1use ark_ff::{
  2    biginteger::{BigInt, BigInteger256 as BigInteger},
  3    fields::{FftParameters, Fp256, Fp256Parameters, FpParameters},
  4};
  5
  6pub type Fr = Fp256<FrParameters>;
  7
  8pub struct FrParameters;
  9
 10impl Fp256Parameters for FrParameters {}
 11impl FftParameters for FrParameters {
 12    type BigInt = BigInteger;
 13
 14    const TWO_ADICITY: u32 = 32;
 15
 16    #[rustfmt::skip]
 17    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInt::new([
 18        0xb9b58d8c5f0e466a,
 19        0x5b1b4c801819d7ec,
 20        0xaf53ae352a31e64,
 21        0x5bf3adda19e9b27b,
 22    ]);
 23}
 24impl FpParameters for FrParameters {
 25    /// MODULUS = 52435875175126190479447740508185965837690552500527637822603658699938581184513
 26    #[rustfmt::skip]
 27    const MODULUS: BigInteger = BigInt::new([
 28        0xffffffff00000001,
 29        0x53bda402fffe5bfe,
 30        0x3339d80809a1d805,
 31        0x73eda753299d7d48,
 32    ]);
 33
 34    const MODULUS_BITS: u32 = 255;
 35
 36    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
 37
 38    const REPR_SHAVE_BITS: u32 = 1;
 39
 40    /// R = 10920338887063814464675503992315976177888879664585288394250266608035967270910
 41    #[rustfmt::skip]
 42    const R: BigInteger = BigInt::new([
 43        0x1fffffffe,
 44        0x5884b7fa00034802,
 45        0x998c4fefecbc4ff5,
 46        0x1824b159acc5056f,
 47    ]);
 48
 49    #[rustfmt::skip]
 50    const R2: BigInteger = BigInt::new([
 51        0xc999e990f3f29c6d,
 52        0x2b6cedcb87925c23,
 53        0x5d314967254398f,
 54        0x748d9d99f59ff11,
 55    ]);
 56
 57    const INV: u64 = 0xfffffffeffffffff;
 58
 59    /// GENERATOR = 7
 60    /// Encoded in Montgomery form, so the value here is
 61    /// 7 * R % q = 24006497034320510773280787438025867407531605151569380937148207556313189711857
 62    #[rustfmt::skip]
 63    const GENERATOR: BigInteger = BigInt::new([
 64        0xefffffff1,
 65        0x17e363d300189c0f,
 66        0xff9c57876f8457b0,
 67        0x351332208fc5a8c4,
 68    ]);
 69
 70    #[rustfmt::skip]
 71    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInt::new([
 72        0x7fffffff80000000,
 73        0xa9ded2017fff2dff,
 74        0x199cec0404d0ec02,
 75        0x39f6d3a994cebea4,
 76    ]);
 77
 78    // T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
 79    // For T coprime to 2
 80
 81    // T = (MODULUS - 1) / 2^S =
 82    // 12208678567578594777604504606729831043093128246378069236549469339647
 83    #[rustfmt::skip]
 84    const T: BigInteger = BigInt::new([
 85        0xfffe5bfeffffffff,
 86        0x9a1d80553bda402,
 87        0x299d7d483339d808,
 88        0x73eda753,
 89    ]);
 90
 91    // (T - 1) / 2 =
 92    // 6104339283789297388802252303364915521546564123189034618274734669823
 93    #[rustfmt::skip]
 94    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInt::new([
 95        0x7fff2dff7fffffff,
 96        0x4d0ec02a9ded201,
 97        0x94cebea4199cec04,
 98        0x39f6d3a9,
 99    ]);
100}