1use ark_ff::{
 2    fields::fp3::{Fp3, Fp3Config},
 3    Field, MontFp,
 4};
 5
 6use crate::Fq;
 7
 8pub type Fq3 = Fp3<Fq3Config>;
 9
10pub struct Fq3Config;
11
12impl Fp3Config for Fq3Config {
13    type Fp = Fq;
14
15    /// NONRESIDUE = -4
16    // Fq3 = Fq\[u\]/u^3+4
17    const NONRESIDUE: Fq = MontFp!("-4");
18
19    // (MODULUS^3 - 1) % 2^TWO_ADICITY == 0
20    const TWO_ADICITY: u32 = 1;
21
22    // (T-1)/2 with T = (MODULUS^3-1) / 2^TWO_ADICITY
23    #[rustfmt::skip]
24    const TRACE_MINUS_ONE_DIV_TWO: &'static [u64] = &[
25        0xb5e7c000000a3eac,
26        0xf79b99dbf41cf4ab,
27        0xe9372b1919e55ee5,
28        0xbb7bbc4936c1980b,
29        0x7c0cb9d4399b36e1,
30        0x73304a5507bb1ae0,
31        0x92f639be8963936f,
32        0x4f574ac2439ba816,
33        0x670d9bd389dd29ef,
34        0x606ddf900d2124f1,
35        0x928fb14985ec3270,
36        0x6b2f2428c5f420f3,
37        0xac9ade29d5ab5fbe,
38        0xec0d0434c4005822,
39        0x973f10d7f3c5c108,
40        0x6d5e83fc81095979,
41        0xdac3e6e4e1647752,
42        0x227febf93994603e,
43        0x4ab8755d894167d1,
44        0x4fd2d3f67d8b537a,
45        0x33e196a4d5f4030a,
46        0x88b51fb72092df1a,
47        0xa67e5b1e8fc48316,
48        0xb0855eb2a00d7dab,
49        0xe875dd2da6751442,
50        0x777594a243e25676,
51        0x294e0f70376a85a8,
52        0x83f431c7988e4f18,
53        0x8e8fb6af3ca2f5f1,
54        0x7297896b4b9e90f1,
55        0xff38f54664d66123,
56        0xb5ecf80bfff41e13,
57        0x1662a3666bb8392a,
58        0x07a0968e8742d3e1,
59        0xf12927e564bcdfdc,
60        0x5de9825a0e,
61    ];
62
63    // NONRESIDUE^T % q
64    const QUADRATIC_NONRESIDUE_TO_T: Fq3 = Fq3::new(
65        MontFp!("6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068298"),
66        Fq::ZERO,
67        Fq::ZERO,
68    );
69
70    // NQR ^ (MODULUS^i - 1)/3, i=0,1,2 with NQR = u = (0,1,0)
71    const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
72        Fq::ONE,
73        MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
74        MontFp!("1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
75    ];
76
77    // NQR ^ (2*MODULUS^i - 2)/3, i=0,1,2 with NQR = u = (0,1,0)
78    const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[
79        Fq::ONE,
80        MontFp!("1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
81        MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
82    ];
83
84    #[inline(always)]
85    fn mul_fp_by_nonresidue(fe: &Self::Fp) -> Self::Fp {
86        let original = -(*fe);
87        let double = original + &original;
88        double + &double
89    }
90}