decimal64.hpp

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#pragma once
 
/// @file userver/decimal64/decimal64.hpp
/// @brief Decimal data type for fixed-point arithmetic
/// @ingroup userver_universal
 
// Original source taken from https://github.com/vpiotr/decimal_for_cpp
// Original license:
//
// ==================================================================
// Name:        decimal.h
// Purpose:     Decimal data type support, for COBOL-like fixed-point
//              operations on currency values.
// Author:      Piotr Likus
// Created:     03/01/2011
// Modified:    23/09/2018
// Version:     1.16
// Licence:     BSD
// ==================================================================
 
#include <array>
#include <cassert>
#include <cstdint>
#include <ios>
#include <iosfwd>
#include <istream>
#include <limits>
#include <numeric>
#include <optional>
#include <stdexcept>
#include <string>
#include <string_view>
#include <type_traits>
 
#include <fmt/compile.h>
#include <fmt/format.h>
 
#include <userver/compiler/impl/three_way_comparison.hpp>
#include <userver/decimal64/format_options.hpp>
#include <userver/formats/common/meta.hpp>
#include <userver/utils/assert.hpp>
#include <userver/utils/flags.hpp>
#include <userver/utils/meta_light.hpp>
 
USERVER_NAMESPACE_BEGIN
 
namespace logging {
 
class LogHelper;
 
}  // namespace logging
 
/// Fixed-point decimal data type and related functions
namespace decimal64 {
 
/// The base class for Decimal-related exceptions
class DecimalError : public std::runtime_error {
public:
    using std::runtime_error::runtime_error;
};
 
/// Thrown on all errors related to parsing `Decimal` from string
class ParseError : public DecimalError {
public:
    using DecimalError::DecimalError;
};
 
/// Thrown on overflow in `Decimal` arithmetic
class OutOfBoundsError : public DecimalError {
public:
    OutOfBoundsError();
};
 
/// Thrown on division by zero in `Decimal` arithmetic
class DivisionByZeroError : public DecimalError {
public:
    DivisionByZeroError();
};
 
namespace impl {
 
inline constexpr auto kMaxInt64 = std::numeric_limits<int64_t>::max();
inline constexpr auto kMinInt64 = std::numeric_limits<int64_t>::min();
 
// Note: static_cast may introduce an inaccuracy. To be on the safe side,
// we'd have to call std::nextafter, but it's not constexpr until C++23.
inline constexpr auto kMinRepresentableLongDouble =
    static_cast<long double>(impl::kMinInt64) * (1 - 2 * std::numeric_limits<long double>::epsilon());
inline constexpr auto kMaxRepresentableLongDouble =
    static_cast<long double>(impl::kMaxInt64) * (1 - 2 * std::numeric_limits<long double>::epsilon());
 
template <typename T>
using EnableIfInt = std::enable_if_t<meta::kIsInteger<T>, int>;
 
template <typename T>
using EnableIfFloat = std::enable_if_t<std::is_floating_point_v<T>, int>;
 
template <int MaxExp>
constexpr std::array<int64_t, MaxExp + 1> PowSeries(int64_t base) {
    int64_t pow = 1;
    std::array<int64_t, MaxExp + 1> result{};
    for (int i = 0; i < MaxExp; ++i) {
        result[i] = pow;
        if (pow > kMaxInt64 / base) {
            throw OutOfBoundsError();
        }
        pow *= base;
    }
    result[MaxExp] = pow;
    return result;
}
 
inline constexpr int kMaxDecimalDigits = 18;
inline constexpr auto kPowSeries10 = PowSeries<kMaxDecimalDigits>(10);
 
// Check that kMaxDecimalDigits is indeed max integer x such that 10^x is valid
static_assert(kMaxInt64 / 10 < kPowSeries10[kMaxDecimalDigits]);
 
template <typename RoundPolicy>
constexpr int64_t Div(int64_t nominator, int64_t denominator, bool extra_odd_quotient = false) {
    // RoundPolicies don't protect against arithmetic errors
    if (denominator == 0) throw DivisionByZeroError();
    if (denominator == -1) {
        if (nominator == kMinInt64) throw OutOfBoundsError();
        return -nominator;  // RoundPolicies behave badly for denominator == -1
    }
 
    return RoundPolicy::DivRounded(nominator, denominator, extra_odd_quotient);
}
 
// result = (value1 * value2) / divisor
template <typename RoundPolicy>
constexpr int64_t MulDiv(int64_t value1, int64_t value2, int64_t divisor) {
    if (divisor == 0) throw DivisionByZeroError();
 
#if __x86_64__ || __ppc64__ || __aarch64__
    using LongInt = __int128_t;
    static_assert(sizeof(void*) == 8);
#else
    using LongInt = int64_t;
    static_assert(sizeof(void*) == 4);
#endif
 
    LongInt prod{};
    if constexpr (sizeof(void*) == 4) {
        if (__builtin_mul_overflow(static_cast<LongInt>(value1), static_cast<LongInt>(value2), &prod)) {
            throw OutOfBoundsError();
        }
    } else {
        prod = static_cast<LongInt>(value1) * value2;
    }
    const auto whole = prod / divisor;
    const auto rem = static_cast<int64_t>(prod % divisor);
 
    if (whole <= kMinInt64 || whole >= kMaxInt64) throw OutOfBoundsError();
 
    const auto whole64 = static_cast<int64_t>(whole);
    const bool extra_odd_quotient = whole64 % 2 != 0;
    const int64_t rem_divided = Div<RoundPolicy>(rem, divisor, extra_odd_quotient);
    UASSERT(rem_divided == -1 || rem_divided == 0 || rem_divided == 1);
 
    return whole64 + rem_divided;
}
 
constexpr int Sign(int64_t value) { return (value > 0) - (value < 0); }
 
// Needed because std::abs is not constexpr
constexpr int64_t Abs(int64_t value) {
    if (value == kMinInt64) throw OutOfBoundsError();
    return value >= 0 ? value : -value;
}
 
// Needed because std::abs is not constexpr
// Insignificantly less performant
template <typename T>
constexpr int64_t Abs(T value) {
    static_assert(std::is_floating_point_v<T>);
    return value >= 0 ? value : -value;
}
 
// Needed because std::floor is not constexpr
// Insignificantly less performant
template <typename T>
constexpr int64_t Floor(T value) {
    if (static_cast<int64_t>(value) <= value) {  // whole or positive
        return static_cast<int64_t>(value);
    } else {
        return static_cast<int64_t>(value) - 1;
    }
}
 
// Needed because std::ceil is not constexpr
// Insignificantly less performant
template <typename T>
constexpr int64_t Ceil(T value) {
    if (static_cast<int64_t>(value) >= value) {  // whole or negative
        return static_cast<int64_t>(value);
    } else {
        return static_cast<int64_t>(value) + 1;
    }
}
 
template <typename Int>
constexpr int64_t ToInt64(Int value) {
    static_assert(meta::kIsInteger<Int>);
    static_assert(sizeof(Int) <= sizeof(int64_t));
 
    if constexpr (sizeof(Int) == sizeof(int64_t)) {
        if (value > kMaxInt64) throw OutOfBoundsError();
    }
    return static_cast<int64_t>(value);
}
 
class HalfUpPolicy final {
public:
    // returns 'true' iff 'abs' should be rounded away from 0
    template <typename T>
    [[nodiscard]] static constexpr bool ShouldRoundAwayFromZero(T abs) {
        const T abs_remainder = abs - static_cast<int64_t>(abs);
        return abs_remainder >= 0.5;
    }
 
    // returns 'true' iff 'a / b' should be rounded away from 0
    static constexpr bool ShouldRoundAwayFromZeroDiv(int64_t a, int64_t b, bool /*extra_odd_quotient*/) {
        const int64_t abs_a = impl::Abs(a);
        const int64_t abs_b = impl::Abs(b);
        const int64_t half_b = abs_b / 2;
        const int64_t abs_remainder = abs_a % abs_b;
        return abs_b % 2 == 0 ? abs_remainder >= half_b : abs_remainder > half_b;
    }
};
 
class HalfDownPolicy final {
public:
    // returns 'true' iff 'abs' should be rounded away from 0
    template <typename T>
    [[nodiscard]] static constexpr bool ShouldRoundAwayFromZero(T abs) {
        const T abs_remainder = abs - static_cast<int64_t>(abs);
        return abs_remainder > 0.5;
    }
 
    // returns 'true' iff 'a / b' should be rounded away from 0
    static constexpr bool ShouldRoundAwayFromZeroDiv(int64_t a, int64_t b, bool /*extra_odd_quotient*/) {
        const int64_t abs_a = impl::Abs(a);
        const int64_t abs_b = impl::Abs(b);
        const int64_t half_b = abs_b / 2;
        const int64_t abs_remainder = abs_a % abs_b;
        return abs_remainder > half_b;
    }
};
 
class HalfEvenPolicy final {
public:
    // returns 'true' iff 'abs' should be rounded away from 0
    template <typename T>
    [[nodiscard]] static constexpr bool ShouldRoundAwayFromZero(T abs) {
        const T abs_remainder = abs - static_cast<int64_t>(abs);
        return abs_remainder == 0.5 ? impl::Floor(abs) % 2 != 0 : abs_remainder > 0.5;
    }
 
    // returns 'true' iff 'a / b' should be rounded away from 0
    static constexpr bool ShouldRoundAwayFromZeroDiv(int64_t a, int64_t b, bool extra_odd_quotient) {
        const int64_t abs_a = impl::Abs(a);
        const int64_t abs_b = impl::Abs(b);
        const int64_t half_b = abs_b / 2;
        const int64_t abs_remainder = abs_a % abs_b;
        return (abs_b % 2 == 0 && abs_remainder == half_b) ? ((abs_a / abs_b) % 2 == 0) == extra_odd_quotient
                                                           : abs_remainder > half_b;
    }
};
 
template <typename HalfPolicy>
class HalfRoundPolicyBase {
public:
    template <typename T>
    [[nodiscard]] static constexpr int64_t Round(T value) {
        if ((value >= 0.0) == HalfPolicy::ShouldRoundAwayFromZero(value)) {
            return impl::Ceil(value);
        } else {
            return impl::Floor(value);
        }
    }
 
    [[nodiscard]] static constexpr int64_t DivRounded(int64_t a, int64_t b, bool extra_odd_quotient) {
        if (HalfPolicy::ShouldRoundAwayFromZeroDiv(a, b, extra_odd_quotient)) {
            const auto quotient_sign = impl::Sign(a) * impl::Sign(b);
            return (a / b) + quotient_sign;  // round away from 0
        } else {
            return a / b;  // round towards 0
        }
    }
};
 
}  // namespace impl
 
/// A fast, constexpr-friendly power of 10
constexpr int64_t Pow10(int exp) {
    if (exp < 0 || exp > impl::kMaxDecimalDigits) {
        throw std::runtime_error("Pow10: invalid power of 10");
    }
    return impl::kPowSeries10[static_cast<size_t>(exp)];
}
 
/// A guaranteed-compile-time power of 10
template <int Exp>
inline constexpr int64_t kPow10 = Pow10(Exp);
 
/// @brief Default rounding. Fast, rounds to nearest.
///
/// On 0.5, rounds away from zero. Also, sometimes rounds up numbers
/// in the neighborhood of 0.5, e.g. 0.49999999999999994 -> 1.
class DefRoundPolicy final {
public:
    template <typename T>
    [[nodiscard]] static constexpr int64_t Round(T value) {
        return static_cast<int64_t>(value + (value < 0 ? -0.5 : 0.5));
    }
 
    [[nodiscard]] static constexpr int64_t DivRounded(int64_t a, int64_t b, bool /*extra_odd_quotient*/) {
        const int64_t divisor_corr = impl::Abs(b / 2);
        if (a >= 0) {
            if (impl::kMaxInt64 - a < divisor_corr) throw OutOfBoundsError();
            return (a + divisor_corr) / b;
        } else {
            if (-(impl::kMinInt64 - a) < divisor_corr) throw OutOfBoundsError();
            return (a - divisor_corr) / b;
        }
    }
};
 
/// Round to nearest, 0.5 towards zero
class HalfDownRoundPolicy final : public impl::HalfRoundPolicyBase<impl::HalfDownPolicy> {};
 
/// Round to nearest, 0.5 away from zero
class HalfUpRoundPolicy final : public impl::HalfRoundPolicyBase<impl::HalfUpPolicy> {};
 
/// Round to nearest, 0.5 towards number with even last digit
class HalfEvenRoundPolicy final : public impl::HalfRoundPolicyBase<impl::HalfEvenPolicy> {};
 
/// Round towards +infinity
class CeilingRoundPolicy {
public:
    template <typename T>
    [[nodiscard]] static constexpr int64_t Round(T value) {
        return impl::Ceil(value);
    }
 
    [[nodiscard]] static constexpr int64_t DivRounded(int64_t a, int64_t b, bool /*extra_odd_quotient*/) {
        const bool quotient_positive = (a >= 0) == (b >= 0);
        return (a / b) + (a % b != 0 && quotient_positive);
    }
};
 
/// Round towards -infinity
class FloorRoundPolicy final {
public:
    template <typename T>
    [[nodiscard]] static constexpr int64_t Round(T value) {
        return impl::Floor(value);
    }
 
    [[nodiscard]] static constexpr int64_t DivRounded(int64_t a, int64_t b, bool /*extra_odd_quotient*/) {
        const bool quotient_negative = (a < 0) != (b < 0);
        return (a / b) - (a % b != 0 && quotient_negative);
    }
};
 
/// Round towards zero. The fastest rounding.
class RoundDownRoundPolicy final {
public:
    template <typename T>
    [[nodiscard]] static constexpr int64_t Round(T value) {
        return static_cast<int64_t>(value);
    }
 
    [[nodiscard]] static constexpr int64_t DivRounded(int64_t a, int64_t b, bool /*extra_odd_quotient*/) {
        return a / b;
    }
};
 
/// Round away from zero
class RoundUpRoundPolicy final {
public:
    template <typename T>
    [[nodiscard]] static constexpr int64_t Round(T value) {
        if (value >= 0.0) {
            return impl::Ceil(value);
        } else {
            return impl::Floor(value);
        }
    }
 
    [[nodiscard]] static constexpr int64_t DivRounded(int64_t a, int64_t b, bool /*extra_odd_quotient*/) {
        const auto quotient_sign = impl::Sign(a) * impl::Sign(b);
        return (a / b) + (a % b != 0) * quotient_sign;
    }
};
 
/// @ingroup userver_universal userver_containers
///
/// @brief Fixed-point decimal data type for use in deterministic calculations,
/// oftentimes involving money
///
/// @tparam Prec The number of fractional digits
/// @tparam RoundPolicy Specifies how to round in lossy operations
///
/// Decimal is internally represented as `int64_t`. It means that it can be
/// passed around by value. It also means that operations with huge
/// numbers can overflow and trap. For example, with `Prec == 6`, the maximum
/// representable number is about 10 trillion.
///
/// Decimal should be serialized and stored as a string, NOT as `double`. Use
/// `Decimal{str}` constructor (or `Decimal::FromStringPermissive` if rounding
/// is allowed) to read a `Decimal`, and `ToString(dec)`
/// (or `ToStringTrailingZeros(dec)`/`ToStringFixed<N>(dec)`) to write a
/// `Decimal`.
///
/// Use arithmetic with caution! Multiplication and division operations involve
/// rounding. You may want to cast to `Decimal` with another `Prec`
/// or `RoundPolicy` beforehand. For that purpose you can use
/// `decimal64::decimal_cast<NewDec>(dec)`.
///
/// Usage example:
/// @code{.cpp}
/// // create a single alias instead of specifying Decimal everywhere
/// using Money = decimal64::Decimal<4, decimal64::HalfEvenRoundPolicy>;
///
/// std::vector<std::string> cart = ...;
/// Money sum{0};
/// for (const std::string& cost_string : cart) {
///   // or use FromStringPermissive to enable rounding
///   sum += Money{cost_string};
/// }
/// return ToString(sum);
/// @endcode
template <int Prec, typename TRoundPolicy = DefRoundPolicy>
class Decimal {
public:
    /// The number of fractional digits
    static constexpr int kDecimalPoints = Prec;
 
    /// Specifies how to round in lossy operations
    using RoundPolicy = TRoundPolicy;
 
    /// The denominator of the decimal fraction
    static constexpr int64_t kDecimalFactor = kPow10<Prec>;
 
    /// Zero by default
    constexpr Decimal() noexcept = default;
 
    /// @brief Convert from an integer
    template <typename Int, impl::EnableIfInt<Int> = 0>
    explicit constexpr Decimal(Int value) : Decimal(FromDecimal(Decimal<0>::FromUnbiased(impl::ToInt64(value)))) {}
 
    /// @brief Convert from a string
    ///
    /// The string must match the following regexp exactly:
    ///
    ///     [+-]?\d+(\.\d+)?
    ///
    /// No extra characters, including spaces, are allowed. Extra leading
    /// and trailing zeros (within `Prec`) are discarded. Input containing more
    /// fractional digits that `Prec` is not allowed (no implicit rounding).
    ///
    /// @throw decimal64::ParseError on invalid input
    /// @see FromStringPermissive
    explicit constexpr Decimal(std::string_view value);
 
    /// @brief Lossy conversion from a floating-point number
    ///
    /// To somewhat resist the accumulated error, the number is always rounded
    /// to the nearest Decimal, regardless of `RoundPolicy`.
    ///
    /// @warning Prefer storing and sending `Decimal` as string, and performing
    /// the computations between `Decimal`s.
    template <typename T>
    static constexpr Decimal FromFloatInexact(T value) {
        static_assert(std::is_floating_point_v<T>);
        // Check that overflow does not occur when converting to int64_t
        // (constexpr detects UB).
        static_assert(DefRoundPolicy::Round(impl::kMinRepresentableLongDouble) < 0);
        static_assert(DefRoundPolicy::Round(impl::kMaxRepresentableLongDouble) > 0);
 
        const auto unbiased_float = static_cast<long double>(value) * kDecimalFactor;
        if (unbiased_float < impl::kMinRepresentableLongDouble || unbiased_float > impl::kMaxRepresentableLongDouble) {
            throw OutOfBoundsError();
        }
        return FromUnbiased(DefRoundPolicy::Round(unbiased_float));
    }
 
    /// @brief Convert from a string, allowing rounding, spaces and boundary dot
    ///
    /// In addition to the `Decimal(str)` constructor, allows:
    /// - rounding (as per `RoundPolicy`), e.g. "12.3456789" with `Prec == 2`
    /// - space characters, e.g. " \t42  \n"
    /// - leading and trailing dot, e.g. "5." and ".5"
    ///
    /// @throw decimal64::ParseError on invalid input
    /// @see Decimal(std::string_view)
    static constexpr Decimal FromStringPermissive(std::string_view input);
 
    /// @brief Reconstruct from the internal representation, as acquired
    /// with `AsUnbiased`
    ///
    /// The Decimal value will be equal to `value/kDecimalFactor`.
    ///
    /// @see AsUnbiased
    static constexpr Decimal FromUnbiased(int64_t value) noexcept {
        Decimal result;
        result.value_ = value;
        return result;
    }
 
    /// @brief Convert from `original_unbiased / 10^original_precision`, rounding
    /// according to `RoundPolicy` if necessary
    ///
    /// Usage examples:
    ///
    ///     Decimal<4>::FromBiased(123, 6) -> 0.0001
    ///     Decimal<4>::FromBiased(123, 2) -> 1.23
    ///     Decimal<4>::FromBiased(123, -1) -> 1230
    ///
    /// @param original_unbiased The original mantissa
    /// @param original_precision The original precision (negated exponent)
    static constexpr Decimal FromBiased(int64_t original_unbiased, int original_precision) {
        const int exponent_for_pack = Prec - original_precision;
 
        if (exponent_for_pack >= 0) {
            return FromUnbiased(original_unbiased) * Pow10(exponent_for_pack);
        } else {
            return FromUnbiased(impl::Div<RoundPolicy>(original_unbiased, Pow10(-exponent_for_pack)));
        }
    }
 
    /// @brief Assignment from another `Decimal`
    ///
    /// The assignment is allowed as long as `RoundPolicy` is the same. Rounding
    /// will be performed according to `RoundPolicy` if necessary.
    template <int Prec2>
    Decimal& operator=(Decimal<Prec2, RoundPolicy> rhs) {
        *this = FromDecimal(rhs);
        return *this;
    }
 
    /// @brief Assignment from an integer
    template <typename Int, impl::EnableIfInt<Int> = 0>
    constexpr Decimal& operator=(Int rhs) {
        *this = Decimal{rhs};
        return *this;
    }
 
#ifdef USERVER_IMPL_HAS_THREE_WAY_COMPARISON
    constexpr auto operator<=>(const Decimal& rhs) const = default;
#else
    constexpr bool operator==(Decimal rhs) const { return value_ == rhs.value_; }
 
    constexpr bool operator!=(Decimal rhs) const { return value_ != rhs.value_; }
 
    constexpr bool operator<(Decimal rhs) const { return value_ < rhs.value_; }
 
    constexpr bool operator<=(Decimal rhs) const { return value_ <= rhs.value_; }
 
    constexpr bool operator>(Decimal rhs) const { return value_ > rhs.value_; }
 
    constexpr bool operator>=(Decimal rhs) const { return value_ >= rhs.value_; }
#endif
 
    constexpr Decimal operator+() const { return *this; }
 
    constexpr Decimal operator-() const {
        if (value_ == impl::kMinInt64) throw OutOfBoundsError();
        return FromUnbiased(-value_);
    }
 
    template <int Prec2>
    constexpr auto operator+(Decimal<Prec2, RoundPolicy> rhs) const {
        if constexpr (Prec2 > Prec) {
            return Decimal<Prec2, RoundPolicy>::FromDecimal(*this) + rhs;
        } else if constexpr (Prec2 < Prec) {
            return *this + FromDecimal(rhs);
        } else {
            int64_t result{};
            if (__builtin_add_overflow(AsUnbiased(), rhs.AsUnbiased(), &result)) {
                throw OutOfBoundsError();
            }
            return FromUnbiased(result);
        }
    }
 
    template <typename Int, impl::EnableIfInt<Int> = 0>
    constexpr Decimal operator+(Int rhs) const {
        return *this + Decimal{rhs};
    }
 
    template <typename Int, impl::EnableIfInt<Int> = 0>
    friend constexpr Decimal operator+(Int lhs, Decimal rhs) {
        return Decimal{lhs} + rhs;
    }
 
    template <int Prec2>
    constexpr Decimal& operator+=(Decimal<Prec2, RoundPolicy> rhs) {
        static_assert(Prec2 <= Prec, "Implicit cast to Decimal of lower precision in assignment");
        *this = *this + rhs;
        return *this;
    }
 
    template <typename Int, impl::EnableIfInt<Int> = 0>
    constexpr Decimal& operator+=(Int rhs) {
        *this = *this + rhs;
        return *this;
    }
 
    template <int Prec2>
    constexpr auto operator-(Decimal<Prec2, RoundPolicy> rhs) const {
        if constexpr (Prec2 > Prec) {
            return Decimal<Prec2, RoundPolicy>::FromDecimal(*this) - rhs;
        } else if constexpr (Prec2 < Prec) {
            return *this - FromDecimal(rhs);
        } else {
            int64_t result{};
            if (__builtin_sub_overflow(AsUnbiased(), rhs.AsUnbiased(), &result)) {
                throw OutOfBoundsError();
            }
            return FromUnbiased(result);
        }
    }
 
    template <typename Int, impl::EnableIfInt<Int> = 0>
    constexpr Decimal operator-(Int rhs) const {
        return *this - Decimal{rhs};
    }
 
    template <typename Int, impl::EnableIfInt<Int> = 0>
    friend constexpr Decimal operator-(Int lhs, Decimal rhs) {
        return Decimal{lhs} - rhs;
    }
 
    template <int Prec2>
    constexpr Decimal& operator-=(Decimal<Prec2, RoundPolicy> rhs) {
        static_assert(Prec2 <= Prec, "Implicit cast to Decimal of lower precision in assignment");
        *this = *this - rhs;
        return *this;
    }
 
    template <typename Int, impl::EnableIfInt<Int> = 0>
    constexpr Decimal& operator-=(Int rhs) {
        *this = *this - rhs;
        return *this;
    }
 
    template <typename Int, typename = impl::EnableIfInt<Int>>
    constexpr Decimal operator*(Int rhs) const {
        int64_t result{};
        if (rhs > impl::kMaxInt64 || __builtin_mul_overflow(value_, static_cast<int64_t>(rhs), &result)) {
            throw OutOfBoundsError();
        }
        return FromUnbiased(result);
    }
 
    template <typename Int, impl::EnableIfInt<Int> = 0>
    friend constexpr Decimal operator*(Int lhs, Decimal rhs) {
        return rhs * lhs;
    }
 
    template <typename Int, impl::EnableIfInt<Int> = 0>
    constexpr Decimal& operator*=(Int rhs) {
        *this = *this * rhs;
        return *this;
    }
 
    template <int Prec2>
    constexpr Decimal operator*(Decimal<Prec2, RoundPolicy> rhs) const {
        return FromUnbiased(impl::MulDiv<RoundPolicy>(AsUnbiased(), rhs.AsUnbiased(), kPow10<Prec2>));
    }
 
    template <int Prec2>
    constexpr Decimal& operator*=(Decimal<Prec2, RoundPolicy> rhs) {
        *this = *this * rhs;
        return *this;
    }
 
    template <typename Int, typename = impl::EnableIfInt<Int>>
    constexpr Decimal operator/(Int rhs) const {
        return FromUnbiased(impl::Div<RoundPolicy>(AsUnbiased(), rhs));
    }
 
    template <typename Int, typename = impl::EnableIfInt<Int>>
    friend constexpr Decimal operator/(Int lhs, Decimal rhs) {
        return Decimal{lhs} / rhs;
    }
 
    template <typename Int, typename = impl::EnableIfInt<Int>>
    constexpr Decimal& operator/=(Int rhs) {
        *this = *this / rhs;
        return *this;
    }
 
    template <int Prec2>
    constexpr Decimal operator/(Decimal<Prec2, RoundPolicy> rhs) const {
        return FromUnbiased(impl::MulDiv<RoundPolicy>(AsUnbiased(), kPow10<Prec2>, rhs.AsUnbiased()));
    }
 
    template <int Prec2>
    constexpr Decimal& operator/=(Decimal<Prec2, RoundPolicy> rhs) {
        *this = *this / rhs;
        return *this;
    }
 
    /// Returns one of {-1, 0, +1}, depending on the sign of the `Decimal`
    constexpr int Sign() const { return impl::Sign(value_); }
 
    /// Returns the absolute value of the `Decimal`
    constexpr Decimal Abs() const { return FromUnbiased(impl::Abs(value_)); }
 
    /// Rounds `this` to the nearest multiple of `base` according to `RoundPolicy`
    constexpr Decimal RoundToMultipleOf(Decimal base) const {
        if (base < Decimal{0}) throw OutOfBoundsError();
        return *this / base.AsUnbiased() * base.AsUnbiased();
    }
 
    /// Returns the value rounded to integer using the active rounding policy
    constexpr int64_t ToInteger() const { return impl::Div<RoundPolicy>(value_, kDecimalFactor); }
 
    /// @brief Returns the value converted to `double`
    ///
    /// @warning Operations with `double`, and even the returned value,
    /// is inexact. Prefer storing and sending `Decimal` as string, and performing
    /// the computations between `Decimal`s.
    ///
    /// @see FromFloatInexact
    constexpr double ToDoubleInexact() const {
        // maximum number that can be represented without modification
        constexpr std::int64_t kLossLimit = (static_cast<std::int64_t>(1) << std::numeric_limits<double>::digits);
 
        if (value_ > -kLossLimit && value_ < kLossLimit) {
            return static_cast<double>(value_) / kDecimalFactor;
        }
 
        constexpr int kCoef =
            1 << (std::max(
                std::numeric_limits<std::int64_t>::digits - std::numeric_limits<double>::digits - 3 * Prec, 0
            ));
 
        // divide the value into two parts (each no more than kLossLimit)
        const std::int64_t p1 = value_ / (kDecimalFactor * kCoef) * kCoef;
        const std::int64_t p2 = value_ % (kDecimalFactor * kCoef);
 
        // combine without loss of accuracy
        return p1 + static_cast<double>(p2) / kDecimalFactor;
    }
 
    /// @brief Retrieve the internal representation
    ///
    /// The internal representation of `Decimal` is `real_value * kDecimalFactor`.
    /// Use for storing the value of Decimal efficiently when `Prec` is guaranteed
    /// not to change.
    ///
    /// @see FromUnbiased
    constexpr int64_t AsUnbiased() const { return value_; }
 
private:
    template <int Prec2, typename RoundPolicy2>
    static constexpr Decimal FromDecimal(Decimal<Prec2, RoundPolicy2> source) {
        if constexpr (Prec > Prec2) {
            int64_t result{};
            if (__builtin_mul_overflow(source.AsUnbiased(), kPow10<Prec - Prec2>, &result)) {
                throw OutOfBoundsError();
            }
            return FromUnbiased(result);
        } else if constexpr (Prec < Prec2) {
            return FromUnbiased(impl::Div<RoundPolicy>(source.AsUnbiased(), kPow10<Prec2 - Prec>));
        } else {
            return FromUnbiased(source.AsUnbiased());
        }
    }
 
    template <int Prec2, typename RoundPolicy2>
    friend class Decimal;
 
    template <typename T, int OldPrec, typename OldRound>
    friend constexpr T decimal_cast(Decimal<OldPrec, OldRound> arg);
 
    int64_t value_{0};
};
 
namespace impl {
 
template <typename T>
struct IsDecimal : std::false_type {};
 
template <int Prec, typename RoundPolicy>
struct IsDecimal<Decimal<Prec, RoundPolicy>> : std::true_type {};
 
}  // namespace impl
 
/// `true` if the type is an instantiation of `Decimal`
template <typename T>
inline constexpr bool kIsDecimal = impl::IsDecimal<T>::value;
 
/// @brief Cast one `Decimal` to another `Decimal` type
///
/// When casting to a `Decimal` with a lower `Prec`, rounding is performed
/// according to the new `RoundPolicy`.
///
/// Usage example:
/// @code{.cpp}
/// using Money = decimal64::Decimal<4>;
/// using Discount = decimal64::Decimal<4, FloorRoundPolicy>;
///
/// Money cost = ...;
/// auto discount = decimal64::decimal_cast<Discount>(cost) * Discount{"0.05"};
/// @endcode
template <typename T, int OldPrec, typename OldRound>
constexpr T decimal_cast(Decimal<OldPrec, OldRound> arg) {
    static_assert(kIsDecimal<T>);
    return T::FromDecimal(arg);
}
 
namespace impl {
 
// FromUnpacked<Decimal<4>>(12, 34) -> 12.0034
// FromUnpacked<Decimal<4>>(-12, -34) -> -12.0034
// FromUnpacked<Decimal<4>>(0, -34) -> -0.0034
template <int Prec, typename RoundPolicy>
constexpr Decimal<Prec, RoundPolicy> FromUnpacked(int64_t before, int64_t after) {
    using Dec = Decimal<Prec, RoundPolicy>;
    UASSERT(((before >= 0) && (after >= 0)) || ((before <= 0) && (after <= 0)));
 
    int64_t result{};
    if (__builtin_mul_overflow(before, Dec::kDecimalFactor, &result) ||
        __builtin_add_overflow(result, after, &result)) {
        throw OutOfBoundsError();
    }
 
    return Dec::FromUnbiased(result);
}
 
// FromUnpacked<Decimal<4>>(12, 34, 3) -> 12.034
template <int Prec, typename RoundPolicy>
constexpr Decimal<Prec, RoundPolicy> FromUnpacked(int64_t before, int64_t after, int original_precision) {
    UASSERT(((before >= 0) && (after >= 0)) || ((before <= 0) && (after <= 0)));
    UASSERT(after > -Pow10(original_precision) && after < Pow10(original_precision));
 
    if (original_precision <= Prec) {
        // direct mode
        const int missing_digits = Prec - original_precision;
        const int64_t factor = Pow10(missing_digits);
        return FromUnpacked<Prec, RoundPolicy>(before, after * factor);
    } else {
        // rounding mode
        const int extra_digits = original_precision - Prec;
        const int64_t factor = Pow10(extra_digits);
        // note: if rounded up, rounded_after may represent a "fractional part"
        // greater than 1.0, which is ok
        const int64_t rounded_after = Div<RoundPolicy>(after, factor);
        return FromUnpacked<Prec, RoundPolicy>(before, rounded_after);
    }
}
 
template <int Prec, typename RoundPolicy>
constexpr Decimal<Prec, RoundPolicy> FromUnpackedWithExponent(
    int64_t before,
    int64_t after,
    int original_precision,
    int exponent,
    bool is_negative_exponent,
    int leading_zeros
) {
    UASSERT(((before >= 0) && (after >= 0)) || ((before <= 0) && (after <= 0)));
    UASSERT(after > -Pow10(original_precision) && after < Pow10(original_precision));
 
    if (before == 0 && after == 0) {
        return Decimal<Prec, RoundPolicy>::FromUnbiased(0);
    }
 
    const int effective_exponent = is_negative_exponent ? -exponent : exponent;
 
    if (effective_exponent + Prec < -kMaxDecimalDigits) {
        return Decimal<Prec, RoundPolicy>::FromUnbiased(0);
    }
 
    int total_scale = effective_exponent + Prec - original_precision;
 
    if (before == 0 && after != 0) {
        if (!is_negative_exponent) {
            if (exponent >= leading_zeros) {
                exponent -= leading_zeros;
                original_precision -= leading_zeros;
            } else {
                original_precision -= exponent;
                exponent = 0;
            }
        }
    }
 
    int64_t value = before;
 
    if (__builtin_mul_overflow(value, Pow10(original_precision), &value) ||
        __builtin_add_overflow(value, after, &value)) {
        throw OutOfBoundsError();
    }
 
    if (total_scale > 0) {
        if (total_scale > kMaxDecimalDigits) {
            throw OutOfBoundsError();
        }
        if (__builtin_mul_overflow(value, Pow10(total_scale), &value)) {
            throw OutOfBoundsError();
        }
    } else if (total_scale < 0) {
        const int64_t divisor = Pow10(-total_scale);
        value = Div<RoundPolicy>(value, divisor);
    }
 
    return Decimal<Prec, RoundPolicy>::FromUnbiased(value);
}
 
struct UnpackedDecimal {
    int64_t before;
    int64_t after;
};
 
// AsUnpacked(Decimal<4>{"3.14"}) -> {3, 1400}
// AsUnpacked(Decimal<4>{"-3.14"}) -> {-3, -1400}
// AsUnpacked(Decimal<4>{"-0.14"}) -> {0, -1400}
template <int Prec, typename RoundPolicy>
constexpr UnpackedDecimal AsUnpacked(Decimal<Prec, RoundPolicy> dec) {
    using Dec = Decimal<Prec, RoundPolicy>;
    return {dec.AsUnbiased() / Dec::kDecimalFactor, dec.AsUnbiased() % Dec::kDecimalFactor};
}
 
// AsUnpacked(Decimal<4>{"3.14"}, 5) -> {3, 14000}
// AsUnpacked(Decimal<4>{"-3.14"}, 6) -> {-3, -140000}
// AsUnpacked(Decimal<4>{"-0.14"}, 1) -> {0, -1}
template <int Prec, typename RoundPolicy>
UnpackedDecimal AsUnpacked(Decimal<Prec, RoundPolicy> dec, int new_prec) {
    if (new_prec == Prec) {
        return AsUnpacked(dec);
    }
    int64_t result{};
    if (new_prec > Prec) {
        if (__builtin_mul_overflow(dec.AsUnbiased(), Pow10(new_prec - Prec), &result)) {
            throw OutOfBoundsError();
        }
    } else {
        result = impl::Div<RoundPolicy>(dec.AsUnbiased(), Pow10(Prec - new_prec));
    }
    const auto dec_factor = Pow10(new_prec);
    return {result / dec_factor, result % dec_factor};
}
 
template <typename CharT>
constexpr bool IsSpace(CharT c) {
    return c == ' ' || c == '\t' || c == '\r' || c == '\n' || c == '\v';
}
 
template <typename CharT, typename Traits>
class StringCharSequence {
public:
    explicit constexpr StringCharSequence(std::basic_string_view<CharT, Traits> sv)
        : current_(sv.begin()), end_(sv.end()) {}
 
    // on sequence end, returns '\0'
    constexpr CharT Get() { return current_ == end_ ? CharT{'\0'} : *current_++; }
 
    constexpr void Unget() { --current_; }
 
private:
    typename std::basic_string_view<CharT, Traits>::iterator current_;
    typename std::basic_string_view<CharT, Traits>::iterator end_;
};
 
template <typename CharT, typename Traits>
class StreamCharSequence {
public:
    explicit StreamCharSequence(std::basic_istream<CharT, Traits>& in) : in_(&in) {}
 
    // on sequence end, returns '\0'
    CharT Get() {
        constexpr CharT kEof = std::basic_istream<CharT, Traits>::traits_type::eof();
        if (!in_->good()) {
            return CharT{'\0'};
        }
        const CharT c = in_->peek();
        if (c == kEof) {
            return CharT{'\0'};
        }
        in_->ignore();
        return c;
    }
 
    void Unget() { in_->unget(); }
 
private:
    std::basic_istream<CharT, Traits>* in_;
};
 
enum class ParseOptions {
    kNone = 0,
 
    /// Allow space characters in the beginning or in the end
    /// " 42  "
    kAllowSpaces = 1 << 0,
 
    /// Allow any trailing characters
    /// "42ABC"
    kAllowTrailingJunk = 1 << 1,
 
    /// Allow leading or trailing dot
    /// "42.", ".42"
    kAllowBoundaryDot = 1 << 2,
 
    /// Allow decimal digits beyond Prec, round according to RoundPolicy
    /// "0.123456" -> "0.1234" or "0.1235"
    kAllowRounding = 1 << 3,
 
    /// Allow using exponential format (e or E)
    /// 1e2 -> 100 or 1E2 -> 100
    kAllowExponent = 1 << 4
};
 
enum class ParseErrorCode : uint8_t {
    /// An unexpected character has been met
    kWrongChar,
 
    /// No digits before or after dot
    kNoDigits,
 
    /// The integral part does not fit in a Decimal
    kOverflow,
 
    /// The string contains leading spaces, while disallowed by options
    kSpace,
 
    /// The string contains trailing junk, while disallowed by options
    kTrailingJunk,
 
    /// On inputs like "42." or ".42" if disallowed by options
    kBoundaryDot,
 
    /// When there are more decimal digits than in any Decimal and rounding is
    /// disallowed by options
    kRounding,
 
    /// On inputs like "1e2" or "1E2" if exponent is not allowed by options
    kExponentNotAllowed,
 
    /// When there are no numbers after the exponent character (or after exponent sign if it exist)
    /// On inputs like "1e" or "1E+" or "1e-"
    kNoExponentDigits
};
 
struct ParseUnpackedResult {
    int64_t before{0};
    int64_t after{0};
    uint8_t decimal_digits{0};
    bool is_negative{false};
    uint8_t exponent{0};
    bool is_negative_exponent{false};
    std::optional<ParseErrorCode> error;
    uint32_t error_position{-1U};
    int zeros_after_dec{0};
};
 
enum class ParseState {
    /// Before reading any part of the Decimal
    kSign,
 
    /// After reading a sign
    kBeforeFirstDig,
 
    /// Only leading zeros (at least one) have been met
    kLeadingZeros,
 
    /// At least one digit before dot has been met
    kBeforeDec,
 
    /// Reading fractional digits
    kAfterDec,
 
    /// Only zeros (at least one) have been met after dot
    kZerosAfterDec,
 
    /// Reading and rounding extra fractional digits
    kIgnoringAfterDec,
 
    /// Exponent sign
    kExpSign,
 
    // First digit after sign
    kExpFirstDigit,
 
    /// Exponent digits
    kExpDigits,
 
    /// A character unrelated to the Decimal has been met
    kEnd
};
 
constexpr inline void
StateToExpSign(std::optional<ParseErrorCode>& error, ParseState& state, utils::Flags<ParseOptions>& options) {
    if (!error && !(options & ParseOptions::kAllowExponent)) {
        error = ParseErrorCode::kExponentNotAllowed;
    }
    state = ParseState::kExpSign;
}
 
/// Extract values from a CharSequence ready to be packed to Decimal
template <typename CharSequence>
[[nodiscard]] constexpr ParseUnpackedResult ParseUnpacked(CharSequence input, utils::Flags<ParseOptions> options) {
    constexpr char dec_point = '.';
 
    int64_t before = 0;
    int64_t after = 0;
    bool is_negative = false;
 
    ptrdiff_t position = -1;
    auto state = ParseState::kSign;
    std::optional<ParseErrorCode> error;
    int before_digit_count = 0;
    uint8_t after_digit_count = 0;
    bool is_negative_exp = false;
    uint8_t exponent = 0;
    int zeros_after_dec = 0;
 
    while (state != ParseState::kEnd) {
        const auto c = input.Get();
        if (c == '\0') break;
        if (!error) ++position;
 
        switch (state) {
            case ParseState::kSign:
                if (c == '-') {
                    is_negative = true;
                    state = ParseState::kBeforeFirstDig;
                } else if (c == '+') {
                    state = ParseState::kBeforeFirstDig;
                } else if (c == '0') {
                    state = ParseState::kLeadingZeros;
                    before_digit_count = 1;
                } else if ((c >= '1') && (c <= '9')) {
                    state = ParseState::kBeforeDec;
                    before = static_cast<int>(c - '0');
                    before_digit_count = 1;
                } else if (c == dec_point) {
                    if (!(options & ParseOptions::kAllowBoundaryDot) && !error) {
                        error = ParseErrorCode::kBoundaryDot;  // keep reading digits
                    }
                    state = ParseState::kZerosAfterDec;
                } else if (IsSpace(c)) {
                    if (!(options & ParseOptions::kAllowSpaces)) {
                        state = ParseState::kEnd;
                        error = ParseErrorCode::kSpace;
                    }
                } else {
                    state = ParseState::kEnd;
                    error = ParseErrorCode::kWrongChar;
                }
                break;
            case ParseState::kBeforeFirstDig:
                if (c == '0') {
                    state = ParseState::kLeadingZeros;
                    before_digit_count = 1;
                } else if ((c >= '1') && (c <= '9')) {
                    state = ParseState::kBeforeDec;
                    before = static_cast<int>(c - '0');
                    before_digit_count = 1;
                } else if (c == dec_point) {
                    if (!(options & ParseOptions::kAllowBoundaryDot) && !error) {
                        error = ParseErrorCode::kBoundaryDot;  // keep reading digits
                    }
                    state = ParseState::kAfterDec;
                } else {
                    state = ParseState::kEnd;
                    error = ParseErrorCode::kWrongChar;
                }
                break;
            case ParseState::kLeadingZeros:
                if (c == '0') {
                    // skip
                } else if ((c >= '1') && (c <= '9')) {
                    state = ParseState::kBeforeDec;
                    before = static_cast<int>(c - '0');
                } else if (c == dec_point) {
                    state = ParseState::kZerosAfterDec;
                } else if (c == 'e' || c == 'E') {
                    StateToExpSign(/*error*/ error, /*state*/ state, /*options*/ options);
                } else {
                    state = ParseState::kEnd;
                }
                break;
            case ParseState::kBeforeDec:
                if ((c >= '0') && (c <= '9')) {
                    if (before_digit_count < kMaxDecimalDigits) {
                        before = 10 * before + static_cast<int>(c - '0');
                        before_digit_count++;
                    } else if (!error) {
                        error = ParseErrorCode::kOverflow;  // keep reading digits
                    }
                } else if (c == dec_point) {
                    state = ParseState::kZerosAfterDec;
                } else if (c == 'e' || c == 'E') {
                    StateToExpSign(/*error*/ error, /*state*/ state, /*options*/ options);
                } else {
                    state = ParseState::kEnd;
                }
                break;
 
            case ParseState::kZerosAfterDec:
                if (c == '0') {
                    zeros_after_dec++;
                    after_digit_count++;
                    break;
                }
                [[fallthrough]];
 
            case ParseState::kAfterDec:
                state = ParseState::kAfterDec;
                if ((c >= '0') && (c <= '9')) {
                    if (after_digit_count < kMaxDecimalDigits) {
                        after = 10 * after + static_cast<int>(c - '0');
                        after_digit_count++;
                    } else {
                        if (!(options & ParseOptions::kAllowRounding) && !error) {
                            error = ParseErrorCode::kRounding;  // keep reading digits
                        }
                        state = ParseState::kIgnoringAfterDec;
                        if (c >= '5') {
                            // round half up
                            after++;
                        }
                    }
 
                } else if (c == 'e' || c == 'E') {
                    StateToExpSign(/*error*/ error, /*state*/ state, /*options*/ options);
                } else {
                    if (!(options & ParseOptions::kAllowBoundaryDot) && after_digit_count == 0 && !error) {
                        error = ParseErrorCode::kBoundaryDot;
                    }
                    state = ParseState::kEnd;
                }
                break;
 
            case ParseState::kIgnoringAfterDec:
                if ((c >= '0') && (c <= '9')) {
                    // skip
                } else if (c == 'e' || c == 'E') {
                    StateToExpSign(/*error*/ error, /*state*/ state, /*options*/ options);
                } else {
                    state = ParseState::kEnd;
                }
                break;
 
            case ParseState::kExpSign:
                if (c == '+') {
                    is_negative_exp = false;
                    state = ParseState::kExpFirstDigit;
                } else if (c == '-') {
                    is_negative_exp = true;
                    state = ParseState::kExpFirstDigit;
                } else if (c >= '0' && c <= '9') {
                    exponent = static_cast<int>(c - '0');
                    state = ParseState::kExpDigits;
                } else {
                    if (!error) {
                        error = ParseErrorCode::kWrongChar;
                    }
                    state = ParseState::kEnd;
                }
                break;
 
            case ParseState::kExpFirstDigit:
                if (c >= '0' && c <= '9') {
                    exponent = static_cast<int>(c - '0');
                    state = ParseState::kExpDigits;
                } else {
                    state = ParseState::kEnd;
                    if (!error) error = ParseErrorCode::kWrongChar;
                }
                break;
 
            case ParseState::kExpDigits:
                if (c >= '0' && c <= '9') {
                    if ((__builtin_mul_overflow(10, exponent, &exponent) ||
                         __builtin_add_overflow(static_cast<int>(c - '0'), exponent, &exponent))) {
                        if (is_negative_exp && !(options & ParseOptions::kAllowRounding) && !error) {
                            error = ParseErrorCode::kRounding;  // keep reading digits
                        }
                        if (!is_negative_exp && !error) {
                            error = ParseErrorCode::kOverflow;  // keep reading digits
                        }
                    }
                } else {
                    state = ParseState::kEnd;
                }
                break;
 
            case ParseState::kEnd:
                UASSERT(false);
                break;
        }  // switch state
    }      // while has more chars & not end
 
    if (state == ParseState::kEnd) {
        input.Unget();
 
        if (!error && !(options & ParseOptions::kAllowTrailingJunk)) {
            if (!(options & ParseOptions::kAllowSpaces)) {
                error = ParseErrorCode::kSpace;
            }
            --position;
 
            while (true) {
                const auto c = input.Get();
                if (c == '\0') break;
                ++position;
                if (!IsSpace(c)) {
                    error = ParseErrorCode::kTrailingJunk;
                    input.Unget();
                    break;
                }
            }
        }
    }
 
    if (!error && before_digit_count == 0 && after_digit_count == 0) {
        error = ParseErrorCode::kNoDigits;
    }
 
    if (!error && state == ParseState::kZerosAfterDec && !(options & ParseOptions::kAllowBoundaryDot) &&
        after_digit_count == 0) {
        error = ParseErrorCode::kBoundaryDot;
    }
 
    if ((!error && state == ParseState::kExpSign) || (!error && state == ParseState::kExpFirstDigit)) {
        error = ParseErrorCode::kNoExponentDigits;
    }
 
    if (zeros_after_dec >= kMaxDecimalDigits) {
        after_digit_count = 0;
        after = 0;
        zeros_after_dec = 0;
    }
 
    return {
        before,
        after,
        after_digit_count,
        is_negative,
        exponent,
        is_negative_exp,
        error,
        static_cast<uint32_t>(position),
        zeros_after_dec,
 
    };
}
 
template <int Prec, typename RoundPolicy>
struct ParseResult {
    Decimal<Prec, RoundPolicy> decimal;
    std::optional<ParseErrorCode> error;
    uint32_t error_position{-1U};
};
 
/// Parse Decimal from a CharSequence
template <int Prec, typename RoundPolicy, typename CharSequence>
[[nodiscard]] constexpr ParseResult<Prec, RoundPolicy> Parse(CharSequence input, utils::Flags<ParseOptions> options) {
    ParseUnpackedResult parsed = ParseUnpacked(input, options);
 
    if (parsed.error) {
        return {{}, parsed.error, parsed.error_position};
    }
 
    if (!(options & ParseOptions::kAllowRounding) && parsed.decimal_digits > Prec) {
        return {{}, ParseErrorCode::kRounding, 0};
    }
 
    if (parsed.before >= kMaxInt64 / kPow10<Prec>) {
        return {{}, ParseErrorCode::kOverflow, 0};
    }
 
    if (parsed.after == 0 && parsed.decimal_digits > 0) {
        parsed.after = 0;
        parsed.decimal_digits = 0;
        parsed.zeros_after_dec = 0;
    }
 
    if (parsed.is_negative) {
        parsed.before = -parsed.before;
        parsed.after = -parsed.after;
    }
 
    if (parsed.exponent != 0) {
        return {
            FromUnpackedWithExponent<Prec, RoundPolicy>(
                parsed.before,
                parsed.after,
                parsed.decimal_digits,
                parsed.exponent,
                parsed.is_negative_exponent,
                parsed.zeros_after_dec
            ),
            {},
            0,
        };
    }
 
    return {FromUnpacked<Prec, RoundPolicy>(parsed.before, parsed.after, parsed.decimal_digits), {}, 0};
}
 
std::string GetErrorMessage(std::string_view source, std::string_view path, size_t position, ParseErrorCode reason);
 
/// removes the zeros on the right in after
/// saves the updated precision in after_precision
void TrimTrailingZeros(int64_t& after, int& after_precision);
 
std::string ToString(int64_t before, int64_t after, int precision, const FormatOptions& format_options);
 
}  // namespace impl
 
template <int Prec, typename RoundPolicy>
constexpr Decimal<Prec, RoundPolicy>::Decimal(std::string_view value) {
    const auto result = impl::Parse<Prec, RoundPolicy>(impl::StringCharSequence(value), impl::ParseOptions::kNone);
 
    if (result.error) {
        throw ParseError(impl::GetErrorMessage(value, "<string>", result.error_position, *result.error));
    }
    *this = result.decimal;
}
 
template <int Prec, typename RoundPolicy>
constexpr Decimal<Prec, RoundPolicy> Decimal<Prec, RoundPolicy>::FromStringPermissive(std::string_view input) {
    const auto result = impl::Parse<Prec, RoundPolicy>(
        impl::StringCharSequence(input),
        {impl::ParseOptions::kAllowSpaces,
         impl::ParseOptions::kAllowBoundaryDot,
         impl::ParseOptions::kAllowRounding,
         impl::ParseOptions::kAllowExponent}
    );
 
    if (result.error) {
        throw ParseError(impl::GetErrorMessage(input, "<string>", result.error_position, *result.error));
    }
    return result.decimal;
}
 
/// @brief Converts Decimal to a string
///
/// Usage example:
///
///     ToString(decimal64::Decimal<4>{"1.5"}) -> 1.5
///
/// @see ToStringTrailingZeros
/// @see ToStringFixed
template <int Prec, typename RoundPolicy>
std::string ToString(Decimal<Prec, RoundPolicy> dec) {
    return fmt::to_string(dec);
}
 
/// @brief Converts Decimal to a string
///
/// Usage example:
///
///     ToString(decimal64::Decimal<4>{"-1234.1234"},
///              {"||", "**", "\1", "<>", {}, true}))   -> "<>1**2**3**4||1234"
///     ToString(decimal64::Decimal<4>{"-1234.1234"},
///              {",", " ", "\3", "-", 6, true}))       -> "-1 234,123400"
///
/// @see ToStringTrailingZeros
/// @see ToStringFixed
template <int Prec, typename RoundPolicy>
std::string ToString(const Decimal<Prec, RoundPolicy>& dec, const FormatOptions& format_options) {
    auto precision = format_options.precision.value_or(Prec);
    if (!format_options.is_fixed) {
        precision = std::min(precision, Prec);
    }
    auto [before, after] = impl::AsUnpacked(dec, precision);
    return impl::ToString(before, after, precision, format_options);
}
 
/// @brief Converts Decimal to a string, writing exactly `Prec` decimal digits
///
/// Usage example:
///
///     ToStringTrailingZeros(decimal64::Decimal<4>{"1.5"}) -> 1.5000
///
/// @see ToString
/// @see ToStringFixed
template <int Prec, typename RoundPolicy>
std::string ToStringTrailingZeros(Decimal<Prec, RoundPolicy> dec) {
    return fmt::format(FMT_COMPILE("{:f}"), dec);
}
 
/// @brief Converts Decimal to a string with exactly `NewPrec` decimal digits
///
/// Usage example:
///
///     ToStringFixed<3>(decimal64::Decimal<4>{"1.5"}) -> 1.500
///
/// @see ToString
/// @see ToStringTrailingZeros
template <int NewPrec, int Prec, typename RoundPolicy>
std::string ToStringFixed(Decimal<Prec, RoundPolicy> dec) {
    return ToStringTrailingZeros(decimal64::decimal_cast<Decimal<NewPrec, RoundPolicy>>(dec));
}
 
/// @brief Parses a `Decimal` from the `istream`
///
/// Acts like the `Decimal(str)` constructor, except that it allows junk that
/// immediately follows the number. Sets the stream's fail bit on failure.
///
/// Usage example:
///
///     if (os >> dec) {
///       // success
///     } else {
///       // failure
///     }
///
/// @see Decimal::Decimal(std::string_view)
template <typename CharT, typename Traits, int Prec, typename RoundPolicy>
std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, Decimal<Prec, RoundPolicy>& d) {
    if (is.flags() & std::ios_base::skipws) {
        std::ws(is);
    }
    const auto result = impl::Parse<Prec, RoundPolicy>(
        impl::StreamCharSequence(is), {impl::ParseOptions::kAllowTrailingJunk, impl::ParseOptions::kAllowExponent}
    );
 
    if (result.error) {
        is.setstate(std::ios_base::failbit);
    } else {
        d = result.decimal;
    }
    return is;
}
 
/// @brief Writes the `Decimal` to the `ostream`
/// @see ToString
template <typename CharT, typename Traits, int Prec, typename RoundPolicy>
std::basic_ostream<CharT, Traits>&
operator<<(std::basic_ostream<CharT, Traits>& os, const Decimal<Prec, RoundPolicy>& d) {
    os << ToString(d);
    return os;
}
 
/// @brief Writes the `Decimal` to the logger
/// @see ToString
template <int Prec, typename RoundPolicy>
logging::LogHelper& operator<<(logging::LogHelper& lh, const Decimal<Prec, RoundPolicy>& d) {
    lh << ToString(d);
    return lh;
}
 
/// @brief Parses the `Decimal` from the string
/// @see Decimal::Decimal(std::string_view)
template <int Prec, typename RoundPolicy, typename Value>
std::enable_if_t<formats::common::kIsFormatValue<Value>, Decimal<Prec, RoundPolicy>>
Parse(const Value& value, formats::parse::To<Decimal<Prec, RoundPolicy>>) {
    const std::string input = value.template As<std::string>();
 
    const auto result =
        impl::Parse<Prec, RoundPolicy>(impl::StringCharSequence(std::string_view{input}), impl::ParseOptions::kNone);
 
    if (result.error) {
        throw ParseError(impl::GetErrorMessage(input, value.GetPath(), result.error_position, *result.error));
    }
    return result.decimal;
}
 
/// @brief Serializes the `Decimal` to string
/// @see ToString
template <int Prec, typename RoundPolicy, typename TargetType>
TargetType Serialize(const Decimal<Prec, RoundPolicy>& object, formats::serialize::To<TargetType>) {
    return typename TargetType::Builder(ToString(object)).ExtractValue();
}
 
/// @brief Writes the `Decimal` to stream
/// @see ToString
template <int Prec, typename RoundPolicy, typename StringBuilder>
void WriteToStream(const Decimal<Prec, RoundPolicy>& object, StringBuilder& sw) {
    WriteToStream(ToString(object), sw);
}
 
/// gtest formatter for decimal64::Decimal
template <int Prec, typename RoundPolicy>
void PrintTo(const Decimal<Prec, RoundPolicy>& v, std::ostream* os) {
    *os << v;
}
 
}  // namespace decimal64
 
USERVER_NAMESPACE_END
 
/// std::hash support
template <int Prec, typename RoundPolicy>
struct std::hash<USERVER_NAMESPACE::decimal64::Decimal<Prec, RoundPolicy>> {
    using Decimal = USERVER_NAMESPACE::decimal64::Decimal<Prec, RoundPolicy>;
 
    std::size_t operator()(const Decimal& v) const noexcept { return std::hash<int64_t>{}(v.AsUnbiased()); }
};
 
/// @brief fmt support
///
/// Spec format:
/// - {} trims any trailing zeros;
/// - {:f} writes exactly `Prec` decimal digits, including trailing zeros
///   if needed.
/// - {:.N} writes exactly `N` decimal digits, including trailing zeros
///   if needed.
template <int Prec, typename RoundPolicy, typename Char>
class fmt::formatter<USERVER_NAMESPACE::decimal64::Decimal<Prec, RoundPolicy>, Char> {
public:
    constexpr auto parse(fmt::basic_format_parse_context<Char>& ctx) {
        const auto* it = ctx.begin();
        const auto* end = ctx.end();
 
        if (it != end && *it == '.') {
            remove_trailing_zeros_ = false;
            custom_precision_ = 0;
            ++it;
            while (it != end && *it >= '0' && *it <= '9') {
                *custom_precision_ = *custom_precision_ * 10 + (*it - '0');
                ++it;
            }
        }
 
        if (!custom_precision_ && it != end && *it == 'f') {
            remove_trailing_zeros_ = false;
            ++it;
        }
 
        if (it != end && *it != '}') {
            throw format_error("invalid format");
        }
 
        return it;
    }
 
    template <typename FormatContext>
    auto format(const USERVER_NAMESPACE::decimal64::Decimal<Prec, RoundPolicy>& dec, FormatContext& ctx) const {
        int after_digits = custom_precision_.value_or(Prec);
        auto [before, after] = USERVER_NAMESPACE::decimal64::impl::AsUnpacked(dec, after_digits);
        if (remove_trailing_zeros_) {
            USERVER_NAMESPACE::decimal64::impl::TrimTrailingZeros(after, after_digits);
        }
 
        if (after_digits > 0) {
            if (dec.Sign() == -1) {
                return fmt::format_to(ctx.out(), FMT_COMPILE("-{}.{:0{}}"), -before, -after, after_digits);
            } else {
                return fmt::format_to(ctx.out(), FMT_COMPILE("{}.{:0{}}"), before, after, after_digits);
            }
        } else {
            return fmt::format_to(ctx.out(), FMT_COMPILE("{}"), before);
        }
    }
 
private:
    bool remove_trailing_zeros_ = true;
    std::optional<int> custom_precision_;
};