From 7032a1fd26da03b3466534aa023c348732452ea5 Mon Sep 17 00:00:00 2001
From: Miao Wang <miaowang@google.com>
Date: Thu, 17 Jan 2019 19:01:01 -0800
Subject: Add scalar_logistic_op to Eigen

Test: mm
Change-Id: Ib09c5bb5adeef356fc42cbe8a2edfda4c727c536
---
 Eigen/src/Core/functors/UnaryFunctors.h | 1134 +++++++++++++++++++------------
 1 file changed, 698 insertions(+), 436 deletions(-)

diff --git a/Eigen/src/Core/functors/UnaryFunctors.h b/Eigen/src/Core/functors/UnaryFunctors.h
index 2e6a00ffd..c396db393 100644
--- a/Eigen/src/Core/functors/UnaryFunctors.h
+++ b/Eigen/src/Core/functors/UnaryFunctors.h
@@ -15,40 +15,52 @@ namespace Eigen {
 namespace internal {
 
 /** \internal
-  * \brief Template functor to compute the opposite of a scalar
-  *
-  * \sa class CwiseUnaryOp, MatrixBase::operator-
-  */
-template<typename Scalar> struct scalar_opposite_op {
+ * \brief Template functor to compute the opposite of a scalar
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::operator-
+ */
+template <typename Scalar>
+struct scalar_opposite_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_opposite_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return -a; }
-  template<typename Packet>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
-  { return internal::pnegate(a); }
-};
-template<typename Scalar>
-struct functor_traits<scalar_opposite_op<Scalar> >
-{ enum {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar
+  operator()(const Scalar& a) const {
+    return -a;
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet
+  packetOp(const Packet& a) const {
+    return internal::pnegate(a);
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_opposite_op<Scalar> > {
+  enum {
     Cost = NumTraits<Scalar>::AddCost,
-    PacketAccess = packet_traits<Scalar>::HasNegate };
+    PacketAccess = packet_traits<Scalar>::HasNegate
+  };
 };
 
 /** \internal
-  * \brief Template functor to compute the absolute value of a scalar
-  *
-  * \sa class CwiseUnaryOp, Cwise::abs
-  */
-template<typename Scalar> struct scalar_abs_op {
+ * \brief Template functor to compute the absolute value of a scalar
+ *
+ * \sa class CwiseUnaryOp, Cwise::abs
+ */
+template <typename Scalar>
+struct scalar_abs_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_abs_op)
   typedef typename NumTraits<Scalar>::Real result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return numext::abs(a); }
-  template<typename Packet>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
-  { return internal::pabs(a); }
-};
-template<typename Scalar>
-struct functor_traits<scalar_abs_op<Scalar> >
-{
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type
+  operator()(const Scalar& a) const {
+    return numext::abs(a);
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet
+  packetOp(const Packet& a) const {
+    return internal::pabs(a);
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_abs_op<Scalar> > {
   enum {
     Cost = NumTraits<Scalar>::AddCost,
     PacketAccess = packet_traits<Scalar>::HasAbs
@@ -56,66 +68,90 @@ struct functor_traits<scalar_abs_op<Scalar> >
 };
 
 /** \internal
-  * \brief Template functor to compute the score of a scalar, to chose a pivot
-  *
-  * \sa class CwiseUnaryOp
-  */
-template<typename Scalar> struct scalar_score_coeff_op : scalar_abs_op<Scalar>
-{
+ * \brief Template functor to compute the score of a scalar, to chose a pivot
+ *
+ * \sa class CwiseUnaryOp
+ */
+template <typename Scalar>
+struct scalar_score_coeff_op : scalar_abs_op<Scalar> {
   typedef void Score_is_abs;
 };
-template<typename Scalar>
-struct functor_traits<scalar_score_coeff_op<Scalar> > : functor_traits<scalar_abs_op<Scalar> > {};
+template <typename Scalar>
+struct functor_traits<scalar_score_coeff_op<Scalar> >
+    : functor_traits<scalar_abs_op<Scalar> > {};
 
-/* Avoid recomputing abs when we know the score and they are the same. Not a true Eigen functor.  */
-template<typename Scalar, typename=void> struct abs_knowing_score
-{
+/* Avoid recomputing abs when we know the score and they are the same. Not a
+ * true Eigen functor.  */
+template <typename Scalar, typename = void>
+struct abs_knowing_score {
   EIGEN_EMPTY_STRUCT_CTOR(abs_knowing_score)
   typedef typename NumTraits<Scalar>::Real result_type;
-  template<typename Score>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a, const Score&) const { return numext::abs(a); }
+  template <typename Score>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type
+  operator()(const Scalar& a, const Score&) const {
+    return numext::abs(a);
+  }
 };
-template<typename Scalar> struct abs_knowing_score<Scalar, typename scalar_score_coeff_op<Scalar>::Score_is_abs>
-{
+template <typename Scalar>
+struct abs_knowing_score<Scalar,
+                         typename scalar_score_coeff_op<Scalar>::Score_is_abs> {
   EIGEN_EMPTY_STRUCT_CTOR(abs_knowing_score)
   typedef typename NumTraits<Scalar>::Real result_type;
-  template<typename Scal>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scal&, const result_type& a) const { return a; }
+  template <typename Scal>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type
+  operator()(const Scal&, const result_type& a) const {
+    return a;
+  }
 };
 
 /** \internal
-  * \brief Template functor to compute the squared absolute value of a scalar
-  *
-  * \sa class CwiseUnaryOp, Cwise::abs2
-  */
-template<typename Scalar> struct scalar_abs2_op {
+ * \brief Template functor to compute the squared absolute value of a scalar
+ *
+ * \sa class CwiseUnaryOp, Cwise::abs2
+ */
+template <typename Scalar>
+struct scalar_abs2_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_abs2_op)
   typedef typename NumTraits<Scalar>::Real result_type;
   EIGEN_DEVICE_FUNC
-  EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return numext::abs2(a); }
-  template<typename Packet>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
-  { return internal::pmul(a,a); }
+  EIGEN_STRONG_INLINE const result_type operator()(const Scalar& a) const {
+    return numext::abs2(a);
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet
+  packetOp(const Packet& a) const {
+    return internal::pmul(a, a);
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_abs2_op<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::MulCost,
+    PacketAccess = packet_traits<Scalar>::HasAbs2
+  };
 };
-template<typename Scalar>
-struct functor_traits<scalar_abs2_op<Scalar> >
-{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasAbs2 }; };
 
 /** \internal
-  * \brief Template functor to compute the conjugate of a complex value
-  *
-  * \sa class CwiseUnaryOp, MatrixBase::conjugate()
-  */
-template<typename Scalar> struct scalar_conjugate_op {
+ * \brief Template functor to compute the conjugate of a complex value
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::conjugate()
+ */
+template <typename Scalar>
+struct scalar_conjugate_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_conjugate_op)
   EIGEN_DEVICE_FUNC
-  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { using numext::conj; return conj(a); }
-  template<typename Packet>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const { return internal::pconj(a); }
+  EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& a) const {
+    using numext::conj;
+    return conj(a);
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet
+  packetOp(const Packet& a) const {
+    return internal::pconj(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_conjugate_op<Scalar> >
-{
+template <typename Scalar>
+struct functor_traits<scalar_conjugate_op<Scalar> > {
   enum {
     Cost = NumTraits<Scalar>::IsComplex ? NumTraits<Scalar>::AddCost : 0,
     PacketAccess = packet_traits<Scalar>::HasConj
@@ -123,221 +159,281 @@ struct functor_traits<scalar_conjugate_op<Scalar> >
 };
 
 /** \internal
-  * \brief Template functor to compute the phase angle of a complex
-  *
-  * \sa class CwiseUnaryOp, Cwise::arg
-  */
-template<typename Scalar> struct scalar_arg_op {
+ * \brief Template functor to compute the phase angle of a complex
+ *
+ * \sa class CwiseUnaryOp, Cwise::arg
+ */
+template <typename Scalar>
+struct scalar_arg_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_arg_op)
   typedef typename NumTraits<Scalar>::Real result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { using numext::arg; return arg(a); }
-  template<typename Packet>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
-  { return internal::parg(a); }
-};
-template<typename Scalar>
-struct functor_traits<scalar_arg_op<Scalar> >
-{
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type
+  operator()(const Scalar& a) const {
+    using numext::arg;
+    return arg(a);
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet
+  packetOp(const Packet& a) const {
+    return internal::parg(a);
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_arg_op<Scalar> > {
   enum {
-    Cost = NumTraits<Scalar>::IsComplex ? 5 * NumTraits<Scalar>::MulCost : NumTraits<Scalar>::AddCost,
+    Cost = NumTraits<Scalar>::IsComplex ? 5 * NumTraits<Scalar>::MulCost
+                                        : NumTraits<Scalar>::AddCost,
     PacketAccess = packet_traits<Scalar>::HasArg
   };
 };
 /** \internal
-  * \brief Template functor to cast a scalar to another type
-  *
-  * \sa class CwiseUnaryOp, MatrixBase::cast()
-  */
-template<typename Scalar, typename NewType>
+ * \brief Template functor to cast a scalar to another type
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::cast()
+ */
+template <typename Scalar, typename NewType>
 struct scalar_cast_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cast_op)
   typedef NewType result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const NewType operator() (const Scalar& a) const { return cast<Scalar, NewType>(a); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const NewType
+  operator()(const Scalar& a) const {
+    return cast<Scalar, NewType>(a);
+  }
+};
+template <typename Scalar, typename NewType>
+struct functor_traits<scalar_cast_op<Scalar, NewType> > {
+  enum {
+    Cost = is_same<Scalar, NewType>::value ? 0 : NumTraits<NewType>::AddCost,
+    PacketAccess = false
+  };
 };
-template<typename Scalar, typename NewType>
-struct functor_traits<scalar_cast_op<Scalar,NewType> >
-{ enum { Cost = is_same<Scalar, NewType>::value ? 0 : NumTraits<NewType>::AddCost, PacketAccess = false }; };
 
 /** \internal
-  * \brief Template functor to extract the real part of a complex
-  *
-  * \sa class CwiseUnaryOp, MatrixBase::real()
-  */
-template<typename Scalar>
+ * \brief Template functor to extract the real part of a complex
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::real()
+ */
+template <typename Scalar>
 struct scalar_real_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_real_op)
   typedef typename NumTraits<Scalar>::Real result_type;
   EIGEN_DEVICE_FUNC
-  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return numext::real(a); }
+  EIGEN_STRONG_INLINE result_type operator()(const Scalar& a) const {
+    return numext::real(a);
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_real_op<Scalar> > {
+  enum { Cost = 0, PacketAccess = false };
 };
-template<typename Scalar>
-struct functor_traits<scalar_real_op<Scalar> >
-{ enum { Cost = 0, PacketAccess = false }; };
 
 /** \internal
-  * \brief Template functor to extract the imaginary part of a complex
-  *
-  * \sa class CwiseUnaryOp, MatrixBase::imag()
-  */
-template<typename Scalar>
+ * \brief Template functor to extract the imaginary part of a complex
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::imag()
+ */
+template <typename Scalar>
 struct scalar_imag_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_imag_op)
   typedef typename NumTraits<Scalar>::Real result_type;
   EIGEN_DEVICE_FUNC
-  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return numext::imag(a); }
+  EIGEN_STRONG_INLINE result_type operator()(const Scalar& a) const {
+    return numext::imag(a);
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_imag_op<Scalar> > {
+  enum { Cost = 0, PacketAccess = false };
 };
-template<typename Scalar>
-struct functor_traits<scalar_imag_op<Scalar> >
-{ enum { Cost = 0, PacketAccess = false }; };
 
 /** \internal
-  * \brief Template functor to extract the real part of a complex as a reference
-  *
-  * \sa class CwiseUnaryOp, MatrixBase::real()
-  */
-template<typename Scalar>
+ * \brief Template functor to extract the real part of a complex as a reference
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::real()
+ */
+template <typename Scalar>
 struct scalar_real_ref_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_real_ref_op)
   typedef typename NumTraits<Scalar>::Real result_type;
   EIGEN_DEVICE_FUNC
-  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return numext::real_ref(*const_cast<Scalar*>(&a)); }
+  EIGEN_STRONG_INLINE result_type& operator()(const Scalar& a) const {
+    return numext::real_ref(*const_cast<Scalar*>(&a));
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_real_ref_op<Scalar> > {
+  enum { Cost = 0, PacketAccess = false };
 };
-template<typename Scalar>
-struct functor_traits<scalar_real_ref_op<Scalar> >
-{ enum { Cost = 0, PacketAccess = false }; };
 
 /** \internal
-  * \brief Template functor to extract the imaginary part of a complex as a reference
-  *
-  * \sa class CwiseUnaryOp, MatrixBase::imag()
-  */
-template<typename Scalar>
+ * \brief Template functor to extract the imaginary part of a complex as a
+ * reference
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::imag()
+ */
+template <typename Scalar>
 struct scalar_imag_ref_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_imag_ref_op)
   typedef typename NumTraits<Scalar>::Real result_type;
   EIGEN_DEVICE_FUNC
-  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return numext::imag_ref(*const_cast<Scalar*>(&a)); }
+  EIGEN_STRONG_INLINE result_type& operator()(const Scalar& a) const {
+    return numext::imag_ref(*const_cast<Scalar*>(&a));
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_imag_ref_op<Scalar> > {
+  enum { Cost = 0, PacketAccess = false };
 };
-template<typename Scalar>
-struct functor_traits<scalar_imag_ref_op<Scalar> >
-{ enum { Cost = 0, PacketAccess = false }; };
 
 /** \internal
-  *
-  * \brief Template functor to compute the exponential of a scalar
-  *
-  * \sa class CwiseUnaryOp, Cwise::exp()
-  */
-template<typename Scalar> struct scalar_exp_op {
+ *
+ * \brief Template functor to compute the exponential of a scalar
+ *
+ * \sa class CwiseUnaryOp, Cwise::exp()
+ */
+template <typename Scalar>
+struct scalar_exp_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_exp_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::exp(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    return numext::exp(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pexp(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::pexp(a);
+  }
 };
 template <typename Scalar>
 struct functor_traits<scalar_exp_op<Scalar> > {
   enum {
     PacketAccess = packet_traits<Scalar>::HasExp,
-    // The following numbers are based on the AVX implementation.
+  // The following numbers are based on the AVX implementation.
 #ifdef EIGEN_VECTORIZE_FMA
     // Haswell can issue 2 add/mul/madd per cycle.
     Cost =
-    (sizeof(Scalar) == 4
-     // float: 8 pmadd, 4 pmul, 2 padd/psub, 6 other
-     ? (8 * NumTraits<Scalar>::AddCost + 6 * NumTraits<Scalar>::MulCost)
-     // double: 7 pmadd, 5 pmul, 3 padd/psub, 1 div,  13 other
-     : (14 * NumTraits<Scalar>::AddCost +
-        6 * NumTraits<Scalar>::MulCost +
-        scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value))
+        (sizeof(Scalar) == 4
+             // float: 8 pmadd, 4 pmul, 2 padd/psub, 6 other
+             ? (8 * NumTraits<Scalar>::AddCost + 6 * NumTraits<Scalar>::MulCost)
+             // double: 7 pmadd, 5 pmul, 3 padd/psub, 1 div,  13 other
+             : (14 * NumTraits<Scalar>::AddCost +
+                6 * NumTraits<Scalar>::MulCost +
+                scalar_div_cost<Scalar, packet_traits<Scalar>::HasDiv>::value))
 #else
     Cost =
-    (sizeof(Scalar) == 4
-     // float: 7 pmadd, 6 pmul, 4 padd/psub, 10 other
-     ? (21 * NumTraits<Scalar>::AddCost + 13 * NumTraits<Scalar>::MulCost)
-     // double: 7 pmadd, 5 pmul, 3 padd/psub, 1 div,  13 other
-     : (23 * NumTraits<Scalar>::AddCost +
-        12 * NumTraits<Scalar>::MulCost +
-        scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value))
+        (sizeof(Scalar) == 4
+             // float: 7 pmadd, 6 pmul, 4 padd/psub, 10 other
+             ? (21 * NumTraits<Scalar>::AddCost +
+                13 * NumTraits<Scalar>::MulCost)
+             // double: 7 pmadd, 5 pmul, 3 padd/psub, 1 div,  13 other
+             : (23 * NumTraits<Scalar>::AddCost +
+                12 * NumTraits<Scalar>::MulCost +
+                scalar_div_cost<Scalar, packet_traits<Scalar>::HasDiv>::value))
 #endif
   };
 };
 
 /** \internal
-  *
-  * \brief Template functor to compute the logarithm of a scalar
-  *
-  * \sa class CwiseUnaryOp, ArrayBase::log()
-  */
-template<typename Scalar> struct scalar_log_op {
+ *
+ * \brief Template functor to compute the logarithm of a scalar
+ *
+ * \sa class CwiseUnaryOp, ArrayBase::log()
+ */
+template <typename Scalar>
+struct scalar_log_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_log_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::log(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    return numext::log(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::plog(a);
+  }
 };
 template <typename Scalar>
 struct functor_traits<scalar_log_op<Scalar> > {
   enum {
     PacketAccess = packet_traits<Scalar>::HasLog,
-    Cost =
-    (PacketAccess
-     // The following numbers are based on the AVX implementation.
+    Cost = (PacketAccess
+  // The following numbers are based on the AVX implementation.
 #ifdef EIGEN_VECTORIZE_FMA
-     // 8 pmadd, 6 pmul, 8 padd/psub, 16 other, can issue 2 add/mul/madd per cycle.
-     ? (20 * NumTraits<Scalar>::AddCost + 7 * NumTraits<Scalar>::MulCost)
+                // 8 pmadd, 6 pmul, 8 padd/psub, 16 other, can issue 2
+                // add/mul/madd per cycle.
+                ? (20 * NumTraits<Scalar>::AddCost +
+                   7 * NumTraits<Scalar>::MulCost)
 #else
-     // 8 pmadd, 6 pmul, 8 padd/psub, 20 other
-     ? (36 * NumTraits<Scalar>::AddCost + 14 * NumTraits<Scalar>::MulCost)
+                // 8 pmadd, 6 pmul, 8 padd/psub, 20 other
+                ? (36 * NumTraits<Scalar>::AddCost +
+                   14 * NumTraits<Scalar>::MulCost)
 #endif
-     // Measured cost of std::log.
-     : sizeof(Scalar)==4 ? 40 : 85)
+                // Measured cost of std::log.
+                : sizeof(Scalar) == 4 ? 40 : 85)
   };
 };
 
 /** \internal
-  *
-  * \brief Template functor to compute the logarithm of 1 plus a scalar value
-  *
-  * \sa class CwiseUnaryOp, ArrayBase::log1p()
-  */
-template<typename Scalar> struct scalar_log1p_op {
+ *
+ * \brief Template functor to compute the logarithm of 1 plus a scalar value
+ *
+ * \sa class CwiseUnaryOp, ArrayBase::log1p()
+ */
+template <typename Scalar>
+struct scalar_log1p_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_log1p_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::log1p(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    return numext::log1p(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog1p(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::plog1p(a);
+  }
 };
 template <typename Scalar>
 struct functor_traits<scalar_log1p_op<Scalar> > {
   enum {
     PacketAccess = packet_traits<Scalar>::HasLog1p,
-    Cost = functor_traits<scalar_log_op<Scalar> >::Cost // TODO measure cost of log1p
+    Cost = functor_traits<scalar_log_op<Scalar> >::Cost  // TODO measure cost of
+                                                         // log1p
   };
 };
 
 /** \internal
-  *
-  * \brief Template functor to compute the base-10 logarithm of a scalar
-  *
-  * \sa class CwiseUnaryOp, Cwise::log10()
-  */
-template<typename Scalar> struct scalar_log10_op {
+ *
+ * \brief Template functor to compute the base-10 logarithm of a scalar
+ *
+ * \sa class CwiseUnaryOp, Cwise::log10()
+ */
+template <typename Scalar>
+struct scalar_log10_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_log10_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { EIGEN_USING_STD_MATH(log10) return log10(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    EIGEN_USING_STD_MATH(log10) return log10(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog10(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::plog10(a);
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_log10_op<Scalar> > {
+  enum {
+    Cost = 5 * NumTraits<Scalar>::MulCost,
+    PacketAccess = packet_traits<Scalar>::HasLog10
+  };
 };
-template<typename Scalar>
-struct functor_traits<scalar_log10_op<Scalar> >
-{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasLog10 }; };
 
 /** \internal
-  * \brief Template functor to compute the square root of a scalar
-  * \sa class CwiseUnaryOp, Cwise::sqrt()
-  */
-template<typename Scalar> struct scalar_sqrt_op {
+ * \brief Template functor to compute the square root of a scalar
+ * \sa class CwiseUnaryOp, Cwise::sqrt()
+ */
+template <typename Scalar>
+struct scalar_sqrt_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_sqrt_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::sqrt(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    return numext::sqrt(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psqrt(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::psqrt(a);
+  }
 };
 template <typename Scalar>
 struct functor_traits<scalar_sqrt_op<Scalar> > {
@@ -357,37 +453,46 @@ struct functor_traits<scalar_sqrt_op<Scalar> > {
 };
 
 /** \internal
-  * \brief Template functor to compute the reciprocal square root of a scalar
-  * \sa class CwiseUnaryOp, Cwise::rsqrt()
-  */
-template<typename Scalar> struct scalar_rsqrt_op {
+ * \brief Template functor to compute the reciprocal square root of a scalar
+ * \sa class CwiseUnaryOp, Cwise::rsqrt()
+ */
+template <typename Scalar>
+struct scalar_rsqrt_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_rsqrt_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return Scalar(1)/numext::sqrt(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    return Scalar(1) / numext::sqrt(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::prsqrt(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::prsqrt(a);
+  }
 };
 
-template<typename Scalar>
-struct functor_traits<scalar_rsqrt_op<Scalar> >
-{ enum {
+template <typename Scalar>
+struct functor_traits<scalar_rsqrt_op<Scalar> > {
+  enum {
     Cost = 5 * NumTraits<Scalar>::MulCost,
     PacketAccess = packet_traits<Scalar>::HasRsqrt
   };
 };
 
 /** \internal
-  * \brief Template functor to compute the cosine of a scalar
-  * \sa class CwiseUnaryOp, ArrayBase::cos()
-  */
-template<typename Scalar> struct scalar_cos_op {
+ * \brief Template functor to compute the cosine of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::cos()
+ */
+template <typename Scalar>
+struct scalar_cos_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cos_op)
-  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return numext::cos(a); }
+  EIGEN_DEVICE_FUNC inline Scalar operator()(const Scalar& a) const {
+    return numext::cos(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pcos(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::pcos(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_cos_op<Scalar> >
-{
+template <typename Scalar>
+struct functor_traits<scalar_cos_op<Scalar> > {
   enum {
     Cost = 5 * NumTraits<Scalar>::MulCost,
     PacketAccess = packet_traits<Scalar>::HasCos
@@ -395,38 +500,45 @@ struct functor_traits<scalar_cos_op<Scalar> >
 };
 
 /** \internal
-  * \brief Template functor to compute the sine of a scalar
-  * \sa class CwiseUnaryOp, ArrayBase::sin()
-  */
-template<typename Scalar> struct scalar_sin_op {
+ * \brief Template functor to compute the sine of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::sin()
+ */
+template <typename Scalar>
+struct scalar_sin_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_sin_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::sin(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    return numext::sin(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psin(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::psin(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_sin_op<Scalar> >
-{
+template <typename Scalar>
+struct functor_traits<scalar_sin_op<Scalar> > {
   enum {
     Cost = 5 * NumTraits<Scalar>::MulCost,
     PacketAccess = packet_traits<Scalar>::HasSin
   };
 };
 
-
 /** \internal
-  * \brief Template functor to compute the tan of a scalar
-  * \sa class CwiseUnaryOp, ArrayBase::tan()
-  */
-template<typename Scalar> struct scalar_tan_op {
+ * \brief Template functor to compute the tan of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::tan()
+ */
+template <typename Scalar>
+struct scalar_tan_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_tan_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::tan(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    return numext::tan(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::ptan(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::ptan(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_tan_op<Scalar> >
-{
+template <typename Scalar>
+struct functor_traits<scalar_tan_op<Scalar> > {
   enum {
     Cost = 5 * NumTraits<Scalar>::MulCost,
     PacketAccess = packet_traits<Scalar>::HasTan
@@ -434,18 +546,22 @@ struct functor_traits<scalar_tan_op<Scalar> >
 };
 
 /** \internal
-  * \brief Template functor to compute the arc cosine of a scalar
-  * \sa class CwiseUnaryOp, ArrayBase::acos()
-  */
-template<typename Scalar> struct scalar_acos_op {
+ * \brief Template functor to compute the arc cosine of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::acos()
+ */
+template <typename Scalar>
+struct scalar_acos_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_acos_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::acos(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    return numext::acos(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pacos(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::pacos(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_acos_op<Scalar> >
-{
+template <typename Scalar>
+struct functor_traits<scalar_acos_op<Scalar> > {
   enum {
     Cost = 5 * NumTraits<Scalar>::MulCost,
     PacketAccess = packet_traits<Scalar>::HasACos
@@ -453,38 +569,45 @@ struct functor_traits<scalar_acos_op<Scalar> >
 };
 
 /** \internal
-  * \brief Template functor to compute the arc sine of a scalar
-  * \sa class CwiseUnaryOp, ArrayBase::asin()
-  */
-template<typename Scalar> struct scalar_asin_op {
+ * \brief Template functor to compute the arc sine of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::asin()
+ */
+template <typename Scalar>
+struct scalar_asin_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_asin_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::asin(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    return numext::asin(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pasin(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::pasin(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_asin_op<Scalar> >
-{
+template <typename Scalar>
+struct functor_traits<scalar_asin_op<Scalar> > {
   enum {
     Cost = 5 * NumTraits<Scalar>::MulCost,
     PacketAccess = packet_traits<Scalar>::HasASin
   };
 };
 
-
 /** \internal
-  * \brief Template functor to compute the atan of a scalar
-  * \sa class CwiseUnaryOp, ArrayBase::atan()
-  */
-template<typename Scalar> struct scalar_atan_op {
+ * \brief Template functor to compute the atan of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::atan()
+ */
+template <typename Scalar>
+struct scalar_atan_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_atan_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::atan(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    return numext::atan(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::patan(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::patan(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_atan_op<Scalar> >
-{
+template <typename Scalar>
+struct functor_traits<scalar_atan_op<Scalar> > {
   enum {
     Cost = 5 * NumTraits<Scalar>::MulCost,
     PacketAccess = packet_traits<Scalar>::HasATan
@@ -492,55 +615,65 @@ struct functor_traits<scalar_atan_op<Scalar> >
 };
 
 /** \internal
-  * \brief Template functor to compute the tanh of a scalar
-  * \sa class CwiseUnaryOp, ArrayBase::tanh()
-  */
+ * \brief Template functor to compute the tanh of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::tanh()
+ */
 template <typename Scalar>
 struct scalar_tanh_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_tanh_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const { return numext::tanh(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    return numext::tanh(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& x) const { return ptanh(x); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& x) const {
+    return ptanh(x);
+  }
 };
 
 template <typename Scalar>
 struct functor_traits<scalar_tanh_op<Scalar> > {
   enum {
     PacketAccess = packet_traits<Scalar>::HasTanh,
-    Cost = ( (EIGEN_FAST_MATH && is_same<Scalar,float>::value)
+    Cost =
+        ((EIGEN_FAST_MATH && is_same<Scalar, float>::value)
 // The following numbers are based on the AVX implementation,
 #ifdef EIGEN_VECTORIZE_FMA
-                // Haswell can issue 2 add/mul/madd per cycle.
-                // 9 pmadd, 2 pmul, 1 div, 2 other
-                ? (2 * NumTraits<Scalar>::AddCost +
-                   6 * NumTraits<Scalar>::MulCost +
-                   scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value)
+             // Haswell can issue 2 add/mul/madd per cycle.
+             // 9 pmadd, 2 pmul, 1 div, 2 other
+             ? (2 * NumTraits<Scalar>::AddCost +
+                6 * NumTraits<Scalar>::MulCost +
+                scalar_div_cost<Scalar, packet_traits<Scalar>::HasDiv>::value)
 #else
-                ? (11 * NumTraits<Scalar>::AddCost +
-                   11 * NumTraits<Scalar>::MulCost +
-                   scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value)
+             ? (11 * NumTraits<Scalar>::AddCost +
+                11 * NumTraits<Scalar>::MulCost +
+                scalar_div_cost<Scalar, packet_traits<Scalar>::HasDiv>::value)
 #endif
-                // This number assumes a naive implementation of tanh
-                : (6 * NumTraits<Scalar>::AddCost +
-                   3 * NumTraits<Scalar>::MulCost +
-                   2 * scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value +
-                   functor_traits<scalar_exp_op<Scalar> >::Cost))
+             // This number assumes a naive implementation of tanh
+             : (6 * NumTraits<Scalar>::AddCost +
+                3 * NumTraits<Scalar>::MulCost +
+                2 * scalar_div_cost<Scalar,
+                                    packet_traits<Scalar>::HasDiv>::value +
+                functor_traits<scalar_exp_op<Scalar> >::Cost))
   };
 };
 
 /** \internal
-  * \brief Template functor to compute the sinh of a scalar
-  * \sa class CwiseUnaryOp, ArrayBase::sinh()
-  */
-template<typename Scalar> struct scalar_sinh_op {
+ * \brief Template functor to compute the sinh of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::sinh()
+ */
+template <typename Scalar>
+struct scalar_sinh_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_sinh_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::sinh(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    return numext::sinh(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psinh(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::psinh(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_sinh_op<Scalar> >
-{
+template <typename Scalar>
+struct functor_traits<scalar_sinh_op<Scalar> > {
   enum {
     Cost = 5 * NumTraits<Scalar>::MulCost,
     PacketAccess = packet_traits<Scalar>::HasSinh
@@ -548,18 +681,22 @@ struct functor_traits<scalar_sinh_op<Scalar> >
 };
 
 /** \internal
-  * \brief Template functor to compute the cosh of a scalar
-  * \sa class CwiseUnaryOp, ArrayBase::cosh()
-  */
-template<typename Scalar> struct scalar_cosh_op {
+ * \brief Template functor to compute the cosh of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::cosh()
+ */
+template <typename Scalar>
+struct scalar_cosh_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cosh_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::cosh(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    return numext::cosh(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pcosh(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::pcosh(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_cosh_op<Scalar> >
-{
+template <typename Scalar>
+struct functor_traits<scalar_cosh_op<Scalar> > {
   enum {
     Cost = 5 * NumTraits<Scalar>::MulCost,
     PacketAccess = packet_traits<Scalar>::HasCosh
@@ -567,66 +704,92 @@ struct functor_traits<scalar_cosh_op<Scalar> >
 };
 
 /** \internal
-  * \brief Template functor to compute the inverse of a scalar
-  * \sa class CwiseUnaryOp, Cwise::inverse()
-  */
-template<typename Scalar>
+ * \brief Template functor to compute the inverse of a scalar
+ * \sa class CwiseUnaryOp, Cwise::inverse()
+ */
+template <typename Scalar>
 struct scalar_inverse_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_inverse_op)
-  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return Scalar(1)/a; }
-  template<typename Packet>
-  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
-  { return internal::pdiv(pset1<Packet>(Scalar(1)),a); }
+  EIGEN_DEVICE_FUNC inline Scalar operator()(const Scalar& a) const {
+    return Scalar(1) / a;
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const {
+    return internal::pdiv(pset1<Packet>(Scalar(1)), a);
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_inverse_op<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::MulCost,
+    PacketAccess = packet_traits<Scalar>::HasDiv
+  };
 };
-template<typename Scalar>
-struct functor_traits<scalar_inverse_op<Scalar> >
-{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasDiv }; };
 
 /** \internal
-  * \brief Template functor to compute the square of a scalar
-  * \sa class CwiseUnaryOp, Cwise::square()
-  */
-template<typename Scalar>
+ * \brief Template functor to compute the square of a scalar
+ * \sa class CwiseUnaryOp, Cwise::square()
+ */
+template <typename Scalar>
 struct scalar_square_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_square_op)
-  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return a*a; }
-  template<typename Packet>
-  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
-  { return internal::pmul(a,a); }
+  EIGEN_DEVICE_FUNC inline Scalar operator()(const Scalar& a) const {
+    return a * a;
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const {
+    return internal::pmul(a, a);
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_square_op<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::MulCost,
+    PacketAccess = packet_traits<Scalar>::HasMul
+  };
 };
-template<typename Scalar>
-struct functor_traits<scalar_square_op<Scalar> >
-{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
 
 /** \internal
-  * \brief Template functor to compute the cube of a scalar
-  * \sa class CwiseUnaryOp, Cwise::cube()
-  */
-template<typename Scalar>
+ * \brief Template functor to compute the cube of a scalar
+ * \sa class CwiseUnaryOp, Cwise::cube()
+ */
+template <typename Scalar>
 struct scalar_cube_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cube_op)
-  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return a*a*a; }
-  template<typename Packet>
-  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
-  { return internal::pmul(a,pmul(a,a)); }
+  EIGEN_DEVICE_FUNC inline Scalar operator()(const Scalar& a) const {
+    return a * a * a;
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const {
+    return internal::pmul(a, pmul(a, a));
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_cube_op<Scalar> > {
+  enum {
+    Cost = 2 * NumTraits<Scalar>::MulCost,
+    PacketAccess = packet_traits<Scalar>::HasMul
+  };
 };
-template<typename Scalar>
-struct functor_traits<scalar_cube_op<Scalar> >
-{ enum { Cost = 2*NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
 
 /** \internal
-  * \brief Template functor to compute the rounded value of a scalar
-  * \sa class CwiseUnaryOp, ArrayBase::round()
-  */
-template<typename Scalar> struct scalar_round_op {
+ * \brief Template functor to compute the rounded value of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::round()
+ */
+template <typename Scalar>
+struct scalar_round_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_round_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::round(a); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar
+  operator()(const Scalar& a) const {
+    return numext::round(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pround(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::pround(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_round_op<Scalar> >
-{
+template <typename Scalar>
+struct functor_traits<scalar_round_op<Scalar> > {
   enum {
     Cost = NumTraits<Scalar>::MulCost,
     PacketAccess = packet_traits<Scalar>::HasRound
@@ -634,18 +797,23 @@ struct functor_traits<scalar_round_op<Scalar> >
 };
 
 /** \internal
-  * \brief Template functor to compute the floor of a scalar
-  * \sa class CwiseUnaryOp, ArrayBase::floor()
-  */
-template<typename Scalar> struct scalar_floor_op {
+ * \brief Template functor to compute the floor of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::floor()
+ */
+template <typename Scalar>
+struct scalar_floor_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_floor_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::floor(a); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar
+  operator()(const Scalar& a) const {
+    return numext::floor(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pfloor(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::pfloor(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_floor_op<Scalar> >
-{
+template <typename Scalar>
+struct functor_traits<scalar_floor_op<Scalar> > {
   enum {
     Cost = NumTraits<Scalar>::MulCost,
     PacketAccess = packet_traits<Scalar>::HasFloor
@@ -653,18 +821,23 @@ struct functor_traits<scalar_floor_op<Scalar> >
 };
 
 /** \internal
-  * \brief Template functor to compute the ceil of a scalar
-  * \sa class CwiseUnaryOp, ArrayBase::ceil()
-  */
-template<typename Scalar> struct scalar_ceil_op {
+ * \brief Template functor to compute the ceil of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::ceil()
+ */
+template <typename Scalar>
+struct scalar_ceil_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_ceil_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::ceil(a); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar
+  operator()(const Scalar& a) const {
+    return numext::ceil(a);
+  }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pceil(a); }
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+    return internal::pceil(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_ceil_op<Scalar> >
-{
+template <typename Scalar>
+struct functor_traits<scalar_ceil_op<Scalar> > {
   enum {
     Cost = NumTraits<Scalar>::MulCost,
     PacketAccess = packet_traits<Scalar>::HasCeil
@@ -672,121 +845,210 @@ struct functor_traits<scalar_ceil_op<Scalar> >
 };
 
 /** \internal
-  * \brief Template functor to compute whether a scalar is NaN
-  * \sa class CwiseUnaryOp, ArrayBase::isnan()
-  */
-template<typename Scalar> struct scalar_isnan_op {
+ * \brief Template functor to compute whether a scalar is NaN
+ * \sa class CwiseUnaryOp, ArrayBase::isnan()
+ */
+template <typename Scalar>
+struct scalar_isnan_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_isnan_op)
   typedef bool result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return (numext::isnan)(a); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type
+  operator()(const Scalar& a) const {
+    return (numext::isnan)(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_isnan_op<Scalar> >
-{
-  enum {
-    Cost = NumTraits<Scalar>::MulCost,
-    PacketAccess = false
-  };
+template <typename Scalar>
+struct functor_traits<scalar_isnan_op<Scalar> > {
+  enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = false };
 };
 
 /** \internal
-  * \brief Template functor to check whether a scalar is +/-inf
-  * \sa class CwiseUnaryOp, ArrayBase::isinf()
-  */
-template<typename Scalar> struct scalar_isinf_op {
+ * \brief Template functor to check whether a scalar is +/-inf
+ * \sa class CwiseUnaryOp, ArrayBase::isinf()
+ */
+template <typename Scalar>
+struct scalar_isinf_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_isinf_op)
   typedef bool result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return (numext::isinf)(a); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type
+  operator()(const Scalar& a) const {
+    return (numext::isinf)(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_isinf_op<Scalar> >
-{
-  enum {
-    Cost = NumTraits<Scalar>::MulCost,
-    PacketAccess = false
-  };
+template <typename Scalar>
+struct functor_traits<scalar_isinf_op<Scalar> > {
+  enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = false };
 };
 
 /** \internal
-  * \brief Template functor to check whether a scalar has a finite value
-  * \sa class CwiseUnaryOp, ArrayBase::isfinite()
-  */
-template<typename Scalar> struct scalar_isfinite_op {
+ * \brief Template functor to check whether a scalar has a finite value
+ * \sa class CwiseUnaryOp, ArrayBase::isfinite()
+ */
+template <typename Scalar>
+struct scalar_isfinite_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_isfinite_op)
   typedef bool result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return (numext::isfinite)(a); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type
+  operator()(const Scalar& a) const {
+    return (numext::isfinite)(a);
+  }
 };
-template<typename Scalar>
-struct functor_traits<scalar_isfinite_op<Scalar> >
-{
-  enum {
-    Cost = NumTraits<Scalar>::MulCost,
-    PacketAccess = false
-  };
+template <typename Scalar>
+struct functor_traits<scalar_isfinite_op<Scalar> > {
+  enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = false };
 };
 
 /** \internal
-  * \brief Template functor to compute the logical not of a boolean
-  *
-  * \sa class CwiseUnaryOp, ArrayBase::operator!
-  */
-template<typename Scalar> struct scalar_boolean_not_op {
+ * \brief Template functor to compute the logical not of a boolean
+ *
+ * \sa class CwiseUnaryOp, ArrayBase::operator!
+ */
+template <typename Scalar>
+struct scalar_boolean_not_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_not_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a) const { return !a; }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const bool& a) const {
+    return !a;
+  }
 };
-template<typename Scalar>
+template <typename Scalar>
 struct functor_traits<scalar_boolean_not_op<Scalar> > {
-  enum {
-    Cost = NumTraits<bool>::AddCost,
-    PacketAccess = false
-  };
+  enum { Cost = NumTraits<bool>::AddCost, PacketAccess = false };
 };
 
 /** \internal
-  * \brief Template functor to compute the signum of a scalar
-  * \sa class CwiseUnaryOp, Cwise::sign()
-  */
-template<typename Scalar,bool iscpx=(NumTraits<Scalar>::IsComplex!=0) > struct scalar_sign_op;
-template<typename Scalar>
-struct scalar_sign_op<Scalar,false> {
+ * \brief Template functor to compute the signum of a scalar
+ * \sa class CwiseUnaryOp, Cwise::sign()
+ */
+template <typename Scalar, bool iscpx = (NumTraits<Scalar>::IsComplex != 0)>
+struct scalar_sign_op;
+template <typename Scalar>
+struct scalar_sign_op<Scalar, false> {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_sign_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const
-  {
-      return Scalar( (a>Scalar(0)) - (a<Scalar(0)) );
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
+    return Scalar((a > Scalar(0)) - (a < Scalar(0)));
   }
-  //TODO
-  //template <typename Packet>
-  //EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psign(a); }
+  // TODO
+  // template <typename Packet>
+  // EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return
+  // internal::psign(a); }
 };
-template<typename Scalar>
-struct scalar_sign_op<Scalar,true> {
+template <typename Scalar>
+struct scalar_sign_op<Scalar, true> {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_sign_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const
-  {
+  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
     typedef typename NumTraits<Scalar>::Real real_type;
     real_type aa = numext::abs(a);
-    if (aa==real_type(0))
-      return Scalar(0);
-    aa = real_type(1)/aa;
-    return Scalar(real(a)*aa, imag(a)*aa );
-  }
-  //TODO
-  //template <typename Packet>
-  //EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psign(a); }
-};
-template<typename Scalar>
-struct functor_traits<scalar_sign_op<Scalar> >
-{ enum {
-    Cost = 
-        NumTraits<Scalar>::IsComplex
-        ? ( 8*NumTraits<Scalar>::MulCost  ) // roughly
-        : ( 3*NumTraits<Scalar>::AddCost),
+    if (aa == real_type(0)) return Scalar(0);
+    aa = real_type(1) / aa;
+    return Scalar(real(a) * aa, imag(a) * aa);
+  }
+  // TODO
+  // template <typename Packet>
+  // EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return
+  // internal::psign(a); }
+};
+template <typename Scalar>
+struct functor_traits<scalar_sign_op<Scalar> > {
+  enum {
+    Cost = NumTraits<Scalar>::IsComplex
+               ? (8 * NumTraits<Scalar>::MulCost)  // roughly
+               : (3 * NumTraits<Scalar>::AddCost),
     PacketAccess = packet_traits<Scalar>::HasSign
   };
 };
 
-} // end namespace internal
+/** \internal
+ * \brief Template functor to compute the logistic function of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::logistic()
+ */
+template <typename T>
+struct scalar_logistic_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_logistic_op)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T operator()(const T& x) const {
+    const T one = T(1);
+    return one / (one + numext::exp(-x));
+  }
+
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+    const Packet one = pset1<Packet>(T(1));
+    return pdiv(one, padd(one, pexp(pnegate(x))));
+  }
+};
+template <typename T>
+struct functor_traits<scalar_logistic_op<T> > {
+  enum {
+    Cost = NumTraits<T>::AddCost * 2 + NumTraits<T>::MulCost * 6,
+    PacketAccess = packet_traits<T>::HasAdd && packet_traits<T>::HasDiv &&
+                   packet_traits<T>::HasNegate && packet_traits<T>::HasExp
+  };
+};
+
+/** \internal
+ * \brief Template specialization of the logistic function for float.
+ *
+ *  Uses just a 9/10-degree rational interpolant which
+ *  interpolates 1/(1+exp(-x)) - 0.5 up to a couple of ulp in the range
+ *  [-18, 18], outside of which the fl(logistic(x)) = {0|1}. The shifted
+ *  logistic is interpolated because it was easier to make the fit converge.
+ *
+ */
+
+template <>
+struct scalar_logistic_op<float> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_logistic_op)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float operator()(const float& x) const {
+    const float one = 1.0f;
+    return one / (one + numext::exp(-x));
+  }
+
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet
+  packetOp(const Packet& _x) const {
+    // Clamp the inputs to the range [-18, 18] since anything outside
+    // this range is 0.0f or 1.0f in single-precision.
+    const Packet x = pmax(pmin(_x, pset1<Packet>(18.0)), pset1<Packet>(-18.0));
+
+    // The monomial coefficients of the numerator polynomial (odd).
+    const Packet alpha_1 = pset1<Packet>(2.48287947061529e-01);
+    const Packet alpha_3 = pset1<Packet>(8.51377133304701e-03);
+    const Packet alpha_5 = pset1<Packet>(6.08574864600143e-05);
+    const Packet alpha_7 = pset1<Packet>(1.15627324459942e-07);
+    const Packet alpha_9 = pset1<Packet>(4.37031012579801e-11);
+
+    // The monomial coefficients of the denominator polynomial (even).
+    const Packet beta_0 = pset1<Packet>(9.93151921023180e-01);
+    const Packet beta_2 = pset1<Packet>(1.16817656904453e-01);
+    const Packet beta_4 = pset1<Packet>(1.70198817374094e-03);
+    const Packet beta_6 = pset1<Packet>(6.29106785017040e-06);
+    const Packet beta_8 = pset1<Packet>(5.76102136993427e-09);
+    const Packet beta_10 = pset1<Packet>(6.10247389755681e-13);
+
+    // Since the polynomials are odd/even, we need x^2.
+    const Packet x2 = pmul(x, x);
+
+    // Evaluate the numerator polynomial p.
+    Packet p = pmadd(x2, alpha_9, alpha_7);
+    p = pmadd(x2, p, alpha_5);
+    p = pmadd(x2, p, alpha_3);
+    p = pmadd(x2, p, alpha_1);
+    p = pmul(x, p);
+
+    // Evaluate the denominator polynomial p.
+    Packet q = pmadd(x2, beta_10, beta_8);
+    q = pmadd(x2, q, beta_6);
+    q = pmadd(x2, q, beta_4);
+    q = pmadd(x2, q, beta_2);
+    q = pmadd(x2, q, beta_0);
+
+    // Divide the numerator by the denominator and shift it up.
+    return pmax(pmin(padd(pdiv(p, q), pset1<Packet>(0.5)), pset1<Packet>(1.0)),
+                pset1<Packet>(0.0));
+  }
+};
+
+}  // end namespace internal
 
-} // end namespace Eigen
+}  // end namespace Eigen
 
-#endif // EIGEN_FUNCTORS_H
+#endif  // EIGEN_FUNCTORS_H
-- 
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