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
use crate::arithmetic::{bits_256::to_bits, utils::*};
#[inline]
pub const fn add(a: [u64; 4], b: [u64; 4], p: [u64; 4]) -> [u64; 4] {
let (l0, c) = adc(a[0], b[0], 0);
let (l1, c) = adc(a[1], b[1], c);
let (l2, c) = adc(a[2], b[2], c);
let (l3, _) = adc(a[3], b[3], c);
sub([l0, l1, l2, l3], p, p)
}
#[inline]
pub const fn sub(a: [u64; 4], b: [u64; 4], p: [u64; 4]) -> [u64; 4] {
let (l0, brw) = sbb(a[0], b[0], 0);
let (l1, brw) = sbb(a[1], b[1], brw);
let (l2, brw) = sbb(a[2], b[2], brw);
let (l3, brw) = sbb(a[3], b[3], brw);
let (l0, c) = adc(l0, p[0] & brw, 0);
let (l1, c) = adc(l1, p[1] & brw, c);
let (l2, c) = adc(l2, p[2] & brw, c);
let (l3, _) = adc(l3, p[3] & brw, c);
[l0, l1, l2, l3]
}
#[inline]
pub const fn double(a: [u64; 4], p: [u64; 4]) -> [u64; 4] {
add(a, a, p)
}
#[inline]
pub const fn mul(a: [u64; 4], b: [u64; 4], p: [u64; 4], inv: u64) -> [u64; 4] {
let (l0, c) = mac(0, a[0], b[0], 0);
let (l1, c) = mac(0, a[0], b[1], c);
let (l2, c) = mac(0, a[0], b[2], c);
let (l3, l4) = mac(0, a[0], b[3], c);
let (l1, c) = mac(l1, a[1], b[0], 0);
let (l2, c) = mac(l2, a[1], b[1], c);
let (l3, c) = mac(l3, a[1], b[2], c);
let (l4, l5) = mac(l4, a[1], b[3], c);
let (l2, c) = mac(l2, a[2], b[0], 0);
let (l3, c) = mac(l3, a[2], b[1], c);
let (l4, c) = mac(l4, a[2], b[2], c);
let (l5, l6) = mac(l5, a[2], b[3], c);
let (l3, c) = mac(l3, a[3], b[0], 0);
let (l4, c) = mac(l4, a[3], b[1], c);
let (l5, c) = mac(l5, a[3], b[2], c);
let (l6, l7) = mac(l6, a[3], b[3], c);
mont([l0, l1, l2, l3, l4, l5, l6, l7], p, inv)
}
#[inline]
pub const fn square(a: [u64; 4], p: [u64; 4], inv: u64) -> [u64; 4] {
mul(a, a, p, inv)
}
#[inline]
pub const fn neg(a: [u64; 4], p: [u64; 4]) -> [u64; 4] {
if (a[0] | a[1] | a[2] | a[3]) == 0 {
a
} else {
sub(p, a, p)
}
}
#[inline]
pub const fn mont(a: [u64; 8], p: [u64; 4], inv: u64) -> [u64; 4] {
let rhs = a[0].wrapping_mul(inv);
let (_, d) = mac(a[0], rhs, p[0], 0);
let (l1, d) = mac(a[1], rhs, p[1], d);
let (l2, d) = mac(a[2], rhs, p[2], d);
let (l3, d) = mac(a[3], rhs, p[3], d);
let (l4, e) = adc(a[4], 0, d);
let rhs = l1.wrapping_mul(inv);
let (_, d) = mac(l1, rhs, p[0], 0);
let (l2, d) = mac(l2, rhs, p[1], d);
let (l3, d) = mac(l3, rhs, p[2], d);
let (l4, d) = mac(l4, rhs, p[3], d);
let (l5, e) = adc(a[5], e, d);
let rhs = l2.wrapping_mul(inv);
let (_, d) = mac(l2, rhs, p[0], 0);
let (l3, d) = mac(l3, rhs, p[1], d);
let (l4, d) = mac(l4, rhs, p[2], d);
let (l5, d) = mac(l5, rhs, p[3], d);
let (l6, e) = adc(a[6], e, d);
let rhs = l3.wrapping_mul(inv);
let (_, d) = mac(l3, rhs, p[0], 0);
let (l4, d) = mac(l4, rhs, p[1], d);
let (l5, d) = mac(l5, rhs, p[2], d);
let (l6, d) = mac(l6, rhs, p[3], d);
let (l7, _) = adc(a[7], e, d);
sub([l4, l5, l6, l7], p, p)
}
#[inline]
pub fn invert(
a: [u64; 4],
little_fermat: [u64; 4],
identity: [u64; 4],
p: [u64; 4],
inv: u64,
) -> Option<[u64; 4]> {
let zero: [u64; 4] = [0; 4];
if a == zero {
None
} else {
Some(pow(a, little_fermat, identity, p, inv))
}
}
pub fn pow(a: [u64; 4], b: [u64; 4], mut identity: [u64; 4], p: [u64; 4], inv: u64) -> [u64; 4] {
let bits = to_bits(b);
for &bit in bits.iter() {
identity = square(identity, p, inv);
if bit == 1 {
identity = mul(identity, a, p, inv);
}
}
identity
}