miden_field/native/

mod.rs

//! Off-chain implementation of [`crate::Felt`].

use alloc::{format, vec, vec::Vec};
use core::{
    array, fmt,
    hash::{Hash, Hasher},
    iter::{Product, Sum},
    mem::{align_of, size_of},
    ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
};

use miden_serde_utils::{
    ByteReader, ByteWriter, Deserializable, DeserializationError, Serializable,
};
use num_bigint::BigUint;
use p3_challenger::UniformSamplingField;
use p3_field::{
    Field, InjectiveMonomial, Packable, PermutationMonomial, PrimeCharacteristicRing, PrimeField,
    PrimeField64, RawDataSerializable, TwoAdicField,
    extension::{
        Binomial, BinomiallyExtendable, ExtensionAlgebra, HasTwoAdicBinomialExtension,
        binomial_mul, binomial_square,
    },
    impl_raw_serializable_primefield64,
    integers::QuotientMap,
    quotient_map_large_iint, quotient_map_large_uint, quotient_map_small_int,
};
use p3_goldilocks::Goldilocks;
use p3_util::flatten_to_base;
use rand::{
    Rng,
    distr::{Distribution, StandardUniform},
};
use subtle::{ConditionallySelectable, ConstantTimeLess};

#[cfg(any(
    all(target_arch = "x86_64", target_feature = "avx2"),
    all(target_arch = "aarch64", target_feature = "neon"),
    all(target_arch = "wasm32", target_feature = "simd128"),
))]
mod packed;
#[cfg(any(
    all(target_arch = "x86_64", target_feature = "avx2"),
    all(target_arch = "aarch64", target_feature = "neon"),
    all(target_arch = "wasm32", target_feature = "simd128"),
))]
pub use packed::PackedFelt;

#[cfg(test)]
mod tests;

// FELT
// ================================================================================================

/// A `Felt` backed by Plonky3's Goldilocks field element.
///
/// Round-trip equality is safe even though `Felt` may hold non-canonical internal values:
/// `PartialEq for Felt` delegates to `Goldilocks::eq`, which compares `as_canonical_u64()` on
/// both sides, so canonicalization by serialization is invisible to equality.
#[derive(Copy, Clone, Default, serde::Serialize, serde::Deserialize)]
#[repr(transparent)]
#[cfg_attr(
    all(feature = "arbitrary", test),
    miden_test_serialization_macros::serialization_test
)]
pub struct Felt(Goldilocks);

impl Felt {
    /// Order of the field.
    pub const ORDER: u64 = <Goldilocks as PrimeField64>::ORDER_U64;

    pub const ZERO: Self = Self(Goldilocks::ZERO);
    pub const ONE: Self = Self(Goldilocks::ONE);

    /// The largest valid field element, equal to `ORDER - 1`.
    pub const MAX: Self = Self::new_unchecked(Self::ORDER - 1);

    /// The number of bytes which this field element occupies in memory.
    pub const NUM_BYTES: usize = Goldilocks::NUM_BYTES;

    /// Constructs a new field element from the provided `value`.
    ///
    /// # Errors
    ///
    /// - [`FeltFromIntError`] if the provided `value` is not a valid input.
    pub fn new(value: u64) -> Result<Self, FeltFromIntError> {
        Felt::from_canonical_checked(value).ok_or(FeltFromIntError(value))
    }

    /// Creates a new field element from any `u64` without performing reduction.
    ///
    /// Any `u64` value is accepted. No reduction is performed since Goldilocks uses a
    /// non-canonical internal representation.
    #[inline]
    pub const fn new_unchecked(value: u64) -> Self {
        Self(Goldilocks::new(value))
    }

    /// Constructs a field element from a `u8`.
    #[inline]
    pub const fn from_u8(value: u8) -> Self {
        Self::new_unchecked(value as u64)
    }

    /// Constructs a field element from a `u16`.
    #[inline]
    pub const fn from_u16(value: u16) -> Self {
        Self::new_unchecked(value as u64)
    }

    /// Constructs a field element from a `u32`.
    #[inline]
    pub const fn from_u32(value: u32) -> Self {
        Self::new_unchecked(value as u64)
    }

    /// The elementary function `double(a) = 2*a`.
    #[inline]
    pub fn double(&self) -> Self {
        <Self as PrimeCharacteristicRing>::double(self)
    }

    /// The elementary function `square(a) = a^2`.
    #[inline]
    pub fn square(&self) -> Self {
        <Self as PrimeCharacteristicRing>::square(self)
    }

    /// Exponentiation by a `u64` power.
    #[inline]
    pub fn exp_u64(&self, power: u64) -> Self {
        <Self as PrimeCharacteristicRing>::exp_u64(self, power)
    }

    /// Exponentiation by a small constant power.
    #[inline]
    pub fn exp_const_u64<const POWER: u64>(&self) -> Self {
        <Self as PrimeCharacteristicRing>::exp_const_u64::<POWER>(self)
    }

    /// Return the representative of element in canonical form which lies in the range
    /// `0 <= x < ORDER`.
    #[inline]
    pub fn as_canonical_u64(&self) -> u64 {
        <Self as PrimeField64>::as_canonical_u64(self)
    }

    /// Constant-time equivalent of `as_canonical_u64()` using the same reduction logic as
    /// Plonky3's Goldilocks implementation.
    #[inline]
    pub fn as_canonical_u64_ct(&self) -> u64 {
        let raw = raw_felt_u64(*self);
        // Mirrors Goldilocks::as_canonical_u64: conditional subtraction of ORDER.
        // A single subtraction is sufficient for any u64 value since 2*ORDER > u64::MAX.
        let reduced = raw.wrapping_sub(Self::ORDER);
        let reduce = !raw.ct_lt(&Self::ORDER);
        u64::conditional_select(&raw, &reduced, reduce)
    }
}

#[inline]
fn raw_felt_u64(value: Felt) -> u64 {
    const _: () = {
        assert!(size_of::<Felt>() == size_of::<u64>());
        assert!(align_of::<Felt>() == align_of::<u64>());
        assert!(2u128 * (Felt::ORDER as u128) > u64::MAX as u128);
    };
    // SAFETY: Felt is repr(transparent) over Goldilocks, which is repr(transparent) over u64.
    unsafe { core::mem::transmute_copy(&value) }
}

/// Reinterprets a `Felt` slice as `Goldilocks`.
///
/// # Safety
///
/// `Felt` is `#[repr(transparent)]` over `Goldilocks`, so the element layout matches.
#[inline]
fn felts_as_goldilocks_slice(s: &[Felt]) -> &[Goldilocks] {
    // SAFETY: `Felt` is `#[repr(transparent)]` over `Goldilocks`, so the element layout matches.
    unsafe { core::slice::from_raw_parts(s.as_ptr().cast::<Goldilocks>(), s.len()) }
}

/// Reinterprets a `Felt` array as `Goldilocks`.
///
/// # Safety
///
/// `Felt` is `#[repr(transparent)]` over `Goldilocks`, so `[Felt; N]` matches `[Goldilocks; N]`.
#[inline]
fn felts_as_goldilocks_array<const N: usize>(a: &[Felt; N]) -> &[Goldilocks; N] {
    // SAFETY: same layout as `felts_as_goldilocks_slice`, for a fixed `N`.
    unsafe { &*(a as *const [Felt; N] as *const [Goldilocks; N]) }
}

impl fmt::Display for Felt {
    #[inline]
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        fmt::Display::fmt(&self.0, f)
    }
}

impl fmt::Debug for Felt {
    #[inline]
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        fmt::Debug::fmt(&self.0, f)
    }
}

impl Hash for Felt {
    #[inline]
    fn hash<H: Hasher>(&self, state: &mut H) {
        state.write_u64(self.as_canonical_u64());
    }
}

// FIELD
// ================================================================================================

impl Field for Felt {
    #[cfg(all(target_arch = "x86_64", target_feature = "avx2", not(target_feature = "avx512f")))]
    type Packing = PackedFelt;

    #[cfg(all(target_arch = "x86_64", target_feature = "avx512f"))]
    type Packing = PackedFelt;

    #[cfg(all(target_arch = "aarch64", target_feature = "neon"))]
    type Packing = PackedFelt;

    #[cfg(all(target_arch = "wasm32", target_feature = "simd128"))]
    type Packing = PackedFelt;

    #[cfg(not(any(
        all(target_arch = "x86_64", target_feature = "avx2", not(target_feature = "avx512f")),
        all(target_arch = "x86_64", target_feature = "avx512f"),
        target_arch = "aarch64",
        all(target_arch = "wasm32", target_feature = "simd128"),
    )))]
    type Packing = Self;

    const GENERATOR: Self = Self(Goldilocks::GENERATOR);

    #[inline]
    fn is_zero(&self) -> bool {
        self.0.is_zero()
    }

    #[inline]
    fn try_inverse(&self) -> Option<Self> {
        self.0.try_inverse().map(Self)
    }

    #[inline]
    fn order() -> BigUint {
        <Goldilocks as Field>::order()
    }
}

impl Packable for Felt {}

impl PrimeCharacteristicRing for Felt {
    type PrimeSubfield = Goldilocks;

    const ZERO: Self = Self(Goldilocks::ZERO);
    const ONE: Self = Self(Goldilocks::ONE);
    const TWO: Self = Self(Goldilocks::TWO);
    const NEG_ONE: Self = Self(Goldilocks::NEG_ONE);

    #[inline]
    fn from_prime_subfield(f: Self::PrimeSubfield) -> Self {
        Self(f)
    }

    #[inline]
    fn from_bool(value: bool) -> Self {
        Self::new_unchecked(value.into())
    }

    #[inline]
    fn halve(&self) -> Self {
        Self(self.0.halve())
    }

    #[inline]
    fn mul_2exp_u64(&self, exp: u64) -> Self {
        Self(self.0.mul_2exp_u64(exp))
    }

    #[inline]
    fn div_2exp_u64(&self, exp: u64) -> Self {
        Self(self.0.div_2exp_u64(exp))
    }

    #[inline]
    fn exp_u64(&self, power: u64) -> Self {
        self.0.exp_u64(power).into()
    }

    #[inline]
    fn sum_array<const N: usize>(input: &[Self]) -> Self {
        assert_eq!(N, input.len());
        let g = felts_as_goldilocks_slice(input);
        Self(Goldilocks::sum_array::<N>(g))
    }

    #[inline]
    fn dot_product<const N: usize>(lhs: &[Self; N], rhs: &[Self; N]) -> Self {
        let lhs_g = felts_as_goldilocks_array(lhs);
        let rhs_g = felts_as_goldilocks_array(rhs);
        Self(Goldilocks::dot_product(lhs_g, rhs_g))
    }

    #[inline]
    fn zero_vec(len: usize) -> Vec<Self> {
        // SAFETY:
        // Due to `#[repr(transparent)]`, Felt, Goldilocks and u64 have the same size,
        // alignment and memory layout making `flatten_to_base` safe.
        // This will create a vector of Felt elements with value set to 0.
        unsafe { flatten_to_base(vec![0u64; len]) }
    }
}

quotient_map_small_int!(Felt, u64, [u8, u16, u32]);
quotient_map_small_int!(Felt, i64, [i8, i16, i32]);

quotient_map_large_uint!(
    Felt,
    u64,
    Felt::ORDER_U64,
    "`[0, 2^64 - 2^32]`",
    "`[0, 2^64 - 1]`",
    [u128]
);
quotient_map_large_iint!(
    Felt,
    i64,
    "`[-(2^63 - 2^31), 2^63 - 2^31]`",
    "`[1 + 2^32 - 2^64, 2^64 - 1]`",
    [(i128, u128)]
);

impl QuotientMap<u64> for Felt {
    #[inline]
    fn from_int(int: u64) -> Self {
        Goldilocks::from_int(int).into()
    }

    #[inline]
    fn from_canonical_checked(int: u64) -> Option<Self> {
        Goldilocks::from_canonical_checked(int).map(From::from)
    }

    #[inline(always)]
    unsafe fn from_canonical_unchecked(int: u64) -> Self {
        Goldilocks::new(int).into()
    }
}

impl QuotientMap<i64> for Felt {
    #[inline]
    fn from_int(int: i64) -> Self {
        Goldilocks::from_int(int).into()
    }

    #[inline]
    fn from_canonical_checked(int: i64) -> Option<Self> {
        Goldilocks::from_canonical_checked(int).map(From::from)
    }

    #[inline(always)]
    unsafe fn from_canonical_unchecked(int: i64) -> Self {
        unsafe { Goldilocks::from_canonical_unchecked(int).into() }
    }
}

impl PrimeField for Felt {
    #[inline]
    fn as_canonical_biguint(&self) -> BigUint {
        <Goldilocks as PrimeField>::as_canonical_biguint(&self.0)
    }
}

impl PrimeField64 for Felt {
    const ORDER_U64: u64 = <Goldilocks as PrimeField64>::ORDER_U64;

    #[inline]
    fn as_canonical_u64(&self) -> u64 {
        self.0.as_canonical_u64()
    }
}

impl TwoAdicField for Felt {
    const TWO_ADICITY: usize = <Goldilocks as TwoAdicField>::TWO_ADICITY;

    #[inline]
    fn two_adic_generator(bits: usize) -> Self {
        Self(<Goldilocks as TwoAdicField>::two_adic_generator(bits))
    }
}

// EXTENSION FIELDS
// ================================================================================================

impl ExtensionAlgebra<Self, 2, Binomial<Self>> for Felt {
    #[inline]
    fn ext_mul(a: &[Self; 2], b: &[Self; 2], res: &mut [Self; 2]) {
        binomial_mul::<Self, Self, Self, 2>(a, b, res, <Self as BinomiallyExtendable<2>>::W);
    }

    #[inline]
    fn ext_square(a: &[Self; 2], res: &mut [Self; 2]) {
        binomial_square::<Self, Self, 2>(a, res, <Self as BinomiallyExtendable<2>>::W);
    }
}

impl BinomiallyExtendable<2> for Felt {
    fn binomial_algebra_id() -> Vec<u8> {
        <Goldilocks as BinomiallyExtendable<2>>::binomial_algebra_id()
    }

    const W: Self = Self(<Goldilocks as BinomiallyExtendable<2>>::W);

    const DTH_ROOT: Self = Self(<Goldilocks as BinomiallyExtendable<2>>::DTH_ROOT);

    const EXT_GENERATOR: [Self; 2] = [
        Self(<Goldilocks as BinomiallyExtendable<2>>::EXT_GENERATOR[0]),
        Self(<Goldilocks as BinomiallyExtendable<2>>::EXT_GENERATOR[1]),
    ];
}

impl HasTwoAdicBinomialExtension<2> for Felt {
    const EXT_TWO_ADICITY: usize = <Goldilocks as HasTwoAdicBinomialExtension<2>>::EXT_TWO_ADICITY;

    #[inline]
    fn ext_two_adic_generator(bits: usize) -> [Self; 2] {
        let [a, b] = <Goldilocks as HasTwoAdicBinomialExtension<2>>::ext_two_adic_generator(bits);
        [Self(a), Self(b)]
    }
}

impl ExtensionAlgebra<Self, 5, Binomial<Self>> for Felt {
    #[inline]
    fn ext_mul(a: &[Self; 5], b: &[Self; 5], res: &mut [Self; 5]) {
        binomial_mul::<Self, Self, Self, 5>(a, b, res, <Self as BinomiallyExtendable<5>>::W);
    }

    #[inline]
    fn ext_square(a: &[Self; 5], res: &mut [Self; 5]) {
        binomial_square::<Self, Self, 5>(a, res, <Self as BinomiallyExtendable<5>>::W);
    }
}

impl BinomiallyExtendable<5> for Felt {
    fn binomial_algebra_id() -> Vec<u8> {
        <Goldilocks as BinomiallyExtendable<5>>::binomial_algebra_id()
    }

    const W: Self = Self(<Goldilocks as BinomiallyExtendable<5>>::W);

    const DTH_ROOT: Self = Self(<Goldilocks as BinomiallyExtendable<5>>::DTH_ROOT);

    const EXT_GENERATOR: [Self; 5] = [
        Self(<Goldilocks as BinomiallyExtendable<5>>::EXT_GENERATOR[0]),
        Self(<Goldilocks as BinomiallyExtendable<5>>::EXT_GENERATOR[1]),
        Self(<Goldilocks as BinomiallyExtendable<5>>::EXT_GENERATOR[2]),
        Self(<Goldilocks as BinomiallyExtendable<5>>::EXT_GENERATOR[3]),
        Self(<Goldilocks as BinomiallyExtendable<5>>::EXT_GENERATOR[4]),
    ];
}

impl HasTwoAdicBinomialExtension<5> for Felt {
    const EXT_TWO_ADICITY: usize = <Goldilocks as HasTwoAdicBinomialExtension<5>>::EXT_TWO_ADICITY;

    #[inline]
    fn ext_two_adic_generator(bits: usize) -> [Self; 5] {
        let ext_generator =
            <Goldilocks as HasTwoAdicBinomialExtension<5>>::ext_two_adic_generator(bits);
        [
            Self(ext_generator[0]),
            Self(ext_generator[1]),
            Self(ext_generator[2]),
            Self(ext_generator[3]),
            Self(ext_generator[4]),
        ]
    }
}

impl RawDataSerializable for Felt {
    impl_raw_serializable_primefield64!();
}

impl Distribution<Felt> for StandardUniform {
    #[inline]
    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Felt {
        let inner = <StandardUniform as Distribution<Goldilocks>>::sample(self, rng);
        Felt(inner)
    }
}

impl UniformSamplingField for Felt {
    const MAX_SINGLE_SAMPLE_BITS: usize =
        <Goldilocks as UniformSamplingField>::MAX_SINGLE_SAMPLE_BITS;
    const SAMPLING_BITS_M: [u64; 64] = <Goldilocks as UniformSamplingField>::SAMPLING_BITS_M;
}

impl InjectiveMonomial<7> for Felt {}

impl PermutationMonomial<7> for Felt {
    #[inline]
    fn injective_exp_root_n(&self) -> Self {
        Self(self.0.injective_exp_root_n())
    }
}

// CONVERSIONS
// ================================================================================================

impl From<u8> for Felt {
    fn from(int: u8) -> Self {
        Self::from_u8(int)
    }
}

impl From<u16> for Felt {
    fn from(int: u16) -> Self {
        Self::from_u16(int)
    }
}

impl From<u32> for Felt {
    fn from(int: u32) -> Self {
        Self::from_u32(int)
    }
}

impl TryFrom<u64> for Felt {
    type Error = FeltFromIntError;

    fn try_from(int: u64) -> Result<Felt, Self::Error> {
        Felt::new(int)
    }
}

#[derive(Debug, thiserror::Error)]
#[error("integer {0} is equal to or exceeds the felt modulus {modulus}", modulus = Felt::ORDER)]
pub struct FeltFromIntError(u64);

impl FeltFromIntError {
    /// Returns the integer for which the conversion failed.
    pub fn as_u64(&self) -> u64 {
        self.0
    }
}

impl From<Goldilocks> for Felt {
    #[inline]
    fn from(value: Goldilocks) -> Self {
        Self(value)
    }
}

impl From<Felt> for Goldilocks {
    #[inline]
    fn from(value: Felt) -> Self {
        value.0
    }
}

// ARITHMETIC OPERATIONS
// ================================================================================================

impl Add for Felt {
    type Output = Self;

    #[inline]
    fn add(self, other: Self) -> Self {
        Self(self.0 + other.0)
    }
}

impl AddAssign for Felt {
    #[inline]
    fn add_assign(&mut self, other: Self) {
        *self = *self + other;
    }
}

impl Sub for Felt {
    type Output = Self;

    #[inline]
    fn sub(self, other: Self) -> Self {
        Self(self.0 - other.0)
    }
}

impl SubAssign for Felt {
    #[inline]
    fn sub_assign(&mut self, other: Self) {
        *self = *self - other;
    }
}

impl Mul for Felt {
    type Output = Self;

    #[inline]
    fn mul(self, other: Self) -> Self {
        Self(self.0 * other.0)
    }
}

impl MulAssign for Felt {
    #[inline]
    fn mul_assign(&mut self, other: Self) {
        *self = *self * other;
    }
}

impl Div for Felt {
    type Output = Self;

    #[inline]
    fn div(self, other: Self) -> Self {
        Self(self.0 / other.0)
    }
}

impl DivAssign for Felt {
    #[inline]
    fn div_assign(&mut self, other: Self) {
        *self = *self / other;
    }
}

impl Neg for Felt {
    type Output = Self;

    #[inline]
    fn neg(self) -> Self {
        Self(-self.0)
    }
}

impl Sum for Felt {
    #[inline]
    fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
        Self(iter.map(|x| x.0).sum())
    }
}

impl<'a> Sum<&'a Felt> for Felt {
    #[inline]
    fn sum<I: Iterator<Item = &'a Felt>>(iter: I) -> Self {
        Self(iter.map(|x| x.0).sum())
    }
}

impl Product for Felt {
    #[inline]
    fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
        Self(iter.map(|x| x.0).product())
    }
}

impl<'a> Product<&'a Felt> for Felt {
    #[inline]
    fn product<I: Iterator<Item = &'a Felt>>(iter: I) -> Self {
        Self(iter.map(|x| x.0).product())
    }
}

// EQUALITY AND COMPARISON OPERATIONS
// ================================================================================================

impl PartialEq for Felt {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.0 == other.0
    }
}

impl PartialEq<Goldilocks> for Felt {
    #[inline]
    fn eq(&self, other: &Goldilocks) -> bool {
        self.0 == *other
    }
}

impl Eq for Felt {}

impl PartialOrd for Felt {
    #[inline]
    fn partial_cmp(&self, other: &Self) -> Option<core::cmp::Ordering> {
        Some(self.cmp(other))
    }
}

impl Ord for Felt {
    #[inline]
    fn cmp(&self, other: &Self) -> core::cmp::Ordering {
        self.0.cmp(&other.0)
    }
}

// SERIALIZATION
// ================================================================================================

impl Serializable for Felt {
    fn write_into<W: ByteWriter>(&self, target: &mut W) {
        target.write_u64(self.as_canonical_u64());
    }

    fn get_size_hint(&self) -> usize {
        size_of::<u64>()
    }
}

impl Deserializable for Felt {
    fn read_from<R: ByteReader>(source: &mut R) -> Result<Self, DeserializationError> {
        let value = source.read_u64()?;
        Self::from_canonical_checked(value).ok_or_else(|| {
            DeserializationError::InvalidValue(format!("value {value} is not a valid felt"))
        })
    }
}

// ARBITRARY (proptest)
// ================================================================================================

#[cfg(all(any(test, feature = "arbitrary"), not(all(target_family = "wasm", miden))))]
mod arbitrary {
    use proptest::prelude::*;

    use super::Felt;

    impl Arbitrary for Felt {
        type Parameters = ();
        type Strategy = BoxedStrategy<Self>;

        fn arbitrary_with(_args: Self::Parameters) -> Self::Strategy {
            prop_oneof![4 => arb_felt_canonical(), 1 => arb_felt_noncanonical()].boxed()
        }
    }

    /// Boundary values of the canonical regime, hit by construction: zero,
    /// one, both sides of the 2^32 seam, and the two elements adjacent to
    /// the modulus. The edge index derives from `r / 8` — a component
    /// independent of the branch gate `r % 8` (the run-#84 correlation
    /// lesson).
    pub(super) const CANONICAL_EDGES: [u64; 6] =
        [0, 1, (1 << 32) - 1, 1 << 32, Felt::ORDER - 2, Felt::ORDER - 1];

    /// Generates field elements with canonical representations: ~7/8 of
    /// draws are uniform over `[0, ORDER)` and ~1/8 are boundary values
    /// hit by construction (uniform sampling leaves them measure-zero,
    /// which under-covers every wire test's Felt fields). The branch gate
    /// and the value draw are INDEPENDENT components — deriving both from
    /// one `u64` would remove every canonical value congruent to the gate
    /// class from the generator's range (the run-#84 correlation lesson at
    /// full depth).
    pub fn arb_felt_canonical() -> impl Strategy<Value = Felt> {
        (any::<u64>(), any::<u64>()).prop_map(|(gate, value)| {
            if gate % 8 == 7 {
                Felt::new_unchecked(CANONICAL_EDGES[(gate / 8) as usize % CANONICAL_EDGES.len()])
            } else {
                Felt::new_unchecked(value % Felt::ORDER)
            }
        })
    }

    /// Boundary values of the non-canonical regime: the first and last
    /// non-canonical representations (ORDER aliases canonical zero;
    /// u64::MAX is the largest).
    pub(super) const NONCANONICAL_EDGES: [u64; 3] = [Felt::ORDER, u64::MAX - 1, u64::MAX];

    /// Generates field elements with non-canonical representations: ~3/4
    /// uniform over `[ORDER, u64::MAX]` and ~1/4 boundary values, with the
    /// same independent gate/value components as the canonical adapter.
    pub fn arb_felt_noncanonical() -> impl Strategy<Value = Felt> {
        (any::<u64>(), any::<u64>()).prop_map(|(gate, value)| {
            if gate % 4 == 3 {
                Felt::new_unchecked(
                    NONCANONICAL_EDGES[(gate / 4) as usize % NONCANONICAL_EDGES.len()],
                )
            } else {
                Felt::new_unchecked(Felt::ORDER + value % (u64::MAX - Felt::ORDER + 1))
            }
        })
    }
}

#[cfg(all(any(test, feature = "arbitrary"), not(all(target_family = "wasm", miden))))]
pub use arbitrary::{arb_felt_canonical, arb_felt_noncanonical};

#[cfg(all(test, not(all(target_family = "wasm", miden))))]
mod arbitrary_boundary_tests {
    use proptest::{
        strategy::{Strategy, ValueTree},
        test_runner::TestRunner,
    };

    use super::{
        Felt,
        arbitrary::{
            CANONICAL_EDGES, NONCANONICAL_EDGES, arb_felt_canonical, arb_felt_noncanonical,
        },
    };

    /// The boundary values are reachable BY CONSTRUCTION — pin it
    /// empirically so a future refactor of the branch gating cannot
    /// silently drop edges (the run-#84 correlation regression).
    #[test]
    fn boundary_values_are_reached_by_construction() {
        let mut runner = TestRunner::deterministic();
        let samples = 10_000;

        let mut canonical_hits = [0usize; CANONICAL_EDGES.len()];
        for _ in 0..samples {
            let felt = arb_felt_canonical().new_tree(&mut runner).unwrap().current();
            for (i, edge) in CANONICAL_EDGES.iter().enumerate() {
                if super::raw_felt_u64(felt) == *edge {
                    canonical_hits[i] += 1;
                }
            }
        }
        for (edge, hits) in CANONICAL_EDGES.iter().zip(canonical_hits) {
            assert!(hits > 0, "canonical boundary {edge} never sampled");
        }

        let mut noncanonical_hits = [0usize; NONCANONICAL_EDGES.len()];
        for _ in 0..samples {
            let felt = arb_felt_noncanonical().new_tree(&mut runner).unwrap().current();
            for (i, edge) in NONCANONICAL_EDGES.iter().enumerate() {
                if super::raw_felt_u64(felt) == *edge {
                    noncanonical_hits[i] += 1;
                }
            }
        }
        for (edge, hits) in NONCANONICAL_EDGES.iter().zip(noncanonical_hits) {
            assert!(hits > 0, "non-canonical boundary {edge} never sampled");
        }

        // The canonical adapter never leaves the canonical regime.
        for _ in 0..samples {
            let felt = arb_felt_canonical().new_tree(&mut runner).unwrap().current();
            assert!(
                super::raw_felt_u64(felt) < Felt::ORDER,
                "canonical adapter emitted a non-canonical element",
            );
        }

        // Every residue class mod 8 must occur among NON-boundary draws —
        // pinning that the gate and the value are independent components
        // (deriving both from one u64 removes the gate class from the
        // generator's range, the run-#430 regression).
        let mut residue_seen = [false; 8];
        for _ in 0..samples {
            let felt = arb_felt_canonical().new_tree(&mut runner).unwrap().current();
            let raw = super::raw_felt_u64(felt);
            if !CANONICAL_EDGES.contains(&raw) {
                residue_seen[(raw % 8) as usize] = true;
            }
        }
        assert!(
            residue_seen.iter().all(|&seen| seen),
            "a residue class mod 8 is missing from non-boundary draws: {residue_seen:?}",
        );
    }
}