1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173

// Copyright 2023-2024 Ulvetanna 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)
	}
}

/// The trait represents the relation between the packed fields of the same bit size
/// where one scalar is the extension of the other one.
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_mut(&mut self) -> &mut Self::PackedSubfield;

	fn cast_ext(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_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_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())
	}
}

/// 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)
	}
}