math.cuh File Reference

Templatized mathematical function definitions for integer and floating-point types. More...

#include "common.cuh"
#include "constexpr_math.cuh"
#include <kat/on_device/builtins.cuh>
#include <type_traits>

Functions
template<typename I >
KAT_FD unsigned	kat::log2_of_power_of_2 (I p)
	compute the base-two logarithm of a number known to be a power of 2. More...
template<typename T , typename S >
KAT_FD T	kat::div_by_power_of_2_rounding_up (const T &dividend, const S &divisor)
	A variant of div_rounding_up (which you can find in constexpr_math.cuh), which has (non-constexpr, unfortunately) optimizations based on the knowledge the divisor is a power of 2. More...
template<typename I , typename P >
constexpr KAT_FD I	kat::div_by_power_of_2 (I dividend, P power_of_2)
template<typename T >
constexpr KAT_FD T	kat::gcd (T u, T v)
	compute the greatest common divisor (gcd) of two values. More...
template<typename I >
KAT_FD I	kat::lcm (I u, I v)
	compute the least common multiple (LCM) of two integer values More...
template<typename I >
KAT_FD int	kat::detail::count_leading_zeros (I x)
	Return the number of bits, beginning from the least-significant, which are all 0 ("leading" zeros) More...
template<typename I >
KAT_FD unsigned	kat::log2 (I x)
	compute the (integral) base-two logarithm of a number More...
template<typename T >
KAT_FD T	kat::detail::minimum (std::integral_constant< bool, false >, T x, T y)
template<typename T >
KAT_FD T	kat::detail::minimum (std::integral_constant< bool, true >, T x, T y)
template<typename T >
KAT_FD T	kat::detail::maximum (std::integral_constant< bool, false >, T x, T y)
template<typename T >
KAT_FD T	kat::detail::maximum (std::integral_constant< bool, true >, T x, T y)
template<typename T >
KAT_FD T	kat::detail::absolute_value (std::integral_constant< bool, false >, T x)
template<typename T >
KAT_FD T	kat::detail::absolute_value (std::integral_constant< bool, true >, T x)
template<typename T >
KAT_FD T	kat::minimum (T x, T y)
template<typename T >
KAT_FD T	kat::maximum (T x, T y)
template<typename T >
KAT_FD T	kat::absolute_value (T x)

Detailed Description

Templatized mathematical function definitions for integer and floating-point types.

CUDA has many mathematical primitives - which are already found in builtins.cuh. However, they are often not defined for all types; and - some functions are missing (e.g. gcd()) or can benefit from specialization (e.g. division by a power of 2). This file has the wider selection of functions, utilizing a primitive (from builtins::) when relevant, and multi-instruction implementation otherwise.

Note

Including this file is sufficient for accessing all functions in constexpr_math.cuh.

Function Documentation

count_leading_zeros()

template<typename I >

KAT_FD int kat::detail::count_leading_zeros ( I  x )

delete

Return the number of bits, beginning from the least-significant, which are all 0 ("leading" zeros)

Returns

The number of leading zeros, between 0 and the size of I in bits.

div_by_power_of_2_rounding_up()

template<typename T , typename S >

KAT_FD T kat::div_by_power_of_2_rounding_up	(	const T &	dividend,
		const S &	divisor
	)

A variant of div_rounding_up (which you can find in constexpr_math.cuh), which has (non-constexpr, unfortunately) optimizations based on the knowledge the divisor is a power of 2.

Returns

The smallest multiple of divisor above dividend / divisor

gcd()

template<typename T >

constexpr KAT_FD T kat::gcd	(	T	u,
		T	v
	)

compute the greatest common divisor (gcd) of two values.

Parameters

u	One integral value (prefer making this the larger one)
v	Another integral value (prefer making this the smaller one)

Returns

the largest I value d such that d divides u and d divides v.

lcm()

template<typename I >

KAT_FD I kat::lcm	(	I	u,
		I	v
	)

compute the least common multiple (LCM) of two integer values

Template Parameters

I	an integral (or integral-number-like) type

Parameters

u	One of the numbers which the result must divide
v	Another one of the numbers which the result must divide

Returns

The highest I value which divides both u and v.

log2()

template<typename I >

KAT_FD unsigned kat::log2

(

I

x

)

compute the (integral) base-two logarithm of a number

Note

Yes, this is trivial to do, but:

1. This says what you're doing, not how you do it (e.g. left-shifting bits and such)
2. There's a device-side optimization here (which isn't constexpr)

Parameters

x	a non-negative value

Returns

floor(log2(x)), i.e. the least exponent l such than 2^l >= x

log2_of_power_of_2()

template<typename I >

KAT_FD unsigned kat::log2_of_power_of_2

(

I

p

)

compute the base-two logarithm of a number known to be a power of 2.

Note

Yes, this is trivial to do, but:

1. This says what you're doing, not how you do it (e.g. left-shifting bits and such)
2. There's a device-side optimization here (which isn't constexpr)

Parameters

p	an integral power of 2

Returns

the exponent l such than 2^l equals p