binius_field/arch/portable/
pairwise_table_arithmetic.rs

1// Copyright 2024-2025 Irreducible Inc.
2// Copyright 2026 The Binius Developers
3
4use bytemuck::TransparentWrapper;
5
6use super::packed::PackedPrimitiveType;
7use crate::{
8	AESTowerField8b,
9	aes_field::aes_mul_8b,
10	arithmetic_traits::{InvertOrZero, Square, WideMul},
11};
12
13/// Widening multiply for the portable 1×8b AES packing: a direct log/exp-table multiply (shared
14/// with the scalar via [`aes_mul_8b`]). The wide product is already the reduced byte, so `reduce`
15/// is the identity. Wider AES packings reach this per lane through the `Divide<u8, _, N>` strategy
16/// (see [`Divide`](crate::arch::Divide)).
17#[repr(transparent)]
18#[derive(TransparentWrapper)]
19pub struct AesLookupWideMul<T>(T);
20
21impl WideMul for AesLookupWideMul<PackedPrimitiveType<u8, AESTowerField8b>> {
22	type Output = PackedPrimitiveType<u8, AESTowerField8b>;
23
24	#[inline]
25	fn wide_mul(a: Self, b: Self) -> Self::Output {
26		let a = Self::peel(a).to_underlier();
27		let b = Self::peel(b).to_underlier();
28		PackedPrimitiveType::from_underlier(aes_mul_8b(a, b))
29	}
30
31	#[inline]
32	fn reduce(wide: Self::Output) -> Self {
33		Self::wrap(wide)
34	}
35}
36
37/// Square and invert strategy for the 1×8b AES packing: a direct table lookup on the underlying
38/// byte. Wider AES packings reach this one byte at a time through the
39/// [`Divide`](crate::arch::Divide) strategy, so no AES arithmetic is ever defined in terms of
40/// (packed) scalar iteration.
41#[repr(transparent)]
42#[derive(TransparentWrapper)]
43pub struct BytewiseLookup<T>(T);
44
45impl Square for BytewiseLookup<PackedPrimitiveType<u8, AESTowerField8b>> {
46	#[inline]
47	fn square(self) -> Self {
48		let byte = Self::peel(self).to_underlier();
49		Self::wrap(PackedPrimitiveType::from_underlier(AES_TOWER_8B_SQUARE_MAP[byte as usize]))
50	}
51}
52
53impl InvertOrZero for BytewiseLookup<PackedPrimitiveType<u8, AESTowerField8b>> {
54	#[inline]
55	fn invert_or_zero(self) -> Self {
56		let byte = Self::peel(self).to_underlier();
57		Self::wrap(PackedPrimitiveType::from_underlier(AES_TOWER_8B_INVERT_MAP[byte as usize]))
58	}
59}
60
61#[rustfmt::skip]
62const AES_TOWER_8B_SQUARE_MAP: [u8; 256] = [
63    0x00, 0x01, 0x04, 0x05, 0x10, 0x11, 0x14, 0x15, 0x40, 0x41, 0x44, 0x45, 0x50, 0x51, 0x54, 0x55,
64    0x1b, 0x1a, 0x1f, 0x1e, 0x0b, 0x0a, 0x0f, 0x0e, 0x5b, 0x5a, 0x5f, 0x5e, 0x4b, 0x4a, 0x4f, 0x4e,
65    0x6c, 0x6d, 0x68, 0x69, 0x7c, 0x7d, 0x78, 0x79, 0x2c, 0x2d, 0x28, 0x29, 0x3c, 0x3d, 0x38, 0x39,
66    0x77, 0x76, 0x73, 0x72, 0x67, 0x66, 0x63, 0x62, 0x37, 0x36, 0x33, 0x32, 0x27, 0x26, 0x23, 0x22,
67    0xab, 0xaa, 0xaf, 0xae, 0xbb, 0xba, 0xbf, 0xbe, 0xeb, 0xea, 0xef, 0xee, 0xfb, 0xfa, 0xff, 0xfe,
68    0xb0, 0xb1, 0xb4, 0xb5, 0xa0, 0xa1, 0xa4, 0xa5, 0xf0, 0xf1, 0xf4, 0xf5, 0xe0, 0xe1, 0xe4, 0xe5,
69    0xc7, 0xc6, 0xc3, 0xc2, 0xd7, 0xd6, 0xd3, 0xd2, 0x87, 0x86, 0x83, 0x82, 0x97, 0x96, 0x93, 0x92,
70    0xdc, 0xdd, 0xd8, 0xd9, 0xcc, 0xcd, 0xc8, 0xc9, 0x9c, 0x9d, 0x98, 0x99, 0x8c, 0x8d, 0x88, 0x89,
71    0x9a, 0x9b, 0x9e, 0x9f, 0x8a, 0x8b, 0x8e, 0x8f, 0xda, 0xdb, 0xde, 0xdf, 0xca, 0xcb, 0xce, 0xcf,
72    0x81, 0x80, 0x85, 0x84, 0x91, 0x90, 0x95, 0x94, 0xc1, 0xc0, 0xc5, 0xc4, 0xd1, 0xd0, 0xd5, 0xd4,
73    0xf6, 0xf7, 0xf2, 0xf3, 0xe6, 0xe7, 0xe2, 0xe3, 0xb6, 0xb7, 0xb2, 0xb3, 0xa6, 0xa7, 0xa2, 0xa3,
74    0xed, 0xec, 0xe9, 0xe8, 0xfd, 0xfc, 0xf9, 0xf8, 0xad, 0xac, 0xa9, 0xa8, 0xbd, 0xbc, 0xb9, 0xb8,
75    0x31, 0x30, 0x35, 0x34, 0x21, 0x20, 0x25, 0x24, 0x71, 0x70, 0x75, 0x74, 0x61, 0x60, 0x65, 0x64,
76    0x2a, 0x2b, 0x2e, 0x2f, 0x3a, 0x3b, 0x3e, 0x3f, 0x6a, 0x6b, 0x6e, 0x6f, 0x7a, 0x7b, 0x7e, 0x7f,
77    0x5d, 0x5c, 0x59, 0x58, 0x4d, 0x4c, 0x49, 0x48, 0x1d, 0x1c, 0x19, 0x18, 0x0d, 0x0c, 0x09, 0x08,
78    0x46, 0x47, 0x42, 0x43, 0x56, 0x57, 0x52, 0x53, 0x06, 0x07, 0x02, 0x03, 0x16, 0x17, 0x12, 0x13,
79];
80
81#[rustfmt::skip]
82const AES_TOWER_8B_INVERT_MAP: [u8; 256] = [
83    0x00, 0x01, 0x8d, 0xf6, 0xcb, 0x52, 0x7b, 0xd1, 0xe8, 0x4f, 0x29, 0xc0, 0xb0, 0xe1, 0xe5, 0xc7,
84    0x74, 0xb4, 0xaa, 0x4b, 0x99, 0x2b, 0x60, 0x5f, 0x58, 0x3f, 0xfd, 0xcc, 0xff, 0x40, 0xee, 0xb2,
85    0x3a, 0x6e, 0x5a, 0xf1, 0x55, 0x4d, 0xa8, 0xc9, 0xc1, 0x0a, 0x98, 0x15, 0x30, 0x44, 0xa2, 0xc2,
86    0x2c, 0x45, 0x92, 0x6c, 0xf3, 0x39, 0x66, 0x42, 0xf2, 0x35, 0x20, 0x6f, 0x77, 0xbb, 0x59, 0x19,
87    0x1d, 0xfe, 0x37, 0x67, 0x2d, 0x31, 0xf5, 0x69, 0xa7, 0x64, 0xab, 0x13, 0x54, 0x25, 0xe9, 0x09,
88    0xed, 0x5c, 0x05, 0xca, 0x4c, 0x24, 0x87, 0xbf, 0x18, 0x3e, 0x22, 0xf0, 0x51, 0xec, 0x61, 0x17,
89    0x16, 0x5e, 0xaf, 0xd3, 0x49, 0xa6, 0x36, 0x43, 0xf4, 0x47, 0x91, 0xdf, 0x33, 0x93, 0x21, 0x3b,
90    0x79, 0xb7, 0x97, 0x85, 0x10, 0xb5, 0xba, 0x3c, 0xb6, 0x70, 0xd0, 0x06, 0xa1, 0xfa, 0x81, 0x82,
91    0x83, 0x7e, 0x7f, 0x80, 0x96, 0x73, 0xbe, 0x56, 0x9b, 0x9e, 0x95, 0xd9, 0xf7, 0x02, 0xb9, 0xa4,
92    0xde, 0x6a, 0x32, 0x6d, 0xd8, 0x8a, 0x84, 0x72, 0x2a, 0x14, 0x9f, 0x88, 0xf9, 0xdc, 0x89, 0x9a,
93    0xfb, 0x7c, 0x2e, 0xc3, 0x8f, 0xb8, 0x65, 0x48, 0x26, 0xc8, 0x12, 0x4a, 0xce, 0xe7, 0xd2, 0x62,
94    0x0c, 0xe0, 0x1f, 0xef, 0x11, 0x75, 0x78, 0x71, 0xa5, 0x8e, 0x76, 0x3d, 0xbd, 0xbc, 0x86, 0x57,
95    0x0b, 0x28, 0x2f, 0xa3, 0xda, 0xd4, 0xe4, 0x0f, 0xa9, 0x27, 0x53, 0x04, 0x1b, 0xfc, 0xac, 0xe6,
96    0x7a, 0x07, 0xae, 0x63, 0xc5, 0xdb, 0xe2, 0xea, 0x94, 0x8b, 0xc4, 0xd5, 0x9d, 0xf8, 0x90, 0x6b,
97    0xb1, 0x0d, 0xd6, 0xeb, 0xc6, 0x0e, 0xcf, 0xad, 0x08, 0x4e, 0xd7, 0xe3, 0x5d, 0x50, 0x1e, 0xb3,
98    0x5b, 0x23, 0x38, 0x34, 0x68, 0x46, 0x03, 0x8c, 0xdd, 0x9c, 0x7d, 0xa0, 0xcd, 0x1a, 0x41, 0x1c,
99];
100
101// Correctness of the byte-lookup square/invert is covered end-to-end by the
102// `PackedAESBinaryField1x8b` square/invert proptests in `packed_aes.rs`, which route
103// `Square`/`InvertOrZero` through this strategy.
binius_field/arch/portable/pairwise_table_arithmetic.rs

binius_field/arch/portable/
pairwise_table_arithmetic.rs
