NumTraits.h

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// 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_NUMTRAITS_H
#define EIGEN_NUMTRAITS_H
 
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
 
// default implementation of digits(), based on numeric_limits if specialized,
// 0 for integer types, and log2(epsilon()) otherwise.
template <typename T, bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
          bool is_integer = NumTraits<T>::IsInteger>
struct default_digits_impl {
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return std::numeric_limits<T>::digits; }
};
 
template <typename T>
struct default_digits_impl<T, false, false>  // Floating point
{
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() {
    using std::ceil;
    using std::log2;
    typedef typename NumTraits<T>::Real Real;
    return int(ceil(-log2(NumTraits<Real>::epsilon())));
  }
};
 
template <typename T>
struct default_digits_impl<T, false, true>  // Integer
{
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return 0; }
};
 
// default implementation of digits10(), based on numeric_limits if specialized,
// 0 for integer types, and floor((digits()-1)*log10(2)) otherwise.
template <typename T, bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
          bool is_integer = NumTraits<T>::IsInteger>
struct default_digits10_impl {
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return std::numeric_limits<T>::digits10; }
};
 
template <typename T>
struct default_digits10_impl<T, false, false>  // Floating point
{
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() {
    using std::floor;
    using std::log10;
    typedef typename NumTraits<T>::Real Real;
    return int(floor((internal::default_digits_impl<Real>::run() - 1) * log10(2)));
  }
};
 
template <typename T>
struct default_digits10_impl<T, false, true>  // Integer
{
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return 0; }
};
 
// default implementation of max_digits10(), based on numeric_limits if specialized,
// 0 for integer types, and log10(2) * digits() + 1 otherwise.
template <typename T, bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
          bool is_integer = NumTraits<T>::IsInteger>
struct default_max_digits10_impl {
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return std::numeric_limits<T>::max_digits10; }
};
 
template <typename T>
struct default_max_digits10_impl<T, false, false>  // Floating point
{
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() {
    using std::ceil;
    using std::log10;
    typedef typename NumTraits<T>::Real Real;
    return int(ceil(internal::default_digits_impl<Real>::run() * log10(2) + 1));
  }
};
 
template <typename T>
struct default_max_digits10_impl<T, false, true>  // Integer
{
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return 0; }
};
 
}  // end namespace internal
 
namespace numext {
// TODO: Replace by std::bit_cast (available in C++20)
template <typename Tgt, typename Src>
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Tgt bit_cast(const Src& src) {
  // The behaviour of memcpy is not specified for non-trivially copyable types
  EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Src>::value, THIS_TYPE_IS_NOT_SUPPORTED)
  EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Tgt>::value && std::is_default_constructible<Tgt>::value,
                      THIS_TYPE_IS_NOT_SUPPORTED)
  EIGEN_STATIC_ASSERT(sizeof(Src) == sizeof(Tgt), THIS_TYPE_IS_NOT_SUPPORTED)
 
  Tgt tgt;
  // Load src into registers first. This allows the memcpy to be elided by CUDA.
  const Src staged = src;
  EIGEN_USING_STD(memcpy)
  memcpy(static_cast<void*>(&tgt), static_cast<const void*>(&staged), sizeof(Tgt));
  return tgt;
}
}  // namespace numext
 
template <typename T>
struct GenericNumTraits {
  enum {
    IsInteger = std::numeric_limits<T>::is_integer,
    IsSigned = std::numeric_limits<T>::is_signed,
    IsComplex = 0,
    RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1,
    ReadCost = 1,
    AddCost = 1,
    MulCost = 1
  };
 
  typedef T Real;
  typedef std::conditional_t<IsInteger, std::conditional_t<sizeof(T) <= 2, float, double>, T> NonInteger;
  typedef T Nested;
  typedef T Literal;
 
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real epsilon() { return numext::numeric_limits<T>::epsilon(); }
 
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int digits10() { return internal::default_digits10_impl<T>::run(); }
 
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int max_digits10() {
    return internal::default_max_digits10_impl<T>::run();
  }
 
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int digits() { return internal::default_digits_impl<T>::run(); }
 
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int min_exponent() { return numext::numeric_limits<T>::min_exponent; }
 
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int max_exponent() { return numext::numeric_limits<T>::max_exponent; }
 
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real dummy_precision() {
    // make sure to override this for floating-point types
    return Real(0);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T highest() { return (numext::numeric_limits<T>::max)(); }
 
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T lowest() { return (numext::numeric_limits<T>::lowest)(); }
 
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T infinity() { return numext::numeric_limits<T>::infinity(); }
 
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T quiet_NaN() { return numext::numeric_limits<T>::quiet_NaN(); }
};
 
template <typename T>
struct NumTraits : GenericNumTraits<T> {};
 
template <>
struct NumTraits<float> : GenericNumTraits<float> {
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline float dummy_precision() { return 1e-5f; }
};
 
template <>
struct NumTraits<double> : GenericNumTraits<double> {
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline double dummy_precision() { return 1e-12; }
};
 
// GPU devices treat `long double` as `double`.
#ifndef EIGEN_GPU_COMPILE_PHASE
template <>
struct NumTraits<long double> : GenericNumTraits<long double> {
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline long double dummy_precision() {
    return static_cast<long double>(1e-15l);
  }
 
#if defined(EIGEN_ARCH_PPC) && (__LDBL_MANT_DIG__ == 106)
  // PowerPC double double causes issues with some values
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline long double epsilon() {
    // 2^(-(__LDBL_MANT_DIG__)+1)
    return static_cast<long double>(2.4651903288156618919116517665087e-32l);
  }
#endif
};
#endif
 
template <typename Real_>
struct NumTraits<std::complex<Real_> > : GenericNumTraits<std::complex<Real_> > {
  typedef Real_ Real;
  typedef typename NumTraits<Real_>::Literal Literal;
  enum {
    IsComplex = 1,
    IsSigned = NumTraits<Real_>::IsSigned,
    RequireInitialization = NumTraits<Real_>::RequireInitialization,
    ReadCost = 2 * NumTraits<Real_>::ReadCost,
    AddCost = 2 * NumTraits<Real>::AddCost,
    MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
  };
 
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int digits10() { return NumTraits<Real>::digits10(); }
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int max_digits10() { return NumTraits<Real>::max_digits10(); }
};
 
template <typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > {
  typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType;
  typedef typename NumTraits<Scalar>::Real RealScalar;
  typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real;
  typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;
  typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;
  typedef ArrayType& Nested;
  typedef typename NumTraits<Scalar>::Literal Literal;
 
  enum {
    IsComplex = NumTraits<Scalar>::IsComplex,
    IsInteger = NumTraits<Scalar>::IsInteger,
    IsSigned = NumTraits<Scalar>::IsSigned,
    RequireInitialization = 1,
    ReadCost = ArrayType::SizeAtCompileTime == Dynamic
                   ? HugeCost
                   : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::ReadCost),
    AddCost = ArrayType::SizeAtCompileTime == Dynamic ? HugeCost
                                                      : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::AddCost),
    MulCost = ArrayType::SizeAtCompileTime == Dynamic ? HugeCost
                                                      : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::MulCost)
  };
 
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline RealScalar dummy_precision() {
    return NumTraits<RealScalar>::dummy_precision();
  }
 
  EIGEN_CONSTEXPR
  static inline int digits10() { return NumTraits<Scalar>::digits10(); }
  EIGEN_CONSTEXPR
  static inline int max_digits10() { return NumTraits<Scalar>::max_digits10(); }
};
 
template <>
struct NumTraits<std::string> : GenericNumTraits<std::string> {
  enum { RequireInitialization = 1, ReadCost = HugeCost, AddCost = HugeCost, MulCost = HugeCost };
 
  EIGEN_CONSTEXPR
  static inline int digits10() { return 0; }
  EIGEN_CONSTEXPR
  static inline int max_digits10() { return 0; }
 
 private:
  static inline std::string epsilon();
  static inline std::string dummy_precision();
  static inline std::string lowest();
  static inline std::string highest();
  static inline std::string infinity();
  static inline std::string quiet_NaN();
};
 
// Empty specialization for void to allow template specialization based on NumTraits<T>::Real with T==void and SFINAE.
template <>
struct NumTraits<void> {};
 
template <>
struct NumTraits<bool> : GenericNumTraits<bool> {};
 
}  // end namespace Eigen
 
#endif  // EIGEN_NUMTRAITS_H