A Proposal to add wide

Green lines are notes for the editor or for the SG6 that must not be treated as part of the wording.

I. Introduction and Motivation

Current standard provides signed and unsigned int8_t, int16_t, int32_t, int64_t. It is usually enough for every day tasks, but sometimes appears a need in big numbers: for cryptography, IPv6, very big counters etc. Non-standard type __int128 which is provided by gcc and clang illuminates this need. But there is no cross-platform solution and no way to satisfy future needs in even more big numbers.

II. Changelog

III. Proposed wording

[Note to SG6: Following 4 paragraphs affect all the new numeric class proposals. - end note]

18.3.4 Class template numeric_limits[numeric.limits]

[Note to editor: Add the following sentence after the sentence "Specializations shall be provided for each arithmetic type, both floating-point and integer, including bool." (first sentence in fourth paragraph in [numeric.limits]) - end note]

Specializations shall be also provided for wide_integer type. [Note: If there is a built-in integral type Integral that has the same signedness and width as wide_integer<MachineWords, S>, then numeric_limits<wide_integer<MachineWords, S>> specialized in the same way as numeric_limits<Integral>- end note]

26.2 Definitions[numerics.defns]

[Note to editor: Add the following paragraph to the end of [numerics.defns] - end note]

Define CT as common_type_t<A, B>, where A and B are the types of the two function arguments.

26.3 Numeric type requirements[numeric.requirements]

[Note to editor: Add the following paragraphs to the end of [numeric.requirements] - end note]

Functions that accept template parameters starting with Arithmetic shall not participate in overload resolution unless std::numeric_limits<Arithmetic>::is_specialized is true.

Functions that accept template parameters starting with Integral shall not participate in overload resolution unless std::numeric_limits<Integral>::is_integer is true.

26.4 Numeric types interoperability[numeric.interop]

[Note to SG6: This is an early attempt to make it possible for different numeric types to inter-operate. It works for wide_integer@built-in, but this approach requires additional study and common_type fixes for new Arithmetic types. - end note]

Following operators are defined for types T and U if T and U have a defined common_type_t<T, U> and satisfy the Arithmetic or Integral requirements from [numeric.requirements] [Note: Implementations are encouraged to provide optimized specializations of the following operators - end note]:

[Note to SG6: We may add to Arithmetic and Integral concepts additional requirement that std::numeric_limits<Integral-or-Arithmetic>::is_interoprable shall be true. In that case no user code will be broken even if user already added following operators. However this seems to be an overkill. - end note]

template<typename Arithmetic1, typename Arithmetic2>
  common_type_t<Arithmetic1, Arithmetic2>
  constexpr operator*(const Arithmetic1& lhs, const Arithmetic2& rhs);

Returns: CT(lhs) * CT(rhs).

template<typename Arithmetic1, typename Arithmetic2>
  common_type_t<Arithmetic1, Arithmetic2>
  constexpr operator/(const Arithmetic1& lhs, const Arithmetic2& rhs);

Returns: CT(lhs) / CT(rhs).

template<typename Arithmetic1, typename Arithmetic2>
  common_type_t<Arithmetic1, Arithmetic2>
  constexpr operator+(const Arithmetic1& lhs, const Arithmetic2& rhs);

Returns: CT(lhs) + CT(rhs).

template<typename Arithmetic1, typename Arithmetic2>
  common_type_t<Arithmetic1, Arithmetic2>
  constexpr operator-(const Arithmetic1& lhs, const Arithmetic2& rhs);

Returns: CT(lhs) - CT(rhs).

template<typename Integral1, typename Integral2>
  common_type_t<Integral1, Integral2>
  constexpr operator%(const Integral1& lhs, const Integral2& rhs);

Returns: CT(lhs) % CT(rhs).

template<typename Integral1, typename Integral2>
  common_type_t<Integral1, Integral2>
  constexpr operator&(const Integral1& lhs, const Integral2& rhs);

Returns: CT(lhs) & CT(rhs).

template<typename Integral1, typename Integral2>
  common_type_t<Integral1, Integral2>
  constexpr operator|(const Integral1& lhs, const Integral2& rhs);

Returns: CT(lhs) | CT(rhs).

template<typename Integral1, typename Integral2>
  common_type_t<Integral1, Integral2>
  constexpr operator^(const Integral1& lhs, const Integral2& rhs);

Returns: CT(lhs) ^ CT(rhs).

template<typename Integral1, typename Integral2>
  common_type_t<Integral1, size_t>
  constexpr operator<<(const Integral1& lhs, const Integral2& rhs);

Returns: common_type_t<Integral1, size_t>(lhs) << static_cast<size_t>(rhs).

template<typename Integral1, typename Integral2>
  common_type_t<Integral1, size_t>
  constexpr operator>>(const Integral1& lhs, const Integral2& rhs);

Returns: common_type_t<Integral1, size_t>(lhs) >> static_cast<size_t>(rhs).

template<typename Arithmetic1, typename Arithmetic2>
  constexpr bool operator<(const Arithmetic1& lhs, const Arithmetic2& rhs);

Returns: CT(lhs) < CT(rhs).

template<typename Arithmetic1, typename Arithmetic2>
  constexpr bool operator>(const Arithmetic1& lhs, const Arithmetic2& rhs);

Returns: CT(lhs) > CT(rhs).

template<typename Arithmetic1, typename Arithmetic2>
  constexpr bool operator<=(const Arithmetic1& lhs, const Arithmetic2& rhs);

Returns: CT(lhs) <= CT(rhs).

template<typename Arithmetic1, typename Arithmetic2>
  constexpr bool operator>=(const Arithmetic1& lhs, const Arithmetic2& rhs);

Returns: CT(lhs) >= CT(rhs).

template<typename Arithmetic1, typename Arithmetic2>
  constexpr bool operator==(const Arithmetic1& lhs, const Arithmetic2& rhs);

Returns: CT(lhs) == CT(rhs).

template<typename Arithmetic1, typename Arithmetic2>
  constexpr bool operator!=(const Arithmetic1& lhs, const Arithmetic2& rhs);

Returns: !(lhs == rhs).

26.??.1 Header <wide_integer> synopsis[numeric.wide_integer.syn]

[Note to SG6: Following part requires updated P0102R0 proposal with exact_2int, fast_2int, least_2int, exact_2uint, fast_2uint, least_2uint specializations for wide_integer. - end note]

The header <wide_integer> defines class template wide_integer and a set of operators for representing and manipulating integers of specified width.

26.??.2 Template class wide_integer overview[numeric.wide_integer.overview]

The class template wide_integer<size_t MachineWords, signedness S> is a POD class that behaves as an integer type of a compile time specified width. Template parameter MachineWords specifies significantexact machine words count to store the integer value. [Note: sizeof(wide_integer<MachineWords, signedness::Unsigned>) and sizeof(wide_integer<MachineWords, signedness::Signed>) are not required to be equal to MachineWords * sizeof(machine-word). - end note] Template parameter S specifies signedness of the stored integer value.

[Note to SG6: Definition for machine words must be provided somewhere and referenced from the above paragraph. - end note]

26.??.2.?? wide_integer constructors [numeric.wide_integer.cons]

26.??.2.?? wide_integer assignments [numeric.wide_integer.assign]

26.??.2.?? wide_integer compound assignments [numeric.wide_integer.cassign]

26.??.2.?? wide_integer observers [numeric.wide_integer.observers]

26.??.?? Specializations of common_type [numeric.wide_integer.traits.specializations]

[Note: common_type follows the usual arithmetic conversions design. - end note]

[Note to SG6: common_type attempts to follow the usual arithmetic conversions design here for interoperability between different numeric types. Following two specializations must be moved to a more generic place and enriched with usual arithmetic conversion rules for all the other numeric classes that specialize std::numeric_limits- end note]

26.??.?? Unary operators [numeric.wide_integer.unary_ops]

26.??.?? Binary operators [numeric.wide_integer.binary_ops]

In the function descriptions that follow, CT represents common_type_t<A, B>, where A and B are the types of the two arguments to the function.

Functions that accept Integral parameter shall not participate in overload resolution unless is_integral_v<Integral> is true.

Functions that accept Arithmetic parameter shall not participate in overload resolution unless is_arithmetic_v<Arithmetic> is true.

[Note: To reduce template instantiations count operators that accept Integral and Arithmetic parameter convert to common type first, as the common type may be a built-in type. - end note]

26.??.?? Numeric conversions [numeric.wide_integer.conversions]

template <size_t MachineWords, signedness S>
to_chars_result to_chars(char* first,
                       char* last,
                       const wide_integer<MachineWords, S>& value,
                       int base = 10);

Behavior of wide_integer overload is subject to the usual rules of primitive numeric output conversion functions [utility.to.chars].

template <size_t MachineWords, signedness S>
from_chars_result from_chars(const char* first,
                           const char* last,
                           wide_integer<MachineWords, S>& value,
                           int base = 10);

Behavior of wide_integer overload is subject to the usual rules of primitive numeric input conversion functions [utility.from.chars].

26.??.?? iostream specializations [numeric.wide_integer.io]

26.??.?? Hash support [numeric.wide_integer.hash]

The specialization is enabled (20.14.14). If there is a built-in integral type Integral that has the same signedness and width as wide_integer<MachineWords, S>, and wi is an object of type wide_integer<MachineWords, S>, then hash<wide_integer<MachineWords, S>>()(wi) == hash<Integral>()(Integral(wi)).

26.??.?? numeric_limits specialization [wide_integer.numeric_limits]

Specialization follows the rules described in [numeric.limits.members]. If there is a built-in integral type Integral that has the same signedness and width as wide_integer<MachineWords, S>, then numeric_limits<wide_integer<MachineWords, S>> specialized in the same way as numeric_limits<Integral>.

IV. Feature-testing macro

For the purposes of SG10 it is sufficient to check for header <wide_integer> using __has_include.

For the purposes of SG10we recommend the feature-testing macro name __cpp_lib_wide_integer.

A Proposal to add wide_int Template Class