EIP7594-Polynomial-Commitments-Tests: Extend Tests for FFT and Coset FFT.

tests/core/pyspec/eth2spec/test/eip7594/unittests/polynomial_commitments/test_polynomial_commitments.py

@@ -15,35 +15,74 @@
 @spec_test
 @single_phase
 def test_fft(spec):
+
+    # in this test we sample a random polynomial in coefficient form
+    # then we apply an FFT to get evaluations over the roots of unity
+    # we then apply an inverse FFT to the evaluations to get coefficients
+
+    # we check two things:
+    # 1) the original coefficients and the resulting coefficients match
+    # 2) the evaluations that we got are the same as if we would have evaluated individually
+
     rng = random.Random(5566)
 
     roots_of_unity = spec.compute_roots_of_unity(spec.FIELD_ELEMENTS_PER_BLOB)
 
+    # sample a random polynomial
     poly_coeff = [rng.randint(0, BLS_MODULUS - 1) for _ in range(spec.FIELD_ELEMENTS_PER_BLOB)]
 
+    # do an FFT and then an inverse FFT
     poly_eval = spec.fft_field(poly_coeff, roots_of_unity)
     poly_coeff_inversed = spec.fft_field(poly_eval, roots_of_unity, inv=True)
 
+    # first check: inverse FFT after FFT results in original coefficients
     assert len(poly_eval) == len(poly_coeff) == len(poly_coeff_inversed)
     assert poly_coeff_inversed == poly_coeff
 
+    # second check: result of FFT are really the evaluations
+    for i, w in enumerate(roots_of_unity):
+        individual_evaluation = spec.evaluate_polynomialcoeff(poly_coeff, w)
+        assert individual_evaluation == poly_eval[i]
+
 
 @with_eip7594_and_later
 @spec_test
 @single_phase
 def test_coset_fft(spec):
+
+    # in this test we sample a random polynomial in coefficient form
+    # then we apply a Coset FFT to get evaluations over the coset of the roots of unity
+    # we then apply an inverse Coset FFT to the evaluations to get coefficients
+
+    # we check two things:
+    # 1) the original coefficients and the resulting coefficients match
+    # 2) the evaluations that we got are the same as if we would have evaluated individually
+
     rng = random.Random(5566)
 
     roots_of_unity = spec.compute_roots_of_unity(spec.FIELD_ELEMENTS_PER_BLOB)
 
+    # this is the shift that generates the coset
+    coset_shift = spec.PRIMITIVE_ROOT_OF_UNITY
+
+    # sample a random polynomial
     poly_coeff = [rng.randint(0, BLS_MODULUS - 1) for _ in range(spec.FIELD_ELEMENTS_PER_BLOB)]
 
+    # do a coset FFT and then an inverse coset FFT
     poly_eval = spec.coset_fft_field(poly_coeff, roots_of_unity)
     poly_coeff_inversed = spec.coset_fft_field(poly_eval, roots_of_unity, inv=True)
 
+    # first check: inverse coset FFT after coset FFT results in original coefficients
     assert len(poly_eval) == len(poly_coeff) == len(poly_coeff_inversed)
     assert poly_coeff_inversed == poly_coeff
 
+    # second check: result of FFT are really the evaluations over the coset
+    for i, w in enumerate(roots_of_unity):
+        # the element of the coset is coset_shift * w
+        shifted_w = spec.BLSFieldElement((coset_shift * int(w)) % BLS_MODULUS)
+        individual_evaluation = spec.evaluate_polynomialcoeff(poly_coeff, shifted_w)
+        assert individual_evaluation == poly_eval[i]
+
 
 @with_eip7594_and_later
 @spec_test