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This is cppad-20221105 documentation. Here is a link to its
current documentation
.
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 sumwhile(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;
}
