The following operators, functions, and language features are available in Expressions and the Math Node.
Use this page as a reference when you need to transform a value, constrain a variable, or build a procedural calculation inside the Math node.
Common Operators
| Type |
Available syntax |
| Arithmetic |
+, -, *, /, %, ^ |
| Equality and comparison |
=, ==, <>, !=, <, <=, >, >= |
| Assignment |
:=, +=, -=, *=, /=, %= |
| Logic |
and, nand, nor, not, or, xor, xnor, mand, mor |
Numeric Functions
| Use |
Functions |
| Basic values |
abs, sgn, floor, ceil, round, roundn, trunc, frac |
| Bounds and ranges |
clamp, iclamp, inrange, min, max |
| Aggregation |
avg, sum, mul |
| Powers and roots |
pow, sqrt, root, hypot |
| Logs and exponentials |
exp, expm1, log, log10, log1p, log2, logn |
| Remainders |
mod |
| Probability and error functions |
erf, erfc, ncdf |
| Comparison helpers |
equal, not_equal |
| Value exchange |
swap |
Trigonometry
| Use |
Functions |
| Standard trig |
sin, cos, tan, cot, sec, csc, sinc |
| Inverse trig |
asin, acos, atan, atan2 |
| Hyperbolic trig |
sinh, cosh, tanh |
| Inverse hyperbolic trig |
asinh, acosh, atanh |
| Unit conversion |
deg2rad, rad2deg, deg2grad, grad2deg |
Flow Control
| Feature |
Use it for |
if-then-else |
Branching between values or calculations. |
| Ternary conditional |
Compact conditional expressions. |
switch / case |
Choosing between several possible branches. |
return |
Ending a calculation and returning a value. |
while |
Repeating while a condition remains true. |
for |
Repeating with a counter or bounded iteration. |
repeat until |
Repeating until a condition becomes true. |
break and continue |
Controlling loop execution. |
Variables, Strings, and Composition
| Feature |
Notes |
| Expression local variables |
Store intermediate values inside an expression. |
| User-defined variables |
Use values exposed through Gaea variables. |
| Vectors and strings |
Create and manipulate vector or string values. |
| String operations |
Equality, inequality, logical operations, concatenation, and sub-ranges. |
| Constants and user functions |
Define reusable values and helper functions. |
| Multivariate function composition |
Build functions that depend on multiple inputs. |
| Multiple sequence points |
Use multiple sub-expressions in a single calculation. |
Advanced Facilities
These features are available for more complex Math node and expression work. Use them when a simple value transform is not enough.
| Area |
Facilities |
| Optimization |
Constant folding, strength reduction, operator coupling, special functions, and dead code elimination. |
| Runtime checks |
Vector bounds, string bounds, loop iteration and execution-time bounds, and assert statements. |
| Compile-time checks |
Function parameter type checking, compilation stack overflow checks, evaluation stack overflow checks, and compilation running time checks. |
| Numerical methods |
Numerical integration and differentiation. |
Vector Processing
| Area |
Facilities |
| BLAS-L1 style operations |
axpy, axpby, axpb |
| Boolean checks |
All true, any true, all false, any false |
| Vector manipulation |
assign, copy, reverse, rotate-left, rotate-right, shift-left, shift-right, sort, nth_element, iota |
| Vector analysis |
count, sum, kahan-sum, dot-product, diff, thresholding |
File I/O
The File I/O package includes routines such as open, close, read, write, and getline, with support for binary and text modes.
For typical parameter work, prefer Variables and Expressions before reaching for File I/O or vector-processing features.
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