VXL reference: functions

Grammar. The expression grammar, with every built-in name and declared user-function ids:

expr    := sum
sum     := product (("+" | "-") product)*
product := unary (("*" | "/") unary)*
unary   := "-" unary | power
power   := primary ("^" INT)?
primary := NUMBER UNIT? | NAME | ENUMLIT | call | "(" expr ")"
call    := (FN | USER_ID) "(" args? ")"
FN      := abs min max clamp sqrt cbrt sin cos tan asin acos atan atan2 exp ln gauss hypot if floor ceil round fract mod sign smoothstep lerp lookup
USER_ID := a declared user-function id

Built-in functions. Every call is pure; function names are reserved identifiers (§3.1).

Call	Arguments	Returns	Semantics
`abs(x)`	any numeric `x`	same dimension as `x`	Absolute value.
`min(a, b, …)`	two or more numerics of one dimension	that dimension	Smallest argument.
`max(a, b, …)`	two or more numerics of one dimension	that dimension	Largest argument.
`clamp(x, low, high)`	`x`, `low`, `high` of one dimension	same dimension as `x`	`x` constrained to the interval `[low, high]`.
`sqrt(x)`	unitless number, or an area	unitless number, or a length	Square root; the dimension must have an exact degree-2 root.
`cbrt(x)`	unitless number, or a volume	unitless number, or a length	Cube root; the dimension must have an exact degree-3 root.
`sin(angle)`	angle in degrees	unitless	Sine.
`cos(angle)`	angle in degrees	unitless	Cosine.
`tan(angle)`	angle in degrees	unitless	Tangent.
`asin(x)`	unitless `x`	angle in degrees	Inverse sine.
`acos(x)`	unitless `x`	angle in degrees	Inverse cosine.
`atan(x)`	unitless `x`	angle in degrees	Inverse tangent.
`atan2(y, x)`	`y` and `x` of one dimension	angle in degrees	Four-quadrant angle of the point (x, y).
`exp(x)`	unitless `x`	unitless	Natural exponential e^x.
`ln(x)`	unitless `x`	unitless	Natural logarithm.
`gauss(x, y, cx, cy, sx, sy)`	six unitless numbers; `sx` and `sy` positive	unitless	Gaussian bump `exp(-0.5((x-cx)/sx)^2 - 0.5((y-cy)/sy)^2)`.
`hypot(x, y, [z])`	two or three numbers of one dimension; `z` optional	the argument dimension	Euclidean norm; with three arguments, `hypot(hypot(x, y), z)`.
`if(cond, a, b)`	boolean `cond`; `a` and `b` of one kind	the kind of `a` and `b`	Selects `a` when `cond` is true and `b` when false; a value, never a statement.
`floor(x)`	unitless `x`	unitless	Largest integer not greater than `x`.
`ceil(x)`	unitless `x`	unitless	Smallest integer not less than `x`.
`round(x)`	unitless `x`	unitless	Nearest integer; halfway cases round away from zero.
`fract(x)`	unitless `x`	unitless	`x - floor(x)`, including for negative `x`.
`mod(x, y)`	unitless `x`, `y`; `y` nonzero	unitless	Floored modulo `x - y * floor(x / y)`.
`sign(x)`	unitless `x`	unitless	Returns 0 for zero; otherwise -1 or +1 according to the sign of `x`.
`smoothstep(lo, hi, x)`	`lo`, `hi`, `x` of one dimension; `lo < hi`	unitless	Clamp `t = (x - lo) / (hi - lo)` to [0, 1], then return `tt(3 - 2*t)`.
`lerp(a, b, t)`	`a`, `b` of one dimension; unitless `t`	the dimension of `a` and `b`	Linear interpolation `a + (b - a) * t`; `t` is not clamped.
`lookup(table, key, column)`	table id, enum-valued `key`, column id	the column's declared type	Resolved during elaboration; it never reaches the evaluator. A missing row or column is `VXL-E212`.