diff --git a/docs/docs/noir/concepts/data_types/integers.md b/docs/docs/noir/concepts/data_types/integers.md index 7d1e83cf4e9..b95cd8dc837 100644 --- a/docs/docs/noir/concepts/data_types/integers.md +++ b/docs/docs/noir/concepts/data_types/integers.md @@ -51,6 +51,55 @@ If you are using the default proving backend with Noir, both even (e.g. _u2_, _i ::: + +## 128 bits Unsigned Integers + +The built-in structure `U128` allows you to use 128-bit unsigned integers almost like a native integer type. However, there are some differences to keep in mind: +- You cannot cast between a native integer and `U128` +- There is a higher performance cost when using `U128`, compared to a native type. + +Conversion between unsigned integer types and U128 are done through the use of `from_integer` and `to_integer` functions. + +```rust +fn main() { + let x = U128::from_integer(23); + let y = U128::from_hex("0x7"); + let z = x + y; + assert(z.to_integer() == 30); +} +``` + +`U128` is implemented with two 64 bits limbs, representing the low and high bits, which explains the performance cost. You should expect `U128` to be twice more costly for addition and four times more costly for multiplication. +You can construct a U128 from its limbs: +```rust +fn main(x: u64, y: u64) { + let x = U128::from_u64s_be(x,y); + assert(z.hi == x as Field); + assert(z.lo == y as Field); +} +``` + +Note that the limbs are stored as Field elements in order to avoid unnecessary conversions. +Apart from this, most operations will work as usual: + +```rust +fn main(x: U128, y: U128) { + // multiplication + let c = x * y; + // addition and subtraction + let c = c - x + y; + // division + let c = x / y; + // bit operation; + let c = x & y | y; + // bit shift + let c = x << y; + // comparisons; + let c = x < y; + let c = x == y; +} +``` + ## Overflows Computations that exceed the type boundaries will result in overflow errors. This happens with both signed and unsigned integers. For example, attempting to prove: