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<?php namespace PhpOffice\PhpSpreadsheet\Calculation\Engineering; use PhpOffice\PhpSpreadsheet\Calculation\Exception; use PhpOffice\PhpSpreadsheet\Calculation\Functions; class BesselY { /** * BESSELY. * * Returns the Bessel function, which is also called the Weber function or the Neumann function. * * Excel Function: * BESSELY(x,ord) * * @param mixed $x A float value at which to evaluate the function. * If x is nonnumeric, BESSELY returns the #VALUE! error value. * @param mixed $ord The integer order of the Bessel function. * If ord is not an integer, it is truncated. * If $ord is nonnumeric, BESSELY returns the #VALUE! error value. * If $ord < 0, BESSELY returns the #NUM! error value. * * @return float|string Result, or a string containing an error */ public static function BESSELY($x, $ord) { $x = Functions::flattenSingleValue($x); $ord = Functions::flattenSingleValue($ord); try { $x = EngineeringValidations::validateFloat($x); $ord = EngineeringValidations::validateInt($ord); } catch (Exception $e) { return $e->getMessage(); } if (($ord < 0) || ($x <= 0.0)) { return Functions::NAN(); } $fBy = self::calculate($x, $ord); return (is_nan($fBy)) ? Functions::NAN() : $fBy; } private static function calculate(float $x, int $ord): float { // special cases switch ($ord) { case 0: return self::besselY0($x); case 1: return self::besselY1($x); } return self::besselY2($x, $ord); } private static function besselY0(float $x): float { if ($x < 8.0) { $y = ($x * $x); $ans1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y * (-86327.92757 + $y * 228.4622733)))); $ans2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y * (47447.26470 + $y * (226.1030244 + $y)))); return $ans1 / $ans2 + 0.636619772 * BesselJ::BESSELJ($x, 0) * log($x); } $z = 8.0 / $x; $y = ($z * $z); $xx = $x - 0.785398164; $ans1 = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6))); $ans2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y * (-0.934945152e-7)))); return sqrt(0.636619772 / $x) * (sin($xx) * $ans1 + $z * cos($xx) * $ans2); } private static function besselY1(float $x): float { if ($x < 8.0) { $y = ($x * $x); $ans1 = $x * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y * (0.7349264551e9 + $y * (-0.4237922726e7 + $y * 0.8511937935e4))))); $ans2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y * (0.1020426050e6 + $y * (0.3549632885e3 + $y))))); return ($ans1 / $ans2) + 0.636619772 * (BesselJ::BESSELJ($x, 1) * log($x) - 1 / $x); } $z = 8.0 / $x; $y = $z * $z; $xx = $x - 2.356194491; $ans1 = 1.0 + $y * (0.183105e-2 + $y * (-0.3516396496e-4 + $y * (0.2457520174e-5 + $y * (-0.240337019e-6)))); $ans2 = 0.04687499995 + $y * (-0.2002690873e-3 + $y * (0.8449199096e-5 + $y * (-0.88228987e-6 + $y * 0.105787412e-6))); return sqrt(0.636619772 / $x) * (sin($xx) * $ans1 + $z * cos($xx) * $ans2); } private static function besselY2(float $x, int $ord): float { $fTox = 2.0 / $x; $fBym = self::besselY0($x); $fBy = self::besselY1($x); for ($n = 1; $n < $ord; ++$n) { $fByp = $n * $fTox * $fBy - $fBym; $fBym = $fBy; $fBy = $fByp; } return $fBy; } }