binius_field/arch/portable/
pairwise_table_arithmetic.rs

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// Copyright 2024-2025 Irreducible Inc.

use super::packed::PackedPrimitiveType;
use crate::{
	arch::PairwiseTableStrategy,
	arithmetic_traits::{TaggedInvertOrZero, TaggedMul, TaggedMulAlpha, TaggedSquare},
	packed::PackedField,
	underlier::UnderlierType,
	AESTowerField8b, BinaryField2b, BinaryField4b, BinaryField8b,
};

impl<U: UnderlierType> TaggedMul<PairwiseTableStrategy> for PackedPrimitiveType<U, BinaryField2b>
where
	Self: PackedField<Scalar = BinaryField2b>,
{
	#[inline]
	fn mul(self, rhs: Self) -> Self {
		Self::from_fn(|i| mul_binary_tower_4b(self.get(i).into(), rhs.get(i).into()).into())
	}
}

impl<U: UnderlierType> TaggedMul<PairwiseTableStrategy> for PackedPrimitiveType<U, BinaryField4b>
where
	Self: PackedField<Scalar = BinaryField4b>,
{
	#[inline]
	fn mul(self, rhs: Self) -> Self {
		Self::from_fn(|i| mul_binary_tower_4b(self.get(i).into(), rhs.get(i).into()).into())
	}
}

const fn mul_binary_tower_4b(a: u8, b: u8) -> u8 {
	#[rustfmt::skip]
	const MUL_4B_LOOKUP: [u8; 128] = [
		0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
		0x10, 0x32, 0x54, 0x76, 0x98, 0xba, 0xdc, 0xfe,
		0x20, 0x13, 0xa8, 0x9b, 0xec, 0xdf, 0x64, 0x57,
		0x30, 0x21, 0xfc, 0xed, 0x74, 0x65, 0xb8, 0xa9,
		0x40, 0xc8, 0xd9, 0x51, 0xae, 0x26, 0x37, 0xbf,
		0x50, 0xfa, 0x8d, 0x27, 0x36, 0x9c, 0xeb, 0x41,
		0x60, 0xdb, 0x71, 0xca, 0x42, 0xf9, 0x53, 0xe8,
		0x70, 0xe9, 0x25, 0xbc, 0xda, 0x43, 0x8f, 0x16,
		0x80, 0x4c, 0x6e, 0xa2, 0xf7, 0x3b, 0x19, 0xd5,
		0x90, 0x7e, 0x3a, 0xd4, 0x6f, 0x81, 0xc5, 0x2b,
		0xa0, 0x5f, 0xc6, 0x39, 0x1b, 0xe4, 0x7d, 0x82,
		0xb0, 0x6d, 0x92, 0x4f, 0x83, 0x5e, 0xa1, 0x7c,
		0xc0, 0x84, 0xb7, 0xf3, 0x59, 0x1d, 0x2e, 0x6a,
		0xd0, 0xb6, 0xe3, 0x85, 0xc1, 0xa7, 0xf2, 0x94,
		0xe0, 0x97, 0x1f, 0x68, 0xb5, 0xc2, 0x4a, 0x3d,
		0xf0, 0xa5, 0x4b, 0x1e, 0x2d, 0x78, 0x96, 0xc3,
	];
	let idx = a << 4 | b;
	(MUL_4B_LOOKUP[idx as usize >> 1] >> ((idx & 1) * 4)) & 0x0f
}

impl<U: UnderlierType> TaggedMul<PairwiseTableStrategy> for PackedPrimitiveType<U, BinaryField8b>
where
	Self: PackedField<Scalar = BinaryField8b>,
{
	#[inline]
	fn mul(self, rhs: Self) -> Self {
		#[rustfmt::skip]
        const EXP_TABLE: [u8; 256] = [
            0x1,  0x13, 0x43, 0x66, 0xab, 0x8c, 0x60, 0xc6, 0x91, 0xca, 0x59, 0xb2, 0x6a, 0x63, 0xf4, 0x53,
            0x17, 0x0f, 0xfa, 0xba, 0xee, 0x87, 0xd6, 0xe0, 0x6e, 0x2f, 0x68, 0x42, 0x75, 0xe8, 0xea, 0xcb,
            0x4a, 0xf1, 0x0c, 0xc8, 0x78, 0x33, 0xd1, 0x9e, 0x30, 0xe3, 0x5c, 0xed, 0xb5, 0x14, 0x3d, 0x38,
            0x67, 0xb8, 0xcf, 0x06, 0x6d, 0x1d, 0xaa, 0x9f, 0x23, 0xa0, 0x3a, 0x46, 0x39, 0x74, 0xfb, 0xa9,
            0xad, 0xe1, 0x7d, 0x6c, 0x0e, 0xe9, 0xf9, 0x88, 0x2c, 0x5a, 0x80, 0xa8, 0xbe, 0xa2, 0x1b, 0xc7,
            0x82, 0x89, 0x3f, 0x19, 0xe6, 0x03, 0x32, 0xc2, 0xdd, 0x56, 0x48, 0xd0, 0x8d, 0x73, 0x85, 0xf7,
            0x61, 0xd5, 0xd2, 0xac, 0xf2, 0x3e, 0x0a, 0xa5, 0x65, 0x99, 0x4e, 0xbd, 0x90, 0xd9, 0x1a, 0xd4,
            0xc1, 0xef, 0x94, 0x95, 0x86, 0xc5, 0xa3, 0x08, 0x84, 0xe4, 0x22, 0xb3, 0x79, 0x20, 0x92, 0xf8,
            0x9b, 0x6f, 0x3c, 0x2b, 0x24, 0xde, 0x64, 0x8a, 0xd,  0xdb, 0x3b, 0x55, 0x7a, 0x12, 0x50, 0x25,
            0xcd, 0x27, 0xec, 0xa6, 0x57, 0x5b, 0x93, 0xeb, 0xd8, 0x09, 0x97, 0xa7, 0x44, 0x18, 0xf5, 0x40,
            0x54, 0x69, 0x51, 0x36, 0x8e, 0x41, 0x47, 0x2a, 0x37, 0x9d, 0x02, 0x21, 0x81, 0xbb, 0xfd, 0xc4,
            0xb0, 0x4b, 0xe2, 0x4f, 0xae, 0xd3, 0xbf, 0xb1, 0x58, 0xa1, 0x29, 0x05, 0x5f, 0xdf, 0x77, 0xc9,
            0x6b, 0x70, 0xb7, 0x35, 0xbc, 0x83, 0x9a, 0x7c, 0x7f, 0x4d, 0x8f, 0x52, 0x04, 0x4c, 0x9c, 0x11,
            0x62, 0xe7, 0x10, 0x71, 0xa4, 0x76, 0xda, 0x28, 0x16, 0x1c, 0xb9, 0xdc, 0x45, 0x0b, 0xb6, 0x26,
            0xff, 0xe5, 0x31, 0xf0, 0x1f, 0x8b, 0x1e, 0x98, 0x5d, 0xfe, 0xf6, 0x72, 0x96, 0xb4, 0x07, 0x7e,
            0x5e, 0xcc, 0x34, 0xaf, 0xc0, 0xfc, 0xd7, 0xf3, 0x2d, 0x49, 0xc3, 0xce, 0x15, 0x2e, 0x7b, 0x00,
        ];
		#[rustfmt::skip]
        const LOG_TABLE: [u8; 256] = [
            0x00, 0x00, 0xaa, 0x55, 0xcc, 0xbb, 0x33, 0xee, 0x77, 0x99, 0x66, 0xdd, 0x22, 0x88, 0x44, 0x11,
            0xd2, 0xcf, 0x8d, 0x01, 0x2d, 0xfc, 0xd8, 0x10, 0x9d, 0x53, 0x6e, 0x4e, 0xd9, 0x35, 0xe6, 0xe4,
            0x7d, 0xab, 0x7a, 0x38, 0x84, 0x8f, 0xdf, 0x91, 0xd7, 0xba, 0xa7, 0x83, 0x48, 0xf8, 0xfd, 0x19,
            0x28, 0xe2, 0x56, 0x25, 0xf2, 0xc3, 0xa3, 0xa8, 0x2f, 0x3c, 0x3a, 0x8a, 0x82, 0x2e, 0x65, 0x52,
            0x9f, 0xa5, 0x1b, 0x02, 0x9c, 0xdc, 0x3b, 0xa6, 0x5a, 0xf9, 0x20, 0xb1, 0xcd, 0xc9, 0x6a, 0xb3,
            0x8e, 0xa2, 0xcb, 0x0f, 0xa0, 0x8b, 0x59, 0x94, 0xb8, 0x0a, 0x49, 0x95, 0x2a, 0xe8, 0xf0, 0xbc,
            0x06, 0x60, 0xd0, 0x0d, 0x86, 0x68, 0x03, 0x30, 0x1a, 0xa1, 0x0c, 0xc0, 0x43, 0x34, 0x18, 0x81,
            0xc1, 0xd3, 0xeb, 0x5d, 0x3d, 0x1c, 0xd5, 0xbe, 0x24, 0x7c, 0x8c, 0xfe, 0xc7, 0x42, 0xef, 0xc8,
            0x4a, 0xac, 0x50, 0xc5, 0x78, 0x5e, 0x74, 0x15, 0x47, 0x51, 0x87, 0xe5, 0x05, 0x5c, 0xa4, 0xca,
            0x6c, 0x08, 0x7e, 0x96, 0x72, 0x73, 0xec, 0x9a, 0xe7, 0x69, 0xc6, 0x80, 0xce, 0xa9, 0x27, 0x37,
            0x39, 0xb9, 0x4d, 0x76, 0xd4, 0x67, 0x93, 0x9b, 0x4b, 0x3f, 0x36, 0x04, 0x63, 0x40, 0xb4, 0xf3,
            0xb0, 0xb7, 0x0b, 0x7b, 0xed, 0x2c, 0xde, 0xc2, 0x31, 0xda, 0x13, 0xad, 0xc4, 0x6b, 0x4c, 0xb6,
            0xf4, 0x70, 0x57, 0xfa, 0xaf, 0x75, 0x07, 0x4f, 0x23, 0xbf, 0x09, 0x1f, 0xf1, 0x90, 0xfb, 0x32,
            0x5b, 0x26, 0x62, 0xb5, 0x6f, 0x61, 0x16, 0xf6, 0x98, 0x6d, 0xd6, 0x89, 0xdb, 0x58, 0x85, 0xbd,
            0x17, 0x41, 0xb2, 0x29, 0x79, 0xe1, 0x54, 0xd1, 0x1d, 0x45, 0x1e, 0x97, 0x92, 0x2b, 0x14, 0x71,
            0xe3, 0x21, 0x64, 0xf7, 0x0e, 0x9e, 0xea, 0x5f, 0x7f, 0x46, 0x12, 0x3e, 0xf5, 0xae, 0xe9, 0xe0,
        ];

		Self::from_fn(|i| {
			multiply_8b_using_log_table(self.get(i).val(), rhs.get(i).val(), &LOG_TABLE, &EXP_TABLE)
				.into()
		})
	}
}

impl<U: UnderlierType> TaggedMul<PairwiseTableStrategy> for PackedPrimitiveType<U, AESTowerField8b>
where
	Self: PackedField<Scalar = AESTowerField8b>,
{
	#[inline]
	fn mul(self, rhs: Self) -> Self {
		#[rustfmt::skip]
		const AES_EXP_TABLE: [u8; 256] = [
			0x01, 0x03, 0x05, 0x0f, 0x11, 0x33, 0x55, 0xff, 0x1a, 0x2e, 0x72, 0x96, 0xa1, 0xf8, 0x13, 0x35,
			0x5f, 0xe1, 0x38, 0x48, 0xd8, 0x73, 0x95, 0xa4, 0xf7, 0x02, 0x06, 0x0a, 0x1e, 0x22, 0x66, 0xaa,
			0xe5, 0x34, 0x5c, 0xe4, 0x37, 0x59, 0xeb, 0x26, 0x6a, 0xbe, 0xd9, 0x70, 0x90, 0xab, 0xe6, 0x31,
			0x53, 0xf5, 0x04, 0x0c, 0x14, 0x3c, 0x44, 0xcc, 0x4f, 0xd1, 0x68, 0xb8, 0xd3, 0x6e, 0xb2, 0xcd,
			0x4c, 0xd4, 0x67, 0xa9, 0xe0, 0x3b, 0x4d, 0xd7, 0x62, 0xa6, 0xf1, 0x08, 0x18, 0x28, 0x78, 0x88,
			0x83, 0x9e, 0xb9, 0xd0, 0x6b, 0xbd, 0xdc, 0x7f, 0x81, 0x98, 0xb3, 0xce, 0x49, 0xdb, 0x76, 0x9a,
			0xb5, 0xc4, 0x57, 0xf9, 0x10, 0x30, 0x50, 0xf0, 0x0b, 0x1d, 0x27, 0x69, 0xbb, 0xd6, 0x61, 0xa3,
			0xfe, 0x19, 0x2b, 0x7d, 0x87, 0x92, 0xad, 0xec, 0x2f, 0x71, 0x93, 0xae, 0xe9, 0x20, 0x60, 0xa0,
			0xfb, 0x16, 0x3a, 0x4e, 0xd2, 0x6d, 0xb7, 0xc2, 0x5d, 0xe7, 0x32, 0x56, 0xfa, 0x15, 0x3f, 0x41,
			0xc3, 0x5e, 0xe2, 0x3d, 0x47, 0xc9, 0x40, 0xc0, 0x5b, 0xed, 0x2c, 0x74, 0x9c, 0xbf, 0xda, 0x75,
			0x9f, 0xba, 0xd5, 0x64, 0xac, 0xef, 0x2a, 0x7e, 0x82, 0x9d, 0xbc, 0xdf, 0x7a, 0x8e, 0x89, 0x80,
			0x9b, 0xb6, 0xc1, 0x58, 0xe8, 0x23, 0x65, 0xaf, 0xea, 0x25, 0x6f, 0xb1, 0xc8, 0x43, 0xc5, 0x54,
			0xfc, 0x1f, 0x21, 0x63, 0xa5, 0xf4, 0x07, 0x09, 0x1b, 0x2d, 0x77, 0x99, 0xb0, 0xcb, 0x46, 0xca,
			0x45, 0xcf, 0x4a, 0xde, 0x79, 0x8b, 0x86, 0x91, 0xa8, 0xe3, 0x3e, 0x42, 0xc6, 0x51, 0xf3, 0x0e,
			0x12, 0x36, 0x5a, 0xee, 0x29, 0x7b, 0x8d, 0x8c, 0x8f, 0x8a, 0x85, 0x94, 0xa7, 0xf2, 0x0d, 0x17,
			0x39, 0x4b, 0xdd, 0x7c, 0x84, 0x97, 0xa2, 0xfd, 0x1c, 0x24, 0x6c, 0xb4, 0xc7, 0x52, 0xf6, 0x0
		];

		#[rustfmt::skip]
		const AES_LOG_TABLE: [u8; 256] = [
			0x00, 0x00, 0x19, 0x01, 0x32, 0x02, 0x1a, 0xc6, 0x4b, 0xc7, 0x1b, 0x68, 0x33, 0xee, 0xdf, 0x03,
			0x64, 0x04, 0xe0, 0x0e, 0x34, 0x8d, 0x81, 0xef, 0x4c, 0x71, 0x08, 0xc8, 0xf8, 0x69, 0x1c, 0xc1,
			0x7d, 0xc2, 0x1d, 0xb5, 0xf9, 0xb9, 0x27, 0x6a, 0x4d, 0xe4, 0xa6, 0x72, 0x9a, 0xc9, 0x09, 0x78,
			0x65, 0x2f, 0x8a, 0x05, 0x21, 0x0f, 0xe1, 0x24, 0x12, 0xf0, 0x82, 0x45, 0x35, 0x93, 0xda, 0x8e,
			0x96, 0x8f, 0xdb, 0xbd, 0x36, 0xd0, 0xce, 0x94, 0x13, 0x5c, 0xd2, 0xf1, 0x40, 0x46, 0x83, 0x38,
			0x66, 0xdd, 0xfd, 0x30, 0xbf, 0x06, 0x8b, 0x62, 0xb3, 0x25, 0xe2, 0x98, 0x22, 0x88, 0x91, 0x10,
			0x7e, 0x6e, 0x48, 0xc3, 0xa3, 0xb6, 0x1e, 0x42, 0x3a, 0x6b, 0x28, 0x54, 0xfa, 0x85, 0x3d, 0xba,
			0x2b, 0x79, 0x0a, 0x15, 0x9b, 0x9f, 0x5e, 0xca, 0x4e, 0xd4, 0xac, 0xe5, 0xf3, 0x73, 0xa7, 0x57,
			0xaf, 0x58, 0xa8, 0x50, 0xf4, 0xea, 0xd6, 0x74, 0x4f, 0xae, 0xe9, 0xd5, 0xe7, 0xe6, 0xad, 0xe8,
			0x2c, 0xd7, 0x75, 0x7a, 0xeb, 0x16, 0x0b, 0xf5, 0x59, 0xcb, 0x5f, 0xb0, 0x9c, 0xa9, 0x51, 0xa0,
			0x7f, 0x0c, 0xf6, 0x6f, 0x17, 0xc4, 0x49, 0xec, 0xd8, 0x43, 0x1f, 0x2d, 0xa4, 0x76, 0x7b, 0xb7,
			0xcc, 0xbb, 0x3e, 0x5a, 0xfb, 0x60, 0xb1, 0x86, 0x3b, 0x52, 0xa1, 0x6c, 0xaa, 0x55, 0x29, 0x9d,
			0x97, 0xb2, 0x87, 0x90, 0x61, 0xbe, 0xdc, 0xfc, 0xbc, 0x95, 0xcf, 0xcd, 0x37, 0x3f, 0x5b, 0xd1,
			0x53, 0x39, 0x84, 0x3c, 0x41, 0xa2, 0x6d, 0x47, 0x14, 0x2a, 0x9e, 0x5d, 0x56, 0xf2, 0xd3, 0xab,
			0x44, 0x11, 0x92, 0xd9, 0x23, 0x20, 0x2e, 0x89, 0xb4, 0x7c, 0xb8, 0x26, 0x77, 0x99, 0xe3, 0xa5,
			0x67, 0x4a, 0xed, 0xde, 0xc5, 0x31, 0xfe, 0x18, 0x0d, 0x63, 0x8c, 0x80, 0xc0, 0xf7, 0x70, 0x07,
		];

		Self::from_fn(|i| {
			multiply_8b_using_log_table(
				self.get(i).val(),
				rhs.get(i).val(),
				&AES_LOG_TABLE,
				&AES_EXP_TABLE,
			)
			.into()
		})
	}
}

#[inline]
fn multiply_8b_using_log_table(
	lhs: u8,
	rhs: u8,
	log_table: &[u8; 256],
	exp_table: &[u8; 256],
) -> u8 {
	let result = if lhs != 0 && rhs != 0 {
		let log_table_index = log_table[lhs as usize] as usize + log_table[rhs as usize] as usize;
		let log_table_index = if log_table_index > 254 {
			log_table_index - 255
		} else {
			log_table_index
		};

		unsafe {
			// Safety: `log_table_index` is smaller than 255 because:
			// - all values in `LOG_TABLE` do not exceed 254
			// - sum of two values do not exceed 254*2
			// - the previous line reduces `log_table_index` by 255 if it is
			// bigger than 254
			*exp_table.get_unchecked(log_table_index)
		}
	} else {
		0
	};

	result
}

/// Return the result of the operation by a table search for each scalar value
#[inline(always)]
fn unary_op_with_table<PT>(val: PT, table: &[u8; 256]) -> PT
where
	PT: PackedField,
	PT::Scalar: From<u8>,
	u8: From<PT::Scalar>,
{
	PT::from_fn(|i| table[u8::from(val.get(i)) as usize].into())
}

/// Implement unary operation with a table search
macro_rules! impl_unary_ops {
	($tagged_op_type:ident, $method_name:ident, $table:ident, $field:ty) => {
		impl<U: UnderlierType> $tagged_op_type<PairwiseTableStrategy>
			for PackedPrimitiveType<U, $field>
		where
			Self: PackedField<Scalar = $field>,
		{
			#[inline(always)]
			fn $method_name(self) -> Self {
				unary_op_with_table(self, &$table)
			}
		}
	};
}

#[rustfmt::skip]
static BINARY_TOWER_8B_SQUARE_MAP: [u8; 256] = [
    0x00, 0x01, 0x03, 0x02, 0x09, 0x08, 0x0a, 0x0b, 0x07, 0x06, 0x04, 0x05, 0x0e, 0x0f, 0x0d, 0x0c,
    0x41, 0x40, 0x42, 0x43, 0x48, 0x49, 0x4b, 0x4a, 0x46, 0x47, 0x45, 0x44, 0x4f, 0x4e, 0x4c, 0x4d,
    0xc3, 0xc2, 0xc0, 0xc1, 0xca, 0xcb, 0xc9, 0xc8, 0xc4, 0xc5, 0xc7, 0xc6, 0xcd, 0xcc, 0xce, 0xcf,
    0x82, 0x83, 0x81, 0x80, 0x8b, 0x8a, 0x88, 0x89, 0x85, 0x84, 0x86, 0x87, 0x8c, 0x8d, 0x8f, 0x8e,
    0xa9, 0xa8, 0xaa, 0xab, 0xa0, 0xa1, 0xa3, 0xa2, 0xae, 0xaf, 0xad, 0xac, 0xa7, 0xa6, 0xa4, 0xa5,
    0xe8, 0xe9, 0xeb, 0xea, 0xe1, 0xe0, 0xe2, 0xe3, 0xef, 0xee, 0xec, 0xed, 0xe6, 0xe7, 0xe5, 0xe4,
    0x6a, 0x6b, 0x69, 0x68, 0x63, 0x62, 0x60, 0x61, 0x6d, 0x6c, 0x6e, 0x6f, 0x64, 0x65, 0x67, 0x66,
    0x2b, 0x2a, 0x28, 0x29, 0x22, 0x23, 0x21, 0x20, 0x2c, 0x2d, 0x2f, 0x2e, 0x25, 0x24, 0x26, 0x27,
    0x57, 0x56, 0x54, 0x55, 0x5e, 0x5f, 0x5d, 0x5c, 0x50, 0x51, 0x53, 0x52, 0x59, 0x58, 0x5a, 0x5b,
    0x16, 0x17, 0x15, 0x14, 0x1f, 0x1e, 0x1c, 0x1d, 0x11, 0x10, 0x12, 0x13, 0x18, 0x19, 0x1b, 0x1a,
    0x94, 0x95, 0x97, 0x96, 0x9d, 0x9c, 0x9e, 0x9f, 0x93, 0x92, 0x90, 0x91, 0x9a, 0x9b, 0x99, 0x98,
    0xd5, 0xd4, 0xd6, 0xd7, 0xdc, 0xdd, 0xdf, 0xde, 0xd2, 0xd3, 0xd1, 0xd0, 0xdb, 0xda, 0xd8, 0xd9,
    0xfe, 0xff, 0xfd, 0xfc, 0xf7, 0xf6, 0xf4, 0xf5, 0xf9, 0xf8, 0xfa, 0xfb, 0xf0, 0xf1, 0xf3, 0xf2,
    0xbf, 0xbe, 0xbc, 0xbd, 0xb6, 0xb7, 0xb5, 0xb4, 0xb8, 0xb9, 0xbb, 0xba, 0xb1, 0xb0, 0xb2, 0xb3,
    0x3d, 0x3c, 0x3e, 0x3f, 0x34, 0x35, 0x37, 0x36, 0x3a, 0x3b, 0x39, 0x38, 0x33, 0x32, 0x30, 0x31,
    0x7c, 0x7d, 0x7f, 0x7e, 0x75, 0x74, 0x76, 0x77, 0x7b, 0x7a, 0x78, 0x79, 0x72, 0x73, 0x71, 0x70,
];

impl_unary_ops!(TaggedSquare, square, BINARY_TOWER_8B_SQUARE_MAP, BinaryField8b);

#[rustfmt::skip]
const AES_TOWER_8B_SQUARE_MAP: [u8; 256] = [
    0x00, 0x01, 0x04, 0x05, 0x10, 0x11, 0x14, 0x15, 0x40, 0x41, 0x44, 0x45, 0x50, 0x51, 0x54, 0x55,
    0x1b, 0x1a, 0x1f, 0x1e, 0x0b, 0x0a, 0x0f, 0x0e, 0x5b, 0x5a, 0x5f, 0x5e, 0x4b, 0x4a, 0x4f, 0x4e,
    0x6c, 0x6d, 0x68, 0x69, 0x7c, 0x7d, 0x78, 0x79, 0x2c, 0x2d, 0x28, 0x29, 0x3c, 0x3d, 0x38, 0x39,
    0x77, 0x76, 0x73, 0x72, 0x67, 0x66, 0x63, 0x62, 0x37, 0x36, 0x33, 0x32, 0x27, 0x26, 0x23, 0x22,
    0xab, 0xaa, 0xaf, 0xae, 0xbb, 0xba, 0xbf, 0xbe, 0xeb, 0xea, 0xef, 0xee, 0xfb, 0xfa, 0xff, 0xfe,
    0xb0, 0xb1, 0xb4, 0xb5, 0xa0, 0xa1, 0xa4, 0xa5, 0xf0, 0xf1, 0xf4, 0xf5, 0xe0, 0xe1, 0xe4, 0xe5,
    0xc7, 0xc6, 0xc3, 0xc2, 0xd7, 0xd6, 0xd3, 0xd2, 0x87, 0x86, 0x83, 0x82, 0x97, 0x96, 0x93, 0x92,
    0xdc, 0xdd, 0xd8, 0xd9, 0xcc, 0xcd, 0xc8, 0xc9, 0x9c, 0x9d, 0x98, 0x99, 0x8c, 0x8d, 0x88, 0x89,
    0x9a, 0x9b, 0x9e, 0x9f, 0x8a, 0x8b, 0x8e, 0x8f, 0xda, 0xdb, 0xde, 0xdf, 0xca, 0xcb, 0xce, 0xcf,
    0x81, 0x80, 0x85, 0x84, 0x91, 0x90, 0x95, 0x94, 0xc1, 0xc0, 0xc5, 0xc4, 0xd1, 0xd0, 0xd5, 0xd4,
    0xf6, 0xf7, 0xf2, 0xf3, 0xe6, 0xe7, 0xe2, 0xe3, 0xb6, 0xb7, 0xb2, 0xb3, 0xa6, 0xa7, 0xa2, 0xa3,
    0xed, 0xec, 0xe9, 0xe8, 0xfd, 0xfc, 0xf9, 0xf8, 0xad, 0xac, 0xa9, 0xa8, 0xbd, 0xbc, 0xb9, 0xb8,
    0x31, 0x30, 0x35, 0x34, 0x21, 0x20, 0x25, 0x24, 0x71, 0x70, 0x75, 0x74, 0x61, 0x60, 0x65, 0x64,
    0x2a, 0x2b, 0x2e, 0x2f, 0x3a, 0x3b, 0x3e, 0x3f, 0x6a, 0x6b, 0x6e, 0x6f, 0x7a, 0x7b, 0x7e, 0x7f,
    0x5d, 0x5c, 0x59, 0x58, 0x4d, 0x4c, 0x49, 0x48, 0x1d, 0x1c, 0x19, 0x18, 0x0d, 0x0c, 0x09, 0x08,
    0x46, 0x47, 0x42, 0x43, 0x56, 0x57, 0x52, 0x53, 0x06, 0x07, 0x02, 0x03, 0x16, 0x17, 0x12, 0x13,
];

impl_unary_ops!(TaggedSquare, square, AES_TOWER_8B_SQUARE_MAP, AESTowerField8b);

#[rustfmt::skip]
const BINARY_TOWER_8B_MUL_ALPHA_MAP: [u8; 256] = [
    0x00, 0x10, 0x20, 0x30, 0x40, 0x50, 0x60, 0x70, 0x80, 0x90, 0xa0, 0xb0, 0xc0, 0xd0, 0xe0, 0xf0,
    0x41, 0x51, 0x61, 0x71, 0x01, 0x11, 0x21, 0x31, 0xc1, 0xd1, 0xe1, 0xf1, 0x81, 0x91, 0xa1, 0xb1,
    0x82, 0x92, 0xa2, 0xb2, 0xc2, 0xd2, 0xe2, 0xf2, 0x02, 0x12, 0x22, 0x32, 0x42, 0x52, 0x62, 0x72,
    0xc3, 0xd3, 0xe3, 0xf3, 0x83, 0x93, 0xa3, 0xb3, 0x43, 0x53, 0x63, 0x73, 0x03, 0x13, 0x23, 0x33,
    0x94, 0x84, 0xb4, 0xa4, 0xd4, 0xc4, 0xf4, 0xe4, 0x14, 0x04, 0x34, 0x24, 0x54, 0x44, 0x74, 0x64,
    0xd5, 0xc5, 0xf5, 0xe5, 0x95, 0x85, 0xb5, 0xa5, 0x55, 0x45, 0x75, 0x65, 0x15, 0x05, 0x35, 0x25,
    0x16, 0x06, 0x36, 0x26, 0x56, 0x46, 0x76, 0x66, 0x96, 0x86, 0xb6, 0xa6, 0xd6, 0xc6, 0xf6, 0xe6,
    0x57, 0x47, 0x77, 0x67, 0x17, 0x07, 0x37, 0x27, 0xd7, 0xc7, 0xf7, 0xe7, 0x97, 0x87, 0xb7, 0xa7,
    0xe8, 0xf8, 0xc8, 0xd8, 0xa8, 0xb8, 0x88, 0x98, 0x68, 0x78, 0x48, 0x58, 0x28, 0x38, 0x08, 0x18,
    0xa9, 0xb9, 0x89, 0x99, 0xe9, 0xf9, 0xc9, 0xd9, 0x29, 0x39, 0x09, 0x19, 0x69, 0x79, 0x49, 0x59,
    0x6a, 0x7a, 0x4a, 0x5a, 0x2a, 0x3a, 0x0a, 0x1a, 0xea, 0xfa, 0xca, 0xda, 0xaa, 0xba, 0x8a, 0x9a,
    0x2b, 0x3b, 0x0b, 0x1b, 0x6b, 0x7b, 0x4b, 0x5b, 0xab, 0xbb, 0x8b, 0x9b, 0xeb, 0xfb, 0xcb, 0xdb,
    0x7c, 0x6c, 0x5c, 0x4c, 0x3c, 0x2c, 0x1c, 0x0c, 0xfc, 0xec, 0xdc, 0xcc, 0xbc, 0xac, 0x9c, 0x8c,
    0x3d, 0x2d, 0x1d, 0x0d, 0x7d, 0x6d, 0x5d, 0x4d, 0xbd, 0xad, 0x9d, 0x8d, 0xfd, 0xed, 0xdd, 0xcd,
    0xfe, 0xee, 0xde, 0xce, 0xbe, 0xae, 0x9e, 0x8e, 0x7e, 0x6e, 0x5e, 0x4e, 0x3e, 0x2e, 0x1e, 0x0e,
    0xbf, 0xaf, 0x9f, 0x8f, 0xff, 0xef, 0xdf, 0xcf, 0x3f, 0x2f, 0x1f, 0x0f, 0x7f, 0x6f, 0x5f, 0x4f,
];

impl_unary_ops!(TaggedMulAlpha, mul_alpha, BINARY_TOWER_8B_MUL_ALPHA_MAP, BinaryField8b);

#[rustfmt::skip]
const AES_TOWER_8B_MUL_ALPHA_MAP: [u8; 256] = [
    0x00, 0xd3, 0xbd, 0x6e, 0x61, 0xb2, 0xdc, 0x0f, 0xc2, 0x11, 0x7f, 0xac, 0xa3, 0x70, 0x1e, 0xcd,
    0x9f, 0x4c, 0x22, 0xf1, 0xfe, 0x2d, 0x43, 0x90, 0x5d, 0x8e, 0xe0, 0x33, 0x3c, 0xef, 0x81, 0x52,
    0x25, 0xf6, 0x98, 0x4b, 0x44, 0x97, 0xf9, 0x2a, 0xe7, 0x34, 0x5a, 0x89, 0x86, 0x55, 0x3b, 0xe8,
    0xba, 0x69, 0x07, 0xd4, 0xdb, 0x08, 0x66, 0xb5, 0x78, 0xab, 0xc5, 0x16, 0x19, 0xca, 0xa4, 0x77,
    0x4a, 0x99, 0xf7, 0x24, 0x2b, 0xf8, 0x96, 0x45, 0x88, 0x5b, 0x35, 0xe6, 0xe9, 0x3a, 0x54, 0x87,
    0xd5, 0x06, 0x68, 0xbb, 0xb4, 0x67, 0x09, 0xda, 0x17, 0xc4, 0xaa, 0x79, 0x76, 0xa5, 0xcb, 0x18,
    0x6f, 0xbc, 0xd2, 0x01, 0x0e, 0xdd, 0xb3, 0x60, 0xad, 0x7e, 0x10, 0xc3, 0xcc, 0x1f, 0x71, 0xa2,
    0xf0, 0x23, 0x4d, 0x9e, 0x91, 0x42, 0x2c, 0xff, 0x32, 0xe1, 0x8f, 0x5c, 0x53, 0x80, 0xee, 0x3d,
    0x94, 0x47, 0x29, 0xfa, 0xf5, 0x26, 0x48, 0x9b, 0x56, 0x85, 0xeb, 0x38, 0x37, 0xe4, 0x8a, 0x59,
    0x0b, 0xd8, 0xb6, 0x65, 0x6a, 0xb9, 0xd7, 0x04, 0xc9, 0x1a, 0x74, 0xa7, 0xa8, 0x7b, 0x15, 0xc6,
    0xb1, 0x62, 0x0c, 0xdf, 0xd0, 0x03, 0x6d, 0xbe, 0x73, 0xa0, 0xce, 0x1d, 0x12, 0xc1, 0xaf, 0x7c,
    0x2e, 0xfd, 0x93, 0x40, 0x4f, 0x9c, 0xf2, 0x21, 0xec, 0x3f, 0x51, 0x82, 0x8d, 0x5e, 0x30, 0xe3,
    0xde, 0x0d, 0x63, 0xb0, 0xbf, 0x6c, 0x02, 0xd1, 0x1c, 0xcf, 0xa1, 0x72, 0x7d, 0xae, 0xc0, 0x13,
    0x41, 0x92, 0xfc, 0x2f, 0x20, 0xf3, 0x9d, 0x4e, 0x83, 0x50, 0x3e, 0xed, 0xe2, 0x31, 0x5f, 0x8c,
    0xfb, 0x28, 0x46, 0x95, 0x9a, 0x49, 0x27, 0xf4, 0x39, 0xea, 0x84, 0x57, 0x58, 0x8b, 0xe5, 0x36,
    0x64, 0xb7, 0xd9, 0x0a, 0x05, 0xd6, 0xb8, 0x6b, 0xa6, 0x75, 0x1b, 0xc8, 0xc7, 0x14, 0x7a, 0xa9,
];

impl_unary_ops!(TaggedMulAlpha, mul_alpha, AES_TOWER_8B_MUL_ALPHA_MAP, AESTowerField8b);

#[rustfmt::skip]
const BINARY_TOWER_8B_INVERT_MAP : [u8; 256] = [
	0x00, 0x01, 0x03, 0x02, 0x06, 0x0e, 0x04, 0x0f, 0x0d, 0x0a, 0x09, 0x0c, 0x0b, 0x08, 0x05, 0x07,
	0x14, 0x67, 0x94, 0x7b, 0x10, 0x66, 0x9e, 0x7e, 0xd2, 0x81, 0x27, 0x4b, 0xd1, 0x8f, 0x2f, 0x42,
	0x3c, 0xe6, 0xde, 0x7c, 0xb3, 0xc1, 0x4a, 0x1a, 0x30, 0xe9, 0xdd, 0x79, 0xb1, 0xc6, 0x43, 0x1e,
	0x28, 0xe8, 0x9d, 0xb9, 0x63, 0x39, 0x8d, 0xc2, 0x62, 0x35, 0x83, 0xc5, 0x20, 0xe7, 0x97, 0xbb,
	0x61, 0x48, 0x1f, 0x2e, 0xac, 0xc8, 0xbc, 0x56, 0x41, 0x60, 0x26, 0x1b, 0xcf, 0xaa, 0x5b, 0xbe,
	0xef, 0x73, 0x6d, 0x5e, 0xf7, 0x86, 0x47, 0xbd, 0x88, 0xfc, 0xbf, 0x4e, 0x76, 0xe0, 0x53, 0x6c,
	0x49, 0x40, 0x38, 0x34, 0xe4, 0xeb, 0x15, 0x11, 0x8b, 0x85, 0xaf, 0xa9, 0x5f, 0x52, 0x98, 0x92,
	0xfb, 0xb5, 0xee, 0x51, 0xb7, 0xf0, 0x5c, 0xe1, 0xdc, 0x2b, 0x95, 0x13, 0x23, 0xdf, 0x17, 0x9f,
	0xd3, 0x19, 0xc4, 0x3a, 0x8a, 0x69, 0x55, 0xf6, 0x58, 0xfd, 0x84, 0x68, 0xc3, 0x36, 0xd0, 0x1d,
	0xa6, 0xf3, 0x6f, 0x99, 0x12, 0x7a, 0xba, 0x3e, 0x6e, 0x93, 0xa0, 0xf8, 0xb8, 0x32, 0x16, 0x7f,
	0x9a, 0xf9, 0xe2, 0xdb, 0xed, 0xd8, 0x90, 0xf2, 0xae, 0x6b, 0x4d, 0xce, 0x44, 0xc9, 0xa8, 0x6a,
	0xc7, 0x2c, 0xc0, 0x24, 0xfa, 0x71, 0xf1, 0x74, 0x9c, 0x33, 0x96, 0x3f, 0x46, 0x57, 0x4f, 0x5a,
	0xb2, 0x25, 0x37, 0x8c, 0x82, 0x3b, 0x2d, 0xb0, 0x45, 0xad, 0xd7, 0xff, 0xf4, 0xd4, 0xab, 0x4c,
	0x8e, 0x1c, 0x18, 0x80, 0xcd, 0xf5, 0xfe, 0xca, 0xa5, 0xec, 0xe3, 0xa3, 0x78, 0x2a, 0x22, 0x7d,
	0x5d, 0x77, 0xa2, 0xda, 0x64, 0xea, 0x21, 0x3d, 0x31, 0x29, 0xe5, 0x65, 0xd9, 0xa4, 0x72, 0x50,
	0x75, 0xb6, 0xa7, 0x91, 0xcc, 0xd5, 0x87, 0x54, 0x9b, 0xa1, 0xb4, 0x70, 0x59, 0x89, 0xd6, 0xcb,
];

impl_unary_ops!(TaggedInvertOrZero, invert_or_zero, BINARY_TOWER_8B_INVERT_MAP, BinaryField8b);
impl_unary_ops!(TaggedInvertOrZero, invert_or_zero, BINARY_TOWER_8B_INVERT_MAP, BinaryField4b);
impl_unary_ops!(TaggedInvertOrZero, invert_or_zero, BINARY_TOWER_8B_INVERT_MAP, BinaryField2b);

#[rustfmt::skip]
const AES_TOWER_8B_INVERT_MAP: [u8; 256] = [
    0x00, 0x01, 0x8d, 0xf6, 0xcb, 0x52, 0x7b, 0xd1, 0xe8, 0x4f, 0x29, 0xc0, 0xb0, 0xe1, 0xe5, 0xc7,
    0x74, 0xb4, 0xaa, 0x4b, 0x99, 0x2b, 0x60, 0x5f, 0x58, 0x3f, 0xfd, 0xcc, 0xff, 0x40, 0xee, 0xb2,
    0x3a, 0x6e, 0x5a, 0xf1, 0x55, 0x4d, 0xa8, 0xc9, 0xc1, 0x0a, 0x98, 0x15, 0x30, 0x44, 0xa2, 0xc2,
    0x2c, 0x45, 0x92, 0x6c, 0xf3, 0x39, 0x66, 0x42, 0xf2, 0x35, 0x20, 0x6f, 0x77, 0xbb, 0x59, 0x19,
    0x1d, 0xfe, 0x37, 0x67, 0x2d, 0x31, 0xf5, 0x69, 0xa7, 0x64, 0xab, 0x13, 0x54, 0x25, 0xe9, 0x09,
    0xed, 0x5c, 0x05, 0xca, 0x4c, 0x24, 0x87, 0xbf, 0x18, 0x3e, 0x22, 0xf0, 0x51, 0xec, 0x61, 0x17,
    0x16, 0x5e, 0xaf, 0xd3, 0x49, 0xa6, 0x36, 0x43, 0xf4, 0x47, 0x91, 0xdf, 0x33, 0x93, 0x21, 0x3b,
    0x79, 0xb7, 0x97, 0x85, 0x10, 0xb5, 0xba, 0x3c, 0xb6, 0x70, 0xd0, 0x06, 0xa1, 0xfa, 0x81, 0x82,
    0x83, 0x7e, 0x7f, 0x80, 0x96, 0x73, 0xbe, 0x56, 0x9b, 0x9e, 0x95, 0xd9, 0xf7, 0x02, 0xb9, 0xa4,
    0xde, 0x6a, 0x32, 0x6d, 0xd8, 0x8a, 0x84, 0x72, 0x2a, 0x14, 0x9f, 0x88, 0xf9, 0xdc, 0x89, 0x9a,
    0xfb, 0x7c, 0x2e, 0xc3, 0x8f, 0xb8, 0x65, 0x48, 0x26, 0xc8, 0x12, 0x4a, 0xce, 0xe7, 0xd2, 0x62,
    0x0c, 0xe0, 0x1f, 0xef, 0x11, 0x75, 0x78, 0x71, 0xa5, 0x8e, 0x76, 0x3d, 0xbd, 0xbc, 0x86, 0x57,
    0x0b, 0x28, 0x2f, 0xa3, 0xda, 0xd4, 0xe4, 0x0f, 0xa9, 0x27, 0x53, 0x04, 0x1b, 0xfc, 0xac, 0xe6,
    0x7a, 0x07, 0xae, 0x63, 0xc5, 0xdb, 0xe2, 0xea, 0x94, 0x8b, 0xc4, 0xd5, 0x9d, 0xf8, 0x90, 0x6b,
    0xb1, 0x0d, 0xd6, 0xeb, 0xc6, 0x0e, 0xcf, 0xad, 0x08, 0x4e, 0xd7, 0xe3, 0x5d, 0x50, 0x1e, 0xb3,
    0x5b, 0x23, 0x38, 0x34, 0x68, 0x46, 0x03, 0x8c, 0xdd, 0x9c, 0x7d, 0xa0, 0xcd, 0x1a, 0x41, 0x1c,
];

impl_unary_ops!(TaggedInvertOrZero, invert_or_zero, AES_TOWER_8B_INVERT_MAP, AESTowerField8b);

#[cfg(test)]
mod tests {
	use super::*;
	use crate::test_utils::{
		define_invert_tests, define_mul_alpha_tests, define_multiply_tests, define_square_tests,
	};

	define_multiply_tests!(TaggedMul<PairwiseTableStrategy>::mul, TaggedMul<PairwiseTableStrategy>);

	define_square_tests!(
		TaggedSquare<PairwiseTableStrategy>::square,
		TaggedSquare<PairwiseTableStrategy>
	);

	define_invert_tests!(
		TaggedInvertOrZero<PairwiseTableStrategy>::invert_or_zero,
		TaggedInvertOrZero<PairwiseTableStrategy>
	);

	define_mul_alpha_tests!(
		TaggedMulAlpha<PairwiseTableStrategy>::mul_alpha,
		TaggedMulAlpha<PairwiseTableStrategy>
	);
}
binius_field/arch/portable/pairwise_table_arithmetic.rs

binius_field/arch/portable/
pairwise_table_arithmetic.rs
