Function Root

extern/ttmath/ttmath.h:2068–2117

	*/
	template<class ValueType>
	ValueType Root(ValueType x, const ValueType & index, ErrorCode * err = 0)
	{
		using namespace auxiliaryfunctions;

		if( x.IsNan() || index.IsNan() )
		{
			if( err )
				*err = err_improper_argument;

			x.SetNan();

		return x;
		}

		if( RootCheckIndexSign(x, index, err) ) return x;
		if( RootCheckIndexZero(x, index, err) ) return x;
		if( RootCheckIndexOne (   index, err) ) return x;
		if( RootCheckIndexTwo (x, index, err) ) return x;
		if( RootCheckIndexFrac(x, index, err) ) return x;
		if( RootCheckXZero    (x,        err) ) return x;

		// index integer and index!=0
		// x!=0

		ValueType old_x(x);
		bool change_sign;

		if( RootCheckIndex(x, index, err, &change_sign ) ) return x;

		ValueType temp;
		uint c = 0;

		// we're using the formula: root(x ; n) = exp( ln(x) / n )
		c += temp.Ln(x);
		c += temp.Div(index);
		c += x.Exp(temp);

		if( change_sign )
		{
			// x is different from zero
			x.SetSign();
		}

		c += RootCorrectInteger(old_x, x, index);

		if( err )
			*err = c ? err_overflow : err_ok;

	return x;
	}