#ifndef STAN_MATH_REV_SCAL_FUN_ATANH_HPP
#define STAN_MATH_REV_SCAL_FUN_ATANH_HPP

#include <stan/math/prim/scal/fun/atanh.hpp>
#include <stan/math/rev/core.hpp>
#include <limits>

namespace stan {
namespace math {

namespace {
class atanh_vari : public op_v_vari {
 public:
  atanh_vari(double val, vari* avi) : op_v_vari(val, avi) {}
  void chain() { avi_->adj_ += adj_ / (1.0 - avi_->val_ * avi_->val_); }
};
}  // namespace

/**
 * The inverse hyperbolic tangent function for variables (C99).
 *
 * The derivative is defined by
 *
 * \f$\frac{d}{dx} \mbox{atanh}(x) = \frac{1}{1 - x^2}\f$.
 *
   \f[
   \mbox{atanh}(x) =
   \begin{cases}
     \textrm{NaN} & \mbox{if } x < -1\\
     \tanh^{-1}(x) & \mbox{if } -1\leq x \leq 1 \\
     \textrm{NaN} & \mbox{if } x > 1\\[6pt]
     \textrm{NaN} & \mbox{if } x = \textrm{NaN}
   \end{cases}
   \f]

   \f[
   \frac{\partial\, \mbox{atanh}(x)}{\partial x} =
   \begin{cases}
     \textrm{NaN} & \mbox{if } x < -1\\
     \frac{\partial\, \tanh^{-1}(x)}{\partial x} & \mbox{if } -1\leq x\leq 1 \\
     \textrm{NaN} & \mbox{if } x > 1\\[6pt]
     \textrm{NaN} & \mbox{if } x = \textrm{NaN}
   \end{cases}
   \f]

   \f[
   \tanh^{-1}(x)=\frac{1}{2}\ln\left(\frac{1+x}{1-x}\right)
   \f]

   \f[
   \frac{\partial \, \tanh^{-1}(x)}{\partial x} = \frac{1}{1-x^2}
   \f]
   *
   * @param a The variable.
   * @return Inverse hyperbolic tangent of the variable.
   * @throw std::domain_error if a < -1 or a > 1
   */
inline var atanh(const var& a) {
  return var(new atanh_vari(atanh(a.val()), a.vi_));
}

}  // namespace math
}  // namespace stan
#endif
