<?php
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namespace PhpOffice\PhpSpreadsheet\Calculation\Engineering;
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use PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
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use PhpOffice\PhpSpreadsheet\Calculation\Functions;
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use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
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class ErfC
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{
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use ArrayEnabled;
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/**
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* ERFC.
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*
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* Returns the complementary ERF function integrated between x and infinity
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*
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* Note: In Excel 2007 or earlier, if you input a negative value for the lower bound argument,
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* the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
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* improved, so that it can now calculate the function for both positive and negative x values.
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* PhpSpreadsheet follows Excel 2010 behaviour, and accepts nagative arguments.
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*
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* Excel Function:
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* ERFC(x)
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*
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* @param mixed $value The float lower bound for integrating ERFC
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* Or can be an array of values
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*
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* @return array|float|string If an array of numbers is passed as an argument, then the returned result will also be an array
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* with the same dimensions
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*/
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public static function ERFC(mixed $value)
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{
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if (is_array($value)) {
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return self::evaluateSingleArgumentArray([self::class, __FUNCTION__], $value);
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}
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if (is_numeric($value)) {
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return self::erfcValue($value);
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}
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return ExcelError::VALUE();
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}
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private const ONE_SQRT_PI = 0.564189583547756287;
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/**
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* Method to calculate the erfc value.
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*/
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private static function erfcValue(float|int|string $value): float|int
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{
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$value = (float) $value;
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if (abs($value) < 2.2) {
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return 1 - Erf::erfValue($value);
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}
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if ($value < 0) {
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return 2 - self::erfcValue(-$value);
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}
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$a = $n = 1;
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$b = $c = $value;
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$d = ($value * $value) + 0.5;
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$q2 = $b / $d;
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do {
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$t = $a * $n + $b * $value;
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$a = $b;
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$b = $t;
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$t = $c * $n + $d * $value;
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$c = $d;
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$d = $t;
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$n += 0.5;
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$q1 = $q2;
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$q2 = $b / $d;
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} while ((abs($q1 - $q2) / $q2) > Functions::PRECISION);
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return self::ONE_SQRT_PI * exp(-$value * $value) * $q2;
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}
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}
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