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function.h File Reference

Math functions and function templates on simple types or generic container and vector concepts. More...

Go to the source code of this file.

Classes

struct  mi::math::functor::Operator_equal_equal
 Functor for the equality comparison operator, ==. More...
 
struct  mi::math::functor::Operator_not_equal
 Functor for the inequality comparison operator, !=. More...
 
struct  mi::math::functor::Operator_less
 Functor for the less-than comparison operator, <. More...
 
struct  mi::math::functor::Operator_less_equal
 Functor for the less-than-or-equal comparison operator, <=. More...
 
struct  mi::math::functor::Operator_greater
 Functor for the greater-than comparison operator, >. More...
 
struct  mi::math::functor::Operator_greater_equal
 Functor for the greater-than-or-equal comparison operator, >=. More...
 
struct  mi::math::functor::Operator_plus
 Functor for the plus operator, +. More...
 
struct  mi::math::functor::Operator_minus
 Functor for the minus operator, -, unary and binary. More...
 
struct  mi::math::functor::Operator_multiply
 Functor for the multiplication operator, *. More...
 
struct  mi::math::functor::Operator_divide
 Functor for the division operator, /. More...
 
struct  mi::math::functor::Operator_and_and
 Functor for the logical and operator, &&. More...
 
struct  mi::math::functor::Operator_or_or
 Functor for the logical or operator, ||. More...
 
struct  mi::math::functor::Operator_xor
 Functor for the xor operator, ^. More...
 
struct  mi::math::functor::Operator_not
 Functor for the logical not operator, !. More...
 
struct  mi::math::functor::Operator_pre_incr
 Functor for the pre-increment operator, ++. More...
 
struct  mi::math::functor::Operator_post_incr
 Functor for the post-increment operator, ++. More...
 
struct  mi::math::functor::Operator_pre_decr
 Functor for the pre-decrement operator, --. More...
 
struct  mi::math::functor::Operator_post_decr
 Functor for the post-decrement operator, --. More...
 

Namespaces

 mi
 Common namespace for APIs of NVIDIA Advanced Rendering Center GmbH.
 
 mi::math
 Namespace for the Math API.
 
 mi::math::functor
 Namespace for basic math functors in the Math API.
 
 mi::math::general
 Namespace for generic functions in the Math API.
 

Constant Groups

 mi
 Common namespace for APIs of NVIDIA Advanced Rendering Center GmbH.
 
 mi::math
 Namespace for the Math API.
 
 mi::math::functor
 Namespace for basic math functors in the Math API.
 
 mi::math::general
 Namespace for generic functions in the Math API.
 

Functions

template<class Vector , class ResultVector , class UnaryFunctor >
void mi::math::general::transform (const Vector &vec, ResultVector &result, UnaryFunctor f)
 Generic transform function that applies a unary functor (return value). More...
 
template<class Vector1 , class Vector2 , class ResultVector , class BinaryFunctor >
void mi::math::general::transform (const Vector1 &vec1, const Vector2 &vec2, ResultVector &result, BinaryFunctor f)
 Generic transform function that applies a binary functor (return value). More...
 
template<class Scalar , class Vector , class ResultVector , class BinaryFunctor >
void mi::math::general::transform_left_scalar (const Scalar &s, const Vector &vec, ResultVector &result, BinaryFunctor f)
 Generic transform function that applies a binary functor (return value, LHS scalar). More...
 
template<class Scalar , class Vector , class ResultVector , class BinaryFunctor >
void mi::math::general::transform_right_scalar (const Vector &vec, const Scalar &s, ResultVector &result, BinaryFunctor f)
 Generic transform function that applies a binary functor (return value, RHS scalar). More...
 
template<class Vector , class UnaryFunctor >
void mi::math::general::for_each (Vector &vec, UnaryFunctor f)
 Generic transform function that applies a unary functor (in-place). More...
 
template<class Vector1 , class Vector2 , class BinaryFunctor >
void mi::math::general::for_each (Vector1 &vec1, const Vector2 &vec2, BinaryFunctor f)
 Generic transform function that applies a binary functor (in-place). More...
 
Float32 mi::math::exp (Float32 s)
 Returns the constant e to the power of s (exponential function). More...
 
Float64 mi::math::exp (Float64 s)
 Returns the constant e to the power of s (exponential function). More...
 
Float32 mi::math::log (Float32 s)
 Returns the natural logarithm of s. More...
 
Float64 mi::math::log (Float64 s)
 Returns the natural logarithm of s. More...
 
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

Math functions and function templates on simple types or generic container and vector concepts.

See Math Functions.