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eigen/Eigen/src/Core/MathFunctions.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_MATHFUNCTIONS_H
#define EIGEN_MATHFUNCTIONS_H
// source: http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html
#define EIGEN_PI 3.141592653589793238462643383279502884197169399375105820974944592307816406
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 \struct 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> {};
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> {};
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_impl
{
EIGEN_DEVICE_FUNC
static inline Scalar run(const Scalar& x)
{
return x;
}
};
template<typename Scalar>
struct conj_impl<Scalar,true>
{
EIGEN_DEVICE_FUNC
static inline Scalar run(const Scalar& x)
{
using std::conj;
return conj(x);
}
};
template<typename Scalar>
struct conj_retval
{
typedef Scalar type;
};
/****************************************************************************
* Implementation of abs2 *
****************************************************************************/
template<typename Scalar>
struct abs2_impl
{
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar run(const Scalar& x)
{
return x*x;
}
};
template<typename RealScalar>
struct abs2_impl<std::complex<RealScalar> >
{
EIGEN_DEVICE_FUNC
static inline RealScalar run(const std::complex<RealScalar>& x)
{
return real(x)*real(x) + imag(x)*imag(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
{
typedef typename NumTraits<Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC
static inline RealScalar run(const Scalar& x)
{
EIGEN_USING_STD_MATH(abs);
return abs(real(x)) + abs(imag(x));
}
};
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
{
typedef typename NumTraits<Scalar>::Real RealScalar;
static inline RealScalar run(const Scalar& x, const Scalar& y)
{
EIGEN_USING_STD_MATH(max);
EIGEN_USING_STD_MATH(min);
EIGEN_USING_STD_MATH(abs);
EIGEN_USING_STD_MATH(sqrt);
RealScalar _x = abs(x);
RealScalar _y = abs(y);
Scalar p, qp;
if(_x>_y)
{
p = _x;
qp = _y / p;
}
else
{
p = _y;
qp = _x / p;
}
if(p==RealScalar(0)) return RealScalar(0);
return p * sqrt(RealScalar(1) + qp*qp);
}
};
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 {
static inline Scalar run(const Scalar& x)
{
EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)
using std::round;
return round(x);
}
};
#else
template<typename Scalar>
struct round_impl
{
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 arg *
****************************************************************************/
#if EIGEN_HAS_CXX11_MATH
template<typename Scalar>
struct arg_impl {
static inline Scalar run(const Scalar& x)
{
EIGEN_USING_STD_MATH(arg);
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 log1p *
****************************************************************************/
template<typename Scalar, bool isComplex = NumTraits<Scalar>::IsComplex >
struct log1p_impl
{
static inline Scalar run(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;
return ( x1p == Scalar(1) ) ? x : x * ( log(x1p) / (x1p - RealScalar(1)) );
}
};
#if EIGEN_HAS_CXX11_MATH
template<typename Scalar>
struct log1p_impl<Scalar, false> {
static inline Scalar run(const Scalar& x)
{
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
using std::log1p;
return log1p(x);
}
};
#endif
template<typename Scalar>
struct log1p_retval
{
typedef Scalar type;
};
/****************************************************************************
* Implementation of pow *
****************************************************************************/
template<typename Scalar, bool IsInteger>
struct pow_default_impl
{
typedef Scalar retval;
static inline Scalar run(const Scalar& x, const Scalar& y)
{
EIGEN_USING_STD_MATH(pow);
return pow(x, y);
}
};
template<typename Scalar>
struct pow_default_impl<Scalar, true>
{
static inline Scalar run(Scalar x, Scalar y)
{
Scalar res(1);
eigen_assert(!NumTraits<Scalar>::IsSigned || y >= 0);
if(y & 1) res *= x;
y >>= 1;
while(y)
{
x *= x;
if(y&1) res *= x;
y >>= 1;
}
return res;
}
};
template<typename Scalar>
struct pow_impl : pow_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
template<typename Scalar>
struct pow_retval
{
typedef Scalar type;
};
/****************************************************************************
* 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)
{
using std::max;
using std::min;
typedef typename conditional<NumTraits<Scalar>::IsSigned,std::ptrdiff_t,std::size_t>::type ScalarX;
if(y<x)
return x;
std::size_t range = ScalarX(y)-ScalarX(x);
std::size_t offset = 0;
// rejection sampling
std::size_t divisor = (range+RAND_MAX-1)/(range+1);
std::size_t multiplier = (range+RAND_MAX-1)/std::size_t(RAND_MAX);
do {
offset = ( (std::size_t(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(real(x), real(y)),
random(imag(x), imag(y)));
}
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();
}
} // end namespace internal
/****************************************************************************
* Generic math functions *
****************************************************************************/
namespace numext {
template<typename T>
EIGEN_DEVICE_FUNC
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
inline T maxi(const T& x, const T& y)
{
EIGEN_USING_STD_MATH(max);
return max EIGEN_NOT_A_MACRO (x,y);
}
template<typename Scalar>
EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
}
template<typename Scalar>
EIGEN_DEVICE_FUNC
inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x)
{
return internal::real_ref_impl<Scalar>::run(x);
}
template<typename Scalar>
EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
}
template<typename Scalar>
EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
}
template<typename Scalar>
EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(arg, Scalar) arg(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(arg, Scalar)::run(x);
}
template<typename Scalar>
EIGEN_DEVICE_FUNC
inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x)
{
return internal::imag_ref_impl<Scalar>::run(x);
}
template<typename Scalar>
EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);
}
template<typename Scalar>
EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
}
template<typename Scalar>
EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);
}
template<typename Scalar>
EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
}
template<typename Scalar>
EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)
{
return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
}
template<typename Scalar>
EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(log1p, Scalar) log1p(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(log1p, Scalar)::run(x);
}
template<typename Scalar>
EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(pow, Scalar) pow(const Scalar& x, const Scalar& y)
{
return EIGEN_MATHFUNC_IMPL(pow, Scalar)::run(x, y);
}
template<typename T>
EIGEN_DEVICE_FUNC
bool (isfinite)(const T& x)
{
#if EIGEN_HAS_CXX11_MATH
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
bool (isnan)(const T& x)
{
#if EIGEN_HAS_CXX11_MATH
using std::isnan;
return isnan EIGEN_NOT_A_MACRO (x);
#else
return x != x;
#endif
}
template<typename T>
EIGEN_DEVICE_FUNC
bool (isinf)(const T& x)
{
#if EIGEN_HAS_CXX11_MATH
using std::isinf;
return isinf EIGEN_NOT_A_MACRO (x);
#else
return x>NumTraits<T>::highest() || x<NumTraits<T>::lowest();
#endif
}
template<typename T>
bool (isfinite)(const std::complex<T>& x)
{
return (numext::isfinite)(numext::real(x)) && (numext::isfinite)(numext::imag(x));
}
template<typename T>
bool (isnan)(const std::complex<T>& x)
{
return (numext::isnan)(numext::real(x)) || (numext::isnan)(numext::imag(x));
}
template<typename T>
bool (isinf)(const std::complex<T>& x)
{
return ((numext::isinf)(numext::real(x)) || (numext::isinf)(numext::imag(x))) && (!(numext::isnan)(x));
}
template<typename Scalar>
EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(round, Scalar) round(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(round, Scalar)::run(x);
}
template<typename T>
EIGEN_DEVICE_FUNC
T (floor)(const T& x)
{
EIGEN_USING_STD_MATH(floor);
return floor(x);
}
template<typename T>
EIGEN_DEVICE_FUNC
T (ceil)(const T& x)
{
EIGEN_USING_STD_MATH(ceil);
return ceil(x);
}
// Log base 2 for 32 bits positive integers.
// Conveniently returns 0 for x==0.
inline int log2(int x)
{
eigen_assert(x>=0);
unsigned int v(x);
static const int table[32] = { 0, 9, 1, 10, 13, 21, 2, 29, 11, 14, 16, 18, 22, 25, 3, 30, 8, 12, 20, 28, 15, 17, 24, 7, 19, 27, 23, 6, 26, 5, 4, 31 };
v |= v >> 1;
v |= v >> 2;
v |= v >> 4;
v |= v >> 8;
v |= v >> 16;
return table[(v * 0x07C4ACDDU) >> 27];
}
} // end namespace numext
namespace internal {
/****************************************************************************
* Implementation of fuzzy comparisons *
****************************************************************************/
template<typename Scalar,
bool IsComplex,
bool IsInteger>
struct scalar_fuzzy_default_impl {};
template<typename Scalar>
struct scalar_fuzzy_default_impl<Scalar, false, false>
{
typedef typename NumTraits<Scalar>::Real RealScalar;
template<typename OtherScalar> EIGEN_DEVICE_FUNC
static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
{
EIGEN_USING_STD_MATH(abs);
return abs(x) <= abs(y) * prec;
}
EIGEN_DEVICE_FUNC
static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
{
EIGEN_USING_STD_MATH(min);
EIGEN_USING_STD_MATH(abs);
return abs(x - y) <= (min)(abs(x), abs(y)) * prec;
}
EIGEN_DEVICE_FUNC
static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec)
{
return x <= y || isApprox(x, y, prec);
}
};
template<typename Scalar>
struct scalar_fuzzy_default_impl<Scalar, false, true>
{
typedef typename NumTraits<Scalar>::Real RealScalar;
template<typename OtherScalar> EIGEN_DEVICE_FUNC
static inline bool isMuchSmallerThan(const Scalar& x, const Scalar&, const RealScalar&)
{
return x == Scalar(0);
}
EIGEN_DEVICE_FUNC
static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar&)
{
return x == y;
}
EIGEN_DEVICE_FUNC
static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar&)
{
return x <= y;
}
};
template<typename Scalar>
struct scalar_fuzzy_default_impl<Scalar, true, false>
{
typedef typename NumTraits<Scalar>::Real RealScalar;
template<typename OtherScalar>
static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
{
return numext::abs2(x) <= numext::abs2(y) * prec * prec;
}
static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
{
EIGEN_USING_STD_MATH(min);
return numext::abs2(x - y) <= (min)(numext::abs2(x), numext::abs2(y)) * prec * prec;
}
};
template<typename Scalar>
struct scalar_fuzzy_impl : scalar_fuzzy_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
template<typename Scalar, typename OtherScalar> EIGEN_DEVICE_FUNC
inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y,
typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
{
return scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision);
}
template<typename Scalar> EIGEN_DEVICE_FUNC
inline bool isApprox(const Scalar& x, const Scalar& y,
typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
{
return scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision);
}
template<typename Scalar> EIGEN_DEVICE_FUNC
inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y,
typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
{
return scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision);
}
/******************************************
*** The special case of the bool type ***
******************************************/
template<> struct random_impl<bool>
{
static inline bool run()
{
return random<int>(0,1)==0 ? false : true;
}
};
template<> struct scalar_fuzzy_impl<bool>
{
typedef bool RealScalar;
template<typename OtherScalar> EIGEN_DEVICE_FUNC
static inline bool isMuchSmallerThan(const bool& x, const bool&, const bool&)
{
return !x;
}
EIGEN_DEVICE_FUNC
static inline bool isApprox(bool x, bool y, bool)
{
return x == y;
}
EIGEN_DEVICE_FUNC
static inline bool isApproxOrLessThan(const bool& x, const bool& y, const bool&)
{
return (!x) || y;
}
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_MATHFUNCTIONS_H
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