If you are re-using the same value multiple times, or if you wish to organise your equations, defining your own variables can be very useful (and sometimes even more efficient!).

Variable Syntax:

• The variable name appears on the left, followed by an equals sign (=), your expression, and finally a semi-colon (;).
• Example:

• The semi-colon is very important. It must be there to separate the declaration of each variable.

Operator     Description

    +              Addition

    -               Subtraction

    *               Multiplication

    /               Division

   %              Modulo: A%B yields the remainder of A divided by B

    ^              Power: A^B raises A to the power of B

In the absence of any operator, multiplication is assumed. Thus, 5 a will be interpreted as 5 * a. For other operators, see also the Conditions sections for boolean operations, and the Bitwise Operators section below.

Maths operations support a number of bitwise operators. These can be useful for setting flags in headers, but these are not boolean operations. Some care must be taken:

• Only the integer part of a value is considered
• Operations consider which bits are set in that integer value

As a consequence, these differ from conditional operations (if, && etc) which treat any non-zero value as one (true)

a xor b    Exclusive OR: sets bits in the output only where they differ in the inputs, according to the following table.

a & b    Bitwise AND: performs a logical AND on each bit in the inputs, and sets the corresponding output bit to the result.

a | b    Bitwise OR: performs a logical OR on each bit in the inputs, and sets the corresponding output bit to the result.

~a    1's complement: performs a bitwise NOT, inverting all bits in the value. Note that the integer representation is signed, so this is equivalent to (-a - 1).

* Simplified to show an 8 bit representation

You can build complex expressions that result in different behaviour in different situations. Conditional statements take the form:

if  ( condition ,  true statement ,  false statement )

where the true statement is used if the condition is true, or vice-versa. Note that those statements can themselves be arbitrary expressions, such as another conditional statement.

Standard comparison operators may be used, which may be combined with standard boolean operators. You can preface any boolean expression with a ! to negate it:

Conditional Examples:

If both a and b are less than zero, use the value of c; otherwise use the sum of a and b

A more-complicated way of writing the same thing, using one conditional inside another.

If either a or b are NaN (invalid), use 1500; otherwise use the sum of a and b

The most natural-seeming way to merge two things together would be to "add" them, as in a + b + c. But this doesn't work, for two reasons.

First, in places where they overlap, that would give you the arithmetic sum of the values at that location -- which is probably not what you intend.

Second, missing values are generally represented by the value NaN (not-a-number). NaN plus any other value remains NaN, so this would have the effect of producing output only at locations where all inputs are defined. This is also probably not what you intend.

To simplify this, Insight provides several functions to make combining easy:

• merge(a, b, c, ...) - combines any number of items, in order of precedence. i.e. where they overlap, the first available value in the list will be used.
• min(a, b, c, ...) - combines any number of items, using the smallest available value
• max(a, b, c, ...) - combines any number of items, using the largest available value
• sum(a, b, c, ...) - arithmetic sum of any number of items, ignoring those that aren't defined at a location
• avg(a, b, c, ...) - arithmetic mean of any number of items, ignoring those that aren't defined at a location
• random(max) - generate a random number between 0 and max (inclusive)
• random(min, max) - generate a random number between min and max (inclusive)
• lerp(v0, v1, t) - linearly interpolates between two inputs (v0, v1) for a parameter (t) in the closed unit interval [0, 1]. Parameter t is clamped between 0 and 1.

You can use comments to explain your formulas to other users.

Comment Syntax:

• Comments are started by a hash #, and extend to the end of that line. Anything written within a comment will be ignored in the formula.
• Example:     
  
  # Comments can appear on their own line.     
  a = v1 * 2;     
  res = a + sin(v1); # Or at the end of other lines.