#ifndef STAN_MATH_REV_SCAL_FUN_CEIL_HPP
#define STAN_MATH_REV_SCAL_FUN_CEIL_HPP

#include <stan/math/rev/core.hpp>
#include <stan/math/prim/scal/fun/is_nan.hpp>
#include <stan/math/prim/scal/meta/likely.hpp>
#include <cmath>
#include <limits>

namespace stan {
  namespace math {

    namespace {
      class ceil_vari : public op_v_vari {
      public:
        explicit ceil_vari(vari* avi) :
          op_v_vari(std::ceil(avi->val_), avi) {
        }
        void chain() {
          if (unlikely(is_nan(avi_->val_)))
            avi_->adj_ = std::numeric_limits<double>::quiet_NaN();
        }
      };
    }

    /**
     * Return the ceiling of the specified variable (cmath).
     *
     * The derivative of the ceiling function is defined and
     * zero everywhere but at integers, and we set them to zero for
     * convenience,
     *
     * \f$\frac{d}{dx} {\lceil x \rceil} = 0\f$.
     *
     * The ceiling function rounds up.  For double values, this is the
     * smallest integral value that is not less than the specified
     * value.  Although this function is not differentiable because it
     * is discontinuous at integral values, its gradient is returned
     * as zero everywhere.
     *
       \f[
       \mbox{ceil}(x) =
       \begin{cases}
         \lceil x\rceil & \mbox{if } -\infty\leq x \leq \infty \\[6pt]
         \textrm{NaN} & \mbox{if } x = \textrm{NaN}
       \end{cases}
       \f]

       \f[
       \frac{\partial\, \mbox{ceil}(x)}{\partial x} =
       \begin{cases}
         0 & \mbox{if } -\infty\leq x\leq \infty \\[6pt]
         \textrm{NaN} & \mbox{if } x = \textrm{NaN}
       \end{cases}
       \f]
     *
     * @param a Input variable.
     * @return Ceiling of the variable.
     */
    inline var ceil(const var& a) {
      return var(new ceil_vari(a.vi_));
    }

  }
}
#endif
