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MathFunctions.h
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// Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// 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_MATHFUNCTIONS_H
#define EIGEN_MATHFUNCTIONS_H
// source: http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html
// TODO this should better be moved to NumTraits
#define EIGEN_PI \
3.141592653589793238462643383279502884197169399375105820974944592307816406L
namespace Eigen {
// On WINCE, std::abs is defined for int only, so let's defined our own
// overloads:
// This issue has been confirmed with MSVC 2008 only, but the issue might exist
// for more recent versions too.
#if EIGEN_OS_WINCE && EIGEN_COMP_MSVC && EIGEN_COMP_MSVC <= 1500
long abs(long x) { return (labs(x)); }
double abs(double x) { return (fabs(x)); }
float abs(float x) { return (fabsf(x)); }
long double abs(long double x) { return (fabsl(x)); }
#endif
namespace internal {
/** \internal \class global_math_functions_filtering_base
*
* What it does:
* Defines a typedef 'type' as follows:
* - if type T has a member typedef
* Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl, then
* global_math_functions_filtering_base<T>::type is a typedef for it.
* - otherwise, global_math_functions_filtering_base<T>::type is a typedef for
* T.
*
* How it's used:
* To allow to defined the global math functions (like sin...) in certain
* cases, like the Array expressions.
* When you do sin(array1+array2), the object array1+array2 has a complicated
* expression type, all what you want to know
* is that it inherits ArrayBase. So we implement a partial specialization of
* sin_impl for ArrayBase<Derived>.
* So we must make sure to use sin_impl<ArrayBase<Derived> > and not
* sin_impl<Derived>, otherwise our partial specialization
* won't be used. How does sin know that? That's exactly what
* global_math_functions_filtering_base tells it.
*
* How it's implemented:
* SFINAE in the style of enable_if. Highly susceptible of breaking compilers.
* With GCC, it sure does work, but if you replace
* the typename dummy by an integer template parameter, it doesn't work
* anymore!
*/
template <typename T, typename dummy = void>
struct global_math_functions_filtering_base {
typedef T type;
};
template <typename T>
struct always_void {
typedef void type;
};
template <typename T>
struct global_math_functions_filtering_base<
T,
typename always_void<
typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl>::
type> {
typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type;
};
#define EIGEN_MATHFUNC_IMPL(func, scalar) \
Eigen::internal::func##_impl< \
typename Eigen::internal::global_math_functions_filtering_base< \
scalar>::type>
#define EIGEN_MATHFUNC_RETVAL(func, scalar) \
typename Eigen::internal::func##_retval< \
typename Eigen::internal::global_math_functions_filtering_base< \
scalar>::type>::type
/****************************************************************************
* Implementation of real *
****************************************************************************/
template <typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
struct real_default_impl {
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar run(const Scalar& x) { return x; }
};
template <typename Scalar>
struct real_default_impl<Scalar, true> {
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar run(const Scalar& x) {
using std::real;
return real(x);
}
};
template <typename Scalar>
struct real_impl : real_default_impl<Scalar> {};
#if defined(EIGEN_GPU_COMPILE_PHASE)
template <typename T>
struct real_impl<std::complex<T>> {
typedef T RealScalar;
EIGEN_DEVICE_FUNC
static inline T run(const std::complex<T>& x) { return x.real(); }
};
#endif
template <typename Scalar>
struct real_retval {
typedef typename NumTraits<Scalar>::Real type;
};
/****************************************************************************
* Implementation of imag *
****************************************************************************/
template <typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
struct imag_default_impl {
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar run(const Scalar&) { return RealScalar(0); }
};
template <typename Scalar>
struct imag_default_impl<Scalar, true> {
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar run(const Scalar& x) {
using std::imag;
return imag(x);
}
};
template <typename Scalar>
struct imag_impl : imag_default_impl<Scalar> {};
#if defined(EIGEN_GPU_COMPILE_PHASE)
template <typename T>
struct imag_impl<std::complex<T>> {
typedef T RealScalar;
EIGEN_DEVICE_FUNC
static inline T run(const std::complex<T>& x) { return x.imag(); }
};
#endif
template <typename Scalar>
struct imag_retval {
typedef typename NumTraits<Scalar>::Real type;
};
/****************************************************************************
* Implementation of real_ref *
****************************************************************************/
template <typename Scalar>
struct real_ref_impl {
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar& run(Scalar& x) {
return reinterpret_cast<RealScalar*>(&x)[0];
}
EIGEN_DEVICE_FUNC
static inline const RealScalar& run(const Scalar& x) {
return reinterpret_cast<const RealScalar*>(&x)[0];
}
};
template <typename Scalar>
struct real_ref_retval {
typedef typename NumTraits<Scalar>::Real& type;
};
/****************************************************************************
* Implementation of imag_ref *
****************************************************************************/
template <typename Scalar, bool IsComplex>
struct imag_ref_default_impl {
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar& run(Scalar& x) {
return reinterpret_cast<RealScalar*>(&x)[1];
}
EIGEN_DEVICE_FUNC
static inline const RealScalar& run(const Scalar& x) {
return reinterpret_cast<RealScalar*>(&x)[1];
}
};
template <typename Scalar>
struct imag_ref_default_impl<Scalar, false> {
EIGEN_DEVICE_FUNC
static inline Scalar run(Scalar&) { return Scalar(0); }
EIGEN_DEVICE_FUNC
static inline const Scalar run(const Scalar&) { return Scalar(0); }
};
template <typename Scalar>
struct imag_ref_impl
: imag_ref_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
template <typename Scalar>
struct imag_ref_retval {
typedef typename NumTraits<Scalar>::Real& type;
};
/****************************************************************************
* Implementation of conj *
****************************************************************************/
template <typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
struct conj_default_impl {
EIGEN_DEVICE_FUNC
static inline Scalar run(const Scalar& x) { return x; }
};
template <typename Scalar>
struct conj_default_impl<Scalar, true> {
EIGEN_DEVICE_FUNC
static inline Scalar run(const Scalar& x) {
using std::conj;
return conj(x);
}
};
template <typename Scalar>
struct conj_impl : conj_default_impl<Scalar> {};
#if defined(EIGEN_GPU_COMPILE_PHASE)
template <typename T>
struct conj_impl<std::complex<T>> {
EIGEN_DEVICE_FUNC
static inline std::complex<T> run(const std::complex<T>& x) {
return std::complex<T>(x.real(), -x.imag());
}
};
#endif
template <typename Scalar>
struct conj_retval {
typedef Scalar type;
};
/****************************************************************************
* Implementation of abs2 *
****************************************************************************/
template <typename Scalar, bool IsComplex>
struct abs2_impl_default {
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar run(const Scalar& x) { return x * x; }
};
template <typename Scalar>
struct abs2_impl_default<Scalar, true> // IsComplex
{
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar run(const Scalar& x) {
return x.real() * x.real() + x.imag() * x.imag();
}
};
template <typename Scalar>
struct abs2_impl {
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar run(const Scalar& x) {
return abs2_impl_default<Scalar, NumTraits<Scalar>::IsComplex>::run(x);
}
};
template <typename Scalar>
struct abs2_retval {
typedef typename NumTraits<Scalar>::Real type;
};
/****************************************************************************
* Implementation of norm1 *
****************************************************************************/
template <typename Scalar, bool IsComplex>
struct norm1_default_impl;
template <typename Scalar>
struct norm1_default_impl<Scalar, true> {
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar run(const Scalar& x) {
EIGEN_USING_STD_MATH(abs);
return abs(x.real()) + abs(x.imag());
}
};
template <typename Scalar>
struct norm1_default_impl<Scalar, false> {
EIGEN_DEVICE_FUNC
static inline Scalar run(const Scalar& x) {
EIGEN_USING_STD_MATH(abs);
return abs(x);
}
};
template <typename Scalar>
struct norm1_impl : norm1_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
template <typename Scalar>
struct norm1_retval {
typedef typename NumTraits<Scalar>::Real type;
};
/****************************************************************************
* Implementation of hypot *
****************************************************************************/
template <typename Scalar>
struct hypot_impl;
template <typename Scalar>
struct hypot_retval {
typedef typename NumTraits<Scalar>::Real type;
};
/****************************************************************************
* Implementation of cast *
****************************************************************************/
template <typename OldType, typename NewType>
struct cast_impl {
EIGEN_DEVICE_FUNC
static inline NewType run(const OldType& x) {
return static_cast<NewType>(x);
}
};
// here, for once, we're plainly returning NewType: we don't want cast to do
// weird things.
template <typename OldType, typename NewType>
EIGEN_DEVICE_FUNC inline NewType cast(const OldType& x) {
return cast_impl<OldType, NewType>::run(x);
}
/****************************************************************************
* Implementation of round *
****************************************************************************/
#if EIGEN_HAS_CXX11_MATH
template <typename Scalar>
struct round_impl {
EIGEN_DEVICE_FUNC
static inline Scalar run(const Scalar& x) {
EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex),
NUMERIC_TYPE_MUST_BE_REAL)
EIGEN_USING_STD_MATH(round);
return round(x);
}
};
#else
template <typename Scalar>
struct round_impl {
EIGEN_DEVICE_FUNC
static inline Scalar run(const Scalar& x) {
EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex),
NUMERIC_TYPE_MUST_BE_REAL)
EIGEN_USING_STD_MATH(floor);
EIGEN_USING_STD_MATH(ceil);
return (x > Scalar(0)) ? floor(x + Scalar(0.5)) : ceil(x - Scalar(0.5));
}
};
#endif
template <typename Scalar>
struct round_retval {
typedef Scalar type;
};
/****************************************************************************
* Implementation of rint *
****************************************************************************/
template <typename Scalar>
struct rint_impl {
EIGEN_DEVICE_FUNC
static inline Scalar run(const Scalar& x) {
EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex),
NUMERIC_TYPE_MUST_BE_REAL)
#if EIGEN_HAS_CXX11_MATH
EIGEN_USING_STD_MATH(rint);
#endif
return rint(x);
}
};
#if !EIGEN_HAS_CXX11_MATH
template <>
struct rint_impl<double> {
EIGEN_DEVICE_FUNC
static inline double run(const double& x) { return ::rint(x); }
};
template <>
struct rint_impl<float> {
EIGEN_DEVICE_FUNC
static inline float run(const float& x) { return ::rintf(x); }
};
#endif
template <typename Scalar>
struct rint_retval {
typedef Scalar type;
};
/****************************************************************************
* Implementation of arg *
****************************************************************************/
#if EIGEN_HAS_CXX11_MATH
template <typename Scalar>
struct arg_impl {
EIGEN_DEVICE_FUNC
static inline Scalar run(const Scalar& x) {
#if defined(EIGEN_HIP_DEVICE_COMPILE)
// HIP does not seem to have a native device side implementation for the
// math routine "arg"
using std::arg;
#else
EIGEN_USING_STD_MATH(arg);
#endif
return arg(x);
}
};
#else
template <typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
struct arg_default_impl {
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar run(const Scalar& x) {
return (x < Scalar(0)) ? Scalar(EIGEN_PI) : Scalar(0);
}
};
template <typename Scalar>
struct arg_default_impl<Scalar, true> {
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar run(const Scalar& x) {
EIGEN_USING_STD_MATH(arg);
return arg(x);
}
};
template <typename Scalar>
struct arg_impl : arg_default_impl<Scalar> {};
#endif
template <typename Scalar>
struct arg_retval {
typedef typename NumTraits<Scalar>::Real type;
};
/****************************************************************************
* Implementation of expm1 *
****************************************************************************/
// This implementation is based on GSL Math's expm1.
namespace std_fallback {
// fallback expm1 implementation in case there is no expm1(Scalar) function in
// namespace of Scalar,
// or that there is no suitable std::expm1 function available. Implementation
// attributed to Kahan. See: http://www.plunk.org/~hatch/rightway.php.
template <typename Scalar>
EIGEN_DEVICE_FUNC inline Scalar expm1(const Scalar& x) {
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_USING_STD_MATH(exp);
Scalar u = exp(x);
if (numext::equal_strict(u, Scalar(1))) {
return x;
}
Scalar um1 = u - RealScalar(1);
if (numext::equal_strict(um1, Scalar(-1))) {
return RealScalar(-1);
}
EIGEN_USING_STD_MATH(log);
Scalar logu = log(u);
return numext::equal_strict(u, logu) ? u : (u - RealScalar(1)) * x / logu;
}
}
template <typename Scalar>
struct expm1_impl {
EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x) {
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
#if EIGEN_HAS_CXX11_MATH
using std::expm1;
#else
using std_fallback::expm1;
#endif
return expm1(x);
}
};
// Specialization for complex types that are not supported by std::expm1.
template <typename RealScalar>
struct expm1_impl<std::complex<RealScalar>> {
EIGEN_DEVICE_FUNC static inline std::complex<RealScalar> run(
const std::complex<RealScalar>& x) {
EIGEN_STATIC_ASSERT_NON_INTEGER(RealScalar)
RealScalar xr = x.real();
RealScalar xi = x.imag();
// expm1(z) = exp(z) - 1
// = exp(x + i * y) - 1
// = exp(x) * (cos(y) + i * sin(y)) - 1
// = exp(x) * cos(y) - 1 + i * exp(x) * sin(y)
// Imag(expm1(z)) = exp(x) * sin(y)
// Real(expm1(z)) = exp(x) * cos(y) - 1
// = exp(x) * cos(y) - 1.
// = expm1(x) + exp(x) * (cos(y) - 1)
// = expm1(x) + exp(x) * (2 * sin(y / 2) ** 2)
// TODO better use numext::expm1 and numext::sin (but that would require
// forward declarations or moving this specialization down).
RealScalar erm1 = expm1_impl<RealScalar>::run(xr);
RealScalar er = erm1 + RealScalar(1.);
EIGEN_USING_STD_MATH(sin);
RealScalar sin2 = sin(xi / RealScalar(2.));
sin2 = sin2 * sin2;
RealScalar s = sin(xi);
RealScalar real_part = erm1 - RealScalar(2.) * er * sin2;
return std::complex<RealScalar>(real_part, er * s);
}
};
template <typename Scalar>
struct expm1_retval {
typedef Scalar type;
};
/****************************************************************************
* Implementation of log1p *
****************************************************************************/
namespace std_fallback {
// fallback log1p implementation in case there is no log1p(Scalar) function in
// namespace of Scalar,
// or that there is no suitable std::log1p function available
template <typename Scalar>
EIGEN_DEVICE_FUNC inline Scalar log1p(const Scalar& x) {
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_USING_STD_MATH(log);
Scalar x1p = RealScalar(1) + x;
Scalar log_1p = log(x1p);
const bool is_small = numext::equal_strict(x1p, Scalar(1));
const bool is_inf = numext::equal_strict(x1p, log_1p);
return (is_small || is_inf) ? x : x * (log_1p / (x1p - RealScalar(1)));
}
}
template <typename Scalar>
struct log1p_impl {
EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x) {
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
#if EIGEN_HAS_CXX11_MATH
using std::log1p;
#else
using std_fallback::log1p;
#endif
return log1p(x);
}
};
// Specialization for complex types that are not supported by std::log1p.
template <typename RealScalar>
struct log1p_impl<std::complex<RealScalar>> {
EIGEN_DEVICE_FUNC static inline std::complex<RealScalar> run(
const std::complex<RealScalar>& x) {
EIGEN_STATIC_ASSERT_NON_INTEGER(RealScalar)
return std_fallback::log1p(x);
}
};
template <typename Scalar>
struct log1p_retval {
typedef Scalar type;
};
/****************************************************************************
* Implementation of pow *
****************************************************************************/
template <typename ScalarX,
typename ScalarY,
bool IsInteger =
NumTraits<ScalarX>::IsInteger&& NumTraits<ScalarY>::IsInteger>
struct pow_impl {
// typedef Scalar retval;
typedef typename ScalarBinaryOpTraits<
ScalarX,
ScalarY,
internal::scalar_pow_op<ScalarX, ScalarY>>::ReturnType result_type;
static EIGEN_DEVICE_FUNC inline result_type run(const ScalarX& x,
const ScalarY& y) {
EIGEN_USING_STD_MATH(pow);
return pow(x, y);
}
};
template <typename ScalarX, typename ScalarY>
struct pow_impl<ScalarX, ScalarY, true> {
typedef ScalarX result_type;
static EIGEN_DEVICE_FUNC inline ScalarX run(ScalarX x, ScalarY y) {
ScalarX res(1);
eigen_assert(!NumTraits<ScalarY>::IsSigned || y >= 0);
if (y & 1) res *= x;
y >>= 1;
while (y) {
x *= x;
if (y & 1) res *= x;
y >>= 1;
}
return res;
}
};
/****************************************************************************
* Implementation of random *
****************************************************************************/
template <typename Scalar, bool IsComplex, bool IsInteger>
struct random_default_impl {};
template <typename Scalar>
struct random_impl : random_default_impl<Scalar,
NumTraits<Scalar>::IsComplex,
NumTraits<Scalar>::IsInteger> {};
template <typename Scalar>
struct random_retval {
typedef Scalar type;
};
template <typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(random, Scalar)
random(const Scalar& x, const Scalar& y);
template <typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random();
template <typename Scalar>
struct random_default_impl<Scalar, false, false> {
static inline Scalar run(const Scalar& x, const Scalar& y) {
return x + (y - x) * Scalar(std::rand()) / Scalar(RAND_MAX);
}
static inline Scalar run() {
return run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1));
}
};
enum {
meta_floor_log2_terminate,
meta_floor_log2_move_up,
meta_floor_log2_move_down,
meta_floor_log2_bogus
};
template <unsigned int n, int lower, int upper>
struct meta_floor_log2_selector {
enum {
middle = (lower + upper) / 2,
value = (upper <= lower + 1)
? int(meta_floor_log2_terminate)
: (n < (1 << middle)) ? int(meta_floor_log2_move_down)
: (n == 0) ? int(meta_floor_log2_bogus)
: int(meta_floor_log2_move_up)
};
};
template <unsigned int n,
int lower = 0,
int upper = sizeof(unsigned int) * CHAR_BIT - 1,
int selector = meta_floor_log2_selector<n, lower, upper>::value>
struct meta_floor_log2 {};
template <unsigned int n, int lower, int upper>
struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_down> {
enum {
value = meta_floor_log2<
n,
lower,
meta_floor_log2_selector<n, lower, upper>::middle>::value
};
};
template <unsigned int n, int lower, int upper>
struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_up> {
enum {
value = meta_floor_log2<n,
meta_floor_log2_selector<n, lower, upper>::middle,
upper>::value
};
};
template <unsigned int n, int lower, int upper>
struct meta_floor_log2<n, lower, upper, meta_floor_log2_terminate> {
enum {
value = (n >= ((unsigned int)(1) << (lower + 1))) ? lower + 1 : lower
};
};
template <unsigned int n, int lower, int upper>
struct meta_floor_log2<n, lower, upper, meta_floor_log2_bogus> {
// no value, error at compile time
};
template <typename Scalar>
struct random_default_impl<Scalar, false, true> {
static inline Scalar run(const Scalar& x, const Scalar& y) {
if (y <= x) return x;
// ScalarU is the unsigned counterpart of Scalar, possibly Scalar itself.
typedef typename make_unsigned<Scalar>::type ScalarU;
// ScalarX is the widest of ScalarU and unsigned int.
// We'll deal only with ScalarX and unsigned int below thus avoiding signed
// types and arithmetic and signed overflows (which are undefined behavior).
typedef typename conditional<(ScalarU(-1) > unsigned(-1)),
ScalarU,
unsigned>::type ScalarX;
// The following difference doesn't overflow, provided our integer types are
// two's
// complement and have the same number of padding bits in signed and
// unsigned variants.
// This is the case in most modern implementations of C++.
ScalarX range = ScalarX(y) - ScalarX(x);
ScalarX offset = 0;
ScalarX divisor = 1;
ScalarX multiplier = 1;
const unsigned rand_max = RAND_MAX;
if (range <= rand_max)
divisor = (rand_max + 1) / (range + 1);
else
multiplier = 1 + range / (rand_max + 1);
// Rejection sampling.
do {
offset = (unsigned(std::rand()) * multiplier) / divisor;
} while (offset > range);
return Scalar(ScalarX(x) + offset);
}
static inline Scalar run() {
#ifdef EIGEN_MAKING_DOCS
return run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10));
#else
enum {
rand_bits = meta_floor_log2<(unsigned int)(RAND_MAX) + 1>::value,
scalar_bits = sizeof(Scalar) * CHAR_BIT,
shift = EIGEN_PLAIN_ENUM_MAX(0, int(rand_bits) - int(scalar_bits)),
offset = NumTraits<Scalar>::IsSigned
? (1 << (EIGEN_PLAIN_ENUM_MIN(rand_bits, scalar_bits) - 1))
: 0};
return Scalar((std::rand() >> shift) - offset);
#endif
}
};
template <typename Scalar>
struct random_default_impl<Scalar, true, false> {
static inline Scalar run(const Scalar& x, const Scalar& y) {
return Scalar(random(x.real(), y.real()), random(x.imag(), y.imag()));
}
static inline Scalar run() {
typedef typename NumTraits<Scalar>::Real RealScalar;
return Scalar(random<RealScalar>(), random<RealScalar>());
}
};
template <typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(random, Scalar)
random(const Scalar& x, const Scalar& y) {
return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);
}
template <typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random() {
return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
}
// Implementation of is* functions
// std::is* do not work with fast-math and gcc, std::is* are available on MSVC
// 2013 and newer, as well as in clang.
#if (EIGEN_HAS_CXX11_MATH && \
!(EIGEN_COMP_GNUC_STRICT && __FINITE_MATH_ONLY__)) || \
(EIGEN_COMP_MSVC >= 1800) || (EIGEN_COMP_CLANG)
#define EIGEN_USE_STD_FPCLASSIFY 1
#else
#define EIGEN_USE_STD_FPCLASSIFY 0
#endif
template <typename T>
EIGEN_DEVICE_FUNC
typename internal::enable_if<internal::is_integral<T>::value, bool>::type
isnan_impl(const T&) {
return false;
}
template <typename T>
EIGEN_DEVICE_FUNC
typename internal::enable_if<internal::is_integral<T>::value, bool>::type
isinf_impl(const T&) {
return false;
}
template <typename T>
EIGEN_DEVICE_FUNC
typename internal::enable_if<internal::is_integral<T>::value, bool>::type
isfinite_impl(const T&) {
return true;
}
template <typename T>
EIGEN_DEVICE_FUNC
typename internal::enable_if<(!internal::is_integral<T>::value) &&
(!NumTraits<T>::IsComplex),
bool>::type
isfinite_impl(const T& x) {
#if defined(EIGEN_GPU_COMPILE_PHASE)
return (::isfinite)(x);
#elif EIGEN_USE_STD_FPCLASSIFY
using std::isfinite;
return isfinite EIGEN_NOT_A_MACRO(x);
#else
return x <= NumTraits<T>::highest() && x >= NumTraits<T>::lowest();
#endif
}
template <typename T>
EIGEN_DEVICE_FUNC
typename internal::enable_if<(!internal::is_integral<T>::value) &&
(!NumTraits<T>::IsComplex),
bool>::type
isinf_impl(const T& x) {
#if defined(EIGEN_GPU_COMPILE_PHASE)
return (::isinf)(x);
#elif EIGEN_USE_STD_FPCLASSIFY
using std::isinf;
return isinf EIGEN_NOT_A_MACRO(x);
#else
return x > NumTraits<T>::highest() || x < NumTraits<T>::lowest();
#endif
}
template <typename T>
EIGEN_DEVICE_FUNC
typename internal::enable_if<(!internal::is_integral<T>::value) &&
(!NumTraits<T>::IsComplex),
bool>::type
isnan_impl(const T& x) {
#if defined(EIGEN_GPU_COMPILE_PHASE)
return (::isnan)(x);
#elif EIGEN_USE_STD_FPCLASSIFY
using std::isnan;
return isnan EIGEN_NOT_A_MACRO(x);
#else
return x != x;
#endif
}
#if (!EIGEN_USE_STD_FPCLASSIFY)
#if EIGEN_COMP_MSVC
template <typename T>
EIGEN_DEVICE_FUNC bool isinf_msvc_helper(T x) {
return _fpclass(x) == _FPCLASS_NINF || _fpclass(x) == _FPCLASS_PINF;
}
// MSVC defines a _isnan builtin function, but for double only
EIGEN_DEVICE_FUNC inline bool isnan_impl(const long double& x) {
return _isnan(x) != 0;
}
EIGEN_DEVICE_FUNC inline bool isnan_impl(const double& x) {
return _isnan(x) != 0;
}
EIGEN_DEVICE_FUNC inline bool isnan_impl(const float& x) {
return _isnan(x) != 0;
}
EIGEN_DEVICE_FUNC inline bool isinf_impl(const long double& x) {
return isinf_msvc_helper(x);
}
EIGEN_DEVICE_FUNC inline bool isinf_impl(const double& x) {
return isinf_msvc_helper(x);
}
EIGEN_DEVICE_FUNC inline bool isinf_impl(const float& x) {
return isinf_msvc_helper(x);
}
#elif (defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ && EIGEN_COMP_GNUC)
#if EIGEN_GNUC_AT_LEAST(5, 0)
#define EIGEN_TMP_NOOPT_ATTRIB \
EIGEN_DEVICE_FUNC inline __attribute__((optimize("no-finite-math-only")))
#else
// NOTE the inline qualifier and noinline attribute are both needed: the former
// is to avoid linking issue (duplicate symbol),
// while the second prevent too aggressive optimizations in fast-math mode:
#define EIGEN_TMP_NOOPT_ATTRIB \
EIGEN_DEVICE_FUNC inline \
__attribute__((noinline, optimize("no-finite-math-only")))
#endif
template <>
EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const long double& x) {
return __builtin_isnan(x);
}
template <>
EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const double& x) {
return __builtin_isnan(x);
}
template <>
EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const float& x) {
return __builtin_isnan(x);
}
template <>
EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const double& x) {
return __builtin_isinf(x);
}
template <>
EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const float& x) {
return __builtin_isinf(x);
}
template <>
EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const long double& x) {
return __builtin_isinf(x);
}
#undef EIGEN_TMP_NOOPT_ATTRIB
#endif
#endif
// The following overload are defined at the end of this file
template <typename T>
EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x);
template <typename T>
EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x);
template <typename T>
EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x);
template <typename T>
T generic_fast_tanh_float(const T& a_x);
} // end namespace internal
/****************************************************************************
* Generic math functions *
****************************************************************************/
namespace numext {
#if (!defined(EIGEN_GPUCC))
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y) {
EIGEN_USING_STD_MATH(min);
return min EIGEN_NOT_A_MACRO(x, y);
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y) {