@math:sqrt

Integer square root (floor).

Returns: number

Syntax

@math:sqrt(...expression)

Arguments

Name	Type	Description
[...expression]	number	Unsigned numeric expression to take the square root of

Examples

load math

set $pool 0x0102030405060708090a0b0c0d0e0f1011121314

# The AMM invariant, computed on-chain at execution time
assert @sqrt!($pool::{reserve0()(uint256)} * $pool::{reserve1()(uint256)}) >= 1e18

# Plain face: floor integer square root off-chain (plain helpers need the
# module prefix; only the `!` faces resolve unqualified)
set $side @math:sqrt(1e18)

See Also

• @math:min!, @math:max!, @math:absDiff!

On-chain face (@math:sqrt!)

Integer square root as one sqrt read: floor(sqrt(x)), so @sqrt!(8) is 2.

The argument is a full expression rather than a single operand, so @sqrt!($a::x() * $b::y()) compiles the product first and takes the root of the result — which is how a geometric mean is written without a temporary.

Notes

• Unsigned only; a negative constant or an Int operand is rejected.
• Not fixed point: taking the root of a wad gives a wad-of-half-scale, so scale it yourself if you need one back.