Phi.hpp

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#ifndef STAN__MATH__FUNCTIONS__PHI_HPP
#define STAN__MATH__FUNCTIONS__PHI_HPP

#include <boost/math/tools/promotion.hpp>
#include <boost/math/special_functions/erf.hpp>
#include <stan/math/constants.hpp>
#include <stan/math/error_handling/check_not_nan.hpp>

namespace stan {
  namespace math {

    template <typename T>
    inline typename boost::math::tools::promote_args<T>::type
    Phi(const T x) {
      // overridden in fvar and var, so can hard-code boost versions
      // here for scalars only
      check_not_nan("Phi(%1%)", x, "x", static_cast<double*>(0));
      if (x < -37.5)
        return 0;
      else if (x < -5.0)
        return 0.5 * boost::math::erfc(-INV_SQRT_2 * x);
      else if (x > 8.25)
        return 1;
      else
        return 0.5 * (1.0 + boost::math::erf(INV_SQRT_2 * x));
    }

  }
}

#endif