Numbers

Use this when doing arithmetic, comparisons, aggregation, or numeric conversions.

Arithmetic operators

Operator	Description	Example	Result
+	Add	+3 4	7
-	Subtract	-10 3	7
*	Multiply	*3 4	12
/	Divide	/10 2	5
%	Modulo	%10 3	1

Bitwise operators

Work on u32, u64, and i64 integer types.

Operator	Description	Example
band	Bitwise AND	band 0xF0u 0x0Fu -> 0u
bor	Bitwise OR	bor 0xF0u 0x0Fu -> 0xFFu
bxor	Bitwise XOR	bxor 0xFFu 0x0Fu -> 0xF0u
bnot	Bitwise NOT (complement)	bnot 0u -> 0xFFFFFFFFu
shl	Left shift	shl 1u 4 -> 16u
shr	Right shift (logical for u32/u64, arithmetic for i64)	shr 16u 4 -> 1u

64-bit variants (band64, bor64, bxor64, bnot64, shl64, shr64) operate on u64 and i64 values, allowing full 64-bit integer manipulation for crypto, binary codecs, and WASM interop.

Comparison operators

Operator	Description	Example
==	Equal	==a b
!=	Not equal	!=a b
>	Greater than	>a b
<	Less than	<a b
>=	Greater or equal	>=a b
<=	Less or equal	<=a b

All comparisons return b.

Logic

Operator	Description	Example
&	Logical AND	&a b
|	Logical OR	|a b
!	Logical NOT	!a

Math

Function	Signature	Description	Example
abs	n > n	Absolute value	abs -5 -> 5
flr	n > n	Floor	flr 3.7 -> 3
cel	n > n	Ceiling	cel 3.2 -> 4
rou	n > n	Round to nearest integer (banker’s rounding)	rou 3.7 -> 4
rnd	> n	Random float in [0, 1). Aliases: rand, random. Read this as random, not round; for rounding use rou.	rnd -> 0.42…
rnd	n n > n	Random integer in [a, b] inclusive	rnd 1 6 -> dice
rndn	n n > n	One sample from N(mu, sigma) (Box-Muller)	rndn 0 1 -> 0.34…
seed	n > _	Set the shared PRNG state (SplitMix64). All subsequent rnd/rndn on every engine use this state. Default seed is deterministic (no wall-clock). Returns _. For entropy: seed (now-ms).	seed 42

Aggregation

Function	Signature	Description	Example
sum	L n > n	Sum a list of numbers	sum [1,2,3] -> 6
avg	L n > n	Average of a list of numbers	avg [2,4,6] -> 4
min	L n > n	Minimum element of a numeric list (error if empty)	min [3,1,4,1,5] -> 1
max	L n > n	Maximum element of a numeric list (error if empty)	max [3,1,4,1,5] -> 5
min	n n > n	Minimum of two numbers	min 3 7 -> 3
max	n n > n	Maximum of two numbers	max 3 7 -> 7
median	L n > n	Median of a numeric list	median [1,2,3,4,5] -> 3
stdev	L n > n	Sample standard deviation (divides by N-1)	stdev [2,4,4,4,5,5,7,9]
variance	L n > n	Sample variance (divides by N-1)	variance [...]
argmax	L n > n	Index of max element (first occurrence wins on ties; errors on empty)	argmax [3,1,9,2] -> 2
argmin	L n > n	Index of min element (first occurrence wins on ties; errors on empty)	argmin [3,1,9,2] -> 1
argsort	L n > L n	Sorted-index permutation ascending (stable; empty returns [])	argsort [3,1,2] -> [1,2,0]

Numeric prelude (list constructors)

Function	Signature	Description	Example
linspace	n n n > L n	n evenly-spaced floats from a to b inclusive (numpy endpoint=True). n=0 returns []; n=1 returns [a]. Last element pinned to b to avoid float-accumulated drift.	linspace 0 10 5 -> [0, 2.5, 5, 7.5, 10]
ones	n > L n	n copies of 1.0. n=0 returns []. Saves the design-matrix-column map (i:n>n;1) (range 0 n) cascade.	ones 5 -> [1, 1, 1, 1, 1]
rep	n T > L T	n copies of any value (element type follows the value). n=0 returns []. Saves map (i:n>T;v) (range 0 n) for accumulator seeding and constant tables.	rep 3 7 -> [7, 7, 7], rep 3 "x" -> ["x", "x", "x"]

All three reject negative n with ILO-R009 and cap at 1,000,000 elements.

Conversions

Function	Signature	Description	Example
str	_ > t	Convert to string	str 42 -> "42"
num	t|n > R n t	Polymorphic: parse text or identity-wrap a number as Ok. Saves the num (str x) roundtrip when x may already be numeric (e.g. from jpar! on a JSON number)	num "42" -> Ok 42, num 42 -> Ok 42

Aliases

Long form	Short form
average	avg
floor	flr
ceil	cel
round	rou
random	rnd
rand	rnd
number	num
string	str