snarkvm_fields/traits/
field.rs

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// Copyright 2024 Aleo Network Foundation
// This file is part of the snarkVM library.

// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at:

// http://www.apache.org/licenses/LICENSE-2.0

// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

use crate::{One, PrimeField, Zero};
use snarkvm_utilities::{
    FromBytes,
    ToBits,
    ToBytes,
    bititerator::BitIteratorBE,
    rand::Uniform,
    serialize::{
        CanonicalDeserialize,
        CanonicalDeserializeWithFlags,
        CanonicalSerialize,
        CanonicalSerializeWithFlags,
        EmptyFlags,
        Flags,
    },
};

use std::{
    fmt::{Debug, Display},
    hash::Hash,
    ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
};

use serde::{Deserialize, Serialize};

/// The interface for a generic field.
pub trait Field:
    'static
    + ToBits
    + ToBytes
    + FromBytes
    + Copy
    + Clone
    + Debug
    + Display
    + Default
    + Send
    + Sync
    + Eq
    + One
    + Ord
    + Neg<Output = Self>
    + Uniform
    + Zero
    + Sized
    + Hash
    + From<u128>
    + From<u64>
    + From<u32>
    + From<u16>
    + From<u8>
    + Add<Self, Output = Self>
    + Sub<Self, Output = Self>
    + Mul<Self, Output = Self>
    + Div<Self, Output = Self>
    + AddAssign<Self>
    + SubAssign<Self>
    + MulAssign<Self>
    + DivAssign<Self>
    + for<'a> Add<&'a Self, Output = Self>
    + for<'a> Sub<&'a Self, Output = Self>
    + for<'a> Mul<&'a Self, Output = Self>
    + for<'a> Div<&'a Self, Output = Self>
    + for<'a> AddAssign<&'a Self>
    + for<'a> SubAssign<&'a Self>
    + for<'a> MulAssign<&'a Self>
    + for<'a> DivAssign<&'a Self>
    + core::iter::Sum<Self>
    + for<'a> core::iter::Sum<&'a Self>
    + core::iter::Product<Self>
    + for<'a> core::iter::Product<&'a Self>
    + CanonicalSerialize
    + CanonicalSerializeWithFlags
    + CanonicalDeserialize
    + CanonicalDeserializeWithFlags
    + Serialize
    + for<'a> Deserialize<'a>
{
    type BasePrimeField: PrimeField;

    /// Constructs an element of `Self` from an element of the base
    /// prime field.
    fn from_base_prime_field(other: Self::BasePrimeField) -> Self;

    /// Returns the constant 2^{-1}.
    fn half() -> Self {
        Self::from_base_prime_field(Self::BasePrimeField::half())
    }

    /// Returns the characteristic of the field.
    fn characteristic<'a>() -> &'a [u64];

    /// Returns `self + self`.
    #[must_use]
    fn double(&self) -> Self;

    /// Doubles `self` in place.
    fn double_in_place(&mut self);

    /// Returns `self * self`.
    #[must_use]
    fn square(&self) -> Self;

    /// Squares `self` in place.
    fn square_in_place(&mut self) -> &mut Self;

    fn sum_of_products<'a>(
        a: impl Iterator<Item = &'a Self> + Clone,
        b: impl Iterator<Item = &'a Self> + Clone,
    ) -> Self {
        a.zip(b).map(|(a, b)| *a * b).sum::<Self>()
    }

    /// Computes the multiplicative inverse of `self` if `self` is nonzero.
    #[must_use]
    fn inverse(&self) -> Option<Self>;

    /// Sets `self` to `self`'s inverse if it exists. Otherwise it is a no-op.
    fn inverse_in_place(&mut self) -> Option<&mut Self>;

    /// Exponentiates this element by a power of the base prime modulus via
    /// the Frobenius automorphism.
    fn frobenius_map(&mut self, power: usize);

    /// Exponentiates this element by a number represented with `u64` limbs,
    /// least significant limb first.
    #[must_use]
    fn pow<S: AsRef<[u64]>>(&self, exp: S) -> Self {
        let mut res = Self::one();

        let mut found_one = false;

        for i in BitIteratorBE::new(exp) {
            if !found_one {
                if i {
                    found_one = true;
                } else {
                    continue;
                }
            }

            res.square_in_place();

            if i {
                res *= self;
            }
        }
        res
    }

    /// Returns a field element if the set of bytes forms a valid field element,
    /// otherwise returns None. This function is primarily intended for sampling
    /// random field elements from a hash-function or RNG output.
    fn from_random_bytes(bytes: &[u8]) -> Option<Self> {
        Self::from_random_bytes_with_flags::<EmptyFlags>(bytes).map(|f| f.0)
    }

    /// Returns a field element with an extra sign bit used for group parsing if
    /// the set of bytes forms a valid field element, otherwise returns
    /// None. This function is primarily intended for sampling
    /// random field elements from a hash-function or RNG output.
    fn from_random_bytes_with_flags<F: Flags>(bytes: &[u8]) -> Option<(Self, F)>;
}