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exp_eps: Implementation
 
template <class Type>
Type exp_eps(const Type &x, const Type &epsilon)
{	// abs_x = |x|
	Type abs_x = x;
	if( Type(0) > x )
		abs_x = - x;
	// initialize
	int  k    = 0;          // initial order 
	Type term = 1.;         // term = |x|^k / k !
	Type sum  = term;       // initial sum
	while(term > epsilon)
	{	k         = k + 1;          // order for next term
		Type temp = term * abs_x;   // term = |x|^k / (k-1)!
		term      = temp / Type(k); // term = |x|^k / k !
		sum       = sum + term;     // sum  = 1 + ... + |x|^k / k !
	}
	// In the case where x is negative, use exp(x) = 1 / exp(-|x|)
	if( Type(0) > x ) 
		sum = Type(1) / sum;
	return sum;
}

Input File: introduction/exp_apx/exp_eps.omh