MATH

This is the addition function.
The result is A + B.
A and B can be floats, points, normals, vectors or colors.
The result will be a float if both A and B are floats.
The result will be a point if either A or B is a point.
The result will be a color if either A or B is a color.
A type mis-match will result from the addition of points and colors.

This is the subtraction function.
The result is A - B.
A and B can be floats, points, normals, vectors or colors.
The result will be a float if both A and B are floats.
The result will be a point if both A and B are points or B is a float.
The result will be a color if both A and B are colors or B is a float.
A type mis-match will result from the subtraction of points or colors
from floats or mixing colors and points.

This is the multiplication function.  The result is A * B.
A and B can be floats, points, normals, vectors or colors.
The result will be a float if both A and B are floats.
The result will be a point if either A or B is a point.
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 can be floats, points, normals, vectors or colors.
The result will be a float if both A and B are floats.
The result will be a point if both A and B are points or B is a float.
The result will be a color if both A and B are colors or B is a float.
A type mis-match will result from the division of floats by anything
but another float or mixing colors and points.

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

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

Result is -A, the negative of input A.
The result will be the same data type.
A can be a float, point, normal, vector or color.

This is a floating point modulus function
The result is a float, 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].  Vectors should be normalized.

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.
The result will be the same data type.

This is the average function.
The result is the average value of all the inputs.
The inputs can be floats, points, normals, vectors or colors
but all inputs must be of the same data type.

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

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

Result is 1-A.  This is the complement of A. 
A may be a float, point, normal, vector 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, points, normals or vectors,
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, normals, vectors 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 can be floats, points, normals, vectors 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 A squared.

This function returns the square root of A.

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.

Result is e raised to the power of A.

Input X is raised to 1/G.

The result is the natural logarithm of 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 float 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 float between [-1,1], the cosine of angle A.

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

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

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

This function converts degrees to radians.
It returns a float, A in radians.

This function converts radians to degrees.
It returns a float, A in degrees.

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

This function returns the maximum of all 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].
The data type returned will be the same type as the inputs.

This function computes the derivative of A with respect to u.
The result will be the same data type as A.
It will be 0 if A does not vary.

This function computes the derivative of A with respect to v.
The result will be the same data type as A.
It will be 0 if A does not vary.

This function computes the derivative of A with respect to B.
Deriv(A,B) = Du(A)/Du(B) + Dv(A)/Dv(B).
The result will be the same data type as A and B.
The results are only useful if both A and B are varying expressions.