Fields

The field type corresponds to the native field type of the proving backend.

The size of a Noir field depends on the elliptic curve's finite field for the proving backend adopted. For example, a field would be a 254-bit integer when paired with the default backend that spans the Grumpkin curve.

Fields support integer arithmetic and are often used as the default numeric type in Noir:

fn main(x : Field, y : Field)  {
    let z = x + y;
}

x, y and z are all private fields in this example. Using the let keyword we defined a new private value z constrained to be equal to x + y.

If proving efficiency is of priority, fields should be used as a default for solving problems. Smaller integer types (e.g. u64) incur extra range constraints.

Methods

After declaring a Field, you can use these common methods on it:

to_le_bits

Transforms the field into an array of bits, Little Endian.

to_le_bits

pub fn to_le_bits<let N: u32>(self: Self) -> [u1; N] {}

^{_{Source code: noir_stdlib/src/field/mod.nr#L32-L34}}

example:

to_le_bits_example

fn test_to_le_bits() {
        let field = 2;
        let bits: [u1; 8] = field.to_le_bits();
        assert_eq(bits, [0, 1, 0, 0, 0, 0, 0, 0]);
    }

^{_{Source code: noir_stdlib/src/field/mod.nr#L260-L266}}

to_be_bits

Transforms the field into an array of bits, Big Endian.

to_be_bits

pub fn to_be_bits<let N: u32>(self: Self) -> [u1; N] {}

^{_{Source code: noir_stdlib/src/field/mod.nr#L48-L50}}

example:

to_be_bits_example

fn test_to_be_bits() {
        let field = 2;
        let bits: [u1; 8] = field.to_be_bits();
        assert_eq(bits, [0, 0, 0, 0, 0, 0, 1, 0]);
    }

^{_{Source code: noir_stdlib/src/field/mod.nr#L251-L257}}

to_le_bytes

Transforms into an array of bytes, Little Endian

to_le_bytes

pub fn to_le_bytes<let N: u32>(self: Self) -> [u8; N] {

^{_{Source code: noir_stdlib/src/field/mod.nr#L61-L63}}

example:

to_le_bytes_example

fn test_to_le_bytes() {
        let field = 2;
        let bits: [u8; 8] = field.to_le_bytes();
        assert_eq(bits, [2, 0, 0, 0, 0, 0, 0, 0]);
        assert_eq(Field::from_le_bytes::<8>(bits), field);
    }

^{_{Source code: noir_stdlib/src/field/mod.nr#L279-L286}}

to_be_bytes

Transforms into an array of bytes, Big Endian

to_be_bytes

pub fn to_be_bytes<let N: u32>(self: Self) -> [u8; N] {

^{_{Source code: noir_stdlib/src/field/mod.nr#L94-L96}}

example:

to_be_bytes_example

fn test_to_be_bytes() {
        let field = 2;
        let bits: [u8; 8] = field.to_be_bytes();
        assert_eq(bits, [0, 0, 0, 0, 0, 0, 0, 2]);
        assert_eq(Field::from_be_bytes::<8>(bits), field);
    }

^{_{Source code: noir_stdlib/src/field/mod.nr#L269-L276}}

to_le_radix

Decomposes into an array over the specified base, Little Endian

to_le_radix

pub fn to_le_radix<let N: u32>(self: Self, radix: u32) -> [u8; N] {
        // Brillig does not need an immediate radix
        if !crate::runtime::is_unconstrained() {
            crate::assert_constant(radix);
        }
        self.__to_le_radix(radix)
    }

^{_{Source code: noir_stdlib/src/field/mod.nr#L118-L126}}

example:

to_le_radix_example

fn test_to_le_radix() {
        let field = 2;
        let bits: [u8; 8] = field.to_le_radix(256);
        assert_eq(bits, [2, 0, 0, 0, 0, 0, 0, 0]);
        assert_eq(Field::from_le_bytes::<8>(bits), field);
    }

^{_{Source code: noir_stdlib/src/field/mod.nr#L299-L306}}

to_be_radix

Decomposes into an array over the specified base, Big Endian

to_be_radix

pub fn to_be_radix<let N: u32>(self: Self, radix: u32) -> [u8; N] {
        // Brillig does not need an immediate radix
        if !crate::runtime::is_unconstrained() {
            crate::assert_constant(radix);
        }
        self.__to_be_radix(radix)
    }

^{_{Source code: noir_stdlib/src/field/mod.nr#L128-L136}}

example:

to_be_radix_example

fn test_to_be_radix() {
        let field = 2;
        let bits: [u8; 8] = field.to_be_radix(256);
        assert_eq(bits, [0, 0, 0, 0, 0, 0, 0, 2]);
        assert_eq(Field::from_be_bytes::<8>(bits), field);
    }

^{_{Source code: noir_stdlib/src/field/mod.nr#L289-L296}}

pow_32

Returns the value to the power of the specified exponent

fn pow_32(self, exponent: Field) -> Field

example:

fn main() {
    let field = 2
    let pow = field.pow_32(4);
    assert(pow == 16);
}

assert_max_bit_size

Adds a constraint to specify that the field can be represented with bit_size number of bits

assert_max_bit_size

pub fn assert_max_bit_size<let BIT_SIZE: u32>(self) {

^{_{Source code: noir_stdlib/src/field/mod.nr#L10-L12}}

example:

fn main() {
    let field = 2
    field.assert_max_bit_size(32);
}

sgn0

Parity of (prime) Field element, i.e. sgn0(x mod p) = 0 if x ∈ {0, ..., p-1} is even, otherwise sgn0(x mod p) = 1.

fn sgn0(self) -> u1

lt

Returns true if the field is less than the other field

pub fn lt(self, another: Field) -> bool