exp_eps: Implementation
Keywords: exp_eps: implementation exp_eps

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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