binius_field/
packed_extension.rs

Help
// Copyright 2023-2025 Irreducible Inc.

use crate::{
	as_packed_field::PackScalar,
	underlier::{Divisible, WithUnderlier},
	ExtensionField, Field, PackedField,
};

/// A [`PackedField`] that can be safely cast to indexable slices of scalars.
///
/// Not all packed fields can index individual scalar elements. Notably, packed fields of
/// $\mathbb{F}_2$ elements can pack multiple scalars into a single byte.
///
///
/// # Safety
///
/// In order for the above relation to be guaranteed, the memory representation of a slice of
/// `PackedExtensionIndexable` elements must be the same as a slice of the underlying scalar
/// elements, differing only in the slice lengths.
pub unsafe trait PackedFieldIndexable: PackedField {
	fn unpack_scalars(packed: &[Self]) -> &[Self::Scalar];
	fn unpack_scalars_mut(packed: &mut [Self]) -> &mut [Self::Scalar];
}

unsafe impl<S, P> PackedFieldIndexable for P
where
	S: Field,
	P: PackedDivisible<S, Scalar = S>,
{
	fn unpack_scalars(packed: &[Self]) -> &[Self::Scalar] {
		P::divide(packed)
	}

	fn unpack_scalars_mut(packed: &mut [Self]) -> &mut [Self::Scalar] {
		P::divide_mut(packed)
	}
}

/// Trait represents a relationship between a packed struct of field elements and a packed struct
/// of elements from an extension field.
///
/// This trait guarantees that one packed type has the same
/// memory representation as the other, differing only in the scalar type and preserving the order
/// of smaller elements.
///
/// This trait relation guarantees that the following iterators yield the same sequence of scalar
/// elements:
///
/// ```
/// use binius_field::{ExtensionField, PackedExtension, PackedField, Field};
///
/// fn ext_then_bases<'a, F, PE>(packed: &'a PE) -> impl Iterator<Item=F> + 'a
///     where
///         PE: PackedField<Scalar: ExtensionField<F>>,
///         F: Field,
/// {
///     packed.iter().flat_map(|ext| ext.into_iter_bases())
/// }
///
/// fn cast_then_iter<'a, F, PE>(packed: &'a PE) -> impl Iterator<Item=F> + 'a
///     where
///         PE: PackedExtension<F, Scalar: ExtensionField<F>>,
///         F: Field,
/// {
///     PE::cast_base_ref(packed).into_iter()
/// }
/// ```
///
/// # Safety
///
/// In order for the above relation to be guaranteed, the memory representation of
/// `PackedExtensionField` element must be the same as a slice of the underlying `PackedField`
/// element.
pub trait PackedExtension<FS: Field>: PackedField
where
	Self::Scalar: ExtensionField<FS>,
{
	type PackedSubfield: PackedField<Scalar = FS>;

	fn cast_bases(packed: &[Self]) -> &[Self::PackedSubfield];
	fn cast_bases_mut(packed: &mut [Self]) -> &mut [Self::PackedSubfield];

	fn cast_exts(packed: &[Self::PackedSubfield]) -> &[Self];
	fn cast_exts_mut(packed: &mut [Self::PackedSubfield]) -> &mut [Self];

	fn cast_base(self) -> Self::PackedSubfield;
	fn cast_base_ref(&self) -> &Self::PackedSubfield;
	fn cast_base_mut(&mut self) -> &mut Self::PackedSubfield;

	fn cast_ext(base: Self::PackedSubfield) -> Self;
	fn cast_ext_ref(base: &Self::PackedSubfield) -> &Self;
	fn cast_ext_mut(base: &mut Self::PackedSubfield) -> &mut Self;
}

impl<PT, FS> PackedExtension<FS> for PT
where
	FS: Field,
	PT: PackedField<Scalar: ExtensionField<FS>> + WithUnderlier<Underlier: PackScalar<FS>>,
{
	type PackedSubfield = <PT::Underlier as PackScalar<FS>>::Packed;

	fn cast_bases(packed: &[Self]) -> &[Self::PackedSubfield] {
		Self::PackedSubfield::from_underliers_ref(Self::to_underliers_ref(packed))
	}

	fn cast_bases_mut(packed: &mut [Self]) -> &mut [Self::PackedSubfield] {
		Self::PackedSubfield::from_underliers_ref_mut(Self::to_underliers_ref_mut(packed))
	}

	fn cast_exts(base: &[Self::PackedSubfield]) -> &[Self] {
		Self::from_underliers_ref(Self::PackedSubfield::to_underliers_ref(base))
	}

	fn cast_exts_mut(base: &mut [Self::PackedSubfield]) -> &mut [Self] {
		Self::from_underliers_ref_mut(Self::PackedSubfield::to_underliers_ref_mut(base))
	}

	fn cast_base(self) -> Self::PackedSubfield {
		Self::PackedSubfield::from_underlier(self.to_underlier())
	}

	fn cast_base_ref(&self) -> &Self::PackedSubfield {
		Self::PackedSubfield::from_underlier_ref(self.to_underlier_ref())
	}

	fn cast_base_mut(&mut self) -> &mut Self::PackedSubfield {
		Self::PackedSubfield::from_underlier_ref_mut(self.to_underlier_ref_mut())
	}

	fn cast_ext(base: Self::PackedSubfield) -> Self {
		Self::from_underlier(base.to_underlier())
	}

	fn cast_ext_ref(base: &Self::PackedSubfield) -> &Self {
		Self::from_underlier_ref(base.to_underlier_ref())
	}

	fn cast_ext_mut(base: &mut Self::PackedSubfield) -> &mut Self {
		Self::from_underlier_ref_mut(base.to_underlier_ref_mut())
	}
}

/// Convenient type alias that returns the packed field type for the scalar field `F` and packed
/// extension `P`.
pub type PackedSubfield<P, F> = <P as PackedExtension<F>>::PackedSubfield;

/// Recast a packed field from one subfield of a packed extension to another.
pub fn recast_packed<P, FSub1, FSub2>(elem: PackedSubfield<P, FSub1>) -> PackedSubfield<P, FSub2>
where
	P: PackedField + PackedExtension<FSub1> + PackedExtension<FSub2>,
	P::Scalar: ExtensionField<FSub1> + ExtensionField<FSub2>,
	FSub1: Field,
	FSub2: Field,
{
	<P as PackedExtension<FSub2>>::cast_base(<P as PackedExtension<FSub1>>::cast_ext(elem))
}

/// Recast a slice of packed field elements from one subfield of a packed extension to another.
pub fn recast_packed_slice<P, FSub1, FSub2>(
	elems: &[PackedSubfield<P, FSub1>],
) -> &[PackedSubfield<P, FSub2>]
where
	P: PackedField + PackedExtension<FSub1> + PackedExtension<FSub2>,
	P::Scalar: ExtensionField<FSub1> + ExtensionField<FSub2>,
	FSub1: Field,
	FSub2: Field,
{
	<P as PackedExtension<FSub2>>::cast_bases(<P as PackedExtension<FSub1>>::cast_exts(elems))
}

/// Recast a mutable slice of packed field elements from one subfield of a packed extension to
/// another.
pub fn recast_packed_mut<P, FSub1, FSub2>(
	elems: &mut [PackedSubfield<P, FSub1>],
) -> &mut [PackedSubfield<P, FSub2>]
where
	P: PackedField + PackedExtension<FSub1> + PackedExtension<FSub2>,
	P::Scalar: ExtensionField<FSub1> + ExtensionField<FSub2>,
	FSub1: Field,
	FSub2: Field,
{
	<P as PackedExtension<FSub2>>::cast_bases_mut(<P as PackedExtension<FSub1>>::cast_exts_mut(
		elems,
	))
}

/// This trait is a shorthand for the case `PackedExtension<P::Scalar, PackedSubfield = P>` which is a
/// quite common case in our codebase.
pub trait RepackedExtension<P: PackedField>:
	PackedExtension<P::Scalar, PackedSubfield = P>
where
	Self::Scalar: ExtensionField<P::Scalar>,
{
}

impl<PT1, PT2> RepackedExtension<PT1> for PT2
where
	PT1: PackedField,
	PT2: PackedExtension<PT1::Scalar, PackedSubfield = PT1, Scalar: ExtensionField<PT1::Scalar>>,
{
}

/// This trait adds shortcut methods for the case `PackedExtension<F, PackedSubfield: PackedFieldIndexable>` which is a
/// quite common case in our codebase.
pub trait PackedExtensionIndexable<F: Field>: PackedExtension<F>
where
	Self::Scalar: ExtensionField<F>,
	Self::PackedSubfield: PackedFieldIndexable,
{
	fn unpack_base_scalars(packed: &[Self]) -> &[F] {
		Self::PackedSubfield::unpack_scalars(Self::cast_bases(packed))
	}

	fn unpack_base_scalars_mut(packed: &mut [Self]) -> &mut [F] {
		Self::PackedSubfield::unpack_scalars_mut(Self::cast_bases_mut(packed))
	}
}

impl<F, PT> PackedExtensionIndexable<F> for PT
where
	F: Field,
	PT: PackedExtension<F, Scalar: ExtensionField<F>, PackedSubfield: PackedFieldIndexable>,
{
}

/// Trait represents a relationship between a packed struct of field elements and a smaller packed
/// struct the same field elements.
///
/// This trait can be used to safely cast memory slices from larger packed fields to smaller ones.
///
/// # Safety
///
/// In order for the above relation to be guaranteed, the memory representation of a slice of
/// `PackedDivisible` elements must be the same as a slice of the underlying `PackedField`
/// elements, differing only in the slice lengths.
pub unsafe trait PackedDivisible<P>: PackedField
where
	P: PackedField<Scalar = Self::Scalar>,
{
	fn divide(packed: &[Self]) -> &[P];
	fn divide_mut(packed: &mut [Self]) -> &mut [P];
}

unsafe impl<PT1, PT2> PackedDivisible<PT2> for PT1
where
	PT2: PackedField + WithUnderlier,
	PT1: PackedField<Scalar = PT2::Scalar> + WithUnderlier<Underlier: Divisible<PT2::Underlier>>,
{
	fn divide(packed: &[Self]) -> &[PT2] {
		let underliers = PT1::to_underliers_ref(packed);
		let underliers: &[PT2::Underlier] = PT1::Underlier::split_slice(underliers);
		PT2::from_underliers_ref(underliers)
	}

	fn divide_mut(packed: &mut [Self]) -> &mut [PT2] {
		let underliers = PT1::to_underliers_ref_mut(packed);
		let underliers: &mut [PT2::Underlier] = PT1::Underlier::split_slice_mut(underliers);
		PT2::from_underliers_ref_mut(underliers)
	}
}
binius_field/packed_extension.rs

binius_field/
packed_extension.rs
