math.hpp File Reference

Contains some portable math functions. More...

#include "LvArrayConfig.hpp"
#include "Macros.hpp"
#include <cmath>
#include <type_traits>

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Classes
struct	LvArray::math::internal::SingleType< T >
	The type of a single value of type T. More...

Namespaces
	LvArray
	The top level namespace.
	LvArray::math
	Contains protable wrappers around cmath functions and some cuda specific functions.

Functions
template<typename T , typename U >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr T	LvArray::math::internal::convert (T const, U const u)
	Convert u to type. More...
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr int	LvArray::math::internal::numValues (T const)
	Return the number of values stored in. More...
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr SingleType< T >	LvArray::math::internal::getFirst (T const x)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr SingleType< T >	LvArray::math::internal::getSecond (T const x)
template<typename T >
LVARRAY_HOST_DEVICE constexpr T	LvArray::math::internal::lessThan (T const x, T const y)
template<typename T >
LVARRAY_DEVICE LVARRAY_FORCE_INLINE T	LvArray::math::internal::asinImpl (T const x)
template<typename T >
LVARRAY_DEVICE LVARRAY_FORCE_INLINE T	LvArray::math::internal::acosImpl (T const x)
template<typename T >
LVARRAY_DEVICE LVARRAY_FORCE_INLINE T	LvArray::math::internal::atan2Impl (T const y, T const x)
Square root and inverse square root.
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE float	LvArray::math::sqrt (float const x)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE double	LvArray::math::sqrt (T const x)
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE float	LvArray::math::invSqrt (float const x)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE double	LvArray::math::invSqrt (T const x)
Trigonometric functions
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE float	LvArray::math::sin (float const theta)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE double	LvArray::math::sin (T const theta)
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE float	LvArray::math::cos (float const theta)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE double	LvArray::math::cos (T const theta)
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE void	LvArray::math::sincos (float const theta, float &sinTheta, float &cosTheta)
	Compute the sine and cosine of theta. More...
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE void	LvArray::math::sincos (double const theta, double &sinTheta, double &cosTheta)
	Compute the sine and cosine of theta. More...
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE void	LvArray::math::sincos (T const theta, double &sinTheta, double &cosTheta)
	Compute the sine and cosine of theta. More...
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE float	LvArray::math::tan (float const theta)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE double	LvArray::math::tan (T const theta)
Inverse trigonometric functions
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE float	LvArray::math::asin (float const x)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE double	LvArray::math::asin (T const x)
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE float	LvArray::math::acos (float const x)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE double	LvArray::math::acos (T const x)
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE float	LvArray::math::atan2 (float const y, float const x)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE double	LvArray::math::atan2 (T const y, T const x)
Exponential functions
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE float	LvArray::math::exp (float const x)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE double	LvArray::math::exp (T const x)
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE float	LvArray::math::log (float const x)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE double	LvArray::math::log (T const x)

General purpose functions
template<typename T >
using	LvArray::math::SingleType = typename internal::SingleType< T >::type
	The type of a single value of type T. More...
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr int	LvArray::math::numValues ()
	Return the number of values stored in type. More...
template<typename T , typename U >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr T	LvArray::math::convert (U const u)
	Convert u to type. More...
template<typename T , typename U , typename V >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr T	LvArray::math::convert (U const u, V const v)
	Convert u and v to a dual type. More...
template<typename T >
LVARRAY_DEVICE LVARRAY_FORCE_INLINE SingleType< T >	LvArray::math::getFirst (T const x)
template<typename T >
LVARRAY_DEVICE LVARRAY_FORCE_INLINE SingleType< T >	LvArray::math::getSecond (T const x)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr std::enable_if_t< std::is_arithmetic< T >::value, T >	LvArray::math::max (T const a, T const b)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr std::enable_if_t< std::is_arithmetic< T >::value, T >	LvArray::math::min (T const a, T const b)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr T	LvArray::math::abs (T const x)
template<typename T >
LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr T	LvArray::math::square (T const x)

Detailed Description

Contains some portable math functions.

Function Documentation

acosImpl()

template<typename T >

LVARRAY_DEVICE LVARRAY_FORCE_INLINE T LvArray::math::internal::acosImpl

(

T const

x

)

Returns

The arcsine of x.

Parameters

x	The value to get the arcsine of, must be in [-1, 1].

Has a max error of 2.64e-3 and max relative error of 1.37e-3 for half precision.

Note

Modified from https://developer.download.nvidia.com/cg/acos.html

asinImpl()

template<typename T >

LVARRAY_DEVICE LVARRAY_FORCE_INLINE T LvArray::math::internal::asinImpl

(

T const

x

)

Returns

The arcsine of x.

Parameters

x	The value to get the arcsine of, must be in [-1, 1].

Has a max error of 1.36e-3 and max relative error of 6.95e-3 for half precision. The largeish relative error occurs where the algorithm transitions away from the small value approximation. The original algorithm didn't the small value approximation and it had huge (~3.0x) relative error, I believe due to the poor cancellation when subtracting from pi/2. acos doesn't have this problem and calculating asin as

pi/2 - acos 

led to the the same error. To improve precision you could always add in another term in the taylor series (x^3 / 6) but I don't think it's worth it.

Note

Modified from https://developer.download.nvidia.com/cg/asin.html

atan2Impl()

template<typename T >

LVARRAY_DEVICE LVARRAY_FORCE_INLINE T LvArray::math::internal::atan2Impl	(	T const	y,
		T const	x
	)

Returns

The arctangent of the point x, y.

Parameters

y	The y coordinate.
x	The x coordinate.

Has a max error of 2.29e-3 and max relative error of 1.51e-3 for half precision.

Note

Modified from https://developer.download.nvidia.com/cg/atan2.html

convert()

template<typename T , typename U >

LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr T LvArray::math::internal::convert	(	T	const,
		U const	u
	)

Convert u to type.

Template Parameters

T.
T	The type to convert to.
U	The type to convert from.

Parameters

u	The value to convert.

Note

No checking is done to ensure the conversion is safe. Ie you could convert -1 to uint.

Returns

u converted to

Template Parameters

T.

getFirst()

template<typename T >

LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr SingleType< T > LvArray::math::internal::getFirst

(

T const

x

)

Returns

x.

Template Parameters

T	The type of x.

Parameters

x	The value to return.

getSecond()

template<typename T >

LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr SingleType< T > LvArray::math::internal::getSecond

(

T const

x

)

Returns

x.

Template Parameters

T	The type of x.

Parameters

x	The value to return.

lessThan()

template<typename T >

LVARRAY_HOST_DEVICE constexpr T LvArray::math::internal::lessThan ( T const  x, T const  y  )

inline

Returns

1 if x is less than y, else 0.

Template Parameters

T	The type of x and y.

Parameters

x	The first value.
y	The second value.

numValues()

template<typename T >

LVARRAY_HOST_DEVICE LVARRAY_FORCE_INLINE constexpr int LvArray::math::internal::numValues

(

T

const

)

Return the number of values stored in.

Template Parameters

T,by	default this is 1.
T	The type to query.

Returns

The number of values stored in

Template Parameters

T,by	default this is 1.