unity_root.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
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#ifndef CRYPTO3_MATH_UNITY_ROOT_HPP
#define CRYPTO3_MATH_UNITY_ROOT_HPP
 
#include <type_traits>
#include <complex>
 
#include <boost/math/constants/constants.hpp>
#include <nil/crypto3/algebra/fields/params.hpp>
 
namespace nil {
    namespace crypto3 {
        namespace math {
 
            template<typename FieldType>
            constexpr typename std::enable_if<std::is_same<typename FieldType::value_type, std::complex<double>>::value,
                                              typename FieldType::value_type>::type
                unity_root(const std::size_t n) {
                const double PI = boost::math::constants::pi<double>();
 
                return typename FieldType::value_type(cos(2 * PI / n), sin(2 * PI / n));
            }
 
            template<typename FieldType>
            constexpr
                typename std::enable_if<!std::is_same<typename FieldType::value_type, std::complex<double>>::value,
                                        typename FieldType::value_type>::type
                unity_root(const std::size_t n) {
 
                typedef typename FieldType::value_type value_type;
 
                const std::size_t logn = std::ceil(std::log2(n));
 
                if (n != (1u << logn)) {
                    throw std::invalid_argument("expected n == (1u << logn)");
                }
                if (logn > algebra::fields::arithmetic_params<FieldType>::s) {
                    throw std::invalid_argument("expected logn <= arithmetic_params<FieldType>::s");
                }
 
                value_type omega = value_type(algebra::fields::arithmetic_params<FieldType>::root_of_unity);
                for (std::size_t i = algebra::fields::arithmetic_params<FieldType>::s; i > logn; --i) {
                    omega *= omega;
                }
 
                return omega;
            }
        }    // namespace math
    }        // namespace crypto3
}    // namespace nil
 
#endif    // CRYPTO3_MATH_UNITY_ROOT_HPP