hermes::Numbers Struct Reference

Number functions. More...

#include <numeric.h>

Public Member Functions
template<>
HERMES_DEVICE_CALLABLE constexpr f64	lowest ()
	Gets lowest representable 64 bit floating point.
template<>
HERMES_DEVICE_CALLABLE constexpr f32	lowest ()
	Gets lowest representable 32 bit floating point.
template<>
HERMES_DEVICE_CALLABLE constexpr f32	greatest ()
	Gets greatest 32 bit floating point number.
template<>
HERMES_DEVICE_CALLABLE constexpr f64	greatest ()
	Gets greatest 64 bit floating point number.

Static Public Member Functions
static HERMES_DEVICE_CALLABLE constexpr f64	lowest_f64 ()
	Gets lowest representable 64 bit floating point.
static HERMES_DEVICE_CALLABLE constexpr f32	lowest_f32 ()
	Gets lowest representable 64 bit floating point.
template<typename T >
static HERMES_DEVICE_CALLABLE constexpr T	lowest ()
	Gets lowest representable floating point.
static HERMES_DEVICE_CALLABLE constexpr f64	greatest_f32 ()
	Gets greatest representable 32 bit floating point.
static HERMES_DEVICE_CALLABLE constexpr f64	greatest_f64 ()
	Gets greatest representable 64 bit floating point.
template<typename T >
static HERMES_DEVICE_CALLABLE constexpr T	greatest ()
	Gets greatest representable floating point.
template<typename T >
static HERMES_DEVICE_CALLABLE constexpr T	min (const T &a, const T &b)
	Computes minimum between two numbers.
template<typename T >
static HERMES_DEVICE_CALLABLE constexpr T	max (const T &a, const T &b)
	Computes maximum between two numbers.
template<typename T >
static HERMES_DEVICE_CALLABLE constexpr T	min (std::initializer_list< T > l)
	Computes minimum value from input.
template<typename T >
static HERMES_DEVICE_CALLABLE constexpr T	max (std::initializer_list< T > l)
	Computes maximum value from input.
template<typename T >
static HERMES_DEVICE_CALLABLE u8	countHexDigits (T n)
	Counts hexadecimal digits.
template<typename T >
static HERMES_DEVICE_CALLABLE T	clamp (const T &n, const T &l, const T &u)
	Clamps value to closed interval.
template<typename T >
static HERMES_DEVICE_CALLABLE void	swap (T &a, T &b)
	Swaps values.
template<typename T >
static HERMES_DEVICE_CALLABLE constexpr T	sqr (T a)
template<typename T >
static HERMES_DEVICE_CALLABLE constexpr T	cube (T a)
	Computes square.
template<typename T >
static HERMES_DEVICE_CALLABLE int	sign (T a)
	Computes sign.
template<typename T >
static HERMES_DEVICE_CALLABLE constexpr T	sqrt (T a)
	Computes square root.
template<typename T >
static HERMES_DEVICE_CALLABLE T	FMA (T a, T b, T c)
	Computes a * b + c.
template<typename Ta , typename Tb , typename Tc , typename Td >
static HERMES_DEVICE_CALLABLE auto	differenceOfProducts (Ta a, Tb b, Tc c, Td d)
	Computes difference of products.
template<typename T , typename C >
static HERMES_DEVICE_CALLABLE constexpr T	evaluatePolynomial (T t, C c)
	Solves polynomial.
template<typename T , typename C , typename... Args>
static HERMES_DEVICE_CALLABLE constexpr T	evaluatePolynomial (T t, C c, Args... cs)
	Solves polynomial.
template<typename Predicate >
static HERMES_DEVICE_CALLABLE size_t	findInterval (size_t sz, const Predicate &pred)
	Bisect range based on predicate.
static HERMES_DEVICE_CALLABLE u32	separateBitsBy1 (u32 n)
	Separate bits by 1 bit-space.
static HERMES_DEVICE_CALLABLE u32	separateBitsBy2 (u32 n)
	Separate bits by 2 bit-spaces.
static HERMES_DEVICE_CALLABLE u32	interleaveBits (u32 x, u32 y, u32 z)
	Interleaves bits of three integers.
static HERMES_DEVICE_CALLABLE u32	interleaveBits (u32 x, u32 y)
	Interleaves bits of two integers.
static HERMES_DEVICE_CALLABLE int	floatExponent (f32 v)
	Extracts exponent from floating-point number.
static HERMES_DEVICE_CALLABLE int	floatSignificand (f32 v)
	Extracts significand bits.
static HERMES_DEVICE_CALLABLE uint32_t	floatSignBit (f32 v)
	Extracts sign bit.
static HERMES_DEVICE_CALLABLE uint32_t	floatToBits (f32 f)
	Interprets a floating-point value into a integer type.
static HERMES_DEVICE_CALLABLE f32	bitsToFloat (uint32_t ui)
	Fills a f32 variable data.
static HERMES_DEVICE_CALLABLE uint64_t	floatToBits (f64 d)
	Interprets a f64-point value into a integer type.
static HERMES_DEVICE_CALLABLE f64	bitsToDouble (uint64_t ui)
	Fills a f64 variable data.
static HERMES_DEVICE_CALLABLE f32	nextFloatUp (f32 v)
	Computes the next greater representable floating-point value.
static HERMES_DEVICE_CALLABLE f32	nextFloatDown (f32 v)
	Computes the next smaller representable floating-point value.
static HERMES_DEVICE_CALLABLE f64	nextDoubleUp (f64 v)
	Computes the next greater representable floating-point value.
static HERMES_DEVICE_CALLABLE f64	nextDoubleDown (f64 v)
	Computes the next smaller representable floating-point value.
static HERMES_DEVICE_CALLABLE constexpr int	lowest_int ()
	Gets minimum representable 32 bit signed integer.
static HERMES_DEVICE_CALLABLE constexpr int	greatest_int ()
	Gets maximum representable 32 bit signed integer.
static HERMES_DEVICE_CALLABLE constexpr bool	isPowerOf2 (int v)
	Checks if integer is power of 2.
static HERMES_DEVICE_CALLABLE int	mod (int a, int b)
	Computes modulus.
static HERMES_DEVICE_CALLABLE int	ceil2Int (float f)
	rounds up
static HERMES_DEVICE_CALLABLE int	floor2Int (float f)
	rounds down
static HERMES_DEVICE_CALLABLE int	round2Int (float f)
	rounds to closest integer
static HERMES_DEVICE_CALLABLE u8	countDigits (u64 t, u8 base=10)
	Computes number of digits.
static HERMES_DEVICE_CALLABLE real_t	fract (real_t x)
	Extract decimal fraction from x.
static HERMES_DEVICE_CALLABLE real_t	mulRoundDown (real_t a, real_t b)
	Multiplies and rounds down to the next smaller float value.
static HERMES_DEVICE_CALLABLE real_t	mulRoundUp (real_t a, real_t b)
	Multiplies and rounds up to the next float value.
static HERMES_DEVICE_CALLABLE real_t	divRoundDown (real_t a, real_t b)
	Divides and rounds down to the next smaller float value.
static HERMES_DEVICE_CALLABLE real_t	divRoundUp (real_t a, real_t b)
	Divides and rounds up to the next float value.
static HERMES_DEVICE_CALLABLE real_t	addRoundDown (real_t a, real_t b)
	Adds and rounds down to the next smaller float value.
static HERMES_DEVICE_CALLABLE real_t	addRoundUp (real_t a, real_t b)
	Adds and rounds up to the next float value.
static HERMES_DEVICE_CALLABLE real_t	subRoundDown (real_t a, real_t b)
	Subtracts and rounds down to the next smaller float value.
static HERMES_DEVICE_CALLABLE real_t	subRoundUp (real_t a, real_t b)
	Subtracts and rounds up to the next float value.
static HERMES_DEVICE_CALLABLE real_t	sqrtRoundDown (real_t a)
	Computes square root rounded down to the next smaller float value.
static HERMES_DEVICE_CALLABLE real_t	sqrtRoundUp (real_t a)
	Computes square root rounded up to the next float value.
static HERMES_DEVICE_CALLABLE f32	log2 (f32 x)
	Computes base 2 log.
static HERMES_DEVICE_CALLABLE f32	safe_sqrt (f32 x)
	Computes square root with clamped input.
template<int n>
static HERMES_DEVICE_CALLABLE constexpr real_t	pow (real_t b)
	Computes b to the power of n.
static HERMES_DEVICE_CALLABLE real_t	fastExp (real_t x)
	Computes fast exponential.
static HERMES_DEVICE_CALLABLE constexpr real_t	gamma (i32 n)
	Computes conservative bounds in error.
template<>
HERMES_DEVICE_CALLABLE constexpr float	pow (float v)
	Computes v to the power of 1.
template<>
HERMES_DEVICE_CALLABLE constexpr float	pow (float v)
	Computes v to the power of 0.

Detailed Description

Number functions.

Member Function Documentation

addRoundDown()

static HERMES_DEVICE_CALLABLE real_t hermes::Numbers::addRoundDown ( real_t  a, real_t  b  )

inlinestatic

Adds and rounds down to the next smaller float value.

Parameters

a
b

Returns

addRoundUp()

static HERMES_DEVICE_CALLABLE real_t hermes::Numbers::addRoundUp ( real_t  a, real_t  b  )

inlinestatic

Adds and rounds up to the next float value.

Parameters

a
b

Returns

bitsToDouble()

static HERMES_DEVICE_CALLABLE f64 hermes::Numbers::bitsToDouble ( uint64_t  ui )

inlinestatic

Fills a f64 variable data.

Parameters

ui

bits

Returns

a f64 built from bits of ui

bitsToFloat()

static HERMES_DEVICE_CALLABLE f32 hermes::Numbers::bitsToFloat ( uint32_t  ui )

inlinestatic

Fills a f32 variable data.

Parameters

ui

bits

Returns

a f32 built from bits of ui

ceil2Int()

static HERMES_DEVICE_CALLABLE int hermes::Numbers::ceil2Int ( float  f )

inlinestatic

rounds up

Parameters

f

[in]

Returns

ceil of f

clamp()

template<typename T >

static HERMES_DEVICE_CALLABLE T hermes::Numbers::clamp ( const T &  n, const T &  l, const T &  u  )

inlinestatic

Clamps value to closed interval.

Parameters

n	[in] value
l	[in] low
u	[in] high

Returns

clamp b to be in [l, h]

countDigits()

static HERMES_DEVICE_CALLABLE u8 hermes::Numbers::countDigits ( u64  t, u8  base = 10  )

inlinestatic

Computes number of digits.

Parameters

t
base

Returns

countHexDigits()

template<typename T >

static HERMES_DEVICE_CALLABLE u8 hermes::Numbers::countHexDigits ( T  n )

inlinestatic

Counts hexadecimal digits.

Template Parameters

T

Parameters

n

Returns

cube()

template<typename T >

static HERMES_DEVICE_CALLABLE constexpr T hermes::Numbers::cube ( T  a )

inlinestaticconstexpr

Computes square.

Template Parameters

T

Parameters

a

Returns

differenceOfProducts()

template<typename Ta , typename Tb , typename Tc , typename Td >

static HERMES_DEVICE_CALLABLE auto hermes::Numbers::differenceOfProducts ( Ta  a, Tb  b, Tc  c, Td  d  )

inlinestatic

Computes difference of products.

Template Parameters

Ta
Tb
Tc
Td

Parameters

a
b
c
d

Returns

divRoundDown()

static HERMES_DEVICE_CALLABLE real_t hermes::Numbers::divRoundDown ( real_t  a, real_t  b  )

inlinestatic

Divides and rounds down to the next smaller float value.

Parameters

a
b

Returns

divRoundUp()

static HERMES_DEVICE_CALLABLE real_t hermes::Numbers::divRoundUp ( real_t  a, real_t  b  )

inlinestatic

Divides and rounds up to the next float value.

Parameters

a
b

Returns

evaluatePolynomial() [1/2]

template<typename T , typename C >

static HERMES_DEVICE_CALLABLE constexpr T hermes::Numbers::evaluatePolynomial ( T  t, C  c  )

inlinestaticconstexpr

Solves polynomial.

Template Parameters

T
C

Parameters

t
c

Returns

evaluatePolynomial() [2/2]

template<typename T , typename C , typename... Args>

static HERMES_DEVICE_CALLABLE constexpr T hermes::Numbers::evaluatePolynomial ( T  t, C  c, Args...  cs  )

inlinestaticconstexpr

Solves polynomial.

Template Parameters

T
C
Args

Parameters

t
c
cs

Returns

fastExp()

static HERMES_DEVICE_CALLABLE real_t hermes::Numbers::fastExp ( real_t  x )

inlinestatic

Computes fast exponential.

Parameters

x

Returns

findInterval()

template<typename Predicate >

static HERMES_DEVICE_CALLABLE size_t hermes::Numbers::findInterval ( size_t  sz, const Predicate &  pred  )

inlinestatic

Bisect range based on predicate.

Template Parameters

Predicate

Parameters

sz
pred

Returns

floatExponent()

static HERMES_DEVICE_CALLABLE int hermes::Numbers::floatExponent ( f32  v )

inlinestatic

Extracts exponent from floating-point number.

Parameters

v

Returns

floatSignBit()

static HERMES_DEVICE_CALLABLE uint32_t hermes::Numbers::floatSignBit ( f32  v )

inlinestatic

Extracts sign bit.

Parameters

v

Returns

floatSignificand()

static HERMES_DEVICE_CALLABLE int hermes::Numbers::floatSignificand ( f32  v )

inlinestatic

Extracts significand bits.

Parameters

v

Returns

floatToBits() [1/2]

static HERMES_DEVICE_CALLABLE uint32_t hermes::Numbers::floatToBits ( f32  f )

inlinestatic

Interprets a floating-point value into a integer type.

Parameters

f

f32 value

Returns

a 32 bit unsigned integer containing the bits of f

floatToBits() [2/2]

static HERMES_DEVICE_CALLABLE uint64_t hermes::Numbers::floatToBits ( f64  d )

inlinestatic

Interprets a f64-point value into a integer type.

Parameters

d

f64 value

Returns

a 64 bit unsigned integer containing the bits of f

floor2Int()

static HERMES_DEVICE_CALLABLE int hermes::Numbers::floor2Int ( float  f )

inlinestatic

rounds down

Parameters

f

[in]

Returns

floor of f

FMA()

template<typename T >

static HERMES_DEVICE_CALLABLE T hermes::Numbers::FMA ( T  a, T  b, T  c  )

inlinestatic

Computes a * b + c.

Template Parameters

T

Parameters

a
b
c

Returns

fract()

static HERMES_DEVICE_CALLABLE real_t hermes::Numbers::fract ( real_t  x )

inlinestatic

Extract decimal fraction from x.

Parameters

x

Returns

gamma()

static HERMES_DEVICE_CALLABLE constexpr real_t hermes::Numbers::gamma ( i32  n )

inlinestaticconstexpr

Computes conservative bounds in error.

Parameters

n

Returns

greatest() [1/3]

template<typename T >

static HERMES_DEVICE_CALLABLE constexpr T hermes::Numbers::greatest ( )

inlinestaticconstexpr

Gets greatest representable floating point.

Template Parameters

T

Returns

greatest() [2/3]

template<>

HERMES_DEVICE_CALLABLE constexpr f32 hermes::Numbers::greatest ( )

inlineconstexpr

Gets greatest 32 bit floating point number.

Returns

greatest() [3/3]

template<>

HERMES_DEVICE_CALLABLE constexpr f64 hermes::Numbers::greatest ( )

inlineconstexpr

Gets greatest 64 bit floating point number.

Returns

greatest_f32()

static HERMES_DEVICE_CALLABLE constexpr f64 hermes::Numbers::greatest_f32 ( )

inlinestaticconstexpr

Gets greatest representable 32 bit floating point.

Returns

greatest_f64()

static HERMES_DEVICE_CALLABLE constexpr f64 hermes::Numbers::greatest_f64 ( )

inlinestaticconstexpr

Gets greatest representable 64 bit floating point.

Returns

greatest_int()

static HERMES_DEVICE_CALLABLE constexpr int hermes::Numbers::greatest_int ( )

inlinestaticconstexpr

Gets maximum representable 32 bit signed integer.

Returns

interleaveBits() [1/2]

static HERMES_DEVICE_CALLABLE u32 hermes::Numbers::interleaveBits ( u32  x, u32  y  )

inlinestatic

Interleaves bits of two integers.

Parameters

x
y

Returns

interleaveBits() [2/2]

static HERMES_DEVICE_CALLABLE u32 hermes::Numbers::interleaveBits ( u32  x, u32  y, u32  z  )

inlinestatic

Interleaves bits of three integers.

Parameters

x
y
z

Returns

isPowerOf2()

static HERMES_DEVICE_CALLABLE constexpr bool hermes::Numbers::isPowerOf2 ( int  v )

inlinestaticconstexpr

Checks if integer is power of 2.

Parameters

v	[in] value

Returns

true if v is power of 2

log2()

static HERMES_DEVICE_CALLABLE f32 hermes::Numbers::log2 ( f32  x )

inlinestatic

Computes base 2 log.

Parameters

x	[in] value

Returns

base-2 logarithm of x

lowest() [1/3]

template<typename T >

static HERMES_DEVICE_CALLABLE constexpr T hermes::Numbers::lowest ( )

inlinestaticconstexpr

Gets lowest representable floating point.

Template Parameters

T

Returns

lowest() [2/3]

template<>

HERMES_DEVICE_CALLABLE constexpr f64 hermes::Numbers::lowest ( )

inlineconstexpr

Gets lowest representable 64 bit floating point.

Returns

lowest() [3/3]

template<>

HERMES_DEVICE_CALLABLE constexpr f32 hermes::Numbers::lowest ( )

inlineconstexpr

Gets lowest representable 32 bit floating point.

Returns

lowest_f32()

static HERMES_DEVICE_CALLABLE constexpr f32 hermes::Numbers::lowest_f32 ( )

inlinestaticconstexpr

Gets lowest representable 64 bit floating point.

Template Parameters

T

Returns

lowest_f64()

static HERMES_DEVICE_CALLABLE constexpr f64 hermes::Numbers::lowest_f64 ( )

inlinestaticconstexpr

Gets lowest representable 64 bit floating point.

Template Parameters

T

Returns

lowest_int()

static HERMES_DEVICE_CALLABLE constexpr int hermes::Numbers::lowest_int ( )

inlinestaticconstexpr

Gets minimum representable 32 bit signed integer.

Returns

max() [1/2]

template<typename T >

static HERMES_DEVICE_CALLABLE constexpr T hermes::Numbers::max ( const T &  a, const T &  b  )

inlinestaticconstexpr

Computes maximum between two numbers.

Template Parameters

T

Parameters

a
b

Returns

max() [2/2]

template<typename T >

static HERMES_DEVICE_CALLABLE constexpr T hermes::Numbers::max ( std::initializer_list< T >  l )

inlinestaticconstexpr

Computes maximum value from input.

Template Parameters

T

Parameters

l

Returns

min() [1/2]

template<typename T >

static HERMES_DEVICE_CALLABLE constexpr T hermes::Numbers::min ( const T &  a, const T &  b  )

inlinestaticconstexpr

Computes minimum between two numbers.

Template Parameters

T

Parameters

a
b

Returns

min() [2/2]

template<typename T >

static HERMES_DEVICE_CALLABLE constexpr T hermes::Numbers::min ( std::initializer_list< T >  l )

inlinestaticconstexpr

Computes minimum value from input.

Template Parameters

T

Parameters

l

Returns

mod()

static HERMES_DEVICE_CALLABLE int hermes::Numbers::mod ( int  a, int  b  )

inlinestatic

Computes modulus.

Parameters

a	[in]
b	[in]

Returns

the remainder of a / b

mulRoundDown()

static HERMES_DEVICE_CALLABLE real_t hermes::Numbers::mulRoundDown ( real_t  a, real_t  b  )

inlinestatic

Multiplies and rounds down to the next smaller float value.

Parameters

a
b

Returns

mulRoundUp()

static HERMES_DEVICE_CALLABLE real_t hermes::Numbers::mulRoundUp ( real_t  a, real_t  b  )

inlinestatic

Multiplies and rounds up to the next float value.

Parameters

a
b

Returns

nextDoubleDown()

static HERMES_DEVICE_CALLABLE f64 hermes::Numbers::nextDoubleDown ( f64  v )

inlinestatic

Computes the next smaller representable floating-point value.

Parameters

v	floating point value

Returns

the next smaller floating point value

nextDoubleUp()

static HERMES_DEVICE_CALLABLE f64 hermes::Numbers::nextDoubleUp ( f64  v )

inlinestatic

Computes the next greater representable floating-point value.

Parameters

v	floating point value

Returns

the next greater floating point value

nextFloatDown()

static HERMES_DEVICE_CALLABLE f32 hermes::Numbers::nextFloatDown ( f32  v )

inlinestatic

Computes the next smaller representable floating-point value.

Parameters

v	floating point value

Returns

the next smaller floating point value

nextFloatUp()

static HERMES_DEVICE_CALLABLE f32 hermes::Numbers::nextFloatUp ( f32  v )

inlinestatic

Computes the next greater representable floating-point value.

Parameters

v	floating point value

Returns

the next greater floating point value

pow() [1/3]

template<>

HERMES_DEVICE_CALLABLE constexpr float hermes::Numbers::pow ( float  v )

inlinestaticconstexpr

Computes v to the power of 1.

Parameters

v

Returns

pow() [2/3]

template<>

HERMES_DEVICE_CALLABLE constexpr float hermes::Numbers::pow ( float  v )

inlinestaticconstexpr

Computes v to the power of 0.

Parameters

v

Returns

pow() [3/3]

template<int n>

static HERMES_DEVICE_CALLABLE constexpr real_t hermes::Numbers::pow ( real_t  b )

inlinestaticconstexpr

Computes b to the power of n.

Template Parameters

n

Parameters

b

Returns

round2Int()

static HERMES_DEVICE_CALLABLE int hermes::Numbers::round2Int ( float  f )

inlinestatic

rounds to closest integer

Parameters

f

[in]

Returns

next integer greater or equal to f

safe_sqrt()

static HERMES_DEVICE_CALLABLE f32 hermes::Numbers::safe_sqrt ( f32  x )

inlinestatic

Computes square root with clamped input.

Parameters

x

Returns

separateBitsBy1()

static HERMES_DEVICE_CALLABLE u32 hermes::Numbers::separateBitsBy1 ( u32  n )

inlinestatic

Separate bits by 1 bit-space.

Parameters

n

Returns

separateBitsBy2()

static HERMES_DEVICE_CALLABLE u32 hermes::Numbers::separateBitsBy2 ( u32  n )

inlinestatic

Separate bits by 2 bit-spaces.

Parameters

n

Returns

sign()

template<typename T >

static HERMES_DEVICE_CALLABLE int hermes::Numbers::sign ( T  a )

inlinestatic

Computes sign.

Template Parameters

T

Parameters

a

Returns

sqr()

template<typename T >

static HERMES_DEVICE_CALLABLE constexpr T hermes::Numbers::sqr ( T  a )

inlinestaticconstexpr

Template Parameters

T

Parameters

a

Returns

sqrt()

template<typename T >

static HERMES_DEVICE_CALLABLE constexpr T hermes::Numbers::sqrt ( T  a )

inlinestaticconstexpr

Computes square root.

Template Parameters

T

Parameters

a

Returns

sqrtRoundDown()

static HERMES_DEVICE_CALLABLE real_t hermes::Numbers::sqrtRoundDown ( real_t  a )

inlinestatic

Computes square root rounded down to the next smaller float value.

Parameters

a

Returns

sqrtRoundUp()

static HERMES_DEVICE_CALLABLE real_t hermes::Numbers::sqrtRoundUp ( real_t  a )

inlinestatic

Computes square root rounded up to the next float value.

Parameters

a

Returns

subRoundDown()

static HERMES_DEVICE_CALLABLE real_t hermes::Numbers::subRoundDown ( real_t  a, real_t  b  )

inlinestatic

Subtracts and rounds down to the next smaller float value.

Parameters

a
b

Returns

subRoundUp()

static HERMES_DEVICE_CALLABLE real_t hermes::Numbers::subRoundUp ( real_t  a, real_t  b  )

inlinestatic

Subtracts and rounds up to the next float value.

Parameters

a
b

Returns

swap()

template<typename T >

static HERMES_DEVICE_CALLABLE void hermes::Numbers::swap ( T &  a, T &  b  )

inlinestatic

Swaps values.

Template Parameters

T

Parameters

a
b

---

The documentation for this struct was generated from the following file:

• hermes/numeric/numeric.h