feat(math): implement (I)FFT #71
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fakedev9999
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I think |
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Could you please separate file relocations from commit |
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Plus, you forgot to update include guard macro. |
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When seeing the commit body of |
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This gives a better performance if the type `T` meets some conditions and can be implemented with fewer lines. See https://google.github.io/styleguide/cppguide.html#noexcept
There are multiple definitions of `SparseCoefficients` in `univaraite/sparse_coefficients.h` and `multivariate/sparse_coefficients.h`. This prevents symbol conflict by adding prefix `Multivariate` and `Univariate` respectively. In addition, this renames followings in a similar way. - `SparseUnivaraitePolynomial` -> `UnivariateSparsePolynomial` - `DenseUnivariatePolynomial` -> `UnivariateDensePolynomial` - `SparseMultivariatePolynomial` -> `MultivariateSparsePolynomial` - `DenseCoefficients` -> `UnivariateDenseCoefficients`
This computes quotient and remainder for polynomial at once.
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LGTM |
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To test `MixedRadixEvaluationDomain` we need a prime field such that `MixedRadixEvaluationDomain` is constructable. Existing prime fields does not fit to construct `MixedRadixEvaluationDomain`, so bn384_small_two_adicity is added.
We have to use `omp_get_max_threads()` to adjust thread nums by such environment variable `OMP_NUM_THREADS`. See https://www.openmp.org/spec-html/5.0/openmpse50.html
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Description
This PR implements (I)FFT over dense univariate polynomial.
To do (I)FFT over a polynomial, an evaluation domain must exist, so this PR also implements evaluation domains. Evaluation domain is basically a domain over which finite field (I)FFTs can be performed.
GeneralEvaluationDomainis a wrapper overRadix2EvaluationDomainandMixedRadixEvaluationDomainwhere it generally tries to build aRadix2EvaluationDomainand falls back to aMixedRadixEvaluationDomainif the radix-2 multiplicative subgroup is too small.Radix2EvaluationDomainis anEvaluationDomainfor performing various kinds of polynomial arithmetic on top of fields that are FFT-friendly.Radix2EvaluationDomainsupports (I)FFTs of size at most 2^two-adicity.MixedRadixEvaluationDomainis anEvaluationDomainfor performing various kinds of polynomial arithmetic on top of fields that are FFT-friendly but do not have high-enough two-adicity to perform the FFT efficiently.MixedRadixEvaluationDomainresolves this issue by using a larger subgroup obtained by combining G with another subgroup of sizeF::Config::kSmallSubgroupBase^F::Config::kSmallSubgroupAdicity, to obtain a subgroup generated byF::Config::kLargeSubgroupRootOfUnity.