/**
* Raise e to the power of this.
* @param number $precision the precision we want to return this to (default = DEFAULT_PRECISION).
* @return BigNumber e raised to the power of *this.
*/
public function Exp($precision = self::BIGNUMBER_DEFAULT_PRECISION)
{
// shortcut
if ($this->IsZero()) {
// reset this to 1
$this->_Copy(BigNumberConstants::One());
// done
return $this->PerformPostOperations($precision);
}
// get the integer part of the number.
$integer = (new BigNumber($this))->Integer();
// now get the decimal part of the number
$fraction = (new BigNumber($this))->Frac();
// reset 'this' to 1
$this->_Copy(BigNumberConstants::One());
// the two sides of the equation
// the whole number.
if (!$integer->IsZero()) {
// get the value of e
$e = BigNumberConstants::e();
// truncate the precision so we do not do too many multiplications.
// add a bit of room for more accurate precision.
$e->Trunc(BigNumberConstants::PrecisionPadding($precision));
// then raise it.
$this->_Copy($e->Pow($integer, BigNumberConstants::PrecisionPadding($precision)));
}
if (!$fraction->IsZero()) {
// x^1 x^2 x^3
// 1 + --- + --- + --- ...
// 1! 2! 3!
$fact = BigNumberConstants::One();
$base = new BigNumber($fraction);
$power = new BigNumber($base);
$result = BigNumberConstants::One();
$paddedPrecision = BigNumberConstants::PrecisionPadding($precision);
for ($i = 1; $i < self::BIGNUMBER_MAX_EXP_ITERATIONS; ++$i) {
// calculate the number up to the precision we are after.
$calulatedNumber = (new BigNumber($power))->Div($fact, $paddedPrecision);
if ($calulatedNumber->IsZero()) {
break;
}
// add it to our number.
$result->Add($calulatedNumber);
// x * x * x ...
$power->Mul($base, $paddedPrecision);
// 1 * 2 * 3 ...
$fact->Mul((int) ($i + 1), $paddedPrecision);
}
// the decimal part of the number.
$fraction = $result;
// multiply the decimal number with the fraction.
$this->Mul($fraction, BigNumberConstants::PrecisionPadding($precision));
}
// clean up and return.
return $this->PerformPostOperations($precision);
}