Upgrade to work with latest ark-ff (#95)

Co-authored-by: Sun <huachuang20@gmail.com>
2026-01-09 07:21:30 +01:00 · 2022-03-07 13:12:03 -08:00
parent d0dc200f22
commit 1551d6d76c
231 changed files with 2830 additions and 4343 deletions
--- a/ed_on_bls12_381_bandersnatch/Cargo.toml
+++ b/ed_on_bls12_381_bandersnatch/Cargo.toml
@@ -25,10 +25,10 @@ ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-featu

 [features]
 default = []
-std = [ 
-    "ark-std/std", 
-    "ark-ff/std", 
-    "ark-ec/std", 
-    "ark-bls12-381/std" 
+std = [
+    "ark-std/std",
+    "ark-ff/std",
+    "ark-ec/std",
+    "ark-bls12-381/std"
 ]
 r1cs = ["ark-r1cs-std"]
--- a/ed_on_bls12_381_bandersnatch/scripts/base_field.sage
+++ b/ed_on_bls12_381_bandersnatch/scripts/base_field.sage
@@ -0,0 +1,28 @@
+modulus = 52435875175126190479447740508185965837690552500527637822603658699938581184513
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)
--- a/ed_on_bls12_381_bandersnatch/scripts/scalar_field.sage
+++ b/ed_on_bls12_381_bandersnatch/scripts/scalar_field.sage
@@ -0,0 +1,28 @@
+modulus = 13108968793781547619861935127046491459309155893440570251786403306729687672801
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)
--- a/ed_on_bls12_381_bandersnatch/src/constraints/curves.rs
+++ b/ed_on_bls12_381_bandersnatch/src/constraints/curves.rs
@@ -1,6 +1,7 @@
-use crate::{constraints::FqVar, *};
 use ark_r1cs_std::groups::curves::{short_weierstrass::ProjectiveVar, twisted_edwards::AffineVar};

+use crate::{constraints::FqVar, *};
+
 /// A variable that is the R1CS equivalent of `crate::BandersnatchParameters`.
 pub type EdwardsVar = AffineVar<BandersnatchParameters, FqVar>;

--- a/ed_on_bls12_381_bandersnatch/src/curves/mod.rs
+++ b/ed_on_bls12_381_bandersnatch/src/curves/mod.rs
@@ -1,4 +1,3 @@
-use crate::{Fq, Fr};
 use ark_ec::{
    models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
    short_weierstrass_jacobian::{
@@ -7,7 +6,9 @@ use ark_ec::{
    twisted_edwards_extended::{GroupAffine, GroupProjective},
    SWModelParameters,
 };
-use ark_ff::{field_new, Field};
+use ark_ff::{Field, MontFp};
+
+use crate::{Fq, Fr};

 #[cfg(test)]
 mod tests;
@@ -18,8 +19,8 @@ pub type EdwardsProjective = GroupProjective<BandersnatchParameters>;
 pub type SWAffine = SWGroupAffine<BandersnatchParameters>;
 pub type SWProjective = SWGroupProjective<BandersnatchParameters>;

-/// `bandersnatch` is a twisted Edwards curve. These curves have equations of the
-/// form: ax² + y² = 1 - dx²y².
+/// `bandersnatch` is a twisted Edwards curve. These curves have equations of
+/// the form: ax² + y² = 1 - dx²y².
 /// over some base finite field Fq.
 ///
 /// bandersnatch's curve equation: -5x² + y² = 1 - dx²y²
@@ -50,7 +51,6 @@ pub type SWProjective = SWGroupProjective<BandersnatchParameters>;
 ///
 /// Script to transfer between different curves are available
 /// <https://github.com/zhenfeizhang/bandersnatch/blob/main/bandersnatch/script/bandersnatch.sage>
-///
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct BandersnatchParameters;

@@ -66,18 +66,22 @@ impl ModelParameters for BandersnatchParameters {

    /// COFACTOR^(-1) mod r =
    /// 9831726595336160714896451345284868594481866920080427688839802480047265754601
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "9831726595336160714896451345284868594481866920080427688839802480047265754601");
+    const COFACTOR_INV: Fr = MontFp!(
+        Fr,
+        "9831726595336160714896451345284868594481866920080427688839802480047265754601"
+    );
 }

 impl TEModelParameters for BandersnatchParameters {
    /// COEFF_A = -5
-    const COEFF_A: Fq = field_new!(Fq, "-5");
+    const COEFF_A: Fq = MontFp!(Fq, "-5");

    /// COEFF_D = (138827208126141220649022263972958607803/
    /// 171449701953573178309673572579671231137) mod q
-    #[rustfmt::skip]
-    const COEFF_D: Fq = field_new!(Fq, "45022363124591815672509500913686876175488063829319466900776701791074614335719");
+    const COEFF_D: Fq = MontFp!(
+        Fq,
+        "45022363124591815672509500913686876175488063829319466900776701791074614335719"
+    );

    /// AFFINE_GENERATOR_COEFFS = (GENERATOR_X, GENERATOR_Y)
    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
@@ -95,44 +99,65 @@ impl TEModelParameters for BandersnatchParameters {

 impl MontgomeryModelParameters for BandersnatchParameters {
    /// COEFF_A = 29978822694968839326280996386011761570173833766074948509196803838190355340952
-    #[rustfmt::skip]
-    const COEFF_A: Fq = field_new!(Fq, "29978822694968839326280996386011761570173833766074948509196803838190355340952");
+    const COEFF_A: Fq = MontFp!(
+        Fq,
+        "29978822694968839326280996386011761570173833766074948509196803838190355340952"
+    );

    /// COEFF_B = 25465760566081946422412445027709227188579564747101592991722834452325077642517
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, "25465760566081946422412445027709227188579564747101592991722834452325077642517");
+    const COEFF_B: Fq = MontFp!(
+        Fq,
+        "25465760566081946422412445027709227188579564747101592991722834452325077642517"
+    );

    type TEModelParameters = BandersnatchParameters;
 }

 // The TE form generator is generated following Zcash's fashion:
-//  "The generators of G1 and G2 are computed by finding the lexicographically smallest
-//   valid x-coordinate, and its lexicographically smallest y-coordinate and scaling it
-//   by the cofactor such that the result is not the point at infinity."
-// The SW form generator is the same TE generator converted into SW form, obtained from the scripts:
+//  "The generators of G1 and G2 are computed by finding the lexicographically
+//   smallest valid x-coordinate, and its lexicographically smallest
+//   y-coordinate and scaling it by the cofactor such that the result is not
+//   the point at infinity."
+// The SW form generator is the same TE generator converted into SW form,
+// obtained from the scripts:
 //   <https://github.com/zhenfeizhang/bandersnatch/blob/main/bandersnatch/script/bandersnatch.sage>

 /// x coordinate for TE curve generator
-#[rustfmt::skip]
-const TE_GENERATOR_X: Fq = field_new!(Fq, "18886178867200960497001835917649091219057080094937609519140440539760939937304");
+const TE_GENERATOR_X: Fq = MontFp!(
+    Fq,
+    "18886178867200960497001835917649091219057080094937609519140440539760939937304"
+);
+
 /// y coordinate for TE curve generator
-#[rustfmt::skip]
-const TE_GENERATOR_Y: Fq = field_new!(Fq, "19188667384257783945677642223292697773471335439753913231509108946878080696678");
+const TE_GENERATOR_Y: Fq = MontFp!(
+    Fq,
+    "19188667384257783945677642223292697773471335439753913231509108946878080696678"
+);
+
 /// x coordinate for SW curve generator
-#[rustfmt::skip]
-const SW_GENERATOR_X: Fq = field_new!(Fq, "30900340493481298850216505686589334086208278925799850409469406976849338430199");
+const SW_GENERATOR_X: Fq = MontFp!(
+    Fq,
+    "30900340493481298850216505686589334086208278925799850409469406976849338430199"
+);
+
 /// y coordinate for SW curve generator
-#[rustfmt::skip]
-const SW_GENERATOR_Y: Fq = field_new!(Fq, "12663882780877899054958035777720958383845500985908634476792678820121468453298");
+const SW_GENERATOR_Y: Fq = MontFp!(
+    Fq,
+    "12663882780877899054958035777720958383845500985908634476792678820121468453298"
+);

 impl SWModelParameters for BandersnatchParameters {
    /// COEFF_A = 10773120815616481058602537765553212789256758185246796157495669123169359657269
-    #[rustfmt::skip]
-    const COEFF_A: Self::BaseField = field_new!(Fq, "10773120815616481058602537765553212789256758185246796157495669123169359657269");
+    const COEFF_A: Self::BaseField = MontFp!(
+        Fq,
+        "10773120815616481058602537765553212789256758185246796157495669123169359657269"
+    );

    /// COEFF_B = 29569587568322301171008055308580903175558631321415017492731745847794083609535
-    #[rustfmt::skip]
-    const COEFF_B: Self::BaseField = field_new!(Fq, "29569587568322301171008055308580903175558631321415017492731745847794083609535");
+    const COEFF_B: Self::BaseField = MontFp!(
+        Fq,
+        "29569587568322301171008055308580903175558631321415017492731745847794083609535"
+    );

    /// generators
    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
--- a/ed_on_bls12_381_bandersnatch/src/curves/tests.rs
+++ b/ed_on_bls12_381_bandersnatch/src/curves/tests.rs
@@ -1,9 +1,10 @@
-use crate::*;
 use ark_algebra_test_templates::{curves::*, groups::*};
 use ark_ec::{AffineCurve, ProjectiveCurve};
 use ark_ff::{bytes::FromBytes, Zero};
 use ark_std::{rand::Rng, str::FromStr, test_rng};

+use crate::*;
+
 #[test]
 fn test_projective_curve() {
    curve_tests::<EdwardsProjective>();
--- a/ed_on_bls12_381_bandersnatch/src/fields/fq.rs
+++ b/ed_on_bls12_381_bandersnatch/src/fields/fq.rs
@@ -1 +1 @@
-pub use ark_bls12_381::{Fr as Fq, FrParameters as FqParameters};
+pub use ark_bls12_381::{Fr as Fq, FrConfig as FqConfig};
--- a/ed_on_bls12_381_bandersnatch/src/fields/fr.rs
+++ b/ed_on_bls12_381_bandersnatch/src/fields/fr.rs
@@ -1,115 +1,7 @@
-use ark_ff::{
-    biginteger::{BigInt, BigInteger256 as BigInteger},
-    fields::{FftParameters, Fp256, Fp256Parameters, FpParameters},
-};
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};

-pub type Fr = Fp256<FrParameters>;
-
-pub struct FrParameters;
-
-impl Fp256Parameters for FrParameters {}
-impl FftParameters for FrParameters {
-    type BigInt = BigInteger;
-
-    /// Let `N` be the size of the multiplicative group defined by the field.
-    /// Then `TWO_ADICITY` is the two-adicity of `N`, i.e. the integer `s`
-    /// such that `N = 2^s * t` for some odd integer `t`.
-    const TWO_ADICITY: u32 = 5;
-
-    /// 2^s root of unity computed by GENERATOR^t
-    /// 4740934665446857387895054948191089665295030226009829406950782728666658007874
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInt::new([
-        0xa4dcdba087826b42,
-        0x6e4ab162f57f862a,
-        0xabc5492749348d6a,
-        0xa7b462035f8c169,
-    ]);
-}
-impl FpParameters for FrParameters {
-    /// The modulus of the field.
-    /// MODULUS = 13108968793781547619861935127046491459309155893440570251786403306729687672801.
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInt::new([
-        0x74fd06b52876e7e1,
-        0xff8f870074190471,
-        0x0cce760202687600,
-        0x1cfb69d4ca675f52,
-    ]);
-
-    /// The number of bits needed to represent the `Self::MODULUS`.
-    const MODULUS_BITS: u32 = 253;
-
-    /// The number of bits that can be reliably stored.
-    /// (Should equal `SELF::MODULUS_BITS - 1`)
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    /// The number of bits that must be shaved from the beginning of
-    /// the representation when randomly sampling.
-    const REPR_SHAVE_BITS: u32 = 4;
-
-    /// Let `M` be the power of 2^64 nearest to `Self::MODULUS_BITS`. Then
-    /// `R = M % Self::MODULUS`.
-    /// R = 10920338887063814464675503992315976178796737518116002025166357554075628257528
-    #[rustfmt::skip]
-    const R: BigInteger = BigInt::new([
-        0x5817ca56bc48c0f8,
-        0x0383c7fc5f37dc74,
-        0x998c4fefecbc4ff8,
-        0x1824b159acc5056f,
-    ]);
-
-    /// R2 = R^2 % Self::MODULUS
-    /// R2 = 4932290691328759802879919559207542894238895193980447506221046538067943049163
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInt::new([
-        0xdbb4f5d658db47cb,
-        0x40fa7ca27fecb938,
-        0xaa9e6daec0055cea,
-        0xae793ddb14aec7d
-    ]);
-
-    /// INV = -MODULUS^{-1} mod 2^64
-    /// INV = 17410672245482742751
-    const INV: u64 = 0xf19f22295cc063df;
-
-    /// A multiplicative generator of the field.
-    /// `Self::GENERATOR` is an element having multiplicative order
-    /// `Self::MODULUS - 1`.
-    /// n = 9962557815892774795293348142308860067333132192265356416788884706064406244838
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInt::new([
-        0x56b6f3ab7b616de6,
-        0x114f419d6c9083e5,
-        0xbf518d217780c4b9,
-        0x16069b9f45dbce7f,
-    ]);
-
-    /// (Self::MODULUS - 1) / 2
-    /// 6554484396890773809930967563523245729654577946720285125893201653364843836400
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInt::new([
-        0xba7e835a943b73f0,
-        0x7fc7c3803a0c8238,
-        0x06673b0101343b00,
-        0xe7db4ea6533afa9,
-    ]);
-
-    /// t for 2^s * t = MODULUS - 1, and t coprime to 2.
-    /// t = 409655274805673363120685472720202858103411121670017820368325103335302739775
-    ///   = (modulus-1)/2^5
-    const T: BigInteger = BigInt::new([
-        0x8ba7e835a943b73f,
-        0x07fc7c3803a0c823,
-        0x906673b0101343b0,
-        0xe7db4ea6533afa,
-    ]);
-
-    /// (t - 1) / 2
-    ///  = 204827637402836681560342736360101429051705560835008910184162551667651369887
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInt::new([
-        0xc5d3f41ad4a1db9f,
-        0x03fe3e1c01d06411,
-        0x483339d80809a1d8,
-        0x73eda753299d7d,
-    ]);
-}
+#[derive(MontConfig)]
+#[modulus = "13108968793781547619861935127046491459309155893440570251786403306729687672801"]
+#[generator = "7"]
+pub struct FrConfig;
+pub type Fr = Fp256<MontBackend<FrConfig, 4>>;
--- a/ed_on_bls12_381_bandersnatch/src/fields/mod.rs
+++ b/ed_on_bls12_381_bandersnatch/src/fields/mod.rs
@@ -4,5 +4,5 @@ pub mod fr;
 pub use fq::*;
 pub use fr::*;

-#[cfg(all(feature = "ed_on_bls12_381_bandersnatch", test))]
+#[cfg(test)]
 mod tests;
--- a/ed_on_bls12_381_bandersnatch/src/fields/tests.rs
+++ b/ed_on_bls12_381_bandersnatch/src/fields/tests.rs
@@ -1,30 +1,20 @@
-use crate::{Fq, Fr};
-use ark_algebra_test_templates::fields::*;
+use ark_algebra_test_templates::{
+    fields::*, generate_field_serialization_test, generate_field_test,
+};
 use ark_ff::{
    biginteger::BigInteger256 as BigInteger,
    bytes::{FromBytes, ToBytes},
-    fields::{Field, LegendreSymbol::*, SquareRootField},
-    One, Zero,
+    fields::{Field, LegendreSymbol::*, PrimeField, SquareRootField},
+    One, UniformRand, Zero,
 };
+use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
 use ark_std::{rand::Rng, str::FromStr, test_rng};
+use core::ops::{AddAssign, MulAssign, SubAssign};

-#[test]
-fn test_fr() {
-    let mut rng = test_rng();
-    let a: Fr = rng.gen();
-    let b: Fr = rng.gen();
-    field_test(a, b);
-    primefield_test::<Fr>();
-}
+use crate::{Fq, FqConfig, Fr, FrConfig};

-#[test]
-fn test_fq() {
-    let mut rng = test_rng();
-    let a: Fq = rng.gen();
-    let b: Fq = rng.gen();
-    field_test(a, b);
-    primefield_test::<Fq>();
-}
+generate_field_test!(ed_on_bls12_381_bandersnatch; mont(4, 4); );
+generate_field_serialization_test!(ed_on_bls12_381_bandersnatch;);

 #[test]
 fn test_fq_add() {
@@ -145,22 +135,6 @@ fn test_fq_sub() {
    assert_eq!(f1 - &f2, f3);
 }

-#[test]
-fn test_fq_double_in_place() {
-    let mut f1 = Fq::from_str(
-        "29729289787452206300641229002276778748586801323231253291984198106063944136114",
-    )
-    .unwrap();
-    let f3 = Fq::from_str(
-        "7022704399778222121834717496367591659483050145934868761364737512189307087715",
-    )
-    .unwrap();
-    assert!(!f1.is_zero());
-    assert!(!f3.is_zero());
-    f1.double_in_place();
-    assert_eq!(f1, f3);
-}
-
 #[test]
 fn test_fq_double_in_place_thrice() {
    let mut f1 = Fq::from_str(
@@ -277,22 +251,9 @@ fn test_fq_square_in_place() {
    assert_eq!(f1, f3);
 }

-#[test]
-fn test_fq_sqrt() {
-    let f1 = Fq::from_str(
-        "10875927553327821418567659853801220899541454800710193788767706167237535308235",
-    )
-    .unwrap();
-    let f3 = Fq::from_str(
-        "10816221372957505053219354782681292880545918527618367765651802809826238616708",
-    )
-    .unwrap();
-    assert_eq!(f1.sqrt().unwrap(), f3);
-}
-
 #[test]
 fn test_fq_from_str() {
-    let f1_from_repr = Fq::from(BigInteger([
+    let f1_from_repr = Fq::from(BigInteger::new([
        0xab8a2535947d1a77,
        0x9ba74cbfda0bbcda,
        0xe928b59724d60baf,
@@ -302,7 +263,7 @@ fn test_fq_from_str() {
        "13026376210409056429264774981357153555336288129100724591327877625017068755575",
    )
    .unwrap();
-    let f2_from_repr = Fq::from(BigInteger([
+    let f2_from_repr = Fq::from(BigInteger::new([
        0x97e9103775d2f35c,
        0xbe6756b6c587544b,
        0x6ee38c3afd88ef4b,
@@ -321,14 +282,14 @@ fn test_fq_legendre() {
    assert_eq!(QuadraticResidue, Fq::one().legendre());
    assert_eq!(Zero, Fq::zero().legendre());

-    let e = BigInteger([
+    let e = BigInteger::new([
        0x0dbc5349cd5664da,
        0x8ac5b6296e3ae29d,
        0x127cb819feceaa3b,
        0x3a6b21fb03867191,
    ]);
    assert_eq!(QuadraticResidue, Fq::from(e).legendre());
-    let e = BigInteger([
+    let e = BigInteger::new([
        0x96341aefd047c045,
        0x9b5f4254500a4d65,
        0x1ee08223b68ac240,
@@ -339,7 +300,7 @@ fn test_fq_legendre() {

 #[test]
 fn test_fq_bytes() {
-    let f1_from_repr = Fq::from(BigInteger([
+    let f1_from_repr = Fq::from(BigInteger::new([
        0xab8a2535947d1a77,
        0x9ba74cbfda0bbcda,
        0xe928b59724d60baf,
@@ -355,19 +316,19 @@ fn test_fq_bytes() {

 #[test]
 fn test_fr_add() {
-    let f1 = Fr::from(BigInteger([
+    let f1 = Fr::from(BigInteger::new([
        0xc81265fb4130fe0c,
        0xb308836c14e22279,
        0x699e887f96bff372,
        0x84ecc7e76c11ad,
    ]));
-    let f2 = Fr::from(BigInteger([
+    let f2 = Fr::from(BigInteger::new([
        0x71875719b422efb8,
        0x0043658e68a93612,
        0x9fa756be2011e833,
        0xaa2b2cb08dac497,
    ]));
-    let f3 = Fr::from(BigInteger([
+    let f3 = Fr::from(BigInteger::new([
        0x3999bd14f553edc4,
        0xb34be8fa7d8b588c,
        0x0945df3db6d1dba5,
@@ -378,19 +339,19 @@ fn test_fr_add() {

 #[test]
 fn test_fr_mul() {
-    let f1 = Fr::from(BigInteger([
+    let f1 = Fr::from(BigInteger::new([
        0xc81265fb4130fe0c,
        0xb308836c14e22279,
        0x699e887f96bff372,
        0x84ecc7e76c11ad,
    ]));
-    let f2 = Fr::from(BigInteger([
+    let f2 = Fr::from(BigInteger::new([
        0x71875719b422efb8,
        0x43658e68a93612,
        0x9fa756be2011e833,
        0xaa2b2cb08dac497,
    ]));
-    let f3 = Fr::from(BigInteger([
+    let f3 = Fr::from(BigInteger::new([
        0xbe3e50c164fe3381,
        0x5ac45bc180974585,
        0x1c234ad6dcdc70c9,
@@ -401,7 +362,7 @@ fn test_fr_mul() {

 #[test]
 fn test_fr_bytes() {
-    let f1_from_repr = Fr::from(BigInteger([
+    let f1_from_repr = Fr::from(BigInteger::new([
        0xc81265fb4130fe0c,
        0xb308836c14e22279,
        0x699e887f96bff372,
@@ -417,7 +378,7 @@ fn test_fr_bytes() {

 #[test]
 fn test_fr_from_str() {
-    let f100_from_repr = Fr::from(BigInteger([0x64, 0, 0, 0]));
+    let f100_from_repr = Fr::from(BigInteger::new([0x64, 0, 0, 0]));
    let f100 = Fr::from_str("100").unwrap();
    assert_eq!(f100_from_repr, f100);
 }