Functions

Functy uses the Symbolic library to allow functions to be interpreted algebraically. This means that functions are kept in the symbolic algebraic form throughout the process, right up until the function needs to be displayed on screen.

This provides a number of benefits, foremost of which is accuracy. For example, it means that the lighting normals for the function surfaces can be calculated at run-time by the shader pipeline based on the surface derivatives. This differs from normal rendering, which uses only an approximation based on the triangle mesh of a surface.

The functions that symbolic recognises are listed below.

Algebra

Unary functions

Name	Symbol	Example
Negative	-	(-x)
Cosec	cosec	cosec(x)
Hyperbolic sin	sinh	sinh(x)
Hyperbolic cos	cosh	cosh(x)
Hyperbolic tan	tanh	tanh(x)
Cosine	cos	cos(x)
Sin	sin	sin(x)
Tan	tan	tan(x)
Sec	sec	sec(x)
Cotangent	cot	cot(x)
Arc sin	asin	asin(x)
Arc cos	acos	acos(x)
Arc tan	atan	atan(x)
Natural log	ln	ln(x)
Exponentiation	exp	exp(x)
Absolute value	abs	abs(x)

Binary functions

Name	Symbol	Example
Power	**	x**y
Addition	+	(x + y)
Subtraction	-	(x - y)
Multiplication	*	(x * y)
Integer divide	DIV	(x DIV y)
Division	/	(x / y)
Remainder	mod	(x mod y)

Comparison

Name	Symbol	Example
Equality	=	(x = y)
Inequality	!=	(x != y)
Less than	<	(x < y)
Less than of equal to	<=	(x <= y)
Greater than	>	(x > y)
Greater than or equal to	>=	(x >= y)

Logic

Unary functions

Name	Symbol	Example
Not	~	(~x)

Binary functions

Name	Symbol	Example
And	^	(x ^ y)
Or	v	(x v y)
Implies	->	(x -> y)

Bitwise

Binary functions

Name	Symbol	Example
Bitwise or	OR	(x OR y)
Bitwise and	AND	(x AND y)
Mask/bitclear	BIC	(x BIC y)
Exclusive or	EOR	(x EOR y)