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Version: v0.28.0

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.

fn to_le_bits(_x : Field, _bit_size: u32) -> [u1]

example:

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

to_be_bits​

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

fn to_be_bits(_x : Field, _bit_size: u32) -> [u1]

example:

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

to_le_bytes​

Transforms into an array of bytes, Little Endian

fn to_le_bytes(_x : Field, byte_size: u32) -> [u8]

example:

fn main() {
    let field = 2;
    let bytes = field.to_le_bytes(4);
}

to_be_bytes​

Transforms into an array of bytes, Big Endian

fn to_be_bytes(_x : Field, byte_size: u32) -> [u8]

example:

fn main() {
    let field = 2;
    let bytes = field.to_be_bytes(4);
}

to_le_radix​

Decomposes into a vector over the specified base, Little Endian

fn to_le_radix(_x : Field, _radix: u32, _result_len: u32) -> [u8]

example:

fn main() {
    let field = 2;
    let radix = field.to_le_radix(256, 4);
}

to_be_radix​

Decomposes into a vector over the specified base, Big Endian

fn to_be_radix(_x : Field, _radix: u32, _result_len: u32) -> [u8]

example:

fn main() {
    let field = 2;
    let radix = field.to_be_radix(256, 4);
}

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

fn assert_max_bit_size(self, bit_size: u32)

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