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Filename : BesselJ.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 BesselJ
{
    use ArrayEnabled;

    /**
     * BESSELJ.
     *
     *    Returns the Bessel function
     *
     *    Excel Function:
     *        BESSELJ(x,ord)
     *
     * NOTE: The MS Excel implementation of the BESSELJ function is still not accurate, particularly for higher order
     *       values with x < -8 and x > 8. This code provides a more accurate calculation
     *
     * @param mixed $x A float value at which to evaluate the function.
     *                                If x is nonnumeric, BESSELJ 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, BESSELJ returns the #VALUE! error value.
     *                                If $ord < 0, BESSELJ returns the #NUM! error value.
     *                      Or can be an array of values
     *
     * @return array|float|string Result, or a string containing an error
     *         If an array of numbers is passed as an argument, then the returned result will also be an array
     *            with the same dimensions
     */
    public static function BESSELJ($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) {
            return ExcelError::NAN();
        }

        $fResult = self::calculate($x, $ord);

        return (is_nan($fResult)) ? ExcelError::NAN() : $fResult;
    }

    private static function calculate(float $x, int $ord): float
    {
        // special cases
        switch ($ord) {
            case 0:
                return self::besselJ0($x);
            case 1:
                return self::besselJ1($x);
        }

        return self::besselJ2($x, $ord);
    }

    private static function besselJ0(float $x): float
    {
        $ax = abs($x);

        if ($ax < 8.0) {
            $y = $x * $x;
            $ans1 = 57568490574.0 + $y * (-13362590354.0 + $y * (651619640.7 + $y * (-11214424.18 + $y *
                            (77392.33017 + $y * (-184.9052456)))));
            $ans2 = 57568490411.0 + $y * (1029532985.0 + $y * (9494680.718 + $y * (59272.64853 + $y *
                            (267.8532712 + $y * 1.0))));

            return $ans1 / $ans2;
        }

        $z = 8.0 / $ax;
        $y = $z * $z;
        $xx = $ax - 0.785398164;
        $ans1 = 1.0 + $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 * 0.934935152e-7)));

        return sqrt(0.636619772 / $ax) * (cos($xx) * $ans1 - $z * sin($xx) * $ans2);
    }

    private static function besselJ1(float $x): float
    {
        $ax = abs($x);

        if ($ax < 8.0) {
            $y = $x * $x;
            $ans1 = $x * (72362614232.0 + $y * (-7895059235.0 + $y * (242396853.1 + $y *
                            (-2972611.439 + $y * (15704.48260 + $y * (-30.16036606))))));
            $ans2 = 144725228442.0 + $y * (2300535178.0 + $y * (18583304.74 + $y * (99447.43394 + $y *
                            (376.9991397 + $y * 1.0))));

            return $ans1 / $ans2;
        }

        $z = 8.0 / $ax;
        $y = $z * $z;
        $xx = $ax - 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)));
        $ans = sqrt(0.636619772 / $ax) * (cos($xx) * $ans1 - $z * sin($xx) * $ans2);

        return ($x < 0.0) ? -$ans : $ans;
    }

    private static function besselJ2(float $x, int $ord): float
    {
        $ax = abs($x);
        if ($ax === 0.0) {
            return 0.0;
        }

        if ($ax > $ord) {
            return self::besselj2a($ax, $ord, $x);
        }

        return self::besselj2b($ax, $ord, $x);
    }

    private static function besselj2a(float $ax, int $ord, float $x)
    {
        $tox = 2.0 / $ax;
        $bjm = self::besselJ0($ax);
        $bj = self::besselJ1($ax);
        for ($j = 1; $j < $ord; ++$j) {
            $bjp = $j * $tox * $bj - $bjm;
            $bjm = $bj;
            $bj = $bjp;
        }
        $ans = $bj;

        return ($x < 0.0 && ($ord % 2) == 1) ? -$ans : $ans;
    }

    private static function besselj2b(float $ax, int $ord, float $x)
    {
        $tox = 2.0 / $ax;
        $jsum = false;
        $bjp = $ans = $sum = 0.0;
        $bj = 1.0;
        for ($j = 2 * ($ord + (int) sqrt(40.0 * $ord)); $j > 0; --$j) {
            $bjm = $j * $tox * $bj - $bjp;
            $bjp = $bj;
            $bj = $bjm;
            if (abs($bj) > 1.0e+10) {
                $bj *= 1.0e-10;
                $bjp *= 1.0e-10;
                $ans *= 1.0e-10;
                $sum *= 1.0e-10;
            }
            if ($jsum === true) {
                $sum += $bj;
            }
            $jsum = !$jsum;
            if ($j === $ord) {
                $ans = $bjp;
            }
        }
        $sum = 2.0 * $sum - $bj;
        $ans /= $sum;

        return ($x < 0.0 && ($ord % 2) === 1) ? -$ans : $ans;
    }
}