arnaucube
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ark-curves-cherry-picked/curve-constraint-tests/src/lib.rs
curve-constraint-tests/src/lib.rsRaw
  1#![macro_use]
  2extern crate ark_relations;
  3
  4pub mod fields {
  5    use ark_ff::{BitIteratorLE, Field, UniformRand};
  6    use ark_r1cs_std::prelude::*;
  7    use ark_relations::r1cs::{ConstraintSystem, SynthesisError};
  8    use ark_std::test_rng;
  9    use ark_std::vec::Vec;
 10
 11    pub fn field_test<F, ConstraintF, AF>() -> Result<(), SynthesisError>
 12    where
 13        F: Field,
 14        ConstraintF: Field,
 15        AF: FieldVar<F, ConstraintF>,
 16        AF: TwoBitLookupGadget<ConstraintF, TableConstant = F>,
 17        for<'a> &'a AF: FieldOpsBounds<'a, F, AF>,
 18    {
 19        let modes = [
 20            AllocationMode::Input,
 21            AllocationMode::Witness,
 22            AllocationMode::Constant,
 23        ];
 24        for &mode in &modes {
 25            let cs = ConstraintSystem::<ConstraintF>::new_ref();
 26
 27            let mut rng = test_rng();
 28            let a_native = F::rand(&mut rng);
 29            let b_native = F::rand(&mut rng);
 30            let a = AF::new_variable(ark_relations::ns!(cs, "generate_a"), || Ok(a_native), mode)?;
 31            let b = AF::new_variable(ark_relations::ns!(cs, "generate_b"), || Ok(b_native), mode)?;
 32            let b_const = AF::new_constant(ark_relations::ns!(cs, "b_as_constant"), b_native)?;
 33
 34            let zero = AF::zero();
 35            let zero_native = zero.value()?;
 36            zero.enforce_equal(&zero)?;
 37
 38            let one = AF::one();
 39            let one_native = one.value()?;
 40            one.enforce_equal(&one)?;
 41
 42            one.enforce_not_equal(&zero)?;
 43
 44            let one_dup = &zero + &one;
 45            one_dup.enforce_equal(&one)?;
 46
 47            let two = &one + &one;
 48            two.enforce_equal(&two)?;
 49            two.enforce_equal(&one.double()?)?;
 50            two.enforce_not_equal(&one)?;
 51            two.enforce_not_equal(&zero)?;
 52
 53            // a + 0 = a
 54            let a_plus_zero = &a + &zero;
 55            assert_eq!(a_plus_zero.value()?, a_native);
 56            a_plus_zero.enforce_equal(&a)?;
 57            a_plus_zero.enforce_not_equal(&a.double()?)?;
 58
 59            // a - 0 = a
 60            let a_minus_zero = &a - &zero;
 61            assert_eq!(a_minus_zero.value()?, a_native);
 62            a_minus_zero.enforce_equal(&a)?;
 63
 64            // a - a = 0
 65            let a_minus_a = &a - &a;
 66            assert_eq!(a_minus_a.value()?, zero_native);
 67            a_minus_a.enforce_equal(&zero)?;
 68
 69            // a + b = b + a
 70            let a_b = &a + &b;
 71            let b_a = &b + &a;
 72            assert_eq!(a_b.value()?, a_native + &b_native);
 73            a_b.enforce_equal(&b_a)?;
 74
 75            // (a + b) + a = a + (b + a)
 76            let ab_a = &a_b + &a;
 77            let a_ba = &a + &b_a;
 78            assert_eq!(ab_a.value()?, a_native + &b_native + &a_native);
 79            ab_a.enforce_equal(&a_ba)?;
 80
 81            let b_times_a_plus_b = &a_b * &b;
 82            let b_times_b_plus_a = &b_a * &b;
 83            assert_eq!(
 84                b_times_a_plus_b.value()?,
 85                b_native * &(b_native + &a_native)
 86            );
 87            assert_eq!(
 88                b_times_a_plus_b.value()?,
 89                (b_native + &a_native) * &b_native
 90            );
 91            assert_eq!(
 92                b_times_a_plus_b.value()?,
 93                (a_native + &b_native) * &b_native
 94            );
 95            b_times_b_plus_a.enforce_equal(&b_times_a_plus_b)?;
 96
 97            // a * 1 = a
 98            assert_eq!((&a * &one).value()?, a_native * &one_native);
 99
100            // a * b = b * a
101            let ab = &a * &b;
102            let ba = &b * &a;
103            assert_eq!(ab.value()?, ba.value()?);
104            assert_eq!(ab.value()?, a_native * &b_native);
105
106            let ab_const = &a * &b_const;
107            let b_const_a = &b_const * &a;
108            assert_eq!(ab_const.value()?, b_const_a.value()?);
109            assert_eq!(ab_const.value()?, ab.value()?);
110            assert_eq!(ab_const.value()?, a_native * &b_native);
111
112            // (a * b) * a = a * (b * a)
113            let ab_a = &ab * &a;
114            let a_ba = &a * &ba;
115            assert_eq!(ab_a.value()?, a_ba.value()?);
116            assert_eq!(ab_a.value()?, a_native * &b_native * &a_native);
117
118            let aa = &a * &a;
119            let a_squared = a.square()?;
120            a_squared.enforce_equal(&aa)?;
121            assert_eq!(aa.value()?, a_squared.value()?);
122            assert_eq!(aa.value()?, a_native.square());
123
124            let aa = &a * a_native;
125            a_squared.enforce_equal(&aa)?;
126            assert_eq!(aa.value()?, a_squared.value()?);
127            assert_eq!(aa.value()?, a_native.square());
128
129            let a_b2 = &a + b_native;
130            a_b.enforce_equal(&a_b2)?;
131            assert_eq!(a_b.value()?, a_b2.value()?);
132
133            let a_inv = a.inverse()?;
134            a_inv.mul_equals(&a, &one)?;
135            assert_eq!(a_inv.value()?, a.value()?.inverse().unwrap());
136            assert_eq!(a_inv.value()?, a_native.inverse().unwrap());
137
138            let a_b_inv = a.mul_by_inverse(&b)?;
139            a_b_inv.mul_equals(&b, &a)?;
140            assert_eq!(a_b_inv.value()?, a_native * b_native.inverse().unwrap());
141
142            // a * a * a = a^3
143            let bits = BitIteratorLE::without_trailing_zeros([3u64])
144                .map(Boolean::constant)
145                .collect::<Vec<_>>();
146            assert_eq!(a_native.pow([0x3]), a.pow_le(&bits)?.value()?);
147
148            // a * a * a = a^3
149            assert_eq!(a_native.pow([0x3]), a.pow_by_constant(&[0x3])?.value()?);
150            assert!(cs.is_satisfied().unwrap());
151
152            let mut constants = [F::zero(); 4];
153            for c in &mut constants {
154                *c = UniformRand::rand(&mut test_rng());
155            }
156            let bits = [
157                Boolean::<ConstraintF>::constant(false),
158                Boolean::constant(true),
159            ];
160            let lookup_result = AF::two_bit_lookup(&bits, constants.as_ref())?;
161            assert_eq!(lookup_result.value()?, constants[2]);
162            assert!(cs.is_satisfied().unwrap());
163
164            let f = F::from(1u128 << 64);
165            let f_bits = ark_ff::BitIteratorLE::new(&[0u64, 1u64]).collect::<Vec<_>>();
166            let fv = AF::new_variable(ark_relations::ns!(cs, "alloc u128"), || Ok(f), mode)?;
167            assert_eq!(fv.to_bits_le()?.value().unwrap()[..128], f_bits[..128]);
168            assert!(cs.is_satisfied().unwrap());
169
170            let r_native: F = UniformRand::rand(&mut test_rng());
171
172            let r = AF::new_variable(ark_relations::ns!(cs, "r_native"), || Ok(r_native), mode)
173                .unwrap();
174            let _ = r.to_non_unique_bits_le()?;
175            assert!(cs.is_satisfied().unwrap());
176            let _ = r.to_bits_le()?;
177            assert!(cs.is_satisfied().unwrap());
178
179            let bytes = r.to_non_unique_bytes()?;
180            assert_eq!(ark_ff::to_bytes!(r_native).unwrap(), bytes.value().unwrap());
181            assert!(cs.is_satisfied().unwrap());
182            let bytes = r.to_bytes()?;
183            assert_eq!(ark_ff::to_bytes!(r_native).unwrap(), bytes.value().unwrap());
184            assert!(cs.is_satisfied().unwrap());
185
186            let ab_false = &a + (AF::from(Boolean::Constant(false)) * b_native);
187            let ab_true = &a + (AF::from(Boolean::Constant(true)) * b_native);
188            assert_eq!(ab_false.value()?, a_native);
189            assert_eq!(ab_true.value()?, a_native + &b_native);
190
191            if !cs.is_satisfied().unwrap() {
192                panic!(
193                    "Unsatisfied in mode {:?}.\n{:?}",
194                    mode,
195                    cs.which_is_unsatisfied().unwrap()
196                );
197            }
198            assert!(cs.is_satisfied().unwrap());
199        }
200        Ok(())
201    }
202
203    pub fn frobenius_tests<F: Field, ConstraintF, AF>(maxpower: usize) -> Result<(), SynthesisError>
204    where
205        F: Field,
206        ConstraintF: Field,
207        AF: FieldVar<F, ConstraintF>,
208        for<'a> &'a AF: FieldOpsBounds<'a, F, AF>,
209    {
210        let modes = [
211            AllocationMode::Input,
212            AllocationMode::Witness,
213            AllocationMode::Constant,
214        ];
215        for &mode in &modes {
216            let cs = ConstraintSystem::<ConstraintF>::new_ref();
217            let mut rng = test_rng();
218            for i in 0..=maxpower {
219                let mut a = F::rand(&mut rng);
220                let mut a_gadget = AF::new_variable(ark_relations::ns!(cs, "a"), || Ok(a), mode)?;
221                a_gadget.frobenius_map_in_place(i)?;
222                a.frobenius_map(i);
223
224                assert_eq!(a_gadget.value()?, a);
225            }
226
227            assert!(cs.is_satisfied().unwrap());
228        }
229        Ok(())
230    }
231}
232
233pub mod curves {
234    use ark_ec::{
235        short_weierstrass_jacobian::GroupProjective as SWProjective,
236        twisted_edwards_extended::GroupProjective as TEProjective, ProjectiveCurve,
237    };
238    use ark_ff::{BitIteratorLE, Field, FpParameters, One, PrimeField};
239    use ark_relations::r1cs::{ConstraintSystem, SynthesisError};
240    use ark_std::{test_rng, vec::Vec, UniformRand};
241
242    use ark_r1cs_std::prelude::*;
243
244    pub fn group_test<C, ConstraintF, GG>() -> Result<(), SynthesisError>
245    where
246        C: ProjectiveCurve,
247        ConstraintF: Field,
248        GG: CurveVar<C, ConstraintF>,
249        for<'a> &'a GG: GroupOpsBounds<'a, C, GG>,
250    {
251        let modes = [
252            AllocationMode::Input,
253            AllocationMode::Witness,
254            AllocationMode::Constant,
255        ];
256        for &mode in &modes {
257            let cs = ConstraintSystem::<ConstraintF>::new_ref();
258
259            let mut rng = test_rng();
260            let a_native = C::rand(&mut rng);
261            let b_native = C::rand(&mut rng);
262            let a = GG::new_variable(ark_relations::ns!(cs, "generate_a"), || Ok(a_native), mode)
263                .unwrap();
264            let b = GG::new_variable(ark_relations::ns!(cs, "generate_b"), || Ok(b_native), mode)
265                .unwrap();
266
267            let zero = GG::zero();
268            assert_eq!(zero.value()?, zero.value()?);
269
270            // a == a
271            assert_eq!(a.value()?, a.value()?);
272            // a + 0 = a
273            assert_eq!((&a + &zero).value()?, a.value()?);
274            // a - 0 = a
275            assert_eq!((&a - &zero).value()?, a.value()?);
276            // a - a = 0
277            assert_eq!((&a - &a).value()?, zero.value()?);
278            // a + b = b + a
279            let a_b = &a + &b;
280            let b_a = &b + &a;
281            assert_eq!(a_b.value()?, b_a.value()?);
282            a_b.enforce_equal(&b_a)?;
283            assert!(cs.is_satisfied().unwrap());
284
285            // (a + b) + a = a + (b + a)
286            let ab_a = &a_b + &a;
287            let a_ba = &a + &b_a;
288            assert_eq!(ab_a.value()?, a_ba.value()?);
289            ab_a.enforce_equal(&a_ba)?;
290            assert!(cs.is_satisfied().unwrap());
291
292            // a.double() = a + a
293            let a_a = &a + &a;
294            let mut a2 = a.clone();
295            a2.double_in_place()?;
296            a2.enforce_equal(&a_a)?;
297            assert_eq!(a2.value()?, a_native.double());
298            assert_eq!(a_a.value()?, a_native.double());
299            assert_eq!(a2.value()?, a_a.value()?);
300            assert!(cs.is_satisfied().unwrap());
301
302            // b.double() = b + b
303            let mut b2 = b.clone();
304            b2.double_in_place()?;
305            let b_b = &b + &b;
306            b2.enforce_equal(&b_b)?;
307            assert!(cs.is_satisfied().unwrap());
308            assert_eq!(b2.value()?, b_b.value()?);
309
310            let _ = a.to_bytes()?;
311            assert!(cs.is_satisfied().unwrap());
312            let _ = a.to_non_unique_bytes()?;
313            assert!(cs.is_satisfied().unwrap());
314
315            let _ = b.to_bytes()?;
316            let _ = b.to_non_unique_bytes()?;
317            if !cs.is_satisfied().unwrap() {
318                panic!(
319                    "Unsatisfied in mode {:?}.\n{:?}",
320                    mode,
321                    cs.which_is_unsatisfied().unwrap()
322                );
323            }
324            assert!(cs.is_satisfied().unwrap());
325
326            let modulus = <C::ScalarField as PrimeField>::Params::MODULUS
327                .as_ref()
328                .to_vec();
329            let mut max = modulus.clone();
330            for limb in &mut max {
331                *limb = u64::MAX;
332            }
333
334            let modulus_last_limb_bits = <C::ScalarField as PrimeField>::Params::MODULUS_BITS % 64;
335            *max.last_mut().unwrap() >>= 64 - modulus_last_limb_bits;
336            let scalars = [
337                C::ScalarField::rand(&mut rng).into_repr().as_ref().to_vec(),
338                vec![u64::rand(&mut rng)],
339                (-C::ScalarField::one()).into_repr().as_ref().to_vec(),
340                <C::ScalarField as PrimeField>::Params::MODULUS
341                    .as_ref()
342                    .to_vec(),
343                max,
344                vec![0; 50],
345                vec![1000012341233u64; 36],
346            ];
347
348            let mut input = vec![];
349
350            // Check scalar mul with edge cases
351            for scalar in scalars.iter() {
352                let native_result = a_native.mul(scalar);
353                let native_result = native_result.into_affine();
354
355                let scalar_bits: Vec<bool> = BitIteratorLE::new(&scalar).collect();
356                input =
357                    Vec::new_witness(ark_relations::ns!(cs, "bits"), || Ok(scalar_bits)).unwrap();
358                let result = a
359                    .scalar_mul_le(input.iter())
360                    .expect(&format!("Mode: {:?}", mode));
361                let result_val = result.value()?.into_affine();
362                assert_eq!(
363                    result_val, native_result,
364                    "gadget & native values are diff. after scalar mul {:?}",
365                    scalar,
366                );
367                assert!(cs.is_satisfied().unwrap());
368            }
369
370            let result = zero.scalar_mul_le(input.iter())?;
371            let result_val = result.value()?.into_affine();
372            result.enforce_equal(&zero)?;
373            assert_eq!(
374                result_val,
375                C::zero().into_affine(),
376                "gadget & native values are diff. after scalar mul of zero"
377            );
378            assert!(cs.is_satisfied().unwrap());
379        }
380        Ok(())
381    }
382
383    pub fn sw_test<P, GG>() -> Result<(), SynthesisError>
384    where
385        P: ark_ec::SWModelParameters,
386        GG: CurveVar<SWProjective<P>, <P::BaseField as Field>::BasePrimeField>,
387        for<'a> &'a GG: GroupOpsBounds<'a, SWProjective<P>, GG>,
388    {
389        group_test::<SWProjective<P>, _, GG>()?;
390        let modes = [
391            AllocationMode::Input,
392            AllocationMode::Witness,
393            AllocationMode::Constant,
394        ];
395        for &mode in &modes {
396            use ark_ec::group::Group;
397
398            let mut rng = test_rng();
399
400            let cs = ConstraintSystem::<<P::BaseField as Field>::BasePrimeField>::new_ref();
401
402            let a = SWProjective::<P>::rand(&mut rng);
403            let b = SWProjective::<P>::rand(&mut rng);
404            let a_affine = a.into_affine();
405            let b_affine = b.into_affine();
406
407            let ns = ark_relations::ns!(cs, "allocating variables");
408            let mut gadget_a = GG::new_variable(cs.clone(), || Ok(a), mode)?;
409            let gadget_b = GG::new_variable(cs.clone(), || Ok(b), mode)?;
410            let zero = GG::zero();
411            drop(ns);
412            assert_eq!(gadget_a.value()?.into_affine().x, a_affine.x);
413            assert_eq!(gadget_a.value()?.into_affine().y, a_affine.y);
414            assert_eq!(gadget_b.value()?.into_affine().x, b_affine.x);
415            assert_eq!(gadget_b.value()?.into_affine().y, b_affine.y);
416            assert_eq!(cs.which_is_unsatisfied().unwrap(), None);
417
418            // Check addition
419            let ab = a + &b;
420            let ab_affine = ab.into_affine();
421            let gadget_ab = &gadget_a + &gadget_b;
422            let gadget_ba = &gadget_b + &gadget_a;
423            gadget_ba.enforce_equal(&gadget_ab)?;
424
425            let ab_val = gadget_ab.value()?.into_affine();
426            assert_eq!(ab_val, ab_affine, "Result of addition is unequal");
427            assert!(cs.is_satisfied().unwrap());
428
429            let gadget_a_zero = &gadget_a + &zero;
430            gadget_a_zero.enforce_equal(&gadget_a)?;
431
432            // Check doubling
433            let aa = Group::double(&a);
434            let aa_affine = aa.into_affine();
435            gadget_a.double_in_place()?;
436            let aa_val = gadget_a.value()?.into_affine();
437            assert_eq!(
438                aa_val, aa_affine,
439                "Gadget and native values are unequal after double."
440            );
441            assert!(cs.is_satisfied().unwrap());
442
443            if !cs.is_satisfied().unwrap() {
444                panic!(
445                    "Unsatisfied in mode {:?}.\n{:?}",
446                    mode,
447                    cs.which_is_unsatisfied().unwrap()
448                );
449            }
450
451            assert!(cs.is_satisfied().unwrap());
452        }
453        Ok(())
454    }
455
456    pub fn te_test<P, GG>() -> Result<(), SynthesisError>
457    where
458        P: ark_ec::TEModelParameters,
459        GG: CurveVar<TEProjective<P>, <P::BaseField as Field>::BasePrimeField>,
460        for<'a> &'a GG: GroupOpsBounds<'a, TEProjective<P>, GG>,
461    {
462        group_test::<TEProjective<P>, _, GG>()?;
463        let modes = [
464            AllocationMode::Input,
465            AllocationMode::Witness,
466            AllocationMode::Constant,
467        ];
468        for &mode in &modes {
469            use ark_ec::group::Group;
470
471            let mut rng = test_rng();
472
473            let cs = ConstraintSystem::<<P::BaseField as Field>::BasePrimeField>::new_ref();
474
475            let a = TEProjective::<P>::rand(&mut rng);
476            let b = TEProjective::<P>::rand(&mut rng);
477            let a_affine = a.into_affine();
478            let b_affine = b.into_affine();
479
480            let ns = ark_relations::ns!(cs, "allocating variables");
481            let mut gadget_a = GG::new_variable(cs.clone(), || Ok(a), mode)?;
482            let gadget_b = GG::new_variable(cs.clone(), || Ok(b), mode)?;
483            drop(ns);
484
485            assert_eq!(gadget_a.value()?.into_affine().x, a_affine.x);
486            assert_eq!(gadget_a.value()?.into_affine().y, a_affine.y);
487            assert_eq!(gadget_b.value()?.into_affine().x, b_affine.x);
488            assert_eq!(gadget_b.value()?.into_affine().y, b_affine.y);
489            assert_eq!(cs.which_is_unsatisfied()?, None);
490
491            // Check addition
492            let ab = a + &b;
493            let ab_affine = ab.into_affine();
494            let gadget_ab = &gadget_a + &gadget_b;
495            let gadget_ba = &gadget_b + &gadget_a;
496            gadget_ba.enforce_equal(&gadget_ab)?;
497
498            let ab_val = gadget_ab.value()?.into_affine();
499            assert_eq!(ab_val, ab_affine, "Result of addition is unequal");
500            assert!(cs.is_satisfied().unwrap());
501
502            // Check doubling
503            let aa = Group::double(&a);
504            let aa_affine = aa.into_affine();
505            gadget_a.double_in_place()?;
506            let aa_val = gadget_a.value()?.into_affine();
507            assert_eq!(
508                aa_val, aa_affine,
509                "Gadget and native values are unequal after double."
510            );
511            assert!(cs.is_satisfied().unwrap());
512
513            if !cs.is_satisfied().unwrap() {
514                panic!(
515                    "Unsatisfied in mode {:?}.\n{:?}",
516                    mode,
517                    cs.which_is_unsatisfied().unwrap()
518                );
519            }
520
521            assert!(cs.is_satisfied().unwrap());
522        }
523        Ok(())
524    }
525}
526
527pub mod pairing {
528    use ark_ec::{PairingEngine, ProjectiveCurve};
529    use ark_ff::{BitIteratorLE, Field, PrimeField};
530    use ark_r1cs_std::prelude::*;
531    use ark_relations::r1cs::{ConstraintSystem, SynthesisError};
532    use ark_std::{test_rng, vec::Vec, UniformRand};
533
534    #[allow(dead_code)]
535    pub fn bilinearity_test<E: PairingEngine, P: PairingVar<E>>() -> Result<(), SynthesisError>
536    where
537        for<'a> &'a P::G1Var: GroupOpsBounds<'a, E::G1Projective, P::G1Var>,
538        for<'a> &'a P::G2Var: GroupOpsBounds<'a, E::G2Projective, P::G2Var>,
539        for<'a> &'a P::GTVar: FieldOpsBounds<'a, E::Fqk, P::GTVar>,
540    {
541        let modes = [
542            AllocationMode::Input,
543            AllocationMode::Witness,
544            AllocationMode::Constant,
545        ];
546        for &mode in &modes {
547            let cs = ConstraintSystem::<E::Fq>::new_ref();
548
549            let mut rng = test_rng();
550            let a = E::G1Projective::rand(&mut rng);
551            let b = E::G2Projective::rand(&mut rng);
552            let s = E::Fr::rand(&mut rng);
553
554            let mut sa = a;
555            sa *= s;
556            let mut sb = b;
557            sb *= s;
558
559            let a_g = P::G1Var::new_variable(cs.clone(), || Ok(a.into_affine()), mode)?;
560            let b_g = P::G2Var::new_variable(cs.clone(), || Ok(b.into_affine()), mode)?;
561            let sa_g = P::G1Var::new_variable(cs.clone(), || Ok(sa.into_affine()), mode)?;
562            let sb_g = P::G2Var::new_variable(cs.clone(), || Ok(sb.into_affine()), mode)?;
563
564            let mut _preparation_num_constraints = cs.num_constraints();
565            let a_prep_g = P::prepare_g1(&a_g)?;
566            let b_prep_g = P::prepare_g2(&b_g)?;
567            _preparation_num_constraints = cs.num_constraints() - _preparation_num_constraints;
568
569            let sa_prep_g = P::prepare_g1(&sa_g)?;
570            let sb_prep_g = P::prepare_g2(&sb_g)?;
571
572            let (ans1_g, ans1_n) = {
573                let _ml_constraints = cs.num_constraints();
574                let ml_g = P::miller_loop(&[sa_prep_g], &[b_prep_g.clone()])?;
575                let _fe_constraints = cs.num_constraints();
576                let ans_g = P::final_exponentiation(&ml_g)?;
577                let ans_n = E::pairing(sa, b);
578                (ans_g, ans_n)
579            };
580
581            let (ans2_g, ans2_n) = {
582                let ans_g = P::pairing(a_prep_g.clone(), sb_prep_g)?;
583                let ans_n = E::pairing(a, sb);
584                (ans_g, ans_n)
585            };
586
587            let (ans3_g, ans3_n) = {
588                let s_iter = BitIteratorLE::without_trailing_zeros(s.into_repr())
589                    .map(Boolean::constant)
590                    .collect::<Vec<_>>();
591
592                let mut ans_g = P::pairing(a_prep_g, b_prep_g)?;
593                let mut ans_n = E::pairing(a, b);
594                ans_n = ans_n.pow(s.into_repr());
595                ans_g = ans_g.pow_le(&s_iter)?;
596
597                (ans_g, ans_n)
598            };
599
600            ans1_g.enforce_equal(&ans2_g)?;
601            ans2_g.enforce_equal(&ans3_g)?;
602
603            assert_eq!(ans1_g.value()?, ans1_n, "Failed native test 1");
604            assert_eq!(ans2_g.value()?, ans2_n, "Failed native test 2");
605            assert_eq!(ans3_g.value()?, ans3_n, "Failed native test 3");
606
607            assert_eq!(ans1_n, ans2_n, "Failed ans1_native == ans2_native");
608            assert_eq!(ans2_n, ans3_n, "Failed ans2_native == ans3_native");
609            assert_eq!(ans1_g.value()?, ans3_g.value()?, "Failed ans1 == ans3");
610            assert_eq!(ans1_g.value()?, ans2_g.value()?, "Failed ans1 == ans2");
611            assert_eq!(ans2_g.value()?, ans3_g.value()?, "Failed ans2 == ans3");
612
613            if !cs.is_satisfied().unwrap() {
614                panic!(
615                    "Unsatisfied in mode {:?}.\n{:?}",
616                    mode,
617                    cs.which_is_unsatisfied().unwrap()
618                );
619            }
620
621            assert!(cs.is_satisfied().unwrap(), "cs is not satisfied");
622        }
623        Ok(())
624    }
625}