MATH

This is the addition function.  The result is A + B + ....
A and B may be scalar, vectors, or colors.
The result will be a scalar if both A and B are scalars.
The result will be a vector if either A or B is a vector.
The result will be a color if either A or B is a color.
A type mis-match will result from the addition of vectors and colors.

This is the subtraction function.  The result is A - B.
A and B can be scalars, vectors, or colors.
The result will be a scalar if both A and B are scalars.
The result will be a vector if either A and B are vectors.
The result will be a color if either A and B are colors.
A type mis-match will result from the subtraction of 
vectors and colors.

This is the multiplication function.  The result is A * B.
A and B can be scalars, vectors, or colors.
The result will be a scalar if both A and B are scalars.
The result will be a vector if either A or B is a vector.
The result will be a color if either A or B is a color.
A type mis-match will result from the multiplication of points and colors.

This is the division function.  The result is the quotient of A / B.
A and B may be scalar, vector, or colors.
The result will be a scalar if both A and B are scalars.
The result will be a vector if either A and B are vectors.
The result will be a color if either A and B are colors.
A type mis-match will result from the division of colors and vectors.

This function returns the absolute value of A: |A|

This function returns either +1 or -1 based on the sign of the input.

This function returns -A, the negative of input A.

This function returns the remainder of A divided by B.

This is function returns mod(A*FQ, 1).
This is the percentage of 1, which that frequency of A represents.

The result is (A+1)/2.  
This shifts the range of A from [-1,1] to [0,1].
Inputs should lie in the range [-1,1].

This function can increase or decrease the contrast of A.
If SHF is negative and GAIN is > 1 this will increase the contrast.
If SHF is positive and GAIN is < 1 the contrast will be decreased.
The result will be the same data type as A.

This function returns the inverse of A: 1/A.

Result is 1-A.  This reverses the direction of A.
Inputs should lie in the range [0,1].  
Vectors should be normalized.

This is the average function.
The result is the average value of all the inputs.
The inputs may be scalars, vectors, or colors, 
but all inputs must be of the same type.

Returns the factorial of A.
OUT = 1 * 2 * 3 .. A

The result is a random scalar in the range [0,1].

Result is 1-A.  This is the complement of A. 
A may be a float, point or color. The result will be the same data type.
A should lie in the range [0,1].  Vectors should be normalized.

This returns the difference of A and B.  
The result is A - AB.
A and B may be floats, colors or points, but they must be the same type.

The result is A * B.  This is the intersection of A and B.
A and B can be floats, points or colors, but they must be
the same data type.  Output will be the same data type.

The result is A + B - (A * B).  This is the union of A and B.
A and B may be floats, points or colors, but they must be the 
same data type.  Output will be the same data type.

This function returns A cubed.

Result of this function is A raised to the power of B;
Example: pow(2,3.0) = 2*2*2 = 8;
Example: pow(4,0.5) = sqrt(4) = 2;

This function returns the square root of A.

This function returns A squared.

This function returns the inverse of the square root of A.

This is the constant e ~ 2.718281828459
e denotes the unquie positive real number such that log(e) = 1.

The result is e raised to the power of A.

The result is e raised to the power of A minus 1.0.

This function returns X raised to 1/G.

The result is the natural logarithm of A;

The result is the natural logarithm to base 10 of A;

The result is the natural logarithm of (1+A);

This is the constant PI ~ 3.1415927

This is the constant 2*PI ~ 6.2831853

This is the constant PI/2 ~ 1.5707963

This function returns a float between [-1,1], the sine of angle A.

This function returns a scalar between [-PI/2,PI/2], the arcsine of A.
Arcsine is the inverse of the sine function where the
asin(x) = y if and only if sin(y) = x.

This function returns a scalar between [-1,1], the cosine of angle A.

This function returns a scalar between [0,PI], the arccosine of A.
Arccosine is the inverse of the cosine function where the
acos(x) = y if and only if cos(y) = x.

This function returns a scalar which runs to infinity as
the angle A approachs PI/2, the tangent of angle A.

This fucntion returns a scalar between [-PI/2,PI/2], 
the arctangent of A.  Arctangent is the inverse of the tangent 
function where the atan(x) = y if and only if tan(y) = x.

This function returns a scalar between [-PI,PI].
The sign of the inputs determines which quadrant the result will be.
Arctangent is the inverse of the tangent function.
atan2(b,a) = y/x if and only if tan(y/x) = b/a.

This function returns the radius of a circle 
inscribed in the square defined by A and B.
For best results A and B should be perpendicular.
Such as u and v or the lengths of two perpendicular vectors.

This function converts degrees to radians.
It returns the input scalar, A in radians.

This function converts radians to degrees.
It returns the input scalar, A in degrees.

This function returns the minimum of the input values.
The value returned will be of the same data type as the inputs.

This function returns the maximum of the input values.
The value returned will be of the same data type as the inputs.

This function returns the smallest integer greater than or equal to A.

This function returns the largest integer less than or equal to A.

This function returns the closest integer A.

This function clamps A to the range [MIN, MAX].
Returns MIN if A < MIN or MAX if A > MAX otherwise it returns A.
The data type returned will be the same type as the inputs.
All inputs must be of the same type.

This returns the vector describing the direction of the motion.
It is used in calculating motion blur. 
If there is no motion a null vector is returned.

This vector represents the rate of change in the surface 
with respect to u and v.  A vector is returned only for free-form 
surface objects, for polygonal objects the vector is null.