Eigen/src/Core/functors/NullaryFunctors.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_NULLARY_FUNCTORS_H
#define EIGEN_NULLARY_FUNCTORS_H

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

namespace Eigen {

namespace internal {

template <typename Scalar>
struct scalar_constant_op {
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_constant_op(const scalar_constant_op& other) : m_other(other.m_other) {}
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_constant_op(const Scalar& other) : m_other(other) {}
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()() const { return m_other; }
  template <typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const PacketType packetOp() const {
    return internal::pset1<PacketType>(m_other);
  }
  const Scalar m_other;
};
template <typename Scalar>
struct functor_traits<scalar_constant_op<Scalar> > {
  enum {
    Cost = 0 /* as the constant value should be loaded in register only once for the whole expression */,
    PacketAccess = packet_traits<Scalar>::Vectorizable,
    IsRepeatable = true
  };
};

template <typename Scalar>
struct scalar_identity_op {
  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(IndexType row, IndexType col) const {
    return row == col ? Scalar(1) : Scalar(0);
  }
};
template <typename Scalar>
struct functor_traits<scalar_identity_op<Scalar> > {
  enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = false, IsRepeatable = true };
};

template <typename Scalar, bool IsInteger>
struct linspaced_op_impl;

template <typename Scalar>
struct linspaced_op_impl<Scalar, /*IsInteger*/ false> {
  typedef typename NumTraits<Scalar>::Real RealScalar;

  EIGEN_DEVICE_FUNC linspaced_op_impl(const Scalar& low, const Scalar& high, Index num_steps)
      : m_low(low),
        m_high(high),
        m_size1(num_steps == 1 ? 1 : num_steps - 1),
        m_step(num_steps == 1 ? Scalar() : Scalar((high - low) / RealScalar(num_steps - 1))),
        m_flip(numext::abs(high) < numext::abs(low)) {}

  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(IndexType i) const {
    if (m_flip)
      return (i == 0) ? m_low : Scalar(m_high - RealScalar(m_size1 - i) * m_step);
    else
      return (i == m_size1) ? m_high : Scalar(m_low + RealScalar(i) * m_step);
  }

  template <typename Packet, typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(IndexType i) const {
    // Principle:
    // [low, ..., low] + ( [step, ..., step] * ( [i, ..., i] + [0, ..., size] ) )
    if (m_flip) {
      Packet pi = plset<Packet>(Scalar(i - m_size1));
      Packet res = padd(pset1<Packet>(m_high), pmul(pset1<Packet>(m_step), pi));
      if (EIGEN_PREDICT_TRUE(i != 0)) return res;
      Packet mask = pcmp_lt(pset1<Packet>(0), plset<Packet>(0));
      return pselect<Packet>(mask, res, pset1<Packet>(m_low));
    } else {
      Packet pi = plset<Packet>(Scalar(i));
      Packet res = padd(pset1<Packet>(m_low), pmul(pset1<Packet>(m_step), pi));
      if (EIGEN_PREDICT_TRUE(i != m_size1 - unpacket_traits<Packet>::size + 1)) return res;
      Packet mask = pcmp_lt(plset<Packet>(0), pset1<Packet>(unpacket_traits<Packet>::size - 1));
      return pselect<Packet>(mask, res, pset1<Packet>(m_high));
    }
  }

  const Scalar m_low;
  const Scalar m_high;
  const Index m_size1;
  const Scalar m_step;
  const bool m_flip;
};

template <typename Scalar>
struct linspaced_op_impl<Scalar, /*IsInteger*/ true> {
  EIGEN_DEVICE_FUNC linspaced_op_impl(const Scalar& low, const Scalar& high, Index num_steps)
      : m_low(low),
        m_multiplier((high - low) / convert_index<Scalar>(num_steps <= 1 ? 1 : num_steps - 1)),
        m_divisor(convert_index<Scalar>((high >= low ? num_steps : -num_steps) + (high - low)) /
                  ((numext::abs(high - low) + 1) == 0 ? 1 : (numext::abs(high - low) + 1))),
        m_use_divisor(num_steps > 1 && (numext::abs(high - low) + 1) < num_steps) {}

  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(IndexType i) const {
    if (m_use_divisor)
      return m_low + convert_index<Scalar>(i) / m_divisor;
    else
      return m_low + convert_index<Scalar>(i) * m_multiplier;
  }

  const Scalar m_low;
  const Scalar m_multiplier;
  const Scalar m_divisor;
  const bool m_use_divisor;
};

// ----- Linspace functor ----------------------------------------------------------------

// Forward declaration (we default to random access which does not really give
// us a speed gain when using packet access but it allows to use the functor in
// nested expressions).
template <typename Scalar>
struct linspaced_op;
template <typename Scalar>
struct functor_traits<linspaced_op<Scalar> > {
  enum {
    Cost = 1,
    PacketAccess =
        (!NumTraits<Scalar>::IsInteger) && packet_traits<Scalar>::HasSetLinear && packet_traits<Scalar>::HasBlend,
    /*&& ((!NumTraits<Scalar>::IsInteger) || packet_traits<Scalar>::HasDiv),*/  // <- vectorization for integer is
                                                                                // currently disabled
    IsRepeatable = true
  };
};
template <typename Scalar>
struct linspaced_op {
  EIGEN_DEVICE_FUNC linspaced_op(const Scalar& low, const Scalar& high, Index num_steps)
      : impl((num_steps == 1 ? high : low), high, num_steps) {}

  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(IndexType i) const {
    return impl(i);
  }

  template <typename Packet, typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(IndexType i) const {
    return impl.template packetOp<Packet>(i);
  }

  // This proxy object handles the actual required temporaries and the different
  // implementations (integer vs. floating point).
  const linspaced_op_impl<Scalar, NumTraits<Scalar>::IsInteger> impl;
};

template <typename Scalar>
struct equalspaced_op {
  typedef typename NumTraits<Scalar>::Real RealScalar;

  EIGEN_DEVICE_FUNC equalspaced_op(const Scalar& start, const Scalar& step) : m_start(start), m_step(step) {}
  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(IndexType i) const {
    return m_start + m_step * static_cast<Scalar>(i);
  }
  template <typename Packet, typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(IndexType i) const {
    const Packet cst_start = pset1<Packet>(m_start);
    const Packet cst_step = pset1<Packet>(m_step);
    const Packet cst_lin0 = plset<Packet>(Scalar(0));
    const Packet cst_offset = pmadd(cst_lin0, cst_step, cst_start);

    Packet i_packet = pset1<Packet>(static_cast<Scalar>(i));
    return pmadd(i_packet, cst_step, cst_offset);
  }
  const Scalar m_start;
  const Scalar m_step;
};

template <typename Scalar>
struct functor_traits<equalspaced_op<Scalar> > {
  enum {
    Cost = NumTraits<Scalar>::AddCost + NumTraits<Scalar>::MulCost,
    PacketAccess =
        packet_traits<Scalar>::HasSetLinear && packet_traits<Scalar>::HasMul && packet_traits<Scalar>::HasAdd,
    IsRepeatable = true
  };
};

// Linear access is automatically determined from the operator() prototypes available for the given functor.
// If it exposes an operator()(i,j), then we assume the i and j coefficients are required independently
// and linear access is not possible. In all other cases, linear access is enabled.
// Users should not have to deal with this structure.
template <typename Functor>
struct functor_has_linear_access {
  enum { ret = !has_binary_operator<Functor>::value };
};

// For unreliable compilers, let's specialize the has_*ary_operator
// helpers so that at least built-in nullary functors work fine.
#if !(EIGEN_COMP_MSVC || EIGEN_COMP_GNUC || (EIGEN_COMP_ICC >= 1600))
template <typename Scalar, typename IndexType>
struct has_nullary_operator<scalar_constant_op<Scalar>, IndexType> {
  enum { value = 1 };
};
template <typename Scalar, typename IndexType>
struct has_unary_operator<scalar_constant_op<Scalar>, IndexType> {
  enum { value = 0 };
};
template <typename Scalar, typename IndexType>
struct has_binary_operator<scalar_constant_op<Scalar>, IndexType> {
  enum { value = 0 };
};

template <typename Scalar, typename IndexType>
struct has_nullary_operator<scalar_identity_op<Scalar>, IndexType> {
  enum { value = 0 };
};
template <typename Scalar, typename IndexType>
struct has_unary_operator<scalar_identity_op<Scalar>, IndexType> {
  enum { value = 0 };
};
template <typename Scalar, typename IndexType>
struct has_binary_operator<scalar_identity_op<Scalar>, IndexType> {
  enum { value = 1 };
};

template <typename Scalar, typename IndexType>
struct has_nullary_operator<linspaced_op<Scalar>, IndexType> {
  enum { value = 0 };
};
template <typename Scalar, typename IndexType>
struct has_unary_operator<linspaced_op<Scalar>, IndexType> {
  enum { value = 1 };
};
template <typename Scalar, typename IndexType>
struct has_binary_operator<linspaced_op<Scalar>, IndexType> {
  enum { value = 0 };
};

template <typename Scalar, typename IndexType>
struct has_nullary_operator<scalar_random_op<Scalar>, IndexType> {
  enum { value = 1 };
};
template <typename Scalar, typename IndexType>
struct has_unary_operator<scalar_random_op<Scalar>, IndexType> {
  enum { value = 0 };
};
template <typename Scalar, typename IndexType>
struct has_binary_operator<scalar_random_op<Scalar>, IndexType> {
  enum { value = 0 };
};
#endif

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_NULLARY_FUNCTORS_H