private static function simplePowerSerie (Decimal $x, Decimal $firstTerm, int $scale): Decimal
    {
        $approx = $firstTerm;
        $change = DecimalConstants::One();

        $xPowerN = DecimalConstants::One();     // Calculates x^n
        $sign = DecimalConstants::One();      // Calculates a_n

        for ($i = 1; !$change->floor($scale + 2)->isZero(); $i++) {
            $xPowerN = $xPowerN->mul($x);

            if ($i % 2 === 0) {
                $factorN = DecimalConstants::zero();
            } else {
                 if ($i % 4 === 1) {
                     $factorN = DecimalConstants::one()->div(Decimal::fromInteger($i), $scale + 2);
                 } else {
                     $factorN = DecimalConstants::negativeOne()->div(Decimal::fromInteger($i), $scale + 2);
                 }
            }

            if (!$factorN->isZero()) {
                $change = $factorN->mul($xPowerN, $scale + 2);
                $approx = $approx->add($change, $scale + 2);
            }
        }

        return $approx->round($scale);
    }
private static function simplePowerSerie (Decimal $x, Decimal $firstTerm, int $scale): Decimal
    {
        $approx = $firstTerm;
        $change = DecimalConstants::One();

        $xPowerN = DecimalConstants::One();     // Calculates x^n
        $sign = DecimalConstants::One();      // Calculates a_n

        for ($i = 1; !$change->floor($scale + 2)->isZero(); $i++) {
            $xPowerN = $xPowerN->mul($x);

            if ($i % 2 === 0) {
                $factorN = DecimalConstants::zero();
            } else {
                 if ($i % 4 === 1) {
                     $factorN = DecimalConstants::one()->div(Decimal::fromInteger($i), $scale + 2);
                 } else {
                     $factorN = DecimalConstants::negativeOne()->div(Decimal::fromInteger($i), $scale + 2);
                 }
            }

            if (!$factorN->isZero()) {
                $change = $factorN->mul($xPowerN, $scale + 2);
                $approx = $approx->add($change, $scale + 2);
            }
        }

        return $approx->round($scale);
    }
private static function simplePowerSerie ( Decimal $ x , Decimal $ firstTerm , int $ scale ) : Decimal { $ approx = $ firstTerm ; $ change = DecimalConstants :: One ( ) ; $ xPowerN = DecimalConstants :: One ( ) ; // Calculates x^n $ sign = DecimalConstants :: One ( ) ; // Calculates a_n for ( $ i = 1 ; ! $ change -> floor ( $ scale + 2 ) -> isZero ( ) ; $ i ++ ) { $ xPowerN = $ xPowerN -> mul ( $ x ) ; if ( $ i % 2 === 0 ) { $ factorN = DecimalConstants :: zero ( ) ; } else { if ( $ i % 4 === 1 ) { $ factorN = DecimalConstants :: one ( ) -> div ( Decimal :: fromInteger ( $ i ) , $ scale + 2 ) ; } else { $ factorN = DecimalConstants :: negativeOne ( ) -> div ( Decimal :: fromInteger ( $ i ) , $ scale + 2 ) ; } } if ( ! $ factorN -> isZero ( ) ) { $ change = $ factorN -> mul ( $ xPowerN , $ scale + 2 ) ; $ approx = $ approx -> add ( $ change , $ scale + 2 ) ; } } return $ approx -> round ( $ scale ) ; }
Internal method used to compute arctan and arccotan

@param Decimal $x
@param Decimal $firstTerm
@param $scale
@return Decimal
Internal method used to compute arctan and arccotan