1use ark_ff::{
  2    biginteger::BigInteger768 as BigInteger,
  3    fields::{FftParameters, Fp768, Fp768Parameters, FpParameters},
  4};
  5
  6pub type Fq = Fp768<FqParameters>;
  7
  8pub struct FqParameters;
  9
 10impl Fp768Parameters for FqParameters {}
 11impl FftParameters for FqParameters {
 12    type BigInt = BigInteger;
 13
 14    const TWO_ADICITY: u32 = 15;
 15
 16    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
 17        0x3b079c7556ac378,
 18        0x2c8c74d04a3f00d4,
 19        0xd3b001061b90d4cf,
 20        0x946e77514891b0e6,
 21        0x79caec8ad6dc9ea1,
 22        0xbefd780edc81435d,
 23        0xe093d4dca630b154,
 24        0x43a0f673199f1c12,
 25        0x92276c78436253ff,
 26        0xe249d1cf014fcd24,
 27        0x96f36471fb7c3ec5,
 28        0x1080b8906b7c4,
 29    ]);
 30
 31    const SMALL_SUBGROUP_BASE: Option<u32> = Some(5);
 32    const SMALL_SUBGROUP_BASE_ADICITY: Option<u32> = Some(2);
 33    /// LARGE_SUBGROUP_ROOT_OF_UNITY =
 34    /// 12249458902762217747626832919710926618510011455364963726393752854649914979954138109976331601455448780251166045203053508523342111624583986869301658366625356826888785691823710598470775453742133593634524619429629803955083254436531
 35    const LARGE_SUBGROUP_ROOT_OF_UNITY: Option<BigInteger> = Some(BigInteger([
 36        8926681816978929800,
 37        10873079436792120119,
 38        6519893728366769435,
 39        7899277225737766970,
 40        8416573500933450083,
 41        12951641800297678468,
 42        7093775028595490583,
 43        14327009285082556021,
 44        18228411097456927576,
 45        2823658094446565457,
 46        1708328092507553067,
 47        109589007594791,
 48    ]));
 49}
 50impl FpParameters for FqParameters {
 51    /// MODULUS = 41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888253786114353726529584385201591605722013126468931404347949840543007986327743462853720628051692141265303114721689601
 52    const MODULUS: BigInteger = BigInteger([
 53        0x5e9063de245e8001,
 54        0xe39d54522cdd119f,
 55        0x638810719ac425f0,
 56        0x685acce9767254a4,
 57        0xb80f0da5cb537e38,
 58        0xb117e776f218059d,
 59        0x99d124d9a15af79d,
 60        0x7fdb925e8a0ed8d,
 61        0x5eb7e8f96c97d873,
 62        0xb7f997505b8fafed,
 63        0x10229022eee2cdad,
 64        0x1c4c62d92c411,
 65    ]);
 66
 67    const MODULUS_BITS: u32 = 753;
 68
 69    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
 70
 71    const REPR_SHAVE_BITS: u32 = 15;
 72
 73    const R: BigInteger = BigInteger([
 74        0x98a8ecabd9dc6f42,
 75        0x91cd31c65a034686,
 76        0x97c3e4a0cd14572e,
 77        0x79589819c788b601,
 78        0xed269c942108976f,
 79        0x1e0f4d8acf031d68,
 80        0x320c3bb713338559,
 81        0x598b4302d2f00a62,
 82        0x4074c9cbfd8ca621,
 83        0xfa47edb3865e88c,
 84        0x95455fb31ff9a195,
 85        0x7b479ec8e242,
 86    ]);
 87
 88    const R2: BigInteger = BigInteger([
 89        0x84717088cfd190c8,
 90        0xc7d9ff8e7df03c0a,
 91        0xa24bea56242b3507,
 92        0xa896a656a0714c7d,
 93        0x80a46659ff6f3ddf,
 94        0x2f47839ef88d7ce8,
 95        0xa8c86d4604a3b597,
 96        0xe03c79cac4f7ef07,
 97        0x2505daf1f4a81245,
 98        0x8e4605754c381723,
 99        0xb081f15bcbfdacaf,
100        0x2a33e89cb485,
101    ]);
102
103    const INV: u64 = 0xf2044cfbe45e7fff;
104
105    const GENERATOR: BigInteger = BigInteger([
106        0xa8f627f0e629635e,
107        0x202afce346c36872,
108        0x85e1ece733493254,
109        0x6d76e610664ac389,
110        0xdf542f3f04441585,
111        0x3aa4885bf6d4dd80,
112        0xeb8b63c1c0fffc74,
113        0xd2488e985f6cfa4e,
114        0xcce1c2a623f7a66a,
115        0x2a060f4d5085b19a,
116        0xa9111a596408842f,
117        0x11ca8d50bf627,
118    ]);
119
120    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
121        0xaf4831ef122f4000,
122        0x71ceaa29166e88cf,
123        0x31c40838cd6212f8,
124        0x342d6674bb392a52,
125        0xdc0786d2e5a9bf1c,
126        0xd88bf3bb790c02ce,
127        0xcce8926cd0ad7bce,
128        0x83fedc92f45076c6,
129        0xaf5bf47cb64bec39,
130        0xdbfccba82dc7d7f6,
131        0x88114811777166d6,
132        0xe26316c96208,
133    ]);
134
135    // T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
136
137    /// T = (MODULUS - 1) / 2^S =
138    /// 1278640471433073529124274133033466709233725278318907137200424283478556909563327233064541435662546964154604216671394463687571830033251476599169665701965732619291119517454523942352538645255842982596454713491581459512424155325
139    const T: BigInteger = BigInteger([
140        0x233ebd20c7bc48bd,
141        0x4be1c73aa8a459ba,
142        0xa948c71020e33588,
143        0xfc70d0b599d2ece4,
144        0xb3b701e1b4b96a6,
145        0xef3b622fceede430,
146        0xdb1b33a249b342b5,
147        0xb0e60ffb724bd141,
148        0x5fdabd6fd1f2d92f,
149        0x9b5b6ff32ea0b71f,
150        0x882220452045ddc5,
151        0x3898c5b25,
152    ]);
153
154    /// (T - 1) / 2 =
155    /// 639320235716536764562137066516733354616862639159453568600212141739278454781663616532270717831273482077302108335697231843785915016625738299584832850982866309645559758727261971176269322627921491298227356745790729756212077662
156    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
157        0x119f5e9063de245e,
158        0x25f0e39d54522cdd,
159        0x54a4638810719ac4,
160        0x7e38685acce97672,
161        0x59db80f0da5cb53,
162        0xf79db117e776f218,
163        0xed8d99d124d9a15a,
164        0xd87307fdb925e8a0,
165        0xafed5eb7e8f96c97,
166        0xcdadb7f997505b8f,
167        0xc41110229022eee2,
168        0x1c4c62d92,
169    ]);
170}