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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
+
+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;
+};
+
+/** \internal
+ * \brief Template functor to compute the sum of two scalars
+ *
+ * \sa class CwiseBinaryOp, MatrixBase::operator+, class VectorwiseOp, DenseBase::sum()
+ */
+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;
+#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_sum_op)
+#else
+ scalar_sum_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::padd(a,b); }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const 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 = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2, // rough estimate!
+ PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasAdd && packet_traits<RhsScalar>::HasAdd
+ // TODO vectorize mixed sum
+ };
+};
+
+/** \internal
+ * \brief Template specialization to deprecate the summation of boolean expressions.
+ * This is required to solve Bug 426.
+ * \sa DenseBase::count(), DenseBase::any(), ArrayBase::cast(), MatrixBase::cast()
+ */
+template<> struct scalar_sum_op<bool,bool> : scalar_sum_op<int,int> {
+ EIGEN_DEPRECATED
+ scalar_sum_op() {}
+};
+
+
+/** \internal
+ * \brief Template functor to compute the product of two scalars
+ *
+ * \sa class CwiseBinaryOp, Cwise::operator*(), class VectorwiseOp, MatrixBase::redux()
+ */
+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;
+#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_product_op)
+#else
+ scalar_product_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::pmul(a,b); }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const 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 = (NumTraits<LhsScalar>::MulCost + NumTraits<RhsScalar>::MulCost)/2, // rough estimate!
+ PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasMul && packet_traits<RhsScalar>::HasMul
+ // TODO vectorize mixed product
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the conjugate product of two scalars
+ *
+ * This is a short cut for conj(x) * y which is needed for optimization purpose; in Eigen2 support mode, this becomes x * conj(y)
+ */
+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_EMPTY_STRUCT_CTOR(scalar_conj_product_op)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const 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 const 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
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the min of two scalars
+ *
+ * \sa class CwiseBinaryOp, MatrixBase::cwiseMin, class VectorwiseOp, MatrixBase::minCoeff()
+ */
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_min_op : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_min_op>::ReturnType result_type;
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_min_op)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return numext::mini(a, b); }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pmin(a,b); }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type predux(const Packet& a) const
+ { return internal::predux_min(a); }
+};
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_min_op<LhsScalar,RhsScalar> > {
+ enum {
+ Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
+ PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMin
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the max of two scalars
+ *
+ * \sa class CwiseBinaryOp, MatrixBase::cwiseMax, class VectorwiseOp, MatrixBase::maxCoeff()
+ */
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_max_op : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_max_op>::ReturnType result_type;
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_max_op)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return numext::maxi(a, b); }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pmax(a,b); }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type predux(const Packet& a) const
+ { return internal::predux_max(a); }
+};
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_max_op<LhsScalar,RhsScalar> > {
+ enum {
+ Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
+ PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMax
+ };
+};
+
+/** \internal
+ * \brief Template functors for comparison of two scalars
+ * \todo Implement packet-comparisons
+ */
+template<typename LhsScalar, typename RhsScalar, ComparisonName cmp> struct scalar_cmp_op;
+
+template<typename LhsScalar, typename RhsScalar, ComparisonName cmp>
+struct functor_traits<scalar_cmp_op<LhsScalar,RhsScalar, cmp> > {
+ enum {
+ Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
+ PacketAccess = false
+ };
+};
+
+template<ComparisonName Cmp, typename LhsScalar, typename RhsScalar>
+struct result_of<scalar_cmp_op<LhsScalar, RhsScalar, Cmp>(LhsScalar,RhsScalar)> {
+ typedef bool type;
+};
+
+
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_EQ> : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef bool result_type;
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a==b;}
+};
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_LT> : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef bool result_type;
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a<b;}
+};
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_LE> : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef bool result_type;
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a<=b;}
+};
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_GT> : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef bool result_type;
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a>b;}
+};
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_GE> : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef bool result_type;
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a>=b;}
+};
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_UNORD> : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef bool result_type;
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return !(a<=b || b<=a);}
+};
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_NEQ> : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef bool result_type;
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a!=b;}
+};
+
+
+/** \internal
+ * \brief Template functor to compute the hypot of two scalars
+ *
+ * \sa MatrixBase::stableNorm(), class Redux
+ */
+template<typename Scalar>
+struct scalar_hypot_op<Scalar,Scalar> : binary_op_base<Scalar,Scalar>
+{
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_hypot_op)
+// typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& _x, const Scalar& _y) const
+ {
+ EIGEN_USING_STD_MATH(sqrt)
+ Scalar p, qp;
+ if(_x>_y)
+ {
+ p = _x;
+ qp = _y / p;
+ }
+ else
+ {
+ p = _y;
+ qp = _x / p;
+ }
+ return p * sqrt(Scalar(1) + qp*qp);
+ }
+};
+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
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the pow of two scalars
+ */
+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;
+#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_pow_op)
+#else
+ 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 Scalar, typename Exponent>
+struct functor_traits<scalar_pow_op<Scalar,Exponent> > {
+ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false };
+};
+
+
+
+//---------- non associative binary functors ----------
+
+/** \internal
+ * \brief Template functor to compute the difference of two scalars
+ *
+ * \sa class CwiseBinaryOp, MatrixBase::operator-
+ */
+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;
+#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_difference_op)
+#else
+ 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 = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
+ PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasSub && packet_traits<RhsScalar>::HasSub
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the quotient of two scalars
+ *
+ * \sa class CwiseBinaryOp, Cwise::operator/()
+ */
+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;
+#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_quotient_op)
+#else
+ 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
+ { 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
+ };
+};
+
+
+
+/** \internal
+ * \brief Template functor to compute the and of two booleans
+ *
+ * \sa class CwiseBinaryOp, ArrayBase::operator&&
+ */
+struct scalar_boolean_and_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_and_op)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a && b; }
+};
+template<> struct functor_traits<scalar_boolean_and_op> {
+ enum {
+ Cost = NumTraits<bool>::AddCost,
+ PacketAccess = false
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the or of two booleans
+ *
+ * \sa class CwiseBinaryOp, ArrayBase::operator||
+ */
+struct scalar_boolean_or_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_or_op)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a || b; }
+};
+template<> struct functor_traits<scalar_boolean_or_op> {
+ enum {
+ Cost = NumTraits<bool>::AddCost,
+ PacketAccess = false
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the xor of two booleans
+ *
+ * \sa class CwiseBinaryOp, ArrayBase::operator^
+ */
+struct scalar_boolean_xor_op {
+ EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_xor_op)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a ^ b; }
+};
+template<> struct functor_traits<scalar_boolean_xor_op> {
+ enum {
+ Cost = NumTraits<bool>::AddCost,
+ PacketAccess = false
+ };
+};
+
+
+
+//---------- 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;
+
+ 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;
+
+ 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