binius_field/arch/portable/byte_sliced/

packed_byte_sliced.rs

// Copyright 2024-2025 Irreducible Inc.

use std::{
	array,
	fmt::Debug,
	iter::{Product, Sum, zip},
	ops::{Add, AddAssign, Mul, MulAssign, Sub, SubAssign},
};

use binius_utils::checked_arithmetics::checked_log_2;
use bytemuck::{Pod, Zeroable};

use super::{invert::invert_or_zero, multiply::mul, square::square};
use crate::{
	AESTowerField8b, AESTowerField16b, AESTowerField32b, AESTowerField64b, AESTowerField128b,
	BinaryField1b, ExtensionField, PackedAESBinaryField16x8b, PackedAESBinaryField64x8b,
	PackedBinaryField128x1b, PackedBinaryField256x1b, PackedBinaryField512x1b, PackedExtension,
	PackedField,
	arch::{
		byte_sliced::underlier::ByteSlicedUnderlier, portable::packed_scaled::ScaledPackedField,
	},
	as_packed_field::{PackScalar, PackedType},
	binary_field::BinaryField,
	linear_transformation::{
		FieldLinearTransformation, IDTransformation, PackedTransformationFactory, Transformation,
	},
	packed_aes_field::PackedAESBinaryField32x8b,
	tower_levels::{TowerLevel, TowerLevel1, TowerLevel2, TowerLevel4, TowerLevel8, TowerLevel16},
	underlier::{UnderlierWithBitOps, WithUnderlier},
};

/// Packed transformation for byte-sliced fields with a scalar bigger than 8b.
///
/// `N` is the number of bytes in the scalar.
pub struct TransformationWrapperNxN<Inner, const N: usize>([[Inner; N]; N]);

/// Byte-sliced packed field with a fixed size (16x$packed_storage).
/// For example for 32-bit scalar the data layout is the following:
///
/// ```plain
/// [ element_0[0], element_4[0], ... ]
/// [ element_0[1], element_4[1], ... ]
/// [ element_0[2], element_4[2], ... ]
/// [ element_0[3], element_4[3], ... ]
/// [ element_1[0], element_5[0], ... ]
/// [ element_1[1], element_5[1], ... ]
/// ...
/// ```
macro_rules! define_byte_sliced_3d {
	($name:ident, $scalar_type:ty, $packed_storage:ty, $scalar_tower_level: ty, $storage_tower_level: ty) => {
		#[derive(Clone, Copy, PartialEq, Eq, Pod, Zeroable)]
		#[repr(transparent)]
		pub struct $name {
			pub(super) data: [[$packed_storage; <$scalar_tower_level as TowerLevel>::WIDTH]; <$storage_tower_level as TowerLevel>::WIDTH / <$scalar_tower_level as TowerLevel>::WIDTH],
		}

		impl $name {
			pub const BYTES: usize = <$storage_tower_level as TowerLevel>::WIDTH * <$packed_storage>::WIDTH;

			const SCALAR_BYTES: usize = <$scalar_type>::N_BITS / 8;
			pub const HEIGHT_BYTES: usize = <$storage_tower_level as TowerLevel>::WIDTH;
			const HEIGHT: usize = Self::HEIGHT_BYTES / Self::SCALAR_BYTES;
			const LOG_HEIGHT: usize = checked_log_2(Self::HEIGHT);

			/// Get the byte at the given index.
			///
			/// # Safety
			/// The caller must ensure that `byte_index` is less than `BYTES`.
			#[allow(clippy::modulo_one)]
			#[inline(always)]
			pub unsafe fn get_byte_unchecked(&self, byte_index: usize) -> u8 {
				let row = byte_index % Self::HEIGHT_BYTES;
				unsafe {
					self.data
						.get_unchecked(row / Self::SCALAR_BYTES)
						.get_unchecked(row % Self::SCALAR_BYTES)
						.get_unchecked(byte_index / Self::HEIGHT_BYTES)
						.to_underlier()
				}
			}

			/// Convert the byte-sliced field to an array of "ordinary" packed fields preserving the order of scalars.
			#[inline]
			pub fn transpose_to(&self, out: &mut [<<$packed_storage as WithUnderlier>::Underlier as PackScalar<$scalar_type>>::Packed; Self::HEIGHT_BYTES]) {
				let underliers = WithUnderlier::to_underliers_arr_ref_mut(out);
				*underliers = bytemuck::must_cast(self.data);

				UnderlierWithBitOps::transpose_bytes_from_byte_sliced::<$storage_tower_level>(underliers);
			}

			/// Convert an array of "ordinary" packed fields to a byte-sliced field preserving the order of scalars.
			#[inline]
			pub fn transpose_from(
				underliers: &[<<$packed_storage as WithUnderlier>::Underlier as PackScalar<$scalar_type>>::Packed; Self::HEIGHT_BYTES],
			) -> Self {
				let mut result = Self {
					data: bytemuck::must_cast(*underliers),
				};

				<$packed_storage as WithUnderlier>::Underlier::transpose_bytes_to_byte_sliced::<$storage_tower_level>(bytemuck::must_cast_mut(&mut result.data));

				result
			}
		}

		impl Default for $name {
			fn default() -> Self {
				Self {
					data: bytemuck::Zeroable::zeroed(),
				}
			}
		}

		impl Debug for $name {
			fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
				let values_str = self
					.iter()
					.map(|value| format!("{}", value))
					.collect::<Vec<_>>()
					.join(",");

				write!(f, "ByteSlicedAES{}x{}([{}])", Self::WIDTH, <$scalar_type>::N_BITS, values_str)
			}
		}

		impl PackedField for $name {
			type Scalar = $scalar_type;

			const LOG_WIDTH: usize = <$packed_storage>::LOG_WIDTH + Self::LOG_HEIGHT;

			#[allow(clippy::modulo_one)]
			#[inline(always)]
			unsafe fn get_unchecked(&self, i: usize) -> Self::Scalar {
				let element_rows = unsafe { self.data.get_unchecked(i % Self::HEIGHT) };
				Self::Scalar::from_bases((0..Self::SCALAR_BYTES).map(|byte_index| unsafe {
					element_rows
						.get_unchecked(byte_index)
						.get_unchecked(i / Self::HEIGHT)
				}))
				.expect("byte index is within bounds")
			}

			#[allow(clippy::modulo_one)]
			#[inline(always)]
			unsafe fn set_unchecked(&mut self, i: usize, scalar: Self::Scalar) {
				let element_rows = unsafe { self.data.get_unchecked_mut(i % Self::HEIGHT) };
				for byte_index in 0..Self::SCALAR_BYTES {
					unsafe {
						element_rows
							.get_unchecked_mut(byte_index)
							.set_unchecked(
								i / Self::HEIGHT,
								scalar.get_base_unchecked(byte_index),
							);
					}
				}
			}

			fn random(mut rng: impl rand::RngCore) -> Self {
				let data = array::from_fn(|_| array::from_fn(|_| <$packed_storage>::random(&mut rng)));
				Self { data }
			}

			#[allow(unreachable_patterns)]
			#[inline]
			fn broadcast(scalar: Self::Scalar) -> Self {
				let data: [[$packed_storage; Self::SCALAR_BYTES]; Self::HEIGHT] = match Self::SCALAR_BYTES {
					1 => {
						let packed_broadcast =
							<$packed_storage>::broadcast(unsafe { scalar.get_base_unchecked(0) });
						array::from_fn(|_| array::from_fn(|_| packed_broadcast))
					}
					Self::HEIGHT_BYTES => array::from_fn(|_| array::from_fn(|byte_index| {
						<$packed_storage>::broadcast(unsafe {
							scalar.get_base_unchecked(byte_index)
						})
					})),
					_ => {
						let mut data = <[[$packed_storage; Self::SCALAR_BYTES]; Self::HEIGHT]>::zeroed();
						for byte_index in 0..Self::SCALAR_BYTES {
							let broadcast = <$packed_storage>::broadcast(unsafe {
								scalar.get_base_unchecked(byte_index)
							});

							for i in 0..Self::HEIGHT {
								data[i][byte_index] = broadcast;
							}
						}

						data
					}
				};

				Self { data }
			}

			impl_init_with_transpose!($packed_storage, $scalar_type, $storage_tower_level);

			// Transposing values first is faster. Also we know that the scalar is at least 8b,
			// so we can cast the transposed array to the array of scalars.
			#[inline]
			fn iter(&self) -> impl Iterator<Item = Self::Scalar> + Clone + Send + '_ {
				type TransposePacked = <<$packed_storage as WithUnderlier>::Underlier as PackScalar<$scalar_type>>::Packed;

				let mut data: [TransposePacked; Self::HEIGHT_BYTES] = bytemuck::must_cast(self.data);
				let mut underliers = WithUnderlier::to_underliers_arr_ref_mut(&mut data);
				UnderlierWithBitOps::transpose_bytes_from_byte_sliced::<$storage_tower_level>(&mut underliers);

				let data: [Self::Scalar; {Self::WIDTH}] = bytemuck::must_cast(data);
				data.into_iter()
			}

			#[inline]
			fn into_iter(self) -> impl Iterator<Item = Self::Scalar> + Clone + Send {
				type TransposePacked = <<$packed_storage as WithUnderlier>::Underlier as PackScalar<$scalar_type>>::Packed;

				let mut data: [TransposePacked; Self::HEIGHT_BYTES] = bytemuck::must_cast(self.data);
				let mut underliers = WithUnderlier::to_underliers_arr_ref_mut(&mut data);
				UnderlierWithBitOps::transpose_bytes_from_byte_sliced::<$storage_tower_level>(&mut underliers);

				let data: [Self::Scalar; {Self::WIDTH}] = bytemuck::must_cast(data);
				data.into_iter()
			}

			#[inline]
			fn square(self) -> Self {
				let mut result = Self::default();

				for i in 0..Self::HEIGHT {
					square::<$packed_storage, $scalar_tower_level>(
						&self.data[i],
						&mut result.data[i],
					);
				}

				result
			}

			#[inline]
			fn invert_or_zero(self) -> Self {
				let mut result = Self::default();

				for i in 0..Self::HEIGHT {
					invert_or_zero::<$packed_storage, $scalar_tower_level>(
						&self.data[i],
						&mut result.data[i],
					);
				}

				result
			}

			#[inline(always)]
			fn interleave(self, other: Self, log_block_len: usize) -> (Self, Self) {

				let self_data: &[$packed_storage; Self::HEIGHT_BYTES] = bytemuck::must_cast_ref(&self.data);
				let other_data: &[$packed_storage; Self::HEIGHT_BYTES] = bytemuck::must_cast_ref(&other.data);

				// This implementation is faster than using a loop with `copy_from_slice` for the first 4 cases
				let (data_1, data_2) = interleave_byte_sliced(self_data, other_data, log_block_len + checked_log_2(Self::SCALAR_BYTES));
				(
					Self {
						data: bytemuck::must_cast(data_1),
					},
					Self {
						data: bytemuck::must_cast(data_2),
					},
				)
			}

			#[inline]
			fn unzip(self, other: Self, log_block_len: usize) -> (Self, Self) {
				let (result1, result2) = unzip_byte_sliced::<$packed_storage, {Self::HEIGHT_BYTES}, {Self::SCALAR_BYTES}>(bytemuck::must_cast_ref(&self.data), bytemuck::must_cast_ref(&other.data), log_block_len + checked_log_2(Self::SCALAR_BYTES));

				(
					Self {
						data: bytemuck::must_cast(result1),
					},
					Self {
						data: bytemuck::must_cast(result2),
					},
				)
			}

			impl_spread!($name, $scalar_type, $packed_storage, $storage_tower_level);
		}

		impl Mul for $name {
			type Output = Self;

			#[inline]
			fn mul(self, rhs: Self) -> Self {
				let mut result = Self::default();

				for i in 0..Self::HEIGHT {
					mul::<$packed_storage, $scalar_tower_level>(
						&self.data[i],
						&rhs.data[i],
						&mut result.data[i],
					);
				}

				result
			}
		}

		impl Add for $name {
			type Output = Self;

			#[inline]
			fn add(self, rhs: Self) -> Self {
				Self {
					data: array::from_fn(|byte_number| {
						array::from_fn(|column|
							self.data[byte_number][column] + rhs.data[byte_number][column]
						)
					}),
				}
			}
		}

		impl AddAssign for $name {
			#[inline]
			fn add_assign(&mut self, rhs: Self) {
				for (data, rhs) in zip(&mut self.data, &rhs.data) {
					for (data, rhs) in zip(data, rhs) {
						*data += *rhs
					}
				}
			}
		}

		byte_sliced_common!($name, $packed_storage, $scalar_type, $storage_tower_level);

		impl<Inner: Transformation<$packed_storage, $packed_storage>> Transformation<$name, $name> for TransformationWrapperNxN<Inner, {<$scalar_tower_level as TowerLevel>::WIDTH}> {
			fn transform(&self, data: &$name) -> $name {
				let mut result = <$name>::default();

				for row in 0..<$name>::SCALAR_BYTES {
					for col in 0..<$name>::SCALAR_BYTES {
						let transformation = &self.0[col][row];

						for i in 0..<$name>::HEIGHT {
							result.data[i][row] += transformation.transform(&data.data[i][col]);
						}
					}
				}

				result
			}
		}

		impl PackedTransformationFactory<$name> for $name {
			type PackedTransformation<Data: AsRef<[<$name as PackedField>::Scalar]> + Sync> = TransformationWrapperNxN<<$packed_storage as  PackedTransformationFactory<$packed_storage>>::PackedTransformation::<[AESTowerField8b; 8]>, {<$scalar_tower_level as TowerLevel>::WIDTH}>;

			fn make_packed_transformation<Data: AsRef<[<$name as PackedField>::Scalar]> + Sync>(
				transformation: FieldLinearTransformation<<$name as PackedField>::Scalar, Data>,
			) -> Self::PackedTransformation<Data> {
				let transformations_8b = array::from_fn(|row| {
					array::from_fn(|col| {
						let row = row * 8;
						let linear_transformation_8b = array::from_fn::<_, 8, _>(|row_8b| unsafe {
							<<$name as PackedField>::Scalar as ExtensionField<AESTowerField8b>>::get_base_unchecked(&transformation.bases()[row + row_8b], col)
						});

						<$packed_storage as PackedTransformationFactory<$packed_storage
						>>::make_packed_transformation(FieldLinearTransformation::new(linear_transformation_8b))
					})
				});

				TransformationWrapperNxN(transformations_8b)
			}
		}
	};
}

/// This macro implements the `from_fn` and `from_scalars` methods for byte-sliced packed fields
/// using transpose operations. This is faster both for 1b and non-1b scalars.
macro_rules! impl_init_with_transpose {
	($packed_storage:ty, $scalar_type:ty, $storage_tower_level:ty) => {
		#[inline]
		fn from_fn(mut f: impl FnMut(usize) -> Self::Scalar) -> Self {
			type TransposePacked =
				<<$packed_storage as WithUnderlier>::Underlier as PackScalar<$scalar_type>>::Packed;

			let mut data: [TransposePacked; Self::HEIGHT_BYTES] = array::from_fn(|i| {
				PackedField::from_fn(|j| f((i << TransposePacked::LOG_WIDTH) + j))
			});
			let mut underliers = WithUnderlier::to_underliers_arr_ref_mut(&mut data);
			UnderlierWithBitOps::transpose_bytes_to_byte_sliced::<$storage_tower_level>(
				&mut underliers,
			);

			Self {
				data: bytemuck::must_cast(data),
			}
		}

		#[inline]
		fn from_scalars(scalars: impl IntoIterator<Item = Self::Scalar>) -> Self {
			type TransposePacked =
				<<$packed_storage as WithUnderlier>::Underlier as PackScalar<$scalar_type>>::Packed;

			let mut data = [TransposePacked::default(); Self::HEIGHT_BYTES];
			let mut iter = scalars.into_iter();
			for v in data.iter_mut() {
				*v = TransposePacked::from_scalars(&mut iter);
			}

			let mut underliers = WithUnderlier::to_underliers_arr_ref_mut(&mut data);
			UnderlierWithBitOps::transpose_bytes_to_byte_sliced::<$storage_tower_level>(
				&mut underliers,
			);

			Self {
				data: bytemuck::must_cast(data),
			}
		}
	};
}

macro_rules! impl_spread {
	($name:ident, $scalar_type:ty, $packed_storage:ty, $storage_tower_level:ty) => {
		#[inline]
		unsafe fn spread_unchecked(mut self, log_block_len: usize, block_idx: usize) -> Self {
			{
				let data: &mut [$packed_storage; Self::HEIGHT_BYTES] =
					bytemuck::must_cast_mut(&mut self.data);
				let underliers = WithUnderlier::to_underliers_arr_ref_mut(data);
				UnderlierWithBitOps::transpose_bytes_from_byte_sliced::<$storage_tower_level>(
					underliers,
				);
			}

			type PackedSequentialField =
				<<$packed_storage as WithUnderlier>::Underlier as PackScalar<$scalar_type>>::Packed;
			let scaled_data: ScaledPackedField<PackedSequentialField, { Self::HEIGHT_BYTES }> =
				bytemuck::must_cast(self);

			let mut result = unsafe { scaled_data.spread_unchecked(log_block_len, block_idx) };
			let data: &mut [$packed_storage; Self::HEIGHT_BYTES] =
				bytemuck::must_cast_mut(&mut result);
			let underliers = WithUnderlier::to_underliers_arr_ref_mut(data);
			UnderlierWithBitOps::transpose_bytes_to_byte_sliced::<$storage_tower_level>(underliers);
			bytemuck::must_cast(result)
		}
	};
}

macro_rules! byte_sliced_common {
	($name:ident, $packed_storage:ty, $scalar_type:ty, $storage_level:ty) => {
		impl Add<$scalar_type> for $name {
			type Output = Self;

			#[inline]
			fn add(self, rhs: $scalar_type) -> $name {
				self + Self::broadcast(rhs)
			}
		}

		impl AddAssign<$scalar_type> for $name {
			#[inline]
			fn add_assign(&mut self, rhs: $scalar_type) {
				*self += Self::broadcast(rhs)
			}
		}

		impl Sub<$scalar_type> for $name {
			type Output = Self;

			#[inline]
			fn sub(self, rhs: $scalar_type) -> $name {
				self.add(rhs)
			}
		}

		impl SubAssign<$scalar_type> for $name {
			#[inline]
			fn sub_assign(&mut self, rhs: $scalar_type) {
				self.add_assign(rhs)
			}
		}

		impl Mul<$scalar_type> for $name {
			type Output = Self;

			#[inline]
			fn mul(self, rhs: $scalar_type) -> $name {
				self * Self::broadcast(rhs)
			}
		}

		impl MulAssign<$scalar_type> for $name {
			#[inline]
			fn mul_assign(&mut self, rhs: $scalar_type) {
				*self *= Self::broadcast(rhs);
			}
		}

		impl Sub for $name {
			type Output = Self;

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

		impl SubAssign for $name {
			#[inline]
			fn sub_assign(&mut self, rhs: Self) {
				self.add_assign(rhs);
			}
		}

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

		impl Product for $name {
			fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
				let mut result = Self::one();

				let mut is_first_item = true;
				for item in iter {
					if is_first_item {
						result = item;
					} else {
						result *= item;
					}

					is_first_item = false;
				}

				result
			}
		}

		impl Sum for $name {
			fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
				let mut result = Self::zero();

				for item in iter {
					result += item;
				}

				result
			}
		}

		unsafe impl WithUnderlier for $name {
			type Underlier = ByteSlicedUnderlier<
				<$packed_storage as WithUnderlier>::Underlier,
				{ <$storage_level as TowerLevel>::WIDTH },
			>;

			#[inline(always)]
			fn to_underlier(self) -> Self::Underlier {
				bytemuck::must_cast(self)
			}

			#[inline(always)]
			fn to_underlier_ref(&self) -> &Self::Underlier {
				bytemuck::must_cast_ref(self)
			}

			#[inline(always)]
			fn to_underlier_ref_mut(&mut self) -> &mut Self::Underlier {
				bytemuck::must_cast_mut(self)
			}

			#[inline(always)]
			fn to_underliers_ref(val: &[Self]) -> &[Self::Underlier] {
				bytemuck::must_cast_slice(val)
			}

			#[inline(always)]
			fn to_underliers_ref_mut(val: &mut [Self]) -> &mut [Self::Underlier] {
				bytemuck::must_cast_slice_mut(val)
			}

			#[inline(always)]
			fn from_underlier(val: Self::Underlier) -> Self {
				bytemuck::must_cast(val)
			}

			#[inline(always)]
			fn from_underlier_ref(val: &Self::Underlier) -> &Self {
				bytemuck::must_cast_ref(val)
			}

			#[inline(always)]
			fn from_underlier_ref_mut(val: &mut Self::Underlier) -> &mut Self {
				bytemuck::must_cast_mut(val)
			}

			#[inline(always)]
			fn from_underliers_ref(val: &[Self::Underlier]) -> &[Self] {
				bytemuck::must_cast_slice(val)
			}

			#[inline(always)]
			fn from_underliers_ref_mut(val: &mut [Self::Underlier]) -> &mut [Self] {
				bytemuck::must_cast_slice_mut(val)
			}
		}

		impl PackScalar<$scalar_type>
			for ByteSlicedUnderlier<
				<$packed_storage as WithUnderlier>::Underlier,
				{ <$storage_level as TowerLevel>::WIDTH },
			>
		{
			type Packed = $name;
		}
	};
}

/// Special case: byte-sliced packed 1b-fields. The order of bytes in the layout matches the one
/// for a byte-sliced AES field, each byte contains 1b-scalar elements in the natural order.
macro_rules! define_byte_sliced_3d_1b {
	($name:ident, $packed_storage:ty, $storage_tower_level: ty) => {
		#[derive(Clone, Copy, PartialEq, Eq, Pod, Zeroable)]
		#[repr(transparent)]
		pub struct $name {
			pub(super) data: [$packed_storage; <$storage_tower_level>::WIDTH],
		}

		impl $name {
			pub const BYTES: usize =
				<$storage_tower_level as TowerLevel>::WIDTH * <$packed_storage>::WIDTH;

			pub const HEIGHT_BYTES: usize = <$storage_tower_level as TowerLevel>::WIDTH;
			const LOG_HEIGHT: usize = checked_log_2(Self::HEIGHT_BYTES);

			/// Get the byte at the given index.
			///
			/// # Safety
			/// The caller must ensure that `byte_index` is less than `BYTES`.
			#[allow(clippy::modulo_one)]
			#[inline(always)]
			pub unsafe fn get_byte_unchecked(&self, byte_index: usize) -> u8 {
				type Packed8b =
					PackedType<<$packed_storage as WithUnderlier>::Underlier, AESTowerField8b>;

				unsafe {
					Packed8b::cast_ext_ref(self.data.get_unchecked(byte_index % Self::HEIGHT_BYTES))
						.get_unchecked(byte_index / Self::HEIGHT_BYTES)
						.to_underlier()
				}
			}

			/// Convert the byte-sliced field to an array of "ordinary" packed fields preserving the
			/// order of scalars.
			#[inline]
			pub fn transpose_to(
				&self,
				out: &mut [PackedType<<$packed_storage as WithUnderlier>::Underlier, BinaryField1b>;
					     Self::HEIGHT_BYTES],
			) {
				let underliers = WithUnderlier::to_underliers_arr_ref_mut(out);
				*underliers = WithUnderlier::to_underliers_arr(self.data);

				UnderlierWithBitOps::transpose_bytes_from_byte_sliced::<$storage_tower_level>(
					underliers,
				);
			}

			/// Convert an array of "ordinary" packed fields to a byte-sliced field preserving the
			/// order of scalars.
			#[inline]
			pub fn transpose_from(
				underliers: &[PackedType<<$packed_storage as WithUnderlier>::Underlier, BinaryField1b>;
					 Self::HEIGHT_BYTES],
			) -> Self {
				let mut underliers = WithUnderlier::to_underliers_arr(*underliers);

				<$packed_storage as WithUnderlier>::Underlier::transpose_bytes_to_byte_sliced::<
					$storage_tower_level,
				>(&mut underliers);

				Self {
					data: WithUnderlier::from_underliers_arr(underliers),
				}
			}
		}

		impl Default for $name {
			fn default() -> Self {
				Self {
					data: bytemuck::Zeroable::zeroed(),
				}
			}
		}

		impl Debug for $name {
			fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
				let values_str = self
					.iter()
					.map(|value| format!("{}", value))
					.collect::<Vec<_>>()
					.join(",");

				write!(f, "ByteSlicedAES{}x1b([{}])", Self::WIDTH, values_str)
			}
		}

		impl PackedField for $name {
			type Scalar = BinaryField1b;

			const LOG_WIDTH: usize = <$packed_storage>::LOG_WIDTH + Self::LOG_HEIGHT;

			#[allow(clippy::modulo_one)]
			#[inline(always)]
			unsafe fn get_unchecked(&self, i: usize) -> Self::Scalar {
				unsafe {
					self.data
						.get_unchecked((i / 8) % Self::HEIGHT_BYTES)
						.get_unchecked(8 * (i / (Self::HEIGHT_BYTES * 8)) + i % 8)
				}
			}

			#[allow(clippy::modulo_one)]
			#[inline(always)]
			unsafe fn set_unchecked(&mut self, i: usize, scalar: Self::Scalar) {
				unsafe {
					self.data
						.get_unchecked_mut((i / 8) % Self::HEIGHT_BYTES)
						.set_unchecked(8 * (i / (Self::HEIGHT_BYTES * 8)) + i % 8, scalar);
				}
			}

			fn random(mut rng: impl rand::RngCore) -> Self {
				let data = array::from_fn(|_| <$packed_storage>::random(&mut rng));
				Self { data }
			}

			impl_init_with_transpose!($packed_storage, BinaryField1b, $storage_tower_level);

			// Benchmarks show that transposing before the iteration makes it slower for 1b case,
			// so do not override the default implementations of `iter` and `into_iter`.

			#[allow(unreachable_patterns)]
			#[inline]
			fn broadcast(scalar: Self::Scalar) -> Self {
				let underlier = <$packed_storage as WithUnderlier>::Underlier::fill_with_bit(
					scalar.to_underlier().into(),
				);
				Self {
					data: array::from_fn(|_| WithUnderlier::from_underlier(underlier)),
				}
			}

			#[inline]
			fn square(self) -> Self {
				let data = array::from_fn(|i| self.data[i].clone().square());
				Self { data }
			}

			#[inline]
			fn invert_or_zero(self) -> Self {
				let data = array::from_fn(|i| self.data[i].clone().invert_or_zero());
				Self { data }
			}

			#[inline(always)]
			fn interleave(self, other: Self, log_block_len: usize) -> (Self, Self) {
				type Packed8b =
					PackedType<<$packed_storage as WithUnderlier>::Underlier, AESTowerField8b>;

				if log_block_len < 3 {
					let mut result1 = Self::default();
					let mut result2 = Self::default();

					for i in 0..Self::HEIGHT_BYTES {
						(result1.data[i], result2.data[i]) =
							self.data[i].interleave(other.data[i], log_block_len);
					}

					(result1, result2)
				} else {
					let self_data: &[Packed8b; Self::HEIGHT_BYTES] =
						Packed8b::cast_ext_arr_ref(&self.data);
					let other_data: &[Packed8b; Self::HEIGHT_BYTES] =
						Packed8b::cast_ext_arr_ref(&other.data);

					let (result1, result2) =
						interleave_byte_sliced(self_data, other_data, log_block_len - 3);

					(
						Self {
							data: Packed8b::cast_base_arr(result1),
						},
						Self {
							data: Packed8b::cast_base_arr(result2),
						},
					)
				}
			}

			#[inline]
			fn unzip(self, other: Self, log_block_len: usize) -> (Self, Self) {
				if log_block_len < 3 {
					let mut result1 = Self::default();
					let mut result2 = Self::default();

					for i in 0..Self::HEIGHT_BYTES {
						(result1.data[i], result2.data[i]) =
							self.data[i].unzip(other.data[i], log_block_len);
					}

					(result1, result2)
				} else {
					type Packed8b =
						PackedType<<$packed_storage as WithUnderlier>::Underlier, AESTowerField8b>;

					let self_data: &[Packed8b; Self::HEIGHT_BYTES] =
						Packed8b::cast_ext_arr_ref(&self.data);
					let other_data: &[Packed8b; Self::HEIGHT_BYTES] =
						Packed8b::cast_ext_arr_ref(&other.data);

					let (result1, result2) = unzip_byte_sliced::<Packed8b, { Self::HEIGHT_BYTES }, 1>(
						self_data,
						other_data,
						log_block_len - 3,
					);

					(
						Self {
							data: Packed8b::cast_base_arr(result1),
						},
						Self {
							data: Packed8b::cast_base_arr(result2),
						},
					)
				}
			}

			impl_spread!($name, BinaryField1b, $packed_storage, $storage_tower_level);
		}

		impl Mul for $name {
			type Output = Self;

			#[inline]
			fn mul(self, rhs: Self) -> Self {
				Self {
					data: array::from_fn(|i| self.data[i].clone() * rhs.data[i].clone()),
				}
			}
		}

		impl Add for $name {
			type Output = Self;

			#[inline]
			fn add(self, rhs: Self) -> Self {
				Self {
					data: array::from_fn(|byte_number| {
						self.data[byte_number] + rhs.data[byte_number]
					}),
				}
			}
		}

		impl AddAssign for $name {
			#[inline]
			fn add_assign(&mut self, rhs: Self) {
				for (data, rhs) in zip(&mut self.data, &rhs.data) {
					*data += *rhs
				}
			}
		}

		byte_sliced_common!($name, $packed_storage, BinaryField1b, $storage_tower_level);

		impl PackedTransformationFactory<$name> for $name {
			type PackedTransformation<Data: AsRef<[<$name as PackedField>::Scalar]> + Sync> =
				IDTransformation;

			fn make_packed_transformation<Data: AsRef<[<$name as PackedField>::Scalar]> + Sync>(
				_transformation: FieldLinearTransformation<<$name as PackedField>::Scalar, Data>,
			) -> Self::PackedTransformation<Data> {
				IDTransformation
			}
		}
	};
}

#[inline(always)]
fn interleave_internal_block<P: PackedField, const N: usize, const LOG_BLOCK_LEN: usize>(
	lhs: &[P; N],
	rhs: &[P; N],
) -> ([P; N], [P; N]) {
	debug_assert!(LOG_BLOCK_LEN < checked_log_2(N));

	let result_1 = array::from_fn(|i| {
		let block_index = i >> (LOG_BLOCK_LEN + 1);
		let block_start = block_index << (LOG_BLOCK_LEN + 1);
		let block_offset = i - block_start;

		if block_offset < (1 << LOG_BLOCK_LEN) {
			lhs[i]
		} else {
			rhs[i - (1 << LOG_BLOCK_LEN)]
		}
	});
	let result_2 = array::from_fn(|i| {
		let block_index = i >> (LOG_BLOCK_LEN + 1);
		let block_start = block_index << (LOG_BLOCK_LEN + 1);
		let block_offset = i - block_start;

		if block_offset < (1 << LOG_BLOCK_LEN) {
			lhs[i + (1 << LOG_BLOCK_LEN)]
		} else {
			rhs[i]
		}
	});

	(result_1, result_2)
}

#[inline(always)]
fn interleave_byte_sliced<P: PackedField, const N: usize>(
	lhs: &[P; N],
	rhs: &[P; N],
	log_block_len: usize,
) -> ([P; N], [P; N]) {
	debug_assert!(checked_log_2(N) <= 4);

	match log_block_len {
		x if x >= checked_log_2(N) => interleave_big_block::<P, N>(lhs, rhs, log_block_len),
		0 => interleave_internal_block::<P, N, 0>(lhs, rhs),
		1 => interleave_internal_block::<P, N, 1>(lhs, rhs),
		2 => interleave_internal_block::<P, N, 2>(lhs, rhs),
		3 => interleave_internal_block::<P, N, 3>(lhs, rhs),
		_ => unreachable!(),
	}
}

#[inline(always)]
fn unzip_byte_sliced<P: PackedField, const N: usize, const SCALAR_BYTES: usize>(
	lhs: &[P; N],
	rhs: &[P; N],
	log_block_len: usize,
) -> ([P; N], [P; N]) {
	let mut result1: [P; N] = bytemuck::Zeroable::zeroed();
	let mut result2: [P; N] = bytemuck::Zeroable::zeroed();

	let log_height = checked_log_2(N);
	if log_block_len < log_height {
		let block_size = 1 << log_block_len;
		let half = N / 2;
		for block_offset in (0..half).step_by(block_size) {
			let target_offset = block_offset * 2;

			result1[block_offset..block_offset + block_size]
				.copy_from_slice(&lhs[target_offset..target_offset + block_size]);
			result1[half + target_offset..half + target_offset + block_size]
				.copy_from_slice(&rhs[target_offset..target_offset + block_size]);

			result2[block_offset..block_offset + block_size]
				.copy_from_slice(&lhs[target_offset + block_size..target_offset + 2 * block_size]);
			result2[half + target_offset..half + target_offset + block_size]
				.copy_from_slice(&rhs[target_offset + block_size..target_offset + 2 * block_size]);
		}
	} else {
		for i in 0..N {
			(result1[i], result2[i]) = lhs[i].unzip(rhs[i], log_block_len - log_height);
		}
	}

	(result1, result2)
}

#[inline(always)]
fn interleave_big_block<P: PackedField, const N: usize>(
	lhs: &[P; N],
	rhs: &[P; N],
	log_block_len: usize,
) -> ([P; N], [P; N]) {
	let mut result_1 = <[P; N]>::zeroed();
	let mut result_2 = <[P; N]>::zeroed();

	for i in 0..N {
		(result_1[i], result_2[i]) = lhs[i].interleave(rhs[i], log_block_len - checked_log_2(N));
	}

	(result_1, result_2)
}

// 128 bit
define_byte_sliced_3d!(
	ByteSlicedAES16x128b,
	AESTowerField128b,
	PackedAESBinaryField16x8b,
	TowerLevel16,
	TowerLevel16
);
define_byte_sliced_3d!(
	ByteSlicedAES16x64b,
	AESTowerField64b,
	PackedAESBinaryField16x8b,
	TowerLevel8,
	TowerLevel8
);
define_byte_sliced_3d!(
	ByteSlicedAES2x16x64b,
	AESTowerField64b,
	PackedAESBinaryField16x8b,
	TowerLevel8,
	TowerLevel16
);
define_byte_sliced_3d!(
	ByteSlicedAES16x32b,
	AESTowerField32b,
	PackedAESBinaryField16x8b,
	TowerLevel4,
	TowerLevel4
);
define_byte_sliced_3d!(
	ByteSlicedAES4x16x32b,
	AESTowerField32b,
	PackedAESBinaryField16x8b,
	TowerLevel4,
	TowerLevel16
);
define_byte_sliced_3d!(
	ByteSlicedAES16x16b,
	AESTowerField16b,
	PackedAESBinaryField16x8b,
	TowerLevel2,
	TowerLevel2
);
define_byte_sliced_3d!(
	ByteSlicedAES8x16x16b,
	AESTowerField16b,
	PackedAESBinaryField16x8b,
	TowerLevel2,
	TowerLevel16
);
define_byte_sliced_3d!(
	ByteSlicedAES16x8b,
	AESTowerField8b,
	PackedAESBinaryField16x8b,
	TowerLevel1,
	TowerLevel1
);
define_byte_sliced_3d!(
	ByteSlicedAES16x16x8b,
	AESTowerField8b,
	PackedAESBinaryField16x8b,
	TowerLevel1,
	TowerLevel16
);

define_byte_sliced_3d_1b!(ByteSliced16x128x1b, PackedBinaryField128x1b, TowerLevel16);
define_byte_sliced_3d_1b!(ByteSliced8x128x1b, PackedBinaryField128x1b, TowerLevel8);
define_byte_sliced_3d_1b!(ByteSliced4x128x1b, PackedBinaryField128x1b, TowerLevel4);
define_byte_sliced_3d_1b!(ByteSliced2x128x1b, PackedBinaryField128x1b, TowerLevel2);
define_byte_sliced_3d_1b!(ByteSliced1x128x1b, PackedBinaryField128x1b, TowerLevel1);

// 256 bit
define_byte_sliced_3d!(
	ByteSlicedAES32x128b,
	AESTowerField128b,
	PackedAESBinaryField32x8b,
	TowerLevel16,
	TowerLevel16
);
define_byte_sliced_3d!(
	ByteSlicedAES32x64b,
	AESTowerField64b,
	PackedAESBinaryField32x8b,
	TowerLevel8,
	TowerLevel8
);
define_byte_sliced_3d!(
	ByteSlicedAES2x32x64b,
	AESTowerField64b,
	PackedAESBinaryField32x8b,
	TowerLevel8,
	TowerLevel16
);
define_byte_sliced_3d!(
	ByteSlicedAES32x32b,
	AESTowerField32b,
	PackedAESBinaryField32x8b,
	TowerLevel4,
	TowerLevel4
);
define_byte_sliced_3d!(
	ByteSlicedAES4x32x32b,
	AESTowerField32b,
	PackedAESBinaryField32x8b,
	TowerLevel4,
	TowerLevel16
);
define_byte_sliced_3d!(
	ByteSlicedAES32x16b,
	AESTowerField16b,
	PackedAESBinaryField32x8b,
	TowerLevel2,
	TowerLevel2
);
define_byte_sliced_3d!(
	ByteSlicedAES8x32x16b,
	AESTowerField16b,
	PackedAESBinaryField32x8b,
	TowerLevel2,
	TowerLevel16
);
define_byte_sliced_3d!(
	ByteSlicedAES32x8b,
	AESTowerField8b,
	PackedAESBinaryField32x8b,
	TowerLevel1,
	TowerLevel1
);
define_byte_sliced_3d!(
	ByteSlicedAES16x32x8b,
	AESTowerField8b,
	PackedAESBinaryField32x8b,
	TowerLevel1,
	TowerLevel16
);

define_byte_sliced_3d_1b!(ByteSliced16x256x1b, PackedBinaryField256x1b, TowerLevel16);
define_byte_sliced_3d_1b!(ByteSliced8x256x1b, PackedBinaryField256x1b, TowerLevel8);
define_byte_sliced_3d_1b!(ByteSliced4x256x1b, PackedBinaryField256x1b, TowerLevel4);
define_byte_sliced_3d_1b!(ByteSliced2x256x1b, PackedBinaryField256x1b, TowerLevel2);
define_byte_sliced_3d_1b!(ByteSliced1x256x1b, PackedBinaryField256x1b, TowerLevel1);

// 512 bit
define_byte_sliced_3d!(
	ByteSlicedAES64x128b,
	AESTowerField128b,
	PackedAESBinaryField64x8b,
	TowerLevel16,
	TowerLevel16
);
define_byte_sliced_3d!(
	ByteSlicedAES64x64b,
	AESTowerField64b,
	PackedAESBinaryField64x8b,
	TowerLevel8,
	TowerLevel8
);
define_byte_sliced_3d!(
	ByteSlicedAES2x64x64b,
	AESTowerField64b,
	PackedAESBinaryField64x8b,
	TowerLevel8,
	TowerLevel16
);
define_byte_sliced_3d!(
	ByteSlicedAES64x32b,
	AESTowerField32b,
	PackedAESBinaryField64x8b,
	TowerLevel4,
	TowerLevel4
);
define_byte_sliced_3d!(
	ByteSlicedAES4x64x32b,
	AESTowerField32b,
	PackedAESBinaryField64x8b,
	TowerLevel4,
	TowerLevel16
);
define_byte_sliced_3d!(
	ByteSlicedAES64x16b,
	AESTowerField16b,
	PackedAESBinaryField64x8b,
	TowerLevel2,
	TowerLevel2
);
define_byte_sliced_3d!(
	ByteSlicedAES8x64x16b,
	AESTowerField16b,
	PackedAESBinaryField64x8b,
	TowerLevel2,
	TowerLevel16
);
define_byte_sliced_3d!(
	ByteSlicedAES64x8b,
	AESTowerField8b,
	PackedAESBinaryField64x8b,
	TowerLevel1,
	TowerLevel1
);
define_byte_sliced_3d!(
	ByteSlicedAES16x64x8b,
	AESTowerField8b,
	PackedAESBinaryField64x8b,
	TowerLevel1,
	TowerLevel16
);

define_byte_sliced_3d_1b!(ByteSliced16x512x1b, PackedBinaryField512x1b, TowerLevel16);
define_byte_sliced_3d_1b!(ByteSliced8x512x1b, PackedBinaryField512x1b, TowerLevel8);
define_byte_sliced_3d_1b!(ByteSliced4x512x1b, PackedBinaryField512x1b, TowerLevel4);
define_byte_sliced_3d_1b!(ByteSliced2x512x1b, PackedBinaryField512x1b, TowerLevel2);
define_byte_sliced_3d_1b!(ByteSliced1x512x1b, PackedBinaryField512x1b, TowerLevel1);