basic_radix2_domain.hpp

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//---------------------------------------------------------------------------//
// Copyright (c) 2020-2021 Mikhail Komarov <nemo@nil.foundation>
// Copyright (c) 2020-2021 Nikita Kaskov <nbering@nil.foundation>
//
// MIT License
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
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// in the Software without restriction, including without limitation the rights
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#ifndef CRYPTO3_MATH_BASIC_RADIX2_DOMAIN_HPP
#define CRYPTO3_MATH_BASIC_RADIX2_DOMAIN_HPP
 
#include <vector>
 
#include <nil/crypto3/math/detail/field_utils.hpp>
 
#include <nil/crypto3/math/domains/evaluation_domain.hpp>
#include <nil/crypto3/math/domains/detail/basic_radix2_domain_aux.hpp>
#include <nil/crypto3/math/algorithms/unity_root.hpp>
 
namespace nil {
    namespace crypto3 {
        namespace math {
 
            using namespace nil::crypto3::algebra;
 
            template<typename FieldType>
            class evaluation_domain;
 
            template<typename FieldType>
            class basic_radix2_domain : public evaluation_domain<FieldType> {
                typedef typename FieldType::value_type value_type;
 
            public:
                typedef FieldType field_type;
 
                value_type omega;
 
                basic_radix2_domain(const std::size_t m) : evaluation_domain<FieldType>(m) {
                    if (m <= 1)
                        throw std::invalid_argument("basic_radix2(): expected m > 1");
 
                    if (!std::is_same<value_type, std::complex<double>>::value) {
                        const std::size_t logm = static_cast<std::size_t>(std::ceil(std::log2(m)));
                        if (logm > (fields::arithmetic_params<FieldType>::s))
                            throw std::invalid_argument(
                                "basic_radix2(): expected logm <= fields::arithmetic_params<FieldType>::s");
                    }
 
                    omega = unity_root<FieldType>(m);
                }
 
                void fft(std::vector<value_type> &a) {
                    if (a.size() != this->m) {
                        if (a.size() < this->m) {
                            a.resize(this->m, value_type(0));
                        } else {
                            throw std::invalid_argument("basic_radix2: expected a.size() == this->m");
                        }
                    }
 
                    _basic_radix2_fft<FieldType>(a, omega);
                }
 
                void inverse_fft(std::vector<value_type> &a) {
                    if (a.size() != this->m) {
                        if (a.size() < this->m) {
                            a.resize(this->m, value_type(0));
                        } else {
                            throw std::invalid_argument("basic_radix2: expected a.size() == this->m");
                        }
                    }
 
                    _basic_radix2_fft<FieldType>(a, omega.inversed());
 
                    const value_type sconst = value_type(a.size()).inversed();
                    for (std::size_t i = 0; i < a.size(); ++i) {
                        a[i] *= sconst;
                    }
                }
 
                std::vector<value_type> evaluate_all_lagrange_polynomials(const value_type &t) {
                    return detail::basic_radix2_evaluate_all_lagrange_polynomials<FieldType>(this->m, t);
                }
 
                value_type get_domain_element(const std::size_t idx) {
                    return omega.pow(idx);
                }
 
                value_type compute_vanishing_polynomial(const value_type &t) {
                    return (t.pow(this->m)) - value_type::one();
                }
 
                void add_poly_z(const value_type &coeff, std::vector<value_type> &H) {
                    if (H.size() != this->m + 1)
                        throw std::invalid_argument("basic_radix2: expected H.size() == this->m+1");
 
                    H[this->m] += coeff;
                    H[0] -= coeff;
                }
 
                void divide_by_z_on_coset(std::vector<value_type> &P) {
                    const value_type coset = fields::arithmetic_params<FieldType>::multiplicative_generator;
                    const value_type Z_inverse_at_coset = this->compute_vanishing_polynomial(coset).inversed();
                    for (std::size_t i = 0; i < this->m; ++i) {
                        P[i] *= Z_inverse_at_coset;
                    }
                }
            };
        }    // namespace math
    }        // namespace crypto3
}    // namespace nil
 
#endif    // ALGEBRA_FFT_BASIC_RADIX2_DOMAIN_HPP