BesselY.php
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<?php
namespace PhpOffice\PhpSpreadsheet\Calculation\Engineering;
use PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
use PhpOffice\PhpSpreadsheet\Calculation\Exception;
use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
class BesselY
{
use ArrayEnabled;
/**
* 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.
* Or can be an array of values
* @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 $ord < 0, BESSELY returns the #NUM! error value.
* Or can be an array of values
*
* @return array|float|string Result, or a string containing an error
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function BESSELY($x, $ord)
{
if (is_array($x) || is_array($ord)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $x, $ord);
}
try {
$x = EngineeringValidations::validateFloat($x);
$ord = EngineeringValidations::validateInt($ord);
} catch (Exception $e) {
return $e->getMessage();
}
if (($ord < 0) || ($x <= 0.0)) {
return ExcelError::NAN();
}
$fBy = self::calculate($x, $ord);
return (is_nan($fBy)) ? ExcelError::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);
}
/**
* Mollify Phpstan.
*
* @codeCoverageIgnore
*/
private static function callBesselJ(float $x, int $ord): float
{
$rslt = BesselJ::BESSELJ($x, $ord);
if (!is_float($rslt)) {
throw new Exception('Unexpected array or string');
}
return $rslt;
}
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 / $ans2 + 0.636619772 * self::callBesselJ($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 / $ans2) + 0.636619772 * (self::callBesselJ($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;
}
}