Fast Approximations for float Math Functions

Fast approximations for math functions on limited precision floats. More...

Modules
	Basic Math Functors in the Math API
	Basic math functors in the Math API.

Functions
Float32	mi::math::fast_sqrt (Float32 i)
	A fast implementation of sqrt(x) for floats. More...
Float32	mi::math::fast_exp (Float32 x)
	A fast implementation of exp for floats. More...
Float32	mi::math::fast_pow2 (Float32 x)
	A fast implementation of pow(2,x) for floats. More...
Float32	mi::math::fast_log2 (Float32 i)
	A fast implementation of log2(x) for floats. More...
Float32	mi::math::fast_pow (Float32 b, Float32 e)
	A fast implementation of pow(x,y) for floats. More...
Float32	mi::math::acos (Float32 s)
	Returns the arc cosine of s in radians. More...
Float64	mi::math::acos (Float64 s)
	Returns the arc cosine of s in radians. More...
bool	mi::math::all (Uint8 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Uint16 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Uint32 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Uint64 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Sint8 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Sint16 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Sint32 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Sint64 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Float32 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Float64 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Uint8 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Uint16 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Uint32 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Uint64 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Sint8 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Sint16 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Sint32 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Sint64 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Float32 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Float64 v)
	Returns true if v is not equal to zero. More...
Float32	mi::math::asin (Float32 s)
	Returns the arc sine of s in radians. More...
Float64	mi::math::asin (Float64 s)
	Returns the arc sine of s in radians. More...
Float32	mi::math::atan (Float32 s)
	Returns the arc tangent of s. More...
Float64	mi::math::atan (Float64 s)
	Returns the arc tangent of s. More...
Float32	mi::math::atan2 (Float32 s, Float32 t)
	Returns the arc tangent of s / t. More...
Float64	mi::math::atan2 (Float64 s, Float64 t)
	Returns the arc tangent of s / t. More...
Float32	mi::math::ceil (Float32 s)
	Returns the smallest integral value that is not less than s. More...
Float64	mi::math::ceil (Float64 s)
	Returns the smallest integral value that is not less than s. More...
Uint8	mi::math::clamp (Uint8 s, Uint8 low, Uint8 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Uint16	mi::math::clamp (Uint16 s, Uint16 low, Uint16 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Uint32	mi::math::clamp (Uint32 s, Uint32 low, Uint32 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Uint64	mi::math::clamp (Uint64 s, Uint64 low, Uint64 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Sint8	mi::math::clamp (Sint8 s, Sint8 low, Sint8 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Sint16	mi::math::clamp (Sint16 s, Sint16 low, Sint16 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Sint32	mi::math::clamp (Sint32 s, Sint32 low, Sint32 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Sint64	mi::math::clamp (Sint64 s, Sint64 low, Sint64 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Float32	mi::math::clamp (Float32 s, Float32 low, Float32 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Float64	mi::math::clamp (Float64 s, Float64 low, Float64 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Float32	mi::math::cos (Float32 a)
	Returns the cosine of a. The angle a is specified in radians. More...
Float64	mi::math::cos (Float64 a)
	Returns the cosine of a. The angle a is specified in radians. More...
Float32	mi::math::degrees (Float32 r)
	Converts radians r to degrees. More...
Float64	mi::math::degrees (Float64 r)
	Converts radians r to degrees. More...
Float32	mi::math::exp2 (Float32 s)
	Returns the constant 2 to the power of s (exponential function). More...
Float64	mi::math::exp2 (Float64 s)
	Returns the constant 2 to the power of s (exponential function). More...
Float32	mi::math::floor (Float32 s)
	Returns the largest integral value that is not greater than s. More...
Float64	mi::math::floor (Float64 s)
	Returns the largest integral value that is not greater than s. More...
Float32	mi::math::fmod (Float32 a, Float32 b)
	Returns a modulo b, in other words, the remainder of a/b. More...
Float64	mi::math::fmod (Float64 a, Float64 b)
	Returns a modulo b, in other words, the remainder of a/b. More...
Float32	mi::math::frac (Float32 s)
	Returns the positive fractional part of s. More...
Float64	mi::math::frac (Float64 s)
	Returns the positive fractional part of s. More...
bool	mi::math::is_approx_equal (Float32 left, Float32 right, Float32 e)
	Compares the two given values for equality within the given epsilon. More...
bool	mi::math::is_approx_equal (Float64 left, Float64 right, Float64 e)
	Compares the two given values for equality within the given epsilon. More...
Uint32	mi::math::leading_zeros (Uint32 v)
	Returns the number of leading zeros of v, 32-bit version. More...
Uint32	mi::math::leading_zeros (Uint64 v)
	Returns the number of leading zeros of v, 64-bit version. More...
Float32	mi::math::lerp (Float32 s1, Float32 s2, Float32 t)
	Returns the linear interpolation between s1 and s2, i.e., it returns (1-t) * s1 + t * s2. More...
Float64	mi::math::lerp (Float64 s1, Float64 s2, Float64 t)
	Returns the linear interpolation between s1 and s2, i.e., it returns (1-t) * s1 + t * s2. More...
Float32	mi::math::log2 (Float32 s)
	Returns the base 2 logarithm of s. More...
Float64	mi::math::log2 (Float64 s)
	Returns the base 2 logarithm of s. More...
Sint32	mi::math::log2_int (const Uint32 v)
	Returns the integer log2 of v. More...
Sint32	mi::math::log2_int (const Uint64 v)
	Returns the integer log2 of v. More...
Sint32	mi::math::log2_int (const Float32 v)
	Returns the integer log2 of v. More...
Sint32	mi::math::log2_int (const Float64 v)
	Returns the integer log2 of v. More...
template<typename Integer>
Sint32	mi::math::log2_int_ceil (const Integer v)
	Returns the integer log2 of v, i.e., rounded up to the next integer. More...
Float32	mi::math::log10 (Float32 s)
	Returns the base 10 logarithm of s. More...
Float64	mi::math::log10 (Float64 s)
	Returns the base 10 logarithm of s. More...
Float32	mi::math::modf (Float32 s, Float32 &i)
	Returns the fractional part of s and stores the integral part of s in i. More...
Float64	mi::math::modf (Float64 s, Float64 &i)
	Returns the fractional part of s and stores the integral part of s in i. More...
Uint32	mi::math::pow (Uint32 a, Uint32 b)
	Returns a to the power of b. More...
Uint64	mi::math::pow (Uint64 a, Uint64 b)
	Returns a to the power of b. More...
Sint32	mi::math::pow (Sint32 a, Sint32 b)
	Returns a to the power of b. More...
Sint64	mi::math::pow (Sint64 a, Sint64 b)
	Returns a to the power of b. More...
Float32	mi::math::pow (Float32 a, Float32 b)
	Returns a to the power of b. More...
Float64	mi::math::pow (Float64 a, Float64 b)
	Returns a to the power of b. More...
Float32	mi::math::radians (Float32 d)
	Converts degrees d to radians. More...
Float64	mi::math::radians (Float64 d)
	Converts degrees d to radians. More...
Float32	mi::math::round (Float32 s)
	Returns s rounded to the nearest integer value. More...
Float64	mi::math::round (Float64 s)
	Returns s rounded to the nearest integer value. More...
Float32	mi::math::rsqrt (Float32 s)
	Returns the reciprocal of the square root of s. More...
Float64	mi::math::rsqrt (Float64 s)
	Returns the reciprocal of the square root of s. More...
Float32	mi::math::saturate (Float32 s)
	Returns the value s clamped to the range [0,1]. More...
Float64	mi::math::saturate (Float64 s)
	Returns the value s clamped to the range [0,1]. More...
Sint8	mi::math::sign (Sint8 s)
	Returns -1 if s<0, 0 if s==0, and +1 if s>0. More...
Sint16	mi::math::sign (Sint16 s)
	Returns -1 if s<0, 0 if s==0, and +1 if s>0. More...
Sint32	mi::math::sign (Sint32 s)
	Returns -1 if s<0, 0 if s==0, and +1 if s>0. More...
Sint64	mi::math::sign (Sint64 s)
	Returns -1 if s<0, 0 if s==0, and +1 if s>0. More...
Float32	mi::math::sign (Float32 s)
	Returns -1 if s<0, 0 if s==0, and +1 if s>0. More...
Float64	mi::math::sign (Float64 s)
	Returns -1 if s<0, 0 if s==0, and +1 if s>0. More...
bool	mi::math::sign_bit (Sint8 s)
	Returns true if s<0 and false if s>= 0. More...
bool	mi::math::sign_bit (Sint16 s)
	Returns true if s<0 and false if s>= 0. More...
bool	mi::math::sign_bit (Sint32 s)
	Returns true if s<0 and false if s>= 0. More...
bool	mi::math::sign_bit (Sint64 s)
	Returns true if s<0 and false if s>= 0. More...
bool	mi::math::sign_bit (Float32 s)
	Extracts the sign bit of a single-precision floating point number. More...
bool	mi::math::sign_bit (Float64 s)
	Extracts the sign bit of a double-precision floating point number. More...
bool	mi::math::isinfinite (const Float32 x)
	Checks a single-precision floating point number for "infinity". More...
bool	mi::math::isinfinite (const Float64 x)
	Checks a double-precision floating point number for "infinity". More...
Float32	mi::math::sin (Float32 a)
	Returns the sine of a. The angle a is specified in radians. More...
Float64	mi::math::sin (Float64 a)
	Returns the sine of a. The angle a is specified in radians. More...
void	mi::math::sincos (Float32 a, Float32 &s, Float32 &c)
	Computes the sine s and cosine c of angle a simultaneously. More...
void	mi::math::sincos (Float64 a, Float64 &s, Float64 &c)
	Computes the sine s and cosine c of angle a simultaneously. More...
Float32	mi::math::smoothstep (Float32 a, Float32 b, Float32 x)
	Returns 0 if x is less than a and 1 if x is greater than b. More...
Float64	mi::math::smoothstep (Float64 a, Float64 b, Float64 x)
	Returns 0 if x is less than a and 1 if x is greater than b. More...
Float32	mi::math::sqrt (Float32 s)
	Returns the square root of s. More...
Float64	mi::math::sqrt (Float64 s)
	Returns the square root of s. More...
Float32	mi::math::step (Float32 a, Float32 x)
	Returns 0 if x is less than a and 1 otherwise. More...
Float64	mi::math::step (Float64 a, Float64 x)
	Returns 0 if x is less than a and 1 otherwise. More...
Float32	mi::math::tan (Float32 a)
	Returns the tangent of a. The angle a is specified in radians. More...
Float64	mi::math::tan (Float64 a)
	Returns the tangent of a. The angle a is specified in radians. More...
MI_HOST_DEVICE_INLINE void	mi::math::to_rgbe (const Float32 color[3], Uint32 &rgbe)
	Encodes a color into RGBE representation. More...
MI_HOST_DEVICE_INLINE void	mi::math::to_rgbe (const Float32 color[3], Uint8 rgbe[4])
	Encodes a color into RGBE representation. More...
MI_HOST_DEVICE_INLINE void	mi::math::from_rgbe (const Uint8 rgbe[4], Float32 color[3])
	Decodes a color from RGBE representation. More...
MI_HOST_DEVICE_INLINE void	mi::math::from_rgbe (const Uint32 rgbe, Float32 color[3])
	Decodes a color from RGBE representation. More...
Sint32	mi::math::dot (Sint32 a, Sint32 b)
	Returns the inner product (a.k.a. dot or scalar product) of two integers. More...
Float32	mi::math::dot (Float32 a, Float32 b)
	Returns the inner product (a.k.a. dot or scalar product) of two scalars. More...
Float64	mi::math::dot (Float64 a, Float64 b)
	Returns the inner product (a.k.a. dot or scalar product) of two scalars. More...
template<class V>
V::value_type	mi::math::dot (const V &lhs, const V &rhs)
	Returns the inner product (a.k.a. dot or scalar product) of two vectors. More...
template<class V>
V::value_type	mi::math::square_length (const V &v)
	Returns the squared Euclidean norm of the vector v. More...
Float32	mi::math::length (Float32 a)
	Returns the Euclidean norm of the scalar a (its absolute value). More...
Float64	mi::math::length (Float64 a)
	Returns the Euclidean norm of the scalar a (its absolute value). More...
template<class V>
V::value_type	mi::math::length (const V &v)
	Returns the Euclidean norm of the vector v. More...
template<class V>
V::value_type	mi::math::square_euclidean_distance (const V &lhs, const V &rhs)
	Returns the squared Euclidean distance from the vector lhs to the vector rhs. More...
template<class V>
V::value_type	mi::math::euclidean_distance (const V &lhs, const V &rhs)
	Returns the Euclidean distance from the vector lhs to the vector rhs. More...
template<class V>
void	mi::math::set_bounds (V &v, const V &low, const V &high)
	Bounds the value of vector v elementwise to the given low and high vector values. More...
template<class V>
bool	mi::math::is_equal (const V &lhs, const V &rhs)
	Returns true if vector lhs is elementwise equal to vector rhs, and false otherwise. More...
template<class V>
bool	mi::math::is_not_equal (const V &lhs, const V &rhs)
	Returns true if vector lhs is elementwise not equal to vector rhs, and false otherwise. More...
template<class V>
bool	mi::math::lexicographically_less (const V &lhs, const V &rhs)
	Returns true if vector lhs is lexicographically less than vector rhs, and false otherwise. More...
template<class V>
bool	mi::math::lexicographically_less_or_equal (const V &lhs, const V &rhs)
	Returns true if vector lhs is lexicographically less than or equal to vector rhs, and false otherwise. More...
template<class V>
bool	mi::math::lexicographically_greater (const V &lhs, const V &rhs)
	Returns true if vector lhs is lexicographically greater than vector rhs, and false otherwise. More...
template<class V>
bool	mi::math::lexicographically_greater_or_equal (const V &lhs, const V &rhs)
	Returns true if vector lhs is lexicographically greater than or equal to vector rhs, and false otherwise. More...
template<class V>
Comparison_result	mi::math::lexicographically_compare (const V &lhs, const V &rhs)
	Compares two vectors lexicographically. More...

Detailed Description

Fast approximations for math functions on limited precision floats.

Include File:

#include <mi/math/function.h>

Function Documentation

acos() [1/2]

Float32 mi::math::acos ( Float32  s )

inline

Returns the arc cosine of s in radians.

acos() [2/2]

Float64 mi::math::acos ( Float64  s )

inline

Returns the arc cosine of s in radians.

all() [1/10]

bool mi::math::all ( Float32  v )

inline

Returns true if v is not equal to zero.

all() [2/10]

bool mi::math::all ( Float64  v )

inline

Returns true if v is not equal to zero.

all() [3/10]

bool mi::math::all ( Sint16  v )

inline

Returns true if v is not equal to zero.

all() [4/10]

bool mi::math::all ( Sint32  v )

inline

Returns true if v is not equal to zero.

all() [5/10]

bool mi::math::all ( Sint64  v )

inline

Returns true if v is not equal to zero.

all() [6/10]

bool mi::math::all ( Sint8  v )

inline

Returns true if v is not equal to zero.

all() [7/10]

bool mi::math::all ( Uint16  v )

inline

Returns true if v is not equal to zero.

all() [8/10]

bool mi::math::all ( Uint32  v )

inline

Returns true if v is not equal to zero.

all() [9/10]

bool mi::math::all ( Uint64  v )

inline

Returns true if v is not equal to zero.

all() [10/10]

bool mi::math::all ( Uint8  v )

inline

Returns true if v is not equal to zero.

any() [1/10]

bool mi::math::any ( Float32  v )

inline

Returns true if v is not equal to zero.

any() [2/10]

bool mi::math::any ( Float64  v )

inline

Returns true if v is not equal to zero.

any() [3/10]

bool mi::math::any ( Sint16  v )

inline

Returns true if v is not equal to zero.

any() [4/10]

bool mi::math::any ( Sint32  v )

inline

Returns true if v is not equal to zero.

any() [5/10]

bool mi::math::any ( Sint64  v )

inline

Returns true if v is not equal to zero.

any() [6/10]

bool mi::math::any ( Sint8  v )

inline

Returns true if v is not equal to zero.

any() [7/10]

bool mi::math::any ( Uint16  v )

inline

Returns true if v is not equal to zero.

any() [8/10]

bool mi::math::any ( Uint32  v )

inline

Returns true if v is not equal to zero.

any() [9/10]

bool mi::math::any ( Uint64  v )

inline

Returns true if v is not equal to zero.

any() [10/10]

bool mi::math::any ( Uint8  v )

inline

Returns true if v is not equal to zero.

asin() [1/2]

Float32 mi::math::asin ( Float32  s )

inline

Returns the arc sine of s in radians.

asin() [2/2]

Float64 mi::math::asin ( Float64  s )

inline

Returns the arc sine of s in radians.

atan() [1/2]

Float32 mi::math::atan ( Float32  s )

inline

Returns the arc tangent of s.

atan() [2/2]

Float64 mi::math::atan ( Float64  s )

inline

Returns the arc tangent of s.

atan2() [1/2]

Float32 mi::math::atan2 ( Float32  s, Float32  t  )

inline

Returns the arc tangent of s / t.

The signs of s and t are used to determine the quadrant of the results.

atan2() [2/2]

Float64 mi::math::atan2 ( Float64  s, Float64  t  )

inline

Returns the arc tangent of s / t.

The signs of s and t are used to determine the quadrant of the results.

ceil() [1/2]

Float32 mi::math::ceil ( Float32  s )

inline

Returns the smallest integral value that is not less than s.

ceil() [2/2]

Float64 mi::math::ceil ( Float64  s )

inline

Returns the smallest integral value that is not less than s.

clamp() [1/10]

Float32 mi::math::clamp ( Float32  s, Float32  low, Float32  high  )

inline

Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high.

clamp() [2/10]

Float64 mi::math::clamp ( Float64  s, Float64  low, Float64  high  )

inline

Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high.

clamp() [3/10]

Sint16 mi::math::clamp ( Sint16  s, Sint16  low, Sint16  high  )

inline

Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high.

clamp() [4/10]

Sint32 mi::math::clamp ( Sint32  s, Sint32  low, Sint32  high  )

inline

Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high.

clamp() [5/10]

Sint64 mi::math::clamp ( Sint64  s, Sint64  low, Sint64  high  )

inline

Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high.

clamp() [6/10]

Sint8 mi::math::clamp ( Sint8  s, Sint8  low, Sint8  high  )

inline

Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high.

clamp() [7/10]

Uint16 mi::math::clamp ( Uint16  s, Uint16  low, Uint16  high  )

inline

Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high.

clamp() [8/10]

Uint32 mi::math::clamp ( Uint32  s, Uint32  low, Uint32  high  )

inline

Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high.

clamp() [9/10]

Uint64 mi::math::clamp ( Uint64  s, Uint64  low, Uint64  high  )

inline

Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high.

clamp() [10/10]

Uint8 mi::math::clamp ( Uint8  s, Uint8  low, Uint8  high  )

inline

Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high.

cos() [1/2]

Float32 mi::math::cos ( Float32  a )

inline

Returns the cosine of a. The angle a is specified in radians.

cos() [2/2]

Float64 mi::math::cos ( Float64  a )

inline

Returns the cosine of a. The angle a is specified in radians.

degrees() [1/2]

Float32 mi::math::degrees ( Float32  r )

inline

Converts radians r to degrees.

degrees() [2/2]

Float64 mi::math::degrees ( Float64  r )

inline

Converts radians r to degrees.

dot() [1/4]

template<class V>

V::value_type mi::math::dot ( const V &  lhs, const V &  rhs  )

inline

Returns the inner product (a.k.a. dot or scalar product) of two vectors.

dot() [2/4]

Float32 mi::math::dot ( Float32  a, Float32  b  )

inline

Returns the inner product (a.k.a. dot or scalar product) of two scalars.

dot() [3/4]

Float64 mi::math::dot ( Float64  a, Float64  b  )

inline

Returns the inner product (a.k.a. dot or scalar product) of two scalars.

dot() [4/4]

Sint32 mi::math::dot ( Sint32  a, Sint32  b  )

inline

Returns the inner product (a.k.a. dot or scalar product) of two integers.

euclidean_distance()

template<class V>

V::value_type mi::math::euclidean_distance ( const V &  lhs, const V &  rhs  )

inline

Returns the Euclidean distance from the vector lhs to the vector rhs.

Uses an unqualified call to sqrt(...) on the vector element type.

exp2() [1/2]

Float32 mi::math::exp2 ( Float32  s )

inline

Returns the constant 2 to the power of s (exponential function).

exp2() [2/2]

Float64 mi::math::exp2 ( Float64  s )

inline

Returns the constant 2 to the power of s (exponential function).

fast_exp()

Float32 mi::math::fast_exp ( Float32  x )

inline

A fast implementation of exp for floats.

fast_log2()

Float32 mi::math::fast_log2 ( Float32  i )

inline

A fast implementation of log2(x) for floats.

fast_pow()

Float32 mi::math::fast_pow ( Float32  b, Float32  e  )

inline

A fast implementation of pow(x,y) for floats.

Parameters

b	base
e	exponent

fast_pow2()

Float32 mi::math::fast_pow2 ( Float32  x )

inline

A fast implementation of pow(2,x) for floats.

fast_sqrt()

Float32 mi::math::fast_sqrt ( Float32  i )

inline

A fast implementation of sqrt(x) for floats.

floor() [1/2]

Float32 mi::math::floor ( Float32  s )

inline

Returns the largest integral value that is not greater than s.

floor() [2/2]

Float64 mi::math::floor ( Float64  s )

inline

Returns the largest integral value that is not greater than s.

fmod() [1/2]

Float32 mi::math::fmod ( Float32  a, Float32  b  )

inline

Returns a modulo b, in other words, the remainder of a/b.

The result has the same sign as a.

fmod() [2/2]

Float64 mi::math::fmod ( Float64  a, Float64  b  )

inline

Returns a modulo b, in other words, the remainder of a/b.

The result has the same sign as a.

frac() [1/2]

Float32 mi::math::frac ( Float32  s )

inline

Returns the positive fractional part of s.

frac() [2/2]

Float64 mi::math::frac ( Float64  s )

inline

Returns the positive fractional part of s.

from_rgbe() [1/2]

MI_HOST_DEVICE_INLINE void mi::math::from_rgbe	(	const Uint32	rgbe,
		Float32	color[3]
	)

Decodes a color from RGBE representation.

from_rgbe() [2/2]

MI_HOST_DEVICE_INLINE void mi::math::from_rgbe	(	const Uint8	rgbe[4],
		Float32	color[3]
	)

Decodes a color from RGBE representation.

is_approx_equal() [1/2]

bool mi::math::is_approx_equal ( Float32  left, Float32  right, Float32  e  )

inline

Compares the two given values for equality within the given epsilon.

is_approx_equal() [2/2]

bool mi::math::is_approx_equal ( Float64  left, Float64  right, Float64  e  )

inline

Compares the two given values for equality within the given epsilon.

is_equal()

template<class V>

bool mi::math::is_equal ( const V &  lhs, const V &  rhs  )

inline

Returns true if vector lhs is elementwise equal to vector rhs, and false otherwise.

is_not_equal()

template<class V>

bool mi::math::is_not_equal ( const V &  lhs, const V &  rhs  )

inline

Returns true if vector lhs is elementwise not equal to vector rhs, and false otherwise.

isinfinite() [1/2]

bool mi::math::isinfinite ( const Float32  x )

inline

Checks a single-precision floating point number for "infinity".

The methods relies on the IEEE 754 floating-point standard.

isinfinite() [2/2]

bool mi::math::isinfinite ( const Float64  x )

inline

Checks a double-precision floating point number for "infinity".

The methods relies on the IEEE 754 floating-point standard.

leading_zeros() [1/2]

Uint32 mi::math::leading_zeros ( Uint32  v )

inline

Returns the number of leading zeros of v, 32-bit version.

leading_zeros() [2/2]

Uint32 mi::math::leading_zeros ( Uint64  v )

inline

Returns the number of leading zeros of v, 64-bit version.

length() [1/3]

template<class V>

V::value_type mi::math::length ( const V &  v )

inline

Returns the Euclidean norm of the vector v.

Uses an unqualified call to sqrt(...) on the vector element type.

length() [2/3]

Float32 mi::math::length ( Float32  a )

inline

Returns the Euclidean norm of the scalar a (its absolute value).

length() [3/3]

Float64 mi::math::length ( Float64  a )

inline

Returns the Euclidean norm of the scalar a (its absolute value).

lerp() [1/2]

Float32 mi::math::lerp ( Float32  s1, Float32  s2, Float32  t  )

inline

Returns the linear interpolation between s1 and s2, i.e., it returns (1-t) * s1 + t * s2.

Parameters

s1	one scalar
s2	second scalar
t	interpolation parameter in [0,1]

lerp() [2/2]

Float64 mi::math::lerp ( Float64  s1, Float64  s2, Float64  t  )

inline

Returns the linear interpolation between s1 and s2, i.e., it returns (1-t) * s1 + t * s2.

Parameters

s1	one scalar
s2	second scalar
t	interpolation parameter in [0,1]

lexicographically_compare()

template<class V>

Comparison_result mi::math::lexicographically_compare ( const V &  lhs, const V &  rhs  )

inline

Compares two vectors lexicographically.

Returns LESS if lhs is less than rhs, and correspondingly EQUAL or GREATER for the other cases.

Note

The result of this function is undefined if lhs or rhs contains NaNs.

See also

mi::Comparison_result, Definition: Lexicographic order and comparison

lexicographically_greater()

template<class V>

bool mi::math::lexicographically_greater ( const V &  lhs, const V &  rhs  )

inline

Returns true if vector lhs is lexicographically greater than vector rhs, and false otherwise.

See also

Definition: Lexicographic order and comparison

lexicographically_greater_or_equal()

template<class V>

bool mi::math::lexicographically_greater_or_equal ( const V &  lhs, const V &  rhs  )

inline

Returns true if vector lhs is lexicographically greater than or equal to vector rhs, and false otherwise.

See also

Definition: Lexicographic order and comparison

lexicographically_less()

template<class V>

bool mi::math::lexicographically_less ( const V &  lhs, const V &  rhs  )

inline

Returns true if vector lhs is lexicographically less than vector rhs, and false otherwise.

See also

Definition: Lexicographic order and comparison

lexicographically_less_or_equal()

template<class V>

bool mi::math::lexicographically_less_or_equal ( const V &  lhs, const V &  rhs  )

inline

Returns true if vector lhs is lexicographically less than or equal to vector rhs, and false otherwise.

See also

Definition: Lexicographic order and comparison

log10() [1/2]

Float32 mi::math::log10 ( Float32  s )

inline

Returns the base 10 logarithm of s.

log10() [2/2]

Float64 mi::math::log10 ( Float64  s )

inline

Returns the base 10 logarithm of s.

log2() [1/2]

Float32 mi::math::log2 ( Float32  s )

inline

Returns the base 2 logarithm of s.

log2() [2/2]

Float64 mi::math::log2 ( Float64  s )

inline

Returns the base 2 logarithm of s.

log2_int() [1/4]

Sint32 mi::math::log2_int ( const Float32  v )

inline

Returns the integer log2 of v.

log2_int() [2/4]

Sint32 mi::math::log2_int ( const Float64  v )

inline

Returns the integer log2 of v.

log2_int() [3/4]

Sint32 mi::math::log2_int ( const Uint32  v )

inline

Returns the integer log2 of v.

log2_int() [4/4]

Sint32 mi::math::log2_int ( const Uint64  v )

inline

Returns the integer log2 of v.

log2_int_ceil()

template<typename Integer>

Sint32 mi::math::log2_int_ceil ( const Integer  v )

inline

Returns the integer log2 of v, i.e., rounded up to the next integer.

modf() [1/2]

Float32 mi::math::modf ( Float32  s, Float32 &  i  )

inline

Returns the fractional part of s and stores the integral part of s in i.

Both parts have the same sign as s.

modf() [2/2]

Float64 mi::math::modf ( Float64  s, Float64 &  i  )

inline

Returns the fractional part of s and stores the integral part of s in i.

Both parts have the same sign as s.

pow() [1/6]

Float32 mi::math::pow ( Float32  a, Float32  b  )

inline

Returns a to the power of b.

pow() [2/6]

Float64 mi::math::pow ( Float64  a, Float64  b  )

inline

Returns a to the power of b.

pow() [3/6]

Sint32 mi::math::pow ( Sint32  a, Sint32  b  )

inline

Returns a to the power of b.

pow() [4/6]

Sint64 mi::math::pow ( Sint64  a, Sint64  b  )

inline

Returns a to the power of b.

pow() [5/6]

Uint32 mi::math::pow ( Uint32  a, Uint32  b  )

inline

Returns a to the power of b.

pow() [6/6]

Uint64 mi::math::pow ( Uint64  a, Uint64  b  )

inline

Returns a to the power of b.

radians() [1/2]

Float32 mi::math::radians ( Float32  d )

inline

Converts degrees d to radians.

radians() [2/2]

Float64 mi::math::radians ( Float64  d )

inline

Converts degrees d to radians.

round() [1/2]

Float32 mi::math::round ( Float32  s )

inline

Returns s rounded to the nearest integer value.

round() [2/2]

Float64 mi::math::round ( Float64  s )

inline

Returns s rounded to the nearest integer value.

rsqrt() [1/2]

Float32 mi::math::rsqrt ( Float32  s )

inline

Returns the reciprocal of the square root of s.

rsqrt() [2/2]

Float64 mi::math::rsqrt ( Float64  s )

inline

Returns the reciprocal of the square root of s.

saturate() [1/2]

Float32 mi::math::saturate ( Float32  s )

inline

Returns the value s clamped to the range [0,1].

saturate() [2/2]

Float64 mi::math::saturate ( Float64  s )

inline

Returns the value s clamped to the range [0,1].

set_bounds()

template<class V>

void mi::math::set_bounds ( V &  v, const V &  low, const V &  high  )

inline

Bounds the value of vector v elementwise to the given low and high vector values.

sign() [1/6]

Float32 mi::math::sign ( Float32  s )

inline

Returns -1 if s<0, 0 if s==0, and +1 if s>0.

sign() [2/6]

Float64 mi::math::sign ( Float64  s )

inline

Returns -1 if s<0, 0 if s==0, and +1 if s>0.

sign() [3/6]

Sint16 mi::math::sign ( Sint16  s )

inline

Returns -1 if s<0, 0 if s==0, and +1 if s>0.

sign() [4/6]

Sint32 mi::math::sign ( Sint32  s )

inline

Returns -1 if s<0, 0 if s==0, and +1 if s>0.

sign() [5/6]

Sint64 mi::math::sign ( Sint64  s )

inline

Returns -1 if s<0, 0 if s==0, and +1 if s>0.

sign() [6/6]

Sint8 mi::math::sign ( Sint8  s )

inline

Returns -1 if s<0, 0 if s==0, and +1 if s>0.

sign_bit() [1/6]

bool mi::math::sign_bit ( Float32  s )

inline

Extracts the sign bit of a single-precision floating point number.

The methods relies on the IEEE 754 floating-point standard. Note that the sign bit is set for the special floating-point value -0.0f, so this function returns true for this value.

sign_bit() [2/6]

bool mi::math::sign_bit ( Float64  s )

inline

Extracts the sign bit of a double-precision floating point number.

The methods relies on the IEEE 754 floating-point standard. Note that the sign bit is set for the special floating-point value -0.0f, so this function returns true for this value.

sign_bit() [3/6]

bool mi::math::sign_bit ( Sint16  s )

inline

Returns true if s<0 and false if s>= 0.

sign_bit() [4/6]

bool mi::math::sign_bit ( Sint32  s )

inline

Returns true if s<0 and false if s>= 0.

sign_bit() [5/6]

bool mi::math::sign_bit ( Sint64  s )

inline

Returns true if s<0 and false if s>= 0.

sign_bit() [6/6]

bool mi::math::sign_bit ( Sint8  s )

inline

Returns true if s<0 and false if s>= 0.

sin() [1/2]

Float32 mi::math::sin ( Float32  a )

inline

Returns the sine of a. The angle a is specified in radians.

sin() [2/2]

Float64 mi::math::sin ( Float64  a )

inline

Returns the sine of a. The angle a is specified in radians.

sincos() [1/2]

void mi::math::sincos ( Float32  a, Float32 &  s, Float32 &  c  )

inline

Computes the sine s and cosine c of angle a simultaneously.

The angle a is specified in radians.

sincos() [2/2]

void mi::math::sincos ( Float64  a, Float64 &  s, Float64 &  c  )

inline

Computes the sine s and cosine c of angle a simultaneously.

The angle a is specified in radians.

smoothstep() [1/2]

Float32 mi::math::smoothstep ( Float32  a, Float32  b, Float32  x  )

inline

Returns 0 if x is less than a and 1 if x is greater than b.

A smooth curve is applied in-between so that the return value varies continuously from 0 to 1 as x varies from a to b.

smoothstep() [2/2]

Float64 mi::math::smoothstep ( Float64  a, Float64  b, Float64  x  )

inline

Returns 0 if x is less than a and 1 if x is greater than b.

A smooth curve is applied in-between so that the return value varies continuously from 0 to 1 as x varies from a to b.

sqrt() [1/2]

Float32 mi::math::sqrt ( Float32  s )

inline

Returns the square root of s.

sqrt() [2/2]

Float64 mi::math::sqrt ( Float64  s )

inline

Returns the square root of s.

square_euclidean_distance()

template<class V>

V::value_type mi::math::square_euclidean_distance ( const V &  lhs, const V &  rhs  )

inline

Returns the squared Euclidean distance from the vector lhs to the vector rhs.

square_length()

template<class V>

V::value_type mi::math::square_length ( const V &  v )

inline

Returns the squared Euclidean norm of the vector v.

step() [1/2]

Float32 mi::math::step ( Float32  a, Float32  x  )

inline

Returns 0 if x is less than a and 1 otherwise.

step() [2/2]

Float64 mi::math::step ( Float64  a, Float64  x  )

inline

Returns 0 if x is less than a and 1 otherwise.

tan() [1/2]

Float32 mi::math::tan ( Float32  a )

inline

Returns the tangent of a. The angle a is specified in radians.

tan() [2/2]

Float64 mi::math::tan ( Float64  a )

inline

Returns the tangent of a. The angle a is specified in radians.

to_rgbe() [1/2]

MI_HOST_DEVICE_INLINE void mi::math::to_rgbe	(	const Float32	color[3],
		Uint32 &	rgbe
	)

Encodes a color into RGBE representation.

to_rgbe() [2/2]

MI_HOST_DEVICE_INLINE void mi::math::to_rgbe	(	const Float32	color[3],
		Uint8	rgbe[4]
	)

Encodes a color into RGBE representation.