# tablepress/3.4/libraries/vendor/PhpSpreadsheet/Calculation/Engineering/BesselI.php

TablePress – Tables in WordPress made easy, version 3.4. 145 lines.

- Page: https://pluginprobe.com/plugins/tablepress/3.4/code/libraries/vendor/PhpSpreadsheet/Calculation/Engineering/BesselI.php
- Raw: https://pluginprobe.com/plugins/tablepress/3.4/raw/libraries/vendor/PhpSpreadsheet/Calculation/Engineering/BesselI.php
- Modified: 2025-08-26T04:06:14+00:00

Line numbers below start at 1. Link to a line or a range by appending a fragment to the
page URL, for example `https://pluginprobe.com/plugins/tablepress/3.4/code/libraries/vendor/PhpSpreadsheet/Calculation/Engineering/BesselI.php#L10-L20`.

```php
<?php

namespace TablePress\PhpOffice\PhpSpreadsheet\Calculation\Engineering;

use TablePress\PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
use TablePress\PhpOffice\PhpSpreadsheet\Calculation\Exception;
use TablePress\PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;

class BesselI
{
	use ArrayEnabled;

	/**
	 * BESSELI.
	 *
	 *    Returns the modified Bessel function In(x), which is equivalent to the Bessel function evaluated
	 *        for purely imaginary arguments
	 *
	 *    Excel Function:
	 *        BESSELI(x,ord)
	 *
	 * NOTE: The MS Excel implementation of the BESSELI function is still not accurate.
	 *       This code provides a more accurate calculation
	 *
	 * @param mixed $x A float value at which to evaluate the function.
	 *                                If x is nonnumeric, BESSELI 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, BESSELI returns the #VALUE! error value.
	 *                                If $ord < 0, BESSELI returns the #NUM! error value.
	 *                      Or can be an array of values
	 *
	 * @return array<mixed>|float|string Result, or a string containing an error
	 *         If an array of numbers is passed as an argument, then the returned result will also be an array
	 *            with the same dimensions
	 */
	public static function BESSELI($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 $ord): float
	{
		switch ($ord) {
									case 0:
										return self::besselI0($x);
									case 1:
										return self::besselI1($x);
									default:
										return self::besselI2($x, $ord);
								}
	}

	private static function besselI0(float $x): float
	{
		$ax = abs($x);

		if ($ax < 3.75) {
			$y = $x / 3.75;
			$y = $y * $y;

			return 1.0 + $y * (3.5156229 + $y * (3.0899424 + $y * (1.2067492
								+ $y * (0.2659732 + $y * (0.360768e-1 + $y * 0.45813e-2)))));
		}

		$y = 3.75 / $ax;

		return (exp($ax) / sqrt($ax)) * (0.39894228 + $y * (0.1328592e-1 + $y * (0.225319e-2 + $y * (-0.157565e-2
							+ $y * (0.916281e-2 + $y * (-0.2057706e-1 + $y * (0.2635537e-1
										+ $y * (-0.1647633e-1 + $y * 0.392377e-2))))))));
	}

	private static function besselI1(float $x): float
	{
		$ax = abs($x);

		if ($ax < 3.75) {
			$y = $x / 3.75;
			$y = $y * $y;
			$ans = $ax * (0.5 + $y * (0.87890594 + $y * (0.51498869 + $y * (0.15084934 + $y * (0.2658733e-1
									+ $y * (0.301532e-2 + $y * 0.32411e-3))))));

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

		$y = 3.75 / $ax;
		$ans = 0.2282967e-1 + $y * (-0.2895312e-1 + $y * (0.1787654e-1 - $y * 0.420059e-2));
		$ans = 0.39894228 + $y * (-0.3988024e-1 + $y * (-0.362018e-2 + $y * (0.163801e-2
						+ $y * (-0.1031555e-1 + $y * $ans))));
		$ans *= exp($ax) / sqrt($ax);

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

	private static function besselI2(float $x, int $ord): float
	{
		if ($x === 0.0) {
			return 0.0;
		}

		$tox = 2.0 / abs($x);
		$bip = 0;
		$ans = 0.0;
		$bi = 1.0;

		for ($j = 2 * ($ord + (int) sqrt(40.0 * $ord)); $j > 0; --$j) {
			$bim = $bip + $j * $tox * $bi;
			$bip = $bi;
			$bi = $bim;

			if (abs($bi) > 1.0e+12) {
				$ans *= 1.0e-12;
				$bi *= 1.0e-12;
				$bip *= 1.0e-12;
			}

			if ($j === $ord) {
				$ans = $bip;
			}
		}

		$ans *= self::besselI0($x) / $bi;

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

```