From 7286f8b8d4d54e6c508a874fb5c2db1544a8b976 Mon Sep 17 00:00:00 2001 From: Sean Middleditch Date: Sun, 14 Jan 2024 16:20:38 -0800 Subject: [PATCH] Fix CI software versions (#51) clang-tidy 11 Sphinx 4.2 Catch 3.5.1 Latest Dragonbox (vendored) Warnings fixes for newer toolchains Disabled several clang-tidy checks that either break dragonbox or are buggy --- .clang-tidy | 8 +- .github/workflows/tidy.yml | 7 +- cmake/fetch_catch2.cmake | 2 +- cmake/fetch_dragonbox.cmake | 9 - docs/conf.py | 2 +- docs/requirements.txt | 2 +- include/nanofmt/dragonbox.h | 3075 +++++++++++++++++++++++++++++++++++ source/CMakeLists.txt | 2 - source/charconv.cpp | 16 +- source/format.cpp | 4 +- tests/CMakeLists.txt | 3 +- 11 files changed, 3098 insertions(+), 32 deletions(-) delete mode 100644 cmake/fetch_dragonbox.cmake create mode 100644 include/nanofmt/dragonbox.h diff --git a/.clang-tidy b/.clang-tidy index b2418ba..e2d8f1d 100644 --- a/.clang-tidy +++ b/.clang-tidy @@ -17,15 +17,19 @@ Checks: >- -cppcoreguidelines-pro-type-member-init, -cppcoreguidelines-pro-type-reinterpret-cast, -cppcoreguidelines-pro-type-union-access, + -cppcoreguidelines-pro-type-vararg, -cppcoreguidelines-owning-memory, -modernize-avoid-c-arrays, - -modernize-use-trailing-return-type, -modernize-raw-string-literal, + -modernize-unary-static-assert, + -modernize-use-nodiscard, + -modernize-use-trailing-return-type, -readability-braces-around-statements, -readability-convert-member-functions-to-static, + -readability-else-after-return, -readability-implicit-bool-conversion, -readability-magic-numbers, -readability-named-parameter, - -readability-uppercase-literal-suffix + -readability-uppercase-literal-suffix, HeaderFilterRegex: nanofmt/.*[.]h WarningsAsErrors: "*" diff --git a/.github/workflows/tidy.yml b/.github/workflows/tidy.yml index 46c1a10..972e747 100644 --- a/.github/workflows/tidy.yml +++ b/.github/workflows/tidy.yml @@ -13,18 +13,17 @@ jobs: name: Tidy env: + CXX: clang++ BUILD_TYPE: RELEASE - CLANG_TIDY: clang-tidy-10 + CLANG_TIDY: clang-tidy-11 steps: - uses: actions/checkout@v2 - name: Install - run: sudo apt-get install -y clang-tidy-10 + run: sudo apt-get install -y ${{ env.CLANG_TIDY }} - name: Configure - env: - CXX: ${{ matrix.compiler }} run: cmake -B ${{ github.workspace }}/build -DCMAKE_BUILD_TYPE=${{ matrix.config }} -DCMAKE_EXPORT_COMPILE_COMMANDS:BOOL=ON - name: Tidy diff --git a/cmake/fetch_catch2.cmake b/cmake/fetch_catch2.cmake index 393ec9e..7918d10 100644 --- a/cmake/fetch_catch2.cmake +++ b/cmake/fetch_catch2.cmake @@ -3,7 +3,7 @@ include(FetchContent) FetchContent_Declare( Catch2 GIT_REPOSITORY https://github.com/catchorg/Catch2.git - GIT_TAG v3.0.0-preview3 + GIT_TAG v3.5.1 ) FetchContent_MakeAvailable(Catch2) diff --git a/cmake/fetch_dragonbox.cmake b/cmake/fetch_dragonbox.cmake deleted file mode 100644 index a4f4d77..0000000 --- a/cmake/fetch_dragonbox.cmake +++ /dev/null @@ -1,9 +0,0 @@ -include(FetchContent) - -FetchContent_Declare( - nanofmt_dragonbox - GIT_REPOSITORY https://github.com/jk-jeon/dragonbox - GIT_TAG 1.0.1 -) - -FetchContent_Populate(nanofmt_dragonbox) diff --git a/docs/conf.py b/docs/conf.py index 2fe8a8a..e366d67 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -57,7 +57,7 @@ # # This is also used if you do content translation via gettext catalogs. # Usually you set "language" from the command line for these cases. -language = None +language = 'en' # List of patterns, relative to source directory, that match files and # directories to ignore when looking for source files. diff --git a/docs/requirements.txt b/docs/requirements.txt index 082efc0..fe3a796 100644 --- a/docs/requirements.txt +++ b/docs/requirements.txt @@ -1,3 +1,3 @@ docutils==0.16 -sphinx<4.1 +sphinx>=4.2 sphinx-rtd-theme diff --git a/include/nanofmt/dragonbox.h b/include/nanofmt/dragonbox.h new file mode 100644 index 0000000..50adef3 --- /dev/null +++ b/include/nanofmt/dragonbox.h @@ -0,0 +1,3075 @@ +// Copyright 2020-2023 Junekey Jeon +// +// The contents of this file may be used under the terms of +// the Apache License v2.0 with LLVM Exceptions. +// +// (See accompanying file LICENSE-Apache or copy at +// https://llvm.org/foundation/relicensing/LICENSE.txt) +// +// Alternatively, the contents of this file may be used under the terms of +// the Boost Software License, Version 1.0. +// (See accompanying file LICENSE-Boost or copy at +// https://www.boost.org/LICENSE_1_0.txt) +// +// Unless required by applicable law or agreed to in writing, this software +// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY +// KIND, either express or implied. + + +// Copied to nanofmt from upstream commit 5cf1d3f92f837272517e8e9e13cf9c6162c2e964 +// - Adjusted namespaces and macros to avoid downstream linking issues + +#ifndef NANOFMT_HEADER_DRAGONBOX +#define NANOFMT_HEADER_DRAGONBOX + +#include "config.h" + +#include +#include +#include +#include +#include + +#ifdef __has_include +# if __has_include() +# include +# endif +#endif + +//////////////////////////////////////////////////////////////////////////////////////// +// Language feature detections. +//////////////////////////////////////////////////////////////////////////////////////// + +// C++14 constexpr +#if defined(__cpp_constexpr) && __cpp_constexpr >= 201304L +# define NANOFMT_HAS_CONSTEXPR14 1 +#elif __cplusplus >= 201402L +# define NANOFMT_HAS_CONSTEXPR14 1 +#elif defined(_MSC_VER) && _MSC_VER >= 1910 && _MSVC_LANG >= 201402L +# define NANOFMT_HAS_CONSTEXPR14 1 +#else +# define NANOFMT_HAS_CONSTEXPR14 0 +#endif + +#if NANOFMT_HAS_CONSTEXPR14 +# define NANOFMT_CONSTEXPR14 constexpr +#else +# define NANOFMT_CONSTEXPR14 +#endif + +// C++17 constexpr lambdas +#if defined(__cpp_constexpr) && __cpp_constexpr >= 201603L +# define NANOFMT_HAS_CONSTEXPR17 1 +#elif __cplusplus >= 201703L +# define NANOFMT_HAS_CONSTEXPR17 1 +#elif defined(_MSC_VER) && _MSC_VER >= 1911 && _MSVC_LANG >= 201703L +# define NANOFMT_HAS_CONSTEXPR17 1 +#else +# define NANOFMT_HAS_CONSTEXPR17 0 +#endif + +// C++17 inline variables +#if defined(__cpp_inline_variables) && __cpp_inline_variables >= 201606L +# define NANOFMT_HAS_INLINE_VARIABLE 1 +#elif __cplusplus >= 201703L +# define NANOFMT_HAS_INLINE_VARIABLE 1 +#elif defined(_MSC_VER) && _MSC_VER >= 1912 && _MSVC_LANG >= 201703L +# define NANOFMT_HAS_INLINE_VARIABLE 1 +#else +# define NANOFMT_HAS_INLINE_VARIABLE 0 +#endif + +#if NANOFMT_HAS_INLINE_VARIABLE +# define NANOFMT_INLINE_VARIABLE inline constexpr +#else +# define NANOFMT_INLINE_VARIABLE static constexpr +#endif + +// C++17 if constexpr +#if defined(__cpp_if_constexpr) && __cpp_if_constexpr >= 201606L +# define NANOFMT_HAS_IF_CONSTEXPR 1 +#elif __cplusplus >= 201703L +# define NANOFMT_HAS_IF_CONSTEXPR 1 +#elif defined(_MSC_VER) && _MSC_VER >= 1911 && _MSVC_LANG >= 201703L +# define NANOFMT_HAS_IF_CONSTEXPR 1 +#else +# define NANOFMT_HAS_IF_CONSTEXPR 0 +#endif + +#if NANOFMT_HAS_IF_CONSTEXPR +# define NANOFMT_IF_CONSTEXPR if constexpr +#else +# define NANOFMT_IF_CONSTEXPR if +#endif + +// C++20 std::bit_cast +#if defined(__cpp_lib_bit_cast) && __cpp_lib_bit_cast >= 201806L +# include +# define NANOFMT_HAS_BIT_CAST 1 +#else +# define NANOFMT_HAS_BIT_CAST 0 +#endif + +// C++23 if consteval or C++20 std::is_constant_evaluated +#if defined(__cpp_if_consteval) && __cpp_is_consteval >= 202106L +# define NANOFMT_IF_CONSTEVAL if consteval +# define NANOFMT_IF_NOT_CONSTEVAL if !consteval +# define NANOFMT_CAN_BRANCH_ON_CONSTEVAL 1 +#elif defined(__cpp_lib_is_constant_evaluated) && __cpp_lib_is_constant_evaluated >= 201811L +# define NANOFMT_IF_CONSTEVAL if (std::is_constant_evaluated()) +# define NANOFMT_IF_NOT_CONSTEVAL if (!std::is_constant_evaluated()) +# define NANOFMT_CAN_BRANCH_ON_CONSTEVAL 1 +#elif NANOFMT_HAS_IF_CONSTEXPR +# define NANOFMT_IF_CONSTEVAL if constexpr (false) +# define NANOFMT_IF_NOT_CONSTEVAL if constexpr (true) +# define NANOFMT_CAN_BRANCH_ON_CONSTEVAL 0 +#else +# define NANOFMT_IF_CONSTEVAL if (false) +# define NANOFMT_IF_NOT_CONSTEVAL if (true) +# define NANOFMT_CAN_BRANCH_ON_CONSTEVAL 0 +#endif + +#if NANOFMT_CAN_BRANCH_ON_CONSTEVAL && NANOFMT_HAS_BIT_CAST +# define NANOFMT_CONSTEXPR20 constexpr +#else +# define NANOFMT_CONSTEXPR20 +#endif + +// Suppress additional buffer overrun check. +// I have no idea why MSVC thinks some functions here are vulnerable to the buffer overrun +// attacks. No, they aren't. +#if defined(__GNUC__) || defined(__clang__) +# define NANOFMT_SAFEBUFFERS +# define NANOFMT_FORCEINLINE inline __attribute__((always_inline)) +#elif defined(_MSC_VER) +# define NANOFMT_SAFEBUFFERS __declspec(safebuffers) +# define NANOFMT_FORCEINLINE __forceinline +#else +# define NANOFMT_SAFEBUFFERS +# define NANOFMT_FORCEINLINE inline +#endif + +#if defined(__has_builtin) +# define NANOFMT_HAS_BUILTIN(x) __has_builtin(x) +#else +# define NANOFMT_HAS_BUILTIN(x) false +#endif + +#if defined(_MSC_VER) +# include +#endif + +namespace NANOFMT_NS { + namespace dragonbox { + //////////////////////////////////////////////////////////////////////////////////////// + // Some general utilities for C++11-compatibility + //////////////////////////////////////////////////////////////////////////////////////// + namespace detail { +#if !NANOFMT_HAS_CONSTEXPR17 + template + struct index_sequence {}; + + template + struct make_index_sequence_impl { + using type = typename make_index_sequence_impl::type; + }; + + template + struct make_index_sequence_impl { + using type = index_sequence; + }; + + template + using make_index_sequence = typename make_index_sequence_impl<0, N, void>::type; +#endif + + template + typename std::add_rvalue_reference::type declval() noexcept; + } // namespace detail + + //////////////////////////////////////////////////////////////////////////////////////// + // Some basic features for encoding/decoding IEEE-754 formats. + //////////////////////////////////////////////////////////////////////////////////////// + namespace detail { + template + struct physical_bits { + static constexpr std::size_t value = sizeof(T) * std::numeric_limits::digits; + }; + template + struct value_bits { + static constexpr std::size_t value = + std::numeric_limits::value, T>::type>::digits; + }; + + template + NANOFMT_CONSTEXPR20 To bit_cast(const From& from) { +#if NANOFMT_HAS_BIT_CAST + return std::bit_cast(from); +#else + static_assert(sizeof(From) == sizeof(To), ""); + static_assert(std::is_trivially_copyable::value, ""); + static_assert(std::is_trivially_copyable::value, ""); + To to; + std::memcpy(&to, &from, sizeof(To)); + return to; +#endif + } + } // namespace detail + + // These classes expose encoding specs of IEEE-754-like floating-point formats. + // Currently available formats are IEEE754-binary32 & IEEE754-binary64. + + struct ieee754_binary32 { + static constexpr int significand_bits = 23; + static constexpr int exponent_bits = 8; + static constexpr int min_exponent = -126; + static constexpr int max_exponent = 127; + static constexpr int exponent_bias = -127; + static constexpr int decimal_digits = 9; + }; + struct ieee754_binary64 { + static constexpr int significand_bits = 52; + static constexpr int exponent_bits = 11; + static constexpr int min_exponent = -1022; + static constexpr int max_exponent = 1023; + static constexpr int exponent_bias = -1023; + static constexpr int decimal_digits = 17; + }; + + // A floating-point traits class defines ways to interpret a bit pattern of given size as an + // encoding of floating-point number. This is a default implementation of such a traits + // class, supporting ways to interpret 32-bits into a binary32-encoded floating-point number + // and to interpret 64-bits into a binary64-encoded floating-point number. Users might + // specialize this class to change the default behavior for certain types. + template + struct default_float_traits { + // I don't know if there is a truly reliable way of detecting + // IEEE-754 binary32/binary64 formats; I just did my best here. + static_assert( + std::numeric_limits::is_iec559 && std::numeric_limits::radix == 2 && + (detail::physical_bits::value == 32 || detail::physical_bits::value == 64), + "default_ieee754_traits only works for 32-bits or 64-bits types " + "supporting binary32 or binary64 formats!"); + + // The type that is being viewed. + using type = T; + + // Refers to the format specification class. + using format = typename std:: + conditional::value == 32, ieee754_binary32, ieee754_binary64>::type; + + // Defines an unsigned integer type that is large enough to carry a variable of type T. + // Most of the operations will be done on this integer type. + using carrier_uint = + typename std::conditional::value == 32, std::uint32_t, std::uint64_t>::type; + static_assert(sizeof(carrier_uint) == sizeof(T), ""); + + // Number of bits in the above unsigned integer type. + static constexpr int carrier_bits = int(detail::physical_bits::value); + + // Convert from carrier_uint into the original type. + // Depending on the floating-point encoding format, this operation might not be possible + // for some specific bit patterns. However, the contract is that u always denotes a + // valid bit pattern, so this function must be assumed to be noexcept. + static NANOFMT_CONSTEXPR20 T carrier_to_float(carrier_uint u) noexcept { + return detail::bit_cast(u); + } + + // Same as above. + static NANOFMT_CONSTEXPR20 carrier_uint float_to_carrier(T x) noexcept { + return detail::bit_cast(x); + } + + // Extract exponent bits from a bit pattern. + // The result must be aligned to the LSB so that there is no additional zero paddings + // on the right. This function does not do bias adjustment. + static constexpr unsigned int extract_exponent_bits(carrier_uint u) noexcept { + static_assert(detail::value_bits::value > format::exponent_bits, ""); + return static_cast(u >> format::significand_bits) & + ((static_cast(1) << format::exponent_bits) - 1); + } + + // Extract significand bits from a bit pattern. + // The result must be aligned to the LSB so that there is no additional zero paddings + // on the right. The result does not contain the implicit bit. + static constexpr carrier_uint extract_significand_bits(carrier_uint u) noexcept { + return carrier_uint(u & carrier_uint((carrier_uint(1) << format::significand_bits) - 1)); + } + + // Remove the exponent bits and extract significand bits together with the sign bit. + static constexpr carrier_uint remove_exponent_bits(carrier_uint u, unsigned int exponent_bits) noexcept { + return u ^ (carrier_uint(exponent_bits) << format::significand_bits); + } + + // Shift the obtained signed significand bits to the left by 1 to remove the sign bit. + static constexpr carrier_uint remove_sign_bit_and_shift(carrier_uint u) noexcept { + return carrier_uint(carrier_uint(u) << 1); + } + + // The actual value of exponent is obtained by adding this value to the extracted + // exponent bits. + static constexpr int exponent_bias = 1 - (1 << (carrier_bits - format::significand_bits - 2)); + + // Obtain the actual value of the binary exponent from the extracted exponent bits. + static constexpr int binary_exponent(unsigned int exponent_bits) noexcept { + return exponent_bits == 0 ? format::min_exponent : int(exponent_bits) + format::exponent_bias; + } + + // Obtain the actual value of the binary exponent from the extracted significand bits + // and exponent bits. + static constexpr carrier_uint binary_significand( + carrier_uint significand_bits, + unsigned int exponent_bits) noexcept { + return exponent_bits == 0 ? significand_bits + : (significand_bits | (carrier_uint(1) << format::significand_bits)); + } + + /* Various boolean observer functions */ + + static constexpr bool is_nonzero(carrier_uint u) noexcept { + return (u << 1) != 0; + } + static constexpr bool is_positive(carrier_uint u) noexcept { + return u < (carrier_uint(1) << (format::significand_bits + format::exponent_bits)); + } + static constexpr bool is_negative(carrier_uint u) noexcept { + return !is_positive(u); + } + static constexpr bool is_finite(unsigned int exponent_bits) noexcept { + return exponent_bits != ((1u << format::exponent_bits) - 1); + } + static constexpr bool has_all_zero_significand_bits(carrier_uint u) noexcept { + return (u << 1) == 0; + } + static constexpr bool has_even_significand_bits(carrier_uint u) noexcept { + return u % 2 == 0; + } + }; + + // Convenient wrappers for floating-point traits classes. + // In order to reduce the argument passing overhead, these classes should be as simple as + // possible (e.g., no inheritance, no private non-static data member, etc.; this is an + // unfortunate fact about common ABI convention). + + template > + struct float_bits; + + template > + struct signed_significand_bits; + + template + struct float_bits { + using type = T; + using traits_type = Traits; + using carrier_uint = typename traits_type::carrier_uint; + + carrier_uint u; + + float_bits() = default; + constexpr explicit float_bits(carrier_uint bit_pattern) noexcept : u{bit_pattern} {} + constexpr explicit float_bits(T float_value) noexcept : u{traits_type::float_to_carrier(float_value)} {} + + constexpr T to_float() const noexcept { + return traits_type::carrier_to_float(u); + } + + // Extract exponent bits from a bit pattern. + // The result must be aligned to the LSB so that there is no additional zero paddings + // on the right. This function does not do bias adjustment. + constexpr unsigned int extract_exponent_bits() const noexcept { + return traits_type::extract_exponent_bits(u); + } + + // Extract significand bits from a bit pattern. + // The result must be aligned to the LSB so that there is no additional zero paddings + // on the right. The result does not contain the implicit bit. + constexpr carrier_uint extract_significand_bits() const noexcept { + return traits_type::extract_significand_bits(u); + } + + // Remove the exponent bits and extract significand bits together with the sign bit. + constexpr signed_significand_bits remove_exponent_bits( + unsigned int exponent_bits) const noexcept { + return signed_significand_bits(traits_type::remove_exponent_bits(u, exponent_bits)); + } + + // Obtain the actual value of the binary exponent from the extracted exponent bits. + static constexpr int binary_exponent(unsigned int exponent_bits) noexcept { + return traits_type::binary_exponent(exponent_bits); + } + constexpr int binary_exponent() const noexcept { + return binary_exponent(extract_exponent_bits()); + } + + // Obtain the actual value of the binary exponent from the extracted significand bits + // and exponent bits. + static constexpr carrier_uint binary_significand( + carrier_uint significand_bits, + unsigned int exponent_bits) noexcept { + return traits_type::binary_significand(significand_bits, exponent_bits); + } + constexpr carrier_uint binary_significand() const noexcept { + return binary_significand(extract_significand_bits(), extract_exponent_bits()); + } + + constexpr bool is_nonzero() const noexcept { + return traits_type::is_nonzero(u); + } + constexpr bool is_positive() const noexcept { + return traits_type::is_positive(u); + } + constexpr bool is_negative() const noexcept { + return traits_type::is_negative(u); + } + constexpr bool is_finite(unsigned int exponent_bits) const noexcept { + return traits_type::is_finite(exponent_bits); + } + constexpr bool is_finite() const noexcept { + return traits_type::is_finite(extract_exponent_bits()); + } + constexpr bool has_even_significand_bits() const noexcept { + return traits_type::has_even_significand_bits(u); + } + }; + + template + struct signed_significand_bits { + using type = T; + using traits_type = Traits; + using carrier_uint = typename traits_type::carrier_uint; + + carrier_uint u; + + signed_significand_bits() = default; + constexpr explicit signed_significand_bits(carrier_uint bit_pattern) noexcept : u{bit_pattern} {} + + // Shift the obtained signed significand bits to the left by 1 to remove the sign bit. + constexpr carrier_uint remove_sign_bit_and_shift() const noexcept { + return traits_type::remove_sign_bit_and_shift(u); + } + + constexpr bool is_positive() const noexcept { + return traits_type::is_positive(u); + } + constexpr bool is_negative() const noexcept { + return traits_type::is_negative(u); + } + constexpr bool has_all_zero_significand_bits() const noexcept { + return traits_type::has_all_zero_significand_bits(u); + } + constexpr bool has_even_significand_bits() const noexcept { + return traits_type::has_even_significand_bits(u); + } + }; + + namespace detail { + //////////////////////////////////////////////////////////////////////////////////////// + // Bit operation intrinsics. + //////////////////////////////////////////////////////////////////////////////////////// + + namespace bits { + // Most compilers should be able to optimize this into the ROR instruction. + inline NANOFMT_CONSTEXPR14 std::uint32_t rotr(std::uint32_t n, std::uint32_t r) noexcept { + r &= 31; + return (n >> r) | (n << (32 - r)); + } + inline NANOFMT_CONSTEXPR14 std::uint64_t rotr(std::uint64_t n, std::uint32_t r) noexcept { + r &= 63; + return (n >> r) | (n << (64 - r)); + } + } // namespace bits + + //////////////////////////////////////////////////////////////////////////////////////// + // Utilities for wide unsigned integer arithmetic. + //////////////////////////////////////////////////////////////////////////////////////// + + namespace wuint { + // Compilers might support built-in 128-bit integer types. However, it seems that + // emulating them with a pair of 64-bit integers actually produces a better code, + // so we avoid using those built-ins. That said, they are still useful for + // implementing 64-bit x 64-bit -> 128-bit multiplication. + + // clang-format off +#if defined(__SIZEOF_INT128__) + // To silence "error: ISO C++ does not support '__int128' for 'type name' + // [-Wpedantic]" +#if defined(__GNUC__) + __extension__ +#endif + using builtin_uint128_t = unsigned __int128; +#endif + // clang-format on + + struct uint128 { + uint128() = default; + + std::uint64_t high_; + std::uint64_t low_; + + constexpr uint128(std::uint64_t high, std::uint64_t low) noexcept : high_{high}, low_{low} {} + + constexpr std::uint64_t high() const noexcept { + return high_; + } + constexpr std::uint64_t low() const noexcept { + return low_; + } + + NANOFMT_CONSTEXPR20 uint128& operator+=(std::uint64_t n) & noexcept { + auto const generic_impl = [&] { + auto sum = low_ + n; + high_ += (sum < low_ ? 1 : 0); + low_ = sum; + }; + NANOFMT_IF_CONSTEVAL { + generic_impl(); + return *this; + } +#if NANOFMT_HAS_BUILTIN(__builtin_addcll) + unsigned long long carry{}; + low_ = __builtin_addcll(low_, n, 0, &carry); + high_ = __builtin_addcll(high_, 0, carry, &carry); +#elif NANOFMT_HAS_BUILTIN(__builtin_ia32_addcarryx_u64) + unsigned long long result{}; + auto carry = __builtin_ia32_addcarryx_u64(0, low_, n, &result); + low_ = result; + __builtin_ia32_addcarryx_u64(carry, high_, 0, &result); + high_ = result; +#elif defined(_MSC_VER) && defined(_M_X64) + auto carry = _addcarry_u64(0, low_, n, &low_); + _addcarry_u64(carry, high_, 0, &high_); +#else + generic_impl(); +#endif + return *this; + } + }; + + inline NANOFMT_CONSTEXPR20 std::uint64_t umul64(std::uint32_t x, std::uint32_t y) noexcept { +#if defined(_MSC_VER) && defined(_M_IX86) + NANOFMT_IF_NOT_CONSTEVAL { + return __emulu(x, y); + } +#endif + return x * std::uint64_t(y); + } + + // Get 128-bit result of multiplication of two 64-bit unsigned integers. + NANOFMT_SAFEBUFFERS inline NANOFMT_CONSTEXPR20 uint128 umul128(std::uint64_t x, std::uint64_t y) noexcept { + auto const generic_impl = [&]() -> uint128 { + auto a = std::uint32_t(x >> 32); + auto b = std::uint32_t(x); + auto c = std::uint32_t(y >> 32); + auto d = std::uint32_t(y); + + auto ac = umul64(a, c); + auto bc = umul64(b, c); + auto ad = umul64(a, d); + auto bd = umul64(b, d); + + auto intermediate = (bd >> 32) + std::uint32_t(ad) + std::uint32_t(bc); + + return { + ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32), + (intermediate << 32) + std::uint32_t(bd)}; + }; + NANOFMT_IF_CONSTEVAL { + return generic_impl(); + } +#if defined(__SIZEOF_INT128__) + auto result = builtin_uint128_t(x) * builtin_uint128_t(y); + return {std::uint64_t(result >> 64), std::uint64_t(result)}; +#elif defined(_MSC_VER) && defined(_M_X64) + uint128 result; + result.low_ = _umul128(x, y, &result.high_); + return result; +#else + return generic_impl(); +#endif + } + + NANOFMT_SAFEBUFFERS inline NANOFMT_CONSTEXPR20 std::uint64_t umul128_upper64( + std::uint64_t x, + std::uint64_t y) noexcept { + auto const generic_impl = [&]() -> std::uint64_t { + auto a = std::uint32_t(x >> 32); + auto b = std::uint32_t(x); + auto c = std::uint32_t(y >> 32); + auto d = std::uint32_t(y); + + auto ac = umul64(a, c); + auto bc = umul64(b, c); + auto ad = umul64(a, d); + auto bd = umul64(b, d); + + auto intermediate = (bd >> 32) + std::uint32_t(ad) + std::uint32_t(bc); + + return ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32); + }; + NANOFMT_IF_CONSTEVAL { + return generic_impl(); + } +#if defined(__SIZEOF_INT128__) + auto result = builtin_uint128_t(x) * builtin_uint128_t(y); + return std::uint64_t(result >> 64); +#elif defined(_MSC_VER) && defined(_M_X64) + return __umulh(x, y); +#else + return generic_impl(); +#endif + } + + // Get upper 128-bits of multiplication of a 64-bit unsigned integer and a 128-bit + // unsigned integer. + NANOFMT_SAFEBUFFERS inline NANOFMT_CONSTEXPR20 uint128 umul192_upper128(std::uint64_t x, uint128 y) noexcept { + auto r = umul128(x, y.high()); + r += umul128_upper64(x, y.low()); + return r; + } + + // Get upper 64-bits of multiplication of a 32-bit unsigned integer and a 64-bit + // unsigned integer. + inline NANOFMT_CONSTEXPR20 std::uint64_t umul96_upper64(std::uint32_t x, std::uint64_t y) noexcept { +#if defined(__SIZEOF_INT128__) || (defined(_MSC_VER) && defined(_M_X64)) + return umul128_upper64(std::uint64_t(x) << 32, y); +#else + auto yh = std::uint32_t(y >> 32); + auto yl = std::uint32_t(y); + + auto xyh = umul64(x, yh); + auto xyl = umul64(x, yl); + + return xyh + (xyl >> 32); +#endif + } + + // Get lower 128-bits of multiplication of a 64-bit unsigned integer and a 128-bit + // unsigned integer. + NANOFMT_SAFEBUFFERS inline NANOFMT_CONSTEXPR20 uint128 umul192_lower128(std::uint64_t x, uint128 y) noexcept { + auto high = x * y.high(); + auto high_low = umul128(x, y.low()); + return {high + high_low.high(), high_low.low()}; + } + + // Get lower 64-bits of multiplication of a 32-bit unsigned integer and a 64-bit + // unsigned integer. + constexpr std::uint64_t umul96_lower64(std::uint32_t x, std::uint64_t y) noexcept { + return x * y; + } + } // namespace wuint + + //////////////////////////////////////////////////////////////////////////////////////// + // Some simple utilities for constexpr computation. + //////////////////////////////////////////////////////////////////////////////////////// + + template + constexpr Int compute_power(Int a) noexcept { + static_assert(k >= 0, ""); +#if NANOFMT_HAS_CONSTEXPR14 + Int p = 1; + for (int i = 0; i < k; ++i) { + p *= a; + } + return p; +#else + return k == 0 ? 1 + : k % 2 == 0 ? compute_power(a * a) + : a * compute_power(a * a); +#endif + } + + template + constexpr int count_factors(UInt n) noexcept { + static_assert(a > 1, ""); +#if NANOFMT_HAS_CONSTEXPR14 + int c = 0; + while (n % a == 0) { + n /= a; + ++c; + } + return c; +#else + return n % a == 0 ? count_factors(n / a) + 1 : 0; +#endif + } + + //////////////////////////////////////////////////////////////////////////////////////// + // Utilities for fast/constexpr log computation. + //////////////////////////////////////////////////////////////////////////////////////// + + namespace log { + static_assert((-1 >> 1) == -1, "right-shift for signed integers must be arithmetic"); + + // Compute floor(e * c - s). + enum class multiply : std::uint32_t {}; + enum class subtract : std::uint32_t {}; + enum class shift : std::size_t {}; + enum class min_exponent : std::int32_t {}; + enum class max_exponent : std::int32_t {}; + + template + constexpr int compute(int e) noexcept { +#if NANOFMT_HAS_CONSTEXPR14 + assert(std::int32_t(e_min) <= e && e <= std::int32_t(e_max)); +#endif + return int((std::int32_t(e) * std::int32_t(m) - std::int32_t(f)) >> std::size_t(k)); + } + + // For constexpr computation. + // Returns -1 when n = 0. + template + constexpr int floor_log2(UInt n) noexcept { +#if NANOFMT_HAS_CONSTEXPR14 + int count = -1; + while (n != 0) { + ++count; + n >>= 1; + } + return count; +#else + return n == 0 ? -1 : floor_log2(n / 2) + 1; +#endif + } + + static constexpr int floor_log10_pow2_min_exponent = -2620; + static constexpr int floor_log10_pow2_max_exponent = 2620; + constexpr int floor_log10_pow2(int e) noexcept { + using namespace log; + return compute< + multiply(315653), + subtract(0), + shift(20), + min_exponent(floor_log10_pow2_min_exponent), + max_exponent(floor_log10_pow2_max_exponent)>(e); + } + + static constexpr int floor_log2_pow10_min_exponent = -1233; + static constexpr int floor_log2_pow10_max_exponent = 1233; + constexpr int floor_log2_pow10(int e) noexcept { + using namespace log; + return compute< + multiply(1741647), + subtract(0), + shift(19), + min_exponent(floor_log2_pow10_min_exponent), + max_exponent(floor_log2_pow10_max_exponent)>(e); + } + + static constexpr int floor_log10_pow2_minus_log10_4_over_3_min_exponent = -2985; + static constexpr int floor_log10_pow2_minus_log10_4_over_3_max_exponent = 2936; + constexpr int floor_log10_pow2_minus_log10_4_over_3(int e) noexcept { + using namespace log; + return compute< + multiply(631305), + subtract(261663), + shift(21), + min_exponent(floor_log10_pow2_minus_log10_4_over_3_min_exponent), + max_exponent(floor_log10_pow2_minus_log10_4_over_3_max_exponent)>(e); + } + + static constexpr int floor_log5_pow2_min_exponent = -1831; + static constexpr int floor_log5_pow2_max_exponent = 1831; + constexpr int floor_log5_pow2(int e) noexcept { + using namespace log; + return compute< + multiply(225799), + subtract(0), + shift(19), + min_exponent(floor_log5_pow2_min_exponent), + max_exponent(floor_log5_pow2_max_exponent)>(e); + } + + static constexpr int floor_log5_pow2_minus_log5_3_min_exponent = -3543; + static constexpr int floor_log5_pow2_minus_log5_3_max_exponent = 2427; + constexpr int floor_log5_pow2_minus_log5_3(int e) noexcept { + using namespace log; + return compute< + multiply(451597), + subtract(715764), + shift(20), + min_exponent(floor_log5_pow2_minus_log5_3_min_exponent), + max_exponent(floor_log5_pow2_minus_log5_3_max_exponent)>(e); + } + } // namespace log + + //////////////////////////////////////////////////////////////////////////////////////// + // Utilities for fast divisibility tests. + //////////////////////////////////////////////////////////////////////////////////////// + + namespace div { + // Replace n by floor(n / 10^N). + // Returns true if and only if n is divisible by 10^N. + // Precondition: n <= 10^(N+1) + // !!It takes an in-out parameter!! + template + struct divide_by_pow10_info; + + template <> + struct divide_by_pow10_info<1> { + static constexpr std::uint32_t magic_number = 6554; + static constexpr int shift_amount = 16; + }; + + template <> + struct divide_by_pow10_info<2> { + static constexpr std::uint32_t magic_number = 656; + static constexpr int shift_amount = 16; + }; + + template + NANOFMT_CONSTEXPR14 bool check_divisibility_and_divide_by_pow10(std::uint32_t& n) noexcept { + // Make sure the computation for max_n does not overflow. + static_assert(N + 1 <= log::floor_log10_pow2(31), ""); + assert(n <= compute_power(std::uint32_t(10))); + + using info = divide_by_pow10_info; + n *= info::magic_number; + + constexpr auto mask = std::uint32_t(std::uint32_t(1) << info::shift_amount) - 1; + bool result = ((n & mask) < info::magic_number); + + n >>= info::shift_amount; + return result; + } + + // Compute floor(n / 10^N) for small n and N. + // Precondition: n <= 10^(N+1) + template + NANOFMT_CONSTEXPR14 std::uint32_t small_division_by_pow10(std::uint32_t n) noexcept { + // Make sure the computation for max_n does not overflow. + static_assert(N + 1 <= log::floor_log10_pow2(31), ""); + assert(n <= compute_power(std::uint32_t(10))); + + return (n * divide_by_pow10_info::magic_number) >> divide_by_pow10_info::shift_amount; + } + + // Compute floor(n / 10^N) for small N. + // Precondition: n <= n_max + template + NANOFMT_CONSTEXPR20 UInt divide_by_pow10(UInt n) noexcept { + static_assert(N >= 0, ""); + + // Specialize for 32-bit division by 100. + // Compiler is supposed to generate the identical code for just writing + // "n / 100", but for some reason MSVC generates an inefficient code + // (mul + mov for no apparent reason, instead of single imul), + // so we does this manually. + NANOFMT_IF_CONSTEXPR(std::is_same::value && N == 2) { + return std::uint32_t(wuint::umul64(n, std::uint32_t(1374389535)) >> 37); + } + // Specialize for 64-bit division by 1000. + // Ensure that the correctness condition is met. + else NANOFMT_IF_CONSTEXPR( + std::is_same::value && N == 3 && + n_max <= std::uint64_t(15534100272597517998ull)) { + return wuint::umul128_upper64(n, std::uint64_t(2361183241434822607ull)) >> 7; + } + else { + constexpr auto divisor = compute_power(UInt(10)); + return n / divisor; + } + } + } // namespace div + } // namespace detail + + //////////////////////////////////////////////////////////////////////////////////////// + // Return types for the main interface function. + //////////////////////////////////////////////////////////////////////////////////////// + + template + struct decimal_fp; + + template + struct decimal_fp { + using carrier_uint = UInt; + + carrier_uint significand; + int exponent; + }; + + template + struct decimal_fp { + using carrier_uint = UInt; + + carrier_uint significand; + int exponent; + bool is_negative; + }; + + template + struct decimal_fp { + using carrier_uint = UInt; + + carrier_uint significand; + int exponent; + bool may_have_trailing_zeros; + }; + + template + struct decimal_fp { + using carrier_uint = UInt; + + carrier_uint significand; + int exponent; + bool may_have_trailing_zeros; + bool is_negative; + }; + + template + using unsigned_decimal_fp = decimal_fp; + + template + using signed_decimal_fp = decimal_fp; + + template + constexpr signed_decimal_fp add_sign_to_unsigned_decimal_fp( + bool is_negative, + unsigned_decimal_fp r) noexcept { + return {r.significand, r.exponent, is_negative}; + } + + template + constexpr signed_decimal_fp add_sign_to_unsigned_decimal_fp( + bool is_negative, + unsigned_decimal_fp r) noexcept { + return {r.significand, r.exponent, r.may_have_trailing_zeros, is_negative}; + } + + namespace detail { + template + struct unsigned_decimal_fp_to_signed; + + template + struct unsigned_decimal_fp_to_signed> { + using type = signed_decimal_fp; + }; + + template + using unsigned_decimal_fp_to_signed_t = typename unsigned_decimal_fp_to_signed::type; + } // namespace detail + + //////////////////////////////////////////////////////////////////////////////////////// + // Computed cache entries. + //////////////////////////////////////////////////////////////////////////////////////// + + namespace detail { + template + struct cache_holder; + + template + struct cache_holder { + using cache_entry_type = std::uint64_t; + static constexpr int cache_bits = 64; + static constexpr int min_k = -31; + static constexpr int max_k = 46; + static constexpr cache_entry_type cache[max_k - min_k + 1] = { + 0x81ceb32c4b43fcf5, 0xa2425ff75e14fc32, 0xcad2f7f5359a3b3f, 0xfd87b5f28300ca0e, 0x9e74d1b791e07e49, + 0xc612062576589ddb, 0xf79687aed3eec552, 0x9abe14cd44753b53, 0xc16d9a0095928a28, 0xf1c90080baf72cb2, + 0x971da05074da7bef, 0xbce5086492111aeb, 0xec1e4a7db69561a6, 0x9392ee8e921d5d08, 0xb877aa3236a4b44a, + 0xe69594bec44de15c, 0x901d7cf73ab0acda, 0xb424dc35095cd810, 0xe12e13424bb40e14, 0x8cbccc096f5088cc, + 0xafebff0bcb24aaff, 0xdbe6fecebdedd5bf, 0x89705f4136b4a598, 0xabcc77118461cefd, 0xd6bf94d5e57a42bd, + 0x8637bd05af6c69b6, 0xa7c5ac471b478424, 0xd1b71758e219652c, 0x83126e978d4fdf3c, 0xa3d70a3d70a3d70b, + 0xcccccccccccccccd, 0x8000000000000000, 0xa000000000000000, 0xc800000000000000, 0xfa00000000000000, + 0x9c40000000000000, 0xc350000000000000, 0xf424000000000000, 0x9896800000000000, 0xbebc200000000000, + 0xee6b280000000000, 0x9502f90000000000, 0xba43b74000000000, 0xe8d4a51000000000, 0x9184e72a00000000, + 0xb5e620f480000000, 0xe35fa931a0000000, 0x8e1bc9bf04000000, 0xb1a2bc2ec5000000, 0xde0b6b3a76400000, + 0x8ac7230489e80000, 0xad78ebc5ac620000, 0xd8d726b7177a8000, 0x878678326eac9000, 0xa968163f0a57b400, + 0xd3c21bcecceda100, 0x84595161401484a0, 0xa56fa5b99019a5c8, 0xcecb8f27f4200f3a, 0x813f3978f8940985, + 0xa18f07d736b90be6, 0xc9f2c9cd04674edf, 0xfc6f7c4045812297, 0x9dc5ada82b70b59e, 0xc5371912364ce306, + 0xf684df56c3e01bc7, 0x9a130b963a6c115d, 0xc097ce7bc90715b4, 0xf0bdc21abb48db21, 0x96769950b50d88f5, + 0xbc143fa4e250eb32, 0xeb194f8e1ae525fe, 0x92efd1b8d0cf37bf, 0xb7abc627050305ae, 0xe596b7b0c643c71a, + 0x8f7e32ce7bea5c70, 0xb35dbf821ae4f38c, 0xe0352f62a19e306f}; + }; +#if !NANOFMT_HAS_INLINE_VARIABLE + template + constexpr typename cache_holder::cache_entry_type + cache_holder::cache[]; +#endif + + template + struct cache_holder { + using cache_entry_type = wuint::uint128; + static constexpr int cache_bits = 128; + static constexpr int min_k = -292; + static constexpr int max_k = 326; + static constexpr cache_entry_type cache[max_k - min_k + 1] = { + {0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7b}, {0x9faacf3df73609b1, 0x77b191618c54e9ad}, + {0xc795830d75038c1d, 0xd59df5b9ef6a2418}, {0xf97ae3d0d2446f25, 0x4b0573286b44ad1e}, + {0x9becce62836ac577, 0x4ee367f9430aec33}, {0xc2e801fb244576d5, 0x229c41f793cda740}, + {0xf3a20279ed56d48a, 0x6b43527578c11110}, {0x9845418c345644d6, 0x830a13896b78aaaa}, + {0xbe5691ef416bd60c, 0x23cc986bc656d554}, {0xedec366b11c6cb8f, 0x2cbfbe86b7ec8aa9}, + {0x94b3a202eb1c3f39, 0x7bf7d71432f3d6aa}, {0xb9e08a83a5e34f07, 0xdaf5ccd93fb0cc54}, + {0xe858ad248f5c22c9, 0xd1b3400f8f9cff69}, {0x91376c36d99995be, 0x23100809b9c21fa2}, + {0xb58547448ffffb2d, 0xabd40a0c2832a78b}, {0xe2e69915b3fff9f9, 0x16c90c8f323f516d}, + {0x8dd01fad907ffc3b, 0xae3da7d97f6792e4}, {0xb1442798f49ffb4a, 0x99cd11cfdf41779d}, + {0xdd95317f31c7fa1d, 0x40405643d711d584}, {0x8a7d3eef7f1cfc52, 0x482835ea666b2573}, + {0xad1c8eab5ee43b66, 0xda3243650005eed0}, {0xd863b256369d4a40, 0x90bed43e40076a83}, + {0x873e4f75e2224e68, 0x5a7744a6e804a292}, {0xa90de3535aaae202, 0x711515d0a205cb37}, + {0xd3515c2831559a83, 0x0d5a5b44ca873e04}, {0x8412d9991ed58091, 0xe858790afe9486c3}, + {0xa5178fff668ae0b6, 0x626e974dbe39a873}, {0xce5d73ff402d98e3, 0xfb0a3d212dc81290}, + {0x80fa687f881c7f8e, 0x7ce66634bc9d0b9a}, {0xa139029f6a239f72, 0x1c1fffc1ebc44e81}, + {0xc987434744ac874e, 0xa327ffb266b56221}, {0xfbe9141915d7a922, 0x4bf1ff9f0062baa9}, + {0x9d71ac8fada6c9b5, 0x6f773fc3603db4aa}, {0xc4ce17b399107c22, 0xcb550fb4384d21d4}, + {0xf6019da07f549b2b, 0x7e2a53a146606a49}, {0x99c102844f94e0fb, 0x2eda7444cbfc426e}, + {0xc0314325637a1939, 0xfa911155fefb5309}, {0xf03d93eebc589f88, 0x793555ab7eba27cb}, + {0x96267c7535b763b5, 0x4bc1558b2f3458df}, {0xbbb01b9283253ca2, 0x9eb1aaedfb016f17}, + {0xea9c227723ee8bcb, 0x465e15a979c1cadd}, {0x92a1958a7675175f, 0x0bfacd89ec191eca}, + {0xb749faed14125d36, 0xcef980ec671f667c}, {0xe51c79a85916f484, 0x82b7e12780e7401b}, + {0x8f31cc0937ae58d2, 0xd1b2ecb8b0908811}, {0xb2fe3f0b8599ef07, 0x861fa7e6dcb4aa16}, + {0xdfbdcece67006ac9, 0x67a791e093e1d49b}, {0x8bd6a141006042bd, 0xe0c8bb2c5c6d24e1}, + {0xaecc49914078536d, 0x58fae9f773886e19}, {0xda7f5bf590966848, 0xaf39a475506a899f}, + {0x888f99797a5e012d, 0x6d8406c952429604}, {0xaab37fd7d8f58178, 0xc8e5087ba6d33b84}, + {0xd5605fcdcf32e1d6, 0xfb1e4a9a90880a65}, {0x855c3be0a17fcd26, 0x5cf2eea09a550680}, + {0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481f}, {0xd0601d8efc57b08b, 0xf13b94daf124da27}, + {0x823c12795db6ce57, 0x76c53d08d6b70859}, {0xa2cb1717b52481ed, 0x54768c4b0c64ca6f}, + {0xcb7ddcdda26da268, 0xa9942f5dcf7dfd0a}, {0xfe5d54150b090b02, 0xd3f93b35435d7c4d}, + {0x9efa548d26e5a6e1, 0xc47bc5014a1a6db0}, {0xc6b8e9b0709f109a, 0x359ab6419ca1091c}, + {0xf867241c8cc6d4c0, 0xc30163d203c94b63}, {0x9b407691d7fc44f8, 0x79e0de63425dcf1e}, + {0xc21094364dfb5636, 0x985915fc12f542e5}, {0xf294b943e17a2bc4, 0x3e6f5b7b17b2939e}, + {0x979cf3ca6cec5b5a, 0xa705992ceecf9c43}, {0xbd8430bd08277231, 0x50c6ff782a838354}, + {0xece53cec4a314ebd, 0xa4f8bf5635246429}, {0x940f4613ae5ed136, 0x871b7795e136be9a}, + {0xb913179899f68584, 0x28e2557b59846e40}, {0xe757dd7ec07426e5, 0x331aeada2fe589d0}, + {0x9096ea6f3848984f, 0x3ff0d2c85def7622}, {0xb4bca50b065abe63, 0x0fed077a756b53aa}, + {0xe1ebce4dc7f16dfb, 0xd3e8495912c62895}, {0x8d3360f09cf6e4bd, 0x64712dd7abbbd95d}, + {0xb080392cc4349dec, 0xbd8d794d96aacfb4}, {0xdca04777f541c567, 0xecf0d7a0fc5583a1}, + {0x89e42caaf9491b60, 0xf41686c49db57245}, {0xac5d37d5b79b6239, 0x311c2875c522ced6}, + {0xd77485cb25823ac7, 0x7d633293366b828c}, {0x86a8d39ef77164bc, 0xae5dff9c02033198}, + {0xa8530886b54dbdeb, 0xd9f57f830283fdfd}, {0xd267caa862a12d66, 0xd072df63c324fd7c}, + {0x8380dea93da4bc60, 0x4247cb9e59f71e6e}, {0xa46116538d0deb78, 0x52d9be85f074e609}, + {0xcd795be870516656, 0x67902e276c921f8c}, {0x806bd9714632dff6, 0x00ba1cd8a3db53b7}, + {0xa086cfcd97bf97f3, 0x80e8a40eccd228a5}, {0xc8a883c0fdaf7df0, 0x6122cd128006b2ce}, + {0xfad2a4b13d1b5d6c, 0x796b805720085f82}, {0x9cc3a6eec6311a63, 0xcbe3303674053bb1}, + {0xc3f490aa77bd60fc, 0xbedbfc4411068a9d}, {0xf4f1b4d515acb93b, 0xee92fb5515482d45}, + {0x991711052d8bf3c5, 0x751bdd152d4d1c4b}, {0xbf5cd54678eef0b6, 0xd262d45a78a0635e}, + {0xef340a98172aace4, 0x86fb897116c87c35}, {0x9580869f0e7aac0e, 0xd45d35e6ae3d4da1}, + {0xbae0a846d2195712, 0x8974836059cca10a}, {0xe998d258869facd7, 0x2bd1a438703fc94c}, + {0x91ff83775423cc06, 0x7b6306a34627ddd0}, {0xb67f6455292cbf08, 0x1a3bc84c17b1d543}, + {0xe41f3d6a7377eeca, 0x20caba5f1d9e4a94}, {0x8e938662882af53e, 0x547eb47b7282ee9d}, + {0xb23867fb2a35b28d, 0xe99e619a4f23aa44}, {0xdec681f9f4c31f31, 0x6405fa00e2ec94d5}, + {0x8b3c113c38f9f37e, 0xde83bc408dd3dd05}, {0xae0b158b4738705e, 0x9624ab50b148d446}, + {0xd98ddaee19068c76, 0x3badd624dd9b0958}, {0x87f8a8d4cfa417c9, 0xe54ca5d70a80e5d7}, + {0xa9f6d30a038d1dbc, 0x5e9fcf4ccd211f4d}, 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{0xbfc2ef456ae276e8, 0x9e3fedd8c321a67f}, + {0xefb3ab16c59b14a2, 0xc5cfe94ef3ea101f}, {0x95d04aee3b80ece5, 0xbba1f1d158724a13}, + {0xbb445da9ca61281f, 0x2a8a6e45ae8edc98}, {0xea1575143cf97226, 0xf52d09d71a3293be}, + {0x924d692ca61be758, 0x593c2626705f9c57}, {0xb6e0c377cfa2e12e, 0x6f8b2fb00c77836d}, + {0xe498f455c38b997a, 0x0b6dfb9c0f956448}, {0x8edf98b59a373fec, 0x4724bd4189bd5ead}, + {0xb2977ee300c50fe7, 0x58edec91ec2cb658}, {0xdf3d5e9bc0f653e1, 0x2f2967b66737e3ee}, + {0x8b865b215899f46c, 0xbd79e0d20082ee75}, {0xae67f1e9aec07187, 0xecd8590680a3aa12}, + {0xda01ee641a708de9, 0xe80e6f4820cc9496}, {0x884134fe908658b2, 0x3109058d147fdcde}, + {0xaa51823e34a7eede, 0xbd4b46f0599fd416}, {0xd4e5e2cdc1d1ea96, 0x6c9e18ac7007c91b}, + {0x850fadc09923329e, 0x03e2cf6bc604ddb1}, {0xa6539930bf6bff45, 0x84db8346b786151d}, + {0xcfe87f7cef46ff16, 0xe612641865679a64}, {0x81f14fae158c5f6e, 0x4fcb7e8f3f60c07f}, + {0xa26da3999aef7749, 0xe3be5e330f38f09e}, {0xcb090c8001ab551c, 0x5cadf5bfd3072cc6}, + {0xfdcb4fa002162a63, 0x73d9732fc7c8f7f7}, {0x9e9f11c4014dda7e, 0x2867e7fddcdd9afb}, + {0xc646d63501a1511d, 0xb281e1fd541501b9}, {0xf7d88bc24209a565, 0x1f225a7ca91a4227}, + {0x9ae757596946075f, 0x3375788de9b06959}, {0xc1a12d2fc3978937, 0x0052d6b1641c83af}, + {0xf209787bb47d6b84, 0xc0678c5dbd23a49b}, {0x9745eb4d50ce6332, 0xf840b7ba963646e1}, + {0xbd176620a501fbff, 0xb650e5a93bc3d899}, {0xec5d3fa8ce427aff, 0xa3e51f138ab4cebf}, + {0x93ba47c980e98cdf, 0xc66f336c36b10138}, {0xb8a8d9bbe123f017, 0xb80b0047445d4185}, + {0xe6d3102ad96cec1d, 0xa60dc059157491e6}, {0x9043ea1ac7e41392, 0x87c89837ad68db30}, + {0xb454e4a179dd1877, 0x29babe4598c311fc}, {0xe16a1dc9d8545e94, 0xf4296dd6fef3d67b}, + {0x8ce2529e2734bb1d, 0x1899e4a65f58660d}, {0xb01ae745b101e9e4, 0x5ec05dcff72e7f90}, + {0xdc21a1171d42645d, 0x76707543f4fa1f74}, {0x899504ae72497eba, 0x6a06494a791c53a9}, + {0xabfa45da0edbde69, 0x0487db9d17636893}, {0xd6f8d7509292d603, 0x45a9d2845d3c42b7}, + {0x865b86925b9bc5c2, 0x0b8a2392ba45a9b3}, {0xa7f26836f282b732, 0x8e6cac7768d7141f}, + {0xd1ef0244af2364ff, 0x3207d795430cd927}, {0x8335616aed761f1f, 0x7f44e6bd49e807b9}, + {0xa402b9c5a8d3a6e7, 0x5f16206c9c6209a7}, {0xcd036837130890a1, 0x36dba887c37a8c10}, + {0x802221226be55a64, 0xc2494954da2c978a}, {0xa02aa96b06deb0fd, 0xf2db9baa10b7bd6d}, + {0xc83553c5c8965d3d, 0x6f92829494e5acc8}, {0xfa42a8b73abbf48c, 0xcb772339ba1f17fa}, + {0x9c69a97284b578d7, 0xff2a760414536efc}, {0xc38413cf25e2d70d, 0xfef5138519684abb}, + {0xf46518c2ef5b8cd1, 0x7eb258665fc25d6a}, {0x98bf2f79d5993802, 0xef2f773ffbd97a62}, + {0xbeeefb584aff8603, 0xaafb550ffacfd8fb}, {0xeeaaba2e5dbf6784, 0x95ba2a53f983cf39}, + {0x952ab45cfa97a0b2, 0xdd945a747bf26184}, {0xba756174393d88df, 0x94f971119aeef9e5}, + {0xe912b9d1478ceb17, 0x7a37cd5601aab85e}, {0x91abb422ccb812ee, 0xac62e055c10ab33b}, + {0xb616a12b7fe617aa, 0x577b986b314d600a}, {0xe39c49765fdf9d94, 0xed5a7e85fda0b80c}, + {0x8e41ade9fbebc27d, 0x14588f13be847308}, {0xb1d219647ae6b31c, 0x596eb2d8ae258fc9}, + {0xde469fbd99a05fe3, 0x6fca5f8ed9aef3bc}, {0x8aec23d680043bee, 0x25de7bb9480d5855}, + {0xada72ccc20054ae9, 0xaf561aa79a10ae6b}, {0xd910f7ff28069da4, 0x1b2ba1518094da05}, + {0x87aa9aff79042286, 0x90fb44d2f05d0843}, {0xa99541bf57452b28, 0x353a1607ac744a54}, + {0xd3fa922f2d1675f2, 0x42889b8997915ce9}, {0x847c9b5d7c2e09b7, 0x69956135febada12}, + {0xa59bc234db398c25, 0x43fab9837e699096}, {0xcf02b2c21207ef2e, 0x94f967e45e03f4bc}, + {0x8161afb94b44f57d, 0x1d1be0eebac278f6}, {0xa1ba1ba79e1632dc, 0x6462d92a69731733}, + {0xca28a291859bbf93, 0x7d7b8f7503cfdcff}, {0xfcb2cb35e702af78, 0x5cda735244c3d43f}, + {0x9defbf01b061adab, 0x3a0888136afa64a8}, {0xc56baec21c7a1916, 0x088aaa1845b8fdd1}, + {0xf6c69a72a3989f5b, 0x8aad549e57273d46}, {0x9a3c2087a63f6399, 0x36ac54e2f678864c}, + {0xc0cb28a98fcf3c7f, 0x84576a1bb416a7de}, {0xf0fdf2d3f3c30b9f, 0x656d44a2a11c51d6}, + {0x969eb7c47859e743, 0x9f644ae5a4b1b326}, {0xbc4665b596706114, 0x873d5d9f0dde1fef}, + {0xeb57ff22fc0c7959, 0xa90cb506d155a7eb}, {0x9316ff75dd87cbd8, 0x09a7f12442d588f3}, + {0xb7dcbf5354e9bece, 0x0c11ed6d538aeb30}, {0xe5d3ef282a242e81, 0x8f1668c8a86da5fb}, + {0x8fa475791a569d10, 0xf96e017d694487bd}, {0xb38d92d760ec4455, 0x37c981dcc395a9ad}, + {0xe070f78d3927556a, 0x85bbe253f47b1418}, {0x8c469ab843b89562, 0x93956d7478ccec8f}, + {0xaf58416654a6babb, 0x387ac8d1970027b3}, {0xdb2e51bfe9d0696a, 0x06997b05fcc0319f}, + {0x88fcf317f22241e2, 0x441fece3bdf81f04}, {0xab3c2fddeeaad25a, 0xd527e81cad7626c4}, + {0xd60b3bd56a5586f1, 0x8a71e223d8d3b075}, {0x85c7056562757456, 0xf6872d5667844e4a}, + {0xa738c6bebb12d16c, 0xb428f8ac016561dc}, {0xd106f86e69d785c7, 0xe13336d701beba53}, + {0x82a45b450226b39c, 0xecc0024661173474}, {0xa34d721642b06084, 0x27f002d7f95d0191}, + {0xcc20ce9bd35c78a5, 0x31ec038df7b441f5}, {0xff290242c83396ce, 0x7e67047175a15272}, + {0x9f79a169bd203e41, 0x0f0062c6e984d387}, {0xc75809c42c684dd1, 0x52c07b78a3e60869}, + {0xf92e0c3537826145, 0xa7709a56ccdf8a83}, {0x9bbcc7a142b17ccb, 0x88a66076400bb692}, + {0xc2abf989935ddbfe, 0x6acff893d00ea436}, {0xf356f7ebf83552fe, 0x0583f6b8c4124d44}, + {0x98165af37b2153de, 0xc3727a337a8b704b}, {0xbe1bf1b059e9a8d6, 0x744f18c0592e4c5d}, + {0xeda2ee1c7064130c, 0x1162def06f79df74}, {0x9485d4d1c63e8be7, 0x8addcb5645ac2ba9}, + {0xb9a74a0637ce2ee1, 0x6d953e2bd7173693}, {0xe8111c87c5c1ba99, 0xc8fa8db6ccdd0438}, + {0x910ab1d4db9914a0, 0x1d9c9892400a22a3}, {0xb54d5e4a127f59c8, 0x2503beb6d00cab4c}, + {0xe2a0b5dc971f303a, 0x2e44ae64840fd61e}, {0x8da471a9de737e24, 0x5ceaecfed289e5d3}, + {0xb10d8e1456105dad, 0x7425a83e872c5f48}, {0xdd50f1996b947518, 0xd12f124e28f7771a}, + {0x8a5296ffe33cc92f, 0x82bd6b70d99aaa70}, {0xace73cbfdc0bfb7b, 0x636cc64d1001550c}, + {0xd8210befd30efa5a, 0x3c47f7e05401aa4f}, {0x8714a775e3e95c78, 0x65acfaec34810a72}, + {0xa8d9d1535ce3b396, 0x7f1839a741a14d0e}, {0xd31045a8341ca07c, 0x1ede48111209a051}, + {0x83ea2b892091e44d, 0x934aed0aab460433}, {0xa4e4b66b68b65d60, 0xf81da84d56178540}, + {0xce1de40642e3f4b9, 0x36251260ab9d668f}, {0x80d2ae83e9ce78f3, 0xc1d72b7c6b42601a}, + {0xa1075a24e4421730, 0xb24cf65b8612f820}, {0xc94930ae1d529cfc, 0xdee033f26797b628}, + {0xfb9b7cd9a4a7443c, 0x169840ef017da3b2}, {0x9d412e0806e88aa5, 0x8e1f289560ee864f}, + {0xc491798a08a2ad4e, 0xf1a6f2bab92a27e3}, {0xf5b5d7ec8acb58a2, 0xae10af696774b1dc}, + {0x9991a6f3d6bf1765, 0xacca6da1e0a8ef2a}, {0xbff610b0cc6edd3f, 0x17fd090a58d32af4}, + {0xeff394dcff8a948e, 0xddfc4b4cef07f5b1}, {0x95f83d0a1fb69cd9, 0x4abdaf101564f98f}, + {0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f2}, {0xea53df5fd18d5513, 0x84c86189216dc5ee}, + {0x92746b9be2f8552c, 0x32fd3cf5b4e49bb5}, {0xb7118682dbb66a77, 0x3fbc8c33221dc2a2}, + {0xe4d5e82392a40515, 0x0fabaf3feaa5334b}, {0x8f05b1163ba6832d, 0x29cb4d87f2a7400f}, + {0xb2c71d5bca9023f8, 0x743e20e9ef511013}, {0xdf78e4b2bd342cf6, 0x914da9246b255417}, + {0x8bab8eefb6409c1a, 0x1ad089b6c2f7548f}, {0xae9672aba3d0c320, 0xa184ac2473b529b2}, + {0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741f}, {0x8865899617fb1871, 0x7e2fa67c7a658893}, + {0xaa7eebfb9df9de8d, 0xddbb901b98feeab8}, {0xd51ea6fa85785631, 0x552a74227f3ea566}, + {0x8533285c936b35de, 0xd53a88958f872760}, {0xa67ff273b8460356, 0x8a892abaf368f138}, + {0xd01fef10a657842c, 0x2d2b7569b0432d86}, {0x8213f56a67f6b29b, 0x9c3b29620e29fc74}, + {0xa298f2c501f45f42, 0x8349f3ba91b47b90}, {0xcb3f2f7642717713, 0x241c70a936219a74}, + {0xfe0efb53d30dd4d7, 0xed238cd383aa0111}, {0x9ec95d1463e8a506, 0xf4363804324a40ab}, + {0xc67bb4597ce2ce48, 0xb143c6053edcd0d6}, {0xf81aa16fdc1b81da, 0xdd94b7868e94050b}, + {0x9b10a4e5e9913128, 0xca7cf2b4191c8327}, {0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f1}, + {0xf24a01a73cf2dccf, 0xbc633b39673c8ced}, {0x976e41088617ca01, 0xd5be0503e085d814}, + {0xbd49d14aa79dbc82, 0x4b2d8644d8a74e19}, {0xec9c459d51852ba2, 0xddf8e7d60ed1219f}, + {0x93e1ab8252f33b45, 0xcabb90e5c942b504}, {0xb8da1662e7b00a17, 0x3d6a751f3b936244}, + {0xe7109bfba19c0c9d, 0x0cc512670a783ad5}, {0x906a617d450187e2, 0x27fb2b80668b24c6}, + {0xb484f9dc9641e9da, 0xb1f9f660802dedf7}, {0xe1a63853bbd26451, 0x5e7873f8a0396974}, + {0x8d07e33455637eb2, 0xdb0b487b6423e1e9}, {0xb049dc016abc5e5f, 0x91ce1a9a3d2cda63}, + {0xdc5c5301c56b75f7, 0x7641a140cc7810fc}, {0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9e}, + {0xac2820d9623bf429, 0x546345fa9fbdcd45}, {0xd732290fbacaf133, 0xa97c177947ad4096}, + {0x867f59a9d4bed6c0, 0x49ed8eabcccc485e}, {0xa81f301449ee8c70, 0x5c68f256bfff5a75}, + {0xd226fc195c6a2f8c, 0x73832eec6fff3112}, {0x83585d8fd9c25db7, 0xc831fd53c5ff7eac}, + {0xa42e74f3d032f525, 0xba3e7ca8b77f5e56}, {0xcd3a1230c43fb26f, 0x28ce1bd2e55f35ec}, + {0x80444b5e7aa7cf85, 0x7980d163cf5b81b4}, {0xa0555e361951c366, 0xd7e105bcc3326220}, + {0xc86ab5c39fa63440, 0x8dd9472bf3fefaa8}, {0xfa856334878fc150, 0xb14f98f6f0feb952}, + {0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d4}, {0xc3b8358109e84f07, 0x0a862f80ec4700c9}, + {0xf4a642e14c6262c8, 0xcd27bb612758c0fb}, {0x98e7e9cccfbd7dbd, 0x8038d51cb897789d}, + {0xbf21e44003acdd2c, 0xe0470a63e6bd56c4}, {0xeeea5d5004981478, 0x1858ccfce06cac75}, + {0x95527a5202df0ccb, 0x0f37801e0c43ebc9}, {0xbaa718e68396cffd, 0xd30560258f54e6bb}, + {0xe950df20247c83fd, 0x47c6b82ef32a206a}, {0x91d28b7416cdd27e, 0x4cdc331d57fa5442}, + {0xb6472e511c81471d, 0xe0133fe4adf8e953}, {0xe3d8f9e563a198e5, 0x58180fddd97723a7}, + {0x8e679c2f5e44ff8f, 0x570f09eaa7ea7649}, {0xb201833b35d63f73, 0x2cd2cc6551e513db}, + {0xde81e40a034bcf4f, 0xf8077f7ea65e58d2}, {0x8b112e86420f6191, 0xfb04afaf27faf783}, + {0xadd57a27d29339f6, 0x79c5db9af1f9b564}, {0xd94ad8b1c7380874, 0x18375281ae7822bd}, + {0x87cec76f1c830548, 0x8f2293910d0b15b6}, {0xa9c2794ae3a3c69a, 0xb2eb3875504ddb23}, + {0xd433179d9c8cb841, 0x5fa60692a46151ec}, {0x849feec281d7f328, 0xdbc7c41ba6bcd334}, + {0xa5c7ea73224deff3, 0x12b9b522906c0801}, {0xcf39e50feae16bef, 0xd768226b34870a01}, + {0x81842f29f2cce375, 0xe6a1158300d46641}, {0xa1e53af46f801c53, 0x60495ae3c1097fd1}, + {0xca5e89b18b602368, 0x385bb19cb14bdfc5}, {0xfcf62c1dee382c42, 0x46729e03dd9ed7b6}, + {0x9e19db92b4e31ba9, 0x6c07a2c26a8346d2}, {0xc5a05277621be293, 0xc7098b7305241886}, + {0xf70867153aa2db38, 0xb8cbee4fc66d1ea8}}; + }; +#if !NANOFMT_HAS_INLINE_VARIABLE + template + constexpr typename cache_holder::cache_entry_type + cache_holder::cache[]; +#endif + + // Compressed cache for double + template + struct compressed_cache_detail { + static constexpr int compression_ratio = 27; + static constexpr std::size_t compressed_table_size = + (cache_holder::max_k - cache_holder::min_k + + compression_ratio) / + compression_ratio; + + struct cache_holder_t { + wuint::uint128 table[compressed_table_size]; + }; + struct pow5_holder_t { + std::uint64_t table[compression_ratio]; + }; + +#if NANOFMT_HAS_CONSTEXPR17 + static constexpr cache_holder_t cache = [] { + cache_holder_t res{}; + for (std::size_t i = 0; i < compressed_table_size; ++i) { + res.table[i] = cache_holder::cache[i * compression_ratio]; + } + return res; + }(); + static constexpr pow5_holder_t pow5 = [] { + pow5_holder_t res{}; + std::uint64_t p = 1; + for (std::size_t i = 0; i < compression_ratio; ++i) { + res.table[i] = p; + p *= 5; + } + return res; + }(); +#else + template + static constexpr cache_holder_t make_cache_table(index_sequence) { + return {cache_holder::cache[indices * compression_ratio]...}; + } + static constexpr cache_holder_t cache = make_cache_table(make_index_sequence{}); + + template + static constexpr pow5_holder_t make_pow5_table(index_sequence) { + return {compute_power(std::uint64_t(5))...}; + } + static constexpr pow5_holder_t pow5 = make_pow5_table(make_index_sequence{}); +#endif + }; +#if !NANOFMT_HAS_INLINE_VARIABLE + template + constexpr typename compressed_cache_detail::cache_holder_t compressed_cache_detail::cache; + template + constexpr typename compressed_cache_detail::pow5_holder_t compressed_cache_detail::pow5; +#endif + } // namespace detail + + //////////////////////////////////////////////////////////////////////////////////////// + // Policies. + //////////////////////////////////////////////////////////////////////////////////////// + + namespace detail { + // Forward declare the implementation class. + template > + struct impl; + + namespace policy_impl { + // Sign policies. + namespace sign { + struct base {}; + + struct ignore : base { + using sign_policy = ignore; + static constexpr bool return_has_sign = false; + + template + static constexpr UnsignedDecimalFp handle_sign( + SignedSignificandBits, + UnsignedDecimalFp r) noexcept { + return r; + } + }; + + struct return_sign : base { + using sign_policy = return_sign; + static constexpr bool return_has_sign = true; + + template + static constexpr unsigned_decimal_fp_to_signed_t handle_sign( + SignedSignificandBits s, + UnsignedDecimalFp r) noexcept { + return add_sign_to_unsigned_decimal_fp(s.is_negative(), r); + } + }; + } // namespace sign + + // Trailing zero policies. + namespace trailing_zero { + struct base {}; + + struct ignore : base { + using trailing_zero_policy = ignore; + static constexpr bool report_trailing_zeros = false; + + template + static constexpr ReturnType on_trailing_zeros( + typename Impl::carrier_uint significand, + int exponent) noexcept { + return {significand, exponent}; + } + + template + static constexpr ReturnType no_trailing_zeros( + typename Impl::carrier_uint significand, + int exponent) noexcept { + return {significand, exponent}; + } + }; + + struct remove : base { + using trailing_zero_policy = remove; + static constexpr bool report_trailing_zeros = false; + + template + NANOFMT_FORCEINLINE static constexpr ReturnType on_trailing_zeros( + typename Impl::carrier_uint significand, + int exponent) noexcept { + return {(exponent += Impl::remove_trailing_zeros(significand), significand), exponent}; + } + + template + static constexpr ReturnType no_trailing_zeros( + typename Impl::carrier_uint significand, + int exponent) noexcept { + return {significand, exponent}; + } + }; + + struct report : base { + using trailing_zero_policy = report; + static constexpr bool report_trailing_zeros = true; + + template + static constexpr ReturnType on_trailing_zeros( + typename Impl::carrier_uint significand, + int exponent) noexcept { + return {significand, exponent, true}; + } + + template + static constexpr ReturnType no_trailing_zeros( + typename Impl::carrier_uint significand, + int exponent) noexcept { + return {significand, exponent, false}; + } + }; + } // namespace trailing_zero + + // Decimal-to-binary rounding mode policies. + namespace decimal_to_binary_rounding { + struct base {}; + + enum class tag_t { to_nearest, left_closed_directed, right_closed_directed }; + namespace interval_type { + struct symmetric_boundary { + static constexpr bool is_symmetric = true; + bool is_closed; + constexpr bool include_left_endpoint() const noexcept { + return is_closed; + } + constexpr bool include_right_endpoint() const noexcept { + return is_closed; + } + }; + struct asymmetric_boundary { + static constexpr bool is_symmetric = false; + bool is_left_closed; + constexpr bool include_left_endpoint() const noexcept { + return is_left_closed; + } + constexpr bool include_right_endpoint() const noexcept { + return !is_left_closed; + } + }; + struct closed { + static constexpr bool is_symmetric = true; + static constexpr bool include_left_endpoint() noexcept { + return true; + } + static constexpr bool include_right_endpoint() noexcept { + return true; + } + }; + struct open { + static constexpr bool is_symmetric = true; + static constexpr bool include_left_endpoint() noexcept { + return false; + } + static constexpr bool include_right_endpoint() noexcept { + return false; + } + }; + struct left_closed_right_open { + static constexpr bool is_symmetric = false; + static constexpr bool include_left_endpoint() noexcept { + return true; + } + static constexpr bool include_right_endpoint() noexcept { + return false; + } + }; + struct right_closed_left_open { + static constexpr bool is_symmetric = false; + static constexpr bool include_left_endpoint() noexcept { + return false; + } + static constexpr bool include_right_endpoint() noexcept { + return true; + } + }; + } // namespace interval_type + + struct nearest_to_even : base { + using decimal_to_binary_rounding_policy = nearest_to_even; + static constexpr auto tag = tag_t::to_nearest; + using normal_interval_type = interval_type::symmetric_boundary; + using shorter_interval_type = interval_type::closed; + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}( + declval(), + Args{}...)) + delegate(SignedSignificandBits, Func f, Args... args) noexcept { + return f(nearest_to_even{}, args...); + } + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}..., false)) + invoke_normal_interval_case(SignedSignificandBits s, Func f, Args... args) noexcept { + return f(args..., s.has_even_significand_bits()); + } + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}...)) + invoke_shorter_interval_case(SignedSignificandBits, Func f, Args... args) noexcept { + return f(args...); + } + }; + struct nearest_to_odd : base { + using decimal_to_binary_rounding_policy = nearest_to_odd; + static constexpr auto tag = tag_t::to_nearest; + using normal_interval_type = interval_type::symmetric_boundary; + using shorter_interval_type = interval_type::open; + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}( + declval(), + Args{}...)) + delegate(SignedSignificandBits, Func f, Args... args) noexcept { + return f(nearest_to_odd{}, args...); + } + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}..., false)) + invoke_normal_interval_case(SignedSignificandBits s, Func f, Args... args) noexcept { + return f(args..., !s.has_even_significand_bits()); + } + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}...)) + invoke_shorter_interval_case(SignedSignificandBits, Func f, Args... args) noexcept { + return f(args...); + } + }; + struct nearest_toward_plus_infinity : base { + using decimal_to_binary_rounding_policy = nearest_toward_plus_infinity; + static constexpr auto tag = tag_t::to_nearest; + using normal_interval_type = interval_type::asymmetric_boundary; + using shorter_interval_type = interval_type::asymmetric_boundary; + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}( + declval(), + Args{}...)) + delegate(SignedSignificandBits, Func f, Args... args) noexcept { + return f(nearest_toward_plus_infinity{}, args...); + } + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}..., false)) + invoke_normal_interval_case(SignedSignificandBits s, Func f, Args... args) noexcept { + return f(args..., !s.is_negative()); + } + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}..., false)) + invoke_shorter_interval_case(SignedSignificandBits s, Func f, Args... args) noexcept { + return f(args..., !s.is_negative()); + } + }; + struct nearest_toward_minus_infinity : base { + using decimal_to_binary_rounding_policy = nearest_toward_minus_infinity; + static constexpr auto tag = tag_t::to_nearest; + using normal_interval_type = interval_type::asymmetric_boundary; + using shorter_interval_type = interval_type::asymmetric_boundary; + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}( + declval(), + Args{}...)) + delegate(SignedSignificandBits, Func f, Args... args) noexcept { + return f(nearest_toward_minus_infinity{}, args...); + } + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}..., false)) + invoke_normal_interval_case(SignedSignificandBits s, Func f, Args... args) noexcept { + return f(args..., s.is_negative()); + } + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}..., false)) + invoke_shorter_interval_case(SignedSignificandBits s, Func f, Args... args) noexcept { + return f(args..., s.is_negative()); + } + }; + struct nearest_toward_zero : base { + using decimal_to_binary_rounding_policy = nearest_toward_zero; + static constexpr auto tag = tag_t::to_nearest; + using normal_interval_type = interval_type::right_closed_left_open; + using shorter_interval_type = interval_type::right_closed_left_open; + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}( + declval(), + Args{}...)) + delegate(SignedSignificandBits, Func f, Args... args) noexcept { + return f(nearest_toward_zero{}, args...); + } + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}...)) + invoke_normal_interval_case(SignedSignificandBits, Func f, Args... args) noexcept { + return f(args...); + } + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}...)) + invoke_shorter_interval_case(SignedSignificandBits, Func f, Args... args) noexcept { + return f(args...); + } + }; + struct nearest_away_from_zero : base { + using decimal_to_binary_rounding_policy = nearest_away_from_zero; + static constexpr auto tag = tag_t::to_nearest; + using normal_interval_type = interval_type::left_closed_right_open; + using shorter_interval_type = interval_type::left_closed_right_open; + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}( + declval(), + Args{}...)) + delegate(SignedSignificandBits, Func f, Args... args) noexcept { + return f(nearest_away_from_zero{}, args...); + } + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}...)) + invoke_normal_interval_case(SignedSignificandBits, Func f, Args... args) noexcept { + return f(args...); + } + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}...)) + invoke_shorter_interval_case(SignedSignificandBits, Func f, Args... args) noexcept { + return f(args...); + } + }; + + namespace detail { + struct nearest_always_closed { + static constexpr auto tag = tag_t::to_nearest; + using normal_interval_type = interval_type::closed; + using shorter_interval_type = interval_type::closed; + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}...)) + invoke_normal_interval_case(SignedSignificandBits, Func f, Args... args) noexcept { + return f(args...); + } + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}...)) + invoke_shorter_interval_case(SignedSignificandBits, Func f, Args... args) noexcept { + return f(args...); + } + }; + struct nearest_always_open { + static constexpr auto tag = tag_t::to_nearest; + using normal_interval_type = interval_type::open; + using shorter_interval_type = interval_type::open; + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}...)) + invoke_normal_interval_case(SignedSignificandBits, Func f, Args... args) noexcept { + return f(args...); + } + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}(Args{}...)) + invoke_shorter_interval_case(SignedSignificandBits, Func f, Args... args) noexcept { + return f(args...); + } + }; + } // namespace detail + + struct nearest_to_even_static_boundary : base { + using decimal_to_binary_rounding_policy = nearest_to_even_static_boundary; + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}( + detail::nearest_always_closed{}, + Args{}...)) + delegate(SignedSignificandBits s, Func f, Args... args) noexcept { + return s.has_even_significand_bits() ? f(detail::nearest_always_closed{}, args...) + : f(detail::nearest_always_open{}, args...); + } + }; + struct nearest_to_odd_static_boundary : base { + using decimal_to_binary_rounding_policy = nearest_to_odd_static_boundary; + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}( + detail::nearest_always_closed{}, + Args{}...)) + delegate(SignedSignificandBits s, Func f, Args... args) noexcept { + return s.has_even_significand_bits() ? f(detail::nearest_always_open{}, args...) + : f(detail::nearest_always_closed{}, args...); + } + }; + struct nearest_toward_plus_infinity_static_boundary : base { + using decimal_to_binary_rounding_policy = nearest_toward_plus_infinity_static_boundary; + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}( + nearest_toward_zero{}, + Args{}...)) + delegate(SignedSignificandBits s, Func f, Args... args) noexcept { + return s.is_negative() ? f(nearest_toward_zero{}, args...) + : f(nearest_away_from_zero{}, args...); + } + }; + struct nearest_toward_minus_infinity_static_boundary : base { + using decimal_to_binary_rounding_policy = nearest_toward_minus_infinity_static_boundary; + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}( + nearest_toward_zero{}, + Args{}...)) + delegate(SignedSignificandBits s, Func f, Args... args) noexcept { + return s.is_negative() ? f(nearest_away_from_zero{}, args...) + : f(nearest_toward_zero{}, args...); + } + }; + + namespace detail { + struct left_closed_directed { + static constexpr auto tag = tag_t::left_closed_directed; + }; + struct right_closed_directed { + static constexpr auto tag = tag_t::right_closed_directed; + }; + } // namespace detail + + struct toward_plus_infinity : base { + using decimal_to_binary_rounding_policy = toward_plus_infinity; + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}( + detail::left_closed_directed{}, + Args{}...)) + delegate(SignedSignificandBits s, Func f, Args... args) noexcept { + return s.is_negative() ? f(detail::left_closed_directed{}, args...) + : f(detail::right_closed_directed{}, args...); + } + }; + struct toward_minus_infinity : base { + using decimal_to_binary_rounding_policy = toward_minus_infinity; + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}( + detail::left_closed_directed{}, + Args{}...)) + delegate(SignedSignificandBits s, Func f, Args... args) noexcept { + return s.is_negative() ? f(detail::right_closed_directed{}, args...) + : f(detail::left_closed_directed{}, args...); + } + }; + struct toward_zero : base { + using decimal_to_binary_rounding_policy = toward_zero; + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}( + detail::left_closed_directed{}, + Args{}...)) + delegate(SignedSignificandBits, Func f, Args... args) noexcept { + return f(detail::left_closed_directed{}, args...); + } + }; + struct away_from_zero : base { + using decimal_to_binary_rounding_policy = away_from_zero; + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static constexpr decltype(Func{}( + detail::right_closed_directed{}, + Args{}...)) + delegate(SignedSignificandBits, Func f, Args... args) noexcept { + return f(detail::right_closed_directed{}, args...); + } + }; + } // namespace decimal_to_binary_rounding + + // Binary-to-decimal rounding policies. + // (Always assumes nearest rounding modes.) + namespace binary_to_decimal_rounding { + struct base {}; + + enum class tag_t { do_not_care, to_even, to_odd, away_from_zero, toward_zero }; + + struct do_not_care : base { + using binary_to_decimal_rounding_policy = do_not_care; + static constexpr auto tag = tag_t::do_not_care; + + template + static constexpr bool prefer_round_down(CarrierUInt) noexcept { + return false; + } + }; + + struct to_even : base { + using binary_to_decimal_rounding_policy = to_even; + static constexpr auto tag = tag_t::to_even; + + template + static constexpr bool prefer_round_down(CarrierUInt significand) noexcept { + return significand % 2 != 0; + } + }; + + struct to_odd : base { + using binary_to_decimal_rounding_policy = to_odd; + static constexpr auto tag = tag_t::to_odd; + + template + static constexpr bool prefer_round_down(CarrierUInt significand) noexcept { + return significand % 2 == 0; + } + }; + + struct away_from_zero : base { + using binary_to_decimal_rounding_policy = away_from_zero; + static constexpr auto tag = tag_t::away_from_zero; + + template + static constexpr bool prefer_round_down(CarrierUInt) noexcept { + return false; + } + }; + + struct toward_zero : base { + using binary_to_decimal_rounding_policy = toward_zero; + static constexpr auto tag = tag_t::toward_zero; + + template + static constexpr bool prefer_round_down(CarrierUInt) noexcept { + return true; + } + }; + } // namespace binary_to_decimal_rounding + + // Cache policies. + namespace cache { + struct base {}; + + struct full : base { + using cache_policy = full; + template + static constexpr typename cache_holder::cache_entry_type get_cache( + int k) noexcept { +#if NANOFMT_HAS_CONSTEXPR14 + assert(k >= cache_holder::min_k && k <= cache_holder::max_k); +#endif + return cache_holder::cache[std::size_t(k - cache_holder::min_k)]; + } + }; + + struct compact : base { + using cache_policy = compact; + + template + struct get_cache_impl { + static constexpr typename cache_holder::cache_entry_type get_cache( + int k) noexcept { + return full::get_cache(k); + } + }; + + template + struct get_cache_impl { + static NANOFMT_CONSTEXPR20 cache_holder::cache_entry_type get_cache( + int k) noexcept { + // Compute the base index. + auto const cache_index = + int(std::uint32_t(k - cache_holder::min_k) / + compressed_cache_detail<>::compression_ratio); + auto const kb = cache_index * compressed_cache_detail<>::compression_ratio + + cache_holder::min_k; + auto const offset = k - kb; + + // Get the base cache. + auto const base_cache = compressed_cache_detail<>::cache.table[cache_index]; + + if (offset == 0) { + return base_cache; + } + else { + // Compute the required amount of bit-shift. + auto const alpha = + log::floor_log2_pow10(kb + offset) - log::floor_log2_pow10(kb) - offset; + assert(alpha > 0 && alpha < 64); + + // Try to recover the real cache. + auto const pow5 = compressed_cache_detail<>::pow5.table[offset]; + auto recovered_cache = wuint::umul128(base_cache.high(), pow5); + auto const middle_low = wuint::umul128(base_cache.low(), pow5); + + recovered_cache += middle_low.high(); + + auto const high_to_middle = recovered_cache.high() << (64 - alpha); + auto const middle_to_low = recovered_cache.low() << (64 - alpha); + + recovered_cache = wuint::uint128{ + (recovered_cache.low() >> alpha) | high_to_middle, + ((middle_low.low() >> alpha) | middle_to_low)}; + + assert(recovered_cache.low() + 1 != 0); + recovered_cache = {recovered_cache.high(), recovered_cache.low() + 1}; + + return recovered_cache; + } + } + }; + + template + static NANOFMT_CONSTEXPR20 typename cache_holder::cache_entry_type get_cache( + int k) noexcept { + assert(k >= cache_holder::min_k && k <= cache_holder::max_k); + + return get_cache_impl::get_cache(k); + } + }; + } // namespace cache + } // namespace policy_impl + } // namespace detail + + namespace policy { + namespace sign { + NANOFMT_INLINE_VARIABLE auto ignore = detail::policy_impl::sign::ignore{}; + NANOFMT_INLINE_VARIABLE auto return_sign = detail::policy_impl::sign::return_sign{}; + } // namespace sign + + namespace trailing_zero { + NANOFMT_INLINE_VARIABLE auto ignore = detail::policy_impl::trailing_zero::ignore{}; + NANOFMT_INLINE_VARIABLE auto remove = detail::policy_impl::trailing_zero::remove{}; + NANOFMT_INLINE_VARIABLE auto report = detail::policy_impl::trailing_zero::report{}; + } // namespace trailing_zero + + namespace decimal_to_binary_rounding { + NANOFMT_INLINE_VARIABLE auto nearest_to_even = + detail::policy_impl::decimal_to_binary_rounding::nearest_to_even{}; + NANOFMT_INLINE_VARIABLE auto nearest_to_odd = + detail::policy_impl::decimal_to_binary_rounding::nearest_to_odd{}; + NANOFMT_INLINE_VARIABLE auto nearest_toward_plus_infinity = + detail::policy_impl::decimal_to_binary_rounding::nearest_toward_plus_infinity{}; + NANOFMT_INLINE_VARIABLE auto nearest_toward_minus_infinity = + detail::policy_impl::decimal_to_binary_rounding::nearest_toward_minus_infinity{}; + NANOFMT_INLINE_VARIABLE auto nearest_toward_zero = + detail::policy_impl::decimal_to_binary_rounding::nearest_toward_zero{}; + NANOFMT_INLINE_VARIABLE auto nearest_away_from_zero = + detail::policy_impl::decimal_to_binary_rounding::nearest_away_from_zero{}; + + NANOFMT_INLINE_VARIABLE auto nearest_to_even_static_boundary = + detail::policy_impl::decimal_to_binary_rounding::nearest_to_even_static_boundary{}; + NANOFMT_INLINE_VARIABLE auto nearest_to_odd_static_boundary = + detail::policy_impl::decimal_to_binary_rounding::nearest_to_odd_static_boundary{}; + NANOFMT_INLINE_VARIABLE auto nearest_toward_plus_infinity_static_boundary = + detail::policy_impl::decimal_to_binary_rounding::nearest_toward_plus_infinity_static_boundary{}; + NANOFMT_INLINE_VARIABLE auto nearest_toward_minus_infinity_static_boundary = + detail::policy_impl::decimal_to_binary_rounding::nearest_toward_minus_infinity_static_boundary{}; + + NANOFMT_INLINE_VARIABLE auto toward_plus_infinity = + detail::policy_impl::decimal_to_binary_rounding::toward_plus_infinity{}; + NANOFMT_INLINE_VARIABLE auto toward_minus_infinity = + detail::policy_impl::decimal_to_binary_rounding::toward_minus_infinity{}; + NANOFMT_INLINE_VARIABLE auto toward_zero = detail::policy_impl::decimal_to_binary_rounding::toward_zero{}; + NANOFMT_INLINE_VARIABLE auto away_from_zero = + detail::policy_impl::decimal_to_binary_rounding::away_from_zero{}; + } // namespace decimal_to_binary_rounding + + namespace binary_to_decimal_rounding { + NANOFMT_INLINE_VARIABLE auto do_not_care = detail::policy_impl::binary_to_decimal_rounding::do_not_care{}; + NANOFMT_INLINE_VARIABLE auto to_even = detail::policy_impl::binary_to_decimal_rounding::to_even{}; + NANOFMT_INLINE_VARIABLE auto to_odd = detail::policy_impl::binary_to_decimal_rounding::to_odd{}; + NANOFMT_INLINE_VARIABLE auto away_from_zero = + detail::policy_impl::binary_to_decimal_rounding::away_from_zero{}; + NANOFMT_INLINE_VARIABLE auto toward_zero = detail::policy_impl::binary_to_decimal_rounding::toward_zero{}; + } // namespace binary_to_decimal_rounding + + namespace cache { + NANOFMT_INLINE_VARIABLE auto full = detail::policy_impl::cache::full{}; + NANOFMT_INLINE_VARIABLE auto compact = detail::policy_impl::cache::compact{}; + } // namespace cache + } // namespace policy + + namespace detail { + //////////////////////////////////////////////////////////////////////////////////////// + // The main algorithm. + //////////////////////////////////////////////////////////////////////////////////////// + + template + struct impl + : private FloatTraits + , private FloatTraits::format { + using format = typename FloatTraits::format; + using carrier_uint = typename FloatTraits::carrier_uint; + + using FloatTraits::carrier_bits; + using format::decimal_digits; + using format::exponent_bias; + using format::max_exponent; + using format::min_exponent; + using format::significand_bits; + + static constexpr int kappa = std::is_same::value ? 1 : 2; + static_assert(kappa >= 1, ""); + static_assert(carrier_bits >= significand_bits + 2 + log::floor_log2_pow10(kappa + 1), ""); + + static constexpr int min(int x, int y) noexcept { + return x < y ? x : y; + } + static constexpr int max(int x, int y) noexcept { + return x > y ? x : y; + } + + static constexpr int min_k = + min(-log::floor_log10_pow2_minus_log10_4_over_3(int(max_exponent - significand_bits)), + -log::floor_log10_pow2(int(max_exponent - significand_bits)) + kappa); + static_assert(min_k >= cache_holder::min_k, ""); + + // We do invoke shorter_interval_case for exponent == min_exponent case, + // so we should not add 1 here. + static constexpr int max_k = + max(-log::floor_log10_pow2_minus_log10_4_over_3(int(min_exponent - significand_bits /*+ 1*/)), + -log::floor_log10_pow2(int(min_exponent - significand_bits)) + kappa); + static_assert(max_k <= cache_holder::max_k, ""); + + using cache_entry_type = typename cache_holder::cache_entry_type; + static constexpr auto cache_bits = cache_holder::cache_bits; + + static constexpr int case_shorter_interval_left_endpoint_lower_threshold = 2; + static constexpr int case_shorter_interval_left_endpoint_upper_threshold = + 2 + + log::floor_log2( + compute_power((carrier_uint(1) << (significand_bits + 2)) - 1) + 1>(10) / 3); + + static constexpr int case_shorter_interval_right_endpoint_lower_threshold = 0; + static constexpr int case_shorter_interval_right_endpoint_upper_threshold = + 2 + + log::floor_log2( + compute_power((carrier_uint(1) << (significand_bits + 1)) + 1) + 1>(10) / 3); + + static constexpr int shorter_interval_tie_lower_threshold = + -log::floor_log5_pow2_minus_log5_3(significand_bits + 4) - 2 - significand_bits; + static constexpr int shorter_interval_tie_upper_threshold = + -log::floor_log5_pow2(significand_bits + 2) - 2 - significand_bits; + + struct compute_mul_result { + carrier_uint integer_part; + bool is_integer; + }; + struct compute_mul_parity_result { + bool parity; + bool is_integer; + }; + template + struct compute_mul_impl; + + //// The main algorithm assumes the input is a normal/subnormal finite number + + template < + class ReturnType, + class IntervalType, + class TrailingZeroPolicy, + class BinaryToDecimalRoundingPolicy, + class CachePolicy, + class... AdditionalArgs> + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static NANOFMT_CONSTEXPR20 ReturnType compute_nearest_normal( + carrier_uint const two_fc, + int const binary_exponent, + AdditionalArgs... additional_args) noexcept { + ////////////////////////////////////////////////////////////////////// + // Step 1: Schubfach multiplier calculation + ////////////////////////////////////////////////////////////////////// + + IntervalType interval_type{additional_args...}; + + // Compute k and beta. + int const minus_k = log::floor_log10_pow2(binary_exponent) - kappa; + auto const cache = CachePolicy::template get_cache(-minus_k); + int const beta = binary_exponent + log::floor_log2_pow10(-minus_k); + + // Compute zi and deltai. + // 10^kappa <= deltai < 10^(kappa + 1) + auto const deltai = compute_mul_impl::compute_delta(cache, beta); + // For the case of binary32, the result of integer check is not correct for + // 29711844 * 2^-82 + // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18 + // and 29711844 * 2^-81 + // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17, + // and they are the unique counterexamples. However, since 29711844 is even, + // this does not cause any problem for the endpoints calculations; it can only + // cause a problem when we need to perform integer check for the center. + // Fortunately, with these inputs, that branch is never executed, so we are + // fine. + auto const z_result = compute_mul_impl::compute_mul((two_fc | 1) << beta, cache); + + ////////////////////////////////////////////////////////////////////// + // Step 2: Try larger divisor; remove trailing zeros if necessary + ////////////////////////////////////////////////////////////////////// + + constexpr auto big_divisor = compute_power(std::uint32_t(10)); + constexpr auto small_divisor = compute_power(std::uint32_t(10)); + + // Using an upper bound on zi, we might be able to optimize the division + // better than the compiler; we are computing zi / big_divisor here. + carrier_uint decimal_significand = div::divide_by_pow10< + kappa + 1, + carrier_uint, + (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1>(z_result.integer_part); + auto r = std::uint32_t(z_result.integer_part - big_divisor * decimal_significand); + + do { + if (r < deltai) { + // Exclude the right endpoint if necessary. + if (r == 0 && (z_result.is_integer & !interval_type.include_right_endpoint())) { + NANOFMT_IF_CONSTEXPR( + BinaryToDecimalRoundingPolicy::tag == + policy_impl::binary_to_decimal_rounding::tag_t::do_not_care) { + decimal_significand *= 10; + --decimal_significand; + return TrailingZeroPolicy::template no_trailing_zeros( + decimal_significand, + minus_k + kappa); + } + else { + --decimal_significand; + r = big_divisor; + break; + } + } + } + else if (r > deltai) { + break; + } + else { + // r == deltai; compare fractional parts. + auto const x_result = compute_mul_impl::compute_mul_parity(two_fc - 1, cache, beta); + + if (!(x_result.parity | (x_result.is_integer & interval_type.include_left_endpoint()))) { + break; + } + } + + // We may need to remove trailing zeros. + return TrailingZeroPolicy::template on_trailing_zeros( + decimal_significand, + minus_k + kappa + 1); + } while (false); + + ////////////////////////////////////////////////////////////////////// + // Step 3: Find the significand with the smaller divisor + ////////////////////////////////////////////////////////////////////// + + decimal_significand *= 10; + + NANOFMT_IF_CONSTEXPR( + BinaryToDecimalRoundingPolicy::tag == + policy_impl::binary_to_decimal_rounding::tag_t::do_not_care) { + // Normally, we want to compute + // significand += r / small_divisor + // and return, but we need to take care of the case that the resulting + // value is exactly the right endpoint, while that is not included in the + // interval. + if (!interval_type.include_right_endpoint()) { + // Is r divisible by 10^kappa? + if (z_result.is_integer && div::check_divisibility_and_divide_by_pow10(r)) { + // This should be in the interval. + decimal_significand += r - 1; + } + else { + decimal_significand += r; + } + } + else { + decimal_significand += div::small_division_by_pow10(r); + } + } + else { + auto dist = r - (deltai / 2) + (small_divisor / 2); + bool const approx_y_parity = ((dist ^ (small_divisor / 2)) & 1) != 0; + + // Is dist divisible by 10^kappa? + bool const divisible_by_small_divisor = + div::check_divisibility_and_divide_by_pow10(dist); + + // Add dist / 10^kappa to the significand. + decimal_significand += dist; + + if (divisible_by_small_divisor) { + // Check z^(f) >= epsilon^(f). + // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1, + // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f). + // Since there are only 2 possibilities, we only need to care about the + // parity. Also, zi and r should have the same parity since the divisor + // is an even number. + auto const y_result = compute_mul_impl::compute_mul_parity(two_fc, cache, beta); + if (y_result.parity != approx_y_parity) { + --decimal_significand; + } + else { + // If z^(f) >= epsilon^(f), we might have a tie + // when z^(f) == epsilon^(f), or equivalently, when y is an integer. + // For tie-to-up case, we can just choose the upper one. + if (BinaryToDecimalRoundingPolicy::prefer_round_down(decimal_significand) & + y_result.is_integer) { + --decimal_significand; + } + } + } + } + return TrailingZeroPolicy::template no_trailing_zeros( + decimal_significand, + minus_k + kappa); + } + + template < + class ReturnType, + class IntervalType, + class TrailingZeroPolicy, + class BinaryToDecimalRoundingPolicy, + class CachePolicy, + class... AdditionalArgs> + NANOFMT_SAFEBUFFERS static NANOFMT_CONSTEXPR20 ReturnType + compute_nearest_shorter(int const binary_exponent, AdditionalArgs... additional_args) noexcept { + IntervalType interval_type{additional_args...}; + + // Compute k and beta. + int const minus_k = log::floor_log10_pow2_minus_log10_4_over_3(binary_exponent); + int const beta = binary_exponent + log::floor_log2_pow10(-minus_k); + + // Compute xi and zi. + auto const cache = CachePolicy::template get_cache(-minus_k); + + auto xi = compute_mul_impl::compute_left_endpoint_for_shorter_interval_case(cache, beta); + auto zi = compute_mul_impl::compute_right_endpoint_for_shorter_interval_case(cache, beta); + + // If we don't accept the right endpoint and + // if the right endpoint is an integer, decrease it. + if (!interval_type.include_right_endpoint() && + is_right_endpoint_integer_shorter_interval(binary_exponent)) { + --zi; + } + // If we don't accept the left endpoint or + // if the left endpoint is not an integer, increase it. + if (!interval_type.include_left_endpoint() || + !is_left_endpoint_integer_shorter_interval(binary_exponent)) { + ++xi; + } + + // Try bigger divisor. + carrier_uint decimal_significand = zi / 10; + + // If succeed, remove trailing zeros if necessary and return. + if (decimal_significand * 10 >= xi) { + return TrailingZeroPolicy::template on_trailing_zeros( + decimal_significand, + minus_k + 1); + } + + // Otherwise, compute the round-up of y. + decimal_significand = + compute_mul_impl::compute_round_up_for_shorter_interval_case(cache, beta); + + // When tie occurs, choose one of them according to the rule. + if (BinaryToDecimalRoundingPolicy::prefer_round_down(decimal_significand) && + binary_exponent >= shorter_interval_tie_lower_threshold && + binary_exponent <= shorter_interval_tie_upper_threshold) { + --decimal_significand; + } + else if (decimal_significand < xi) { + ++decimal_significand; + } + return TrailingZeroPolicy::template no_trailing_zeros( + decimal_significand, + minus_k); + } + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static NANOFMT_CONSTEXPR20 ReturnType + compute_left_closed_directed(carrier_uint const two_fc, int binary_exponent) noexcept { + ////////////////////////////////////////////////////////////////////// + // Step 1: Schubfach multiplier calculation + ////////////////////////////////////////////////////////////////////// + + // Compute k and beta. + int const minus_k = log::floor_log10_pow2(binary_exponent) - kappa; + auto const cache = CachePolicy::template get_cache(-minus_k); + int const beta = binary_exponent + log::floor_log2_pow10(-minus_k); + + // Compute xi and deltai. + // 10^kappa <= deltai < 10^(kappa + 1) + auto const deltai = compute_mul_impl::compute_delta(cache, beta); + auto x_result = compute_mul_impl::compute_mul(two_fc << beta, cache); + + // Deal with the unique exceptional cases + // 29711844 * 2^-82 + // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18 + // and 29711844 * 2^-81 + // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17 + // for binary32. + NANOFMT_IF_CONSTEXPR(std::is_same::value) { + if (binary_exponent <= -80) { + x_result.is_integer = false; + } + } + + if (!x_result.is_integer) { + ++x_result.integer_part; + } + + ////////////////////////////////////////////////////////////////////// + // Step 2: Try larger divisor; remove trailing zeros if necessary + ////////////////////////////////////////////////////////////////////// + + constexpr auto big_divisor = compute_power(std::uint32_t(10)); + + // Using an upper bound on xi, we might be able to optimize the division + // better than the compiler; we are computing xi / big_divisor here. + carrier_uint decimal_significand = div::divide_by_pow10< + kappa + 1, + carrier_uint, + (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1>(x_result.integer_part); + auto r = std::uint32_t(x_result.integer_part - big_divisor * decimal_significand); + + if (r != 0) { + ++decimal_significand; + r = big_divisor - r; + } + + do { + if (r > deltai) { + break; + } + else if (r == deltai) { + // Compare the fractional parts. + // This branch is never taken for the exceptional cases + // 2f_c = 29711482, e = -81 + // (6.1442649164096937243516663440523473127541365101933479309082... * + // 10^-18) and 2f_c = 29711482, e = -80 + // (1.2288529832819387448703332688104694625508273020386695861816... * + // 10^-17). + auto const z_result = compute_mul_impl::compute_mul_parity(two_fc + 2, cache, beta); + if (z_result.parity || z_result.is_integer) { + break; + } + } + + // The ceiling is inside, so we are done. + return TrailingZeroPolicy::template on_trailing_zeros( + decimal_significand, + minus_k + kappa + 1); + } while (false); + + ////////////////////////////////////////////////////////////////////// + // Step 3: Find the significand with the smaller divisor + ////////////////////////////////////////////////////////////////////// + + decimal_significand *= 10; + decimal_significand -= div::small_division_by_pow10(r); + return TrailingZeroPolicy::template no_trailing_zeros( + decimal_significand, + minus_k + kappa); + } + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS static NANOFMT_CONSTEXPR20 ReturnType compute_right_closed_directed( + carrier_uint const two_fc, + int const binary_exponent, + bool shorter_interval) noexcept { + ////////////////////////////////////////////////////////////////////// + // Step 1: Schubfach multiplier calculation + ////////////////////////////////////////////////////////////////////// + + // Compute k and beta. + int const minus_k = log::floor_log10_pow2(binary_exponent - (shorter_interval ? 1 : 0)) - kappa; + auto const cache = CachePolicy::template get_cache(-minus_k); + int const beta = binary_exponent + log::floor_log2_pow10(-minus_k); + + // Compute zi and deltai. + // 10^kappa <= deltai < 10^(kappa + 1) + auto const deltai = shorter_interval ? compute_mul_impl::compute_delta(cache, beta - 1) + : compute_mul_impl::compute_delta(cache, beta); + carrier_uint const zi = compute_mul_impl::compute_mul(two_fc << beta, cache).integer_part; + + ////////////////////////////////////////////////////////////////////// + // Step 2: Try larger divisor; remove trailing zeros if necessary + ////////////////////////////////////////////////////////////////////// + + constexpr auto big_divisor = compute_power(std::uint32_t(10)); + + // Using an upper bound on zi, we might be able to optimize the division better + // than the compiler; we are computing zi / big_divisor here. + carrier_uint decimal_significand = div::divide_by_pow10< + kappa + 1, + carrier_uint, + (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1>(zi); + auto const r = std::uint32_t(zi - big_divisor * decimal_significand); + + do { + if (r > deltai) { + break; + } + else if (r == deltai) { + // Compare the fractional parts. + if (!compute_mul_impl::compute_mul_parity( + two_fc - (shorter_interval ? 1 : 2), + cache, + beta) + .parity) { + break; + } + } + + // The floor is inside, so we are done. + return TrailingZeroPolicy::template on_trailing_zeros( + decimal_significand, + minus_k + kappa + 1); + } while (false); + + ////////////////////////////////////////////////////////////////////// + // Step 3: Find the significand with the small divisor + ////////////////////////////////////////////////////////////////////// + + decimal_significand *= 10; + decimal_significand += div::small_division_by_pow10(r); + return TrailingZeroPolicy::template no_trailing_zeros( + decimal_significand, + minus_k + kappa); + } + + // Remove trailing zeros from n and return the number of zeros removed. + NANOFMT_FORCEINLINE static NANOFMT_CONSTEXPR20 int remove_trailing_zeros(carrier_uint& n) noexcept { + assert(n != 0); + + NANOFMT_IF_CONSTEXPR(std::is_same::value) { + constexpr auto mod_inv_5 = std::uint32_t(0xcccccccd); + constexpr auto mod_inv_25 = mod_inv_5 * mod_inv_5; + + int s = 0; + while (true) { + auto q = bits::rotr(n * mod_inv_25, 2); + if (q <= std::numeric_limits::max() / 100) { + n = q; + s += 2; + } + else { + break; + } + } + auto q = bits::rotr(n * mod_inv_5, 1); + if (q <= std::numeric_limits::max() / 10) { + n = q; + s |= 1; + } + + return s; + } + else { +#if NANOFMT_HAS_IF_CONSTEXPR + static_assert(std::is_same::value, ""); +#endif + + // Divide by 10^8 and reduce to 32-bits if divisible. + // Since ret_value.significand <= (2^53 * 1000 - 1) / 1000 < 10^16, + // n is at most of 16 digits. + + // This magic number is ceil(2^90 / 10^8). + constexpr auto magic_number = std::uint64_t(12379400392853802749ull); + auto nm = wuint::umul128(n, magic_number); + + // Is n is divisible by 10^8? + if ((nm.high() & ((std::uint64_t(1) << (90 - 64)) - 1)) == 0 && nm.low() < magic_number) { + // If yes, work with the quotient. + auto n32 = std::uint32_t(nm.high() >> (90 - 64)); + + constexpr auto mod_inv_5 = std::uint32_t(0xcccccccd); + constexpr auto mod_inv_25 = mod_inv_5 * mod_inv_5; + + int s = 8; + while (true) { + auto q = bits::rotr(n32 * mod_inv_25, 2); + if (q <= std::numeric_limits::max() / 100) { + n32 = q; + s += 2; + } + else { + break; + } + } + auto q = bits::rotr(n32 * mod_inv_5, 1); + if (q <= std::numeric_limits::max() / 10) { + n32 = q; + s |= 1; + } + + n = n32; + return s; + } + + // If n is not divisible by 10^8, work with n itself. + constexpr auto mod_inv_5 = std::uint64_t(0xcccccccccccccccd); + constexpr auto mod_inv_25 = mod_inv_5 * mod_inv_5; + + int s = 0; + while (true) { + auto q = bits::rotr(n * mod_inv_25, 2); + if (q <= std::numeric_limits::max() / 100) { + n = q; + s += 2; + } + else { + break; + } + } + auto q = bits::rotr(n * mod_inv_5, 1); + if (q <= std::numeric_limits::max() / 10) { + n = q; + s |= 1; + } + + return s; + } + } + + template + struct compute_mul_impl { + static NANOFMT_CONSTEXPR20 compute_mul_result + compute_mul(carrier_uint u, cache_entry_type const& cache) noexcept { + auto r = wuint::umul96_upper64(u, cache); + return {carrier_uint(r >> 32), carrier_uint(r) == 0}; + } + + static constexpr std::uint32_t compute_delta(cache_entry_type const& cache, int beta) noexcept { + return std::uint32_t(cache >> (cache_bits - 1 - beta)); + } + + static NANOFMT_CONSTEXPR20 compute_mul_parity_result + compute_mul_parity(carrier_uint two_f, cache_entry_type const& cache, int beta) noexcept { + assert(beta >= 1); + assert(beta < 64); + + auto r = wuint::umul96_lower64(two_f, cache); + return {((r >> (64 - beta)) & 1) != 0, std::uint32_t(r >> (32 - beta)) == 0}; + } + + static constexpr carrier_uint compute_left_endpoint_for_shorter_interval_case( + cache_entry_type const& cache, + int beta) noexcept { + return carrier_uint( + (cache - (cache >> (significand_bits + 2))) >> (cache_bits - significand_bits - 1 - beta)); + } + + static constexpr carrier_uint compute_right_endpoint_for_shorter_interval_case( + cache_entry_type const& cache, + int beta) noexcept { + return carrier_uint( + (cache + (cache >> (significand_bits + 1))) >> (cache_bits - significand_bits - 1 - beta)); + } + + static constexpr carrier_uint compute_round_up_for_shorter_interval_case( + cache_entry_type const& cache, + int beta) noexcept { + return (carrier_uint(cache >> (cache_bits - significand_bits - 2 - beta)) + 1) / 2; + } + }; + + template + struct compute_mul_impl { + static NANOFMT_CONSTEXPR20 compute_mul_result + compute_mul(carrier_uint u, cache_entry_type const& cache) noexcept { + auto r = wuint::umul192_upper128(u, cache); + return {r.high(), r.low() == 0}; + } + + static constexpr std::uint32_t compute_delta(cache_entry_type const& cache, int beta) noexcept { + return std::uint32_t(cache.high() >> (carrier_bits - 1 - beta)); + } + + static NANOFMT_CONSTEXPR20 compute_mul_parity_result + compute_mul_parity(carrier_uint two_f, cache_entry_type const& cache, int beta) noexcept { + assert(beta >= 1); + assert(beta < 64); + + auto r = wuint::umul192_lower128(two_f, cache); + return { + ((r.high() >> (64 - beta)) & 1) != 0, + ((r.high() << beta) | (r.low() >> (64 - beta))) == 0}; + } + + static constexpr carrier_uint compute_left_endpoint_for_shorter_interval_case( + cache_entry_type const& cache, + int beta) noexcept { + return (cache.high() - (cache.high() >> (significand_bits + 2))) >> + (carrier_bits - significand_bits - 1 - beta); + } + + static constexpr carrier_uint compute_right_endpoint_for_shorter_interval_case( + cache_entry_type const& cache, + int beta) noexcept { + return (cache.high() + (cache.high() >> (significand_bits + 1))) >> + (carrier_bits - significand_bits - 1 - beta); + } + + static constexpr carrier_uint compute_round_up_for_shorter_interval_case( + cache_entry_type const& cache, + int beta) noexcept { + return ((cache.high() >> (carrier_bits - significand_bits - 2 - beta)) + 1) / 2; + } + }; + + static constexpr bool is_right_endpoint_integer_shorter_interval(int exponent) noexcept { + return exponent >= case_shorter_interval_right_endpoint_lower_threshold && + exponent <= case_shorter_interval_right_endpoint_upper_threshold; + } + + static constexpr bool is_left_endpoint_integer_shorter_interval(int exponent) noexcept { + return exponent >= case_shorter_interval_left_endpoint_lower_threshold && + exponent <= case_shorter_interval_left_endpoint_upper_threshold; + } + }; + + //////////////////////////////////////////////////////////////////////////////////////// + // Policy holder. + //////////////////////////////////////////////////////////////////////////////////////// + + namespace policy_impl { + // The library will specify a list of accepted kinds of policies and their defaults, + // and the user will pass a list of policies. The aim of helper classes/functions + // here is to do the following: + // 1. Check if the policy parameters given by the user are all valid; that means, + // each of them should be of the kinds specified by the library. + // If that's not the case, then the compilation fails. + // 2. Check if multiple policy parameters for the same kind is specified by the + // user. + // If that's the case, then the compilation fails. + // 3. Build a class deriving from all policies the user have given, and also from + // the default policies if the user did not specify one for some kinds. + // A policy belongs to a certain kind if it is deriving from a base class. + + // For a given kind, find a policy belonging to that kind. + // Check if there are more than one such policies. + enum class policy_found_info { not_found, unique, repeated }; + template + struct found_policy_pair { + using policy = Policy; + static constexpr auto found_info = info; + }; + + template + struct base_default_pair { + using base = Base; + + template + struct get_found_policy_pair_impl; + + template + struct get_found_policy_pair_impl { + using type = FoundPolicyInfo; + }; + + template + struct get_found_policy_pair_impl { + using type = typename std::conditional< + std::is_base_of::value, + typename std::conditional< + FoundPolicyInfo::found_info == policy_found_info::not_found, + typename get_found_policy_pair_impl< + found_policy_pair, + RemainingPolicies...>::type, + typename get_found_policy_pair_impl< + found_policy_pair, + RemainingPolicies...>::type>::type, + typename get_found_policy_pair_impl::type>::type; + }; + + template + using get_found_policy_pair = typename get_found_policy_pair_impl< + found_policy_pair, + Policies...>::type; + }; + template + struct base_default_pair_list {}; + + // Check if a given policy belongs to one of the kinds specified by the library. + template + constexpr bool check_policy_validity(Policy, base_default_pair_list<>) { + return false; + } + template + constexpr bool check_policy_validity( + Policy, + base_default_pair_list) { + return std::is_base_of::value || + check_policy_validity(Policy{}, base_default_pair_list{}); + } + + template + constexpr bool check_policy_list_validity(BaseDefaultPairList) { + return true; + } + + template + constexpr bool check_policy_list_validity( + BaseDefaultPairList, + FirstPolicy, + RemainingPolicies... remaining_policies) { + return check_policy_validity(FirstPolicy{}, BaseDefaultPairList{}) && + check_policy_list_validity(BaseDefaultPairList{}, remaining_policies...); + } + + // Build policy_holder. + template + struct found_policy_pair_list { + static constexpr bool repeated = repeated_; + }; + + template + struct policy_holder : Policies... {}; + + template + struct make_policy_holder_impl; + + template + struct make_policy_holder_impl< + base_default_pair_list<>, + found_policy_pair_list, + Policies...> { + using type = found_policy_pair_list; + }; + + template < + class FirstBaseDefaultPair, + class... RemainingBaseDefaultPairs, + bool repeated, + class... FoundPolicyPairs, + class... Policies> + struct make_policy_holder_impl< + base_default_pair_list, + found_policy_pair_list, + Policies...> { + using new_found_policy_pair = + typename FirstBaseDefaultPair::template get_found_policy_pair; + + using type = typename make_policy_holder_impl< + base_default_pair_list, + found_policy_pair_list< + (repeated || new_found_policy_pair::found_info == policy_found_info::repeated), + new_found_policy_pair, + FoundPolicyPairs...>, + Policies...>::type; + }; + + template + using policy_pair_list = + typename make_policy_holder_impl, Policies...>:: + type; + + template + struct convert_to_policy_holder_impl; + + template + struct convert_to_policy_holder_impl, RawPolicies...> { + using type = policy_holder; + }; + + template < + bool repeated, + class FirstFoundPolicyPair, + class... RemainingFoundPolicyPairs, + class... RawPolicies> + struct convert_to_policy_holder_impl< + found_policy_pair_list, + RawPolicies...> { + using type = typename convert_to_policy_holder_impl< + found_policy_pair_list, + typename FirstFoundPolicyPair::policy, + RawPolicies...>::type; + }; + + template + using convert_to_policy_holder = typename convert_to_policy_holder_impl::type; + + template + constexpr convert_to_policy_holder> + make_policy_holder(BaseDefaultPairList, Policies... policies) { + static_assert( + check_policy_list_validity(BaseDefaultPairList{}, Policies{}...), + "nanofmt::dragonbox: an invalid policy is specified"); + + static_assert( + !policy_pair_list::repeated, + "nanofmt::dragonbox: each policy should be specified at most once"); + + return {}; + } + } // namespace policy_impl + + template + using to_decimal_policy_holder = decltype(policy_impl::make_policy_holder( + policy_impl::base_default_pair_list< + policy_impl::base_default_pair, + policy_impl:: + base_default_pair, + policy_impl::base_default_pair< + policy_impl::decimal_to_binary_rounding::base, + policy_impl::decimal_to_binary_rounding::nearest_to_even>, + policy_impl::base_default_pair< + policy_impl::binary_to_decimal_rounding::base, + policy_impl::binary_to_decimal_rounding::to_even>, + policy_impl::base_default_pair>{}, + Policies{}...)); + + template + using to_decimal_return_type = decimal_fp< + typename FloatTraits::carrier_uint, + to_decimal_policy_holder::return_has_sign, + to_decimal_policy_holder::report_trailing_zeros>; + + template + struct invoke_shorter_dispatcher { + using unsigned_return_type = + decimal_fp; + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS NANOFMT_CONSTEXPR20 unsigned_return_type operator()(Args... args) noexcept { + return impl::template compute_nearest_shorter< + unsigned_return_type, + typename IntervalTypeProvider::shorter_interval_type, + typename PolicyHolder::trailing_zero_policy, + typename PolicyHolder::binary_to_decimal_rounding_policy, + typename PolicyHolder::cache_policy>(args...); + } + }; + + template + struct invoke_normal_dispatcher { + using unsigned_return_type = + decimal_fp; + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS NANOFMT_CONSTEXPR20 unsigned_return_type operator()(Args... args) noexcept { + return impl::template compute_nearest_normal< + unsigned_return_type, + typename IntervalTypeProvider::normal_interval_type, + typename PolicyHolder::trailing_zero_policy, + typename PolicyHolder::binary_to_decimal_rounding_policy, + typename PolicyHolder::cache_policy>(args...); + } + }; + + template + NANOFMT_SAFEBUFFERS NANOFMT_CONSTEXPR20 decimal_fp< + typename FloatTraits::carrier_uint, + PolicyHolder::return_has_sign, + PolicyHolder::report_trailing_zeros> + to_decimal_impl( + signed_significand_bits signed_significand_bits, + unsigned int exponent_bits) noexcept { + using namespace policy_impl; + using unsigned_return_type = + decimal_fp; + using format = typename FloatTraits::format; + constexpr auto tag = IntervalTypeProvider::tag; + + auto two_fc = signed_significand_bits.remove_sign_bit_and_shift(); + auto exponent = int(exponent_bits); + + NANOFMT_IF_CONSTEXPR(tag == decimal_to_binary_rounding::tag_t::to_nearest) { + // Is the input a normal number? + if (exponent != 0) { + exponent += format::exponent_bias - format::significand_bits; + + // Shorter interval case; proceed like Schubfach. + // One might think this condition is wrong, since when exponent_bits == + // 1 and two_fc == 0, the interval is actually regular. However, it + // turns out that this seemingly wrong condition is actually fine, + // because the end result is anyway the same. + // + // [binary32] + // (fc-1/2) * 2^e = 1.175'494'28... * 10^-38 + // (fc-1/4) * 2^e = 1.175'494'31... * 10^-38 + // fc * 2^e = 1.175'494'35... * 10^-38 + // (fc+1/2) * 2^e = 1.175'494'42... * 10^-38 + // + // Hence, shorter_interval_case will return 1.175'494'4 * 10^-38. + // 1.175'494'3 * 10^-38 is also a correct shortest representation that + // will be rejected if we assume shorter interval, but 1.175'494'4 * + // 10^-38 is closer to the true value so it doesn't matter. + // + // [binary64] + // (fc-1/2) * 2^e = 2.225'073'858'507'201'13... * 10^-308 + // (fc-1/4) * 2^e = 2.225'073'858'507'201'25... * 10^-308 + // fc * 2^e = 2.225'073'858'507'201'38... * 10^-308 + // (fc+1/2) * 2^e = 2.225'073'858'507'201'63... * 10^-308 + // + // Hence, shorter_interval_case will return 2.225'073'858'507'201'4 * + // 10^-308. This is indeed of the shortest length, and it is the unique + // one closest to the true value among valid representations of the same + // length. + static_assert( + std::is_same::value || + std::is_same::value, + ""); + + if (two_fc == 0) { + return PolicyHolder::handle_sign( + signed_significand_bits, + IntervalTypeProvider::invoke_shorter_interval_case( + signed_significand_bits, + invoke_shorter_dispatcher{}, + exponent)); + } + + two_fc |= (decltype(two_fc)(1) << (format::significand_bits + 1)); + } + // Is the input a subnormal number? + else { + exponent = format::min_exponent - format::significand_bits; + } + + return PolicyHolder::handle_sign( + signed_significand_bits, + IntervalTypeProvider::invoke_normal_interval_case( + signed_significand_bits, + invoke_normal_dispatcher{}, + two_fc, + exponent)); + } + else NANOFMT_IF_CONSTEXPR(tag == decimal_to_binary_rounding::tag_t::left_closed_directed) { + // Is the input a normal number? + if (exponent != 0) { + exponent += format::exponent_bias - format::significand_bits; + two_fc |= (decltype(two_fc)(1) << (format::significand_bits + 1)); + } + // Is the input a subnormal number? + else { + exponent = format::min_exponent - format::significand_bits; + } + + return PolicyHolder::handle_sign( + signed_significand_bits, + detail::impl::template compute_left_closed_directed< + unsigned_return_type, + typename PolicyHolder::trailing_zero_policy, + typename PolicyHolder::cache_policy>(two_fc, exponent)); + } + else { +#if NANOFMT_HAS_IF_CONSTEXPR + static_assert(tag == decimal_to_binary_rounding::tag_t::right_closed_directed, ""); +#endif + + bool shorter_interval = false; + + // Is the input a normal number? + if (exponent != 0) { + if (two_fc == 0 && exponent != 1) { + shorter_interval = true; + } + exponent += format::exponent_bias - format::significand_bits; + two_fc |= (decltype(two_fc)(1) << (format::significand_bits + 1)); + } + // Is the input a subnormal number? + else { + exponent = format::min_exponent - format::significand_bits; + } + + return PolicyHolder::handle_sign( + signed_significand_bits, + detail::impl::template compute_right_closed_directed< + unsigned_return_type, + typename PolicyHolder::trailing_zero_policy, + typename PolicyHolder::cache_policy>(two_fc, exponent, shorter_interval)); + } + } + + template + struct to_decimal_dispatcher { + using return_type = decimal_fp< + typename FloatTraits::carrier_uint, + PolicyHolder::return_has_sign, + PolicyHolder::report_trailing_zeros>; + + template + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS NANOFMT_CONSTEXPR20 return_type + operator()(IntervalTypeProvider, Args... args) noexcept { + return to_decimal_impl(args...); + } + }; + } // namespace detail + + //////////////////////////////////////////////////////////////////////////////////////// + // The interface function. + //////////////////////////////////////////////////////////////////////////////////////// + + template , class... Policies> + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS NANOFMT_CONSTEXPR20 detail::to_decimal_return_type + to_decimal( + signed_significand_bits signed_significand_bits, + unsigned int exponent_bits, + Policies...) noexcept { + // Build policy holder type. + using namespace detail::policy_impl; + using policy_holder = detail::to_decimal_policy_holder; + + return policy_holder::delegate( + signed_significand_bits, + detail::to_decimal_dispatcher{}, + signed_significand_bits, + exponent_bits); + } + + template , class... Policies> + NANOFMT_FORCEINLINE NANOFMT_SAFEBUFFERS NANOFMT_CONSTEXPR20 detail::to_decimal_return_type + to_decimal(Float x, Policies... policies) noexcept { + auto const br = float_bits(x); + auto const exponent_bits = br.extract_exponent_bits(); + auto const s = br.remove_exponent_bits(exponent_bits); + assert(br.is_finite()); + + return to_decimal(s, exponent_bits, policies...); + } + } // namespace dragonbox +} // namespace NANOFMT_NS + +#undef NANOFMT_HAS_BUILTIN +#undef NANOFMT_FORCEINLINE +#undef NANOFMT_SAFEBUFFERS +#undef NANOFMT_CONSTEXPR20 +#undef NANOFMT_CAN_BRANCH_ON_CONSTEVAL +#undef NANOFMT_IF_NOT_CONSTEVAL +#undef NANOFMT_IF_CONSTEVAL +#undef NANOFMT_HAS_BIT_CAST +#undef NANOFMT_IF_CONSTEXPR +#undef NANOFMT_HAS_IF_CONSTEXPR +#undef NANOFMT_INLINE_VARIABLE +#undef NANOFMT_HAS_INLINE_VARIABLE +#undef NANOFMT_HAS_CONSTEXPR17 +#undef NANOFMT_CONSTEXPR14 +#undef NANOFMT_HAS_CONSTEXPR14 + +#endif diff --git a/source/CMakeLists.txt b/source/CMakeLists.txt index e396d3d..e83617c 100644 --- a/source/CMakeLists.txt +++ b/source/CMakeLists.txt @@ -1,5 +1,3 @@ -include(fetch_dragonbox) - target_sources(nanofmt PRIVATE "charconv.cpp" "format.cpp" diff --git a/source/charconv.cpp b/source/charconv.cpp index 8387a06..dbc988f 100644 --- a/source/charconv.cpp +++ b/source/charconv.cpp @@ -1,12 +1,8 @@ // Copyright (c) Sean Middleditch and contributors. See accompanying LICENSE.md for copyright details. -// just in case another library links dragonbox, make ours "private" to -// avoid version/ODR problems -#define jkj nanofmt_jkj - #include "nanofmt/charconv.h" #include "numeric_utils.h" -#include "dragonbox/dragonbox.h" +#include "nanofmt/dragonbox.h" #include "nanofmt/format.h" #include @@ -172,12 +168,12 @@ namespace NANOFMT_NS { int exponent = 0; if (value != 0) { - auto const db_result = jkj::dragonbox::to_decimal( + auto const db_result = nanofmt::dragonbox::to_decimal( value, - jkj::dragonbox::policy::sign::ignore, - jkj::dragonbox::policy::cache::compact, - jkj::dragonbox::policy::trailing_zero::remove, - jkj::dragonbox::policy::binary_to_decimal_rounding::to_even); + nanofmt::dragonbox::policy::sign::ignore, + nanofmt::dragonbox::policy::cache::compact, + nanofmt::dragonbox::policy::trailing_zero::remove, + nanofmt::dragonbox::policy::binary_to_decimal_rounding::to_even); significand = db_result.significand; exponent = db_result.exponent; } diff --git a/source/format.cpp b/source/format.cpp index c1fdc16..763772e 100644 --- a/source/format.cpp +++ b/source/format.cpp @@ -521,7 +521,9 @@ namespace NANOFMT_NS { } // binary encoding is the widest; FIXME: this is icky - char chars[sizeof(value) * 8]; + char chars[sizeof(value) * 8] = { + 0, + }; size_t const available = out.end - out.pos; size_t const length = diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt index 74e07cf..85d4942 100644 --- a/tests/CMakeLists.txt +++ b/tests/CMakeLists.txt @@ -2,11 +2,12 @@ include(fetch_catch2) add_executable(nanofmt_test) target_sources(nanofmt_test PRIVATE + "fwd_only_type.h" "test_charconv.cpp" "test_format.cpp" "test_format_args.cpp" "test_utils.h" - "fwd_only_type.h") +) target_link_libraries(nanofmt_test PRIVATE nanofmt Catch2::Catch2WithMain