E.1 Mathematical Functions
Table E-1 lists the mathematical functions that the Cg Standard Library provides. The table includes functions useful for trigonometry, exponentiation, rounding, and vector and matrix manipulations, among others. All functions work on scalars and vectors of all sizes, except where noted.
Table E-1. Mathematical Functions
|
Function |
Description |
|---|---|
|
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:
|
|
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:
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 ) |
xy . |
|
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. |
E.2 Geometric Functions
Table E-2 presents the geometric functions that are provided in the Cg Standard Library.
Table E-2. Geometric Functions
|
Function |
Description |
|---|---|
|
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. |
E.3 Texture Map Functions
Table E-3 presents the texture map functions that are provided in the Cg Standard Library. Currently, these texture functions are fully supported by the ps_2_0 , ps_2_x , arbfp1 , and fp30 profiles (though only OpenGL profiles support the samplerRECT functions). They will also be supported by all future advanced fragment profiles with texture-mapping capabilities. All of the functions listed in Table E-3 return a float4 value.
Table E-3. Texture Map Functions
|
Function |
Description |
|---|---|
|
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) |
Because of the limited pixel programmability of older hardware, the ps_1_1 , ps_1_2 , ps_1_3 , and fp20 profiles have restrictions on the use of texture-mapping functions. See the documentation for these profiles for more information.
In the table, the name of the second argument to each function indicates how its values are used when performing the texture lookup:
- s indicates a one-, two-, or three-component texture coordinate.
- z indicates a depth comparison value for shadow map lookups.
- q indicates a perspective value, and is used to divide the texture coordinate ( s ) before the texture lookup is performed.
When you use the texture functions that allow specifying a depth comparison value, the associated texture unit must be configured for depth-compare texturing. Otherwise, no depth comparison will actually be performed.
E.4 Derivative Functions
Table E-4 presents the derivative functions that are supported by the Cg Standard Library. Vertex profiles do not support these functions.
Table E-4. Derivative Functions
|
Function |
Description |
|---|---|
|
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 |
E.5 Debugging Function
Table E-5 presents the debugging function that is supported by the Cg Standard Library. Vertex profiles are not required to support this function.
Table E-5. Debugging Function
|
Function |
Description |
|---|---|
|
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. |
The intent of the debug function is to allow a program to be compiled twice—once with the DEBUG option and once without. By executing both programs, it is possible to obtain one frame buffer containing the final output of the program and another frame buffer containing an intermediate value to be examined for debugging purposes.