callback = $callback; } /** @return float|string */ public function execute(float $probability) { $xLo = 100; $xHi = 0; $dx = 1; $x = $xNew = 1; $i = 0; while ((abs($dx) > Functions::PRECISION) && ($i++ < self::MAX_ITERATIONS)) { // Apply Newton-Raphson step $result = call_user_func($this->callback, $x); $error = $result - $probability; if ($error == 0.0) { $dx = 0; } elseif ($error < 0.0) { $xLo = $x; } else { $xHi = $x; } // Avoid division by zero if ($result != 0.0) { $dx = $error / $result; $xNew = $x - $dx; } // If the NR fails to converge (which for example may be the // case if the initial guess is too rough) we apply a bisection // step to determine a more narrow interval around the root. if (($xNew < $xLo) || ($xNew > $xHi) || ($result == 0.0)) { $xNew = ($xLo + $xHi) / 2; $dx = $xNew - $x; } $x = $xNew; } if ($i == self::MAX_ITERATIONS) { return ExcelError::NA(); } return $x; } }