1use ark_ff::{
  2    biginteger::{BigInt, BigInteger768 as BigInteger},
  3    fields::{FftParameters, Fp768, Fp768Parameters, FpParameters},
  4};
  5
  6pub type Fr = Fp768<FrParameters>;
  7
  8pub struct FrParameters;
  9
 10impl Fp768Parameters for FrParameters {}
 11impl FftParameters for FrParameters {
 12    type BigInt = BigInteger;
 13
 14    const TWO_ADICITY: u32 = 30;
 15
 16    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInt::new([
 17        0x307f66b297671883,
 18        0xd72a7f2b1e645f4e,
 19        0x67079daa9a902283,
 20        0xf33f7620a86c668b,
 21        0x8878570d66464c12,
 22        0xa557af5b524f522b,
 23        0x5fafa3f6ef19319d,
 24        0x1eb9e04110a65629,
 25        0x3f96feb3c639a0b0,
 26        0x4d4fe37df3ffd732,
 27        0xadc831bd55bcf3e9,
 28        0x1b9f32a8bd6ab,
 29    ]);
 30}
 31impl FpParameters for FrParameters {
 32    /// MODULUS = 41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888458477323173057491593855069696241854796396165721416325350064441470418137846398469611935719059908164220784476160001
 33    const MODULUS: BigInteger = BigInt::new([
 34        0xd90776e240000001,
 35        0x4ea099170fa13a4f,
 36        0xd6c381bc3f005797,
 37        0xb9dff97634993aa4,
 38        0x3eebca9429212636,
 39        0xb26c5c28c859a99b,
 40        0x99d124d9a15af79d,
 41        0x7fdb925e8a0ed8d,
 42        0x5eb7e8f96c97d873,
 43        0xb7f997505b8fafed,
 44        0x10229022eee2cdad,
 45        0x1c4c62d92c411,
 46    ]);
 47
 48    const MODULUS_BITS: u32 = 753;
 49
 50    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
 51
 52    const REPR_SHAVE_BITS: u32 = 15;
 53
 54    const R: BigInteger = BigInt::new([
 55        0xb99680147fff6f42,
 56        0x4eb16817b589cea8,
 57        0xa1ebd2d90c79e179,
 58        0xf725caec549c0da,
 59        0xab0c4ee6d3e6dad4,
 60        0x9fbca908de0ccb62,
 61        0x320c3bb713338498,
 62        0x598b4302d2f00a62,
 63        0x4074c9cbfd8ca621,
 64        0xfa47edb3865e88c,
 65        0x95455fb31ff9a195,
 66        0x7b479ec8e242,
 67    ]);
 68
 69    const R2: BigInteger = BigInt::new([
 70        0x3f9c69c7b7f4c8d1,
 71        0x70a50fa9ee48d127,
 72        0xcdbe6702009569cb,
 73        0x6bd8c6c6c49edc38,
 74        0x7955876cc35ee94e,
 75        0xc7285529be54a3f4,
 76        0xded52121ecec77cf,
 77        0x99be80f2ee12ee8e,
 78        0xc8a0ff01493bdcef,
 79        0xacc27988f3d9a316,
 80        0xd9e817a8fb44b3c9,
 81        0x5b58037e0e4,
 82    ]);
 83
 84    const INV: u64 = 0xc90776e23fffffff;
 85
 86    const GENERATOR: BigInteger = BigInt::new([
 87        0xeee0a5d37ff6635e,
 88        0xff458536cfa1cff4,
 89        0x659af978d8169ab0,
 90        0x1f1841c24780e3f1,
 91        0x602213036dcfef3a,
 92        0xd1d5c8f39d72db20,
 93        0xeb8b63c1c0ffefab,
 94        0xd2488e985f6cfa4e,
 95        0xcce1c2a623f7a66a,
 96        0x2a060f4d5085b19a,
 97        0xa9111a596408842f,
 98        0x11ca8d50bf627,
 99    ]);
100
101    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInt::new([
102        0xec83bb7120000000,
103        0xa7504c8b87d09d27,
104        0x6b61c0de1f802bcb,
105        0x5ceffcbb1a4c9d52,
106        0x9f75e54a1490931b,
107        0xd9362e14642cd4cd,
108        0xcce8926cd0ad7bce,
109        0x83fedc92f45076c6,
110        0xaf5bf47cb64bec39,
111        0xdbfccba82dc7d7f6,
112        0x88114811777166d6,
113        0xe26316c96208,
114    ]);
115
116    // T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
117
118    /// T = (MODULUS - 1) / 2^S =
119    /// 39021010480745652133919498688765463538626870065884617224134041854204007249857398469987226430131438115069708760723898631821547688442835449306011425196003537779414482717728302293895201885929702287178426719326440397855625
120    const T: BigInteger = BigInt::new([
121        0x3e84e93f641ddb89,
122        0xfc015e5d3a82645c,
123        0xd264ea935b0e06f0,
124        0xa48498dae77fe5d8,
125        0x2166a66cfbaf2a50,
126        0x856bde76c9b170a3,
127        0xa283b63667449366,
128        0xb25f61cc1ff6e497,
129        0x6e3ebfb57adfa3e5,
130        0xbb8b36b6dfe65d41,
131        0xb64b1044408a408b,
132        0x71318,
133    ]);
134
135    /// (T - 1) / 2 =
136    /// 19510505240372826066959749344382731769313435032942308612067020927102003624928699234993613215065719057534854380361949315910773844221417724653005712598001768889707241358864151146947600942964851143589213359663220198927812
137    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInt::new([
138        0x1f42749fb20eedc4,
139        0x7e00af2e9d41322e,
140        0x69327549ad870378,
141        0x52424c6d73bff2ec,
142        0x90b353367dd79528,
143        0x42b5ef3b64d8b851,
144        0xd141db1b33a249b3,
145        0xd92fb0e60ffb724b,
146        0xb71f5fdabd6fd1f2,
147        0xddc59b5b6ff32ea0,
148        0x5b25882220452045,
149        0x3898c,
150    ]);
151}