BinaryFunctors.h

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 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_BINARY_FUNCTORS_H
#define EIGEN_BINARY_FUNCTORS_H
 
#include "../InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
 
//---------- associative binary functors ----------
 
template<typename Arg1, typename Arg2>
struct binary_op_base
{
  typedef Arg1 first_argument_type;
  typedef Arg2 second_argument_type;
};
 
template<typename LhsScalar,typename RhsScalar>
struct scalar_sum_op : binary_op_base<LhsScalar,RhsScalar>
{
  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_sum_op>::ReturnType result_type;
#ifdef EIGEN_SCALAR_BINARY_OP_PLUGIN
  scalar_sum_op() {
    EIGEN_SCALAR_BINARY_OP_PLUGIN
  }
#endif
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a + b; }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
  { return internal::padd(a,b); }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type predux(const Packet& a) const
  { return internal::predux(a); }
};
template<typename LhsScalar,typename RhsScalar>
struct functor_traits<scalar_sum_op<LhsScalar,RhsScalar> > {
  enum {
    Cost = (int(NumTraits<LhsScalar>::AddCost) + int(NumTraits<RhsScalar>::AddCost)) / 2, // rough estimate!
    PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasAdd && packet_traits<RhsScalar>::HasAdd
    // TODO vectorize mixed sum
  };
};
 
 
template<>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool scalar_sum_op<bool,bool>::operator() (const bool& a, const bool& b) const { return a || b; }
 
 
template<typename LhsScalar,typename RhsScalar>
struct scalar_product_op  : binary_op_base<LhsScalar,RhsScalar>
{
  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_product_op>::ReturnType result_type;
#ifdef EIGEN_SCALAR_BINARY_OP_PLUGIN
  scalar_product_op() {
    EIGEN_SCALAR_BINARY_OP_PLUGIN
  }
#endif
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a * b; }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
  { return internal::pmul(a,b); }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type predux(const Packet& a) const
  { return internal::predux_mul(a); }
};
template<typename LhsScalar,typename RhsScalar>
struct functor_traits<scalar_product_op<LhsScalar,RhsScalar> > {
  enum {
    Cost = (int(NumTraits<LhsScalar>::MulCost) + int(NumTraits<RhsScalar>::MulCost))/2, // rough estimate!
    PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasMul && packet_traits<RhsScalar>::HasMul
    // TODO vectorize mixed product
  };
};
 
template<>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool scalar_product_op<bool,bool>::operator() (const bool& a, const bool& b) const { return a && b; }
 
 
template<typename LhsScalar,typename RhsScalar>
struct scalar_conj_product_op  : binary_op_base<LhsScalar,RhsScalar>
{
 
  enum {
    Conj = NumTraits<LhsScalar>::IsComplex
  };
 
  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_conj_product_op>::ReturnType result_type;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const LhsScalar& a, const RhsScalar& b) const
  { return conj_helper<LhsScalar,RhsScalar,Conj,false>().pmul(a,b); }
 
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
  { return conj_helper<Packet,Packet,Conj,false>().pmul(a,b); }
};
template<typename LhsScalar,typename RhsScalar>
struct functor_traits<scalar_conj_product_op<LhsScalar,RhsScalar> > {
  enum {
    Cost = NumTraits<LhsScalar>::MulCost,
    PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMul
  };
};
 
template<typename LhsScalar,typename RhsScalar, int NaNPropagation>
struct scalar_min_op : binary_op_base<LhsScalar,RhsScalar>
{
  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_min_op>::ReturnType result_type;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const LhsScalar& a, const RhsScalar& b) const {
    return internal::pmin<NaNPropagation>(a, b);
  }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
  {
    return internal::pmin<NaNPropagation>(a,b);
  }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type predux(const Packet& a) const
  {
    return internal::predux_min<NaNPropagation>(a);
  }
};
 
template<typename LhsScalar,typename RhsScalar, int NaNPropagation>
struct functor_traits<scalar_min_op<LhsScalar,RhsScalar, NaNPropagation> > {
  enum {
    Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
    PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMin
  };
};
 
template<typename LhsScalar,typename RhsScalar, int NaNPropagation>
struct scalar_max_op : binary_op_base<LhsScalar,RhsScalar>
{
  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_max_op>::ReturnType result_type;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const LhsScalar& a, const RhsScalar& b) const {
    return internal::pmax<NaNPropagation>(a,b);
  }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
  {
    return internal::pmax<NaNPropagation>(a,b);
  }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type predux(const Packet& a) const
  {
    return internal::predux_max<NaNPropagation>(a);
  }
};
 
template<typename LhsScalar,typename RhsScalar, int NaNPropagation>
struct functor_traits<scalar_max_op<LhsScalar,RhsScalar, NaNPropagation> > {
  enum {
    Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
    PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMax
  };
};
 
template <typename LhsScalar, typename RhsScalar, ComparisonName cmp,
          bool UseTypedComparators = false>
struct scalar_cmp_op;
 
template <typename LhsScalar, typename RhsScalar, ComparisonName cmp, bool UseTypedComparators>
struct functor_traits<scalar_cmp_op<LhsScalar, RhsScalar, cmp, UseTypedComparators>> {
  enum {
    Cost = (NumTraits<LhsScalar>::AddCost + NumTraits<RhsScalar>::AddCost) / 2,
    PacketAccess = (UseTypedComparators || is_same<LhsScalar, bool>::value) && is_same<LhsScalar, RhsScalar>::value &&
                   packet_traits<LhsScalar>::HasCmp
  };
};
 
template <typename LhsScalar, typename RhsScalar, bool UseTypedComparators>
struct typed_cmp_helper {
  static constexpr bool SameType = is_same<LhsScalar, RhsScalar>::value;
  static constexpr bool IsNumeric = is_arithmetic<typename NumTraits<LhsScalar>::Real>::value;
  static constexpr bool UseTyped = UseTypedComparators && SameType && IsNumeric;
  using type = typename conditional<UseTyped, LhsScalar, bool>::type;
};
 
template <typename LhsScalar, typename RhsScalar, bool UseTypedComparators>
using cmp_return_t = typename typed_cmp_helper<LhsScalar, RhsScalar, UseTypedComparators>::type;
 
template <typename LhsScalar, typename RhsScalar, bool UseTypedComparators>
struct scalar_cmp_op<LhsScalar, RhsScalar, cmp_EQ, UseTypedComparators> : binary_op_base<LhsScalar, RhsScalar> {
  using result_type = cmp_return_t<LhsScalar, RhsScalar, UseTypedComparators>;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator()(const LhsScalar& a, const RhsScalar& b) const {
    return a == b ? result_type(1) : result_type(0);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const {
    const Packet cst_one = pset1<Packet>(result_type(1));
    return pand(pcmp_eq(a, b), cst_one);
  }
};
 
template <typename LhsScalar, typename RhsScalar, bool UseTypedComparators>
struct scalar_cmp_op<LhsScalar, RhsScalar, cmp_LT, UseTypedComparators> : binary_op_base<LhsScalar, RhsScalar> {
  using result_type = cmp_return_t<LhsScalar, RhsScalar, UseTypedComparators>;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator()(const LhsScalar& a, const RhsScalar& b) const {
    return a < b ? result_type(1) : result_type(0);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const {
    const Packet cst_one = pset1<Packet>(result_type(1));
    return pand(pcmp_lt(a, b), cst_one);
  }
};
 
template <typename LhsScalar, typename RhsScalar, bool UseTypedComparators>
struct scalar_cmp_op<LhsScalar, RhsScalar, cmp_LE, UseTypedComparators> : binary_op_base<LhsScalar, RhsScalar> {
  using result_type = cmp_return_t<LhsScalar, RhsScalar, UseTypedComparators>;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator()(const LhsScalar& a, const RhsScalar& b) const {
    return a <= b ? result_type(1) : result_type(0);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const {
    const Packet cst_one = pset1<Packet>(result_type(1));
    return pand(cst_one, pcmp_le(a, b));
  }
};
 
template <typename LhsScalar, typename RhsScalar, bool UseTypedComparators>
struct scalar_cmp_op<LhsScalar, RhsScalar, cmp_GT, UseTypedComparators> : binary_op_base<LhsScalar, RhsScalar> {
  using result_type = cmp_return_t<LhsScalar, RhsScalar, UseTypedComparators>;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator()(const LhsScalar& a, const RhsScalar& b) const {
    return a > b ? result_type(1) : result_type(0);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const {
    const Packet cst_one = pset1<Packet>(result_type(1));
    return pand(cst_one, pcmp_lt(b, a));
  }
};
 
template <typename LhsScalar, typename RhsScalar, bool UseTypedComparators>
struct scalar_cmp_op<LhsScalar, RhsScalar, cmp_GE, UseTypedComparators> : binary_op_base<LhsScalar, RhsScalar> {
  using result_type = cmp_return_t<LhsScalar, RhsScalar, UseTypedComparators>;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator()(const LhsScalar& a, const RhsScalar& b) const {
    return a >= b ? result_type(1) : result_type(0);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const {
    const Packet cst_one = pset1<Packet>(result_type(1));
    return pand(cst_one, pcmp_le(b, a));
  }
};
 
template <typename LhsScalar, typename RhsScalar, bool UseTypedComparators>
struct scalar_cmp_op<LhsScalar, RhsScalar, cmp_UNORD, UseTypedComparators> : binary_op_base<LhsScalar, RhsScalar> {
  using result_type = cmp_return_t<LhsScalar, RhsScalar, UseTypedComparators>;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator()(const LhsScalar& a, const RhsScalar& b) const {
    return !(a <= b || b <= a) ? result_type(1) : result_type(0);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const {
    const Packet cst_one = pset1<Packet>(result_type(1));
    return pandnot(cst_one, por(pcmp_le(a, b), pcmp_le(b, a)));
  }
};
 
template <typename LhsScalar, typename RhsScalar, bool UseTypedComparators>
struct scalar_cmp_op<LhsScalar, RhsScalar, cmp_NEQ, UseTypedComparators> : binary_op_base<LhsScalar, RhsScalar> {
  using result_type = cmp_return_t<LhsScalar, RhsScalar, UseTypedComparators>;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator()(const LhsScalar& a, const RhsScalar& b) const {
    return a != b ? result_type(1) : result_type(0);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const {
    const Packet cst_one = pset1<Packet>(result_type(1));
    return pandnot(cst_one, pcmp_eq(a, b));
  }
};
 
template<typename Scalar>
struct scalar_hypot_op<Scalar,Scalar> : binary_op_base<Scalar,Scalar>
{
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar &x, const Scalar &y) const
  {
    // This functor is used by hypotNorm only for which it is faster to first apply abs
    // on all coefficients prior to reduction through hypot.
    // This way we avoid calling abs on positive and real entries, and this also permits
    // to seamlessly handle complexes. Otherwise we would have to handle both real and complexes
    // through the same functor...
    return internal::positive_real_hypot(x,y);
  }
};
template<typename Scalar>
struct functor_traits<scalar_hypot_op<Scalar,Scalar> > {
  enum
  {
    Cost = 3 * NumTraits<Scalar>::AddCost +
           2 * NumTraits<Scalar>::MulCost +
           2 * scalar_div_cost<Scalar,false>::value,
    PacketAccess = false
  };
};
 
template<typename Scalar, typename Exponent>
struct scalar_pow_op  : binary_op_base<Scalar,Exponent>
{
  typedef typename ScalarBinaryOpTraits<Scalar,Exponent,scalar_pow_op>::ReturnType result_type;
#ifdef EIGEN_SCALAR_BINARY_OP_PLUGIN
  scalar_pow_op() {
    typedef Scalar LhsScalar;
    typedef Exponent RhsScalar;
    EIGEN_SCALAR_BINARY_OP_PLUGIN
  }
#endif
 
  EIGEN_DEVICE_FUNC
  inline result_type operator() (const Scalar& a, const Exponent& b) const { return numext::pow(a, b); }
 
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
  {
    return generic_pow(a,b);
  }
};
 
template<typename Scalar, typename Exponent>
struct functor_traits<scalar_pow_op<Scalar,Exponent> > {
  enum {
    Cost = 5 * NumTraits<Scalar>::MulCost,
    PacketAccess = (!NumTraits<Scalar>::IsComplex && !NumTraits<Scalar>::IsInteger &&
                    packet_traits<Scalar>::HasExp && packet_traits<Scalar>::HasLog &&
                    packet_traits<Scalar>::HasRound && packet_traits<Scalar>::HasCmp &&
                    // Temporarily disable packet access for half/bfloat16 until
                    // accuracy is improved.
                    !is_same<Scalar, half>::value && !is_same<Scalar, bfloat16>::value
                    )
  };
};
 
//---------- non associative binary functors ----------
 
template<typename LhsScalar,typename RhsScalar>
struct scalar_difference_op : binary_op_base<LhsScalar,RhsScalar>
{
  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_difference_op>::ReturnType result_type;
#ifdef EIGEN_SCALAR_BINARY_OP_PLUGIN
  scalar_difference_op() {
    EIGEN_SCALAR_BINARY_OP_PLUGIN
  }
#endif
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a - b; }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
  { return internal::psub(a,b); }
};
template<typename LhsScalar,typename RhsScalar>
struct functor_traits<scalar_difference_op<LhsScalar,RhsScalar> > {
  enum {
    Cost = (int(NumTraits<LhsScalar>::AddCost) + int(NumTraits<RhsScalar>::AddCost)) / 2,
    PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasSub && packet_traits<RhsScalar>::HasSub
  };
};
 
template <typename Packet, bool IsInteger = NumTraits<typename unpacket_traits<Packet>::type>::IsInteger>
struct maybe_raise_div_by_zero {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Packet x) {
    EIGEN_UNUSED_VARIABLE(x);
  }
};
 
#ifndef EIGEN_GPU_COMPILE_PHASE
template <typename Packet>
struct maybe_raise_div_by_zero<Packet, true> {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Packet x) {
    if (EIGEN_PREDICT_FALSE(predux_any(pcmp_eq(x, pzero(x))))) {
      // Use volatile variables to force a division by zero, which will
      // result in the default platform behaviour (usually SIGFPE).
      volatile typename unpacket_traits<Packet>::type zero = 0;
      volatile typename unpacket_traits<Packet>::type val = 1;
      val = val / zero;
    }
  }
};
#endif
 
template<typename LhsScalar,typename RhsScalar>
struct scalar_quotient_op  : binary_op_base<LhsScalar,RhsScalar>
{
  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_quotient_op>::ReturnType result_type;
#ifdef EIGEN_SCALAR_BINARY_OP_PLUGIN
  scalar_quotient_op() {
    EIGEN_SCALAR_BINARY_OP_PLUGIN
  }
#endif
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a / b; }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const {
    maybe_raise_div_by_zero<Packet>::run(b);
    return internal::pdiv(a,b);
  }
};
template<typename LhsScalar,typename RhsScalar>
struct functor_traits<scalar_quotient_op<LhsScalar,RhsScalar> > {
  typedef typename scalar_quotient_op<LhsScalar,RhsScalar>::result_type result_type;
  enum {
    PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasDiv && packet_traits<RhsScalar>::HasDiv,
    Cost = scalar_div_cost<result_type,PacketAccess>::value
  };
};
 
template <typename Scalar>
struct scalar_boolean_and_op {
  using result_type = Scalar;
  // `false` any value `a` that satisfies `a == Scalar(0)`
  // `true` is the complement of `false`
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const Scalar& a, const Scalar& b) const {
    return (a != Scalar(0)) && (b != Scalar(0)) ? Scalar(1) : Scalar(0);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const {
    const Packet cst_one = pset1<Packet>(Scalar(1));
    // and(a,b) == !or(!a,!b)
    Packet not_a = pcmp_eq(a, pzero(a));
    Packet not_b = pcmp_eq(b, pzero(b));
    Packet a_nand_b = por(not_a, not_b);
    return pandnot(cst_one, a_nand_b);
  }
};
template <typename Scalar>
struct functor_traits<scalar_boolean_and_op<Scalar>> {
  enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasCmp };
};
 
template <typename Scalar>
struct scalar_boolean_or_op {
  using result_type = Scalar;
  // `false` any value `a` that satisfies `a == Scalar(0)`
  // `true` is the complement of `false`
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const Scalar& a, const Scalar& b) const {
    return (a != Scalar(0)) || (b != Scalar(0)) ? Scalar(1) : Scalar(0);
  }
  template <typename Packet>
  EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const {
    const Packet cst_one = pset1<Packet>(Scalar(1));
    // if or(a,b) == 0, then a == 0 and b == 0
    // or(a,b) == !nor(a,b)
    Packet a_nor_b = pcmp_eq(por(a, b), pzero(a));
    return pandnot(cst_one, a_nor_b);
  }
};
template <typename Scalar>
struct functor_traits<scalar_boolean_or_op<Scalar>> {
  enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasCmp };
};
 
template <typename Scalar>
struct scalar_boolean_xor_op {
  using result_type = Scalar;
  // `false` any value `a` that satisfies `a == Scalar(0)`
  // `true` is the complement of `false`
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const Scalar& a, const Scalar& b) const {
    return (a != Scalar(0)) != (b != Scalar(0)) ? Scalar(1) : Scalar(0);
  }
  template <typename Packet>
  EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const {
    const Packet cst_one = pset1<Packet>(Scalar(1));
    // xor(a,b) == xor(!a,!b)
    Packet not_a = pcmp_eq(a, pzero(a));
    Packet not_b = pcmp_eq(b, pzero(b));
    Packet a_xor_b = pxor(not_a, not_b);
    return pand(cst_one, a_xor_b);
  }
};
template <typename Scalar>
struct functor_traits<scalar_boolean_xor_op<Scalar>> {
  enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasCmp };
};
 
template <typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
struct bitwise_binary_impl {
  static constexpr size_t Size = sizeof(Scalar);
  using uint_t = typename numext::get_integer_by_size<Size>::unsigned_type;
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_and(const Scalar& a, const Scalar& b) {
    uint_t a_as_uint = numext::bit_cast<uint_t, Scalar>(a);
    uint_t b_as_uint = numext::bit_cast<uint_t, Scalar>(b);
    uint_t result = a_as_uint & b_as_uint;
    return numext::bit_cast<Scalar, uint_t>(result);
  }
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_or(const Scalar& a, const Scalar& b) {
    uint_t a_as_uint = numext::bit_cast<uint_t, Scalar>(a);
    uint_t b_as_uint = numext::bit_cast<uint_t, Scalar>(b);
    uint_t result = a_as_uint | b_as_uint;
    return numext::bit_cast<Scalar, uint_t>(result);
  }
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_xor(const Scalar& a, const Scalar& b) {
    uint_t a_as_uint = numext::bit_cast<uint_t, Scalar>(a);
    uint_t b_as_uint = numext::bit_cast<uint_t, Scalar>(b);
    uint_t result = a_as_uint ^ b_as_uint;
    return numext::bit_cast<Scalar, uint_t>(result);
  }
};
 
template <typename Scalar>
struct bitwise_binary_impl<Scalar, true> {
  using Real = typename NumTraits<Scalar>::Real;
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_and(const Scalar& a, const Scalar& b) {
    Real real_result = bitwise_binary_impl<Real>::run_and(numext::real(a), numext::real(b));
    Real imag_result = bitwise_binary_impl<Real>::run_and(numext::imag(a), numext::imag(b));
    return Scalar(real_result, imag_result);
  }
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_or(const Scalar& a, const Scalar& b) {
    Real real_result = bitwise_binary_impl<Real>::run_or(numext::real(a), numext::real(b));
    Real imag_result = bitwise_binary_impl<Real>::run_or(numext::imag(a), numext::imag(b));
    return Scalar(real_result, imag_result);
  }
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_xor(const Scalar& a, const Scalar& b) {
    Real real_result = bitwise_binary_impl<Real>::run_xor(numext::real(a), numext::real(b));
    Real imag_result = bitwise_binary_impl<Real>::run_xor(numext::imag(a), numext::imag(b));
    return Scalar(real_result, imag_result);
  }
};
 
template <typename Scalar>
struct scalar_bitwise_and_op {
  EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::RequireInitialization,
                      BITWISE OPERATIONS MAY ONLY BE PERFORMED ON PLAIN DATA TYPES)
  EIGEN_STATIC_ASSERT((!internal::is_same<Scalar, bool>::value), DONT USE BITWISE OPS ON BOOLEAN TYPES)
  using result_type = Scalar;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const Scalar& a, const Scalar& b) const {
    return bitwise_binary_impl<Scalar>::run_and(a, b);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const {
    return pand(a, b);
  }
};
template <typename Scalar>
struct functor_traits<scalar_bitwise_and_op<Scalar>> {
  enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = true };
};
 
template <typename Scalar>
struct scalar_bitwise_or_op {
  EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::RequireInitialization,
                      BITWISE OPERATIONS MAY ONLY BE PERFORMED ON PLAIN DATA TYPES)
  EIGEN_STATIC_ASSERT((!internal::is_same<Scalar, bool>::value), DONT USE BITWISE OPS ON BOOLEAN TYPES)
  using result_type = Scalar;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const Scalar& a, const Scalar& b) const {
    return bitwise_binary_impl<Scalar>::run_or(a, b);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const {
    return por(a, b);
  }
};
template <typename Scalar>
struct functor_traits<scalar_bitwise_or_op<Scalar>> {
  enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = true };
};
 
template <typename Scalar>
struct scalar_bitwise_xor_op {
  EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::RequireInitialization,
                      BITWISE OPERATIONS MAY ONLY BE PERFORMED ON PLAIN DATA TYPES)
  EIGEN_STATIC_ASSERT((!internal::is_same<Scalar, bool>::value), DONT USE BITWISE OPS ON BOOLEAN TYPES)
  using result_type = Scalar;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const Scalar& a, const Scalar& b) const {
    return bitwise_binary_impl<Scalar>::run_xor(a, b);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const {
    return pxor(a, b);
  }
};
template <typename Scalar>
struct functor_traits<scalar_bitwise_xor_op<Scalar>> {
  enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = true };
};
 
template<typename LhsScalar,typename RhsScalar>
struct scalar_absolute_difference_op : binary_op_base<LhsScalar,RhsScalar>
{
  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_absolute_difference_op>::ReturnType result_type;
#ifdef EIGEN_SCALAR_BINARY_OP_PLUGIN
  scalar_absolute_difference_op() {
    EIGEN_SCALAR_BINARY_OP_PLUGIN
  }
#endif
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const
  { return numext::absdiff(a,b); }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
  { return internal::pabsdiff(a,b); }
};
template<typename LhsScalar,typename RhsScalar>
struct functor_traits<scalar_absolute_difference_op<LhsScalar,RhsScalar> > {
  enum {
    Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
    PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasAbsDiff
  };
};
 
 
template <typename LhsScalar, typename RhsScalar>
struct scalar_atan2_op {
  using Scalar = LhsScalar;
 
  static constexpr bool Enable = is_same<LhsScalar, RhsScalar>::value && !NumTraits<Scalar>::IsInteger && !NumTraits<Scalar>::IsComplex;
  EIGEN_STATIC_ASSERT(Enable, "LhsScalar and RhsScalar must be the same non-integer, non-complex type")
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const Scalar& y, const Scalar& x) const {
    return numext::atan2(y, x);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& y, const Packet& x) const {
    return internal::patan2(y, x);
  }
};
 
template<typename LhsScalar,typename RhsScalar>
    struct functor_traits<scalar_atan2_op<LhsScalar, RhsScalar>> {
  using Scalar = LhsScalar;
  enum {
    PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<Scalar>::HasATan && packet_traits<Scalar>::HasDiv && !NumTraits<Scalar>::IsInteger && !NumTraits<Scalar>::IsComplex,
    Cost = int(scalar_div_cost<Scalar, PacketAccess>::value) + int(functor_traits<scalar_atan_op<Scalar>>::Cost)
  };
};
 
//---------- binary functors bound to a constant, thus appearing as a unary functor ----------
 
// The following two classes permits to turn any binary functor into a unary one with one argument bound to a constant value.
// They are analogues to std::binder1st/binder2nd but with the following differences:
//  - they are compatible with packetOp
//  - they are portable across C++ versions (the std::binder* are deprecated in C++11)
template<typename BinaryOp> struct bind1st_op : BinaryOp {
 
  typedef typename BinaryOp::first_argument_type  first_argument_type;
  typedef typename BinaryOp::second_argument_type second_argument_type;
  typedef typename BinaryOp::result_type          result_type;
 
  EIGEN_DEVICE_FUNC explicit bind1st_op(const first_argument_type &val) : m_value(val) {}
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const second_argument_type& b) const { return BinaryOp::operator()(m_value,b); }
 
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& b) const
  { return BinaryOp::packetOp(internal::pset1<Packet>(m_value), b); }
 
  first_argument_type m_value;
};
template<typename BinaryOp> struct functor_traits<bind1st_op<BinaryOp> > : functor_traits<BinaryOp> {};
 
 
template<typename BinaryOp> struct bind2nd_op : BinaryOp {
 
  typedef typename BinaryOp::first_argument_type  first_argument_type;
  typedef typename BinaryOp::second_argument_type second_argument_type;
  typedef typename BinaryOp::result_type          result_type;
 
  EIGEN_DEVICE_FUNC explicit bind2nd_op(const second_argument_type &val) : m_value(val) {}
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const first_argument_type& a) const { return BinaryOp::operator()(a,m_value); }
 
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
  { return BinaryOp::packetOp(a,internal::pset1<Packet>(m_value)); }
 
  second_argument_type m_value;
};
template<typename BinaryOp> struct functor_traits<bind2nd_op<BinaryOp> > : functor_traits<BinaryOp> {};
 
 
} // end namespace internal
 
} // end namespace Eigen
 
#endif // EIGEN_BINARY_FUNCTORS_H