3. Math library

Floating point math in general is not bit-precise. Compiler can optimize permutations, replace divisions with multiplications, and some of functions are not bit-exact. If you need precise math use double precision type. All functions and symbols are in “math” module, use require to get access to it.

require math

3.1. Constants

PI = 3.1415927f

The ratio of a circle’s circumference to its diameter. π

DBL_PI = 3.141592653589793lf

The ratio of a circle’s circumference to its diameter. π

FLT_EPSILON = 1.1920929e-07f

the difference between 1 and the smallest floating point number of type float that is greater than 1.

DBL_EPSILON = 2.220446049250313e-16lf

the difference between 1 and the smallest double precision floating point number of type double that is greater than 1.

3.2. Handled structures

float4x4

float4x4 fields are

z	float4
w	float4
y	float4
x	float4

floating point matrix with 4 rows and 4 columns

float3x4

float3x4 fields are

z	float3
w	float3
y	float3
x	float3

floating point matrix with 4 rows and 3 columns

float3x3

float3x3 fields are

z	float3
y	float3
x	float3

floating point matrix with 3 rows and 3 columns

3.3. all numerics (uint*, int*, float*, double)

• min (x:int const;y:int const) : int

• max (x:int const;y:int const) : int

• min (x:int2 const;y:int2 const) : int2

• max (x:int2 const;y:int2 const) : int2

• min (x:int3 const;y:int3 const) : int3

• max (x:int3 const;y:int3 const) : int3

• min (x:int4 const;y:int4 const) : int4

• max (x:int4 const;y:int4 const) : int4

• min (x:uint const;y:uint const) : uint

• max (x:uint const;y:uint const) : uint

• min (x:uint2 const;y:uint2 const) : uint2

• max (x:uint2 const;y:uint2 const) : uint2

• min (x:uint3 const;y:uint3 const) : uint3

• max (x:uint3 const;y:uint3 const) : uint3

• min (x:uint4 const;y:uint4 const) : uint4

• max (x:uint4 const;y:uint4 const) : uint4

• min (x:float const;y:float const) : float

• max (x:float const;y:float const) : float

• min (x:float2 const;y:float2 const) : float2

• max (x:float2 const;y:float2 const) : float2

• min (x:float3 const;y:float3 const) : float3

• max (x:float3 const;y:float3 const) : float3

• min (x:float4 const;y:float4 const) : float4

• max (x:float4 const;y:float4 const) : float4

• min (x:double const;y:double const) : double

• max (x:double const;y:double const) : double

• min (x:int64 const;y:int64 const) : int64

• max (x:int64 const;y:int64 const) : int64

• min (x:uint64 const;y:uint64 const) : uint64

• max (x:uint64 const;y:uint64 const) : uint64

min(x: int const; y: int const)

min returns int

argument	argument type
x	int const
y	int const

returns the minimum of x and y

max(x: int const; y: int const)

max returns int

argument	argument type
x	int const
y	int const

returns the maximum of x and y

min(x: int2 const; y: int2 const)

min returns int2

argument	argument type
x	int2 const
y	int2 const

returns the minimum of x and y

max(x: int2 const; y: int2 const)

max returns int2

argument	argument type
x	int2 const
y	int2 const

returns the maximum of x and y

min(x: int3 const; y: int3 const)

min returns int3

argument	argument type
x	int3 const
y	int3 const

returns the minimum of x and y

max(x: int3 const; y: int3 const)

max returns int3

argument	argument type
x	int3 const
y	int3 const

returns the maximum of x and y

min(x: int4 const; y: int4 const)

min returns int4

argument	argument type
x	int4 const
y	int4 const

returns the minimum of x and y

max(x: int4 const; y: int4 const)

max returns int4

argument	argument type
x	int4 const
y	int4 const

returns the maximum of x and y

min(x: uint const; y: uint const)

min returns uint

argument	argument type
x	uint const
y	uint const

returns the minimum of x and y

max(x: uint const; y: uint const)

max returns uint

argument	argument type
x	uint const
y	uint const

returns the maximum of x and y

min(x: uint2 const; y: uint2 const)

min returns uint2

argument	argument type
x	uint2 const
y	uint2 const

returns the minimum of x and y

max(x: uint2 const; y: uint2 const)

max returns uint2

argument	argument type
x	uint2 const
y	uint2 const

returns the maximum of x and y

min(x: uint3 const; y: uint3 const)

min returns uint3

argument	argument type
x	uint3 const
y	uint3 const

returns the minimum of x and y

max(x: uint3 const; y: uint3 const)

max returns uint3

argument	argument type
x	uint3 const
y	uint3 const

returns the maximum of x and y

min(x: uint4 const; y: uint4 const)

min returns uint4

argument	argument type
x	uint4 const
y	uint4 const

returns the minimum of x and y

max(x: uint4 const; y: uint4 const)

max returns uint4

argument	argument type
x	uint4 const
y	uint4 const

returns the maximum of x and y

min(x: float const; y: float const)

min returns float

argument	argument type
x	float const
y	float const

returns the minimum of x and y

max(x: float const; y: float const)

max returns float

argument	argument type
x	float const
y	float const

returns the maximum of x and y

min(x: float2 const; y: float2 const)

min returns float2

argument	argument type
x	float2 const
y	float2 const

returns the minimum of x and y

max(x: float2 const; y: float2 const)

max returns float2

argument	argument type
x	float2 const
y	float2 const

returns the maximum of x and y

min(x: float3 const; y: float3 const)

min returns float3

argument	argument type
x	float3 const
y	float3 const

returns the minimum of x and y

max(x: float3 const; y: float3 const)

max returns float3

argument	argument type
x	float3 const
y	float3 const

returns the maximum of x and y

min(x: float4 const; y: float4 const)

min returns float4

argument	argument type
x	float4 const
y	float4 const

returns the minimum of x and y

max(x: float4 const; y: float4 const)

max returns float4

argument	argument type
x	float4 const
y	float4 const

returns the maximum of x and y

min(x: double const; y: double const)

min returns double

argument	argument type
x	double const
y	double const

returns the minimum of x and y

max(x: double const; y: double const)

max returns double

argument	argument type
x	double const
y	double const

returns the maximum of x and y

min(x: int64 const; y: int64 const)

min returns int64

argument	argument type
x	int64 const
y	int64 const

returns the minimum of x and y

max(x: int64 const; y: int64 const)

max returns int64

argument	argument type
x	int64 const
y	int64 const

returns the maximum of x and y

min(x: uint64 const; y: uint64 const)

min returns uint64

argument	argument type
x	uint64 const
y	uint64 const

returns the minimum of x and y

max(x: uint64 const; y: uint64 const)

max returns uint64

argument	argument type
x	uint64 const
y	uint64 const

returns the maximum of x and y

3.4. float* and double

• sin (x:float const) : float

• cos (x:float const) : float

• tan (x:float const) : float

• sin (x:float2 const) : float2

• cos (x:float2 const) : float2

• tan (x:float2 const) : float2

• sin (x:float3 const) : float3

• cos (x:float3 const) : float3

• tan (x:float3 const) : float3

• sin (x:float4 const) : float4

• cos (x:float4 const) : float4

• tan (x:float4 const) : float4

• exp (x:float const) : float

• log (x:float const) : float

• exp2 (x:float const) : float

• log2 (x:float const) : float

• rcp (x:float const) : float

• pow (x:float const;y:float const) : float

• exp (x:float2 const) : float2

• log (x:float2 const) : float2

• exp2 (x:float2 const) : float2

• log2 (x:float2 const) : float2

• rcp (x:float2 const) : float2

• pow (x:float2 const;y:float2 const) : float2

• exp (x:float3 const) : float3

• log (x:float3 const) : float3

• exp2 (x:float3 const) : float3

• log2 (x:float3 const) : float3

• rcp (x:float3 const) : float3

• pow (x:float3 const;y:float3 const) : float3

• exp (x:float4 const) : float4

• log (x:float4 const) : float4

• exp2 (x:float4 const) : float4

• log2 (x:float4 const) : float4

• rcp (x:float4 const) : float4

• pow (x:float4 const;y:float4 const) : float4

• floor (x:float const) : float

• ceil (x:float const) : float

• sqrt (x:float const) : float

• saturate (x:float const) : float

• floor (x:float2 const) : float2

• ceil (x:float2 const) : float2

• sqrt (x:float2 const) : float2

• saturate (x:float2 const) : float2

• floor (x:float3 const) : float3

• ceil (x:float3 const) : float3

• sqrt (x:float3 const) : float3

• saturate (x:float3 const) : float3

• floor (x:float4 const) : float4

• ceil (x:float4 const) : float4

• sqrt (x:float4 const) : float4

• saturate (x:float4 const) : float4

• abs (x:int const) : int

• sign (x:int const) : int

• abs (x:int2 const) : int2

• sign (x:int2 const) : int2

• abs (x:int3 const) : int3

• sign (x:int3 const) : int3

• abs (x:int4 const) : int4

• sign (x:int4 const) : int4

• abs (x:uint const) : uint

• sign (x:uint const) : uint

• abs (x:uint2 const) : uint2

• sign (x:uint2 const) : uint2

• abs (x:uint3 const) : uint3

• sign (x:uint3 const) : uint3

• abs (x:uint4 const) : uint4

• sign (x:uint4 const) : uint4

• abs (x:float const) : float

• sign (x:float const) : float

• abs (x:float2 const) : float2

• sign (x:float2 const) : float2

• abs (x:float3 const) : float3

• sign (x:float3 const) : float3

• abs (x:float4 const) : float4

• sign (x:float4 const) : float4

• abs (x:double const) : double

• sign (x:double const) : double

• abs (x:int64 const) : int64

• sign (x:int64 const) : int64

• abs (x:uint64 const) : uint64

• sign (x:uint64 const) : uint64

• is_nan (x:float const) : bool

• is_finite (x:float const) : bool

• is_nan (x:double const) : bool

• is_finite (x:double const) : bool

• sqrt (x:double const) : double

• exp (x:double const) : double

• rcp (x:double const) : double

• log (x:double const) : double

• pow (x:double const;y:double const) : double

• exp2 (x:double const) : double

• log2 (x:double const) : double

• sin (x:double const) : double

• cos (x:double const) : double

• asin (x:double const) : double

• acos (x:double const) : double

• tan (x:double const) : double

• atan (x:double const) : double

• atan2 (y:double const;x:double const) : double

• sincos (x:float const;s:float& implicit;c:float& implicit) : void

• sincos (x:double const;s:double& implicit;c:double& implicit) : void

• asin (x:float const) : float

• acos (x:float const) : float

• atan (x:float const) : float

• atan2 (y:float const;x:float const) : float

• asin (x:float2 const) : float2

• asin (x:float3 const) : float3

• asin (x:float4 const) : float4

• acos (x:float2 const) : float2

• acos (x:float3 const) : float3

• acos (x:float4 const) : float4

• atan (x:float2 const) : float2

• atan (x:float3 const) : float3

• atan (x:float4 const) : float4

• atan2 (y:float2 const;x:float2 const) : float2

• atan2 (y:float3 const;x:float3 const) : float3

• atan2 (y:float4 const;x:float4 const) : float4

sin(x: float const)

sin returns float

argument	argument type
x	float const

returns the sine of x

cos(x: float const)

cos returns float

argument	argument type
x	float const

returns the cosine of x

tan(x: float const)

tan returns float

argument	argument type
x	float const

returns the tangent of x

sin(x: float2 const)

sin returns float2

argument	argument type
x	float2 const

returns the sine of x

cos(x: float2 const)

cos returns float2

argument	argument type
x	float2 const

returns the cosine of x

tan(x: float2 const)

tan returns float2

argument	argument type
x	float2 const

returns the tangent of x

sin(x: float3 const)

sin returns float3

argument	argument type
x	float3 const

returns the sine of x

cos(x: float3 const)

cos returns float3

argument	argument type
x	float3 const

returns the cosine of x

tan(x: float3 const)

tan returns float3

argument	argument type
x	float3 const

returns the tangent of x

sin(x: float4 const)

sin returns float4

argument	argument type
x	float4 const

returns the sine of x

cos(x: float4 const)

cos returns float4

argument	argument type
x	float4 const

returns the cosine of x

tan(x: float4 const)

tan returns float4

argument	argument type
x	float4 const

returns the tangent of x

exp(x: float const)

exp returns float

argument	argument type
x	float const

returns the e^x value of x

log(x: float const)

log returns float

argument	argument type
x	float const

returns the natural logarithm of x

exp2(x: float const)

exp2 returns float

argument	argument type
x	float const

returns the 2^x value of x

log2(x: float const)

log2 returns float

argument	argument type
x	float const

returns the logarithm base-2 of x

rcp(x: float const)

rcp returns float

argument	argument type
x	float const

returns the 1/x

pow(x: float const; y: float const)

pow returns float

argument	argument type
x	float const
y	float const

returns x raised to the power of y

exp(x: float2 const)

exp returns float2

argument	argument type
x	float2 const

returns the e^x value of x

log(x: float2 const)

log returns float2

argument	argument type
x	float2 const

returns the natural logarithm of x

exp2(x: float2 const)

exp2 returns float2

argument	argument type
x	float2 const

returns the 2^x value of x

log2(x: float2 const)

log2 returns float2

argument	argument type
x	float2 const

returns the logarithm base-2 of x

rcp(x: float2 const)

rcp returns float2

argument	argument type
x	float2 const

returns the 1/x

pow(x: float2 const; y: float2 const)

pow returns float2

argument	argument type
x	float2 const
y	float2 const

returns x raised to the power of y

exp(x: float3 const)

exp returns float3

argument	argument type
x	float3 const

returns the e^x value of x

log(x: float3 const)

log returns float3

argument	argument type
x	float3 const

returns the natural logarithm of x

exp2(x: float3 const)

exp2 returns float3

argument	argument type
x	float3 const

returns the 2^x value of x

log2(x: float3 const)

log2 returns float3

argument	argument type
x	float3 const

returns the logarithm base-2 of x

rcp(x: float3 const)

rcp returns float3

argument	argument type
x	float3 const

returns the 1/x

pow(x: float3 const; y: float3 const)

pow returns float3

argument	argument type
x	float3 const
y	float3 const

returns x raised to the power of y

exp(x: float4 const)

exp returns float4

argument	argument type
x	float4 const

returns the e^x value of x

log(x: float4 const)

log returns float4

argument	argument type
x	float4 const

returns the natural logarithm of x

exp2(x: float4 const)

exp2 returns float4

argument	argument type
x	float4 const

returns the 2^x value of x

log2(x: float4 const)

log2 returns float4

argument	argument type
x	float4 const

returns the logarithm base-2 of x

rcp(x: float4 const)

rcp returns float4

argument	argument type
x	float4 const

returns the 1/x

pow(x: float4 const; y: float4 const)

pow returns float4

argument	argument type
x	float4 const
y	float4 const

returns x raised to the power of y

floor(x: float const)

floor returns float

argument	argument type
x	float const

returns a float value representing the largest integer that is less than or equal to x

ceil(x: float const)

ceil returns float

argument	argument type
x	float const

returns a float value representing the smallest integer (type is still float) that is greater than or equal to arg0

sqrt(x: float const)

sqrt returns float

argument	argument type
x	float const

returns the square root of x

saturate(x: float const)

saturate returns float

argument	argument type
x	float const

returns a clamped to [0..1] inclusive range x

floor(x: float2 const)

floor returns float2

argument	argument type
x	float2 const

returns a float value representing the largest integer that is less than or equal to x

ceil(x: float2 const)

ceil returns float2

argument	argument type
x	float2 const

returns a float value representing the smallest integer (type is still float) that is greater than or equal to arg0

sqrt(x: float2 const)

sqrt returns float2

argument	argument type
x	float2 const

returns the square root of x

saturate(x: float2 const)

saturate returns float2

argument	argument type
x	float2 const

returns a clamped to [0..1] inclusive range x

floor(x: float3 const)

floor returns float3

argument	argument type
x	float3 const

returns a float value representing the largest integer that is less than or equal to x

ceil(x: float3 const)

ceil returns float3

argument	argument type
x	float3 const

returns a float value representing the smallest integer (type is still float) that is greater than or equal to arg0

sqrt(x: float3 const)

sqrt returns float3

argument	argument type
x	float3 const

returns the square root of x

saturate(x: float3 const)

saturate returns float3

argument	argument type
x	float3 const

returns a clamped to [0..1] inclusive range x

floor(x: float4 const)

floor returns float4

argument	argument type
x	float4 const

returns a float value representing the largest integer that is less than or equal to x

ceil(x: float4 const)

ceil returns float4

argument	argument type
x	float4 const

returns a float value representing the smallest integer (type is still float) that is greater than or equal to arg0

sqrt(x: float4 const)

sqrt returns float4

argument	argument type
x	float4 const

returns the square root of x

saturate(x: float4 const)

saturate returns float4

argument	argument type
x	float4 const

returns a clamped to [0..1] inclusive range x

abs(x: int const)

abs returns int

argument	argument type
x	int const

returns the absolute value of x

sign(x: int const)

sign returns int

argument	argument type
x	int const

returns sign of x, or 0 if x == 0

abs(x: int2 const)

abs returns int2

argument	argument type
x	int2 const

returns the absolute value of x

sign(x: int2 const)

sign returns int2

argument	argument type
x	int2 const

returns sign of x, or 0 if x == 0

abs(x: int3 const)

abs returns int3

argument	argument type
x	int3 const

returns the absolute value of x

sign(x: int3 const)

sign returns int3

argument	argument type
x	int3 const

returns sign of x, or 0 if x == 0

abs(x: int4 const)

abs returns int4

argument	argument type
x	int4 const

returns the absolute value of x

sign(x: int4 const)

sign returns int4

argument	argument type
x	int4 const

returns sign of x, or 0 if x == 0

abs(x: uint const)

abs returns uint

argument	argument type
x	uint const

returns the absolute value of x

sign(x: uint const)

sign returns uint

argument	argument type
x	uint const

returns sign of x, or 0 if x == 0

abs(x: uint2 const)

abs returns uint2

argument	argument type
x	uint2 const

returns the absolute value of x

sign(x: uint2 const)

sign returns uint2

argument	argument type
x	uint2 const

returns sign of x, or 0 if x == 0

abs(x: uint3 const)

abs returns uint3

argument	argument type
x	uint3 const

returns the absolute value of x

sign(x: uint3 const)

sign returns uint3

argument	argument type
x	uint3 const

returns sign of x, or 0 if x == 0

abs(x: uint4 const)

abs returns uint4

argument	argument type
x	uint4 const

returns the absolute value of x

sign(x: uint4 const)

sign returns uint4

argument	argument type
x	uint4 const

returns sign of x, or 0 if x == 0

abs(x: float const)

abs returns float

argument	argument type
x	float const

returns the absolute value of x

sign(x: float const)

sign returns float

argument	argument type
x	float const

returns sign of x, or 0 if x == 0

abs(x: float2 const)

abs returns float2

argument	argument type
x	float2 const

returns the absolute value of x

sign(x: float2 const)

sign returns float2

argument	argument type
x	float2 const

returns sign of x, or 0 if x == 0

abs(x: float3 const)

abs returns float3

argument	argument type
x	float3 const

returns the absolute value of x

sign(x: float3 const)

sign returns float3

argument	argument type
x	float3 const

returns sign of x, or 0 if x == 0

abs(x: float4 const)

abs returns float4

argument	argument type
x	float4 const

returns the absolute value of x

sign(x: float4 const)

sign returns float4

argument	argument type
x	float4 const

returns sign of x, or 0 if x == 0

abs(x: double const)

abs returns double

argument	argument type
x	double const

returns the absolute value of x

sign(x: double const)

sign returns double

argument	argument type
x	double const

returns sign of x, or 0 if x == 0

abs(x: int64 const)

abs returns int64

argument	argument type
x	int64 const

returns the absolute value of x

sign(x: int64 const)

sign returns int64

argument	argument type
x	int64 const

returns sign of x, or 0 if x == 0

abs(x: uint64 const)

abs returns uint64

argument	argument type
x	uint64 const

returns the absolute value of x

sign(x: uint64 const)

sign returns uint64

argument	argument type
x	uint64 const

returns sign of x, or 0 if x == 0

is_nan(x: float const)

is_nan returns bool

argument	argument type
x	float const

Returns true if x is NaN (not a number)

is_finite(x: float const)

is_finite returns bool

argument	argument type
x	float const

Returns true if x is not a negative or positive infinity

is_nan(x: double const)

is_nan returns bool

argument	argument type
x	double const

Returns true if x is NaN (not a number)

is_finite(x: double const)

is_finite returns bool

argument	argument type
x	double const

Returns true if x is not a negative or positive infinity

sqrt(x: double const)

sqrt returns double

argument	argument type
x	double const

returns the square root of x

exp(x: double const)

exp returns double

argument	argument type
x	double const

returns the e^x value of x

rcp(x: double const)

rcp returns double

argument	argument type
x	double const

returns the 1/x

log(x: double const)

log returns double

argument	argument type
x	double const

returns the natural logarithm of x

pow(x: double const; y: double const)

pow returns double

argument	argument type
x	double const
y	double const

returns x raised to the power of y

exp2(x: double const)

exp2 returns double

argument	argument type
x	double const

returns the 2^x value of x

log2(x: double const)

log2 returns double

argument	argument type
x	double const

returns the logarithm base-2 of x

sin(x: double const)

sin returns double

argument	argument type
x	double const

returns the sine of x

cos(x: double const)

cos returns double

argument	argument type
x	double const

returns the cosine of x

asin(x: double const)

asin returns double

argument	argument type
x	double const

returns the arcsine of x

acos(x: double const)

acos returns double

argument	argument type
x	double const

returns the arccosine of x

tan(x: double const)

tan returns double

argument	argument type
x	double const

returns the tangent of x

atan(x: double const)

atan returns double

argument	argument type
x	double const

returns the arctangent of x

atan2(y: double const; x: double const)

atan2 returns double

argument	argument type
y	double const
x	double const

returns the arctangent of y/x

sincos(x: float const; s: float& implicit; c: float& implicit)

argument	argument type
x	float const
s	float& implicit
c	float& implicit

returns oth sine and cosine of x

sincos(x: double const; s: double& implicit; c: double& implicit)

argument	argument type
x	double const
s	double& implicit
c	double& implicit

returns oth sine and cosine of x

asin(x: float const)

asin returns float

argument	argument type
x	float const

returns the arcsine of x

acos(x: float const)

acos returns float

argument	argument type
x	float const

returns the arccosine of x

atan(x: float const)

atan returns float

argument	argument type
x	float const

returns the arctangent of x

atan2(y: float const; x: float const)

atan2 returns float

argument	argument type
y	float const
x	float const

returns the arctangent of y/x

asin(x: float2 const)

asin returns float2

argument	argument type
x	float2 const

returns the arcsine of x

asin(x: float3 const)

asin returns float3

argument	argument type
x	float3 const

returns the arcsine of x

asin(x: float4 const)

asin returns float4

argument	argument type
x	float4 const

returns the arcsine of x

acos(x: float2 const)

acos returns float2

argument	argument type
x	float2 const

returns the arccosine of x

acos(x: float3 const)

acos returns float3

argument	argument type
x	float3 const

returns the arccosine of x

acos(x: float4 const)

acos returns float4

argument	argument type
x	float4 const

returns the arccosine of x

atan(x: float2 const)

atan returns float2

argument	argument type
x	float2 const

returns the arctangent of x

atan(x: float3 const)

atan returns float3

argument	argument type
x	float3 const

returns the arctangent of x

atan(x: float4 const)

atan returns float4

argument	argument type
x	float4 const

returns the arctangent of x

atan2(y: float2 const; x: float2 const)

atan2 returns float2

argument	argument type
y	float2 const
x	float2 const

returns the arctangent of y/x

atan2(y: float3 const; x: float3 const)

atan2 returns float3

argument	argument type
y	float3 const
x	float3 const

returns the arctangent of y/x

atan2(y: float4 const; x: float4 const)

atan2 returns float4

argument	argument type
y	float4 const
x	float4 const

returns the arctangent of y/x

3.5. float* only

• rcp_est (x:float const) : float

• rcp_est (x:float2 const) : float2

• rcp_est (x:float3 const) : float3

• rcp_est (x:float4 const) : float4

• fract (x:float const) : float

• round (x:float const) : float

• rsqrt (x:float const) : float

• rsqrt_est (x:float const) : float

• fract (x:float2 const) : float2

• round (x:float2 const) : float2

• rsqrt (x:float2 const) : float2

• rsqrt_est (x:float2 const) : float2

• fract (x:float3 const) : float3

• round (x:float3 const) : float3

• rsqrt (x:float3 const) : float3

• rsqrt_est (x:float3 const) : float3

• fract (x:float4 const) : float4

• round (x:float4 const) : float4

• rsqrt (x:float4 const) : float4

• rsqrt_est (x:float4 const) : float4

• atan_est (x:float const) : float

• atan2_est (y:float const;x:float const) : float

• atan_est (x:float2 const) : float2

• atan_est (x:float3 const) : float3

• atan_est (x:float4 const) : float4

• atan2_est (y:float2 const;x:float2 const) : float2

• atan2_est (y:float3 const;x:float3 const) : float3

• atan2_est (y:float4 const;x:float4 const) : float4

• floori (x:float const) : int

• ceili (x:float const) : int

• roundi (x:float const) : int

• trunci (x:float const) : int

• floori (x:double const) : int

• ceili (x:double const) : int

• roundi (x:double const) : int

• trunci (x:double const) : int

• floori (x:float2 const) : int2

• ceili (x:float2 const) : int2

• roundi (x:float2 const) : int2

• trunci (x:float2 const) : int2

• floori (x:float3 const) : int3

• ceili (x:float3 const) : int3

• roundi (x:float3 const) : int3

• trunci (x:float3 const) : int3

• floori (x:float4 const) : int4

• ceili (x:float4 const) : int4

• roundi (x:float4 const) : int4

• trunci (x:float4 const) : int4

• - (x:math::float4x4 const implicit) : math::float4x4

• - (x:math::float3x4 const implicit) : math::float3x4

• - (x:math::float3x3 const implicit) : math::float3x3

rcp_est(x: float const)

rcp_est returns float

argument	argument type
x	float const

returns the fast approximation 1/x

rcp_est(x: float2 const)

rcp_est returns float2

argument	argument type
x	float2 const

returns the fast approximation 1/x

rcp_est(x: float3 const)

rcp_est returns float3

argument	argument type
x	float3 const

returns the fast approximation 1/x

rcp_est(x: float4 const)

rcp_est returns float4

argument	argument type
x	float4 const

returns the fast approximation 1/x

fract(x: float const)

fract returns float

argument	argument type
x	float const

returns a fraction part of x

round(x: float const)

round returns float

argument	argument type
x	float const

Returns the nearest integer to x.

rsqrt(x: float const)

rsqrt returns float

argument	argument type
x	float const

returns 1/sqrt(x)

rsqrt_est(x: float const)

rsqrt_est returns float

argument	argument type
x	float const

returns the fast approximation 1/sqrt(x)

fract(x: float2 const)

fract returns float2

argument	argument type
x	float2 const

returns a fraction part of x

round(x: float2 const)

round returns float2

argument	argument type
x	float2 const

Returns the nearest integer to x.

rsqrt(x: float2 const)

rsqrt returns float2

argument	argument type
x	float2 const

returns 1/sqrt(x)

rsqrt_est(x: float2 const)

rsqrt_est returns float2

argument	argument type
x	float2 const

returns the fast approximation 1/sqrt(x)

fract(x: float3 const)

fract returns float3

argument	argument type
x	float3 const

returns a fraction part of x

round(x: float3 const)

round returns float3

argument	argument type
x	float3 const

Returns the nearest integer to x.

rsqrt(x: float3 const)

rsqrt returns float3

argument	argument type
x	float3 const

returns 1/sqrt(x)

rsqrt_est(x: float3 const)

rsqrt_est returns float3

argument	argument type
x	float3 const

returns the fast approximation 1/sqrt(x)

fract(x: float4 const)

fract returns float4

argument	argument type
x	float4 const

returns a fraction part of x

round(x: float4 const)

round returns float4

argument	argument type
x	float4 const

Returns the nearest integer to x.

rsqrt(x: float4 const)

rsqrt returns float4

argument	argument type
x	float4 const

returns 1/sqrt(x)

rsqrt_est(x: float4 const)

rsqrt_est returns float4

argument	argument type
x	float4 const

returns the fast approximation 1/sqrt(x)

atan_est(x: float const)

atan_est returns float

argument	argument type
x	float const

Fast estimation for the atan.

atan2_est(y: float const; x: float const)

atan2_est returns float

argument	argument type
y	float const
x	float const

returns the fast approximation of arctangent of y/x

atan_est(x: float2 const)

atan_est returns float2

argument	argument type
x	float2 const

Fast estimation for the atan.

atan_est(x: float3 const)

atan_est returns float3

argument	argument type
x	float3 const

Fast estimation for the atan.

atan_est(x: float4 const)

atan_est returns float4

argument	argument type
x	float4 const

Fast estimation for the atan.

atan2_est(y: float2 const; x: float2 const)

atan2_est returns float2

argument	argument type
y	float2 const
x	float2 const

returns the fast approximation of arctangent of y/x

atan2_est(y: float3 const; x: float3 const)

atan2_est returns float3

argument	argument type
y	float3 const
x	float3 const

returns the fast approximation of arctangent of y/x

atan2_est(y: float4 const; x: float4 const)

atan2_est returns float4

argument	argument type
y	float4 const
x	float4 const

returns the fast approximation of arctangent of y/x

floori(x: float const)

floori returns int

argument	argument type
x	float const

returns a integer value representing the largest integer that is less than or equal to x

ceili(x: float const)

ceili returns int

argument	argument type
x	float const

returns a value representing the smallest integer (integer type!) that is greater than or equal to arg0

roundi(x: float const)

roundi returns int

argument	argument type
x	float const

returns a integer value representing the integer that is closest to x

trunci(x: float const)

trunci returns int

argument	argument type
x	float const

returns a integer value representing the float without fraction part of x

floori(x: double const)

floori returns int

argument	argument type
x	double const

returns a integer value representing the largest integer that is less than or equal to x

ceili(x: double const)

ceili returns int

argument	argument type
x	double const

returns a value representing the smallest integer (integer type!) that is greater than or equal to arg0

roundi(x: double const)

roundi returns int

argument	argument type
x	double const

returns a integer value representing the integer that is closest to x

trunci(x: double const)

trunci returns int

argument	argument type
x	double const

returns a integer value representing the float without fraction part of x

floori(x: float2 const)

floori returns int2

argument	argument type
x	float2 const

returns a integer value representing the largest integer that is less than or equal to x

ceili(x: float2 const)

ceili returns int2

argument	argument type
x	float2 const

returns a value representing the smallest integer (integer type!) that is greater than or equal to arg0

roundi(x: float2 const)

roundi returns int2

argument	argument type
x	float2 const

returns a integer value representing the integer that is closest to x

trunci(x: float2 const)

trunci returns int2

argument	argument type
x	float2 const

returns a integer value representing the float without fraction part of x

floori(x: float3 const)

floori returns int3

argument	argument type
x	float3 const

returns a integer value representing the largest integer that is less than or equal to x

ceili(x: float3 const)

ceili returns int3

argument	argument type
x	float3 const

returns a value representing the smallest integer (integer type!) that is greater than or equal to arg0

roundi(x: float3 const)

roundi returns int3

argument	argument type
x	float3 const

returns a integer value representing the integer that is closest to x

trunci(x: float3 const)

trunci returns int3

argument	argument type
x	float3 const

returns a integer value representing the float without fraction part of x

floori(x: float4 const)

floori returns int4

argument	argument type
x	float4 const

returns a integer value representing the largest integer that is less than or equal to x

ceili(x: float4 const)

ceili returns int4

argument	argument type
x	float4 const

returns a value representing the smallest integer (integer type!) that is greater than or equal to arg0

roundi(x: float4 const)

roundi returns int4

argument	argument type
x	float4 const

returns a integer value representing the integer that is closest to x

trunci(x: float4 const)

trunci returns int4

argument	argument type
x	float4 const

returns a integer value representing the float without fraction part of x

operator -(x: float4x4 const implicit)

• returns math::float4x4

argument	argument type
x	math::float4x4 const implicit

returns -x

operator -(x: float3x4 const implicit)

• returns math::float3x4

argument	argument type
x	math::float3x4 const implicit

returns -x

operator -(x: float3x3 const implicit)

• returns math::float3x3

argument	argument type
x	math::float3x3 const implicit

returns -x

3.6. float3 only

• cross (x:float3 const;y:float3 const) : float3

• distance (x:float2 const;y:float2 const) : float

• distance_sq (x:float2 const;y:float2 const) : float

• inv_distance (x:float2 const;y:float2 const) : float

• inv_distance_sq (x:float2 const;y:float2 const) : float

• distance (x:float3 const;y:float3 const) : float

• distance_sq (x:float3 const;y:float3 const) : float

• inv_distance (x:float3 const;y:float3 const) : float

• inv_distance_sq (x:float3 const;y:float3 const) : float

• distance (x:float4 const;y:float4 const) : float

• distance_sq (x:float4 const;y:float4 const) : float

• inv_distance (x:float4 const;y:float4 const) : float

• inv_distance_sq (x:float4 const;y:float4 const) : float

• reflect (v:float3 const;n:float3 const) : float3

• reflect (v:float2 const;n:float2 const) : float2

• refract (v:float3 const;n:float3 const;nint:float const) : float3

• refract (v:float2 const;n:float2 const;nint:float const) : float2

cross(x: float3 const; y: float3 const)

cross returns float3

argument	argument type
x	float3 const
y	float3 const

returns vector representing cross product between x and y

distance(x: float2 const; y: float2 const)

distance returns float

argument	argument type
x	float2 const
y	float2 const

returns a non-negative value representing distance between x and y

distance_sq(x: float2 const; y: float2 const)

distance_sq returns float

argument	argument type
x	float2 const
y	float2 const

returns a non-negative value representing squared distance between x and y

inv_distance(x: float2 const; y: float2 const)

inv_distance returns float

argument	argument type
x	float2 const
y	float2 const

returns a non-negative value representing 1/distance between x and y

inv_distance_sq(x: float2 const; y: float2 const)

inv_distance_sq returns float

argument	argument type
x	float2 const
y	float2 const

returns a non-negative value representing 1/squared distance between x and y

distance(x: float3 const; y: float3 const)

distance returns float

argument	argument type
x	float3 const
y	float3 const

returns a non-negative value representing distance between x and y

distance_sq(x: float3 const; y: float3 const)

distance_sq returns float

argument	argument type
x	float3 const
y	float3 const

returns a non-negative value representing squared distance between x and y

inv_distance(x: float3 const; y: float3 const)

inv_distance returns float

argument	argument type
x	float3 const
y	float3 const

returns a non-negative value representing 1/distance between x and y

inv_distance_sq(x: float3 const; y: float3 const)

inv_distance_sq returns float

argument	argument type
x	float3 const
y	float3 const

returns a non-negative value representing 1/squared distance between x and y

distance(x: float4 const; y: float4 const)

distance returns float

argument	argument type
x	float4 const
y	float4 const

returns a non-negative value representing distance between x and y

distance_sq(x: float4 const; y: float4 const)

distance_sq returns float

argument	argument type
x	float4 const
y	float4 const

returns a non-negative value representing squared distance between x and y

inv_distance(x: float4 const; y: float4 const)

inv_distance returns float

argument	argument type
x	float4 const
y	float4 const

returns a non-negative value representing 1/distance between x and y

inv_distance_sq(x: float4 const; y: float4 const)

inv_distance_sq returns float

argument	argument type
x	float4 const
y	float4 const

returns a non-negative value representing 1/squared distance between x and y

reflect(v: float3 const; n: float3 const)

reflect returns float3

argument	argument type
v	float3 const
n	float3 const

returns vector representing reflection of vector v from normal n same as

def reflect(v, n: float3)
    return v - 2. * dot(v, n) * n

reflect(v: float2 const; n: float2 const)

reflect returns float2

argument	argument type
v	float2 const
n	float2 const

returns vector representing reflection of vector v from normal n same as

def reflect(v, n: float3)
    return v - 2. * dot(v, n) * n

refract(v: float3 const; n: float3 const; nint: float const)

refract returns float3

argument	argument type
v	float3 const
n	float3 const
nint	float const

returns vector representing refractoin of vector v from normal n same as

def refract(v, n: float3; nint: float; outRefracted: float3&)
    let dt = dot(v, n)
    let discr = 1. - nint * nint * (1. - dt * dt)
    if discr > 0.
        outRefracted = nint * (v - n * dt) - n * sqrt(discr)
        return true
    return false

refract(v: float2 const; n: float2 const; nint: float const)

refract returns float2

argument	argument type
v	float2 const
n	float2 const
nint	float const

returns vector representing refractoin of vector v from normal n same as

def refract(v, n: float3; nint: float; outRefracted: float3&)
    let dt = dot(v, n)
    let discr = 1. - nint * nint * (1. - dt * dt)
    if discr > 0.
        outRefracted = nint * (v - n * dt) - n * sqrt(discr)
        return true
    return false

3.7. float2, float3, float4

• dot (x:float2 const;y:float2 const) : float

• dot (x:float3 const;y:float3 const) : float

• dot (x:float4 const;y:float4 const) : float

• fast_normalize (x:float2 const) : float2

• fast_normalize (x:float3 const) : float3

• fast_normalize (x:float4 const) : float4

• normalize (x:float2 const) : float2

• normalize (x:float3 const) : float3

• normalize (x:float4 const) : float4

• length (x:float2 const) : float

• length (x:float3 const) : float

• length (x:float4 const) : float

• inv_length (x:float2 const) : float

• inv_length (x:float3 const) : float

• inv_length (x:float4 const) : float

• inv_length_sq (x:float2 const) : float

• inv_length_sq (x:float3 const) : float

• inv_length_sq (x:float4 const) : float

• length_sq (x:float2 const) : float

• length_sq (x:float3 const) : float

• length_sq (x:float4 const) : float

dot(x: float2 const; y: float2 const)

dot returns float

argument	argument type
x	float2 const
y	float2 const

returns scalar representing dot product between x and y

dot(x: float3 const; y: float3 const)

dot returns float

argument	argument type
x	float3 const
y	float3 const

returns scalar representing dot product between x and y

dot(x: float4 const; y: float4 const)

dot returns float

argument	argument type
x	float4 const
y	float4 const

returns scalar representing dot product between x and y

fast_normalize(x: float2 const)

fast_normalize returns float2

argument	argument type
x	float2 const

returns the fast approximation of normalized x, or nan if length(x) is 0

fast_normalize(x: float3 const)

fast_normalize returns float3

argument	argument type
x	float3 const

returns the fast approximation of normalized x, or nan if length(x) is 0

fast_normalize(x: float4 const)

fast_normalize returns float4

argument	argument type
x	float4 const

returns the fast approximation of normalized x, or nan if length(x) is 0

normalize(x: float2 const)

normalize returns float2

argument	argument type
x	float2 const

returns normalized x, or nan if length(x) is 0

normalize(x: float3 const)

normalize returns float3

argument	argument type
x	float3 const

returns normalized x, or nan if length(x) is 0

normalize(x: float4 const)

normalize returns float4

argument	argument type
x	float4 const

returns normalized x, or nan if length(x) is 0

length(x: float2 const)

length returns float

argument	argument type
x	float2 const

returns a non-negative value representing magnitude of x

length(x: float3 const)

length returns float

argument	argument type
x	float3 const

returns a non-negative value representing magnitude of x

length(x: float4 const)

length returns float

argument	argument type
x	float4 const

returns a non-negative value representing magnitude of x

inv_length(x: float2 const)

inv_length returns float

argument	argument type
x	float2 const

returns a non-negative value representing 1/magnitude of x

inv_length(x: float3 const)

inv_length returns float

argument	argument type
x	float3 const

returns a non-negative value representing 1/magnitude of x

inv_length(x: float4 const)

inv_length returns float

argument	argument type
x	float4 const

returns a non-negative value representing 1/magnitude of x

inv_length_sq(x: float2 const)

inv_length_sq returns float

argument	argument type
x	float2 const

returns a non-negative value representing 1/squared magnitude of x

inv_length_sq(x: float3 const)

inv_length_sq returns float

argument	argument type
x	float3 const

returns a non-negative value representing 1/squared magnitude of x

inv_length_sq(x: float4 const)

inv_length_sq returns float

argument	argument type
x	float4 const

returns a non-negative value representing 1/squared magnitude of x

length_sq(x: float2 const)

length_sq returns float

argument	argument type
x	float2 const

returns a non-negative value representing squared magnitude of x

length_sq(x: float3 const)

length_sq returns float

argument	argument type
x	float3 const

returns a non-negative value representing squared magnitude of x

length_sq(x: float4 const)

length_sq returns float

argument	argument type
x	float4 const

returns a non-negative value representing squared magnitude of x

3.8. Noise functions

• uint32_hash (seed:uint const) : uint

• uint_noise_1D (position:int const;seed:uint const) : uint

• uint_noise_2D (position:int2 const;seed:uint const) : uint

• uint_noise_3D (position:int3 const;seed:uint const) : uint

uint32_hash(seed: uint const)

uint32_hash returns uint

argument	argument type
seed	uint const

returns hashed value of seed

uint_noise_1D(position: int const; seed: uint const)

uint_noise_1D returns uint

argument	argument type
position	int const
seed	uint const

returns noise value of position in the seeded sequence

uint_noise_2D(position: int2 const; seed: uint const)

uint_noise_2D returns uint

argument	argument type
position	int2 const
seed	uint const

returns noise value of position in the seeded sequence

uint_noise_3D(position: int3 const; seed: uint const)

uint_noise_3D returns uint

argument	argument type
position	int3 const
seed	uint const

returns noise value of position in the seeded sequence

3.9. lerp/mad/clamp

• mad (a:float const;b:float const;c:float const) : float

• lerp (a:float const;b:float const;t:float const) : float

• mad (a:float2 const;b:float2 const;c:float2 const) : float2

• lerp (a:float2 const;b:float2 const;t:float2 const) : float2

• mad (a:float3 const;b:float3 const;c:float3 const) : float3

• lerp (a:float3 const;b:float3 const;t:float3 const) : float3

• mad (a:float4 const;b:float4 const;c:float4 const) : float4

• lerp (a:float4 const;b:float4 const;t:float4 const) : float4

• mad (a:float2 const;b:float const;c:float2 const) : float2

• mad (a:float3 const;b:float const;c:float3 const) : float3

• mad (a:float4 const;b:float const;c:float4 const) : float4

• mad (a:int const;b:int const;c:int const) : int

• mad (a:int2 const;b:int2 const;c:int2 const) : int2

• mad (a:int3 const;b:int3 const;c:int3 const) : int3

• mad (a:int4 const;b:int4 const;c:int4 const) : int4

• mad (a:int2 const;b:int const;c:int2 const) : int2

• mad (a:int3 const;b:int const;c:int3 const) : int3

• mad (a:int4 const;b:int const;c:int4 const) : int4

• mad (a:uint const;b:uint const;c:uint const) : uint

• mad (a:uint2 const;b:uint2 const;c:uint2 const) : uint2

• mad (a:uint3 const;b:uint3 const;c:uint3 const) : uint3

• mad (a:uint4 const;b:uint4 const;c:uint4 const) : uint4

• mad (a:uint2 const;b:uint const;c:uint2 const) : uint2

• mad (a:uint3 const;b:uint const;c:uint3 const) : uint3

• mad (a:uint4 const;b:uint const;c:uint4 const) : uint4

• mad (a:double const;b:double const;c:double const) : double

• lerp (a:double const;b:double const;t:double const) : double

• clamp (t:int const;a:int const;b:int const) : int

• clamp (t:int2 const;a:int2 const;b:int2 const) : int2

• clamp (t:int3 const;a:int3 const;b:int3 const) : int3

• clamp (t:int4 const;a:int4 const;b:int4 const) : int4

• clamp (t:uint const;a:uint const;b:uint const) : uint

• clamp (t:uint2 const;a:uint2 const;b:uint2 const) : uint2

• clamp (t:uint3 const;a:uint3 const;b:uint3 const) : uint3

• clamp (t:uint4 const;a:uint4 const;b:uint4 const) : uint4

• clamp (t:float const;a:float const;b:float const) : float

• clamp (t:float2 const;a:float2 const;b:float2 const) : float2

• clamp (t:float3 const;a:float3 const;b:float3 const) : float3

• clamp (t:float4 const;a:float4 const;b:float4 const) : float4

• clamp (t:double const;a:double const;b:double const) : double

• clamp (t:int64 const;a:int64 const;b:int64 const) : int64

• clamp (t:uint64 const;a:uint64 const;b:uint64 const) : uint64

• lerp (a:float2 const;b:float2 const;t:float const) : float2

• lerp (a:float3 const;b:float3 const;t:float const) : float3

• lerp (a:float4 const;b:float4 const;t:float const) : float4

mad(a: float const; b: float const; c: float const)

mad returns float

argument	argument type
a	float const
b	float const
c	float const

returns vector or scalar representing a * b + c

lerp(a: float const; b: float const; t: float const)

lerp returns float

argument	argument type
a	float const
b	float const
t	float const

returns vector or scalar representing a + (b - a) * t

mad(a: float2 const; b: float2 const; c: float2 const)

mad returns float2

argument	argument type
a	float2 const
b	float2 const
c	float2 const

returns vector or scalar representing a * b + c

lerp(a: float2 const; b: float2 const; t: float2 const)

lerp returns float2

argument	argument type
a	float2 const
b	float2 const
t	float2 const

returns vector or scalar representing a + (b - a) * t

mad(a: float3 const; b: float3 const; c: float3 const)

mad returns float3

argument	argument type
a	float3 const
b	float3 const
c	float3 const

returns vector or scalar representing a * b + c

lerp(a: float3 const; b: float3 const; t: float3 const)

lerp returns float3

argument	argument type
a	float3 const
b	float3 const
t	float3 const

returns vector or scalar representing a + (b - a) * t

mad(a: float4 const; b: float4 const; c: float4 const)

mad returns float4

argument	argument type
a	float4 const
b	float4 const
c	float4 const

returns vector or scalar representing a * b + c

lerp(a: float4 const; b: float4 const; t: float4 const)

lerp returns float4

argument	argument type
a	float4 const
b	float4 const
t	float4 const

returns vector or scalar representing a + (b - a) * t

mad(a: float2 const; b: float const; c: float2 const)

mad returns float2

argument	argument type
a	float2 const
b	float const
c	float2 const

returns vector or scalar representing a * b + c

mad(a: float3 const; b: float const; c: float3 const)

mad returns float3

argument	argument type
a	float3 const
b	float const
c	float3 const

returns vector or scalar representing a * b + c

mad(a: float4 const; b: float const; c: float4 const)

mad returns float4

argument	argument type
a	float4 const
b	float const
c	float4 const

returns vector or scalar representing a * b + c

mad(a: int const; b: int const; c: int const)

mad returns int

argument	argument type
a	int const
b	int const
c	int const

returns vector or scalar representing a * b + c

mad(a: int2 const; b: int2 const; c: int2 const)

mad returns int2

argument	argument type
a	int2 const
b	int2 const
c	int2 const

returns vector or scalar representing a * b + c

mad(a: int3 const; b: int3 const; c: int3 const)

mad returns int3

argument	argument type
a	int3 const
b	int3 const
c	int3 const

returns vector or scalar representing a * b + c

mad(a: int4 const; b: int4 const; c: int4 const)

mad returns int4

argument	argument type
a	int4 const
b	int4 const
c	int4 const

returns vector or scalar representing a * b + c

mad(a: int2 const; b: int const; c: int2 const)

mad returns int2

argument	argument type
a	int2 const
b	int const
c	int2 const

returns vector or scalar representing a * b + c

mad(a: int3 const; b: int const; c: int3 const)

mad returns int3

argument	argument type
a	int3 const
b	int const
c	int3 const

returns vector or scalar representing a * b + c

mad(a: int4 const; b: int const; c: int4 const)

mad returns int4

argument	argument type
a	int4 const
b	int const
c	int4 const

returns vector or scalar representing a * b + c

mad(a: uint const; b: uint const; c: uint const)

mad returns uint

argument	argument type
a	uint const
b	uint const
c	uint const

returns vector or scalar representing a * b + c

mad(a: uint2 const; b: uint2 const; c: uint2 const)

mad returns uint2

argument	argument type
a	uint2 const
b	uint2 const
c	uint2 const

returns vector or scalar representing a * b + c

mad(a: uint3 const; b: uint3 const; c: uint3 const)

mad returns uint3

argument	argument type
a	uint3 const
b	uint3 const
c	uint3 const

returns vector or scalar representing a * b + c

mad(a: uint4 const; b: uint4 const; c: uint4 const)

mad returns uint4

argument	argument type
a	uint4 const
b	uint4 const
c	uint4 const

returns vector or scalar representing a * b + c

mad(a: uint2 const; b: uint const; c: uint2 const)

mad returns uint2

argument	argument type
a	uint2 const
b	uint const
c	uint2 const

returns vector or scalar representing a * b + c

mad(a: uint3 const; b: uint const; c: uint3 const)

mad returns uint3

argument	argument type
a	uint3 const
b	uint const
c	uint3 const

returns vector or scalar representing a * b + c

mad(a: uint4 const; b: uint const; c: uint4 const)

mad returns uint4

argument	argument type
a	uint4 const
b	uint const
c	uint4 const

returns vector or scalar representing a * b + c

mad(a: double const; b: double const; c: double const)

mad returns double

argument	argument type
a	double const
b	double const
c	double const

returns vector or scalar representing a * b + c

lerp(a: double const; b: double const; t: double const)

lerp returns double

argument	argument type
a	double const
b	double const
t	double const

returns vector or scalar representing a + (b - a) * t

clamp(t: int const; a: int const; b: int const)

clamp returns int

argument	argument type
t	int const
a	int const
b	int const

returns vector or scalar representing min(max(t, a), b)

clamp(t: int2 const; a: int2 const; b: int2 const)

clamp returns int2

argument	argument type
t	int2 const
a	int2 const
b	int2 const

returns vector or scalar representing min(max(t, a), b)

clamp(t: int3 const; a: int3 const; b: int3 const)

clamp returns int3

argument	argument type
t	int3 const
a	int3 const
b	int3 const

returns vector or scalar representing min(max(t, a), b)

clamp(t: int4 const; a: int4 const; b: int4 const)

clamp returns int4

argument	argument type
t	int4 const
a	int4 const
b	int4 const

returns vector or scalar representing min(max(t, a), b)

clamp(t: uint const; a: uint const; b: uint const)

clamp returns uint

argument	argument type
t	uint const
a	uint const
b	uint const

returns vector or scalar representing min(max(t, a), b)

clamp(t: uint2 const; a: uint2 const; b: uint2 const)

clamp returns uint2

argument	argument type
t	uint2 const
a	uint2 const
b	uint2 const

returns vector or scalar representing min(max(t, a), b)

clamp(t: uint3 const; a: uint3 const; b: uint3 const)

clamp returns uint3

argument	argument type
t	uint3 const
a	uint3 const
b	uint3 const

returns vector or scalar representing min(max(t, a), b)

clamp(t: uint4 const; a: uint4 const; b: uint4 const)

clamp returns uint4

argument	argument type
t	uint4 const
a	uint4 const
b	uint4 const

returns vector or scalar representing min(max(t, a), b)

clamp(t: float const; a: float const; b: float const)

clamp returns float

argument	argument type
t	float const
a	float const
b	float const

returns vector or scalar representing min(max(t, a), b)

clamp(t: float2 const; a: float2 const; b: float2 const)

clamp returns float2

argument	argument type
t	float2 const
a	float2 const
b	float2 const

returns vector or scalar representing min(max(t, a), b)

clamp(t: float3 const; a: float3 const; b: float3 const)

clamp returns float3

argument	argument type
t	float3 const
a	float3 const
b	float3 const

returns vector or scalar representing min(max(t, a), b)

clamp(t: float4 const; a: float4 const; b: float4 const)

clamp returns float4

argument	argument type
t	float4 const
a	float4 const
b	float4 const

returns vector or scalar representing min(max(t, a), b)

clamp(t: double const; a: double const; b: double const)

clamp returns double

argument	argument type
t	double const
a	double const
b	double const

returns vector or scalar representing min(max(t, a), b)

clamp(t: int64 const; a: int64 const; b: int64 const)

clamp returns int64

argument	argument type
t	int64 const
a	int64 const
b	int64 const

returns vector or scalar representing min(max(t, a), b)

clamp(t: uint64 const; a: uint64 const; b: uint64 const)

clamp returns uint64

argument	argument type
t	uint64 const
a	uint64 const
b	uint64 const

returns vector or scalar representing min(max(t, a), b)

lerp(a: float2 const; b: float2 const; t: float const)

lerp returns float2

argument	argument type
a	float2 const
b	float2 const
t	float const

returns vector or scalar representing a + (b - a) * t

lerp(a: float3 const; b: float3 const; t: float const)

lerp returns float3

argument	argument type
a	float3 const
b	float3 const
t	float const

returns vector or scalar representing a + (b - a) * t

lerp(a: float4 const; b: float4 const; t: float const)

lerp returns float4

argument	argument type
a	float4 const
b	float4 const
t	float const

returns vector or scalar representing a + (b - a) * t

3.10. Matrix operations

• * (x:math::float4x4 const implicit;y:math::float4x4 const implicit) : math::float4x4

• == (x:math::float4x4 const implicit;y:math::float4x4 const implicit) : bool

• != (x:math::float4x4 const implicit;y:math::float4x4 const implicit) : bool

• * (x:math::float3x4 const implicit;y:math::float3x4 const implicit) : math::float3x4

• * (x:math::float3x4 const implicit;y:float3 const) : float3

• * (x:math::float4x4 const implicit;y:float4 const) : float4

• == (x:math::float3x4 const implicit;y:math::float3x4 const implicit) : bool

• != (x:math::float3x4 const implicit;y:math::float3x4 const implicit) : bool

• * (x:math::float3x3 const implicit;y:math::float3x3 const implicit) : math::float3x3

• * (x:math::float3x3 const implicit;y:float3 const) : float3

• == (x:math::float3x3 const implicit;y:math::float3x3 const implicit) : bool

• != (x:math::float3x3 const implicit;y:math::float3x3 const implicit) : bool

operator *(x: float4x4 const implicit; y: float4x4 const implicit)

• returns math::float4x4

argument	argument type
x	math::float4x4 const implicit
y	math::float4x4 const implicit

Multiplies x by y.

operator ==(x: float4x4 const implicit; y: float4x4 const implicit)

== returns bool

argument	argument type
x	math::float4x4 const implicit
y	math::float4x4 const implicit

Compares x and y per component. Returns false if at least one component does not match.

operator !=(x: float4x4 const implicit; y: float4x4 const implicit)

!= returns bool

argument	argument type
x	math::float4x4 const implicit
y	math::float4x4 const implicit

Compares x and y per component. Returns true if at least one component does not match.

operator *(x: float3x4 const implicit; y: float3x4 const implicit)

• returns math::float3x4

argument	argument type
x	math::float3x4 const implicit
y	math::float3x4 const implicit

Multiplies x by y.

operator *(x: float3x4 const implicit; y: float3 const)

• returns float3

argument	argument type
x	math::float3x4 const implicit
y	float3 const

Multiplies x by y.

operator *(x: float4x4 const implicit; y: float4 const)

• returns float4

argument	argument type
x	math::float4x4 const implicit
y	float4 const

Multiplies x by y.

operator ==(x: float3x4 const implicit; y: float3x4 const implicit)

== returns bool

argument	argument type
x	math::float3x4 const implicit
y	math::float3x4 const implicit

Compares x and y per component. Returns false if at least one component does not match.

operator !=(x: float3x4 const implicit; y: float3x4 const implicit)

!= returns bool

argument	argument type
x	math::float3x4 const implicit
y	math::float3x4 const implicit

Compares x and y per component. Returns true if at least one component does not match.

operator *(x: float3x3 const implicit; y: float3x3 const implicit)

• returns math::float3x3

argument	argument type
x	math::float3x3 const implicit
y	math::float3x3 const implicit

Multiplies x by y.

operator *(x: float3x3 const implicit; y: float3 const)

• returns float3

argument	argument type
x	math::float3x3 const implicit
y	float3 const

Multiplies x by y.

operator ==(x: float3x3 const implicit; y: float3x3 const implicit)

== returns bool

argument	argument type
x	math::float3x3 const implicit
y	math::float3x3 const implicit

Compares x and y per component. Returns false if at least one component does not match.

operator !=(x: float3x3 const implicit; y: float3x3 const implicit)

!= returns bool

argument	argument type
x	math::float3x3 const implicit
y	math::float3x3 const implicit

Compares x and y per component. Returns true if at least one component does not match.

3.11. Matrix initializers

• float3x3 () : math::float3x3

• float3x4 () : math::float3x4

• float4x4 () : math::float4x4

• float4x4 (arg0:math::float3x4 const implicit) : math::float4x4

• identity4x4 () : math::float4x4

• float3x4 (arg0:math::float4x4 const implicit) : math::float3x4

• identity3x4 () : math::float3x4

• float3x3 (arg0:math::float4x4 const implicit) : math::float3x3

• float3x3 (arg0:math::float3x4 const implicit) : math::float3x3

• identity3x3 () : math::float3x3

float3x3()

float3x3 returns math::float3x3

Returns empty matrix, where each component is 0.

float3x4()

float3x4 returns math::float3x4

Returns empty matrix, where each component is 0.

float4x4()

float4x4 returns math::float4x4

Returns empty matrix, where each component is 0.

float4x4(arg0: float3x4 const implicit)

float4x4 returns math::float4x4

argument	argument type
arg0	math::float3x4 const implicit

Returns empty matrix, where each component is 0.

identity4x4()

identity4x4 returns math::float4x4

Returns identity matrix, where diagonal is 1 and every other component is 0.

float3x4(arg0: float4x4 const implicit)

float3x4 returns math::float3x4

argument	argument type
arg0	math::float4x4 const implicit

Returns empty matrix, where each component is 0.

identity3x4()

identity3x4 returns math::float3x4

Returns identity matrix, where diagonal is 1 and every other component is 0.

float3x3(arg0: float4x4 const implicit)

float3x3 returns math::float3x3

argument	argument type
arg0	math::float4x4 const implicit

Returns empty matrix, where each component is 0.

float3x3(arg0: float3x4 const implicit)

float3x3 returns math::float3x3

argument	argument type
arg0	math::float3x4 const implicit

Returns empty matrix, where each component is 0.

identity3x3()

identity3x3 returns math::float3x3

Returns identity matrix, where diagonal is 1 and every other component is 0.

3.12. Matrix manipulation

• identity (x:math::float4x4 implicit) : void

• translation (xyz:float3 const) : math::float4x4

• transpose (x:math::float4x4 const implicit) : math::float4x4

• persp_forward (wk:float const;hk:float const;zn:float const;zf:float const) : math::float4x4

• persp_reverse (wk:float const;hk:float const;zn:float const;zf:float const) : math::float4x4

• look_at (eye:float3 const;at:float3 const;up:float3 const) : math::float4x4

• compose (pos:float3 const;rot:float4 const;scale:float3 const) : math::float4x4

• decompose (mat:math::float4x4 const implicit;pos:float3& implicit;rot:float4& implicit;scale:float3& implicit) : void

• identity (x:math::float3x4 implicit) : void

• inverse (x:math::float3x4 const implicit) : math::float3x4

• inverse (m:math::float4x4 const implicit) : math::float4x4

• orthonormal_inverse (m:math::float3x3 const implicit) : math::float3x3

• orthonormal_inverse (m:math::float3x4 const implicit) : math::float3x4

• rotate (x:math::float3x4 const implicit;y:float3 const) : float3

• identity (x:math::float3x3 implicit) : void

identity(x: float4x4 implicit)

argument	argument type
x	math::float4x4 implicit

Returns identity matrix, where diagonal is 1 and every other component is 0.

translation(xyz: float3 const)

translation returns math::float4x4

argument	argument type
xyz	float3 const

produces a translation by xyz

1	0	0	0
0	1	0	0
0	0	1	0
x	y	z	1

transpose(x: float4x4 const implicit)

transpose returns math::float4x4

argument	argument type
x	math::float4x4 const implicit

Transposes the specified input matrix x.

persp_forward(wk: float const; hk: float const; zn: float const; zf: float const)

persp_forward returns math::float4x4

argument	argument type
wk	float const
hk	float const
zn	float const
zf	float const

Perspective matrix, zn - 0, zf - 1

persp_reverse(wk: float const; hk: float const; zn: float const; zf: float const)

persp_reverse returns math::float4x4

argument	argument type
wk	float const
hk	float const
zn	float const
zf	float const

Perspective matrix, zn - 1, zf - 0

look_at(eye: float3 const; at: float3 const; up: float3 const)

look_at returns math::float4x4

argument	argument type
eye	float3 const
at	float3 const
up	float3 const

Look-at matrix with the origin at eye, looking at at, with up as up direction.

compose(pos: float3 const; rot: float4 const; scale: float3 const)

compose returns math::float4x4

argument	argument type
pos	float3 const
rot	float4 const
scale	float3 const

Compose transformation out of translation, rotation and scale.

decompose(mat: float4x4 const implicit; pos: float3& implicit; rot: float4& implicit; scale: float3& implicit)

argument	argument type
mat	math::float4x4 const implicit
pos	float3& implicit
rot	float4& implicit
scale	float3& implicit

Decompose transformation into translation, rotation and scale.

identity(x: float3x4 implicit)

argument	argument type
x	math::float3x4 implicit

Returns identity matrix, where diagonal is 1 and every other component is 0.

inverse(x: float3x4 const implicit)

inverse returns math::float3x4

argument	argument type
x	math::float3x4 const implicit

Returns the inverse of the matrix x.

inverse(m: float4x4 const implicit)

inverse returns math::float4x4

argument	argument type
m	math::float4x4 const implicit

Returns the inverse of the matrix x.

orthonormal_inverse(m: float3x3 const implicit)

orthonormal_inverse returns math::float3x3

argument	argument type
m	math::float3x3 const implicit

Fast inverse for the orthonormal matrix.

orthonormal_inverse(m: float3x4 const implicit)

orthonormal_inverse returns math::float3x4

argument	argument type
m	math::float3x4 const implicit

Fast inverse for the orthonormal matrix.

rotate(x: float3x4 const implicit; y: float3 const)

rotate returns float3

argument	argument type
x	math::float3x4 const implicit
y	float3 const

Rotates vector y by 3x4 matrix x. Only 3x3 portion of x is multiplied by y.

identity(x: float3x3 implicit)

argument	argument type
x	math::float3x3 implicit

Returns identity matrix, where diagonal is 1 and every other component is 0.

3.13. Quaternion operations

• quat_from_unit_arc (v0:float3 const;v1:float3 const) : float4

• quat_from_unit_vec_ang (v:float3 const;ang:float const) : float4

• quat_mul (q1:float4 const;q2:float4 const) : float4

• quat_mul_vec (q:float4 const;v:float3 const) : float3

• quat_conjugate (q:float4 const) : float4

quat_from_unit_arc(v0: float3 const; v1: float3 const)

quat_from_unit_arc returns float4

argument	argument type
v0	float3 const
v1	float3 const

Quaternion which represents rotation from v0 to v1, both arguments need to be normalized

quat_from_unit_vec_ang(v: float3 const; ang: float const)

quat_from_unit_vec_ang returns float4

argument	argument type
v	float3 const
ang	float const

Quaternion which represents rotation for ang radians around vector v. v needs to be normalized

quat_mul(q1: float4 const; q2: float4 const)

quat_mul returns float4

argument	argument type
q1	float4 const
q2	float4 const

Quaternion which is multiplication of q1 and q2

quat_mul_vec(q: float4 const; v: float3 const)

quat_mul_vec returns float3

argument	argument type
q	float4 const
v	float3 const

Transform vector v by quaternion q

quat_conjugate(q: float4 const)

quat_conjugate returns float4

argument	argument type
q	float4 const

Quaternion which is conjugate of q

3.14. Packing and unpacking

• pack_float_to_byte (x:float4 const) : uint

• unpack_byte_to_float (x:uint const) : float4

pack_float_to_byte(x: float4 const)

pack_float_to_byte returns uint

argument	argument type
x	float4 const

Packs float4 vector v to byte4 vector and returns it as uint. Each component is clamped to [0..255] range.

unpack_byte_to_float(x: uint const)

unpack_byte_to_float returns float4

argument	argument type
x	uint const

Unpacks byte4 vector to float4 vector.

3.15. Uncategorized

operator [](m: float4x4 implicit ==const; i: int const)

[] returns float4&

argument	argument type
m	math::float4x4 implicit!
i	int const

Returns the component of the matrix m at the specified row.

operator [](m: float4x4 const implicit ==const; i: int const)

[] returns float4 const&

argument	argument type
m	math::float4x4 const implicit!
i	int const

Returns the component of the matrix m at the specified row.

operator [](m: float4x4 implicit ==const; i: uint const)

[] returns float4&

argument	argument type
m	math::float4x4 implicit!
i	uint const

Returns the component of the matrix m at the specified row.

operator [](m: float4x4 const implicit ==const; i: uint const)

[] returns float4 const&

argument	argument type
m	math::float4x4 const implicit!
i	uint const

Returns the component of the matrix m at the specified row.

determinant(x: float4x4 const implicit)

determinant returns float

argument	argument type
x	math::float4x4 const implicit

Returns the determinant of the matrix m.

determinant(x: float3x4 const implicit)

determinant returns float

argument	argument type
x	math::float3x4 const implicit

Returns the determinant of the matrix m.

operator [](m: float3x4 implicit ==const; i: int const)

[] returns float3&

argument	argument type
m	math::float3x4 implicit!
i	int const

Returns the component of the matrix m at the specified row.

operator [](m: float3x4 const implicit ==const; i: int const)

[] returns float3 const&

argument	argument type
m	math::float3x4 const implicit!
i	int const

Returns the component of the matrix m at the specified row.

operator [](m: float3x4 implicit ==const; i: uint const)

[] returns float3&

argument	argument type
m	math::float3x4 implicit!
i	uint const

Returns the component of the matrix m at the specified row.

operator [](m: float3x4 const implicit ==const; i: uint const)

[] returns float3 const&

argument	argument type
m	math::float3x4 const implicit!
i	uint const

Returns the component of the matrix m at the specified row.

quat_from_euler(angles: float3 const)

quat_from_euler returns float4

argument	argument type
angles	float3 const

Construct quaternion from euler angles.

quat_from_euler(x: float const; y: float const; z: float const)

quat_from_euler returns float4

argument	argument type
x	float const
y	float const
z	float const

Construct quaternion from euler angles.

euler_from_quat(angles: float4 const)

euler_from_quat returns float3

argument	argument type
angles	float4 const

Construct euler angles from quaternion.

quat(m: float3x3 const implicit)

quat returns float4

argument	argument type
m	math::float3x3 const implicit

Construct quaternion from matrix.

quat(m: float3x4 const implicit)

quat returns float4

argument	argument type
m	math::float3x4 const implicit

Construct quaternion from matrix.

quat(m: float4x4 const implicit)

quat returns float4

argument	argument type
m	math::float4x4 const implicit

Construct quaternion from matrix.

quat_slerp(t: float const; a: float4 const; b: float4 const)

quat_slerp returns float4

argument	argument type
t	float const
a	float4 const
b	float4 const

Spherical linear interpolation between a and b by t.

determinant(x: float3x3 const implicit)

determinant returns float

argument	argument type
x	math::float3x3 const implicit

Returns the determinant of the matrix m.

operator [](m: float3x3 implicit ==const; i: int const)

[] returns float3&

argument	argument type
m	math::float3x3 implicit!
i	int const

Returns the component of the matrix m at the specified row.

operator [](m: float3x3 const implicit ==const; i: int const)

[] returns float3 const&

argument	argument type
m	math::float3x3 const implicit!
i	int const

Returns the component of the matrix m at the specified row.

operator [](m: float3x3 implicit ==const; i: uint const)

[] returns float3&

argument	argument type
m	math::float3x3 implicit!
i	uint const

Returns the component of the matrix m at the specified row.

operator [](m: float3x3 const implicit ==const; i: uint const)

[] returns float3 const&

argument	argument type
m	math::float3x3 const implicit!
i	uint const

Returns the component of the matrix m at the specified row.