abs( x )

Absolute value of x .

acos( x )

Arccosine of x in range [0, p], x in [–1, 1].

all( x )

Returns true if every component of x is not equal to 0.

Returns false otherwise.

any( x )

Returns true if any component of x is not equal to 0.

Returns false otherwise.

asin( x )

Arcsine of x in range [–p/2, p/2]; x should be in [–1, 1].

atan( x )

Arctangent of x in range [–p/2, p/2].

atan2( y , x )

Arctangent of y / x in range [–p, p].

ceil( x )

Smallest integer not less than x .

clamp( x , a , b )

x clamped to the range [ a , b ] as follows:

• Returns a if x is less than a .
• Returns b if x is greater than b .
• Returns x otherwise.

cos( x )

Cosine of x .

cosh( x )

Hyperbolic cosine of x .

cross( A , B )

Cross product of vectors A and B ;

A and B must be three-component vectors.

degrees( x )

Radian-to-degree conversion.

determinant( M )

Determinant of matrix M .

dot( A , B )

Dot product of vectors A and B .

exp( x )

Exponential function e ^x .

exp2( x )

Exponential function 2 ^x .

floor( x )

Largest integer not greater than x .

fmod( x , y )

Remainder of x / y , with the same sign as x .

If y is 0, the result is implementation-defined.

frac( x )

Fractional part of x .

frexp( x , out exp )

Splits x into a normalized fraction in the interval [½, 1), which is returned, and a power of 2, which is stored in exp .

If x is 0, both parts of the result are 0.

isfinite( x )

Returns true if x is finite.

isinf( x )

Returns true if x is infinite.

isnan( x )

Returns true if x is NaN (Not a Number).

ldexp( x , n )

x x 2 ⁿ .

lerp( a , b , f )

Linear interpolation:

(1 – f )* a + b * f

where a and b are matching vector or scalar types. f can be either a scalar or a vector of the same type as a and b .

lit( NdotL , NdotH , m )

Computes lighting coefficients for ambient, diffuse, and specular light contributions.

Expects the NdotL parameter to contain N • L and the NdotH parameter to contain N • H .

Returns a four-component vector as follows:

• The x component of the result vector contains the ambient coefficient, which is always 1.0.
• The y component contains the diffuse coefficient, which is 0 if ( N • L ) < 0; otherwise ( N • L ).
• The z component contains the specular coefficient, which is 0 if either ( N • L ) < 0 or ( N • H ) < 0; ( N • H ) ^m otherwise.
• The w component is 1.0.

There is no vectorized version of this function.

log( x )

Natural logarithm ln( x ) ; x must be greater than 0.

log2( x )

Base 2 logarithm of x ; x must be greater than 0.

log10( x )

Base 10 logarithm of x ; x must be greater than 0.

max( a , b )

Maximum of a and b .

min( a , b )

Minimum of a and b .

modf( x , out ip )

Splits x into integral and fractional parts, each with the same sign as x .

Stores the integral part in ip and returns the fractional part.

mul( M , N )

Matrix product of matrix M and matrix N , as shown below:

If M has size A x B , and N has size B x C , returns a matrix of size A x C .

mul( M , v )

Product of matrix M and column vector v , as shown below:

If M is an A x B matrix and v is a B x 1 vector, returns an A x 1 vector.

mul( v , M )

Product of row vector v and matrix M , as shown below:

If v is a 1 x A vector and M is an A x B matrix, returns a 1 x B vector.

noise( x )

Either a one-, two-, or three-dimensional noise function, depending on the type of its argument. The returned value is between 0 and 1, and is always the same for a given input value.

pow( x , y )

x^y .

radians( x )

Degree-to-radian conversion.

round( x )

Closest integer to x .

rsqrt( x )

Reciprocal square root of x ; x must be greater than 0.

saturate( x )

Clamps x to the [0, 1] range.

sign( x )

1 if x > 0; –1 if x < 0; 0 otherwise.

sin( x )

Sine of x .

sincos(float x , out s , out c )

s is set to the sine of x , and c is set to the cosine of x .

If both sin( x ) and cos( x ) are needed, this function is more efficient than calculating each individually.

sinh( x )

Hyperbolic sine of x .

smoothstep( min , max , x )

For values of x between min and max , returns a smoothly varying value that ranges from 0 at x = min to 1 at x = max .

x is clamped to the range [ min , max ] and then the interpolation formula is evaluated:

–2*(( x – min )/( max – min ))³ +

3*(( x – min )/( max – min ))²

step( a , x )

0 if x < a ;

1 if x >= a .

sqrt( x )

Square root of x ;

x must be greater than 0.

tan( x )

Tangent of x .

tanh( x )

Hyperbolic tangent of x .

transpose( M )

Matrix transpose of matrix M .

If M is an A x B matrix, the transpose of M is a B x A matrix whose first column is the first row of M , whose second column is the second row of M , whose third column is the third row of M , and so on.

distance( pt1 , pt2 )

Euclidean distance between points pt1 and pt2 .

faceforward( N , I , Ng )

N if dot( Ng , I ) < 0; - N otherwise.

length( v )

Euclidean length of a vector.

normalize( v )

Returns a vector of length 1 that points in the same direction as vector v .

reflect( I , N )

Computes reflection vector from entering ray direction I and surface normal N .

Valid only for three-component vectors.

refract( I , N , eta )

Given entering ray direction I , surface normal N , and relative index of refraction eta , computes refraction vector.

If the angle between I and N is too large for a given eta , returns (0, 0, 0).

Valid only for three-component vectors.

tex1D(sampler1D tex , float s )

1D nonprojective texture query

tex1D(sampler1D tex , float s , float dsdx , float dsdy )

1D nonprojective texture query with derivatives

tex1D(sampler1D tex , float2 sz )

1D nonprojective depth compare texture query

tex1D(sampler1D tex , float2 sz , float dsdx , float dsdy )

1D nonprojective depth compare texture query with derivatives

tex1Dproj(sampler1D tex , float2 sq )

1D projective texture query

tex1Dproj(sampler1D tex , float3 szq )

1D projective depth compare texture query

tex2D(sampler2D tex , float2 s )

2D nonprojective texture query

tex2D(sampler2D tex , float2 s , float2 dsdx , float2 dsdy )

2D nonprojective texture query with derivatives

tex2D(sampler2D tex , float3 sz )

2D nonprojective depth compare texture query

tex2D(sampler2D tex , float3 sz , float2 dsdx , float2 dsdy )

2D nonprojective depth compare texture query with derivatives

tex2Dproj(sampler2D tex , float3 sq )

2D projective texture query

tex2Dproj(sampler2D tex , float4 szq )

2D projective depth compare texture query

texRECT(samplerRECT tex , float2 s )

2D nonprojective texture rectangle texture query (OpenGL only)

texRECT(samplerRECT tex , float2 s , float2 dsdx , float2 dsdy )

2D nonprojective texture rectangle texture query with derivatives (OpenGL only)

texRECT(samplerRECT tex , float3 sz )

2D nonprojective texture rectangle depth compare texture query (OpenGL only)

texRECT(samplerRECT tex , float3 sz , float2 dsdx , float2 dsdy )

2D nonprojective depth compare texture query with derivatives (OpenGL only)

texRECTproj(samplerRECT tex , float3 sq )

2D texture rectangle projective texture query (OpenGL only)

texRECTproj(samplerRECT tex , float3 szq )

2D texture rectangle projective depth compare texture query (OpenGL only)

tex3D(sampler3D tex , float3 s )

3D nonprojective texture query

tex3D(sampler3D tex , float3 s , float3 dsdx , float3 dsdy )

3D nonprojective texture query with derivatives

tex3Dproj(sampler3D tex , float4 sq )

3D projective texture query

texCUBE(samplerCUBE tex , float3 s )

Cube map nonprojective texture query

texCUBE(samplerCUBE tex , float3 s , float3 dsdx , float3 dsdy )

Cube map nonprojective texture query with derivatives

texCUBEproj(samplerCUBE tex , float4 sq )

Cube map projective texture query (ignores q)

ddx( a )

Approximate partial derivative of a with respect to screen-space x coordinate

ddy( a )

Approximate partial derivative of a with respect to screen-space y coordinate

void debug(float4 x )

If the compiler's DEBUG option is enabled, calling this function causes the value x to be copied to the COLOR output of the program, and execution of the program is terminated.

If the compiler's DEBUG option is not enabled, this function does nothing.