> Aztec.nr API reference, v6.0.0 (mainnet and testnet). Index: https://docs.aztec.network/aztec-nr-api/v6.0.0/llms.txt # Primitive type Field Module: `std` 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. 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. ## Implementations ```rust impl Field ``` ```rust pub fn assert_max_bit_size(self) ``` Asserts that `self` can be represented in `bit_size` bits. #### Failures Causes a constraint failure for `Field` values exceeding `2^{bit_size}`. ```rust pub fn to_le_bits(self) -> [bool; N] ``` Decomposes `self` into its little endian bit decomposition as a `[bool; N]` array. This array will be zero padded should not all bits be necessary to represent `self`. #### Failures Causes a constraint failure for `Field` values exceeding `2^N` as the resulting array will not be able to represent the original `Field`. #### Safety The bit decomposition returned is canonical and is guaranteed to not overflow the modulus. ```rust pub fn to_be_bits(self) -> [bool; N] ``` Decomposes `self` into its big endian bit decomposition as a `[bool; N]` array. This array will be zero padded should not all bits be necessary to represent `self`. #### Failures Causes a constraint failure for `Field` values exceeding `2^N` as the resulting array will not be able to represent the original `Field`. #### Safety The bit decomposition returned is canonical and is guaranteed to not overflow the modulus. ```rust pub fn to_le_bytes(self) -> [u8; N] ``` Decomposes `self` into its little endian byte decomposition as a `[u8;N]` array This array will be zero padded should not all bytes be necessary to represent `self`. #### Failures The length N of the array must be big enough to contain all the bytes of the 'self', and no more than the number of bytes required to represent the field modulus #### Safety The result is ensured to be the canonical decomposition of the field element ```rust pub fn to_be_bytes(self) -> [u8; N] ``` Decomposes `self` into its big endian byte decomposition as a `[u8;N]` array of length required to represent the field modulus This array will be zero padded should not all bytes be necessary to represent `self`. #### Failures The length N of the array must be big enough to contain all the bytes of the 'self', and no more than the number of bytes required to represent the field modulus #### Safety The result is ensured to be the canonical decomposition of the field element ```rust pub fn pow_32(self, exponent: Self) -> Self ``` ```rust pub fn sgn0(self) -> bool ``` ```rust pub fn lt(self, another: Self) -> bool ``` ```rust pub fn from_le_bytes(bytes: [u8; N]) -> Self ``` Convert a little endian byte array to a field element. If the provided byte array overflows the field modulus then the Field will silently wrap around. #### Failures `N` must be no greater than the number of bytes required to represent the field modulus ```rust pub fn from_be_bytes(bytes: [u8; N]) -> Self ``` Convert a big endian byte array to a field element. If the provided byte array overflows the field modulus then the Field will silently wrap around. #### Failures `N` must be no greater than the number of bytes required to represent the field modulus ```rust pub fn from_le_bytes_checked(bytes: [u8; N]) -> Self ``` Convert a little endian byte array to a field element, asserting that the input is a canonical representation (strictly less than the field modulus). #### Failures Causes a constraint failure if `bytes` encodes a value greater than or equal to the field modulus. ```rust pub fn from_be_bytes_checked(bytes: [u8; N]) -> Self ``` Convert a big endian byte array to a field element, asserting that the input is a canonical representation (strictly less than the field modulus). #### Failures Causes a constraint failure if `bytes` encodes a value greater than or equal to the field modulus. ## Trait implementations ```rust impl Add for Field ``` ```rust pub fn add(self, other: Self) -> Self ``` ```rust impl AsPrimitive for Field ``` ```rust pub fn as_(self) -> bool ``` ```rust impl AsPrimitive for Field ``` ```rust pub fn as_(self) -> u128 ``` ```rust impl AsPrimitive for Field ``` ```rust pub fn as_(self) -> u16 ``` ```rust impl AsPrimitive for Field ``` ```rust pub fn as_(self) -> u32 ``` ```rust impl AsPrimitive for Field ``` ```rust pub fn as_(self) -> u64 ``` ```rust impl AsPrimitive for Field ``` ```rust pub fn as_(self) -> u8 ``` ```rust impl Default for Field ``` ```rust pub fn default() -> Self ``` ```rust impl Div for Field ``` ```rust pub fn div(self, other: Self) -> Self ``` ```rust impl Eq for Field ``` ```rust pub fn eq(self, other: Self) -> bool ``` ```rust impl From for Field ``` ```rust pub fn from(value: bool) -> Self ``` ```rust impl From for Field ``` ```rust pub fn from(value: u128) -> Self ``` ```rust impl From for Field ``` ```rust pub fn from(value: u16) -> Self ``` ```rust impl From for Field ``` ```rust pub fn from(value: u32) -> Self ``` ```rust impl From for Field ``` ```rust pub fn from(value: u64) -> Self ``` ```rust impl From for Field ``` ```rust pub fn from(value: u8) -> Self ``` ```rust impl Hash for Field ``` ```rust pub fn hash(self, state: &mut H) where H: Hasher ``` ```rust impl Mul for Field ``` ```rust pub fn mul(self, other: Self) -> Self ``` ```rust impl Neg for Field ``` ```rust pub fn neg(self) -> Self ``` ```rust impl Sub for Field ``` ```rust pub fn sub(self, other: Self) -> Self ``` ```rust impl WrappingAdd for Field ``` ```rust pub fn wrapping_add(self, y: Self) -> Self ``` ```rust impl WrappingMul for Field ``` ```rust pub fn wrapping_mul(self, y: Self) -> Self ``` ```rust impl WrappingSub for Field ``` ```rust pub fn wrapping_sub(self, y: Self) -> Self ```