libdpf/include/dpf/fp61.hpp

/// @file dpf/fp61.hpp
/// @brief Prime field \(\mathbb{F}_{2^{61}-1}\) additive output type.
/// @copyright Copyright (c) 2019-2026 Ryan Henry and [others](@ref authors)
/// @license Released under a GNU General Public v2.0 (GPLv2) license;
///          see [LICENSE.md](@ref license) for details.

#ifndef LIBDPF_INCLUDE_DPF_FP61_HPP__
#define LIBDPF_INCLUDE_DPF_FP61_HPP__

#include <cstddef>
#include <cstdint>
#include <cstring>
#include <ostream>
#include <type_traits>

#include "hedley/hedley.h"

#include "dpf/utils.hpp"
#include "dpf/leaf_arithmetic.hpp"

namespace dpf
{

/// @brief Modulus \(p = 2^{61}-1\). `p` itself reduces to 0.
inline constexpr std::uint64_t fp61_mod = (std::uint64_t{1} << 61) - 1;

/// @brief Additive element of \(\mathbb{F}_{2^{61}-1}\).
class fp61
{
  public:
    /// @brief Underlying unsigned word. Values are stored already reduced.
    using integral_type = std::uint64_t;
    static constexpr std::size_t num_bits = 61;
    static constexpr bool dpf_modint = true;
    static constexpr bool dpf_fp61 = true;

    /// @brief Reduce `v` into the field.
    /// @param v the integer to reduce. Defaults to 0
    HEDLEY_NO_THROW
    HEDLEY_ALWAYS_INLINE
    constexpr fp61(integral_type v = 0) noexcept
        : val{reduce(v)}
    { }

    /// @brief Copy constructor.
    HEDLEY_NO_THROW
    HEDLEY_ALWAYS_INLINE
    constexpr fp61(const fp61 &) noexcept = default;
    /// @brief Move constructor.
    HEDLEY_NO_THROW
    HEDLEY_ALWAYS_INLINE
    constexpr fp61(fp61 &&) noexcept = default;
    /// @brief Copy assignment.
    /// @return `*this`
    HEDLEY_NO_THROW
    HEDLEY_ALWAYS_INLINE
    constexpr fp61 & operator=(const fp61 &) noexcept = default;
    /// @brief Move assignment.
    /// @return `*this`
    HEDLEY_NO_THROW
    HEDLEY_ALWAYS_INLINE
    constexpr fp61 & operator=(fp61 &&) noexcept = default;

    /// @brief The reduced representative in `[0, p)`.
    /// @return the stored field element
    HEDLEY_NO_THROW
    HEDLEY_ALWAYS_INLINE
    HEDLEY_PURE
    constexpr integral_type raw() const noexcept { return val; }

    /// @brief Same value as `raw()`.
    /// @return the stored field element
    HEDLEY_NO_THROW
    HEDLEY_ALWAYS_INLINE
    HEDLEY_PURE
    explicit constexpr operator integral_type() const noexcept { return val; }

    /// @brief Mersenne reduction of a 64-bit word.
    /// @param x the integer to reduce
    /// @return `x` modulo `2^61-1`, with `p` itself represented as 0
    HEDLEY_NO_THROW
    HEDLEY_ALWAYS_INLINE
    HEDLEY_CONST
    static constexpr integral_type reduce(integral_type x) noexcept
    {
        x = (x & fp61_mod) + (x >> 61);
        if (x >= fp61_mod)
            x -= fp61_mod;
        return x;
    }

    /// @brief Field addition.
    /// @param a left addend
    /// @param b right addend
    /// @return `a + b` in the field
    HEDLEY_NO_THROW
    HEDLEY_ALWAYS_INLINE
    HEDLEY_CONST
    friend constexpr fp61 operator+(fp61 a, fp61 b) noexcept
    {
        return fp61{a.val + b.val};
    }

    /// @brief Field subtraction.
    /// @param a minuend
    /// @param b subtrahend
    /// @return `a - b` in the field
    HEDLEY_NO_THROW
    HEDLEY_ALWAYS_INLINE
    HEDLEY_CONST
    friend constexpr fp61 operator-(fp61 a, fp61 b) noexcept
    {
        return fp61{a.val + fp61_mod - b.val};
    }

    /// @brief Field negation.
    /// @param a the element to negate
    /// @return `-a`, with `-0 = 0`
    HEDLEY_NO_THROW
    HEDLEY_ALWAYS_INLINE
    HEDLEY_CONST
    friend constexpr fp61 operator-(fp61 a) noexcept
    {
        return fp61{a.val == 0 ? 0 : fp61_mod - a.val};
    }

    /// @brief Field multiplication.
    /// @param a left factor
    /// @param b right factor
    /// @return `a * b` in the field
    HEDLEY_NO_THROW
    HEDLEY_ALWAYS_INLINE
    HEDLEY_CONST
    friend constexpr fp61 operator*(fp61 a, fp61 b) noexcept
    {
        using u128 = unsigned __int128;
        const u128 p = static_cast<u128>(a.val) * static_cast<u128>(b.val);
        const auto lo = static_cast<integral_type>(p) & fp61_mod;
        const auto mid = static_cast<integral_type>(p >> 61) & fp61_mod;
        const auto hi = static_cast<integral_type>(p >> 122);
        return fp61{lo + mid + hi};
    }

    /// @brief Field equality.
    /// @param a left element
    /// @param b right element
    /// @return `true` when the reduced values match
    HEDLEY_NO_THROW
    HEDLEY_ALWAYS_INLINE
    HEDLEY_CONST
    friend constexpr bool operator==(fp61 a, fp61 b) noexcept
    {
        return a.val == b.val;
    }

    /// @brief Field inequality.
    /// @param a left element
    /// @param b right element
    /// @return `true` when the reduced values differ
    HEDLEY_NO_THROW
    HEDLEY_ALWAYS_INLINE
    HEDLEY_CONST
    friend constexpr bool operator!=(fp61 a, fp61 b) noexcept
    {
        return a.val != b.val;
    }

    /// @brief Write the reduced representative in decimal.
    /// @param os the output stream
    /// @param a the element to write
    /// @return `os`
    friend std::ostream & operator<<(std::ostream & os, fp61 a)
    {
        return os << a.val;
    }

  private:
    integral_type val;
};

namespace utils
{

template <>
struct bitlength_of<fp61>
    : std::integral_constant<std::size_t, 61>
{ };

template <>
struct has_characteristic_two<fp61> : std::false_type
{ };

}  // namespace utils

namespace leaf_arithmetic
{

HEDLEY_PRAGMA(GCC diagnostic push)
HEDLEY_PRAGMA(GCC diagnostic ignored "-Wignored-attributes")
template <>
struct add_t<fp61, simde__m128i>
{
    auto operator()(const simde__m128i & a, const simde__m128i & b) const
    {
        return add_t<fp61::integral_type, simde__m128i>{}(a, b);
    }
};

template <>
struct subtract_t<fp61, simde__m128i>
{
    auto operator()(const simde__m128i & a, const simde__m128i & b) const
    {
        return subtract_t<fp61::integral_type, simde__m128i>{}(a, b);
    }
};

template <>
struct add_t<fp61, simde__m256i>
{
    auto operator()(const simde__m256i & a, const simde__m256i & b) const
    {
        return add_t<fp61::integral_type, simde__m256i>{}(a, b);
    }
};

template <>
struct subtract_t<fp61, simde__m256i>
{
    auto operator()(const simde__m256i & a, const simde__m256i & b) const
    {
        return subtract_t<fp61::integral_type, simde__m256i>{}(a, b);
    }
};
HEDLEY_PRAGMA(GCC diagnostic pop)

}  // namespace leaf_arithmetic

}  // namespace dpf

#endif  // LIBDPF_INCLUDE_DPF_FP61_HPP__