// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_SPECIALFUNCTIONS_PACKETMATH_H
#define EIGEN_SPECIALFUNCTIONS_PACKETMATH_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

/** \internal \returns the ln(|gamma(\a a)|) (coeff-wise) */
template <typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet plgamma(const Packet& a) {
  using numext::lgamma;
  return lgamma(a);
}

/** \internal \returns the derivative of lgamma, psi(\a a) (coeff-wise) */
template <typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pdigamma(const Packet& a) {
  using numext::digamma;
  return digamma(a);
}

/** \internal \returns the zeta function of two arguments (coeff-wise) */
template <typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pzeta(const Packet& x, const Packet& q) {
  using numext::zeta;
  return zeta(x, q);
}

/** \internal \returns the polygamma function (coeff-wise) */
template <typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet ppolygamma(const Packet& n, const Packet& x) {
  using numext::polygamma;
  return polygamma(n, x);
}

/** \internal \returns the erf(\a a) (coeff-wise) */
template <typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet perf(const Packet& a) {
  using numext::erf;
  return erf(a);
}

/** \internal \returns the erfc(\a a) (coeff-wise) */
template <typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet perfc(const Packet& a) {
  using numext::erfc;
  return erfc(a);
}

/** \internal \returns the ndtri(\a a) (coeff-wise) */
template <typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pndtri(const Packet& a) {
  typedef typename unpacket_traits<Packet>::type ScalarType;
  using internal::generic_ndtri;
  return generic_ndtri<Packet, ScalarType>(a);
}

/** \internal \returns the incomplete gamma function igamma(\a a, \a x) */
template <typename Packet>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pigamma(const Packet& a, const Packet& x) {
  using numext::igamma;
  return igamma(a, x);
}

/** \internal \returns the derivative of the incomplete gamma function
 * igamma_der_a(\a a, \a x) */
template <typename Packet>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pigamma_der_a(const Packet& a, const Packet& x) {
  using numext::igamma_der_a;
  return igamma_der_a(a, x);
}

/** \internal \returns compute the derivative of the sample
 * of Gamma(alpha, 1) random variable with respect to the parameter a
 * gamma_sample_der_alpha(\a alpha, \a sample) */
template <typename Packet>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pgamma_sample_der_alpha(const Packet& alpha, const Packet& sample) {
  using numext::gamma_sample_der_alpha;
  return gamma_sample_der_alpha(alpha, sample);
}

/** \internal \returns the complementary incomplete gamma function igammac(\a a, \a x) */
template <typename Packet>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pigammac(const Packet& a, const Packet& x) {
  using numext::igammac;
  return igammac(a, x);
}

/** \internal \returns the complementary incomplete gamma function betainc(\a a, \a b, \a x) */
template <typename Packet>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pbetainc(const Packet& a, const Packet& b, const Packet& x) {
  using numext::betainc;
  return betainc(a, b, x);
}

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_SPECIALFUNCTIONS_PACKETMATH_H