
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'pt' => ['Group' => 'Liquid', 'Unit Name' => 'U.S. Pint', 'AllowPrefix' => false], |
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'us_pt' => ['Group' => 'Liquid', 'Unit Name' => 'U.S. Pint', 'AllowPrefix' => false], |
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'uk_pt' => ['Group' => 'Liquid', 'Unit Name' => 'U.K. Pint', 'AllowPrefix' => false], |
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'qt' => ['Group' => 'Liquid', 'Unit Name' => 'Quart', 'AllowPrefix' => false], |
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'gal' => ['Group' => 'Liquid', 'Unit Name' => 'Gallon', 'AllowPrefix' => false], |
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'l' => ['Group' => 'Liquid', 'Unit Name' => 'Litre', 'AllowPrefix' => true], |
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'lt' => ['Group' => 'Liquid', 'Unit Name' => 'Litre', 'AllowPrefix' => true], |
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]; |
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/** |
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* Details of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM(). |
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* |
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* @var mixed[] |
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*/ |
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private static $conversionMultipliers = [ |
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'Y' => ['multiplier' => 1E24, 'name' => 'yotta'], |
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'Z' => ['multiplier' => 1E21, 'name' => 'zetta'], |
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'E' => ['multiplier' => 1E18, 'name' => 'exa'], |
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'P' => ['multiplier' => 1E15, 'name' => 'peta'], |
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'T' => ['multiplier' => 1E12, 'name' => 'tera'], |
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'G' => ['multiplier' => 1E9, 'name' => 'giga'], |
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'M' => ['multiplier' => 1E6, 'name' => 'mega'], |
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'k' => ['multiplier' => 1E3, 'name' => 'kilo'], |
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'h' => ['multiplier' => 1E2, 'name' => 'hecto'], |
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'e' => ['multiplier' => 1E1, 'name' => 'deka'], |
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'd' => ['multiplier' => 1E-1, 'name' => 'deci'], |
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'c' => ['multiplier' => 1E-2, 'name' => 'centi'], |
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'm' => ['multiplier' => 1E-3, 'name' => 'milli'], |
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'u' => ['multiplier' => 1E-6, 'name' => 'micro'], |
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'n' => ['multiplier' => 1E-9, 'name' => 'nano'], |
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'p' => ['multiplier' => 1E-12, 'name' => 'pico'], |
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'f' => ['multiplier' => 1E-15, 'name' => 'femto'], |
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'a' => ['multiplier' => 1E-18, 'name' => 'atto'], |
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'z' => ['multiplier' => 1E-21, 'name' => 'zepto'], |
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'y' => ['multiplier' => 1E-24, 'name' => 'yocto'], |
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]; |
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/** |
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* Details of the Units of measure conversion factors, organised by group. |
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* |
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* @var mixed[] |
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*/ |
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private static $unitConversions = [ |
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'Mass' => [ |
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'g' => [ |
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'g' => 1.0, |
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'sg' => 6.85220500053478E-05, |
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'lbm' => 2.20462291469134E-03, |
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'u' => 6.02217000000000E+23, |
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'ozm' => 3.52739718003627E-02, |
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], |
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'sg' => [ |
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'g' => 1.45938424189287E+04, |
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'sg' => 1.0, |
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'lbm' => 3.21739194101647E+01, |
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'u' => 8.78866000000000E+27, |
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'ozm' => 5.14782785944229E+02, |
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], |
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'lbm' => [ |
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'g' => 4.5359230974881148E+02, |
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'sg' => 3.10810749306493E-02, |
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'lbm' => 1.0, |
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'u' => 2.73161000000000E+26, |
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'ozm' => 1.60000023429410E+01, |
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], |
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'u' => [ |
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'g' => 1.66053100460465E-24, |
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'sg' => 1.13782988532950E-28, |
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'lbm' => 3.66084470330684E-27, |
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'u' => 1.0, |
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'ozm' => 5.85735238300524E-26, |
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], |
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'ozm' => [ |
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'g' => 2.83495152079732E+01, |
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'sg' => 1.94256689870811E-03, |
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'lbm' => 6.24999908478882E-02, |
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'u' => 1.70725600000000E+25, |
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'ozm' => 1.0, |
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], |
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], |
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'Distance' => [ |
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'm' => [ |
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'm' => 1.0, |
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'mi' => 6.21371192237334E-04, |
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'Nmi' => 5.39956803455724E-04, |
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'in' => 3.93700787401575E+01, |
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'ft' => 3.28083989501312E+00, |
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'yd' => 1.09361329797891E+00, |
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'ang' => 1.00000000000000E+10, |
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'Pica' => 2.83464566929116E+03, |
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], |
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'mi' => [ |
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'm' => 1.60934400000000E+03, |
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'mi' => 1.0, |
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'Nmi' => 8.68976241900648E-01, |
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'in' => 6.33600000000000E+04, |
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'ft' => 5.28000000000000E+03, |
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'yd' => 1.76000000000000E+03, |
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'ang' => 1.60934400000000E+13, |
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'Pica' => 4.56191999999971E+06, |
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], |
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'Nmi' => [ |
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'm' => 1.85200000000000E+03, |
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'mi' => 1.15077944802354E+00, |
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'Nmi' => 1.0, |
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'in' => 7.29133858267717E+04, |
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'ft' => 6.07611548556430E+03, |
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'yd' => 2.02537182785694E+03, |
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'ang' => 1.85200000000000E+13, |
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'Pica' => 5.24976377952723E+06, |
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], |
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'in' => [ |
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'm' => 2.54000000000000E-02, |
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'mi' => 1.57828282828283E-05, |
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'Nmi' => 1.37149028077754E-05, |
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'in' => 1.0, |
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'ft' => 8.33333333333333E-02, |
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'yd' => 2.77777777686643E-02, |
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'ang' => 2.54000000000000E+08, |
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'Pica' => 7.19999999999955E+01, |
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], |
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'ft' => [ |
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196
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'm' => 3.04800000000000E-01, |
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'mi' => 1.89393939393939E-04, |
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198
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'Nmi' => 1.64578833693305E-04, |
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199
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'in' => 1.20000000000000E+01, |
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200
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'ft' => 1.0, |
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'yd' => 3.33333333223972E-01, |
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'ang' => 3.04800000000000E+09, |
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'Pica' => 8.63999999999946E+02, |
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], |
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'yd' => [ |
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'm' => 9.14400000300000E-01, |
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'mi' => 5.68181818368230E-04, |
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'Nmi' => 4.93736501241901E-04, |
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209
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'in' => 3.60000000118110E+01, |
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'ft' => 3.00000000000000E+00, |
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'yd' => 1.0, |
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212
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'ang' => 9.14400000300000E+09, |
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213
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'Pica' => 2.59200000085023E+03, |
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214
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], |
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215
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'ang' => [ |
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216
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'm' => 1.00000000000000E-10, |
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217
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'mi' => 6.21371192237334E-14, |
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218
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'Nmi' => 5.39956803455724E-14, |
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219
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'in' => 3.93700787401575E-09, |
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220
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'ft' => 3.28083989501312E-10, |
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221
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'yd' => 1.09361329797891E-10, |
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'ang' => 1.0, |
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'Pica' => 2.83464566929116E-07, |
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], |
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'Pica' => [ |
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'm' => 3.52777777777800E-04, |
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227
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'mi' => 2.19205948372629E-07, |
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228
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'Nmi' => 1.90484761219114E-07, |
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229
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'in' => 1.38888888888898E-02, |
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230
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'ft' => 1.15740740740748E-03, |
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231
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'yd' => 3.85802469009251E-04, |
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232
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'ang' => 3.52777777777800E+06, |
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233
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'Pica' => 1.0, |
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234
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], |
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235
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], |
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236
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'Time' => [ |
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237
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'yr' => [ |
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238
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'yr' => 1.0, |
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239
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'day' => 365.25, |
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240
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'hr' => 8766.0, |
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241
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'mn' => 525960.0, |
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242
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'sec' => 31557600.0, |
|
243
|
|
|
], |
|
244
|
|
|
'day' => [ |
|
245
|
|
|
'yr' => 2.73785078713210E-03, |
|
246
|
|
|
'day' => 1.0, |
|
247
|
|
|
'hr' => 24.0, |
|
248
|
|
|
'mn' => 1440.0, |
|
249
|
|
|
'sec' => 86400.0, |
|
250
|
|
|
], |
|
251
|
|
|
'hr' => [ |
|
252
|
|
|
'yr' => 1.14077116130504E-04, |
|
253
|
|
|
'day' => 4.16666666666667E-02, |
|
254
|
|
|
'hr' => 1.0, |
|
255
|
|
|
'mn' => 60.0, |
|
256
|
|
|
'sec' => 3600.0, |
|
257
|
|
|
], |
|
258
|
|
|
'mn' => [ |
|
259
|
|
|
'yr' => 1.90128526884174E-06, |
|
260
|
|
|
'day' => 6.94444444444444E-04, |
|
261
|
|
|
'hr' => 1.66666666666667E-02, |
|
262
|
|
|
'mn' => 1.0, |
|
263
|
|
|
'sec' => 60.0, |
|
264
|
|
|
], |
|
265
|
|
|
'sec' => [ |
|
266
|
|
|
'yr' => 3.16880878140289E-08, |
|
267
|
|
|
'day' => 1.15740740740741E-05, |
|
268
|
|
|
'hr' => 2.77777777777778E-04, |
|
269
|
|
|
'mn' => 1.66666666666667E-02, |
|
270
|
|
|
'sec' => 1.0, |
|
271
|
|
|
], |
|
272
|
|
|
], |
|
273
|
|
|
'Pressure' => [ |
|
274
|
|
|
'Pa' => [ |
|
275
|
|
|
'Pa' => 1.0, |
|
276
|
|
|
'p' => 1.0, |
|
277
|
|
|
'atm' => 9.86923299998193E-06, |
|
278
|
|
|
'at' => 9.86923299998193E-06, |
|
279
|
|
|
'mmHg' => 7.50061707998627E-03, |
|
280
|
|
|
], |
|
281
|
|
|
'p' => [ |
|
282
|
|
|
'Pa' => 1.0, |
|
283
|
|
|
'p' => 1.0, |
|
284
|
|
|
'atm' => 9.86923299998193E-06, |
|
285
|
|
|
'at' => 9.86923299998193E-06, |
|
286
|
|
|
'mmHg' => 7.50061707998627E-03, |
|
287
|
|
|
], |
|
288
|
|
|
'atm' => [ |
|
289
|
|
|
'Pa' => 1.01324996583000E+05, |
|
290
|
|
|
'p' => 1.01324996583000E+05, |
|
291
|
|
|
'atm' => 1.0, |
|
292
|
|
|
'at' => 1.0, |
|
293
|
|
|
'mmHg' => 760.0, |
|
294
|
|
|
], |
|
295
|
|
|
'at' => [ |
|
296
|
|
|
'Pa' => 1.01324996583000E+05, |
|
297
|
|
|
'p' => 1.01324996583000E+05, |
|
298
|
|
|
'atm' => 1.0, |
|
299
|
|
|
'at' => 1.0, |
|
300
|
|
|
'mmHg' => 760.0, |
|
301
|
|
|
], |
|
302
|
|
|
'mmHg' => [ |
|
303
|
|
|
'Pa' => 1.33322363925000E+02, |
|
304
|
|
|
'p' => 1.33322363925000E+02, |
|
305
|
|
|
'atm' => 1.31578947368421E-03, |
|
306
|
|
|
'at' => 1.31578947368421E-03, |
|
307
|
|
|
'mmHg' => 1.0, |
|
308
|
|
|
], |
|
309
|
|
|
], |
|
310
|
|
|
'Force' => [ |
|
311
|
|
|
'N' => [ |
|
312
|
|
|
'N' => 1.0, |
|
313
|
|
|
'dyn' => 1.0E+5, |
|
314
|
|
|
'dy' => 1.0E+5, |
|
315
|
|
|
'lbf' => 2.24808923655339E-01, |
|
316
|
|
|
], |
|
317
|
|
|
'dyn' => [ |
|
318
|
|
|
'N' => 1.0E-5, |
|
319
|
|
|
'dyn' => 1.0, |
|
320
|
|
|
'dy' => 1.0, |
|
321
|
|
|
'lbf' => 2.24808923655339E-06, |
|
322
|
|
|
], |
|
323
|
|
|
'dy' => [ |
|
324
|
|
|
'N' => 1.0E-5, |
|
325
|
|
|
'dyn' => 1.0, |
|
326
|
|
|
'dy' => 1.0, |
|
327
|
|
|
'lbf' => 2.24808923655339E-06, |
|
328
|
|
|
], |
|
329
|
|
|
'lbf' => [ |
|
330
|
|
|
'N' => 4.448222, |
|
331
|
|
|
'dyn' => 4.448222E+5, |
|
332
|
|
|
'dy' => 4.448222E+5, |
|
333
|
|
|
'lbf' => 1.0, |
|
334
|
|
|
], |
|
335
|
|
|
], |
|
336
|
|
|
'Energy' => [ |
|
337
|
|
|
'J' => [ |
|
338
|
|
|
'J' => 1.0, |
|
339
|
|
|
'e' => 9.99999519343231E+06, |
|
340
|
|
|
'c' => 2.39006249473467E-01, |
|
341
|
|
|
'cal' => 2.38846190642017E-01, |
|
342
|
|
|
'eV' => 6.24145700000000E+18, |
|
343
|
|
|
'ev' => 6.24145700000000E+18, |
|
344
|
|
|
'HPh' => 3.72506430801000E-07, |
|
345
|
|
|
'hh' => 3.72506430801000E-07, |
|
346
|
|
|
'Wh' => 2.77777916238711E-04, |
|
347
|
|
|
'wh' => 2.77777916238711E-04, |
|
348
|
|
|
'flb' => 2.37304222192651E+01, |
|
349
|
|
|
'BTU' => 9.47815067349015E-04, |
|
350
|
|
|
'btu' => 9.47815067349015E-04, |
|
351
|
|
|
], |
|
352
|
|
|
'e' => [ |
|
353
|
|
|
'J' => 1.00000048065700E-07, |
|
354
|
|
|
'e' => 1.0, |
|
355
|
|
|
'c' => 2.39006364353494E-08, |
|
356
|
|
|
'cal' => 2.38846305445111E-08, |
|
357
|
|
|
'eV' => 6.24146000000000E+11, |
|
358
|
|
|
'ev' => 6.24146000000000E+11, |
|
359
|
|
|
'HPh' => 3.72506609848824E-14, |
|
360
|
|
|
'hh' => 3.72506609848824E-14, |
|
361
|
|
|
'Wh' => 2.77778049754611E-11, |
|
362
|
|
|
'wh' => 2.77778049754611E-11, |
|
363
|
|
|
'flb' => 2.37304336254586E-06, |
|
364
|
|
|
'BTU' => 9.47815522922962E-11, |
|
365
|
|
|
'btu' => 9.47815522922962E-11, |
|
366
|
|
|
], |
|
367
|
|
|
'c' => [ |
|
368
|
|
|
'J' => 4.18399101363672E+00, |
|
369
|
|
|
'e' => 4.18398900257312E+07, |
|
370
|
|
|
'c' => 1.0, |
|
371
|
|
|
'cal' => 9.99330315287563E-01, |
|
372
|
|
|
'eV' => 2.61142000000000E+19, |
|
373
|
|
|
'ev' => 2.61142000000000E+19, |
|
374
|
|
|
'HPh' => 1.55856355899327E-06, |
|
375
|
|
|
'hh' => 1.55856355899327E-06, |
|
376
|
|
|
'Wh' => 1.16222030532950E-03, |
|
377
|
|
|
'wh' => 1.16222030532950E-03, |
|
378
|
|
|
'flb' => 9.92878733152102E+01, |
|
379
|
|
|
'BTU' => 3.96564972437776E-03, |
|
380
|
|
|
'btu' => 3.96564972437776E-03, |
|
381
|
|
|
], |
|
382
|
|
|
'cal' => [ |
|
383
|
|
|
'J' => 4.18679484613929E+00, |
|
384
|
|
|
'e' => 4.18679283372801E+07, |
|
385
|
|
|
'c' => 1.00067013349059E+00, |
|
386
|
|
|
'cal' => 1.0, |
|
387
|
|
|
'eV' => 2.61317000000000E+19, |
|
388
|
|
|
'ev' => 2.61317000000000E+19, |
|
389
|
|
|
'HPh' => 1.55960800463137E-06, |
|
390
|
|
|
'hh' => 1.55960800463137E-06, |
|
391
|
|
|
'Wh' => 1.16299914807955E-03, |
|
392
|
|
|
'wh' => 1.16299914807955E-03, |
|
393
|
|
|
'flb' => 9.93544094443283E+01, |
|
394
|
|
|
'BTU' => 3.96830723907002E-03, |
|
395
|
|
|
'btu' => 3.96830723907002E-03, |
|
396
|
|
|
], |
|
397
|
|
|
'eV' => [ |
|
398
|
|
|
'J' => 1.60219000146921E-19, |
|
399
|
|
|
'e' => 1.60218923136574E-12, |
|
400
|
|
|
'c' => 3.82933423195043E-20, |
|
401
|
|
|
'cal' => 3.82676978535648E-20, |
|
402
|
|
|
'eV' => 1.0, |
|
403
|
|
|
'ev' => 1.0, |
|
404
|
|
|
'HPh' => 5.96826078912344E-26, |
|
405
|
|
|
'hh' => 5.96826078912344E-26, |
|
406
|
|
|
'Wh' => 4.45053000026614E-23, |
|
407
|
|
|
'wh' => 4.45053000026614E-23, |
|
408
|
|
|
'flb' => 3.80206452103492E-18, |
|
409
|
|
|
'BTU' => 1.51857982414846E-22, |
|
410
|
|
|
'btu' => 1.51857982414846E-22, |
|
411
|
|
|
], |
|
412
|
|
|
'ev' => [ |
|
413
|
|
|
'J' => 1.60219000146921E-19, |
|
414
|
|
|
'e' => 1.60218923136574E-12, |
|
415
|
|
|
'c' => 3.82933423195043E-20, |
|
416
|
|
|
'cal' => 3.82676978535648E-20, |
|
417
|
|
|
'eV' => 1.0, |
|
418
|
|
|
'ev' => 1.0, |
|
419
|
|
|
'HPh' => 5.96826078912344E-26, |
|
420
|
|
|
'hh' => 5.96826078912344E-26, |
|
421
|
|
|
'Wh' => 4.45053000026614E-23, |
|
422
|
|
|
'wh' => 4.45053000026614E-23, |
|
423
|
|
|
'flb' => 3.80206452103492E-18, |
|
424
|
|
|
'BTU' => 1.51857982414846E-22, |
|
425
|
|
|
'btu' => 1.51857982414846E-22, |
|
426
|
|
|
], |
|
427
|
|
|
'HPh' => [ |
|
428
|
|
|
'J' => 2.68451741316170E+06, |
|
429
|
|
|
'e' => 2.68451612283024E+13, |
|
430
|
|
|
'c' => 6.41616438565991E+05, |
|
431
|
|
|
'cal' => 6.41186757845835E+05, |
|
432
|
|
|
'eV' => 1.67553000000000E+25, |
|
433
|
|
|
'ev' => 1.67553000000000E+25, |
|
434
|
|
|
'HPh' => 1.0, |
|
435
|
|
|
'hh' => 1.0, |
|
436
|
|
|
'Wh' => 7.45699653134593E+02, |
|
437
|
|
|
'wh' => 7.45699653134593E+02, |
|
438
|
|
|
'flb' => 6.37047316692964E+07, |
|
439
|
|
|
'BTU' => 2.54442605275546E+03, |
|
440
|
|
|
'btu' => 2.54442605275546E+03, |
|
441
|
|
|
], |
|
442
|
|
|
'hh' => [ |
|
443
|
|
|
'J' => 2.68451741316170E+06, |
|
444
|
|
|
'e' => 2.68451612283024E+13, |
|
445
|
|
|
'c' => 6.41616438565991E+05, |
|
446
|
|
|
'cal' => 6.41186757845835E+05, |
|
447
|
|
|
'eV' => 1.67553000000000E+25, |
|
448
|
|
|
'ev' => 1.67553000000000E+25, |
|
449
|
|
|
'HPh' => 1.0, |
|
450
|
|
|
'hh' => 1.0, |
|
451
|
|
|
'Wh' => 7.45699653134593E+02, |
|
452
|
|
|
'wh' => 7.45699653134593E+02, |
|
453
|
|
|
'flb' => 6.37047316692964E+07, |
|
454
|
|
|
'BTU' => 2.54442605275546E+03, |
|
455
|
|
|
'btu' => 2.54442605275546E+03, |
|
456
|
|
|
], |
|
457
|
|
|
'Wh' => [ |
|
458
|
|
|
'J' => 3.59999820554720E+03, |
|
459
|
|
|
'e' => 3.59999647518369E+10, |
|
460
|
|
|
'c' => 8.60422069219046E+02, |
|
461
|
|
|
'cal' => 8.59845857713046E+02, |
|
462
|
|
|
'eV' => 2.24692340000000E+22, |
|
463
|
|
|
'ev' => 2.24692340000000E+22, |
|
464
|
|
|
'HPh' => 1.34102248243839E-03, |
|
465
|
|
|
'hh' => 1.34102248243839E-03, |
|
466
|
|
|
'Wh' => 1.0, |
|
467
|
|
|
'wh' => 1.0, |
|
468
|
|
|
'flb' => 8.54294774062316E+04, |
|
469
|
|
|
'BTU' => 3.41213254164705E+00, |
|
470
|
|
|
'btu' => 3.41213254164705E+00, |
|
471
|
|
|
], |
|
472
|
|
|
'wh' => [ |
|
473
|
|
|
'J' => 3.59999820554720E+03, |
|
474
|
|
|
'e' => 3.59999647518369E+10, |
|
475
|
|
|
'c' => 8.60422069219046E+02, |
|
476
|
|
|
'cal' => 8.59845857713046E+02, |
|
477
|
|
|
'eV' => 2.24692340000000E+22, |
|
478
|
|
|
'ev' => 2.24692340000000E+22, |
|
479
|
|
|
'HPh' => 1.34102248243839E-03, |
|
480
|
|
|
'hh' => 1.34102248243839E-03, |
|
481
|
|
|
'Wh' => 1.0, |
|
482
|
|
|
'wh' => 1.0, |
|
483
|
|
|
'flb' => 8.54294774062316E+04, |
|
484
|
|
|
'BTU' => 3.41213254164705E+00, |
|
485
|
|
|
'btu' => 3.41213254164705E+00, |
|
486
|
|
|
], |
|
487
|
|
|
'flb' => [ |
|
488
|
|
|
'J' => 4.21400003236424E-02, |
|
489
|
|
|
'e' => 4.21399800687660E+05, |
|
490
|
|
|
'c' => 1.00717234301644E-02, |
|
491
|
|
|
'cal' => 1.00649785509554E-02, |
|
492
|
|
|
'eV' => 2.63015000000000E+17, |
|
493
|
|
|
'ev' => 2.63015000000000E+17, |
|
494
|
|
|
'HPh' => 1.56974211145130E-08, |
|
495
|
|
|
'hh' => 1.56974211145130E-08, |
|
496
|
|
|
'Wh' => 1.17055614802000E-05, |
|
497
|
|
|
'wh' => 1.17055614802000E-05, |
|
498
|
|
|
'flb' => 1.0, |
|
499
|
|
|
'BTU' => 3.99409272448406E-05, |
|
500
|
|
|
'btu' => 3.99409272448406E-05, |
|
501
|
|
|
], |
|
502
|
|
|
'BTU' => [ |
|
503
|
|
|
'J' => 1.05505813786749E+03, |
|
504
|
|
|
'e' => 1.05505763074665E+10, |
|
505
|
|
|
'c' => 2.52165488508168E+02, |
|
506
|
|
|
'cal' => 2.51996617135510E+02, |
|
507
|
|
|
'eV' => 6.58510000000000E+21, |
|
508
|
|
|
'ev' => 6.58510000000000E+21, |
|
509
|
|
|
'HPh' => 3.93015941224568E-04, |
|
510
|
|
|
'hh' => 3.93015941224568E-04, |
|
511
|
|
|
'Wh' => 2.93071851047526E-01, |
|
512
|
|
|
'wh' => 2.93071851047526E-01, |
|
513
|
|
|
'flb' => 2.50369750774671E+04, |
|
514
|
|
|
'BTU' => 1.0, |
|
515
|
|
|
'btu' => 1.0, |
|
516
|
|
|
], |
|
517
|
|
|
'btu' => [ |
|
518
|
|
|
'J' => 1.05505813786749E+03, |
|
519
|
|
|
'e' => 1.05505763074665E+10, |
|
520
|
|
|
'c' => 2.52165488508168E+02, |
|
521
|
|
|
'cal' => 2.51996617135510E+02, |
|
522
|
|
|
'eV' => 6.58510000000000E+21, |
|
523
|
|
|
'ev' => 6.58510000000000E+21, |
|
524
|
|
|
'HPh' => 3.93015941224568E-04, |
|
525
|
|
|
'hh' => 3.93015941224568E-04, |
|
526
|
|
|
'Wh' => 2.93071851047526E-01, |
|
527
|
|
|
'wh' => 2.93071851047526E-01, |
|
528
|
|
|
'flb' => 2.50369750774671E+04, |
|
529
|
|
|
'BTU' => 1.0, |
|
530
|
|
|
'btu' => 1.0, |
|
531
|
|
|
], |
|
532
|
|
|
], |
|
533
|
|
|
'Power' => [ |
|
534
|
|
|
'HP' => [ |
|
535
|
|
|
'HP' => 1.0, |
|
536
|
|
|
'h' => 1.0, |
|
537
|
|
|
'W' => 7.45701000000000E+02, |
|
538
|
|
|
'w' => 7.45701000000000E+02, |
|
539
|
|
|
], |
|
540
|
|
|
'h' => [ |
|
541
|
|
|
'HP' => 1.0, |
|
542
|
|
|
'h' => 1.0, |
|
543
|
|
|
'W' => 7.45701000000000E+02, |
|
544
|
|
|
'w' => 7.45701000000000E+02, |
|
545
|
|
|
], |
|
546
|
|
|
'W' => [ |
|
547
|
|
|
'HP' => 1.34102006031908E-03, |
|
548
|
|
|
'h' => 1.34102006031908E-03, |
|
549
|
|
|
'W' => 1.0, |
|
550
|
|
|
'w' => 1.0, |
|
551
|
|
|
], |
|
552
|
|
|
'w' => [ |
|
553
|
|
|
'HP' => 1.34102006031908E-03, |
|
554
|
|
|
'h' => 1.34102006031908E-03, |
|
555
|
|
|
'W' => 1.0, |
|
556
|
|
|
'w' => 1.0, |
|
557
|
|
|
], |
|
558
|
|
|
], |
|
559
|
|
|
'Magnetism' => [ |
|
560
|
|
|
'T' => [ |
|
561
|
|
|
'T' => 1.0, |
|
562
|
|
|
'ga' => 10000.0, |
|
563
|
|
|
], |
|
564
|
|
|
'ga' => [ |
|
565
|
|
|
'T' => 0.0001, |
|
566
|
|
|
'ga' => 1.0, |
|
567
|
|
|
], |
|
568
|
|
|
], |
|
569
|
|
|
'Liquid' => [ |
|
570
|
|
|
'tsp' => [ |
|
571
|
|
|
'tsp' => 1.0, |
|
572
|
|
|
'tbs' => 3.33333333333333E-01, |
|
573
|
|
|
'oz' => 1.66666666666667E-01, |
|
574
|
|
|
'cup' => 2.08333333333333E-02, |
|
575
|
|
|
'pt' => 1.04166666666667E-02, |
|
576
|
|
|
'us_pt' => 1.04166666666667E-02, |
|
577
|
|
|
'uk_pt' => 8.67558516821960E-03, |
|
578
|
|
|
'qt' => 5.20833333333333E-03, |
|
579
|
|
|
'gal' => 1.30208333333333E-03, |
|
580
|
|
|
'l' => 4.92999408400710E-03, |
|
581
|
|
|
'lt' => 4.92999408400710E-03, |
|
582
|
|
|
], |
|
583
|
|
|
'tbs' => [ |
|
584
|
|
|
'tsp' => 3.00000000000000E+00, |
|
585
|
|
|
'tbs' => 1.0, |
|
586
|
|
|
'oz' => 5.00000000000000E-01, |
|
587
|
|
|
'cup' => 6.25000000000000E-02, |
|
588
|
|
|
'pt' => 3.12500000000000E-02, |
|
589
|
|
|
'us_pt' => 3.12500000000000E-02, |
|
590
|
|
|
'uk_pt' => 2.60267555046588E-02, |
|
591
|
|
|
'qt' => 1.56250000000000E-02, |
|
592
|
|
|
'gal' => 3.90625000000000E-03, |
|
593
|
|
|
'l' => 1.47899822520213E-02, |
|
594
|
|
|
'lt' => 1.47899822520213E-02, |
|
595
|
|
|
], |
|
596
|
|
|
'oz' => [ |
|
597
|
|
|
'tsp' => 6.00000000000000E+00, |
|
598
|
|
|
'tbs' => 2.00000000000000E+00, |
|
599
|
|
|
'oz' => 1.0, |
|
600
|
|
|
'cup' => 1.25000000000000E-01, |
|
601
|
|
|
'pt' => 6.25000000000000E-02, |
|
602
|
|
|
'us_pt' => 6.25000000000000E-02, |
|
603
|
|
|
'uk_pt' => 5.20535110093176E-02, |
|
604
|
|
|
'qt' => 3.12500000000000E-02, |
|
605
|
|
|
'gal' => 7.81250000000000E-03, |
|
606
|
|
|
'l' => 2.95799645040426E-02, |
|
607
|
|
|
'lt' => 2.95799645040426E-02, |
|
608
|
|
|
], |
|
609
|
|
|
'cup' => [ |
|
610
|
|
|
'tsp' => 4.80000000000000E+01, |
|
611
|
|
|
'tbs' => 1.60000000000000E+01, |
|
612
|
|
|
'oz' => 8.00000000000000E+00, |
|
613
|
|
|
'cup' => 1.0, |
|
614
|
|
|
'pt' => 5.00000000000000E-01, |
|
615
|
|
|
'us_pt' => 5.00000000000000E-01, |
|
616
|
|
|
'uk_pt' => 4.16428088074541E-01, |
|
617
|
|
|
'qt' => 2.50000000000000E-01, |
|
618
|
|
|
'gal' => 6.25000000000000E-02, |
|
619
|
|
|
'l' => 2.36639716032341E-01, |
|
620
|
|
|
'lt' => 2.36639716032341E-01, |
|
621
|
|
|
], |
|
622
|
|
|
'pt' => [ |
|
623
|
|
|
'tsp' => 9.60000000000000E+01, |
|
624
|
|
|
'tbs' => 3.20000000000000E+01, |
|
625
|
|
|
'oz' => 1.60000000000000E+01, |
|
626
|
|
|
'cup' => 2.00000000000000E+00, |
|
627
|
|
|
'pt' => 1.0, |
|
628
|
|
|
'us_pt' => 1.0, |
|
629
|
|
|
'uk_pt' => 8.32856176149081E-01, |
|
630
|
|
|
'qt' => 5.00000000000000E-01, |
|
631
|
|
|
'gal' => 1.25000000000000E-01, |
|
632
|
|
|
'l' => 4.73279432064682E-01, |
|
633
|
|
|
'lt' => 4.73279432064682E-01, |
|
634
|
|
|
], |
|
635
|
|
|
'us_pt' => [ |
|
636
|
|
|
'tsp' => 9.60000000000000E+01, |
|
637
|
|
|
'tbs' => 3.20000000000000E+01, |
|
638
|
|
|
'oz' => 1.60000000000000E+01, |
|
639
|
|
|
'cup' => 2.00000000000000E+00, |
|
640
|
|
|
'pt' => 1.0, |
|
641
|
|
|
'us_pt' => 1.0, |
|
642
|
|
|
'uk_pt' => 8.32856176149081E-01, |
|
643
|
|
|
'qt' => 5.00000000000000E-01, |
|
644
|
|
|
'gal' => 1.25000000000000E-01, |
|
645
|
|
|
'l' => 4.73279432064682E-01, |
|
646
|
|
|
'lt' => 4.73279432064682E-01, |
|
647
|
|
|
], |
|
648
|
|
|
'uk_pt' => [ |
|
649
|
|
|
'tsp' => 1.15266000000000E+02, |
|
650
|
|
|
'tbs' => 3.84220000000000E+01, |
|
651
|
|
|
'oz' => 1.92110000000000E+01, |
|
652
|
|
|
'cup' => 2.40137500000000E+00, |
|
653
|
|
|
'pt' => 1.20068750000000E+00, |
|
654
|
|
|
'us_pt' => 1.20068750000000E+00, |
|
655
|
|
|
'uk_pt' => 1.0, |
|
656
|
|
|
'qt' => 6.00343750000000E-01, |
|
657
|
|
|
'gal' => 1.50085937500000E-01, |
|
658
|
|
|
'l' => 5.68260698087162E-01, |
|
659
|
|
|
'lt' => 5.68260698087162E-01, |
|
660
|
|
|
], |
|
661
|
|
|
'qt' => [ |
|
662
|
|
|
'tsp' => 1.92000000000000E+02, |
|
663
|
|
|
'tbs' => 6.40000000000000E+01, |
|
664
|
|
|
'oz' => 3.20000000000000E+01, |
|
665
|
|
|
'cup' => 4.00000000000000E+00, |
|
666
|
|
|
'pt' => 2.00000000000000E+00, |
|
667
|
|
|
'us_pt' => 2.00000000000000E+00, |
|
668
|
|
|
'uk_pt' => 1.66571235229816E+00, |
|
669
|
|
|
'qt' => 1.0, |
|
670
|
|
|
'gal' => 2.50000000000000E-01, |
|
671
|
|
|
'l' => 9.46558864129363E-01, |
|
672
|
|
|
'lt' => 9.46558864129363E-01, |
|
673
|
|
|
], |
|
674
|
|
|
'gal' => [ |
|
675
|
|
|
'tsp' => 7.68000000000000E+02, |
|
676
|
|
|
'tbs' => 2.56000000000000E+02, |
|
677
|
|
|
'oz' => 1.28000000000000E+02, |
|
678
|
|
|
'cup' => 1.60000000000000E+01, |
|
679
|
|
|
'pt' => 8.00000000000000E+00, |
|
680
|
|
|
'us_pt' => 8.00000000000000E+00, |
|
681
|
|
|
'uk_pt' => 6.66284940919265E+00, |
|
682
|
|
|
'qt' => 4.00000000000000E+00, |
|
683
|
|
|
'gal' => 1.0, |
|
684
|
|
|
'l' => 3.78623545651745E+00, |
|
685
|
|
|
'lt' => 3.78623545651745E+00, |
|
686
|
|
|
], |
|
687
|
|
|
'l' => [ |
|
688
|
|
|
'tsp' => 2.02840000000000E+02, |
|
689
|
|
|
'tbs' => 6.76133333333333E+01, |
|
690
|
|
|
'oz' => 3.38066666666667E+01, |
|
691
|
|
|
'cup' => 4.22583333333333E+00, |
|
692
|
|
|
'pt' => 2.11291666666667E+00, |
|
693
|
|
|
'us_pt' => 2.11291666666667E+00, |
|
694
|
|
|
'uk_pt' => 1.75975569552166E+00, |
|
695
|
|
|
'qt' => 1.05645833333333E+00, |
|
696
|
|
|
'gal' => 2.64114583333333E-01, |
|
697
|
|
|
'l' => 1.0, |
|
698
|
|
|
'lt' => 1.0, |
|
699
|
|
|
], |
|
700
|
|
|
'lt' => [ |
|
701
|
|
|
'tsp' => 2.02840000000000E+02, |
|
702
|
|
|
'tbs' => 6.76133333333333E+01, |
|
703
|
|
|
'oz' => 3.38066666666667E+01, |
|
704
|
|
|
'cup' => 4.22583333333333E+00, |
|
705
|
|
|
'pt' => 2.11291666666667E+00, |
|
706
|
|
|
'us_pt' => 2.11291666666667E+00, |
|
707
|
|
|
'uk_pt' => 1.75975569552166E+00, |
|
708
|
|
|
'qt' => 1.05645833333333E+00, |
|
709
|
|
|
'gal' => 2.64114583333333E-01, |
|
710
|
|
|
'l' => 1.0, |
|
711
|
|
|
'lt' => 1.0, |
|
712
|
|
|
], |
|
713
|
|
|
], |
|
714
|
|
|
]; |
|
715
|
|
|
|
|
716
|
|
|
/** |
|
717
|
|
|
* parseComplex. |
|
718
|
|
|
* |
|
719
|
|
|
* Parses a complex number into its real and imaginary parts, and an I or J suffix |
|
720
|
|
|
* |
|
721
|
|
|
* @param string $complexNumber The complex number |
|
722
|
|
|
* |
|
723
|
|
|
* @return string[] Indexed on "real", "imaginary" and "suffix" |
|
724
|
|
|
*/ |
|
725
|
354 |
|
public static function parseComplex($complexNumber) |
|
726
|
|
|
{ |
|
727
|
354 |
|
$workString = (string) $complexNumber; |
|
728
|
|
|
|
|
729
|
354 |
|
$realNumber = $imaginary = 0; |
|
|
|
|
|
|
730
|
|
|
// Extract the suffix, if there is one |
|
731
|
354 |
|
$suffix = substr($workString, -1); |
|
732
|
354 |
|
if (!is_numeric($suffix)) { |
|
733
|
289 |
|
$workString = substr($workString, 0, -1); |
|
734
|
|
|
} else { |
|
735
|
142 |
|
$suffix = ''; |
|
736
|
|
|
} |
|
737
|
|
|
|
|
738
|
|
|
// Split the input into its Real and Imaginary components |
|
739
|
354 |
|
$leadingSign = 0; |
|
740
|
354 |
|
if (strlen($workString) > 0) { |
|
|
|
|
|
|
741
|
345 |
|
$leadingSign = (($workString[0] == '+') || ($workString[0] == '-')) ? 1 : 0; |
|
742
|
|
|
} |
|
743
|
354 |
|
$power = ''; |
|
744
|
354 |
|
$realNumber = strtok($workString, '+-'); |
|
|
|
|
|
|
745
|
354 |
|
if (strtoupper(substr($realNumber, -1)) == 'E') { |
|
|
|
|
|
|
746
|
8 |
|
$power = strtok('+-'); |
|
|
|
|
|
|
747
|
8 |
|
++$leadingSign; |
|
748
|
|
|
} |
|
749
|
|
|
|
|
750
|
354 |
|
$realNumber = substr($workString, 0, strlen($realNumber) + strlen($power) + $leadingSign); |
|
|
|
|
|
|
751
|
|
|
|
|
752
|
354 |
|
if ($suffix != '') { |
|
753
|
289 |
|
$imaginary = substr($workString, strlen($realNumber)); |
|
754
|
|
|
|
|
755
|
289 |
|
if (($imaginary == '') && (($realNumber == '') || ($realNumber == '+') || ($realNumber == '-'))) { |
|
756
|
24 |
|
$imaginary = $realNumber . '1'; |
|
|
|
|
|
|
757
|
24 |
|
$realNumber = '0'; |
|
758
|
269 |
|
} elseif ($imaginary == '') { |
|
759
|
30 |
|
$imaginary = $realNumber; |
|
760
|
30 |
|
$realNumber = '0'; |
|
761
|
243 |
|
} elseif (($imaginary == '+') || ($imaginary == '-')) { |
|
762
|
96 |
|
$imaginary .= '1'; |
|
763
|
|
|
} |
|
764
|
|
|
} |
|
765
|
|
|
|
|
766
|
|
|
return [ |
|
|
|
|
|
|
767
|
354 |
|
'real' => $realNumber, |
|
768
|
354 |
|
'imaginary' => $imaginary, |
|
769
|
354 |
|
'suffix' => $suffix, |
|
770
|
|
|
]; |
|
771
|
|
|
} |
|
772
|
|
|
|
|
773
|
|
|
/** |
|
774
|
|
|
* Cleans the leading characters in a complex number string. |
|
775
|
|
|
* |
|
776
|
|
|
* @param string $complexNumber The complex number to clean |
|
777
|
|
|
* |
|
778
|
|
|
* @return string The "cleaned" complex number |
|
779
|
|
|
*/ |
|
780
|
38 |
|
private static function cleanComplex($complexNumber) |
|
781
|
|
|
{ |
|
782
|
38 |
|
if ($complexNumber[0] == '+') { |
|
783
|
|
|
$complexNumber = substr($complexNumber, 1); |
|
784
|
|
|
} |
|
785
|
38 |
|
if ($complexNumber[0] == '0') { |
|
786
|
4 |
|
$complexNumber = substr($complexNumber, 1); |
|
|
|
|
|
|
787
|
|
|
} |
|
788
|
38 |
|
if ($complexNumber[0] == '.') { |
|
789
|
4 |
|
$complexNumber = '0' . $complexNumber; |
|
|
|
|
|
|
790
|
|
|
} |
|
791
|
38 |
|
if ($complexNumber[0] == '+') { |
|
792
|
|
|
$complexNumber = substr($complexNumber, 1); |
|
793
|
|
|
} |
|
794
|
|
|
|
|
795
|
38 |
|
return $complexNumber; |
|
|
|
|
|
|
796
|
|
|
} |
|
797
|
|
|
|
|
798
|
|
|
/** |
|
799
|
|
|
* Formats a number base string value with leading zeroes. |
|
800
|
|
|
* |
|
801
|
|
|
* @param string $xVal The "number" to pad |
|
802
|
|
|
* @param int $places The length that we want to pad this value |
|
803
|
|
|
* |
|
804
|
|
|
* @return string The padded "number" |
|
805
|
|
|
*/ |
|
806
|
82 |
|
private static function nbrConversionFormat($xVal, $places) |
|
807
|
|
|
{ |
|
808
|
82 |
|
if ($places !== null) { |
|
809
|
22 |
|
if (is_numeric($places)) { |
|
810
|
18 |
|
$places = (int) $places; |
|
811
|
|
|
} else { |
|
812
|
4 |
|
return Functions::VALUE(); |
|
813
|
|
|
} |
|
814
|
18 |
|
if ($places < 0) { |
|
815
|
4 |
|
return Functions::NAN(); |
|
816
|
|
|
} |
|
817
|
14 |
|
if (strlen($xVal) <= $places) { |
|
818
|
14 |
|
return substr(str_pad($xVal, $places, '0', STR_PAD_LEFT), -10); |
|
|
|
|
|
|
819
|
|
|
} |
|
820
|
|
|
|
|
821
|
|
|
return Functions::NAN(); |
|
822
|
|
|
} |
|
823
|
|
|
|
|
824
|
60 |
|
return substr($xVal, -10); |
|
825
|
|
|
} |
|
826
|
|
|
|
|
827
|
|
|
/** |
|
828
|
|
|
* BESSELI. |
|
829
|
|
|
* |
|
830
|
|
|
* Returns the modified Bessel function In(x), which is equivalent to the Bessel function evaluated |
|
831
|
|
|
* for purely imaginary arguments |
|
832
|
|
|
* |
|
833
|
|
|
* Excel Function: |
|
834
|
|
|
* BESSELI(x,ord) |
|
835
|
|
|
* |
|
836
|
|
|
* @category Engineering Functions |
|
837
|
|
|
* |
|
838
|
|
|
* @param float $x The value at which to evaluate the function. |
|
839
|
|
|
* If x is nonnumeric, BESSELI returns the #VALUE! error value. |
|
840
|
|
|
* @param int $ord The order of the Bessel function. |
|
841
|
|
|
* If ord is not an integer, it is truncated. |
|
842
|
|
|
* If $ord is nonnumeric, BESSELI returns the #VALUE! error value. |
|
843
|
|
|
* If $ord < 0, BESSELI returns the #NUM! error value. |
|
844
|
|
|
* |
|
845
|
|
|
* @return float |
|
846
|
|
|
*/ |
|
847
|
74 |
|
public static function BESSELI($x, $ord) |
|
848
|
|
|
{ |
|
849
|
74 |
|
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x); |
|
850
|
74 |
|
$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord); |
|
851
|
|
|
|
|
852
|
74 |
|
if ((is_numeric($x)) && (is_numeric($ord))) { |
|
853
|
70 |
|
$ord = floor($ord); |
|
854
|
70 |
|
if ($ord < 0) { |
|
855
|
2 |
|
return Functions::NAN(); |
|
|
|
|
|
|
856
|
|
|
} |
|
857
|
|
|
|
|
858
|
68 |
|
if (abs($x) <= 30) { |
|
859
|
68 |
|
$fResult = $fTerm = pow($x / 2, $ord) / MathTrig::FACT($ord); |
|
860
|
68 |
|
$ordK = 1; |
|
861
|
68 |
|
$fSqrX = ($x * $x) / 4; |
|
862
|
|
View Code Duplication |
do { |
|
|
|
|
|
|
863
|
68 |
|
$fTerm *= $fSqrX; |
|
864
|
68 |
|
$fTerm /= ($ordK * ($ordK + $ord)); |
|
865
|
68 |
|
$fResult += $fTerm; |
|
866
|
68 |
|
} while ((abs($fTerm) > 1e-12) && (++$ordK < 100)); |
|
867
|
|
|
} else { |
|
868
|
|
|
$f_2_PI = 2 * M_PI; |
|
869
|
|
|
|
|
870
|
|
|
$fXAbs = abs($x); |
|
871
|
|
|
$fResult = exp($fXAbs) / sqrt($f_2_PI * $fXAbs); |
|
872
|
|
|
if (($ord & 1) && ($x < 0)) { |
|
873
|
|
|
$fResult = -$fResult; |
|
874
|
|
|
} |
|
875
|
|
|
} |
|
876
|
|
|
|
|
877
|
68 |
|
return (is_nan($fResult)) ? Functions::NAN() : $fResult; |
|
|
|
|
|
|
878
|
|
|
} |
|
879
|
|
|
|
|
880
|
4 |
|
return Functions::VALUE(); |
|
|
|
|
|
|
881
|
|
|
} |
|
882
|
|
|
|
|
883
|
|
|
/** |
|
884
|
|
|
* BESSELJ. |
|
885
|
|
|
* |
|
886
|
|
|
* Returns the Bessel function |
|
887
|
|
|
* |
|
888
|
|
|
* Excel Function: |
|
889
|
|
|
* BESSELJ(x,ord) |
|
890
|
|
|
* |
|
891
|
|
|
* @category Engineering Functions |
|
892
|
|
|
* |
|
893
|
|
|
* @param float $x The value at which to evaluate the function. |
|
894
|
|
|
* If x is nonnumeric, BESSELJ returns the #VALUE! error value. |
|
895
|
|
|
* @param int $ord The order of the Bessel function. If n is not an integer, it is truncated. |
|
896
|
|
|
* If $ord is nonnumeric, BESSELJ returns the #VALUE! error value. |
|
897
|
|
|
* If $ord < 0, BESSELJ returns the #NUM! error value. |
|
898
|
|
|
* |
|
899
|
|
|
* @return float |
|
900
|
|
|
*/ |
|
901
|
50 |
|
public static function BESSELJ($x, $ord) |
|
902
|
|
|
{ |
|
903
|
50 |
|
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x); |
|
904
|
50 |
|
$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord); |
|
905
|
|
|
|
|
906
|
50 |
|
if ((is_numeric($x)) && (is_numeric($ord))) { |
|
907
|
48 |
|
$ord = floor($ord); |
|
908
|
48 |
|
if ($ord < 0) { |
|
909
|
1 |
|
return Functions::NAN(); |
|
|
|
|
|
|
910
|
|
|
} |
|
911
|
|
|
|
|
912
|
47 |
|
$fResult = 0; |
|
913
|
47 |
|
if (abs($x) <= 30) { |
|
914
|
47 |
|
$fResult = $fTerm = pow($x / 2, $ord) / MathTrig::FACT($ord); |
|
915
|
47 |
|
$ordK = 1; |
|
916
|
47 |
|
$fSqrX = ($x * $x) / -4; |
|
917
|
|
View Code Duplication |
do { |
|
|
|
|
|
|
918
|
47 |
|
$fTerm *= $fSqrX; |
|
919
|
47 |
|
$fTerm /= ($ordK * ($ordK + $ord)); |
|
920
|
47 |
|
$fResult += $fTerm; |
|
921
|
47 |
|
} while ((abs($fTerm) > 1e-12) && (++$ordK < 100)); |
|
922
|
|
|
} else { |
|
923
|
|
|
$f_PI_DIV_2 = M_PI / 2; |
|
924
|
|
|
$f_PI_DIV_4 = M_PI / 4; |
|
925
|
|
|
|
|
926
|
|
|
$fXAbs = abs($x); |
|
927
|
|
|
$fResult = sqrt(Functions::M_2DIVPI / $fXAbs) * cos($fXAbs - $ord * $f_PI_DIV_2 - $f_PI_DIV_4); |
|
928
|
|
|
if (($ord & 1) && ($x < 0)) { |
|
929
|
|
|
$fResult = -$fResult; |
|
930
|
|
|
} |
|
931
|
|
|
} |
|
932
|
|
|
|
|
933
|
47 |
|
return (is_nan($fResult)) ? Functions::NAN() : $fResult; |
|
|
|
|
|
|
934
|
|
|
} |
|
935
|
|
|
|
|
936
|
2 |
|
return Functions::VALUE(); |
|
|
|
|
|
|
937
|
|
|
} |
|
938
|
|
|
|
|
939
|
22 |
|
private static function besselK0($fNum) |
|
940
|
|
|
{ |
|
941
|
22 |
|
if ($fNum <= 2) { |
|
942
|
14 |
|
$fNum2 = $fNum * 0.5; |
|
943
|
14 |
|
$y = ($fNum2 * $fNum2); |
|
944
|
14 |
|
$fRet = -log($fNum2) * self::BESSELI($fNum, 0) + |
|
945
|
|
|
(-0.57721566 + $y * (0.42278420 + $y * (0.23069756 + $y * (0.3488590e-1 + $y * (0.262698e-2 + $y * |
|
946
|
14 |
|
(0.10750e-3 + $y * 0.74e-5)))))); |
|
947
|
|
View Code Duplication |
} else { |
|
|
|
|
|
|
948
|
8 |
|
$y = 2 / $fNum; |
|
949
|
8 |
|
$fRet = exp(-$fNum) / sqrt($fNum) * |
|
950
|
|
|
(1.25331414 + $y * (-0.7832358e-1 + $y * (0.2189568e-1 + $y * (-0.1062446e-1 + $y * |
|
951
|
8 |
|
(0.587872e-2 + $y * (-0.251540e-2 + $y * 0.53208e-3)))))); |
|
952
|
|
|
} |
|
953
|
|
|
|
|
954
|
22 |
|
return $fRet; |
|
955
|
|
|
} |
|
956
|
|
|
|
|
957
|
30 |
|
private static function besselK1($fNum) |
|
958
|
|
|
{ |
|
959
|
30 |
|
if ($fNum <= 2) { |
|
960
|
17 |
|
$fNum2 = $fNum * 0.5; |
|
961
|
17 |
|
$y = ($fNum2 * $fNum2); |
|
962
|
17 |
|
$fRet = log($fNum2) * self::BESSELI($fNum, 1) + |
|
963
|
|
|
(1 + $y * (0.15443144 + $y * (-0.67278579 + $y * (-0.18156897 + $y * (-0.1919402e-1 + $y * |
|
964
|
17 |
|
(-0.110404e-2 + $y * (-0.4686e-4))))))) / $fNum; |
|
965
|
|
View Code Duplication |
} else { |
|
|
|
|
|
|
966
|
13 |
|
$y = 2 / $fNum; |
|
967
|
13 |
|
$fRet = exp(-$fNum) / sqrt($fNum) * |
|
968
|
|
|
(1.25331414 + $y * (0.23498619 + $y * (-0.3655620e-1 + $y * (0.1504268e-1 + $y * (-0.780353e-2 + $y * |
|
969
|
13 |
|
(0.325614e-2 + $y * (-0.68245e-3))))))); |
|
970
|
|
|
} |
|
971
|
|
|
|
|
972
|
30 |
|
return $fRet; |
|
973
|
|
|
} |
|
974
|
|
|
|
|
975
|
|
|
/** |
|
976
|
|
|
* BESSELK. |
|
977
|
|
|
* |
|
978
|
|
|
* Returns the modified Bessel function Kn(x), which is equivalent to the Bessel functions evaluated |
|
979
|
|
|
* for purely imaginary arguments. |
|
980
|
|
|
* |
|
981
|
|
|
* Excel Function: |
|
982
|
|
|
* BESSELK(x,ord) |
|
983
|
|
|
* |
|
984
|
|
|
* @category Engineering Functions |
|
985
|
|
|
* |
|
986
|
|
|
* @param float $x The value at which to evaluate the function. |
|
987
|
|
|
* If x is nonnumeric, BESSELK returns the #VALUE! error value. |
|
988
|
|
|
* @param int $ord The order of the Bessel function. If n is not an integer, it is truncated. |
|
989
|
|
|
* If $ord is nonnumeric, BESSELK returns the #VALUE! error value. |
|
990
|
|
|
* If $ord < 0, BESSELK returns the #NUM! error value. |
|
991
|
|
|
* |
|
992
|
|
|
* @return float |
|
993
|
|
|
*/ |
|
994
|
38 |
View Code Duplication |
public static function BESSELK($x, $ord) |
|
|
|
|
|
|
995
|
|
|
{ |
|
996
|
38 |
|
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x); |
|
997
|
38 |
|
$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord); |
|
998
|
|
|
|
|
999
|
38 |
|
if ((is_numeric($x)) && (is_numeric($ord))) { |
|
1000
|
36 |
|
if (($ord < 0) || ($x == 0.0)) { |
|
1001
|
4 |
|
return Functions::NAN(); |
|
|
|
|
|
|
1002
|
|
|
} |
|
1003
|
|
|
|
|
1004
|
32 |
|
switch (floor($ord)) { |
|
1005
|
32 |
|
case 0: |
|
1006
|
2 |
|
$fBk = self::besselK0($x); |
|
1007
|
|
|
|
|
1008
|
2 |
|
break; |
|
1009
|
30 |
|
case 1: |
|
1010
|
10 |
|
$fBk = self::besselK1($x); |
|
1011
|
|
|
|
|
1012
|
10 |
|
break; |
|
1013
|
|
|
default: |
|
1014
|
20 |
|
$fTox = 2 / $x; |
|
1015
|
20 |
|
$fBkm = self::besselK0($x); |
|
1016
|
20 |
|
$fBk = self::besselK1($x); |
|
1017
|
20 |
|
for ($n = 1; $n < $ord; ++$n) { |
|
1018
|
20 |
|
$fBkp = $fBkm + $n * $fTox * $fBk; |
|
1019
|
20 |
|
$fBkm = $fBk; |
|
1020
|
20 |
|
$fBk = $fBkp; |
|
1021
|
|
|
} |
|
1022
|
|
|
} |
|
1023
|
|
|
|
|
1024
|
32 |
|
return (is_nan($fBk)) ? Functions::NAN() : $fBk; |
|
|
|
|
|
|
1025
|
|
|
} |
|
1026
|
|
|
|
|
1027
|
2 |
|
return Functions::VALUE(); |
|
|
|
|
|
|
1028
|
|
|
} |
|
1029
|
|
|
|
|
1030
|
11 |
|
private static function besselY0($fNum) |
|
1031
|
|
|
{ |
|
1032
|
11 |
|
if ($fNum < 8.0) { |
|
1033
|
10 |
|
$y = ($fNum * $fNum); |
|
1034
|
10 |
|
$f1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y * (-86327.92757 + $y * 228.4622733)))); |
|
1035
|
10 |
|
$f2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y * (47447.26470 + $y * (226.1030244 + $y)))); |
|
1036
|
10 |
|
$fRet = $f1 / $f2 + 0.636619772 * self::BESSELJ($fNum, 0) * log($fNum); |
|
1037
|
|
|
} else { |
|
1038
|
1 |
|
$z = 8.0 / $fNum; |
|
1039
|
1 |
|
$y = ($z * $z); |
|
1040
|
1 |
|
$xx = $fNum - 0.785398164; |
|
1041
|
1 |
|
$f1 = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6))); |
|
1042
|
1 |
|
$f2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y * (-0.934945152e-7)))); |
|
1043
|
1 |
|
$fRet = sqrt(0.636619772 / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2); |
|
1044
|
|
|
} |
|
1045
|
|
|
|
|
1046
|
11 |
|
return $fRet; |
|
1047
|
|
|
} |
|
1048
|
|
|
|
|
1049
|
16 |
|
private static function besselY1($fNum) |
|
1050
|
|
|
{ |
|
1051
|
16 |
|
if ($fNum < 8.0) { |
|
1052
|
16 |
|
$y = ($fNum * $fNum); |
|
1053
|
|
|
$f1 = $fNum * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y * (0.7349264551e9 + $y * |
|
1054
|
16 |
|
(-0.4237922726e7 + $y * 0.8511937935e4))))); |
|
1055
|
|
|
$f2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y * |
|
1056
|
16 |
|
(0.1020426050e6 + $y * (0.3549632885e3 + $y))))); |
|
1057
|
16 |
|
$fRet = $f1 / $f2 + 0.636619772 * (self::BESSELJ($fNum, 1) * log($fNum) - 1 / $fNum); |
|
1058
|
|
|
} else { |
|
1059
|
|
|
$fRet = sqrt(0.636619772 / $fNum) * sin($fNum - 2.356194491); |
|
1060
|
|
|
} |
|
1061
|
|
|
|
|
1062
|
16 |
|
return $fRet; |
|
1063
|
|
|
} |
|
1064
|
|
|
|
|
1065
|
|
|
/** |
|
1066
|
|
|
* BESSELY. |
|
1067
|
|
|
* |
|
1068
|
|
|
* Returns the Bessel function, which is also called the Weber function or the Neumann function. |
|
1069
|
|
|
* |
|
1070
|
|
|
* Excel Function: |
|
1071
|
|
|
* BESSELY(x,ord) |
|
1072
|
|
|
* |
|
1073
|
|
|
* @category Engineering Functions |
|
1074
|
|
|
* |
|
1075
|
|
|
* @param float $x The value at which to evaluate the function. |
|
1076
|
|
|
* If x is nonnumeric, BESSELK returns the #VALUE! error value. |
|
1077
|
|
|
* @param int $ord The order of the Bessel function. If n is not an integer, it is truncated. |
|
1078
|
|
|
* If $ord is nonnumeric, BESSELK returns the #VALUE! error value. |
|
1079
|
|
|
* If $ord < 0, BESSELK returns the #NUM! error value. |
|
1080
|
|
|
* |
|
1081
|
|
|
* @return float |
|
1082
|
|
|
*/ |
|
1083
|
23 |
View Code Duplication |
public static function BESSELY($x, $ord) |
|
|
|
|
|
|
1084
|
|
|
{ |
|
1085
|
23 |
|
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x); |
|
1086
|
23 |
|
$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord); |
|
1087
|
|
|
|
|
1088
|
23 |
|
if ((is_numeric($x)) && (is_numeric($ord))) { |
|
1089
|
21 |
|
if (($ord < 0) || ($x == 0.0)) { |
|
1090
|
3 |
|
return Functions::NAN(); |
|
|
|
|
|
|
1091
|
|
|
} |
|
1092
|
|
|
|
|
1093
|
18 |
|
switch (floor($ord)) { |
|
1094
|
18 |
|
case 0: |
|
1095
|
2 |
|
$fBy = self::besselY0($x); |
|
1096
|
|
|
|
|
1097
|
2 |
|
break; |
|
1098
|
16 |
|
case 1: |
|
1099
|
7 |
|
$fBy = self::besselY1($x); |
|
1100
|
|
|
|
|
1101
|
7 |
|
break; |
|
1102
|
|
|
default: |
|
1103
|
9 |
|
$fTox = 2 / $x; |
|
1104
|
9 |
|
$fBym = self::besselY0($x); |
|
1105
|
9 |
|
$fBy = self::besselY1($x); |
|
1106
|
9 |
|
for ($n = 1; $n < $ord; ++$n) { |
|
1107
|
9 |
|
$fByp = $n * $fTox * $fBy - $fBym; |
|
1108
|
9 |
|
$fBym = $fBy; |
|
1109
|
9 |
|
$fBy = $fByp; |
|
1110
|
|
|
} |
|
1111
|
|
|
} |
|
1112
|
|
|
|
|
1113
|
18 |
|
return (is_nan($fBy)) ? Functions::NAN() : $fBy; |
|
|
|
|
|
|
1114
|
|
|
} |
|
1115
|
|
|
|
|
1116
|
2 |
|
return Functions::VALUE(); |
|
|
|
|
|
|
1117
|
|
|
} |
|
1118
|
|
|
|
|
1119
|
|
|
/** |
|
1120
|
|
|
* BINTODEC. |
|
1121
|
|
|
* |
|
1122
|
|
|
* Return a binary value as decimal. |
|
1123
|
|
|
* |
|
1124
|
|
|
* Excel Function: |
|
1125
|
|
|
* BIN2DEC(x) |
|
1126
|
|
|
* |
|
1127
|
|
|
* @category Engineering Functions |
|
1128
|
|
|
* |
|
1129
|
|
|
* @param string $x The binary number (as a string) that you want to convert. The number |
|
1130
|
|
|
* cannot contain more than 10 characters (10 bits). The most significant |
|
1131
|
|
|
* bit of number is the sign bit. The remaining 9 bits are magnitude bits. |
|
1132
|
|
|
* Negative numbers are represented using two's-complement notation. |
|
1133
|
|
|
* If number is not a valid binary number, or if number contains more than |
|
1134
|
|
|
* 10 characters (10 bits), BIN2DEC returns the #NUM! error value. |
|
1135
|
|
|
* |
|
1136
|
|
|
* @return string |
|
1137
|
|
|
*/ |
|
1138
|
10 |
|
public static function BINTODEC($x) |
|
1139
|
|
|
{ |
|
1140
|
10 |
|
$x = Functions::flattenSingleValue($x); |
|
1141
|
|
|
|
|
1142
|
10 |
|
if (is_bool($x)) { |
|
1143
|
1 |
|
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) { |
|
1144
|
|
|
$x = (int) $x; |
|
1145
|
|
|
} else { |
|
1146
|
1 |
|
return Functions::VALUE(); |
|
1147
|
|
|
} |
|
1148
|
|
|
} |
|
1149
|
9 |
|
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) { |
|
1150
|
|
|
$x = floor($x); |
|
|
|
|
|
|
1151
|
|
|
} |
|
1152
|
9 |
|
$x = (string) $x; |
|
1153
|
9 |
|
if (strlen($x) > preg_match_all('/[01]/', $x, $out)) { |
|
1154
|
1 |
|
return Functions::NAN(); |
|
1155
|
|
|
} |
|
1156
|
8 |
|
if (strlen($x) > 10) { |
|
1157
|
1 |
|
return Functions::NAN(); |
|
1158
|
7 |
|
} elseif (strlen($x) == 10) { |
|
1159
|
|
|
// Two's Complement |
|
1160
|
2 |
|
$x = substr($x, -9); |
|
1161
|
|
|
|
|
1162
|
2 |
|
return '-' . (512 - bindec($x)); |
|
|
|
|
|
|
1163
|
|
|
} |
|
1164
|
|
|
|
|
1165
|
5 |
|
return bindec($x); |
|
1166
|
|
|
} |
|
1167
|
|
|
|
|
1168
|
|
|
/** |
|
1169
|
|
|
* BINTOHEX. |
|
1170
|
|
|
* |
|
1171
|
|
|
* Return a binary value as hex. |
|
1172
|
|
|
* |
|
1173
|
|
|
* Excel Function: |
|
1174
|
|
|
* BIN2HEX(x[,places]) |
|
1175
|
|
|
* |
|
1176
|
|
|
* @category Engineering Functions |
|
1177
|
|
|
* |
|
1178
|
|
|
* @param string $x The binary number (as a string) that you want to convert. The number |
|
1179
|
|
|
* cannot contain more than 10 characters (10 bits). The most significant |
|
1180
|
|
|
* bit of number is the sign bit. The remaining 9 bits are magnitude bits. |
|
1181
|
|
|
* Negative numbers are represented using two's-complement notation. |
|
1182
|
|
|
* If number is not a valid binary number, or if number contains more than |
|
1183
|
|
|
* 10 characters (10 bits), BIN2HEX returns the #NUM! error value. |
|
1184
|
|
|
* @param int $places The number of characters to use. If places is omitted, BIN2HEX uses the |
|
1185
|
|
|
* minimum number of characters necessary. Places is useful for padding the |
|
1186
|
|
|
* return value with leading 0s (zeros). |
|
1187
|
|
|
* If places is not an integer, it is truncated. |
|
1188
|
|
|
* If places is nonnumeric, BIN2HEX returns the #VALUE! error value. |
|
1189
|
|
|
* If places is negative, BIN2HEX returns the #NUM! error value. |
|
1190
|
|
|
* |
|
1191
|
|
|
* @return string |
|
1192
|
|
|
*/ |
|
1193
|
14 |
View Code Duplication |
public static function BINTOHEX($x, $places = null) |
|
|
|
|
|
|
1194
|
|
|
{ |
|
1195
|
14 |
|
$x = Functions::flattenSingleValue($x); |
|
1196
|
14 |
|
$places = Functions::flattenSingleValue($places); |
|
1197
|
|
|
|
|
1198
|
|
|
// Argument X |
|
1199
|
14 |
|
if (is_bool($x)) { |
|
1200
|
1 |
|
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) { |
|
1201
|
|
|
$x = (int) $x; |
|
1202
|
|
|
} else { |
|
1203
|
1 |
|
return Functions::VALUE(); |
|
1204
|
|
|
} |
|
1205
|
|
|
} |
|
1206
|
13 |
|
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) { |
|
1207
|
|
|
$x = floor($x); |
|
|
|
|
|
|
1208
|
|
|
} |
|
1209
|
13 |
|
$x = (string) $x; |
|
1210
|
13 |
|
if (strlen($x) > preg_match_all('/[01]/', $x, $out)) { |
|
1211
|
1 |
|
return Functions::NAN(); |
|
1212
|
|
|
} |
|
1213
|
12 |
|
if (strlen($x) > 10) { |
|
1214
|
1 |
|
return Functions::NAN(); |
|
1215
|
11 |
|
} elseif (strlen($x) == 10) { |
|
1216
|
|
|
// Two's Complement |
|
1217
|
2 |
|
return str_repeat('F', 8) . substr(strtoupper(dechex(bindec(substr($x, -9)))), -2); |
|
|
|
|
|
|
1218
|
|
|
} |
|
1219
|
9 |
|
$hexVal = (string) strtoupper(dechex(bindec($x))); |
|
1220
|
|
|
|
|
1221
|
9 |
|
return self::nbrConversionFormat($hexVal, $places); |
|
1222
|
|
|
} |
|
1223
|
|
|
|
|
1224
|
|
|
/** |
|
1225
|
|
|
* BINTOOCT. |
|
1226
|
|
|
* |
|
1227
|
|
|
* Return a binary value as octal. |
|
1228
|
|
|
* |
|
1229
|
|
|
* Excel Function: |
|
1230
|
|
|
* BIN2OCT(x[,places]) |
|
1231
|
|
|
* |
|
1232
|
|
|
* @category Engineering Functions |
|
1233
|
|
|
* |
|
1234
|
|
|
* @param string $x The binary number (as a string) that you want to convert. The number |
|
1235
|
|
|
* cannot contain more than 10 characters (10 bits). The most significant |
|
1236
|
|
|
* bit of number is the sign bit. The remaining 9 bits are magnitude bits. |
|
1237
|
|
|
* Negative numbers are represented using two's-complement notation. |
|
1238
|
|
|
* If number is not a valid binary number, or if number contains more than |
|
1239
|
|
|
* 10 characters (10 bits), BIN2OCT returns the #NUM! error value. |
|
1240
|
|
|
* @param int $places The number of characters to use. If places is omitted, BIN2OCT uses the |
|
1241
|
|
|
* minimum number of characters necessary. Places is useful for padding the |
|
1242
|
|
|
* return value with leading 0s (zeros). |
|
1243
|
|
|
* If places is not an integer, it is truncated. |
|
1244
|
|
|
* If places is nonnumeric, BIN2OCT returns the #VALUE! error value. |
|
1245
|
|
|
* If places is negative, BIN2OCT returns the #NUM! error value. |
|
1246
|
|
|
* |
|
1247
|
|
|
* @return string |
|
1248
|
|
|
*/ |
|
1249
|
15 |
View Code Duplication |
public static function BINTOOCT($x, $places = null) |
|
|
|
|
|
|
1250
|
|
|
{ |
|
1251
|
15 |
|
$x = Functions::flattenSingleValue($x); |
|
1252
|
15 |
|
$places = Functions::flattenSingleValue($places); |
|
1253
|
|
|
|
|
1254
|
15 |
|
if (is_bool($x)) { |
|
1255
|
1 |
|
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) { |
|
1256
|
|
|
$x = (int) $x; |
|
1257
|
|
|
} else { |
|
1258
|
1 |
|
return Functions::VALUE(); |
|
1259
|
|
|
} |
|
1260
|
|
|
} |
|
1261
|
14 |
|
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) { |
|
1262
|
|
|
$x = floor($x); |
|
|
|
|
|
|
1263
|
|
|
} |
|
1264
|
14 |
|
$x = (string) $x; |
|
1265
|
14 |
|
if (strlen($x) > preg_match_all('/[01]/', $x, $out)) { |
|
1266
|
1 |
|
return Functions::NAN(); |
|
1267
|
|
|
} |
|
1268
|
13 |
|
if (strlen($x) > 10) { |
|
1269
|
1 |
|
return Functions::NAN(); |
|
1270
|
12 |
|
} elseif (strlen($x) == 10) { |
|
1271
|
|
|
// Two's Complement |
|
1272
|
2 |
|
return str_repeat('7', 7) . substr(strtoupper(decoct(bindec(substr($x, -9)))), -3); |
|
|
|
|
|
|
1273
|
|
|
} |
|
1274
|
10 |
|
$octVal = (string) decoct(bindec($x)); |
|
1275
|
|
|
|
|
1276
|
10 |
|
return self::nbrConversionFormat($octVal, $places); |
|
1277
|
|
|
} |
|
1278
|
|
|
|
|
1279
|
|
|
/** |
|
1280
|
|
|
* DECTOBIN. |
|
1281
|
|
|
* |
|
1282
|
|
|
* Return a decimal value as binary. |
|
1283
|
|
|
* |
|
1284
|
|
|
* Excel Function: |
|
1285
|
|
|
* DEC2BIN(x[,places]) |
|
1286
|
|
|
* |
|
1287
|
|
|
* @category Engineering Functions |
|
1288
|
|
|
* |
|
1289
|
|
|
* @param string $x The decimal integer you want to convert. If number is negative, |
|
1290
|
|
|
* valid place values are ignored and DEC2BIN returns a 10-character |
|
1291
|
|
|
* (10-bit) binary number in which the most significant bit is the sign |
|
1292
|
|
|
* bit. The remaining 9 bits are magnitude bits. Negative numbers are |
|
1293
|
|
|
* represented using two's-complement notation. |
|
1294
|
|
|
* If number < -512 or if number > 511, DEC2BIN returns the #NUM! error |
|
1295
|
|
|
* value. |
|
1296
|
|
|
* If number is nonnumeric, DEC2BIN returns the #VALUE! error value. |
|
1297
|
|
|
* If DEC2BIN requires more than places characters, it returns the #NUM! |
|
1298
|
|
|
* error value. |
|
1299
|
|
|
* @param int $places The number of characters to use. If places is omitted, DEC2BIN uses |
|
1300
|
|
|
* the minimum number of characters necessary. Places is useful for |
|
1301
|
|
|
* padding the return value with leading 0s (zeros). |
|
1302
|
|
|
* If places is not an integer, it is truncated. |
|
1303
|
|
|
* If places is nonnumeric, DEC2BIN returns the #VALUE! error value. |
|
1304
|
|
|
* If places is zero or negative, DEC2BIN returns the #NUM! error value. |
|
1305
|
|
|
* |
|
1306
|
|
|
* @return string |
|
1307
|
|
|
*/ |
|
1308
|
41 |
|
public static function DECTOBIN($x, $places = null) |
|
1309
|
|
|
{ |
|
1310
|
41 |
|
$x = Functions::flattenSingleValue($x); |
|
1311
|
41 |
|
$places = Functions::flattenSingleValue($places); |
|
1312
|
|
|
|
|
1313
|
41 |
|
if (is_bool($x)) { |
|
1314
|
1 |
|
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) { |
|
1315
|
|
|
$x = (int) $x; |
|
1316
|
|
|
} else { |
|
1317
|
1 |
|
return Functions::VALUE(); |
|
1318
|
|
|
} |
|
1319
|
|
|
} |
|
1320
|
40 |
|
$x = (string) $x; |
|
1321
|
40 |
|
if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) { |
|
1322
|
1 |
|
return Functions::VALUE(); |
|
1323
|
|
|
} |
|
1324
|
|
|
|
|
1325
|
39 |
|
$x = (string) floor($x); |
|
|
|
|
|
|
1326
|
39 |
|
if ($x < -512 || $x > 511) { |
|
1327
|
13 |
|
return Functions::NAN(); |
|
1328
|
|
|
} |
|
1329
|
|
|
|
|
1330
|
26 |
|
$r = decbin($x); |
|
|
|
|
|
|
1331
|
|
|
// Two's Complement |
|
1332
|
26 |
|
$r = substr($r, -10); |
|
1333
|
26 |
|
if (strlen($r) >= 11) { |
|
|
|
|
|
|
1334
|
|
|
return Functions::NAN(); |
|
1335
|
|
|
} |
|
1336
|
|
|
|
|
1337
|
26 |
|
return self::nbrConversionFormat($r, $places); |
|
|
|
|
|
|
1338
|
|
|
} |
|
1339
|
|
|
|
|
1340
|
|
|
/** |
|
1341
|
|
|
* DECTOHEX. |
|
1342
|
|
|
* |
|
1343
|
|
|
* Return a decimal value as hex. |
|
1344
|
|
|
* |
|
1345
|
|
|
* Excel Function: |
|
1346
|
|
|
* DEC2HEX(x[,places]) |
|
1347
|
|
|
* |
|
1348
|
|
|
* @category Engineering Functions |
|
1349
|
|
|
* |
|
1350
|
|
|
* @param string $x The decimal integer you want to convert. If number is negative, |
|
1351
|
|
|
* places is ignored and DEC2HEX returns a 10-character (40-bit) |
|
1352
|
|
|
* hexadecimal number in which the most significant bit is the sign |
|
1353
|
|
|
* bit. The remaining 39 bits are magnitude bits. Negative numbers |
|
1354
|
|
|
* are represented using two's-complement notation. |
|
1355
|
|
|
* If number < -549,755,813,888 or if number > 549,755,813,887, |
|
1356
|
|
|
* DEC2HEX returns the #NUM! error value. |
|
1357
|
|
|
* If number is nonnumeric, DEC2HEX returns the #VALUE! error value. |
|
1358
|
|
|
* If DEC2HEX requires more than places characters, it returns the |
|
1359
|
|
|
* #NUM! error value. |
|
1360
|
|
|
* @param int $places The number of characters to use. If places is omitted, DEC2HEX uses |
|
1361
|
|
|
* the minimum number of characters necessary. Places is useful for |
|
1362
|
|
|
* padding the return value with leading 0s (zeros). |
|
1363
|
|
|
* If places is not an integer, it is truncated. |
|
1364
|
|
|
* If places is nonnumeric, DEC2HEX returns the #VALUE! error value. |
|
1365
|
|
|
* If places is zero or negative, DEC2HEX returns the #NUM! error value. |
|
1366
|
|
|
* |
|
1367
|
|
|
* @return string |
|
1368
|
|
|
*/ |
|
1369
|
15 |
View Code Duplication |
public static function DECTOHEX($x, $places = null) |
|
|
|
|
|
|
1370
|
|
|
{ |
|
1371
|
15 |
|
$x = Functions::flattenSingleValue($x); |
|
1372
|
15 |
|
$places = Functions::flattenSingleValue($places); |
|
1373
|
|
|
|
|
1374
|
15 |
|
if (is_bool($x)) { |
|
1375
|
1 |
|
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) { |
|
1376
|
|
|
$x = (int) $x; |
|
1377
|
|
|
} else { |
|
1378
|
1 |
|
return Functions::VALUE(); |
|
1379
|
|
|
} |
|
1380
|
|
|
} |
|
1381
|
14 |
|
$x = (string) $x; |
|
1382
|
14 |
|
if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) { |
|
1383
|
1 |
|
return Functions::VALUE(); |
|
1384
|
|
|
} |
|
1385
|
13 |
|
$x = (string) floor($x); |
|
|
|
|
|
|
1386
|
13 |
|
$r = strtoupper(dechex($x)); |
|
|
|
|
|
|
1387
|
13 |
|
if (strlen($r) == 8) { |
|
1388
|
|
|
// Two's Complement |
|
1389
|
|
|
$r = 'FF' . $r; |
|
1390
|
|
|
} |
|
1391
|
|
|
|
|
1392
|
13 |
|
return self::nbrConversionFormat($r, $places); |
|
1393
|
|
|
} |
|
1394
|
|
|
|
|
1395
|
|
|
/** |
|
1396
|
|
|
* DECTOOCT. |
|
1397
|
|
|
* |
|
1398
|
|
|
* Return an decimal value as octal. |
|
1399
|
|
|
* |
|
1400
|
|
|
* Excel Function: |
|
1401
|
|
|
* DEC2OCT(x[,places]) |
|
1402
|
|
|
* |
|
1403
|
|
|
* @category Engineering Functions |
|
1404
|
|
|
* |
|
1405
|
|
|
* @param string $x The decimal integer you want to convert. If number is negative, |
|
1406
|
|
|
* places is ignored and DEC2OCT returns a 10-character (30-bit) |
|
1407
|
|
|
* octal number in which the most significant bit is the sign bit. |
|
1408
|
|
|
* The remaining 29 bits are magnitude bits. Negative numbers are |
|
1409
|
|
|
* represented using two's-complement notation. |
|
1410
|
|
|
* If number < -536,870,912 or if number > 536,870,911, DEC2OCT |
|
1411
|
|
|
* returns the #NUM! error value. |
|
1412
|
|
|
* If number is nonnumeric, DEC2OCT returns the #VALUE! error value. |
|
1413
|
|
|
* If DEC2OCT requires more than places characters, it returns the |
|
1414
|
|
|
* #NUM! error value. |
|
1415
|
|
|
* @param int $places The number of characters to use. If places is omitted, DEC2OCT uses |
|
1416
|
|
|
* the minimum number of characters necessary. Places is useful for |
|
1417
|
|
|
* padding the return value with leading 0s (zeros). |
|
1418
|
|
|
* If places is not an integer, it is truncated. |
|
1419
|
|
|
* If places is nonnumeric, DEC2OCT returns the #VALUE! error value. |
|
1420
|
|
|
* If places is zero or negative, DEC2OCT returns the #NUM! error value. |
|
1421
|
|
|
* |
|
1422
|
|
|
* @return string |
|
1423
|
|
|
*/ |
|
1424
|
20 |
View Code Duplication |
public static function DECTOOCT($x, $places = null) |
|
|
|
|
|
|
1425
|
|
|
{ |
|
1426
|
20 |
|
$xorig = $x; |
|
|
|
|
|
|
1427
|
20 |
|
$x = Functions::flattenSingleValue($x); |
|
1428
|
20 |
|
$places = Functions::flattenSingleValue($places); |
|
1429
|
|
|
|
|
1430
|
20 |
|
if (is_bool($x)) { |
|
1431
|
1 |
|
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) { |
|
1432
|
|
|
$x = (int) $x; |
|
1433
|
|
|
} else { |
|
1434
|
1 |
|
return Functions::VALUE(); |
|
1435
|
|
|
} |
|
1436
|
|
|
} |
|
1437
|
19 |
|
$x = (string) $x; |
|
1438
|
19 |
|
if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) { |
|
1439
|
1 |
|
return Functions::VALUE(); |
|
1440
|
|
|
} |
|
1441
|
18 |
|
$x = (string) floor($x); |
|
|
|
|
|
|
1442
|
18 |
|
$r = decoct($x); |
|
|
|
|
|
|
1443
|
18 |
|
if (strlen($r) == 11) { |
|
1444
|
|
|
// Two's Complement |
|
1445
|
|
|
$r = substr($r, -10); |
|
1446
|
|
|
} |
|
1447
|
|
|
|
|
1448
|
18 |
|
return self::nbrConversionFormat($r, $places); |
|
|
|
|
|
|
1449
|
|
|
} |
|
1450
|
|
|
|
|
1451
|
|
|
/** |
|
1452
|
|
|
* HEXTOBIN. |
|
1453
|
|
|
* |
|
1454
|
|
|
* Return a hex value as binary. |
|
1455
|
|
|
* |
|
1456
|
|
|
* Excel Function: |
|
1457
|
|
|
* HEX2BIN(x[,places]) |
|
1458
|
|
|
* |
|
1459
|
|
|
* @category Engineering Functions |
|
1460
|
|
|
* |
|
1461
|
|
|
* @param string $x the hexadecimal number you want to convert. |
|
1462
|
|
|
* Number cannot contain more than 10 characters. |
|
1463
|
|
|
* The most significant bit of number is the sign bit (40th bit from the right). |
|
1464
|
|
|
* The remaining 9 bits are magnitude bits. |
|
1465
|
|
|
* Negative numbers are represented using two's-complement notation. |
|
1466
|
|
|
* If number is negative, HEX2BIN ignores places and returns a 10-character binary number. |
|
1467
|
|
|
* If number is negative, it cannot be less than FFFFFFFE00, |
|
1468
|
|
|
* and if number is positive, it cannot be greater than 1FF. |
|
1469
|
|
|
* If number is not a valid hexadecimal number, HEX2BIN returns the #NUM! error value. |
|
1470
|
|
|
* If HEX2BIN requires more than places characters, it returns the #NUM! error value. |
|
1471
|
|
|
* @param int $places The number of characters to use. If places is omitted, |
|
1472
|
|
|
* HEX2BIN uses the minimum number of characters necessary. Places |
|
1473
|
|
|
* is useful for padding the return value with leading 0s (zeros). |
|
1474
|
|
|
* If places is not an integer, it is truncated. |
|
1475
|
|
|
* If places is nonnumeric, HEX2BIN returns the #VALUE! error value. |
|
1476
|
|
|
* If places is negative, HEX2BIN returns the #NUM! error value. |
|
1477
|
|
|
* |
|
1478
|
|
|
* @return string |
|
1479
|
|
|
*/ |
|
1480
|
16 |
View Code Duplication |
public static function HEXTOBIN($x, $places = null) |
|
|
|
|
|
|
1481
|
|
|
{ |
|
1482
|
16 |
|
$x = Functions::flattenSingleValue($x); |
|
1483
|
16 |
|
$places = Functions::flattenSingleValue($places); |
|
1484
|
|
|
|
|
1485
|
16 |
|
if (is_bool($x)) { |
|
1486
|
1 |
|
return Functions::VALUE(); |
|
1487
|
|
|
} |
|
1488
|
15 |
|
$x = (string) $x; |
|
1489
|
15 |
|
if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) { |
|
1490
|
2 |
|
return Functions::NAN(); |
|
1491
|
|
|
} |
|
1492
|
|
|
|
|
1493
|
13 |
|
return self::DECTOBIN(self::HEXTODEC($x), $places); |
|
1494
|
|
|
} |
|
1495
|
|
|
|
|
1496
|
|
|
/** |
|
1497
|
|
|
* HEXTODEC. |
|
1498
|
|
|
* |
|
1499
|
|
|
* Return a hex value as decimal. |
|
1500
|
|
|
* |
|
1501
|
|
|
* Excel Function: |
|
1502
|
|
|
* HEX2DEC(x) |
|
1503
|
|
|
* |
|
1504
|
|
|
* @category Engineering Functions |
|
1505
|
|
|
* |
|
1506
|
|
|
* @param string $x The hexadecimal number you want to convert. This number cannot |
|
1507
|
|
|
* contain more than 10 characters (40 bits). The most significant |
|
1508
|
|
|
* bit of number is the sign bit. The remaining 39 bits are magnitude |
|
1509
|
|
|
* bits. Negative numbers are represented using two's-complement |
|
1510
|
|
|
* notation. |
|
1511
|
|
|
* If number is not a valid hexadecimal number, HEX2DEC returns the |
|
1512
|
|
|
* #NUM! error value. |
|
1513
|
|
|
* |
|
1514
|
|
|
* @return string |
|
1515
|
|
|
*/ |
|
1516
|
37 |
|
public static function HEXTODEC($x) |
|
1517
|
|
|
{ |
|
1518
|
37 |
|
$x = Functions::flattenSingleValue($x); |
|
1519
|
|
|
|
|
1520
|
37 |
|
if (is_bool($x)) { |
|
1521
|
1 |
|
return Functions::VALUE(); |
|
1522
|
|
|
} |
|
1523
|
36 |
|
$x = (string) $x; |
|
1524
|
36 |
|
if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) { |
|
1525
|
3 |
|
return Functions::NAN(); |
|
1526
|
|
|
} |
|
1527
|
|
|
|
|
1528
|
33 |
|
if (strlen($x) > 10) { |
|
1529
|
1 |
|
return Functions::NAN(); |
|
1530
|
|
|
} |
|
1531
|
|
|
|
|
1532
|
32 |
|
$binX = ''; |
|
1533
|
32 |
View Code Duplication |
foreach (str_split($x) as $char) { |
|
|
|
|
|
|
1534
|
32 |
|
$binX .= str_pad(base_convert($char, 16, 2), 4, '0', STR_PAD_LEFT); |
|
1535
|
|
|
} |
|
1536
|
32 |
View Code Duplication |
if (strlen($binX) == 40 && $binX[0] == '1') { |
|
|
|
|
|
|
1537
|
5 |
|
for ($i = 0; $i < 40; ++$i) { |
|
1538
|
5 |
|
$binX[$i] = ($binX[$i] == '1' ? '0' : '1'); |
|
1539
|
|
|
} |
|
1540
|
|
|
|
|
1541
|
5 |
|
return (bindec($binX) + 1) * -1; |
|
1542
|
|
|
} |
|
1543
|
|
|
|
|
1544
|
27 |
|
return bindec($binX); |
|
1545
|
|
|
} |
|
1546
|
|
|
|
|
1547
|
|
|
/** |
|
1548
|
|
|
* HEXTOOCT. |
|
1549
|
|
|
* |
|
1550
|
|
|
* Return a hex value as octal. |
|
1551
|
|
|
* |
|
1552
|
|
|
* Excel Function: |
|
1553
|
|
|
* HEX2OCT(x[,places]) |
|
1554
|
|
|
* |
|
1555
|
|
|
* @category Engineering Functions |
|
1556
|
|
|
* |
|
1557
|
|
|
* @param string $x The hexadecimal number you want to convert. Number cannot |
|
1558
|
|
|
* contain more than 10 characters. The most significant bit of |
|
1559
|
|
|
* number is the sign bit. The remaining 39 bits are magnitude |
|
1560
|
|
|
* bits. Negative numbers are represented using two's-complement |
|
1561
|
|
|
* notation. |
|
1562
|
|
|
* If number is negative, HEX2OCT ignores places and returns a |
|
1563
|
|
|
* 10-character octal number. |
|
1564
|
|
|
* If number is negative, it cannot be less than FFE0000000, and |
|
1565
|
|
|
* if number is positive, it cannot be greater than 1FFFFFFF. |
|
1566
|
|
|
* If number is not a valid hexadecimal number, HEX2OCT returns |
|
1567
|
|
|
* the #NUM! error value. |
|
1568
|
|
|
* If HEX2OCT requires more than places characters, it returns |
|
1569
|
|
|
* the #NUM! error value. |
|
1570
|
|
|
* @param int $places The number of characters to use. If places is omitted, HEX2OCT |
|
1571
|
|
|
* uses the minimum number of characters necessary. Places is |
|
1572
|
|
|
* useful for padding the return value with leading 0s (zeros). |
|
1573
|
|
|
* If places is not an integer, it is truncated. |
|
1574
|
|
|
* If places is nonnumeric, HEX2OCT returns the #VALUE! error |
|
1575
|
|
|
* value. |
|
1576
|
|
|
* If places is negative, HEX2OCT returns the #NUM! error value. |
|
1577
|
|
|
* |
|
1578
|
|
|
* @return string |
|
1579
|
|
|
*/ |
|
1580
|
13 |
|
public static function HEXTOOCT($x, $places = null) |
|
1581
|
|
|
{ |
|
1582
|
13 |
|
$x = Functions::flattenSingleValue($x); |
|
1583
|
13 |
|
$places = Functions::flattenSingleValue($places); |
|
1584
|
|
|
|
|
1585
|
13 |
|
if (is_bool($x)) { |
|
1586
|
1 |
|
return Functions::VALUE(); |
|
1587
|
|
|
} |
|
1588
|
12 |
|
$x = (string) $x; |
|
1589
|
12 |
|
if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) { |
|
1590
|
3 |
|
return Functions::NAN(); |
|
1591
|
|
|
} |
|
1592
|
|
|
|
|
1593
|
9 |
|
$decimal = self::HEXTODEC($x); |
|
1594
|
9 |
|
if ($decimal < -536870912 || $decimal > 536870911) { |
|
1595
|
1 |
|
return Functions::NAN(); |
|
1596
|
|
|
} |
|
1597
|
|
|
|
|
1598
|
8 |
|
return self::DECTOOCT($decimal, $places); |
|
1599
|
|
|
} |
|
1600
|
|
|
|
|
1601
|
|
|
/** |
|
1602
|
|
|
* OCTTOBIN. |
|
1603
|
|
|
* |
|
1604
|
|
|
* Return an octal value as binary. |
|
1605
|
|
|
* |
|
1606
|
|
|
* Excel Function: |
|
1607
|
|
|
* OCT2BIN(x[,places]) |
|
1608
|
|
|
* |
|
1609
|
|
|
* @category Engineering Functions |
|
1610
|
|
|
* |
|
1611
|
|
|
* @param string $x The octal number you want to convert. Number may not |
|
1612
|
|
|
* contain more than 10 characters. The most significant |
|
1613
|
|
|
* bit of number is the sign bit. The remaining 29 bits |
|
1614
|
|
|
* are magnitude bits. Negative numbers are represented |
|
1615
|
|
|
* using two's-complement notation. |
|
1616
|
|
|
* If number is negative, OCT2BIN ignores places and returns |
|
1617
|
|
|
* a 10-character binary number. |
|
1618
|
|
|
* If number is negative, it cannot be less than 7777777000, |
|
1619
|
|
|
* and if number is positive, it cannot be greater than 777. |
|
1620
|
|
|
* If number is not a valid octal number, OCT2BIN returns |
|
1621
|
|
|
* the #NUM! error value. |
|
1622
|
|
|
* If OCT2BIN requires more than places characters, it |
|
1623
|
|
|
* returns the #NUM! error value. |
|
1624
|
|
|
* @param int $places The number of characters to use. If places is omitted, |
|
1625
|
|
|
* OCT2BIN uses the minimum number of characters necessary. |
|
1626
|
|
|
* Places is useful for padding the return value with |
|
1627
|
|
|
* leading 0s (zeros). |
|
1628
|
|
|
* If places is not an integer, it is truncated. |
|
1629
|
|
|
* If places is nonnumeric, OCT2BIN returns the #VALUE! |
|
1630
|
|
|
* error value. |
|
1631
|
|
|
* If places is negative, OCT2BIN returns the #NUM! error |
|
1632
|
|
|
* value. |
|
1633
|
|
|
* |
|
1634
|
|
|
* @return string |
|
1635
|
|
|
*/ |
|
1636
|
13 |
View Code Duplication |
public static function OCTTOBIN($x, $places = null) |
|
|
|
|
|
|
1637
|
|
|
{ |
|
1638
|
13 |
|
$x = Functions::flattenSingleValue($x); |
|
1639
|
13 |
|
$places = Functions::flattenSingleValue($places); |
|
1640
|
|
|
|
|
1641
|
13 |
|
if (is_bool($x)) { |
|
1642
|
1 |
|
return Functions::VALUE(); |
|
1643
|
|
|
} |
|
1644
|
12 |
|
$x = (string) $x; |
|
1645
|
12 |
|
if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) { |
|
1646
|
2 |
|
return Functions::NAN(); |
|
1647
|
|
|
} |
|
1648
|
|
|
|
|
1649
|
10 |
|
return self::DECTOBIN(self::OCTTODEC($x), $places); |
|
1650
|
|
|
} |
|
1651
|
|
|
|
|
1652
|
|
|
/** |
|
1653
|
|
|
* OCTTODEC. |
|
1654
|
|
|
* |
|
1655
|
|
|
* Return an octal value as decimal. |
|
1656
|
|
|
* |
|
1657
|
|
|
* Excel Function: |
|
1658
|
|
|
* OCT2DEC(x) |
|
1659
|
|
|
* |
|
1660
|
|
|
* @category Engineering Functions |
|
1661
|
|
|
* |
|
1662
|
|
|
* @param string $x The octal number you want to convert. Number may not contain |
|
1663
|
|
|
* more than 10 octal characters (30 bits). The most significant |
|
1664
|
|
|
* bit of number is the sign bit. The remaining 29 bits are |
|
1665
|
|
|
* magnitude bits. Negative numbers are represented using |
|
1666
|
|
|
* two's-complement notation. |
|
1667
|
|
|
* If number is not a valid octal number, OCT2DEC returns the |
|
1668
|
|
|
* #NUM! error value. |
|
1669
|
|
|
* |
|
1670
|
|
|
* @return string |
|
1671
|
|
|
*/ |
|
1672
|
25 |
|
public static function OCTTODEC($x) |
|
1673
|
|
|
{ |
|
1674
|
25 |
|
$x = Functions::flattenSingleValue($x); |
|
1675
|
|
|
|
|
1676
|
25 |
|
if (is_bool($x)) { |
|
1677
|
1 |
|
return Functions::VALUE(); |
|
1678
|
|
|
} |
|
1679
|
24 |
|
$x = (string) $x; |
|
1680
|
24 |
|
if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) { |
|
1681
|
2 |
|
return Functions::NAN(); |
|
1682
|
|
|
} |
|
1683
|
22 |
|
$binX = ''; |
|
1684
|
22 |
View Code Duplication |
foreach (str_split($x) as $char) { |
|
|
|
|
|
|
1685
|
22 |
|
$binX .= str_pad(decbin((int) $char), 3, '0', STR_PAD_LEFT); |
|
1686
|
|
|
} |
|
1687
|
22 |
View Code Duplication |
if (strlen($binX) == 30 && $binX[0] == '1') { |
|
|
|
|
|
|
1688
|
4 |
|
for ($i = 0; $i < 30; ++$i) { |
|
1689
|
4 |
|
$binX[$i] = ($binX[$i] == '1' ? '0' : '1'); |
|
1690
|
|
|
} |
|
1691
|
|
|
|
|
1692
|
4 |
|
return (bindec($binX) + 1) * -1; |
|
1693
|
|
|
} |
|
1694
|
|
|
|
|
1695
|
18 |
|
return bindec($binX); |
|
1696
|
|
|
} |
|
1697
|
|
|
|
|
1698
|
|
|
/** |
|
1699
|
|
|
* OCTTOHEX. |
|
1700
|
|
|
* |
|
1701
|
|
|
* Return an octal value as hex. |
|
1702
|
|
|
* |
|
1703
|
|
|
* Excel Function: |
|
1704
|
|
|
* OCT2HEX(x[,places]) |
|
1705
|
|
|
* |
|
1706
|
|
|
* @category Engineering Functions |
|
1707
|
|
|
* |
|
1708
|
|
|
* @param string $x The octal number you want to convert. Number may not contain |
|
1709
|
|
|
* more than 10 octal characters (30 bits). The most significant |
|
1710
|
|
|
* bit of number is the sign bit. The remaining 29 bits are |
|
1711
|
|
|
* magnitude bits. Negative numbers are represented using |
|
1712
|
|
|
* two's-complement notation. |
|
1713
|
|
|
* If number is negative, OCT2HEX ignores places and returns a |
|
1714
|
|
|
* 10-character hexadecimal number. |
|
1715
|
|
|
* If number is not a valid octal number, OCT2HEX returns the |
|
1716
|
|
|
* #NUM! error value. |
|
1717
|
|
|
* If OCT2HEX requires more than places characters, it returns |
|
1718
|
|
|
* the #NUM! error value. |
|
1719
|
|
|
* @param int $places The number of characters to use. If places is omitted, OCT2HEX |
|
1720
|
|
|
* uses the minimum number of characters necessary. Places is useful |
|
1721
|
|
|
* for padding the return value with leading 0s (zeros). |
|
1722
|
|
|
* If places is not an integer, it is truncated. |
|
1723
|
|
|
* If places is nonnumeric, OCT2HEX returns the #VALUE! error value. |
|
1724
|
|
|
* If places is negative, OCT2HEX returns the #NUM! error value. |
|
1725
|
|
|
* |
|
1726
|
|
|
* @return string |
|
1727
|
|
|
*/ |
|
1728
|
9 |
View Code Duplication |
public static function OCTTOHEX($x, $places = null) |
|
|
|
|
|
|
1729
|
|
|
{ |
|
1730
|
9 |
|
$x = Functions::flattenSingleValue($x); |
|
1731
|
9 |
|
$places = Functions::flattenSingleValue($places); |
|
1732
|
|
|
|
|
1733
|
9 |
|
if (is_bool($x)) { |
|
1734
|
1 |
|
return Functions::VALUE(); |
|
1735
|
|
|
} |
|
1736
|
8 |
|
$x = (string) $x; |
|
1737
|
8 |
|
if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) { |
|
1738
|
2 |
|
return Functions::NAN(); |
|
1739
|
|
|
} |
|
1740
|
6 |
|
$hexVal = strtoupper(dechex(self::OCTTODEC($x))); |
|
|
|
|
|
|
1741
|
|
|
|
|
1742
|
6 |
|
return self::nbrConversionFormat($hexVal, $places); |
|
1743
|
|
|
} |
|
1744
|
|
|
|
|
1745
|
|
|
/** |
|
1746
|
|
|
* COMPLEX. |
|
1747
|
|
|
* |
|
1748
|
|
|
* Converts real and imaginary coefficients into a complex number of the form x + yi or x + yj. |
|
1749
|
|
|
* |
|
1750
|
|
|
* Excel Function: |
|
1751
|
|
|
* COMPLEX(realNumber,imaginary[,places]) |
|
1752
|
|
|
* |
|
1753
|
|
|
* @category Engineering Functions |
|
1754
|
|
|
* |
|
1755
|
|
|
* @param float $realNumber the real coefficient of the complex number |
|
1756
|
|
|
* @param float $imaginary the imaginary coefficient of the complex number |
|
1757
|
|
|
* @param string $suffix The suffix for the imaginary component of the complex number. |
|
1758
|
|
|
* If omitted, the suffix is assumed to be "i". |
|
1759
|
|
|
* |
|
1760
|
|
|
* @return string |
|
1761
|
|
|
*/ |
|
1762
|
759 |
|
public static function COMPLEX($realNumber = 0.0, $imaginary = 0.0, $suffix = 'i') |
|
1763
|
|
|
{ |
|
1764
|
759 |
|
$realNumber = ($realNumber === null) ? 0.0 : Functions::flattenSingleValue($realNumber); |
|
1765
|
759 |
|
$imaginary = ($imaginary === null) ? 0.0 : Functions::flattenSingleValue($imaginary); |
|
1766
|
759 |
|
$suffix = ($suffix === null) ? 'i' : Functions::flattenSingleValue($suffix); |
|
1767
|
|
|
|
|
1768
|
759 |
|
if (((is_numeric($realNumber)) && (is_numeric($imaginary))) && |
|
1769
|
759 |
|
(($suffix == 'i') || ($suffix == 'j') || ($suffix == '')) |
|
1770
|
|
|
) { |
|
1771
|
758 |
|
$realNumber = (float) $realNumber; |
|
1772
|
758 |
|
$imaginary = (float) $imaginary; |
|
1773
|
|
|
|
|
1774
|
758 |
|
if ($suffix == '') { |
|
1775
|
|
|
$suffix = 'i'; |
|
1776
|
|
|
} |
|
1777
|
758 |
|
if ($realNumber == 0.0) { |
|
1778
|
65 |
|
if ($imaginary == 0.0) { |
|
1779
|
6 |
|
return (string) '0'; |
|
1780
|
59 |
|
} elseif ($imaginary == 1.0) { |
|
1781
|
5 |
|
return (string) $suffix; |
|
1782
|
54 |
|
} elseif ($imaginary == -1.0) { |
|
1783
|
2 |
|
return (string) '-' . $suffix; |
|
1784
|
|
|
} |
|
1785
|
|
|
|
|
1786
|
52 |
|
return (string) $imaginary . $suffix; |
|
1787
|
693 |
|
} elseif ($imaginary == 0.0) { |
|
1788
|
54 |
|
return (string) $realNumber; |
|
1789
|
639 |
|
} elseif ($imaginary == 1.0) { |
|
1790
|
45 |
|
return (string) $realNumber . '+' . $suffix; |
|
1791
|
594 |
|
} elseif ($imaginary == -1.0) { |
|
1792
|
8 |
|
return (string) $realNumber . '-' . $suffix; |
|
1793
|
|
|
} |
|
1794
|
586 |
|
if ($imaginary > 0) { |
|
1795
|
329 |
|
$imaginary = (string) '+' . $imaginary; |
|
1796
|
|
|
} |
|
1797
|
|
|
|
|
1798
|
586 |
|
return (string) $realNumber . $imaginary . $suffix; |
|
1799
|
|
|
} |
|
1800
|
|
|
|
|
1801
|
1 |
|
return Functions::VALUE(); |
|
1802
|
|
|
} |
|
1803
|
|
|
|
|
1804
|
|
|
/** |
|
1805
|
|
|
* IMAGINARY. |
|
1806
|
|
|
* |
|
1807
|
|
|
* Returns the imaginary coefficient of a complex number in x + yi or x + yj text format. |
|
1808
|
|
|
* |
|
1809
|
|
|
* Excel Function: |
|
1810
|
|
|
* IMAGINARY(complexNumber) |
|
1811
|
|
|
* |
|
1812
|
|
|
* @category Engineering Functions |
|
1813
|
|
|
* |
|
1814
|
|
|
* @param string $complexNumber the complex number for which you want the imaginary |
|
1815
|
|
|
* coefficient |
|
1816
|
|
|
* |
|
1817
|
|
|
* @return float |
|
1818
|
|
|
*/ |
|
1819
|
30 |
|
public static function IMAGINARY($complexNumber) |
|
1820
|
|
|
{ |
|
1821
|
30 |
|
$complexNumber = Functions::flattenSingleValue($complexNumber); |
|
1822
|
|
|
|
|
1823
|
30 |
|
$parsedComplex = self::parseComplex($complexNumber); |
|
1824
|
|
|
|
|
1825
|
30 |
|
return $parsedComplex['imaginary']; |
|
|
|
|
|
|
1826
|
|
|
} |
|
1827
|
|
|
|
|
1828
|
|
|
/** |
|
1829
|
|
|
* IMREAL. |
|
1830
|
|
|
* |
|
1831
|
|
|
* Returns the real coefficient of a complex number in x + yi or x + yj text format. |
|
1832
|
|
|
* |
|
1833
|
|
|
* Excel Function: |
|
1834
|
|
|
* IMREAL(complexNumber) |
|
1835
|
|
|
* |
|
1836
|
|
|
* @category Engineering Functions |
|
1837
|
|
|
* |
|
1838
|
|
|
* @param string $complexNumber the complex number for which you want the real coefficient |
|
1839
|
|
|
* |
|
1840
|
|
|
* @return float |
|
1841
|
|
|
*/ |
|
1842
|
30 |
|
public static function IMREAL($complexNumber) |
|
1843
|
|
|
{ |
|
1844
|
30 |
|
$complexNumber = Functions::flattenSingleValue($complexNumber); |
|
1845
|
|
|
|
|
1846
|
30 |
|
$parsedComplex = self::parseComplex($complexNumber); |
|
1847
|
|
|
|
|
1848
|
30 |
|
return $parsedComplex['real']; |
|
|
|
|
|
|
1849
|
|
|
} |
|
1850
|
|
|
|
|
1851
|
|
|
/** |
|
1852
|
|
|
* IMABS. |
|
1853
|
|
|
* |
|
1854
|
|
|
* Returns the absolute value (modulus) of a complex number in x + yi or x + yj text format. |
|
1855
|
|
|
* |
|
1856
|
|
|
* Excel Function: |
|
1857
|
|
|
* IMABS(complexNumber) |
|
1858
|
|
|
* |
|
1859
|
|
|
* @param string $complexNumber the complex number for which you want the absolute value |
|
1860
|
|
|
* |
|
1861
|
|
|
* @return float |
|
1862
|
|
|
*/ |
|
1863
|
27 |
|
public static function IMABS($complexNumber) |
|
1864
|
|
|
{ |
|
1865
|
27 |
|
$complexNumber = Functions::flattenSingleValue($complexNumber); |
|
1866
|
|
|
|
|
1867
|
27 |
|
$parsedComplex = self::parseComplex($complexNumber); |
|
1868
|
|
|
|
|
1869
|
27 |
|
return sqrt( |
|
1870
|
27 |
|
($parsedComplex['real'] * $parsedComplex['real']) + |
|
1871
|
27 |
|
($parsedComplex['imaginary'] * $parsedComplex['imaginary']) |
|
1872
|
|
|
); |
|
1873
|
|
|
} |
|
1874
|
|
|
|
|
1875
|
|
|
/** |
|
1876
|
|
|
* IMARGUMENT. |
|
1877
|
|
|
* |
|
1878
|
|
|
* Returns the argument theta of a complex number, i.e. the angle in radians from the real |
|
1879
|
|
|
* axis to the representation of the number in polar coordinates. |
|
1880
|
|
|
* |
|
1881
|
|
|
* Excel Function: |
|
1882
|
|
|
* IMARGUMENT(complexNumber) |
|
1883
|
|
|
* |
|
1884
|
|
|
* @param string $complexNumber the complex number for which you want the argument theta |
|
1885
|
|
|
* |
|
1886
|
|
|
* @return float |
|
1887
|
|
|
*/ |
|
1888
|
128 |
|
public static function IMARGUMENT($complexNumber) |
|
1889
|
|
|
{ |
|
1890
|
128 |
|
$complexNumber = Functions::flattenSingleValue($complexNumber); |
|
1891
|
128 |
|
$parsedComplex = self::parseComplex($complexNumber); |
|
1892
|
128 |
|
if ($parsedComplex['real'] == 0.0) { |
|
1893
|
22 |
|
if ($parsedComplex['imaginary'] == 0.0) { |
|
1894
|
2 |
|
return Functions::DIV0(); |
|
|
|
|
|
|
1895
|
20 |
|
} elseif ($parsedComplex['imaginary'] < 0.0) { |
|
1896
|
10 |
|
return M_PI / -2; |
|
1897
|
|
|
} |
|
1898
|
|
|
|
|
1899
|
10 |
|
return M_PI / 2; |
|
1900
|
106 |
|
} elseif ($parsedComplex['real'] > 0.0) { |
|
1901
|
52 |
|
return atan($parsedComplex['imaginary'] / $parsedComplex['real']); |
|
1902
|
54 |
|
} elseif ($parsedComplex['imaginary'] < 0.0) { |
|
1903
|
20 |
|
return 0 - (M_PI - atan(abs($parsedComplex['imaginary']) / abs($parsedComplex['real']))); |
|
1904
|
|
|
} |
|
1905
|
|
|
|
|
1906
|
34 |
|
return M_PI - atan($parsedComplex['imaginary'] / abs($parsedComplex['real'])); |
|
1907
|
|
|
} |
|
1908
|
|
|
|
|
1909
|
|
|
/** |
|
1910
|
|
|
* IMCONJUGATE. |
|
1911
|
|
|
* |
|
1912
|
|
|
* Returns the complex conjugate of a complex number in x + yi or x + yj text format. |
|
1913
|
|
|
* |
|
1914
|
|
|
* Excel Function: |
|
1915
|
|
|
* IMCONJUGATE(complexNumber) |
|
1916
|
|
|
* |
|
1917
|
|
|
* @param string $complexNumber the complex number for which you want the conjugate |
|
1918
|
|
|
* |
|
1919
|
|
|
* @return string |
|
1920
|
|
|
*/ |
|
1921
|
47 |
|
public static function IMCONJUGATE($complexNumber) |
|
1922
|
|
|
{ |
|
1923
|
47 |
|
$complexNumber = Functions::flattenSingleValue($complexNumber); |
|
1924
|
|
|
|
|
1925
|
47 |
|
$parsedComplex = self::parseComplex($complexNumber); |
|
1926
|
|
|
|
|
1927
|
47 |
|
if ($parsedComplex['imaginary'] == 0.0) { |
|
1928
|
9 |
|
return $parsedComplex['real']; |
|
1929
|
|
|
} |
|
1930
|
|
|
|
|
1931
|
38 |
|
return self::cleanComplex( |
|
1932
|
38 |
|
self::COMPLEX( |
|
1933
|
38 |
|
$parsedComplex['real'], |
|
|
|
|
|
|
1934
|
38 |
|
0 - $parsedComplex['imaginary'], |
|
1935
|
38 |
|
$parsedComplex['suffix'] |
|
1936
|
|
|
) |
|
1937
|
|
|
); |
|
1938
|
|
|
} |
|
1939
|
|
|
|
|
1940
|
|
|
/** |
|
1941
|
|
|
* IMCOS. |
|
1942
|
|
|
* |
|
1943
|
|
|
* Returns the cosine of a complex number in x + yi or x + yj text format. |
|
1944
|
|
|
* |
|
1945
|
|
|
* Excel Function: |
|
1946
|
|
|
* IMCOS(complexNumber) |
|
1947
|
|
|
* |
|
1948
|
|
|
* @param string $complexNumber the complex number for which you want the cosine |
|
1949
|
|
|
* |
|
1950
|
|
|
* @return float|string |
|
1951
|
|
|
*/ |
|
1952
|
27 |
View Code Duplication |
public static function IMCOS($complexNumber) |
|
|
|
|
|
|
1953
|
|
|
{ |
|
1954
|
27 |
|
$complexNumber = Functions::flattenSingleValue($complexNumber); |
|
1955
|
|
|
|
|
1956
|
27 |
|
$parsedComplex = self::parseComplex($complexNumber); |
|
1957
|
|
|
|
|
1958
|
27 |
|
if ($parsedComplex['imaginary'] == 0.0) { |
|
1959
|
6 |
|
return cos($parsedComplex['real']); |
|
|
|
|
|
|
1960
|
|
|
} |
|
1961
|
|
|
|
|
1962
|
21 |
|
return self::IMCONJUGATE( |
|
1963
|
21 |
|
self::COMPLEX( |
|
1964
|
21 |
|
cos($parsedComplex['real']) * cosh($parsedComplex['imaginary']), |
|
|
|
|
|
|
1965
|
21 |
|
sin($parsedComplex['real']) * sinh($parsedComplex['imaginary']), |
|
|
|
|
|
|
1966
|
21 |
|
$parsedComplex['suffix'] |
|
1967
|
|
|
) |
|
1968
|
|
|
); |
|
1969
|
|
|
} |
|
1970
|
|
|
|
|
1971
|
|
|
/** |
|
1972
|
|
|
* IMSIN. |
|
1973
|
|
|
* |
|
1974
|
|
|
* Returns the sine of a complex number in x + yi or x + yj text format. |
|
1975
|
|
|
* |
|
1976
|
|
|
* Excel Function: |
|
1977
|
|
|
* IMSIN(complexNumber) |
|
1978
|
|
|
* |
|
1979
|
|
|
* @param string $complexNumber the complex number for which you want the sine |
|
1980
|
|
|
* |
|
1981
|
|
|
* @return float|string |
|
1982
|
|
|
*/ |
|
1983
|
27 |
View Code Duplication |
public static function IMSIN($complexNumber) |
|
|
|
|
|
|
1984
|
|
|
{ |
|
1985
|
27 |
|
$complexNumber = Functions::flattenSingleValue($complexNumber); |
|
1986
|
|
|
|
|
1987
|
27 |
|
$parsedComplex = self::parseComplex($complexNumber); |
|
1988
|
|
|
|
|
1989
|
27 |
|
if ($parsedComplex['imaginary'] == 0.0) { |
|
1990
|
6 |
|
return sin($parsedComplex['real']); |
|
|
|
|
|
|
1991
|
|
|
} |
|
1992
|
|
|
|
|
1993
|
21 |
|
return self::COMPLEX( |
|
1994
|
21 |
|
sin($parsedComplex['real']) * cosh($parsedComplex['imaginary']), |
|
|
|
|
|
|
1995
|
21 |
|
cos($parsedComplex['real']) * sinh($parsedComplex['imaginary']), |
|
|
|
|
|
|
1996
|
21 |
|
$parsedComplex['suffix'] |
|
1997
|
|
|
); |
|
1998
|
|
|
} |
|
1999
|
|
|
|
|
2000
|
|
|
/** |
|
2001
|
|
|
* IMSQRT. |
|
2002
|
|
|
* |
|
2003
|
|
|
* Returns the square root of a complex number in x + yi or x + yj text format. |
|
2004
|
|
|
* |
|
2005
|
|
|
* Excel Function: |
|
2006
|
|
|
* IMSQRT(complexNumber) |
|
2007
|
|
|
* |
|
2008
|
|
|
* @param string $complexNumber the complex number for which you want the square root |
|
2009
|
|
|
* |
|
2010
|
|
|
* @return string |
|
2011
|
|
|
*/ |
|
2012
|
28 |
|
public static function IMSQRT($complexNumber) |
|
2013
|
|
|
{ |
|
2014
|
28 |
|
$complexNumber = Functions::flattenSingleValue($complexNumber); |
|
2015
|
|
|
|
|
2016
|
28 |
|
$parsedComplex = self::parseComplex($complexNumber); |
|
2017
|
|
|
|
|
2018
|
28 |
|
$theta = self::IMARGUMENT($complexNumber); |
|
2019
|
28 |
|
if ($theta === Functions::DIV0()) { |
|
2020
|
1 |
|
return '0'; |
|
2021
|
|
|
} |
|
2022
|
|
|
|
|
2023
|
27 |
|
$d1 = cos($theta / 2); |
|
2024
|
27 |
|
$d2 = sin($theta / 2); |
|
2025
|
27 |
|
$r = sqrt(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']))); |
|
2026
|
|
|
|
|
2027
|
27 |
|
if ($parsedComplex['suffix'] == '') { |
|
2028
|
5 |
|
return self::COMPLEX($d1 * $r, $d2 * $r); |
|
2029
|
|
|
} |
|
2030
|
|
|
|
|
2031
|
22 |
|
return self::COMPLEX($d1 * $r, $d2 * $r, $parsedComplex['suffix']); |
|
2032
|
|
|
} |
|
2033
|
|
|
|
|
2034
|
|
|
/** |
|
2035
|
|
|
* IMLN. |
|
2036
|
|
|
* |
|
2037
|
|
|
* Returns the natural logarithm of a complex number in x + yi or x + yj text format. |
|
2038
|
|
|
* |
|
2039
|
|
|
* Excel Function: |
|
2040
|
|
|
* IMLN(complexNumber) |
|
2041
|
|
|
* |
|
2042
|
|
|
* @param string $complexNumber the complex number for which you want the natural logarithm |
|
2043
|
|
|
* |
|
2044
|
|
|
* @return string |
|
2045
|
|
|
*/ |
|
2046
|
75 |
|
public static function IMLN($complexNumber) |
|
2047
|
|
|
{ |
|
2048
|
75 |
|
$complexNumber = Functions::flattenSingleValue($complexNumber); |
|
2049
|
|
|
|
|
2050
|
75 |
|
$parsedComplex = self::parseComplex($complexNumber); |
|
2051
|
|
|
|
|
2052
|
75 |
|
if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) { |
|
2053
|
1 |
|
return Functions::NAN(); |
|
2054
|
|
|
} |
|
2055
|
|
|
|
|
2056
|
74 |
|
$logR = log(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']))); |
|
2057
|
74 |
|
$t = self::IMARGUMENT($complexNumber); |
|
2058
|
|
|
|
|
2059
|
74 |
|
if ($parsedComplex['suffix'] == '') { |
|
2060
|
8 |
|
return self::COMPLEX($logR, $t); |
|
2061
|
|
|
} |
|
2062
|
|
|
|
|
2063
|
66 |
|
return self::COMPLEX($logR, $t, $parsedComplex['suffix']); |
|
2064
|
|
|
} |
|
2065
|
|
|
|
|
2066
|
|
|
/** |
|
2067
|
|
|
* IMLOG10. |
|
2068
|
|
|
* |
|
2069
|
|
|
* Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format. |
|
2070
|
|
|
* |
|
2071
|
|
|
* Excel Function: |
|
2072
|
|
|
* IMLOG10(complexNumber) |
|
2073
|
|
|
* |
|
2074
|
|
|
* @param string $complexNumber the complex number for which you want the common logarithm |
|
2075
|
|
|
* |
|
2076
|
|
|
* @return string |
|
2077
|
|
|
*/ |
|
2078
|
27 |
View Code Duplication |
public static function IMLOG10($complexNumber) |
|
|
|
|
|
|
2079
|
|
|
{ |
|
2080
|
27 |
|
$complexNumber = Functions::flattenSingleValue($complexNumber); |
|
2081
|
|
|
|
|
2082
|
27 |
|
$parsedComplex = self::parseComplex($complexNumber); |
|
2083
|
|
|
|
|
2084
|
27 |
|
if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) { |
|
2085
|
1 |
|
return Functions::NAN(); |
|
2086
|
26 |
|
} elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) { |
|
2087
|
2 |
|
return log10($parsedComplex['real']); |
|
2088
|
|
|
} |
|
2089
|
|
|
|
|
2090
|
24 |
|
return self::IMPRODUCT(log10(self::EULER), self::IMLN($complexNumber)); |
|
2091
|
|
|
} |
|
2092
|
|
|
|
|
2093
|
|
|
/** |
|
2094
|
|
|
* IMLOG2. |
|
2095
|
|
|
* |
|
2096
|
|
|
* Returns the base-2 logarithm of a complex number in x + yi or x + yj text format. |
|
2097
|
|
|
* |
|
2098
|
|
|
* Excel Function: |
|
2099
|
|
|
* IMLOG2(complexNumber) |
|
2100
|
|
|
* |
|
2101
|
|
|
* @param string $complexNumber the complex number for which you want the base-2 logarithm |
|
2102
|
|
|
* |
|
2103
|
|
|
* @return string |
|
2104
|
|
|
*/ |
|
2105
|
27 |
View Code Duplication |
public static function IMLOG2($complexNumber) |
|
|
|
|
|
|
2106
|
|
|
{ |
|
2107
|
27 |
|
$complexNumber = Functions::flattenSingleValue($complexNumber); |
|
2108
|
|
|
|
|
2109
|
27 |
|
$parsedComplex = self::parseComplex($complexNumber); |
|
2110
|
|
|
|
|
2111
|
27 |
|
if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) { |
|
2112
|
1 |
|
return Functions::NAN(); |
|
2113
|
26 |
|
} elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) { |
|
2114
|
2 |
|
return log($parsedComplex['real'], 2); |
|
2115
|
|
|
} |
|
2116
|
|
|
|
|
2117
|
24 |
|
return self::IMPRODUCT(log(self::EULER, 2), self::IMLN($complexNumber)); |
|
2118
|
|
|
} |
|
2119
|
|
|
|
|
2120
|
|
|
/** |
|
2121
|
|
|
* IMEXP. |
|
2122
|
|
|
* |
|
2123
|
|
|
* Returns the exponential of a complex number in x + yi or x + yj text format. |
|
2124
|
|
|
* |
|
2125
|
|
|
* Excel Function: |
|
2126
|
|
|
* IMEXP(complexNumber) |
|
2127
|
|
|
* |
|
2128
|
|
|
* @param string $complexNumber the complex number for which you want the exponential |
|
2129
|
|
|
* |
|
2130
|
|
|
* @return string |
|
2131
|
|
|
*/ |
|
2132
|
27 |
|
public static function IMEXP($complexNumber) |
|
2133
|
|
|
{ |
|
2134
|
27 |
|
$complexNumber = Functions::flattenSingleValue($complexNumber); |
|
2135
|
|
|
|
|
2136
|
27 |
|
$parsedComplex = self::parseComplex($complexNumber); |
|
2137
|
|
|
|
|
2138
|
27 |
|
if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) { |
|
2139
|
1 |
|
return '1'; |
|
2140
|
|
|
} |
|
2141
|
|
|
|
|
2142
|
26 |
|
$e = exp($parsedComplex['real']); |
|
2143
|
26 |
|
$eX = $e * cos($parsedComplex['imaginary']); |
|
2144
|
26 |
|
$eY = $e * sin($parsedComplex['imaginary']); |
|
2145
|
|
|
|
|
2146
|
26 |
|
if ($parsedComplex['suffix'] == '') { |
|
2147
|
4 |
|
return self::COMPLEX($eX, $eY); |
|
2148
|
|
|
} |
|
2149
|
|
|
|
|
2150
|
22 |
|
return self::COMPLEX($eX, $eY, $parsedComplex['suffix']); |
|
2151
|
|
|
} |
|
2152
|
|
|
|
|
2153
|
|
|
/** |
|
2154
|
|
|
* IMPOWER. |
|
2155
|
|
|
* |
|
2156
|
|
|
* Returns a complex number in x + yi or x + yj text format raised to a power. |
|
2157
|
|
|
* |
|
2158
|
|
|
* Excel Function: |
|
2159
|
|
|
* IMPOWER(complexNumber,realNumber) |
|
2160
|
|
|
* |
|
2161
|
|
|
* @param string $complexNumber the complex number you want to raise to a power |
|
2162
|
|
|
* @param float $realNumber the power to which you want to raise the complex number |
|
2163
|
|
|
* |
|
2164
|
|
|
* @return string |
|
2165
|
|
|
*/ |
|
2166
|
|
|
public static function IMPOWER($complexNumber, $realNumber) |
|
2167
|
|
|
{ |
|
2168
|
|
|
$complexNumber = Functions::flattenSingleValue($complexNumber); |
|
2169
|
|
|
$realNumber = Functions::flattenSingleValue($realNumber); |
|
2170
|
|
|
|
|
2171
|
|
|
if (!is_numeric($realNumber)) { |
|
2172
|
|
|
return Functions::VALUE(); |
|
2173
|
|
|
} |
|
2174
|
|
|
|
|
2175
|
|
|
$parsedComplex = self::parseComplex($complexNumber); |
|
2176
|
|
|
|
|
2177
|
|
|
$r = sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])); |
|
2178
|
|
|
$rPower = pow($r, $realNumber); |
|
2179
|
|
|
$theta = self::IMARGUMENT($complexNumber) * $realNumber; |
|
2180
|
|
|
if ($theta == 0) { |
|
2181
|
|
|
return 1; |
|
2182
|
|
|
} elseif ($parsedComplex['imaginary'] == 0.0) { |
|
2183
|
|
|
return self::COMPLEX($rPower * cos($theta), $rPower * sin($theta), $parsedComplex['suffix']); |
|
2184
|
|
|
} |
|
2185
|
|
|
|
|
2186
|
|
|
return self::COMPLEX($rPower * cos($theta), $rPower * sin($theta), $parsedComplex['suffix']); |
|
2187
|
|
|
} |
|
2188
|
|
|
|
|
2189
|
|
|
/** |
|
2190
|
|
|
* IMDIV. |
|
2191
|
|
|
* |
|
2192
|
|
|
* Returns the quotient of two complex numbers in x + yi or x + yj text format. |
|
2193
|
|
|
* |
|
2194
|
|
|
* Excel Function: |
|
2195
|
|
|
* IMDIV(complexDividend,complexDivisor) |
|
2196
|
|
|
* |
|
2197
|
|
|
* @param string $complexDividend the complex numerator or dividend |
|
2198
|
|
|
* @param string $complexDivisor the complex denominator or divisor |
|
2199
|
|
|
* |
|
2200
|
|
|
* @return string |
|
2201
|
|
|
*/ |
|
2202
|
|
|
public static function IMDIV($complexDividend, $complexDivisor) |
|
2203
|
|
|
{ |
|
2204
|
|
|
$complexDividend = Functions::flattenSingleValue($complexDividend); |
|
2205
|
|
|
$complexDivisor = Functions::flattenSingleValue($complexDivisor); |
|
2206
|
|
|
|
|
2207
|
|
|
$parsedComplexDividend = self::parseComplex($complexDividend); |
|
2208
|
|
|
$parsedComplexDivisor = self::parseComplex($complexDivisor); |
|
2209
|
|
|
|
|
2210
|
|
|
if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] != '') && |
|
2211
|
|
|
($parsedComplexDividend['suffix'] != $parsedComplexDivisor['suffix']) |
|
2212
|
|
|
) { |
|
2213
|
|
|
return Functions::NAN(); |
|
2214
|
|
|
} |
|
2215
|
|
|
if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] == '')) { |
|
2216
|
|
|
$parsedComplexDivisor['suffix'] = $parsedComplexDividend['suffix']; |
|
2217
|
|
|
} |
|
2218
|
|
|
|
|
2219
|
|
|
$d1 = ($parsedComplexDividend['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['imaginary']); |
|
2220
|
|
|
$d2 = ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['real']) - ($parsedComplexDividend['real'] * $parsedComplexDivisor['imaginary']); |
|
2221
|
|
|
$d3 = ($parsedComplexDivisor['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDivisor['imaginary'] * $parsedComplexDivisor['imaginary']); |
|
2222
|
|
|
|
|
2223
|
|
|
$r = $d1 / $d3; |
|
2224
|
|
|
$i = $d2 / $d3; |
|
2225
|
|
|
|
|
2226
|
|
|
if ($i > 0.0) { |
|
2227
|
|
|
return self::cleanComplex($r . '+' . $i . $parsedComplexDivisor['suffix']); |
|
2228
|
|
|
} elseif ($i < 0.0) { |
|
2229
|
|
|
return self::cleanComplex($r . $i . $parsedComplexDivisor['suffix']); |
|
2230
|
|
|
} |
|
2231
|
|
|
|
|
2232
|
|
|
return $r; |
|
2233
|
|
|
} |
|
2234
|
|
|
|
|
2235
|
|
|
/** |
|
2236
|
|
|
* IMSUB. |
|
2237
|
|
|
* |
|
2238
|
|
|
* Returns the difference of two complex numbers in x + yi or x + yj text format. |
|
2239
|
|
|
* |
|
2240
|
|
|
* Excel Function: |
|
2241
|
|
|
* IMSUB(complexNumber1,complexNumber2) |
|
2242
|
|
|
* |
|
2243
|
|
|
* @param string $complexNumber1 the complex number from which to subtract complexNumber2 |
|
2244
|
|
|
* @param string $complexNumber2 the complex number to subtract from complexNumber1 |
|
2245
|
|
|
* |
|
2246
|
|
|
* @return string |
|
2247
|
|
|
*/ |
|
2248
|
|
|
public static function IMSUB($complexNumber1, $complexNumber2) |
|
2249
|
|
|
{ |
|
2250
|
|
|
$complexNumber1 = Functions::flattenSingleValue($complexNumber1); |
|
2251
|
|
|
$complexNumber2 = Functions::flattenSingleValue($complexNumber2); |
|
2252
|
|
|
|
|
2253
|
|
|
$parsedComplex1 = self::parseComplex($complexNumber1); |
|
2254
|
|
|
$parsedComplex2 = self::parseComplex($complexNumber2); |
|
2255
|
|
|
|
|
2256
|
|
|
if ((($parsedComplex1['suffix'] != '') && ($parsedComplex2['suffix'] != '')) && |
|
2257
|
|
|
($parsedComplex1['suffix'] != $parsedComplex2['suffix']) |
|
2258
|
|
|
) { |
|
2259
|
|
|
return Functions::NAN(); |
|
2260
|
|
|
} elseif (($parsedComplex1['suffix'] == '') && ($parsedComplex2['suffix'] != '')) { |
|
2261
|
|
|
$parsedComplex1['suffix'] = $parsedComplex2['suffix']; |
|
2262
|
|
|
} |
|
2263
|
|
|
|
|
2264
|
|
|
$d1 = $parsedComplex1['real'] - $parsedComplex2['real']; |
|
2265
|
|
|
$d2 = $parsedComplex1['imaginary'] - $parsedComplex2['imaginary']; |
|
2266
|
|
|
|
|
2267
|
|
|
return self::COMPLEX($d1, $d2, $parsedComplex1['suffix']); |
|
2268
|
|
|
} |
|
2269
|
|
|
|
|
2270
|
|
|
/** |
|
2271
|
|
|
* IMSUM. |
|
2272
|
|
|
* |
|
2273
|
|
|
* Returns the sum of two or more complex numbers in x + yi or x + yj text format. |
|
2274
|
|
|
* |
|
2275
|
|
|
* Excel Function: |
|
2276
|
|
|
* IMSUM(complexNumber[,complexNumber[,...]]) |
|
2277
|
|
|
* |
|
2278
|
|
|
* @param string ...$complexNumbers Series of complex numbers to add |
|
2279
|
|
|
* |
|
2280
|
|
|
* @return string |
|
2281
|
|
|
*/ |
|
2282
|
10 |
|
public static function IMSUM(...$complexNumbers) |
|
2283
|
|
|
{ |
|
2284
|
|
|
// Return value |
|
2285
|
10 |
|
$returnValue = self::parseComplex('0'); |
|
2286
|
10 |
|
$activeSuffix = ''; |
|
2287
|
|
|
|
|
2288
|
|
|
// Loop through the arguments |
|
2289
|
10 |
|
$aArgs = Functions::flattenArray($complexNumbers); |
|
2290
|
10 |
|
foreach ($aArgs as $arg) { |
|
2291
|
10 |
|
$parsedComplex = self::parseComplex($arg); |
|
2292
|
|
|
|
|
2293
|
10 |
View Code Duplication |
if ($activeSuffix == '') { |
|
|
|
|
|
|
2294
|
10 |
|
$activeSuffix = $parsedComplex['suffix']; |
|
2295
|
10 |
|
} elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) { |
|
2296
|
2 |
|
return Functions::NAN(); |
|
2297
|
|
|
} |
|
2298
|
|
|
|
|
2299
|
10 |
|
$returnValue['real'] += $parsedComplex['real']; |
|
2300
|
10 |
|
$returnValue['imaginary'] += $parsedComplex['imaginary']; |
|
2301
|
|
|
} |
|
2302
|
|
|
|
|
2303
|
8 |
|
if ($returnValue['imaginary'] == 0.0) { |
|
2304
|
|
|
$activeSuffix = ''; |
|
2305
|
|
|
} |
|
2306
|
|
|
|
|
2307
|
8 |
|
return self::COMPLEX($returnValue['real'], $returnValue['imaginary'], $activeSuffix); |
|
2308
|
|
|
} |
|
2309
|
|
|
|
|
2310
|
|
|
/** |
|
2311
|
|
|
* IMPRODUCT. |
|
2312
|
|
|
* |
|
2313
|
|
|
* Returns the product of two or more complex numbers in x + yi or x + yj text format. |
|
2314
|
|
|
* |
|
2315
|
|
|
* Excel Function: |
|
2316
|
|
|
* IMPRODUCT(complexNumber[,complexNumber[,...]]) |
|
2317
|
|
|
* |
|
2318
|
|
|
* @param string ...$complexNumbers Series of complex numbers to multiply |
|
2319
|
|
|
* |
|
2320
|
|
|
* @return string |
|
2321
|
|
|
*/ |
|
2322
|
63 |
|
public static function IMPRODUCT(...$complexNumbers) |
|
2323
|
|
|
{ |
|
2324
|
|
|
// Return value |
|
2325
|
63 |
|
$returnValue = self::parseComplex('1'); |
|
2326
|
63 |
|
$activeSuffix = ''; |
|
2327
|
|
|
|
|
2328
|
|
|
// Loop through the arguments |
|
2329
|
63 |
|
$aArgs = Functions::flattenArray($complexNumbers); |
|
2330
|
63 |
|
foreach ($aArgs as $arg) { |
|
2331
|
63 |
|
$parsedComplex = self::parseComplex($arg); |
|
2332
|
|
|
|
|
2333
|
63 |
|
$workValue = $returnValue; |
|
2334
|
63 |
View Code Duplication |
if (($parsedComplex['suffix'] != '') && ($activeSuffix == '')) { |
|
|
|
|
|
|
2335
|
63 |
|
$activeSuffix = $parsedComplex['suffix']; |
|
2336
|
62 |
|
} elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) { |
|
2337
|
1 |
|
return Functions::NAN(); |
|
2338
|
|
|
} |
|
2339
|
63 |
|
$returnValue['real'] = ($workValue['real'] * $parsedComplex['real']) - ($workValue['imaginary'] * $parsedComplex['imaginary']); |
|
2340
|
63 |
|
$returnValue['imaginary'] = ($workValue['real'] * $parsedComplex['imaginary']) + ($workValue['imaginary'] * $parsedComplex['real']); |
|
2341
|
|
|
} |
|
2342
|
|
|
|
|
2343
|
62 |
|
if ($returnValue['imaginary'] == 0.0) { |
|
2344
|
|
|
$activeSuffix = ''; |
|
2345
|
|
|
} |
|
2346
|
|
|
|
|
2347
|
62 |
|
return self::COMPLEX($returnValue['real'], $returnValue['imaginary'], $activeSuffix); |
|
2348
|
|
|
} |
|
2349
|
|
|
|
|
2350
|
|
|
/** |
|
2351
|
|
|
* DELTA. |
|
2352
|
|
|
* |
|
2353
|
|
|
* Tests whether two values are equal. Returns 1 if number1 = number2; returns 0 otherwise. |
|
2354
|
|
|
* Use this function to filter a set of values. For example, by summing several DELTA |
|
2355
|
|
|
* functions you calculate the count of equal pairs. This function is also known as the |
|
2356
|
|
|
* Kronecker Delta function. |
|
2357
|
|
|
* |
|
2358
|
|
|
* Excel Function: |
|
2359
|
|
|
* DELTA(a[,b]) |
|
2360
|
|
|
* |
|
2361
|
|
|
* @param float $a the first number |
|
2362
|
|
|
* @param float $b The second number. If omitted, b is assumed to be zero. |
|
2363
|
|
|
* |
|
2364
|
|
|
* @return int |
|
2365
|
|
|
*/ |
|
2366
|
25 |
|
public static function DELTA($a, $b = 0) |
|
2367
|
|
|
{ |
|
2368
|
25 |
|
$a = Functions::flattenSingleValue($a); |
|
2369
|
25 |
|
$b = Functions::flattenSingleValue($b); |
|
2370
|
|
|
|
|
2371
|
25 |
|
return (int) ($a == $b); |
|
2372
|
|
|
} |
|
2373
|
|
|
|
|
2374
|
|
|
/** |
|
2375
|
|
|
* GESTEP. |
|
2376
|
|
|
* |
|
2377
|
|
|
* Excel Function: |
|
2378
|
|
|
* GESTEP(number[,step]) |
|
2379
|
|
|
* |
|
2380
|
|
|
* Returns 1 if number >= step; returns 0 (zero) otherwise |
|
2381
|
|
|
* Use this function to filter a set of values. For example, by summing several GESTEP |
|
2382
|
|
|
* functions you calculate the count of values that exceed a threshold. |
|
2383
|
|
|
* |
|
2384
|
|
|
* @param float $number the value to test against step |
|
2385
|
|
|
* @param float $step The threshold value. |
|
2386
|
|
|
* If you omit a value for step, GESTEP uses zero. |
|
2387
|
|
|
* |
|
2388
|
|
|
* @return int |
|
2389
|
|
|
*/ |
|
2390
|
81 |
|
public static function GESTEP($number, $step = 0) |
|
2391
|
|
|
{ |
|
2392
|
81 |
|
$number = Functions::flattenSingleValue($number); |
|
2393
|
81 |
|
$step = Functions::flattenSingleValue($step); |
|
2394
|
|
|
|
|
2395
|
81 |
|
return (int) ($number >= $step); |
|
2396
|
|
|
} |
|
2397
|
|
|
|
|
2398
|
|
|
// |
|
2399
|
|
|
// Private method to calculate the erf value |
|
2400
|
|
|
// |
|
2401
|
|
|
private static $twoSqrtPi = 1.128379167095512574; |
|
2402
|
|
|
|
|
2403
|
148 |
|
public static function erfVal($x) |
|
2404
|
|
|
{ |
|
2405
|
148 |
|
if (abs($x) > 2.2) { |
|
2406
|
67 |
|
return 1 - self::erfcVal($x); |
|
2407
|
|
|
} |
|
2408
|
123 |
|
$sum = $term = $x; |
|
2409
|
123 |
|
$xsqr = ($x * $x); |
|
2410
|
123 |
|
$j = 1; |
|
2411
|
|
|
do { |
|
2412
|
123 |
|
$term *= $xsqr / $j; |
|
2413
|
123 |
|
$sum -= $term / (2 * $j + 1); |
|
2414
|
123 |
|
++$j; |
|
2415
|
123 |
|
$term *= $xsqr / $j; |
|
2416
|
123 |
|
$sum += $term / (2 * $j + 1); |
|
2417
|
123 |
|
++$j; |
|
2418
|
123 |
|
if ($sum == 0.0) { |
|
2419
|
19 |
|
break; |
|
2420
|
|
|
} |
|
2421
|
112 |
|
} while (abs($term / $sum) > Functions::PRECISION); |
|
2422
|
|
|
|
|
2423
|
123 |
|
return self::$twoSqrtPi * $sum; |
|
2424
|
|
|
} |
|
2425
|
|
|
|
|
2426
|
|
|
/** |
|
2427
|
|
|
* ERF. |
|
2428
|
|
|
* |
|
2429
|
|
|
* Returns the error function integrated between the lower and upper bound arguments. |
|
2430
|
|
|
* |
|
2431
|
|
|
* Note: In Excel 2007 or earlier, if you input a negative value for the upper or lower bound arguments, |
|
2432
|
|
|
* the function would return a #NUM! error. However, in Excel 2010, the function algorithm was |
|
2433
|
|
|
* improved, so that it can now calculate the function for both positive and negative ranges. |
|
2434
|
|
|
* PhpSpreadsheet follows Excel 2010 behaviour, and accepts nagative arguments. |
|
2435
|
|
|
* |
|
2436
|
|
|
* Excel Function: |
|
2437
|
|
|
* ERF(lower[,upper]) |
|
2438
|
|
|
* |
|
2439
|
|
|
* @param float $lower lower bound for integrating ERF |
|
2440
|
|
|
* @param float $upper upper bound for integrating ERF. |
|
2441
|
|
|
* If omitted, ERF integrates between zero and lower_limit |
|
2442
|
|
|
* |
|
2443
|
|
|
* @return float |
|
2444
|
|
|
*/ |
|
2445
|
123 |
|
public static function ERF($lower, $upper = null) |
|
2446
|
|
|
{ |
|
2447
|
123 |
|
$lower = Functions::flattenSingleValue($lower); |
|
2448
|
123 |
|
$upper = Functions::flattenSingleValue($upper); |
|
2449
|
|
|
|
|
2450
|
123 |
|
if (is_numeric($lower)) { |
|
2451
|
120 |
|
if ($upper === null) { |
|
2452
|
37 |
|
return self::erfVal($lower); |
|
2453
|
|
|
} |
|
2454
|
83 |
|
if (is_numeric($upper)) { |
|
2455
|
83 |
|
return self::erfVal($upper) - self::erfVal($lower); |
|
2456
|
|
|
} |
|
2457
|
|
|
} |
|
2458
|
|
|
|
|
2459
|
3 |
|
return Functions::VALUE(); |
|
|
|
|
|
|
2460
|
|
|
} |
|
2461
|
|
|
|
|
2462
|
|
|
// |
|
2463
|
|
|
// Private method to calculate the erfc value |
|
2464
|
|
|
// |
|
2465
|
|
|
private static $oneSqrtPi = 0.564189583547756287; |
|
2466
|
|
|
|
|
2467
|
104 |
|
private static function erfcVal($x) |
|
2468
|
|
|
{ |
|
2469
|
104 |
|
if (abs($x) < 2.2) { |
|
2470
|
28 |
|
return 1 - self::erfVal($x); |
|
2471
|
|
|
} |
|
2472
|
76 |
|
if ($x < 0) { |
|
2473
|
1 |
|
return 2 - self::ERFC(-$x); |
|
2474
|
|
|
} |
|
2475
|
76 |
|
$a = $n = 1; |
|
2476
|
76 |
|
$b = $c = $x; |
|
2477
|
76 |
|
$d = ($x * $x) + 0.5; |
|
2478
|
76 |
|
$q1 = $q2 = $b / $d; |
|
|
|
|
|
|
2479
|
76 |
|
$t = 0; |
|
|
|
|
|
|
2480
|
|
|
do { |
|
2481
|
76 |
|
$t = $a * $n + $b * $x; |
|
2482
|
76 |
|
$a = $b; |
|
2483
|
76 |
|
$b = $t; |
|
2484
|
76 |
|
$t = $c * $n + $d * $x; |
|
2485
|
76 |
|
$c = $d; |
|
2486
|
76 |
|
$d = $t; |
|
2487
|
76 |
|
$n += 0.5; |
|
2488
|
76 |
|
$q1 = $q2; |
|
2489
|
76 |
|
$q2 = $b / $d; |
|
2490
|
76 |
|
} while ((abs($q1 - $q2) / $q2) > Functions::PRECISION); |
|
2491
|
|
|
|
|
2492
|
76 |
|
return self::$oneSqrtPi * exp(-$x * $x) * $q2; |
|
2493
|
|
|
} |
|
2494
|
|
|
|
|
2495
|
|
|
/** |
|
2496
|
|
|
* ERFC. |
|
2497
|
|
|
* |
|
2498
|
|
|
* Returns the complementary ERF function integrated between x and infinity |
|
2499
|
|
|
* |
|
2500
|
|
|
* Note: In Excel 2007 or earlier, if you input a negative value for the lower bound argument, |
|
2501
|
|
|
* the function would return a #NUM! error. However, in Excel 2010, the function algorithm was |
|
2502
|
|
|
* improved, so that it can now calculate the function for both positive and negative x values. |
|
2503
|
|
|
* PhpSpreadsheet follows Excel 2010 behaviour, and accepts nagative arguments. |
|
2504
|
|
|
* |
|
2505
|
|
|
* Excel Function: |
|
2506
|
|
|
* ERFC(x) |
|
2507
|
|
|
* |
|
2508
|
|
|
* @param float $x The lower bound for integrating ERFC |
|
2509
|
|
|
* |
|
2510
|
|
|
* @return float |
|
2511
|
|
|
*/ |
|
2512
|
41 |
|
public static function ERFC($x) |
|
2513
|
|
|
{ |
|
2514
|
41 |
|
$x = Functions::flattenSingleValue($x); |
|
2515
|
|
|
|
|
2516
|
41 |
|
if (is_numeric($x)) { |
|
2517
|
38 |
|
return self::erfcVal($x); |
|
2518
|
|
|
} |
|
2519
|
|
|
|
|
2520
|
3 |
|
return Functions::VALUE(); |
|
|
|
|
|
|
2521
|
|
|
} |
|
2522
|
|
|
|
|
2523
|
|
|
/** |
|
2524
|
|
|
* getConversionGroups |
|
2525
|
|
|
* Returns a list of the different conversion groups for UOM conversions. |
|
2526
|
|
|
* |
|
2527
|
|
|
* @return array |
|
2528
|
|
|
*/ |
|
2529
|
1 |
|
public static function getConversionGroups() |
|
2530
|
|
|
{ |
|
2531
|
1 |
|
$conversionGroups = []; |
|
2532
|
1 |
|
foreach (self::$conversionUnits as $conversionUnit) { |
|
2533
|
1 |
|
$conversionGroups[] = $conversionUnit['Group']; |
|
2534
|
|
|
} |
|
2535
|
|
|
|
|
2536
|
1 |
|
return array_merge(array_unique($conversionGroups)); |
|
2537
|
|
|
} |
|
2538
|
|
|
|
|
2539
|
|
|
/** |
|
2540
|
|
|
* getConversionGroupUnits |
|
2541
|
|
|
* Returns an array of units of measure, for a specified conversion group, or for all groups. |
|
2542
|
|
|
* |
|
2543
|
|
|
* @param string $group The group whose units of measure you want to retrieve |
|
2544
|
|
|
* |
|
2545
|
|
|
* @return array |
|
2546
|
|
|
*/ |
|
2547
|
1 |
|
public static function getConversionGroupUnits($group = null) |
|
2548
|
|
|
{ |
|
2549
|
1 |
|
$conversionGroups = []; |
|
2550
|
1 |
|
foreach (self::$conversionUnits as $conversionUnit => $conversionGroup) { |
|
2551
|
1 |
|
if (($group === null) || ($conversionGroup['Group'] == $group)) { |
|
2552
|
1 |
|
$conversionGroups[$conversionGroup['Group']][] = $conversionUnit; |
|
2553
|
|
|
} |
|
2554
|
|
|
} |
|
2555
|
|
|
|
|
2556
|
1 |
|
return $conversionGroups; |
|
2557
|
|
|
} |
|
2558
|
|
|
|
|
2559
|
|
|
/** |
|
2560
|
|
|
* getConversionGroupUnitDetails. |
|
2561
|
|
|
* |
|
2562
|
|
|
* @param string $group The group whose units of measure you want to retrieve |
|
2563
|
|
|
* |
|
2564
|
|
|
* @return array |
|
2565
|
|
|
*/ |
|
2566
|
1 |
|
public static function getConversionGroupUnitDetails($group = null) |
|
2567
|
|
|
{ |
|
2568
|
1 |
|
$conversionGroups = []; |
|
2569
|
1 |
|
foreach (self::$conversionUnits as $conversionUnit => $conversionGroup) { |
|
2570
|
1 |
|
if (($group === null) || ($conversionGroup['Group'] == $group)) { |
|
2571
|
1 |
|
$conversionGroups[$conversionGroup['Group']][] = [ |
|
2572
|
1 |
|
'unit' => $conversionUnit, |
|
2573
|
1 |
|
'description' => $conversionGroup['Unit Name'], |
|
2574
|
|
|
]; |
|
2575
|
|
|
} |
|
2576
|
|
|
} |
|
2577
|
|
|
|
|
2578
|
1 |
|
return $conversionGroups; |
|
2579
|
|
|
} |
|
2580
|
|
|
|
|
2581
|
|
|
/** |
|
2582
|
|
|
* getConversionMultipliers |
|
2583
|
|
|
* Returns an array of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM(). |
|
2584
|
|
|
* |
|
2585
|
|
|
* @return array of mixed |
|
2586
|
|
|
*/ |
|
2587
|
1 |
|
public static function getConversionMultipliers() |
|
2588
|
|
|
{ |
|
2589
|
1 |
|
return self::$conversionMultipliers; |
|
2590
|
|
|
} |
|
2591
|
|
|
|
|
2592
|
|
|
/** |
|
2593
|
|
|
* CONVERTUOM. |
|
2594
|
|
|
* |
|
2595
|
|
|
* Converts a number from one measurement system to another. |
|
2596
|
|
|
* For example, CONVERT can translate a table of distances in miles to a table of distances |
|
2597
|
|
|
* in kilometers. |
|
2598
|
|
|
* |
|
2599
|
|
|
* Excel Function: |
|
2600
|
|
|
* CONVERT(value,fromUOM,toUOM) |
|
2601
|
|
|
* |
|
2602
|
|
|
* @param float $value the value in fromUOM to convert |
|
2603
|
|
|
* @param string $fromUOM the units for value |
|
2604
|
|
|
* @param string $toUOM the units for the result |
|
2605
|
|
|
* |
|
2606
|
|
|
* @return float |
|
2607
|
|
|
*/ |
|
2608
|
24 |
|
public static function CONVERTUOM($value, $fromUOM, $toUOM) |
|
2609
|
|
|
{ |
|
2610
|
24 |
|
$value = Functions::flattenSingleValue($value); |
|
2611
|
24 |
|
$fromUOM = Functions::flattenSingleValue($fromUOM); |
|
2612
|
24 |
|
$toUOM = Functions::flattenSingleValue($toUOM); |
|
2613
|
|
|
|
|
2614
|
24 |
|
if (!is_numeric($value)) { |
|
2615
|
1 |
|
return Functions::VALUE(); |
|
|
|
|
|
|
2616
|
|
|
} |
|
2617
|
23 |
|
$fromMultiplier = 1.0; |
|
2618
|
23 |
View Code Duplication |
if (isset(self::$conversionUnits[$fromUOM])) { |
|
|
|
|
|
|
2619
|
16 |
|
$unitGroup1 = self::$conversionUnits[$fromUOM]['Group']; |
|
2620
|
|
|
} else { |
|
2621
|
7 |
|
$fromMultiplier = substr($fromUOM, 0, 1); |
|
2622
|
7 |
|
$fromUOM = substr($fromUOM, 1); |
|
2623
|
7 |
|
if (isset(self::$conversionMultipliers[$fromMultiplier])) { |
|
2624
|
6 |
|
$fromMultiplier = self::$conversionMultipliers[$fromMultiplier]['multiplier']; |
|
2625
|
|
|
} else { |
|
2626
|
1 |
|
return Functions::NA(); |
|
|
|
|
|
|
2627
|
|
|
} |
|
2628
|
6 |
|
if ((isset(self::$conversionUnits[$fromUOM])) && (self::$conversionUnits[$fromUOM]['AllowPrefix'])) { |
|
2629
|
5 |
|
$unitGroup1 = self::$conversionUnits[$fromUOM]['Group']; |
|
2630
|
|
|
} else { |
|
2631
|
1 |
|
return Functions::NA(); |
|
|
|
|
|
|
2632
|
|
|
} |
|
2633
|
|
|
} |
|
2634
|
21 |
|
$value *= $fromMultiplier; |
|
2635
|
|
|
|
|
2636
|
21 |
|
$toMultiplier = 1.0; |
|
2637
|
21 |
View Code Duplication |
if (isset(self::$conversionUnits[$toUOM])) { |
|
|
|
|
|
|
2638
|
14 |
|
$unitGroup2 = self::$conversionUnits[$toUOM]['Group']; |
|
2639
|
|
|
} else { |
|
2640
|
7 |
|
$toMultiplier = substr($toUOM, 0, 1); |
|
2641
|
7 |
|
$toUOM = substr($toUOM, 1); |
|
2642
|
7 |
|
if (isset(self::$conversionMultipliers[$toMultiplier])) { |
|
2643
|
6 |
|
$toMultiplier = self::$conversionMultipliers[$toMultiplier]['multiplier']; |
|
2644
|
|
|
} else { |
|
2645
|
1 |
|
return Functions::NA(); |
|
|
|
|
|
|
2646
|
|
|
} |
|
2647
|
6 |
|
if ((isset(self::$conversionUnits[$toUOM])) && (self::$conversionUnits[$toUOM]['AllowPrefix'])) { |
|
2648
|
5 |
|
$unitGroup2 = self::$conversionUnits[$toUOM]['Group']; |
|
2649
|
|
|
} else { |
|
2650
|
1 |
|
return Functions::NA(); |
|
|
|
|
|
|
2651
|
|
|
} |
|
2652
|
|
|
} |
|
2653
|
19 |
|
if ($unitGroup1 != $unitGroup2) { |
|
2654
|
2 |
|
return Functions::NA(); |
|
|
|
|
|
|
2655
|
|
|
} |
|
2656
|
|
|
|
|
2657
|
17 |
|
if (($fromUOM == $toUOM) && ($fromMultiplier == $toMultiplier)) { |
|
2658
|
|
|
// We've already factored $fromMultiplier into the value, so we need |
|
2659
|
|
|
// to reverse it again |
|
2660
|
3 |
|
return $value / $fromMultiplier; |
|
2661
|
14 |
|
} elseif ($unitGroup1 == 'Temperature') { |
|
2662
|
9 |
|
if (($fromUOM == 'F') || ($fromUOM == 'fah')) { |
|
2663
|
3 |
|
if (($toUOM == 'F') || ($toUOM == 'fah')) { |
|
2664
|
1 |
|
return $value; |
|
2665
|
|
|
} |
|
2666
|
2 |
|
$value = (($value - 32) / 1.8); |
|
2667
|
2 |
|
if (($toUOM == 'K') || ($toUOM == 'kel')) { |
|
2668
|
1 |
|
$value += 273.15; |
|
2669
|
|
|
} |
|
2670
|
|
|
|
|
2671
|
2 |
|
return $value; |
|
2672
|
6 |
|
} elseif ((($fromUOM == 'K') || ($fromUOM == 'kel')) && |
|
2673
|
6 |
|
(($toUOM == 'K') || ($toUOM == 'kel')) |
|
2674
|
|
|
) { |
|
2675
|
1 |
|
return $value; |
|
2676
|
5 |
|
} elseif ((($fromUOM == 'C') || ($fromUOM == 'cel')) && |
|
2677
|
5 |
|
(($toUOM == 'C') || ($toUOM == 'cel')) |
|
2678
|
|
|
) { |
|
2679
|
1 |
|
return $value; |
|
2680
|
|
|
} |
|
2681
|
4 |
|
if (($toUOM == 'F') || ($toUOM == 'fah')) { |
|
2682
|
2 |
|
if (($fromUOM == 'K') || ($fromUOM == 'kel')) { |
|
2683
|
1 |
|
$value -= 273.15; |
|
2684
|
|
|
} |
|
2685
|
|
|
|
|
2686
|
2 |
|
return ($value * 1.8) + 32; |
|
2687
|
|
|
} |
|
2688
|
2 |
|
if (($toUOM == 'C') || ($toUOM == 'cel')) { |
|
2689
|
1 |
|
return $value - 273.15; |
|
2690
|
|
|
} |
|
2691
|
|
|
|
|
2692
|
1 |
|
return $value + 273.15; |
|
2693
|
|
|
} |
|
2694
|
|
|
|
|
2695
|
5 |
|
return ($value * self::$unitConversions[$unitGroup1][$fromUOM][$toUOM]) / $toMultiplier; |
|
2696
|
|
|
} |
|
2697
|
|
|
} |
|
2698
|
|
|
|
PHPOffice /
PhpSpreadsheet
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