how are the math node operations in cycles calculated? How does the math node do calculations with a specific operation:



the usual operations of add,subtract, multiply and divide are quite understandable and are(empirically) very similar to some of the operations in MixRGB node. But, how do the operations such as Sine, Power, Logarithm, Minimum, Maximum, Modulo, Round, etc,.. interpret with the values. How can we visualize this in realtime?
Here is a list of the mathematical equivalents of each operation.


Add: Out = Value1 + Value2.
Subtract: Out = Value1 - Value2.
Multiply: Out = Value1 * Value2.
Divide: Out = Value1 / Value2.
Sine: Out = Sin(Value1).†
Cosine: Out = Cos(Value1).†
Tangent: Out = Tan(Value1).†
Arcsin: Out = Sin⁻¹(Value1).†
Arccosine: Out = Cos⁻¹(Value1).†
Arctangent: Out = Tan⁻¹(Value1).†
Power: Out = Value1 ^ Value2.
Logarithm: Out = log(Value2, Value1).††
Minimum: Out = Smaller Value of (Value1, Value2).
Maximum: Out = larger value of (Value1, Value2).
Round: Out = Value1 rounded to nearest integer.
Less Than: Out = 1 if Value1 &lt; Value2, else 0'
Greater Than: Out = 1 if Value1 &gt; Value2, else 0'
Modulo: Out = Value1 (mod Value2).‡


Note that some operations use only the first input, in such cases the second input is ignored completely.

†. All trigonometric functions use radians.
††. log(x, y) = the logarithm of x to the base y.
‡. x mod y = the remainder when x is divided by y.