Rename PrimeField -> Field64 (#454)

* Rename `PrimeField` -> `Field64`

And add TODOs for moving around various methods which aren't well-defined in their current traits, or would be well-defined in a supertrait.

* fix test

* TODOs as per PR feedback

field/src/arch/x86_64/avx2_goldilocks_field.rs

@@ -5,7 +5,7 @@ use std::iter::{Product, Sum};
 use std::mem::transmute;
 use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
 
-use crate::field_types::{Field, PrimeField};
+use crate::field_types::{Field, Field64};
 use crate::goldilocks_field::GoldilocksField;
 use crate::ops::Square;
 use crate::packed_field::PackedField;
@@ -510,7 +510,7 @@ unsafe fn interleave2(x: __m256i, y: __m256i) -> (__m256i, __m256i) {
 #[cfg(test)]
 mod tests {
     use crate::arch::x86_64::avx2_goldilocks_field::Avx2GoldilocksField;
-    use crate::field_types::PrimeField;
+    use crate::field_types::Field64;
     use crate::goldilocks_field::GoldilocksField;
     use crate::ops::Square;
     use crate::packed_field::PackedField;

field/src/arch/x86_64/avx512_goldilocks_field.rs

@@ -5,7 +5,7 @@ use std::iter::{Product, Sum};
 use std::mem::transmute;
 use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
 
-use crate::field_types::{Field, PrimeField};
+use crate::field_types::{Field, Field64};
 use crate::goldilocks_field::GoldilocksField;
 use crate::ops::Square;
 use crate::packed_field::PackedField;
@@ -407,7 +407,7 @@ unsafe fn interleave4(x: __m512i, y: __m512i) -> (__m512i, __m512i) {
 #[cfg(test)]
 mod tests {
     use crate::arch::x86_64::avx512_goldilocks_field::Avx512GoldilocksField;
-    use crate::field_types::PrimeField;
+    use crate::field_types::Field64;
     use crate::goldilocks_field::GoldilocksField;
     use crate::ops::Square;
     use crate::packed_field::PackedField;

field/src/field_types.rs

@@ -264,17 +264,25 @@ pub trait Field:
         subgroup.into_iter().map(|x| x * shift).collect()
     }
 
-    // TODO: move these to a new `PrimeField` trait (for all prime fields, not just 64-bit ones)
+    // TODO: The current behavior for composite fields doesn't seem natural or useful.
+    // Rename to `from_noncanonical_biguint` and have it return `n % Self::characteristic()`.
     fn from_biguint(n: BigUint) -> Self;
 
+    // TODO: Move to a new `PrimeField` trait.
     fn to_biguint(&self) -> BigUint;
 
+    /// Returns `n`. Assumes that `n` is already in canonical form, i.e. `n < Self::order()`.
+    // TODO: Should probably be unsafe.
     fn from_canonical_u64(n: u64) -> Self;
 
+    /// Returns `n`. Assumes that `n` is already in canonical form, i.e. `n < Self::order()`.
+    // TODO: Should probably be unsafe.
     fn from_canonical_u32(n: u32) -> Self {
         Self::from_canonical_u64(n as u64)
     }
 
+    /// Returns `n`. Assumes that `n` is already in canonical form, i.e. `n < Self::order()`.
+    // TODO: Should probably be unsafe.
     fn from_canonical_usize(n: usize) -> Self {
         Self::from_canonical_u64(n as u64)
     }
@@ -283,11 +291,11 @@ pub trait Field:
         Self::from_canonical_u64(b as u64)
     }
 
-    /// Returns `n % Self::CHARACTERISTIC`.
+    /// Returns `n % Self::characteristic()`.
     fn from_noncanonical_u128(n: u128) -> Self;
 
-    /// Returns `n % Self::CHARACTERISTIC`. May be cheaper than from_noncanonical_u128 when we know
-    /// that n < 2 ** 96.
+    /// Returns `n % Self::characteristic()`. May be cheaper than from_noncanonical_u128 when we know
+    /// that `n < 2 ** 96`.
     #[inline]
     fn from_noncanonical_u96((n_lo, n_hi): (u64, u32)) -> Self {
         // Default implementation.
@@ -399,22 +407,28 @@ pub trait Field:
     }
 }
 
-/// A finite field of prime order less than 2^64.
-pub trait PrimeField: Field {
+/// A finite field of order less than 2^64.
+pub trait Field64: Field {
     const ORDER: u64;
 
+    // TODO: Only well-defined for prime 64-bit fields. Move to a new PrimeField64 trait?
     fn to_canonical_u64(&self) -> u64;
 
+    // TODO: Only well-defined for prime 64-bit fields. Move to a new PrimeField64 trait?
     fn to_noncanonical_u64(&self) -> u64;
 
+    /// Returns `x % Self::CHARACTERISTIC`.
+    // TODO: Move to `Field`.
     fn from_noncanonical_u64(n: u64) -> Self;
 
     #[inline]
+    // TODO: Move to `Field`.
     fn add_one(&self) -> Self {
         unsafe { self.add_canonical_u64(1) }
     }
 
     #[inline]
+    // TODO: Move to `Field`.
     fn sub_one(&self) -> Self {
         unsafe { self.sub_canonical_u64(1) }
     }
@@ -423,6 +437,7 @@ pub trait PrimeField: Field {
     /// Equivalent to *self + Self::from_canonical_u64(rhs), but may be cheaper. The caller must
     /// ensure that 0 <= rhs < Self::ORDER. The function may return incorrect results if this
     /// precondition is not met. It is marked unsafe for this reason.
+    // TODO: Move to `Field`.
     #[inline]
     unsafe fn add_canonical_u64(&self, rhs: u64) -> Self {
         // Default implementation.
@@ -433,6 +448,7 @@ pub trait PrimeField: Field {
     /// Equivalent to *self - Self::from_canonical_u64(rhs), but may be cheaper. The caller must
     /// ensure that 0 <= rhs < Self::ORDER. The function may return incorrect results if this
     /// precondition is not met. It is marked unsafe for this reason.
+    // TODO: Move to `Field`.
     #[inline]
     unsafe fn sub_canonical_u64(&self, rhs: u64) -> Self {
         // Default implementation.

field/src/goldilocks_field.rs

@@ -12,7 +12,7 @@ use serde::{Deserialize, Serialize};
 use crate::extension_field::quadratic::QuadraticExtension;
 use crate::extension_field::quartic::QuarticExtension;
 use crate::extension_field::{Extendable, Frobenius};
-use crate::field_types::{Field, PrimeField};
+use crate::field_types::{Field, Field64};
 use crate::inversion::try_inverse_u64;
 
 const EPSILON: u64 = (1 << 32) - 1;
@@ -123,7 +123,7 @@ impl Field for GoldilocksField {
     }
 }
 
-impl PrimeField for GoldilocksField {
+impl Field64 for GoldilocksField {
     const ORDER: u64 = 0xFFFFFFFF00000001;
 
     #[inline]

field/src/inversion.rs

@@ -1,4 +1,4 @@
-use crate::field_types::PrimeField;
+use crate::field_types::Field64;
 
 /// This is a 'safe' iteration for the modular inversion algorithm. It
 /// is safe in the sense that it will produce the right answer even
@@ -63,7 +63,7 @@ unsafe fn unsafe_iteration(f: &mut u64, g: &mut u64, c: &mut i128, d: &mut i128,
 /// Elliptic and Hyperelliptic Cryptography, Algorithms 11.6
 /// and 11.12.
 #[allow(clippy::many_single_char_names)]
-pub(crate) fn try_inverse_u64<F: PrimeField>(x: &F) -> Option<F> {
+pub(crate) fn try_inverse_u64<F: Field64>(x: &F) -> Option<F> {
     let mut f = x.to_noncanonical_u64();
     let mut g = F::ORDER;
     // NB: These two are very rarely such that their absolute

field/src/prime_field_testing.rs

@@ -1,4 +1,4 @@
-use crate::field_types::PrimeField;
+use crate::field_types::Field64;
 
 /// Generates a series of non-negative integers less than `modulus` which cover a range of
 /// interesting test values.
@@ -19,7 +19,7 @@ pub fn test_inputs(modulus: u64) -> Vec<u64> {
 /// word_bits)` and panic if the two resulting vectors differ.
 pub fn run_unaryop_test_cases<F, UnaryOp, ExpectedOp>(op: UnaryOp, expected_op: ExpectedOp)
 where
-    F: PrimeField,
+    F: Field64,
     UnaryOp: Fn(F) -> F,
     ExpectedOp: Fn(u64) -> u64,
 {
@@ -43,7 +43,7 @@ where
 /// Apply the binary functions `op` and `expected_op` to each pair of inputs.
 pub fn run_binaryop_test_cases<F, BinaryOp, ExpectedOp>(op: BinaryOp, expected_op: ExpectedOp)
 where
-    F: PrimeField,
+    F: Field64,
     BinaryOp: Fn(F, F) -> F,
     ExpectedOp: Fn(u64, u64) -> u64,
 {
@@ -70,7 +70,7 @@ macro_rules! test_prime_field_arithmetic {
         mod prime_field_arithmetic {
             use std::ops::{Add, Mul, Neg, Sub};
 
-            use crate::field_types::{Field, PrimeField};
+            use crate::field_types::{Field, Field64};
             use crate::ops::Square;
 
             #[test]

plonky2/src/bin/generate_constants.rs

@@ -2,7 +2,7 @@
 
 #![allow(clippy::needless_range_loop)]
 
-use plonky2_field::field_types::PrimeField;
+use plonky2_field::field_types::Field64;
 use plonky2_field::goldilocks_field::GoldilocksField;
 use rand::{Rng, SeedableRng};
 use rand_chacha::ChaCha8Rng;

plonky2/src/gadgets/arithmetic.rs

@@ -1,7 +1,7 @@
 use std::borrow::Borrow;
 
 use plonky2_field::extension_field::Extendable;
-use plonky2_field::field_types::PrimeField;
+use plonky2_field::field_types::Field64;
 
 use crate::gates::arithmetic_base::ArithmeticGate;
 use crate::gates::exponentiation::ExponentiationGate;
@@ -325,7 +325,7 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
 
 /// Represents a base arithmetic operation in the circuit. Used to memoize results.
 #[derive(Copy, Clone, Eq, PartialEq, Hash)]
-pub(crate) struct BaseArithmeticOperation<F: PrimeField> {
+pub(crate) struct BaseArithmeticOperation<F: Field64> {
     const_0: F,
     const_1: F,
     multiplicand_0: Target,

plonky2/src/gadgets/arithmetic_extension.rs

@@ -1,6 +1,6 @@
 use plonky2_field::extension_field::FieldExtension;
 use plonky2_field::extension_field::{Extendable, OEF};
-use plonky2_field::field_types::{Field, PrimeField};
+use plonky2_field::field_types::{Field, Field64};
 use plonky2_util::bits_u64;
 
 use crate::gates::arithmetic_extension::ArithmeticExtensionGate;
@@ -544,7 +544,7 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
 
 /// Represents an extension arithmetic operation in the circuit. Used to memoize results.
 #[derive(Copy, Clone, Eq, PartialEq, Hash)]
-pub(crate) struct ExtensionArithmeticOperation<F: PrimeField + Extendable<D>, const D: usize> {
+pub(crate) struct ExtensionArithmeticOperation<F: Field64 + Extendable<D>, const D: usize> {
     const_0: F,
     const_1: F,
     multiplicand_0: ExtensionTarget<D>,

plonky2/src/gates/assert_le.rs

@@ -1,7 +1,7 @@
 use std::marker::PhantomData;
 
 use plonky2_field::extension_field::Extendable;
-use plonky2_field::field_types::{Field, PrimeField};
+use plonky2_field::field_types::{Field, Field64};
 use plonky2_field::packed_field::PackedField;
 use plonky2_util::{bits_u64, ceil_div_usize};
 
@@ -25,7 +25,7 @@ use crate::plonk::vars::{
 
 /// A gate for checking that one value is less than or equal to another.
 #[derive(Clone, Debug)]
-pub struct AssertLessThanGate<F: PrimeField + Extendable<D>, const D: usize> {
+pub struct AssertLessThanGate<F: Field64 + Extendable<D>, const D: usize> {
     pub(crate) num_bits: usize,
     pub(crate) num_chunks: usize,
     _phantom: PhantomData<F>,
@@ -455,7 +455,7 @@ mod tests {
 
     use anyhow::Result;
     use plonky2_field::extension_field::quartic::QuarticExtension;
-    use plonky2_field::field_types::{Field, PrimeField};
+    use plonky2_field::field_types::{Field, Field64};
     use plonky2_field::goldilocks_field::GoldilocksField;
     use rand::Rng;
 

plonky2/src/gates/base_sum.rs

@@ -1,7 +1,7 @@
 use std::ops::Range;
 
 use plonky2_field::extension_field::Extendable;
-use plonky2_field::field_types::{Field, PrimeField};
+use plonky2_field::field_types::{Field, Field64};
 use plonky2_field::packed_field::PackedField;
 
 use crate::gates::gate::Gate;
@@ -31,7 +31,7 @@ impl<const B: usize> BaseSumGate<B> {
         Self { num_limbs }
     }
 
-    pub fn new_from_config<F: PrimeField>(config: &CircuitConfig) -> Self {
+    pub fn new_from_config<F: Field64>(config: &CircuitConfig) -> Self {
         let num_limbs = F::BITS.min(config.num_routed_wires - Self::START_LIMBS);
         Self::new(num_limbs)
     }

plonky2/src/gates/comparison.rs

@@ -1,7 +1,7 @@
 use std::marker::PhantomData;
 
 use plonky2_field::extension_field::Extendable;
-use plonky2_field::field_types::{Field, PrimeField};
+use plonky2_field::field_types::{Field, Field64};
 use plonky2_field::packed_field::PackedField;
 use plonky2_util::{bits_u64, ceil_div_usize};
 
@@ -23,7 +23,7 @@ use crate::plonk::vars::{
 
 /// A gate for checking that one value is less than or equal to another.
 #[derive(Clone, Debug)]
-pub struct ComparisonGate<F: PrimeField + Extendable<D>, const D: usize> {
+pub struct ComparisonGate<F: Field64 + Extendable<D>, const D: usize> {
     pub(crate) num_bits: usize,
     pub(crate) num_chunks: usize,
     _phantom: PhantomData<F>,
@@ -520,7 +520,7 @@ mod tests {
     use std::marker::PhantomData;
 
     use anyhow::Result;
-    use plonky2_field::field_types::{Field, PrimeField};
+    use plonky2_field::field_types::{Field, Field64};
     use plonky2_field::goldilocks_field::GoldilocksField;
     use rand::Rng;
 

plonky2/src/gates/subtraction_u32.rs

@@ -338,7 +338,7 @@ mod tests {
 
     use anyhow::Result;
     use plonky2_field::extension_field::quartic::QuarticExtension;
-    use plonky2_field::field_types::{Field, PrimeField};
+    use plonky2_field::field_types::{Field, Field64};
     use plonky2_field::goldilocks_field::GoldilocksField;
     use rand::Rng;
 

plonky2/src/hash/arch/aarch64/poseidon_goldilocks_neon.rs

@@ -3,7 +3,7 @@
 use std::arch::aarch64::*;
 use std::arch::asm;
 
-use plonky2_field::field_types::PrimeField;
+use plonky2_field::field_types::Field64;
 use plonky2_field::goldilocks_field::GoldilocksField;
 use plonky2_util::branch_hint;
 use static_assertions::const_assert;

plonky2/src/hash/hash_types.rs

@@ -1,4 +1,4 @@
-use plonky2_field::field_types::{Field, PrimeField};
+use plonky2_field::field_types::{Field, Field64};
 use plonky2_field::goldilocks_field::GoldilocksField;
 use rand::Rng;
 use serde::{Deserialize, Deserializer, Serialize, Serializer};
@@ -8,7 +8,7 @@ use crate::iop::target::Target;
 use crate::plonk::config::GenericHashOut;
 
 /// A prime order field with the features we need to use it as a base field in our argument system.
-pub trait RichField: PrimeField + Poseidon {}
+pub trait RichField: Field64 + Poseidon {}
 
 impl RichField for GoldilocksField {}
 

plonky2/src/hash/poseidon.rs

@@ -2,7 +2,7 @@
 //! https://eprint.iacr.org/2019/458.pdf
 
 use plonky2_field::extension_field::{Extendable, FieldExtension};
-use plonky2_field::field_types::{Field, PrimeField};
+use plonky2_field::field_types::{Field, Field64};
 use unroll::unroll_for_loops;
 
 use crate::gates::gate::Gate;
@@ -35,7 +35,7 @@ fn add_u160_u128((x_lo, x_hi): (u128, u32), y: u128) -> (u128, u32) {
 }
 
 #[inline(always)]
-fn reduce_u160<F: PrimeField>((n_lo, n_hi): (u128, u32)) -> F {
+fn reduce_u160<F: Field64>((n_lo, n_hi): (u128, u32)) -> F {
     let n_lo_hi = (n_lo >> 64) as u64;
     let n_lo_lo = n_lo as u64;
     let reduced_hi: u64 = F::from_noncanonical_u96((n_lo_hi, n_hi)).to_noncanonical_u64();
@@ -148,7 +148,7 @@ pub const ALL_ROUND_CONSTANTS: [u64; MAX_WIDTH * N_ROUNDS]  = [
 ];
 
 const WIDTH: usize = SPONGE_WIDTH;
-pub trait Poseidon: PrimeField {
+pub trait Poseidon: Field64 {
     // Total number of round constants required: width of the input
     // times number of rounds.
     const N_ROUND_CONSTANTS: usize = WIDTH * N_ROUNDS;

plonky2/src/hash/poseidon_goldilocks.rs

@@ -270,7 +270,7 @@ impl Poseidon for GoldilocksField {
 
 #[cfg(test)]
 mod tests {
-    use plonky2_field::field_types::{Field, PrimeField};
+    use plonky2_field::field_types::{Field, Field64};
     use plonky2_field::goldilocks_field::GoldilocksField as F;
 
     use crate::hash::poseidon::test_helpers::{check_consistency, check_test_vectors};

plonky2/src/util/serialization.rs

@@ -3,7 +3,7 @@ use std::io::Cursor;
 use std::io::{Read, Result, Write};
 
 use plonky2_field::extension_field::{Extendable, FieldExtension};
-use plonky2_field::field_types::PrimeField;
+use plonky2_field::field_types::Field64;
 use plonky2_field::polynomial::PolynomialCoeffs;
 
 use crate::fri::proof::{
@@ -53,10 +53,10 @@ impl Buffer {
         Ok(u32::from_le_bytes(buf))
     }
 
-    fn write_field<F: PrimeField>(&mut self, x: F) -> Result<()> {
+    fn write_field<F: Field64>(&mut self, x: F) -> Result<()> {
         self.0.write_all(&x.to_canonical_u64().to_le_bytes())
     }
-    fn read_field<F: PrimeField>(&mut self) -> Result<F> {
+    fn read_field<F: Field64>(&mut self) -> Result<F> {
         let mut buf = [0; std::mem::size_of::<u64>()];
         self.0.read_exact(&mut buf)?;
         Ok(F::from_canonical_u64(u64::from_le_bytes(
@@ -116,13 +116,13 @@ impl Buffer {
         ))
     }
 
-    pub fn write_field_vec<F: PrimeField>(&mut self, v: &[F]) -> Result<()> {
+    pub fn write_field_vec<F: Field64>(&mut self, v: &[F]) -> Result<()> {
         for &a in v {
             self.write_field(a)?;
         }
         Ok(())
     }
-    pub fn read_field_vec<F: PrimeField>(&mut self, length: usize) -> Result<Vec<F>> {
+    pub fn read_field_vec<F: Field64>(&mut self, length: usize) -> Result<Vec<F>> {
         (0..length)
             .map(|_| self.read_field())
             .collect::<Result<Vec<_>>>()

waksman/src/sorting.rs

@@ -183,7 +183,7 @@ impl<F: RichField + Extendable<D>, const D: usize> SimpleGenerator<F>
 #[cfg(test)]
 mod tests {
     use anyhow::Result;
-    use plonky2::field::field_types::{Field, PrimeField};
+    use plonky2::field::field_types::{Field, Field64};
     use plonky2::iop::witness::PartialWitness;
     use plonky2::plonk::circuit_data::CircuitConfig;
     use plonky2::plonk::config::{GenericConfig, PoseidonGoldilocksConfig};