diff options
Diffstat (limited to 'NorthstarDLL/include/spdlog/fmt/bundled/format-inl.h')
| -rw-r--r-- | NorthstarDLL/include/spdlog/fmt/bundled/format-inl.h | 2801 |
1 files changed, 2801 insertions, 0 deletions
diff --git a/NorthstarDLL/include/spdlog/fmt/bundled/format-inl.h b/NorthstarDLL/include/spdlog/fmt/bundled/format-inl.h new file mode 100644 index 00000000..8f2fe735 --- /dev/null +++ b/NorthstarDLL/include/spdlog/fmt/bundled/format-inl.h @@ -0,0 +1,2801 @@ +// Formatting library for C++ - implementation +// +// Copyright (c) 2012 - 2016, Victor Zverovich +// All rights reserved. +// +// For the license information refer to format.h. + +#ifndef FMT_FORMAT_INL_H_ +#define FMT_FORMAT_INL_H_ + +#include <cassert> +#include <cctype> +#include <climits> +#include <cmath> +#include <cstdarg> +#include <cstring> // std::memmove +#include <cwchar> +#include <exception> + +#ifndef FMT_STATIC_THOUSANDS_SEPARATOR +# include <locale> +#endif + +#ifdef _WIN32 +# include <io.h> // _isatty +#endif + +#include "format.h" + +// Dummy implementations of strerror_r and strerror_s called if corresponding +// system functions are not available. +inline fmt::detail::null<> strerror_r(int, char*, ...) { return {}; } +inline fmt::detail::null<> strerror_s(char*, size_t, ...) { return {}; } + +FMT_BEGIN_NAMESPACE +namespace detail { + +FMT_FUNC void assert_fail(const char* file, int line, const char* message) { + // Use unchecked std::fprintf to avoid triggering another assertion when + // writing to stderr fails + std::fprintf(stderr, "%s:%d: assertion failed: %s", file, line, message); + // Chosen instead of std::abort to satisfy Clang in CUDA mode during device + // code pass. + std::terminate(); +} + +#ifndef _MSC_VER +# define FMT_SNPRINTF snprintf +#else // _MSC_VER +inline int fmt_snprintf(char* buffer, size_t size, const char* format, ...) { + va_list args; + va_start(args, format); + int result = vsnprintf_s(buffer, size, _TRUNCATE, format, args); + va_end(args); + return result; +} +# define FMT_SNPRINTF fmt_snprintf +#endif // _MSC_VER + +// A portable thread-safe version of strerror. +// Sets buffer to point to a string describing the error code. +// This can be either a pointer to a string stored in buffer, +// or a pointer to some static immutable string. +// Returns one of the following values: +// 0 - success +// ERANGE - buffer is not large enough to store the error message +// other - failure +// Buffer should be at least of size 1. +inline int safe_strerror(int error_code, char*& buffer, + size_t buffer_size) FMT_NOEXCEPT { + FMT_ASSERT(buffer != nullptr && buffer_size != 0, "invalid buffer"); + + class dispatcher { + private: + int error_code_; + char*& buffer_; + size_t buffer_size_; + + // A noop assignment operator to avoid bogus warnings. + void operator=(const dispatcher&) {} + + // Handle the result of XSI-compliant version of strerror_r. + int handle(int result) { + // glibc versions before 2.13 return result in errno. + return result == -1 ? errno : result; + } + + // Handle the result of GNU-specific version of strerror_r. + FMT_MAYBE_UNUSED + int handle(char* message) { + // If the buffer is full then the message is probably truncated. + if (message == buffer_ && strlen(buffer_) == buffer_size_ - 1) + return ERANGE; + buffer_ = message; + return 0; + } + + // Handle the case when strerror_r is not available. + FMT_MAYBE_UNUSED + int handle(detail::null<>) { + return fallback(strerror_s(buffer_, buffer_size_, error_code_)); + } + + // Fallback to strerror_s when strerror_r is not available. + FMT_MAYBE_UNUSED + int fallback(int result) { + // If the buffer is full then the message is probably truncated. + return result == 0 && strlen(buffer_) == buffer_size_ - 1 ? ERANGE + : result; + } + +#if !FMT_MSC_VER + // Fallback to strerror if strerror_r and strerror_s are not available. + int fallback(detail::null<>) { + errno = 0; + buffer_ = strerror(error_code_); + return errno; + } +#endif + + public: + dispatcher(int err_code, char*& buf, size_t buf_size) + : error_code_(err_code), buffer_(buf), buffer_size_(buf_size) {} + + int run() { return handle(strerror_r(error_code_, buffer_, buffer_size_)); } + }; + return dispatcher(error_code, buffer, buffer_size).run(); +} + +FMT_FUNC void format_error_code(detail::buffer<char>& out, int error_code, + string_view message) FMT_NOEXCEPT { + // Report error code making sure that the output fits into + // inline_buffer_size to avoid dynamic memory allocation and potential + // bad_alloc. + out.try_resize(0); + static const char SEP[] = ": "; + static const char ERROR_STR[] = "error "; + // Subtract 2 to account for terminating null characters in SEP and ERROR_STR. + size_t error_code_size = sizeof(SEP) + sizeof(ERROR_STR) - 2; + auto abs_value = static_cast<uint32_or_64_or_128_t<int>>(error_code); + if (detail::is_negative(error_code)) { + abs_value = 0 - abs_value; + ++error_code_size; + } + error_code_size += detail::to_unsigned(detail::count_digits(abs_value)); + auto it = buffer_appender<char>(out); + if (message.size() <= inline_buffer_size - error_code_size) + format_to(it, "{}{}", message, SEP); + format_to(it, "{}{}", ERROR_STR, error_code); + assert(out.size() <= inline_buffer_size); +} + +FMT_FUNC void report_error(format_func func, int error_code, + string_view message) FMT_NOEXCEPT { + memory_buffer full_message; + func(full_message, error_code, message); + // Don't use fwrite_fully because the latter may throw. + (void)std::fwrite(full_message.data(), full_message.size(), 1, stderr); + std::fputc('\n', stderr); +} + +// A wrapper around fwrite that throws on error. +inline void fwrite_fully(const void* ptr, size_t size, size_t count, + FILE* stream) { + size_t written = std::fwrite(ptr, size, count, stream); + if (written < count) FMT_THROW(system_error(errno, "cannot write to file")); +} +} // namespace detail + +#if !defined(FMT_STATIC_THOUSANDS_SEPARATOR) +namespace detail { + +template <typename Locale> +locale_ref::locale_ref(const Locale& loc) : locale_(&loc) { + static_assert(std::is_same<Locale, std::locale>::value, ""); +} + +template <typename Locale> Locale locale_ref::get() const { + static_assert(std::is_same<Locale, std::locale>::value, ""); + return locale_ ? *static_cast<const std::locale*>(locale_) : std::locale(); +} + +template <typename Char> FMT_FUNC std::string grouping_impl(locale_ref loc) { + return std::use_facet<std::numpunct<Char>>(loc.get<std::locale>()).grouping(); +} +template <typename Char> FMT_FUNC Char thousands_sep_impl(locale_ref loc) { + return std::use_facet<std::numpunct<Char>>(loc.get<std::locale>()) + .thousands_sep(); +} +template <typename Char> FMT_FUNC Char decimal_point_impl(locale_ref loc) { + return std::use_facet<std::numpunct<Char>>(loc.get<std::locale>()) + .decimal_point(); +} +} // namespace detail +#else +template <typename Char> +FMT_FUNC std::string detail::grouping_impl(locale_ref) { + return "\03"; +} +template <typename Char> FMT_FUNC Char detail::thousands_sep_impl(locale_ref) { + return FMT_STATIC_THOUSANDS_SEPARATOR; +} +template <typename Char> FMT_FUNC Char detail::decimal_point_impl(locale_ref) { + return '.'; +} +#endif + +FMT_API FMT_FUNC format_error::~format_error() FMT_NOEXCEPT = default; +FMT_API FMT_FUNC system_error::~system_error() FMT_NOEXCEPT = default; + +FMT_FUNC void system_error::init(int err_code, string_view format_str, + format_args args) { + error_code_ = err_code; + memory_buffer buffer; + format_system_error(buffer, err_code, vformat(format_str, args)); + std::runtime_error& base = *this; + base = std::runtime_error(to_string(buffer)); +} + +namespace detail { + +template <> FMT_FUNC int count_digits<4>(detail::fallback_uintptr n) { + // fallback_uintptr is always stored in little endian. + int i = static_cast<int>(sizeof(void*)) - 1; + while (i > 0 && n.value[i] == 0) --i; + auto char_digits = std::numeric_limits<unsigned char>::digits / 4; + return i >= 0 ? i * char_digits + count_digits<4, unsigned>(n.value[i]) : 1; +} + +template <typename T> +const typename basic_data<T>::digit_pair basic_data<T>::digits[] = { + {'0', '0'}, {'0', '1'}, {'0', '2'}, {'0', '3'}, {'0', '4'}, {'0', '5'}, + {'0', '6'}, {'0', '7'}, {'0', '8'}, {'0', '9'}, {'1', '0'}, {'1', '1'}, + {'1', '2'}, {'1', '3'}, {'1', '4'}, {'1', '5'}, {'1', '6'}, {'1', '7'}, + {'1', '8'}, {'1', '9'}, {'2', '0'}, {'2', '1'}, {'2', '2'}, {'2', '3'}, + {'2', '4'}, {'2', '5'}, {'2', '6'}, {'2', '7'}, {'2', '8'}, {'2', '9'}, + {'3', '0'}, {'3', '1'}, {'3', '2'}, {'3', '3'}, {'3', '4'}, {'3', '5'}, + {'3', '6'}, {'3', '7'}, {'3', '8'}, {'3', '9'}, {'4', '0'}, {'4', '1'}, + {'4', '2'}, {'4', '3'}, {'4', '4'}, {'4', '5'}, {'4', '6'}, {'4', '7'}, + {'4', '8'}, {'4', '9'}, {'5', '0'}, {'5', '1'}, {'5', '2'}, {'5', '3'}, + {'5', '4'}, {'5', '5'}, {'5', '6'}, {'5', '7'}, {'5', '8'}, {'5', '9'}, + {'6', '0'}, {'6', '1'}, {'6', '2'}, {'6', '3'}, {'6', '4'}, {'6', '5'}, + {'6', '6'}, {'6', '7'}, {'6', '8'}, {'6', '9'}, {'7', '0'}, {'7', '1'}, + {'7', '2'}, {'7', '3'}, {'7', '4'}, {'7', '5'}, {'7', '6'}, {'7', '7'}, + {'7', '8'}, {'7', '9'}, {'8', '0'}, {'8', '1'}, {'8', '2'}, {'8', '3'}, + {'8', '4'}, {'8', '5'}, {'8', '6'}, {'8', '7'}, {'8', '8'}, {'8', '9'}, + {'9', '0'}, {'9', '1'}, {'9', '2'}, {'9', '3'}, {'9', '4'}, {'9', '5'}, + {'9', '6'}, {'9', '7'}, {'9', '8'}, {'9', '9'}}; + +template <typename T> +const char basic_data<T>::hex_digits[] = "0123456789abcdef"; + +#define FMT_POWERS_OF_10(factor) \ + factor * 10, (factor)*100, (factor)*1000, (factor)*10000, (factor)*100000, \ + (factor)*1000000, (factor)*10000000, (factor)*100000000, \ + (factor)*1000000000 + +template <typename T> +const uint64_t basic_data<T>::powers_of_10_64[] = { + 1, FMT_POWERS_OF_10(1), FMT_POWERS_OF_10(1000000000ULL), + 10000000000000000000ULL}; + +template <typename T> +const uint32_t basic_data<T>::zero_or_powers_of_10_32[] = {0, + FMT_POWERS_OF_10(1)}; +template <typename T> +const uint64_t basic_data<T>::zero_or_powers_of_10_64[] = { + 0, FMT_POWERS_OF_10(1), FMT_POWERS_OF_10(1000000000ULL), + 10000000000000000000ULL}; + +template <typename T> +const uint32_t basic_data<T>::zero_or_powers_of_10_32_new[] = { + 0, 0, FMT_POWERS_OF_10(1)}; + +template <typename T> +const uint64_t basic_data<T>::zero_or_powers_of_10_64_new[] = { + 0, 0, FMT_POWERS_OF_10(1), FMT_POWERS_OF_10(1000000000ULL), + 10000000000000000000ULL}; + +// Normalized 64-bit significands of pow(10, k), for k = -348, -340, ..., 340. +// These are generated by support/compute-powers.py. +template <typename T> +const uint64_t basic_data<T>::grisu_pow10_significands[] = { + 0xfa8fd5a0081c0288, 0xbaaee17fa23ebf76, 0x8b16fb203055ac76, + 0xcf42894a5dce35ea, 0x9a6bb0aa55653b2d, 0xe61acf033d1a45df, + 0xab70fe17c79ac6ca, 0xff77b1fcbebcdc4f, 0xbe5691ef416bd60c, + 0x8dd01fad907ffc3c, 0xd3515c2831559a83, 0x9d71ac8fada6c9b5, + 0xea9c227723ee8bcb, 0xaecc49914078536d, 0x823c12795db6ce57, + 0xc21094364dfb5637, 0x9096ea6f3848984f, 0xd77485cb25823ac7, + 0xa086cfcd97bf97f4, 0xef340a98172aace5, 0xb23867fb2a35b28e, + 0x84c8d4dfd2c63f3b, 0xc5dd44271ad3cdba, 0x936b9fcebb25c996, + 0xdbac6c247d62a584, 0xa3ab66580d5fdaf6, 0xf3e2f893dec3f126, + 0xb5b5ada8aaff80b8, 0x87625f056c7c4a8b, 0xc9bcff6034c13053, + 0x964e858c91ba2655, 0xdff9772470297ebd, 0xa6dfbd9fb8e5b88f, + 0xf8a95fcf88747d94, 0xb94470938fa89bcf, 0x8a08f0f8bf0f156b, + 0xcdb02555653131b6, 0x993fe2c6d07b7fac, 0xe45c10c42a2b3b06, + 0xaa242499697392d3, 0xfd87b5f28300ca0e, 0xbce5086492111aeb, + 0x8cbccc096f5088cc, 0xd1b71758e219652c, 0x9c40000000000000, + 0xe8d4a51000000000, 0xad78ebc5ac620000, 0x813f3978f8940984, + 0xc097ce7bc90715b3, 0x8f7e32ce7bea5c70, 0xd5d238a4abe98068, + 0x9f4f2726179a2245, 0xed63a231d4c4fb27, 0xb0de65388cc8ada8, + 0x83c7088e1aab65db, 0xc45d1df942711d9a, 0x924d692ca61be758, + 0xda01ee641a708dea, 0xa26da3999aef774a, 0xf209787bb47d6b85, + 0xb454e4a179dd1877, 0x865b86925b9bc5c2, 0xc83553c5c8965d3d, + 0x952ab45cfa97a0b3, 0xde469fbd99a05fe3, 0xa59bc234db398c25, + 0xf6c69a72a3989f5c, 0xb7dcbf5354e9bece, 0x88fcf317f22241e2, + 0xcc20ce9bd35c78a5, 0x98165af37b2153df, 0xe2a0b5dc971f303a, + 0xa8d9d1535ce3b396, 0xfb9b7cd9a4a7443c, 0xbb764c4ca7a44410, + 0x8bab8eefb6409c1a, 0xd01fef10a657842c, 0x9b10a4e5e9913129, + 0xe7109bfba19c0c9d, 0xac2820d9623bf429, 0x80444b5e7aa7cf85, + 0xbf21e44003acdd2d, 0x8e679c2f5e44ff8f, 0xd433179d9c8cb841, + 0x9e19db92b4e31ba9, 0xeb96bf6ebadf77d9, 0xaf87023b9bf0ee6b, +}; + +// Binary exponents of pow(10, k), for k = -348, -340, ..., 340, corresponding +// to significands above. +template <typename T> +const int16_t basic_data<T>::grisu_pow10_exponents[] = { + -1220, -1193, -1166, -1140, -1113, -1087, -1060, -1034, -1007, -980, -954, + -927, -901, -874, -847, -821, -794, -768, -741, -715, -688, -661, + -635, -608, -582, -555, -529, -502, -475, -449, -422, -396, -369, + -343, -316, -289, -263, -236, -210, -183, -157, -130, -103, -77, + -50, -24, 3, 30, 56, 83, 109, 136, 162, 189, 216, + 242, 269, 295, 322, 348, 375, 402, 428, 455, 481, 508, + 534, 561, 588, 614, 641, 667, 694, 720, 747, 774, 800, + 827, 853, 880, 907, 933, 960, 986, 1013, 1039, 1066}; + +template <typename T> +const divtest_table_entry<uint32_t> basic_data<T>::divtest_table_for_pow5_32[] = + {{0x00000001, 0xffffffff}, {0xcccccccd, 0x33333333}, + {0xc28f5c29, 0x0a3d70a3}, {0x26e978d5, 0x020c49ba}, + {0x3afb7e91, 0x0068db8b}, {0x0bcbe61d, 0x0014f8b5}, + {0x68c26139, 0x000431bd}, {0xae8d46a5, 0x0000d6bf}, + {0x22e90e21, 0x00002af3}, {0x3a2e9c6d, 0x00000897}, + {0x3ed61f49, 0x000001b7}}; + +template <typename T> +const divtest_table_entry<uint64_t> basic_data<T>::divtest_table_for_pow5_64[] = + {{0x0000000000000001, 0xffffffffffffffff}, + {0xcccccccccccccccd, 0x3333333333333333}, + {0x8f5c28f5c28f5c29, 0x0a3d70a3d70a3d70}, + {0x1cac083126e978d5, 0x020c49ba5e353f7c}, + {0xd288ce703afb7e91, 0x0068db8bac710cb2}, + {0x5d4e8fb00bcbe61d, 0x0014f8b588e368f0}, + {0x790fb65668c26139, 0x000431bde82d7b63}, + {0xe5032477ae8d46a5, 0x0000d6bf94d5e57a}, + {0xc767074b22e90e21, 0x00002af31dc46118}, + {0x8e47ce423a2e9c6d, 0x0000089705f4136b}, + {0x4fa7f60d3ed61f49, 0x000001b7cdfd9d7b}, + {0x0fee64690c913975, 0x00000057f5ff85e5}, + {0x3662e0e1cf503eb1, 0x000000119799812d}, + {0xa47a2cf9f6433fbd, 0x0000000384b84d09}, + {0x54186f653140a659, 0x00000000b424dc35}, + {0x7738164770402145, 0x0000000024075f3d}, + {0xe4a4d1417cd9a041, 0x000000000734aca5}, + {0xc75429d9e5c5200d, 0x000000000170ef54}, + {0xc1773b91fac10669, 0x000000000049c977}, + {0x26b172506559ce15, 0x00000000000ec1e4}, + {0xd489e3a9addec2d1, 0x000000000002f394}, + {0x90e860bb892c8d5d, 0x000000000000971d}, + {0x502e79bf1b6f4f79, 0x0000000000001e39}, + {0xdcd618596be30fe5, 0x000000000000060b}}; + +template <typename T> +const uint64_t basic_data<T>::dragonbox_pow10_significands_64[] = { + 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, 0x813f3978f8940984, + 0xa18f07d736b90be5, 0xc9f2c9cd04674ede, 0xfc6f7c4045812296, + 0x9dc5ada82b70b59d, 0xc5371912364ce305, 0xf684df56c3e01bc6, + 0x9a130b963a6c115c, 0xc097ce7bc90715b3, 0xf0bdc21abb48db20, + 0x96769950b50d88f4, 0xbc143fa4e250eb31, 0xeb194f8e1ae525fd, + 0x92efd1b8d0cf37be, 0xb7abc627050305ad, 0xe596b7b0c643c719, + 0x8f7e32ce7bea5c6f, 0xb35dbf821ae4f38b, 0xe0352f62a19e306e}; + +template <typename T> +const uint128_wrapper basic_data<T>::dragonbox_pow10_significands_128[] = { +#if FMT_USE_FULL_CACHE_DRAGONBOX + {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}, + {0xd47487cc8470652b, 0x7647c32000696720}, + {0x84c8d4dfd2c63f3b, 0x29ecd9f40041e074}, + {0xa5fb0a17c777cf09, 0xf468107100525891}, + {0xcf79cc9db955c2cc, 0x7182148d4066eeb5}, + {0x81ac1fe293d599bf, 0xc6f14cd848405531}, + {0xa21727db38cb002f, 0xb8ada00e5a506a7d}, + {0xca9cf1d206fdc03b, 0xa6d90811f0e4851d}, + {0xfd442e4688bd304a, 0x908f4a166d1da664}, + {0x9e4a9cec15763e2e, 0x9a598e4e043287ff}, + {0xc5dd44271ad3cdba, 0x40eff1e1853f29fe}, + {0xf7549530e188c128, 0xd12bee59e68ef47d}, + {0x9a94dd3e8cf578b9, 0x82bb74f8301958cf}, + {0xc13a148e3032d6e7, 0xe36a52363c1faf02}, + {0xf18899b1bc3f8ca1, 0xdc44e6c3cb279ac2}, + {0x96f5600f15a7b7e5, 0x29ab103a5ef8c0ba}, + {0xbcb2b812db11a5de, 0x7415d448f6b6f0e8}, + {0xebdf661791d60f56, 0x111b495b3464ad22}, + {0x936b9fcebb25c995, 0xcab10dd900beec35}, + {0xb84687c269ef3bfb, 0x3d5d514f40eea743}, + {0xe65829b3046b0afa, 0x0cb4a5a3112a5113}, + {0x8ff71a0fe2c2e6dc, 0x47f0e785eaba72ac}, + {0xb3f4e093db73a093, 0x59ed216765690f57}, + {0xe0f218b8d25088b8, 0x306869c13ec3532d}, + {0x8c974f7383725573, 0x1e414218c73a13fc}, + {0xafbd2350644eeacf, 0xe5d1929ef90898fb}, + {0xdbac6c247d62a583, 0xdf45f746b74abf3a}, + {0x894bc396ce5da772, 0x6b8bba8c328eb784}, + {0xab9eb47c81f5114f, 0x066ea92f3f326565}, + {0xd686619ba27255a2, 0xc80a537b0efefebe}, + {0x8613fd0145877585, 0xbd06742ce95f5f37}, + {0xa798fc4196e952e7, 0x2c48113823b73705}, + {0xd17f3b51fca3a7a0, 0xf75a15862ca504c6}, + {0x82ef85133de648c4, 0x9a984d73dbe722fc}, + {0xa3ab66580d5fdaf5, 0xc13e60d0d2e0ebbb}, + {0xcc963fee10b7d1b3, 0x318df905079926a9}, + {0xffbbcfe994e5c61f, 0xfdf17746497f7053}, + {0x9fd561f1fd0f9bd3, 0xfeb6ea8bedefa634}, + {0xc7caba6e7c5382c8, 0xfe64a52ee96b8fc1}, + {0xf9bd690a1b68637b, 0x3dfdce7aa3c673b1}, + {0x9c1661a651213e2d, 0x06bea10ca65c084f}, + {0xc31bfa0fe5698db8, 0x486e494fcff30a63}, + {0xf3e2f893dec3f126, 0x5a89dba3c3efccfb}, + {0x986ddb5c6b3a76b7, 0xf89629465a75e01d}, + {0xbe89523386091465, 0xf6bbb397f1135824}, + {0xee2ba6c0678b597f, 0x746aa07ded582e2d}, + {0x94db483840b717ef, 0xa8c2a44eb4571cdd}, + {0xba121a4650e4ddeb, 0x92f34d62616ce414}, + {0xe896a0d7e51e1566, 0x77b020baf9c81d18}, + {0x915e2486ef32cd60, 0x0ace1474dc1d122f}, + {0xb5b5ada8aaff80b8, 0x0d819992132456bb}, + {0xe3231912d5bf60e6, 0x10e1fff697ed6c6a}, + {0x8df5efabc5979c8f, 0xca8d3ffa1ef463c2}, + {0xb1736b96b6fd83b3, 0xbd308ff8a6b17cb3}, + {0xddd0467c64bce4a0, 0xac7cb3f6d05ddbdf}, + {0x8aa22c0dbef60ee4, 0x6bcdf07a423aa96c}, + {0xad4ab7112eb3929d, 0x86c16c98d2c953c7}, + {0xd89d64d57a607744, 0xe871c7bf077ba8b8}, + {0x87625f056c7c4a8b, 0x11471cd764ad4973}, + {0xa93af6c6c79b5d2d, 0xd598e40d3dd89bd0}, + {0xd389b47879823479, 0x4aff1d108d4ec2c4}, + {0x843610cb4bf160cb, 0xcedf722a585139bb}, + {0xa54394fe1eedb8fe, 0xc2974eb4ee658829}, + {0xce947a3da6a9273e, 0x733d226229feea33}, + {0x811ccc668829b887, 0x0806357d5a3f5260}, + {0xa163ff802a3426a8, 0xca07c2dcb0cf26f8}, + {0xc9bcff6034c13052, 0xfc89b393dd02f0b6}, + {0xfc2c3f3841f17c67, 0xbbac2078d443ace3}, + {0x9d9ba7832936edc0, 0xd54b944b84aa4c0e}, + {0xc5029163f384a931, 0x0a9e795e65d4df12}, + {0xf64335bcf065d37d, 0x4d4617b5ff4a16d6}, + {0x99ea0196163fa42e, 0x504bced1bf8e4e46}, + {0xc06481fb9bcf8d39, 0xe45ec2862f71e1d7}, + {0xf07da27a82c37088, 0x5d767327bb4e5a4d}, + {0x964e858c91ba2655, 0x3a6a07f8d510f870}, + {0xbbe226efb628afea, 0x890489f70a55368c}, + {0xeadab0aba3b2dbe5, 0x2b45ac74ccea842f}, + {0x92c8ae6b464fc96f, 0x3b0b8bc90012929e}, + {0xb77ada0617e3bbcb, 0x09ce6ebb40173745}, + {0xe55990879ddcaabd, 0xcc420a6a101d0516}, + {0x8f57fa54c2a9eab6, 0x9fa946824a12232e}, + {0xb32df8e9f3546564, 0x47939822dc96abfa}, + {0xdff9772470297ebd, 0x59787e2b93bc56f8}, + {0x8bfbea76c619ef36, 0x57eb4edb3c55b65b}, + {0xaefae51477a06b03, 0xede622920b6b23f2}, + {0xdab99e59958885c4, 0xe95fab368e45ecee}, + {0x88b402f7fd75539b, 0x11dbcb0218ebb415}, + {0xaae103b5fcd2a881, 0xd652bdc29f26a11a}, + {0xd59944a37c0752a2, 0x4be76d3346f04960}, + {0x857fcae62d8493a5, 0x6f70a4400c562ddc}, + {0xa6dfbd9fb8e5b88e, 0xcb4ccd500f6bb953}, + {0xd097ad07a71f26b2, 0x7e2000a41346a7a8}, + {0x825ecc24c873782f, 0x8ed400668c0c28c9}, + {0xa2f67f2dfa90563b, 0x728900802f0f32fb}, + {0xcbb41ef979346bca, 0x4f2b40a03ad2ffba}, + {0xfea126b7d78186bc, 0xe2f610c84987bfa9}, + {0x9f24b832e6b0f436, 0x0dd9ca7d2df4d7ca}, + {0xc6ede63fa05d3143, 0x91503d1c79720dbc}, + {0xf8a95fcf88747d94, 0x75a44c6397ce912b}, + {0x9b69dbe1b548ce7c, 0xc986afbe3ee11abb}, + {0xc24452da229b021b, 0xfbe85badce996169}, + {0xf2d56790ab41c2a2, 0xfae27299423fb9c4}, + {0x97c560ba6b0919a5, 0xdccd879fc967d41b}, + {0xbdb6b8e905cb600f, 0x5400e987bbc1c921}, + {0xed246723473e3813, 0x290123e9aab23b69}, + {0x9436c0760c86e30b, 0xf9a0b6720aaf6522}, + {0xb94470938fa89bce, 0xf808e40e8d5b3e6a}, + {0xe7958cb87392c2c2, 0xb60b1d1230b20e05}, + {0x90bd77f3483bb9b9, 0xb1c6f22b5e6f48c3}, + {0xb4ecd5f01a4aa828, 0x1e38aeb6360b1af4}, + {0xe2280b6c20dd5232, 0x25c6da63c38de1b1}, + {0x8d590723948a535f, 0x579c487e5a38ad0f}, + {0xb0af48ec79ace837, 0x2d835a9df0c6d852}, + {0xdcdb1b2798182244, 0xf8e431456cf88e66}, + {0x8a08f0f8bf0f156b, 0x1b8e9ecb641b5900}, + {0xac8b2d36eed2dac5, 0xe272467e3d222f40}, + {0xd7adf884aa879177, 0x5b0ed81dcc6abb10}, + {0x86ccbb52ea94baea, 0x98e947129fc2b4ea}, + {0xa87fea27a539e9a5, 0x3f2398d747b36225}, + {0xd29fe4b18e88640e, 0x8eec7f0d19a03aae}, + {0x83a3eeeef9153e89, 0x1953cf68300424ad}, + {0xa48ceaaab75a8e2b, 0x5fa8c3423c052dd8}, + {0xcdb02555653131b6, 0x3792f412cb06794e}, + {0x808e17555f3ebf11, 0xe2bbd88bbee40bd1}, + {0xa0b19d2ab70e6ed6, 0x5b6aceaeae9d0ec5}, + {0xc8de047564d20a8b, 0xf245825a5a445276}, + {0xfb158592be068d2e, 0xeed6e2f0f0d56713}, + {0x9ced737bb6c4183d, 0x55464dd69685606c}, + {0xc428d05aa4751e4c, 0xaa97e14c3c26b887}, + {0xf53304714d9265df, 0xd53dd99f4b3066a9}, + {0x993fe2c6d07b7fab, 0xe546a8038efe402a}, + {0xbf8fdb78849a5f96, 0xde98520472bdd034}, + {0xef73d256a5c0f77c, 0x963e66858f6d4441}, + {0x95a8637627989aad, 0xdde7001379a44aa9}, + {0xbb127c53b17ec159, 0x5560c018580d5d53}, + {0xe9d71b689dde71af, 0xaab8f01e6e10b4a7}, + {0x9226712162ab070d, 0xcab3961304ca70e9}, + {0xb6b00d69bb55c8d1, 0x3d607b97c5fd0d23}, + {0xe45c10c42a2b3b05, 0x8cb89a7db77c506b}, + {0x8eb98a7a9a5b04e3, 0x77f3608e92adb243}, + {0xb267ed1940f1c61c, 0x55f038b237591ed4}, + {0xdf01e85f912e37a3, 0x6b6c46dec52f6689}, + {0x8b61313bbabce2c6, 0x2323ac4b3b3da016}, + {0xae397d8aa96c1b77, 0xabec975e0a0d081b}, + {0xd9c7dced53c72255, 0x96e7bd358c904a22}, + {0x881cea14545c7575, 0x7e50d64177da2e55}, + {0xaa242499697392d2, 0xdde50bd1d5d0b9ea}, + {0xd4ad2dbfc3d07787, 0x955e4ec64b44e865}, + {0x84ec3c97da624ab4, 0xbd5af13bef0b113f}, + {0xa6274bbdd0fadd61, 0xecb1ad8aeacdd58f}, + {0xcfb11ead453994ba, 0x67de18eda5814af3}, + {0x81ceb32c4b43fcf4, 0x80eacf948770ced8}, + {0xa2425ff75e14fc31, 0xa1258379a94d028e}, + {0xcad2f7f5359a3b3e, 0x096ee45813a04331}, + {0xfd87b5f28300ca0d, 0x8bca9d6e188853fd}, + {0x9e74d1b791e07e48, 0x775ea264cf55347e}, + {0xc612062576589dda, 0x95364afe032a819e}, + {0xf79687aed3eec551, 0x3a83ddbd83f52205}, + {0x9abe14cd44753b52, 0xc4926a9672793543}, + {0xc16d9a0095928a27, 0x75b7053c0f178294}, + {0xf1c90080baf72cb1, 0x5324c68b12dd6339}, + {0x971da05074da7bee, 0xd3f6fc16ebca5e04}, + {0xbce5086492111aea, 0x88f4bb1ca6bcf585}, + 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0x7f1839a741a14d0d}, + {0xd31045a8341ca07c, 0x1ede48111209a050}, + {0x83ea2b892091e44d, 0x934aed0aab460432}, + {0xa4e4b66b68b65d60, 0xf81da84d5617853f}, + {0xce1de40642e3f4b9, 0x36251260ab9d668e}, + {0x80d2ae83e9ce78f3, 0xc1d72b7c6b426019}, + {0xa1075a24e4421730, 0xb24cf65b8612f81f}, + {0xc94930ae1d529cfc, 0xdee033f26797b627}, + {0xfb9b7cd9a4a7443c, 0x169840ef017da3b1}, + {0x9d412e0806e88aa5, 0x8e1f289560ee864e}, + {0xc491798a08a2ad4e, 0xf1a6f2bab92a27e2}, + {0xf5b5d7ec8acb58a2, 0xae10af696774b1db}, + {0x9991a6f3d6bf1765, 0xacca6da1e0a8ef29}, + {0xbff610b0cc6edd3f, 0x17fd090a58d32af3}, + {0xeff394dcff8a948e, 0xddfc4b4cef07f5b0}, + {0x95f83d0a1fb69cd9, 0x4abdaf101564f98e}, + {0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f1}, + {0xea53df5fd18d5513, 0x84c86189216dc5ed}, + {0x92746b9be2f8552c, 0x32fd3cf5b4e49bb4}, + {0xb7118682dbb66a77, 0x3fbc8c33221dc2a1}, + {0xe4d5e82392a40515, 0x0fabaf3feaa5334a}, + {0x8f05b1163ba6832d, 0x29cb4d87f2a7400e}, + {0xb2c71d5bca9023f8, 0x743e20e9ef511012}, + {0xdf78e4b2bd342cf6, 0x914da9246b255416}, + {0x8bab8eefb6409c1a, 0x1ad089b6c2f7548e}, + {0xae9672aba3d0c320, 0xa184ac2473b529b1}, + {0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741e}, + {0x8865899617fb1871, 0x7e2fa67c7a658892}, + {0xaa7eebfb9df9de8d, 0xddbb901b98feeab7}, + {0xd51ea6fa85785631, 0x552a74227f3ea565}, + {0x8533285c936b35de, 0xd53a88958f87275f}, + {0xa67ff273b8460356, 0x8a892abaf368f137}, + {0xd01fef10a657842c, 0x2d2b7569b0432d85}, + {0x8213f56a67f6b29b, 0x9c3b29620e29fc73}, + {0xa298f2c501f45f42, 0x8349f3ba91b47b8f}, + {0xcb3f2f7642717713, 0x241c70a936219a73}, + {0xfe0efb53d30dd4d7, 0xed238cd383aa0110}, + {0x9ec95d1463e8a506, 0xf4363804324a40aa}, + {0xc67bb4597ce2ce48, 0xb143c6053edcd0d5}, + {0xf81aa16fdc1b81da, 0xdd94b7868e94050a}, + {0x9b10a4e5e9913128, 0xca7cf2b4191c8326}, + {0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f0}, + {0xf24a01a73cf2dccf, 0xbc633b39673c8cec}, + {0x976e41088617ca01, 0xd5be0503e085d813}, + {0xbd49d14aa79dbc82, 0x4b2d8644d8a74e18}, + {0xec9c459d51852ba2, 0xddf8e7d60ed1219e}, + {0x93e1ab8252f33b45, 0xcabb90e5c942b503}, + {0xb8da1662e7b00a17, 0x3d6a751f3b936243}, + {0xe7109bfba19c0c9d, 0x0cc512670a783ad4}, + {0x906a617d450187e2, 0x27fb2b80668b24c5}, + {0xb484f9dc9641e9da, 0xb1f9f660802dedf6}, + {0xe1a63853bbd26451, 0x5e7873f8a0396973}, + {0x8d07e33455637eb2, 0xdb0b487b6423e1e8}, + {0xb049dc016abc5e5f, 0x91ce1a9a3d2cda62}, + {0xdc5c5301c56b75f7, 0x7641a140cc7810fb}, + {0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9d}, + {0xac2820d9623bf429, 0x546345fa9fbdcd44}, + {0xd732290fbacaf133, 0xa97c177947ad4095}, + {0x867f59a9d4bed6c0, 0x49ed8eabcccc485d}, + {0xa81f301449ee8c70, 0x5c68f256bfff5a74}, + {0xd226fc195c6a2f8c, 0x73832eec6fff3111}, + {0x83585d8fd9c25db7, 0xc831fd53c5ff7eab}, + {0xa42e74f3d032f525, 0xba3e7ca8b77f5e55}, + {0xcd3a1230c43fb26f, 0x28ce1bd2e55f35eb}, + {0x80444b5e7aa7cf85, 0x7980d163cf5b81b3}, + {0xa0555e361951c366, 0xd7e105bcc332621f}, + {0xc86ab5c39fa63440, 0x8dd9472bf3fefaa7}, + {0xfa856334878fc150, 0xb14f98f6f0feb951}, + {0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d3}, + {0xc3b8358109e84f07, 0x0a862f80ec4700c8}, + {0xf4a642e14c6262c8, 0xcd27bb612758c0fa}, + {0x98e7e9cccfbd7dbd, 0x8038d51cb897789c}, + {0xbf21e44003acdd2c, 0xe0470a63e6bd56c3}, + {0xeeea5d5004981478, 0x1858ccfce06cac74}, + {0x95527a5202df0ccb, 0x0f37801e0c43ebc8}, + {0xbaa718e68396cffd, 0xd30560258f54e6ba}, + {0xe950df20247c83fd, 0x47c6b82ef32a2069}, + {0x91d28b7416cdd27e, 0x4cdc331d57fa5441}, + {0xb6472e511c81471d, 0xe0133fe4adf8e952}, + {0xe3d8f9e563a198e5, 0x58180fddd97723a6}, + {0x8e679c2f5e44ff8f, 0x570f09eaa7ea7648}, + {0xb201833b35d63f73, 0x2cd2cc6551e513da}, + {0xde81e40a034bcf4f, 0xf8077f7ea65e58d1}, + {0x8b112e86420f6191, 0xfb04afaf27faf782}, + {0xadd57a27d29339f6, 0x79c5db9af1f9b563}, + {0xd94ad8b1c7380874, 0x18375281ae7822bc}, + {0x87cec76f1c830548, 0x8f2293910d0b15b5}, + {0xa9c2794ae3a3c69a, 0xb2eb3875504ddb22}, + {0xd433179d9c8cb841, 0x5fa60692a46151eb}, + {0x849feec281d7f328, 0xdbc7c41ba6bcd333}, + {0xa5c7ea73224deff3, 0x12b9b522906c0800}, + {0xcf39e50feae16bef, 0xd768226b34870a00}, + {0x81842f29f2cce375, 0xe6a1158300d46640}, + {0xa1e53af46f801c53, 0x60495ae3c1097fd0}, + {0xca5e89b18b602368, 0x385bb19cb14bdfc4}, + {0xfcf62c1dee382c42, 0x46729e03dd9ed7b5}, + {0x9e19db92b4e31ba9, 0x6c07a2c26a8346d1}, + {0xc5a05277621be293, 0xc7098b7305241885}, + {0xf70867153aa2db38, 0xb8cbee4fc66d1ea7} +#else + {0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7b}, + {0xce5d73ff402d98e3, 0xfb0a3d212dc81290}, + {0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481f}, + {0x86a8d39ef77164bc, 0xae5dff9c02033198}, + {0xd98ddaee19068c76, 0x3badd624dd9b0958}, + {0xafbd2350644eeacf, 0xe5d1929ef90898fb}, + {0x8df5efabc5979c8f, 0xca8d3ffa1ef463c2}, + {0xe55990879ddcaabd, 0xcc420a6a101d0516}, + {0xb94470938fa89bce, 0xf808e40e8d5b3e6a}, + {0x95a8637627989aad, 0xdde7001379a44aa9}, + {0xf1c90080baf72cb1, 0x5324c68b12dd6339}, + {0xc350000000000000, 0x0000000000000000}, + {0x9dc5ada82b70b59d, 0xf020000000000000}, + {0xfee50b7025c36a08, 0x02f236d04753d5b4}, + {0xcde6fd5e09abcf26, 0xed4c0226b55e6f86}, + {0xa6539930bf6bff45, 0x84db8346b786151c}, + {0x865b86925b9bc5c2, 0x0b8a2392ba45a9b2}, + {0xd910f7ff28069da4, 0x1b2ba1518094da04}, + {0xaf58416654a6babb, 0x387ac8d1970027b2}, + {0x8da471a9de737e24, 0x5ceaecfed289e5d2}, + {0xe4d5e82392a40515, 0x0fabaf3feaa5334a}, + {0xb8da1662e7b00a17, 0x3d6a751f3b936243}, + {0x95527a5202df0ccb, 0x0f37801e0c43ebc8} +#endif +}; + +#if !FMT_USE_FULL_CACHE_DRAGONBOX +template <typename T> +const uint64_t basic_data<T>::powers_of_5_64[] = { + 0x0000000000000001, 0x0000000000000005, 0x0000000000000019, + 0x000000000000007d, 0x0000000000000271, 0x0000000000000c35, + 0x0000000000003d09, 0x000000000001312d, 0x000000000005f5e1, + 0x00000000001dcd65, 0x00000000009502f9, 0x0000000002e90edd, + 0x000000000e8d4a51, 0x0000000048c27395, 0x000000016bcc41e9, + 0x000000071afd498d, 0x0000002386f26fc1, 0x000000b1a2bc2ec5, + 0x000003782dace9d9, 0x00001158e460913d, 0x000056bc75e2d631, + 0x0001b1ae4d6e2ef5, 0x000878678326eac9, 0x002a5a058fc295ed, + 0x00d3c21bcecceda1, 0x0422ca8b0a00a425, 0x14adf4b7320334b9}; + +template <typename T> +const uint32_t basic_data<T>::dragonbox_pow10_recovery_errors[] = { + 0x50001400, 0x54044100, 0x54014555, 0x55954415, 0x54115555, 0x00000001, + 0x50000000, 0x00104000, 0x54010004, 0x05004001, 0x55555544, 0x41545555, + 0x54040551, 0x15445545, 0x51555514, 0x10000015, 0x00101100, 0x01100015, + 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x04450514, 0x45414110, + 0x55555145, 0x50544050, 0x15040155, 0x11054140, 0x50111514, 0x11451454, + 0x00400541, 0x00000000, 0x55555450, 0x10056551, 0x10054011, 0x55551014, + 0x69514555, 0x05151109, 0x00155555}; +#endif + +template <typename T> +const char basic_data<T>::foreground_color[] = "\x1b[38;2;"; +template <typename T> +const char basic_data<T>::background_color[] = "\x1b[48;2;"; +template <typename T> const char basic_data<T>::reset_color[] = "\x1b[0m"; +template <typename T> const wchar_t basic_data<T>::wreset_color[] = L"\x1b[0m"; +template <typename T> const char basic_data<T>::signs[] = {0, '-', '+', ' '}; +template <typename T> +const char basic_data<T>::left_padding_shifts[] = {31, 31, 0, 1, 0}; +template <typename T> +const char basic_data<T>::right_padding_shifts[] = {0, 31, 0, 1, 0}; + +template <typename T> struct bits { + static FMT_CONSTEXPR_DECL const int value = + static_cast<int>(sizeof(T) * std::numeric_limits<unsigned char>::digits); +}; + +class fp; +template <int SHIFT = 0> fp normalize(fp value); + +// Lower (upper) boundary is a value half way between a floating-point value +// and its predecessor (successor). Boundaries have the same exponent as the +// value so only significands are stored. +struct boundaries { + uint64_t lower; + uint64_t upper; +}; + +// A handmade floating-point number f * pow(2, e). +class fp { + private: + using significand_type = uint64_t; + + template <typename Float> + using is_supported_float = bool_constant<sizeof(Float) == sizeof(uint64_t) || + sizeof(Float) == sizeof(uint32_t)>; + + public: + significand_type f; + int e; + + // All sizes are in bits. + // Subtract 1 to account for an implicit most significant bit in the + // normalized form. + static FMT_CONSTEXPR_DECL const int double_significand_size = + std::numeric_limits<double>::digits - 1; + static FMT_CONSTEXPR_DECL const uint64_t implicit_bit = + 1ULL << double_significand_size; + static FMT_CONSTEXPR_DECL const int significand_size = + bits<significand_type>::value; + + fp() : f(0), e(0) {} + fp(uint64_t f_val, int e_val) : f(f_val), e(e_val) {} + + // Constructs fp from an IEEE754 double. It is a template to prevent compile + // errors on platforms where double is not IEEE754. + template <typename Double> explicit fp(Double d) { assign(d); } + + // Assigns d to this and return true iff predecessor is closer than successor. + template <typename Float, FMT_ENABLE_IF(is_supported_float<Float>::value)> + bool assign(Float d) { + // Assume float is in the format [sign][exponent][significand]. + using limits = std::numeric_limits<Float>; + const int float_significand_size = limits::digits - 1; + const int exponent_size = + bits<Float>::value - float_significand_size - 1; // -1 for sign + const uint64_t float_implicit_bit = 1ULL << float_significand_size; + const uint64_t significand_mask = float_implicit_bit - 1; + const uint64_t exponent_mask = (~0ULL >> 1) & ~significand_mask; + const int exponent_bias = (1 << exponent_size) - limits::max_exponent - 1; + constexpr bool is_double = sizeof(Float) == sizeof(uint64_t); + auto u = bit_cast<conditional_t<is_double, uint64_t, uint32_t>>(d); + f = u & significand_mask; + int biased_e = + static_cast<int>((u & exponent_mask) >> float_significand_size); + // Predecessor is closer if d is a normalized power of 2 (f == 0) other than + // the smallest normalized number (biased_e > 1). + bool is_predecessor_closer = f == 0 && biased_e > 1; + if (biased_e != 0) + f += float_implicit_bit; + else + biased_e = 1; // Subnormals use biased exponent 1 (min exponent). + e = biased_e - exponent_bias - float_significand_size; + return is_predecessor_closer; + } + + template <typename Float, FMT_ENABLE_IF(!is_supported_float<Float>::value)> + bool assign(Float) { + *this = fp(); + return false; + } +}; + +// Normalizes the value converted from double and multiplied by (1 << SHIFT). +template <int SHIFT> fp normalize(fp value) { + // Handle subnormals. + const auto shifted_implicit_bit = fp::implicit_bit << SHIFT; + while ((value.f & shifted_implicit_bit) == 0) { + value.f <<= 1; + --value.e; + } + // Subtract 1 to account for hidden bit. + const auto offset = + fp::significand_size - fp::double_significand_size - SHIFT - 1; + value.f <<= offset; + value.e -= offset; + return value; +} + +inline bool operator==(fp x, fp y) { return x.f == y.f && x.e == y.e; } + +// Computes lhs * rhs / pow(2, 64) rounded to nearest with half-up tie breaking. +inline uint64_t multiply(uint64_t lhs, uint64_t rhs) { +#if FMT_USE_INT128 + auto product = static_cast<__uint128_t>(lhs) * rhs; + auto f = static_cast<uint64_t>(product >> 64); + return (static_cast<uint64_t>(product) & (1ULL << 63)) != 0 ? f + 1 : f; +#else + // Multiply 32-bit parts of significands. + uint64_t mask = (1ULL << 32) - 1; + uint64_t a = lhs >> 32, b = lhs & mask; + uint64_t c = rhs >> 32, d = rhs & mask; + uint64_t ac = a * c, bc = b * c, ad = a * d, bd = b * d; + // Compute mid 64-bit of result and round. + uint64_t mid = (bd >> 32) + (ad & mask) + (bc & mask) + (1U << 31); + return ac + (ad >> 32) + (bc >> 32) + (mid >> 32); +#endif +} + +inline fp operator*(fp x, fp y) { return {multiply(x.f, y.f), x.e + y.e + 64}; } + +// Returns a cached power of 10 `c_k = c_k.f * pow(2, c_k.e)` such that its +// (binary) exponent satisfies `min_exponent <= c_k.e <= min_exponent + 28`. +inline fp get_cached_power(int min_exponent, int& pow10_exponent) { + const int shift = 32; + const auto significand = static_cast<int64_t>(data::log10_2_significand); + int index = static_cast<int>( + ((min_exponent + fp::significand_size - 1) * (significand >> shift) + + ((int64_t(1) << shift) - 1)) // ceil + >> 32 // arithmetic shift + ); + // Decimal exponent of the first (smallest) cached power of 10. + const int first_dec_exp = -348; + // Difference between 2 consecutive decimal exponents in cached powers of 10. + const int dec_exp_step = 8; + index = (index - first_dec_exp - 1) / dec_exp_step + 1; + pow10_exponent = first_dec_exp + index * dec_exp_step; + return {data::grisu_pow10_significands[index], + data::grisu_pow10_exponents[index]}; +} + +// A simple accumulator to hold the sums of terms in bigint::square if uint128_t +// is not available. +struct accumulator { + uint64_t lower; + uint64_t upper; + + accumulator() : lower(0), upper(0) {} + explicit operator uint32_t() const { return static_cast<uint32_t>(lower); } + + void operator+=(uint64_t n) { + lower += n; + if (lower < n) ++upper; + } + void operator>>=(int shift) { + assert(shift == 32); + (void)shift; + lower = (upper << 32) | (lower >> 32); + upper >>= 32; + } +}; + +class bigint { + private: + // A bigint is stored as an array of bigits (big digits), with bigit at index + // 0 being the least significant one. + using bigit = uint32_t; + using double_bigit = uint64_t; + enum { bigits_capacity = 32 }; + basic_memory_buffer<bigit, bigits_capacity> bigits_; + int exp_; + + bigit operator[](int index) const { return bigits_[to_unsigned(index)]; } + bigit& operator[](int index) { return bigits_[to_unsigned(index)]; } + + static FMT_CONSTEXPR_DECL const int bigit_bits = bits<bigit>::value; + + friend struct formatter<bigint>; + + void subtract_bigits(int index, bigit other, bigit& borrow) { + auto result = static_cast<double_bigit>((*this)[index]) - other - borrow; + (*this)[index] = static_cast<bigit>(result); + borrow = static_cast<bigit>(result >> (bigit_bits * 2 - 1)); + } + + void remove_leading_zeros() { + int num_bigits = static_cast<int>(bigits_.size()) - 1; + while (num_bigits > 0 && (*this)[num_bigits] == 0) --num_bigits; + bigits_.resize(to_unsigned(num_bigits + 1)); + } + + // Computes *this -= other assuming aligned bigints and *this >= other. + void subtract_aligned(const bigint& other) { + FMT_ASSERT(other.exp_ >= exp_, "unaligned bigints"); + FMT_ASSERT(compare(*this, other) >= 0, ""); + bigit borrow = 0; + int i = other.exp_ - exp_; + for (size_t j = 0, n = other.bigits_.size(); j != n; ++i, ++j) + subtract_bigits(i, other.bigits_[j], borrow); + while (borrow > 0) subtract_bigits(i, 0, borrow); + remove_leading_zeros(); + } + + void multiply(uint32_t value) { + const double_bigit wide_value = value; + bigit carry = 0; + for (size_t i = 0, n = bigits_.size(); i < n; ++i) { + double_bigit result = bigits_[i] * wide_value + carry; + bigits_[i] = static_cast<bigit>(result); + carry = static_cast<bigit>(result >> bigit_bits); + } + if (carry != 0) bigits_.push_back(carry); + } + + void multiply(uint64_t value) { + const bigit mask = ~bigit(0); + const double_bigit lower = value & mask; + const double_bigit upper = value >> bigit_bits; + double_bigit carry = 0; + for (size_t i = 0, n = bigits_.size(); i < n; ++i) { + double_bigit result = bigits_[i] * lower + (carry & mask); + carry = + bigits_[i] * upper + (result >> bigit_bits) + (carry >> bigit_bits); + bigits_[i] = static_cast<bigit>(result); + } + while (carry != 0) { + bigits_.push_back(carry & mask); + carry >>= bigit_bits; + } + } + + public: + bigint() : exp_(0) {} + explicit bigint(uint64_t n) { assign(n); } + ~bigint() { assert(bigits_.capacity() <= bigits_capacity); } + + bigint(const bigint&) = delete; + void operator=(const bigint&) = delete; + + void assign(const bigint& other) { + auto size = other.bigits_.size(); + bigits_.resize(size); + auto data = other.bigits_.data(); + std::copy(data, data + size, make_checked(bigits_.data(), size)); + exp_ = other.exp_; + } + + void assign(uint64_t n) { + size_t num_bigits = 0; + do { + bigits_[num_bigits++] = n & ~bigit(0); + n >>= bigit_bits; + } while (n != 0); + bigits_.resize(num_bigits); + exp_ = 0; + } + + int num_bigits() const { return static_cast<int>(bigits_.size()) + exp_; } + + FMT_NOINLINE bigint& operator<<=(int shift) { + assert(shift >= 0); + exp_ += shift / bigit_bits; + shift %= bigit_bits; + if (shift == 0) return *this; + bigit carry = 0; + for (size_t i = 0, n = bigits_.size(); i < n; ++i) { + bigit c = bigits_[i] >> (bigit_bits - shift); + bigits_[i] = (bigits_[i] << shift) + carry; + carry = c; + } + if (carry != 0) bigits_.push_back(carry); + return *this; + } + + template <typename Int> bigint& operator*=(Int value) { + FMT_ASSERT(value > 0, ""); + multiply(uint32_or_64_or_128_t<Int>(value)); + return *this; + } + + friend int compare(const bigint& lhs, const bigint& rhs) { + int num_lhs_bigits = lhs.num_bigits(), num_rhs_bigits = rhs.num_bigits(); + if (num_lhs_bigits != num_rhs_bigits) + return num_lhs_bigits > num_rhs_bigits ? 1 : -1; + int i = static_cast<int>(lhs.bigits_.size()) - 1; + int j = static_cast<int>(rhs.bigits_.size()) - 1; + int end = i - j; + if (end < 0) end = 0; + for (; i >= end; --i, --j) { + bigit lhs_bigit = lhs[i], rhs_bigit = rhs[j]; + if (lhs_bigit != rhs_bigit) return lhs_bigit > rhs_bigit ? 1 : -1; + } + if (i != j) return i > j ? 1 : -1; + return 0; + } + + // Returns compare(lhs1 + lhs2, rhs). + friend int add_compare(const bigint& lhs1, const bigint& lhs2, + const bigint& rhs) { + int max_lhs_bigits = (std::max)(lhs1.num_bigits(), lhs2.num_bigits()); + int num_rhs_bigits = rhs.num_bigits(); + if (max_lhs_bigits + 1 < num_rhs_bigits) return -1; + if (max_lhs_bigits > num_rhs_bigits) return 1; + auto get_bigit = [](const bigint& n, int i) -> bigit { + return i >= n.exp_ && i < n.num_bigits() ? n[i - n.exp_] : 0; + }; + double_bigit borrow = 0; + int min_exp = (std::min)((std::min)(lhs1.exp_, lhs2.exp_), rhs.exp_); + for (int i = num_rhs_bigits - 1; i >= min_exp; --i) { + double_bigit sum = + static_cast<double_bigit>(get_bigit(lhs1, i)) + get_bigit(lhs2, i); + bigit rhs_bigit = get_bigit(rhs, i); + if (sum > rhs_bigit + borrow) return 1; + borrow = rhs_bigit + borrow - sum; + if (borrow > 1) return -1; + borrow <<= bigit_bits; + } + return borrow != 0 ? -1 : 0; + } + + // Assigns pow(10, exp) to this bigint. + void assign_pow10(int exp) { + assert(exp >= 0); + if (exp == 0) return assign(1); + // Find the top bit. + int bitmask = 1; + while (exp >= bitmask) bitmask <<= 1; + bitmask >>= 1; + // pow(10, exp) = pow(5, exp) * pow(2, exp). First compute pow(5, exp) by + // repeated squaring and multiplication. + assign(5); + bitmask >>= 1; + while (bitmask != 0) { + square(); + if ((exp & bitmask) != 0) *this *= 5; + bitmask >>= 1; + } + *this <<= exp; // Multiply by pow(2, exp) by shifting. + } + + void square() { + basic_memory_buffer<bigit, bigits_capacity> n(std::move(bigits_)); + int num_bigits = static_cast<int>(bigits_.size()); + int num_result_bigits = 2 * num_bigits; + bigits_.resize(to_unsigned(num_result_bigits)); + using accumulator_t = conditional_t<FMT_USE_INT128, uint128_t, accumulator>; + auto sum = accumulator_t(); + for (int bigit_index = 0; bigit_index < num_bigits; ++bigit_index) { + // Compute bigit at position bigit_index of the result by adding + // cross-product terms n[i] * n[j] such that i + j == bigit_index. + for (int i = 0, j = bigit_index; j >= 0; ++i, --j) { + // Most terms are multiplied twice which can be optimized in the future. + sum += static_cast<double_bigit>(n[i]) * n[j]; + } + (*this)[bigit_index] = static_cast<bigit>(sum); + sum >>= bits<bigit>::value; // Compute the carry. + } + // Do the same for the top half. + for (int bigit_index = num_bigits; bigit_index < num_result_bigits; + ++bigit_index) { + for (int j = num_bigits - 1, i = bigit_index - j; i < num_bigits;) + sum += static_cast<double_bigit>(n[i++]) * n[j--]; + (*this)[bigit_index] = static_cast<bigit>(sum); + sum >>= bits<bigit>::value; + } + --num_result_bigits; + remove_leading_zeros(); + exp_ *= 2; + } + + // If this bigint has a bigger exponent than other, adds trailing zero to make + // exponents equal. This simplifies some operations such as subtraction. + void align(const bigint& other) { + int exp_difference = exp_ - other.exp_; + if (exp_difference <= 0) return; + int num_bigits = static_cast<int>(bigits_.size()); + bigits_.resize(to_unsigned(num_bigits + exp_difference)); + for (int i = num_bigits - 1, j = i + exp_difference; i >= 0; --i, --j) + bigits_[j] = bigits_[i]; + std::uninitialized_fill_n(bigits_.data(), exp_difference, 0); + exp_ -= exp_difference; + } + + // Divides this bignum by divisor, assigning the remainder to this and + // returning the quotient. + int divmod_assign(const bigint& divisor) { + FMT_ASSERT(this != &divisor, ""); + if (compare(*this, divisor) < 0) return 0; + FMT_ASSERT(divisor.bigits_[divisor.bigits_.size() - 1u] != 0, ""); + align(divisor); + int quotient = 0; + do { + subtract_aligned(divisor); + ++quotient; + } while (compare(*this, divisor) >= 0); + return quotient; + } +}; + +enum class round_direction { unknown, up, down }; + +// Given the divisor (normally a power of 10), the remainder = v % divisor for +// some number v and the error, returns whether v should be rounded up, down, or +// whether the rounding direction can't be determined due to error. +// error should be less than divisor / 2. +inline round_direction get_round_direction(uint64_t divisor, uint64_t remainder, + uint64_t error) { + FMT_ASSERT(remainder < divisor, ""); // divisor - remainder won't overflow. + FMT_ASSERT(error < divisor, ""); // divisor - error won't overflow. + FMT_ASSERT(error < divisor - error, ""); // error * 2 won't overflow. + // Round down if (remainder + error) * 2 <= divisor. + if (remainder <= divisor - remainder && error * 2 <= divisor - remainder * 2) + return round_direction::down; + // Round up if (remainder - error) * 2 >= divisor. + if (remainder >= error && + remainder - error >= divisor - (remainder - error)) { + return round_direction::up; + } + return round_direction::unknown; +} + +namespace digits { +enum result { + more, // Generate more digits. + done, // Done generating digits. + error // Digit generation cancelled due to an error. +}; +} + +// Generates output using the Grisu digit-gen algorithm. +// error: the size of the region (lower, upper) outside of which numbers +// definitely do not round to value (Delta in Grisu3). +template <typename Handler> +FMT_ALWAYS_INLINE digits::result grisu_gen_digits(fp value, uint64_t error, + int& exp, Handler& handler) { + const fp one(1ULL << -value.e, value.e); + // The integral part of scaled value (p1 in Grisu) = value / one. It cannot be + // zero because it contains a product of two 64-bit numbers with MSB set (due + // to normalization) - 1, shifted right by at most 60 bits. + auto integral = static_cast<uint32_t>(value.f >> -one.e); + FMT_ASSERT(integral != 0, ""); + FMT_ASSERT(integral == value.f >> -one.e, ""); + // The fractional part of scaled value (p2 in Grisu) c = value % one. + uint64_t fractional = value.f & (one.f - 1); + exp = count_digits(integral); // kappa in Grisu. + // Divide by 10 to prevent overflow. + auto result = handler.on_start(data::powers_of_10_64[exp - 1] << -one.e, + value.f / 10, error * 10, exp); + if (result != digits::more) return result; + // Generate digits for the integral part. This can produce up to 10 digits. + do { + uint32_t digit = 0; + auto divmod_integral = [&](uint32_t divisor) { + digit = integral / divisor; + integral %= divisor; + }; + // This optimization by Milo Yip reduces the number of integer divisions by + // one per iteration. + switch (exp) { + case 10: + divmod_integral(1000000000); + break; + case 9: + divmod_integral(100000000); + break; + case 8: + divmod_integral(10000000); + break; + case 7: + divmod_integral(1000000); + break; + case 6: + divmod_integral(100000); + break; + case 5: + divmod_integral(10000); + break; + case 4: + divmod_integral(1000); + break; + case 3: + divmod_integral(100); + break; + case 2: + divmod_integral(10); + break; + case 1: + digit = integral; + integral = 0; + break; + default: + FMT_ASSERT(false, "invalid number of digits"); + } + --exp; + auto remainder = (static_cast<uint64_t>(integral) << -one.e) + fractional; + result = handler.on_digit(static_cast<char>('0' + digit), + data::powers_of_10_64[exp] << -one.e, remainder, + error, exp, true); + if (result != digits::more) return result; + } while (exp > 0); + // Generate digits for the fractional part. + for (;;) { + fractional *= 10; + error *= 10; + char digit = static_cast<char>('0' + (fractional >> -one.e)); + fractional &= one.f - 1; + --exp; + result = handler.on_digit(digit, one.f, fractional, error, exp, false); + if (result != digits::more) return result; + } +} + +// The fixed precision digit handler. +struct fixed_handler { + char* buf; + int size; + int precision; + int exp10; + bool fixed; + + digits::result on_start(uint64_t divisor, uint64_t remainder, uint64_t error, + int& exp) { + // Non-fixed formats require at least one digit and no precision adjustment. + if (!fixed) return digits::more; + // Adjust fixed precision by exponent because it is relative to decimal + // point. + precision += exp + exp10; + // Check if precision is satisfied just by leading zeros, e.g. + // format("{:.2f}", 0.001) gives "0.00" without generating any digits. + if (precision > 0) return digits::more; + if (precision < 0) return digits::done; + auto dir = get_round_direction(divisor, remainder, error); + if (dir == round_direction::unknown) return digits::error; + buf[size++] = dir == round_direction::up ? '1' : '0'; + return digits::done; + } + + digits::result on_digit(char digit, uint64_t divisor, uint64_t remainder, + uint64_t error, int, bool integral) { + FMT_ASSERT(remainder < divisor, ""); + buf[size++] = digit; + if (!integral && error >= remainder) return digits::error; + if (size < precision) return digits::more; + if (!integral) { + // Check if error * 2 < divisor with overflow prevention. + // The check is not needed for the integral part because error = 1 + // and divisor > (1 << 32) there. + if (error >= divisor || error >= divisor - error) return digits::error; + } else { + FMT_ASSERT(error == 1 && divisor > 2, ""); + } + auto dir = get_round_direction(divisor, remainder, error); + if (dir != round_direction::up) + return dir == round_direction::down ? digits::done : digits::error; + ++buf[size - 1]; + for (int i = size - 1; i > 0 && buf[i] > '9'; --i) { + buf[i] = '0'; + ++buf[i - 1]; + } + if (buf[0] > '9') { + buf[0] = '1'; + if (fixed) + buf[size++] = '0'; + else + ++exp10; + } + return digits::done; + } +}; + +// Implementation of Dragonbox algorithm: https://github.com/jk-jeon/dragonbox. +namespace dragonbox { +// Computes 128-bit result of multiplication of two 64-bit unsigned integers. +FMT_SAFEBUFFERS inline uint128_wrapper umul128(uint64_t x, + uint64_t y) FMT_NOEXCEPT { +#if FMT_USE_INT128 + return static_cast<uint128_t>(x) * static_cast<uint128_t>(y); +#elif defined(_MSC_VER) && defined(_M_X64) + uint128_wrapper result; + result.low_ = _umul128(x, y, &result.high_); + return result; +#else + const uint64_t mask = (uint64_t(1) << 32) - uint64_t(1); + + uint64_t a = x >> 32; + uint64_t b = x & mask; + uint64_t c = y >> 32; + uint64_t d = y & mask; + + uint64_t ac = a * c; + uint64_t bc = b * c; + uint64_t ad = a * d; + uint64_t bd = b * d; + + uint64_t intermediate = (bd >> 32) + (ad & mask) + (bc & mask); + + return {ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32), + (intermediate << 32) + (bd & mask)}; +#endif +} + +// Computes upper 64 bits of multiplication of two 64-bit unsigned integers. +FMT_SAFEBUFFERS inline uint64_t umul128_upper64(uint64_t x, + uint64_t y) FMT_NOEXCEPT { +#if FMT_USE_INT128 + auto p = static_cast<uint128_t>(x) * static_cast<uint128_t>(y); + return static_cast<uint64_t>(p >> 64); +#elif defined(_MSC_VER) && defined(_M_X64) + return __umulh(x, y); +#else + return umul128(x, y).high(); +#endif +} + +// Computes upper 64 bits of multiplication of a 64-bit unsigned integer and a +// 128-bit unsigned integer. +FMT_SAFEBUFFERS inline uint64_t umul192_upper64(uint64_t x, uint128_wrapper y) + FMT_NOEXCEPT { + uint128_wrapper g0 = umul128(x, y.high()); + g0 += umul128_upper64(x, y.low()); + return g0.high(); +} + +// Computes upper 32 bits of multiplication of a 32-bit unsigned integer and a +// 64-bit unsigned integer. +inline uint32_t umul96_upper32(uint32_t x, uint64_t y) FMT_NOEXCEPT { + return static_cast<uint32_t>(umul128_upper64(x, y)); +} + +// Computes middle 64 bits of multiplication of a 64-bit unsigned integer and a +// 128-bit unsigned integer. +FMT_SAFEBUFFERS inline uint64_t umul192_middle64(uint64_t x, uint128_wrapper y) + FMT_NOEXCEPT { + uint64_t g01 = x * y.high(); + uint64_t g10 = umul128_upper64(x, y.low()); + return g01 + g10; +} + +// Computes lower 64 bits of multiplication of a 32-bit unsigned integer and a +// 64-bit unsigned integer. +inline uint64_t umul96_lower64(uint32_t x, uint64_t y) FMT_NOEXCEPT { + return x * y; +} + +// Computes floor(log10(pow(2, e))) for e in [-1700, 1700] using the method from +// https://fmt.dev/papers/Grisu-Exact.pdf#page=5, section 3.4. +inline int floor_log10_pow2(int e) FMT_NOEXCEPT { + FMT_ASSERT(e <= 1700 && e >= -1700, "too large exponent"); + const int shift = 22; + return (e * static_cast<int>(data::log10_2_significand >> (64 - shift))) >> + shift; +} + +// Various fast log computations. +inline int floor_log2_pow10(int e) FMT_NOEXCEPT { + FMT_ASSERT(e <= 1233 && e >= -1233, "too large exponent"); + const uint64_t log2_10_integer_part = 3; + const uint64_t log2_10_fractional_digits = 0x5269e12f346e2bf9; + const int shift_amount = 19; + return (e * static_cast<int>( + (log2_10_integer_part << shift_amount) | + (log2_10_fractional_digits >> (64 - shift_amount)))) >> + shift_amount; +} +inline int floor_log10_pow2_minus_log10_4_over_3(int e) FMT_NOEXCEPT { + FMT_ASSERT(e <= 1700 && e >= -1700, "too large exponent"); + const uint64_t log10_4_over_3_fractional_digits = 0x1ffbfc2bbc780375; + const int shift_amount = 22; + return (e * static_cast<int>(data::log10_2_significand >> + (64 - shift_amount)) - + static_cast<int>(log10_4_over_3_fractional_digits >> + (64 - shift_amount))) >> + shift_amount; +} + +// Returns true iff x is divisible by pow(2, exp). +inline bool divisible_by_power_of_2(uint32_t x, int exp) FMT_NOEXCEPT { + FMT_ASSERT(exp >= 1, ""); + FMT_ASSERT(x != 0, ""); +#ifdef FMT_BUILTIN_CTZ + return FMT_BUILTIN_CTZ(x) >= exp; +#else + return exp < num_bits<uint32_t>() && x == ((x >> exp) << exp); +#endif +} +inline bool divisible_by_power_of_2(uint64_t x, int exp) FMT_NOEXCEPT { + FMT_ASSERT(exp >= 1, ""); + FMT_ASSERT(x != 0, ""); +#ifdef FMT_BUILTIN_CTZLL + return FMT_BUILTIN_CTZLL(x) >= exp; +#else + return exp < num_bits<uint64_t>() && x == ((x >> exp) << exp); +#endif +} + +// Returns true iff x is divisible by pow(5, exp). +inline bool divisible_by_power_of_5(uint32_t x, int exp) FMT_NOEXCEPT { + FMT_ASSERT(exp <= 10, "too large exponent"); + return x * data::divtest_table_for_pow5_32[exp].mod_inv <= + data::divtest_table_for_pow5_32[exp].max_quotient; +} +inline bool divisible_by_power_of_5(uint64_t x, int exp) FMT_NOEXCEPT { + FMT_ASSERT(exp <= 23, "too large exponent"); + return x * data::divtest_table_for_pow5_64[exp].mod_inv <= + data::divtest_table_for_pow5_64[exp].max_quotient; +} + +// Replaces n by floor(n / pow(5, N)) returning true if and only if n is +// divisible by pow(5, N). +// Precondition: n <= 2 * pow(5, N + 1). +template <int N> +bool check_divisibility_and_divide_by_pow5(uint32_t& n) FMT_NOEXCEPT { + static constexpr struct { + uint32_t magic_number; + int bits_for_comparison; + uint32_t threshold; + int shift_amount; + } infos[] = {{0xcccd, 16, 0x3333, 18}, {0xa429, 8, 0x0a, 20}}; + constexpr auto info = infos[N - 1]; + n *= info.magic_number; + const uint32_t comparison_mask = (1u << info.bits_for_comparison) - 1; + bool result = (n & comparison_mask) <= info.threshold; + n >>= info.shift_amount; + return result; +} + +// Computes floor(n / pow(10, N)) for small n and N. +// Precondition: n <= pow(10, N + 1). +template <int N> uint32_t small_division_by_pow10(uint32_t n) FMT_NOEXCEPT { + static constexpr struct { + uint32_t magic_number; + int shift_amount; + uint32_t divisor_times_10; + } infos[] = {{0xcccd, 19, 100}, {0xa3d8, 22, 1000}}; + constexpr auto info = infos[N - 1]; + FMT_ASSERT(n <= info.divisor_times_10, "n is too large"); + return n * info.magic_number >> info.shift_amount; +} + +// Computes floor(n / 10^(kappa + 1)) (float) +inline uint32_t divide_by_10_to_kappa_plus_1(uint32_t n) FMT_NOEXCEPT { + return n / float_info<float>::big_divisor; +} +// Computes floor(n / 10^(kappa + 1)) (double) +inline uint64_t divide_by_10_to_kappa_plus_1(uint64_t n) FMT_NOEXCEPT { + return umul128_upper64(n, 0x83126e978d4fdf3c) >> 9; +} + +// Various subroutines using pow10 cache +template <class T> struct cache_accessor; + +template <> struct cache_accessor<float> { + using carrier_uint = float_info<float>::carrier_uint; + using cache_entry_type = uint64_t; + + static uint64_t get_cached_power(int k) FMT_NOEXCEPT { + FMT_ASSERT(k >= float_info<float>::min_k && k <= float_info<float>::max_k, + "k is out of range"); + return data::dragonbox_pow10_significands_64[k - float_info<float>::min_k]; + } + + static carrier_uint compute_mul(carrier_uint u, + const cache_entry_type& cache) FMT_NOEXCEPT { + return umul96_upper32(u, cache); + } + + static uint32_t compute_delta(const cache_entry_type& cache, + int beta_minus_1) FMT_NOEXCEPT { + return static_cast<uint32_t>(cache >> (64 - 1 - beta_minus_1)); + } + + static bool compute_mul_parity(carrier_uint two_f, + const cache_entry_type& cache, + int beta_minus_1) FMT_NOEXCEPT { + FMT_ASSERT(beta_minus_1 >= 1, ""); + FMT_ASSERT(beta_minus_1 < 64, ""); + + return ((umul96_lower64(two_f, cache) >> (64 - beta_minus_1)) & 1) != 0; + } + + static carrier_uint compute_left_endpoint_for_shorter_interval_case( + const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT { + return static_cast<carrier_uint>( + (cache - (cache >> (float_info<float>::significand_bits + 2))) >> + (64 - float_info<float>::significand_bits - 1 - beta_minus_1)); + } + + static carrier_uint compute_right_endpoint_for_shorter_interval_case( + const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT { + return static_cast<carrier_uint>( + (cache + (cache >> (float_info<float>::significand_bits + 1))) >> + (64 - float_info<float>::significand_bits - 1 - beta_minus_1)); + } + + static carrier_uint compute_round_up_for_shorter_interval_case( + const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT { + return (static_cast<carrier_uint>( + cache >> + (64 - float_info<float>::significand_bits - 2 - beta_minus_1)) + + 1) / + 2; + } +}; + +template <> struct cache_accessor<double> { + using carrier_uint = float_info<double>::carrier_uint; + using cache_entry_type = uint128_wrapper; + + static uint128_wrapper get_cached_power(int k) FMT_NOEXCEPT { + FMT_ASSERT(k >= float_info<double>::min_k && k <= float_info<double>::max_k, + "k is out of range"); + +#if FMT_USE_FULL_CACHE_DRAGONBOX + return data::dragonbox_pow10_significands_128[k - + float_info<double>::min_k]; +#else + static const int compression_ratio = 27; + + // Compute base index. + int cache_index = (k - float_info<double>::min_k) / compression_ratio; + int kb = cache_index * compression_ratio + float_info<double>::min_k; + int offset = k - kb; + + // Get base cache. + uint128_wrapper base_cache = + data::dragonbox_pow10_significands_128[cache_index]; + if (offset == 0) return base_cache; + + // Compute the required amount of bit-shift. + int alpha = floor_log2_pow10(kb + offset) - floor_log2_pow10(kb) - offset; + FMT_ASSERT(alpha > 0 && alpha < 64, "shifting error detected"); + + // Try to recover the real cache. + uint64_t pow5 = data::powers_of_5_64[offset]; + uint128_wrapper recovered_cache = umul128(base_cache.high(), pow5); + uint128_wrapper middle_low = + umul128(base_cache.low() - (kb < 0 ? 1u : 0u), pow5); + + recovered_cache += middle_low.high(); + + uint64_t high_to_middle = recovered_cache.high() << (64 - alpha); + uint64_t middle_to_low = recovered_cache.low() << (64 - alpha); + + recovered_cache = + uint128_wrapper{(recovered_cache.low() >> alpha) | high_to_middle, + ((middle_low.low() >> alpha) | middle_to_low)}; + + if (kb < 0) recovered_cache += 1; + + // Get error. + int error_idx = (k - float_info<double>::min_k) / 16; + uint32_t error = (data::dragonbox_pow10_recovery_errors[error_idx] >> + ((k - float_info<double>::min_k) % 16) * 2) & + 0x3; + + // Add the error back. + FMT_ASSERT(recovered_cache.low() + error >= recovered_cache.low(), ""); + return {recovered_cache.high(), recovered_cache.low() + error}; +#endif + } + + static carrier_uint compute_mul(carrier_uint u, + const cache_entry_type& cache) FMT_NOEXCEPT { + return umul192_upper64(u, cache); + } + + static uint32_t compute_delta(cache_entry_type const& cache, + int beta_minus_1) FMT_NOEXCEPT { + return static_cast<uint32_t>(cache.high() >> (64 - 1 - beta_minus_1)); + } + + static bool compute_mul_parity(carrier_uint two_f, + const cache_entry_type& cache, + int beta_minus_1) FMT_NOEXCEPT { + FMT_ASSERT(beta_minus_1 >= 1, ""); + FMT_ASSERT(beta_minus_1 < 64, ""); + + return ((umul192_middle64(two_f, cache) >> (64 - beta_minus_1)) & 1) != 0; + } + + static carrier_uint compute_left_endpoint_for_shorter_interval_case( + const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT { + return (cache.high() - + (cache.high() >> (float_info<double>::significand_bits + 2))) >> + (64 - float_info<double>::significand_bits - 1 - beta_minus_1); + } + + static carrier_uint compute_right_endpoint_for_shorter_interval_case( + const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT { + return (cache.high() + + (cache.high() >> (float_info<double>::significand_bits + 1))) >> + (64 - float_info<double>::significand_bits - 1 - beta_minus_1); + } + + static carrier_uint compute_round_up_for_shorter_interval_case( + const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT { + return ((cache.high() >> + (64 - float_info<double>::significand_bits - 2 - beta_minus_1)) + + 1) / + 2; + } +}; + +// Various integer checks +template <class T> +bool is_left_endpoint_integer_shorter_interval(int exponent) FMT_NOEXCEPT { + return exponent >= + float_info< + T>::case_shorter_interval_left_endpoint_lower_threshold && + exponent <= + float_info<T>::case_shorter_interval_left_endpoint_upper_threshold; +} +template <class T> +bool is_endpoint_integer(typename float_info<T>::carrier_uint two_f, + int exponent, int minus_k) FMT_NOEXCEPT { + if (exponent < float_info<T>::case_fc_pm_half_lower_threshold) return false; + // For k >= 0. + if (exponent <= float_info<T>::case_fc_pm_half_upper_threshold) return true; + // For k < 0. + if (exponent > float_info<T>::divisibility_check_by_5_threshold) return false; + return divisible_by_power_of_5(two_f, minus_k); +} + +template <class T> +bool is_center_integer(typename float_info<T>::carrier_uint two_f, int exponent, + int minus_k) FMT_NOEXCEPT { + // Exponent for 5 is negative. + if (exponent > float_info<T>::divisibility_check_by_5_threshold) return false; + if (exponent > float_info<T>::case_fc_upper_threshold) + return divisible_by_power_of_5(two_f, minus_k); + // Both exponents are nonnegative. + if (exponent >= float_info<T>::case_fc_lower_threshold) return true; + // Exponent for 2 is negative. + return divisible_by_power_of_2(two_f, minus_k - exponent + 1); +} + +// Remove trailing zeros from n and return the number of zeros removed (float) +FMT_ALWAYS_INLINE int remove_trailing_zeros(uint32_t& n) FMT_NOEXCEPT { +#ifdef FMT_BUILTIN_CTZ + int t = FMT_BUILTIN_CTZ(n); +#else + int t = ctz(n); +#endif + if (t > float_info<float>::max_trailing_zeros) + t = float_info<float>::max_trailing_zeros; + + const uint32_t mod_inv1 = 0xcccccccd; + const uint32_t max_quotient1 = 0x33333333; + const uint32_t mod_inv2 = 0xc28f5c29; + const uint32_t max_quotient2 = 0x0a3d70a3; + + int s = 0; + for (; s < t - 1; s += 2) { + if (n * mod_inv2 > max_quotient2) break; + n *= mod_inv2; + } + if (s < t && n * mod_inv1 <= max_quotient1) { + n *= mod_inv1; + ++s; + } + n >>= s; + return s; +} + +// Removes trailing zeros and returns the number of zeros removed (double) +FMT_ALWAYS_INLINE int remove_trailing_zeros(uint64_t& n) FMT_NOEXCEPT { +#ifdef FMT_BUILTIN_CTZLL + int t = FMT_BUILTIN_CTZLL(n); +#else + int t = ctzll(n); +#endif + if (t > float_info<double>::max_trailing_zeros) + t = float_info<double>::max_trailing_zeros; + // Divide by 10^8 and reduce to 32-bits + // Since ret_value.significand <= (2^64 - 1) / 1000 < 10^17, + // both of the quotient and the r should fit in 32-bits + + const uint32_t mod_inv1 = 0xcccccccd; + const uint32_t max_quotient1 = 0x33333333; + const uint64_t mod_inv8 = 0xc767074b22e90e21; + const uint64_t max_quotient8 = 0x00002af31dc46118; + + // If the number is divisible by 1'0000'0000, work with the quotient + if (t >= 8) { + auto quotient_candidate = n * mod_inv8; + + if (quotient_candidate <= max_quotient8) { + auto quotient = static_cast<uint32_t>(quotient_candidate >> 8); + + int s = 8; + for (; s < t; ++s) { + if (quotient * mod_inv1 > max_quotient1) break; + quotient *= mod_inv1; + } + quotient >>= (s - 8); + n = quotient; + return s; + } + } + + // Otherwise, work with the remainder + auto quotient = static_cast<uint32_t>(n / 100000000); + auto remainder = static_cast<uint32_t>(n - 100000000 * quotient); + + if (t == 0 || remainder * mod_inv1 > max_quotient1) { + return 0; + } + remainder *= mod_inv1; + + if (t == 1 || remainder * mod_inv1 > max_quotient1) { + n = (remainder >> 1) + quotient * 10000000ull; + return 1; + } + remainder *= mod_inv1; + + if (t == 2 || remainder * mod_inv1 > max_quotient1) { + n = (remainder >> 2) + quotient * 1000000ull; + return 2; + } + remainder *= mod_inv1; + + if (t == 3 || remainder * mod_inv1 > max_quotient1) { + n = (remainder >> 3) + quotient * 100000ull; + return 3; + } + remainder *= mod_inv1; + + if (t == 4 || remainder * mod_inv1 > max_quotient1) { + n = (remainder >> 4) + quotient * 10000ull; + return 4; + } + remainder *= mod_inv1; + + if (t == 5 || remainder * mod_inv1 > max_quotient1) { + n = (remainder >> 5) + quotient * 1000ull; + return 5; + } + remainder *= mod_inv1; + + if (t == 6 || remainder * mod_inv1 > max_quotient1) { + n = (remainder >> 6) + quotient * 100ull; + return 6; + } + remainder *= mod_inv1; + + n = (remainder >> 7) + quotient * 10ull; + return 7; +} + +// The main algorithm for shorter interval case +template <class T> +FMT_ALWAYS_INLINE FMT_SAFEBUFFERS decimal_fp<T> shorter_interval_case( + int exponent) FMT_NOEXCEPT { + decimal_fp<T> ret_value; + // Compute k and beta + const int minus_k = floor_log10_pow2_minus_log10_4_over_3(exponent); + const int beta_minus_1 = exponent + floor_log2_pow10(-minus_k); + + // Compute xi and zi + using cache_entry_type = typename cache_accessor<T>::cache_entry_type; + const cache_entry_type cache = cache_accessor<T>::get_cached_power(-minus_k); + + auto xi = cache_accessor<T>::compute_left_endpoint_for_shorter_interval_case( + cache, beta_minus_1); + auto zi = cache_accessor<T>::compute_right_endpoint_for_shorter_interval_case( + cache, beta_minus_1); + + // If the left endpoint is not an integer, increase it + if (!is_left_endpoint_integer_shorter_interval<T>(exponent)) ++xi; + + // Try bigger divisor + ret_value.significand = zi / 10; + + // If succeed, remove trailing zeros if necessary and return + if (ret_value.significand * 10 >= xi) { + ret_value.exponent = minus_k + 1; + ret_value.exponent += remove_trailing_zeros(ret_value.significand); + return ret_value; + } + + // Otherwise, compute the round-up of y + ret_value.significand = + cache_accessor<T>::compute_round_up_for_shorter_interval_case( + cache, beta_minus_1); + ret_value.exponent = minus_k; + + // When tie occurs, choose one of them according to the rule + if (exponent >= float_info<T>::shorter_interval_tie_lower_threshold && + exponent <= float_info<T>::shorter_interval_tie_upper_threshold) { + ret_value.significand = ret_value.significand % 2 == 0 + ? ret_value.significand + : ret_value.significand - 1; + } else if (ret_value.significand < xi) { + ++ret_value.significand; + } + return ret_value; +} + +template <typename T> +FMT_SAFEBUFFERS decimal_fp<T> to_decimal(T x) FMT_NOEXCEPT { + // Step 1: integer promotion & Schubfach multiplier calculation. + + using carrier_uint = typename float_info<T>::carrier_uint; + using cache_entry_type = typename cache_accessor<T>::cache_entry_type; + auto br = bit_cast<carrier_uint>(x); + + // Extract significand bits and exponent bits. + const carrier_uint significand_mask = + (static_cast<carrier_uint>(1) << float_info<T>::significand_bits) - 1; + carrier_uint significand = (br & significand_mask); + int exponent = static_cast<int>((br & exponent_mask<T>()) >> + float_info<T>::significand_bits); + + if (exponent != 0) { // Check if normal. + exponent += float_info<T>::exponent_bias - float_info<T>::significand_bits; + + // Shorter interval case; proceed like Schubfach. + if (significand == 0) return shorter_interval_case<T>(exponent); + + significand |= + (static_cast<carrier_uint>(1) << float_info<T>::significand_bits); + } else { + // Subnormal case; the interval is always regular. + if (significand == 0) return {0, 0}; + exponent = float_info<T>::min_exponent - float_info<T>::significand_bits; + } + + const bool include_left_endpoint = (significand % 2 == 0); + const bool include_right_endpoint = include_left_endpoint; + + // Compute k and beta. + const int minus_k = floor_log10_pow2(exponent) - float_info<T>::kappa; + const cache_entry_type cache = cache_accessor<T>::get_cached_power(-minus_k); + const int beta_minus_1 = exponent + floor_log2_pow10(-minus_k); + + // Compute zi and deltai + // 10^kappa <= deltai < 10^(kappa + 1) + const uint32_t deltai = cache_accessor<T>::compute_delta(cache, beta_minus_1); + const carrier_uint two_fc = significand << 1; + const carrier_uint two_fr = two_fc | 1; + const carrier_uint zi = + cache_accessor<T>::compute_mul(two_fr << beta_minus_1, cache); + + // Step 2: Try larger divisor; remove trailing zeros if necessary + + // 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 + decimal_fp<T> ret_value; + ret_value.significand = divide_by_10_to_kappa_plus_1(zi); + uint32_t r = static_cast<uint32_t>(zi - float_info<T>::big_divisor * + ret_value.significand); + + if (r > deltai) { + goto small_divisor_case_label; + } else if (r < deltai) { + // Exclude the right endpoint if necessary + if (r == 0 && !include_right_endpoint && + is_endpoint_integer<T>(two_fr, exponent, minus_k)) { + --ret_value.significand; + r = float_info<T>::big_divisor; + goto small_divisor_case_label; + } + } else { + // r == deltai; compare fractional parts + // Check conditions in the order different from the paper + // to take advantage of short-circuiting + const carrier_uint two_fl = two_fc - 1; + if ((!include_left_endpoint || + !is_endpoint_integer<T>(two_fl, exponent, minus_k)) && + !cache_accessor<T>::compute_mul_parity(two_fl, cache, beta_minus_1)) { + goto small_divisor_case_label; + } + } + ret_value.exponent = minus_k + float_info<T>::kappa + 1; + + // We may need to remove trailing zeros + ret_value.exponent += remove_trailing_zeros(ret_value.significand); + return ret_value; + + // Step 3: Find the significand with the smaller divisor + +small_divisor_case_label: + ret_value.significand *= 10; + ret_value.exponent = minus_k + float_info<T>::kappa; + + const uint32_t mask = (1u << float_info<T>::kappa) - 1; + auto dist = r - (deltai / 2) + (float_info<T>::small_divisor / 2); + + // Is dist divisible by 2^kappa? + if ((dist & mask) == 0) { + const bool approx_y_parity = + ((dist ^ (float_info<T>::small_divisor / 2)) & 1) != 0; + dist >>= float_info<T>::kappa; + + // Is dist divisible by 5^kappa? + if (check_divisibility_and_divide_by_pow5<float_info<T>::kappa>(dist)) { + ret_value.significand += dist; + + // 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 + if (cache_accessor<T>::compute_mul_parity(two_fc, cache, beta_minus_1) != + approx_y_parity) { + --ret_value.significand; + } else { + // If z^(f) >= epsilon^(f), we might have a tie + // when z^(f) == epsilon^(f), or equivalently, when y is an integer + if (is_center_integer<T>(two_fc, exponent, minus_k)) { + ret_value.significand = ret_value.significand % 2 == 0 + ? ret_value.significand + : ret_value.significand - 1; + } + } + } + // Is dist not divisible by 5^kappa? + else { + ret_value.significand += dist; + } + } + // Is dist not divisible by 2^kappa? + else { + // Since we know dist is small, we might be able to optimize the division + // better than the compiler; we are computing dist / small_divisor here + ret_value.significand += + small_division_by_pow10<float_info<T>::kappa>(dist); + } + return ret_value; +} +} // namespace dragonbox + +// Formats value using a variation of the Fixed-Precision Positive +// Floating-Point Printout ((FPP)^2) algorithm by Steele & White: +// https://fmt.dev/p372-steele.pdf. +template <typename Double> +void fallback_format(Double d, int num_digits, bool binary32, buffer<char>& buf, + int& exp10) { + bigint numerator; // 2 * R in (FPP)^2. + bigint denominator; // 2 * S in (FPP)^2. + // lower and upper are differences between value and corresponding boundaries. + bigint lower; // (M^- in (FPP)^2). + bigint upper_store; // upper's value if different from lower. + bigint* upper = nullptr; // (M^+ in (FPP)^2). + fp value; + // Shift numerator and denominator by an extra bit or two (if lower boundary + // is closer) to make lower and upper integers. This eliminates multiplication + // by 2 during later computations. + const bool is_predecessor_closer = + binary32 ? value.assign(static_cast<float>(d)) : value.assign(d); + int shift = is_predecessor_closer ? 2 : 1; + uint64_t significand = value.f << shift; + if (value.e >= 0) { + numerator.assign(significand); + numerator <<= value.e; + lower.assign(1); + lower <<= value.e; + if (shift != 1) { + upper_store.assign(1); + upper_store <<= value.e + 1; + upper = &upper_store; + } + denominator.assign_pow10(exp10); + denominator <<= shift; + } else if (exp10 < 0) { + numerator.assign_pow10(-exp10); + lower.assign(numerator); + if (shift != 1) { + upper_store.assign(numerator); + upper_store <<= 1; + upper = &upper_store; + } + numerator *= significand; + denominator.assign(1); + denominator <<= shift - value.e; + } else { + numerator.assign(significand); + denominator.assign_pow10(exp10); + denominator <<= shift - value.e; + lower.assign(1); + if (shift != 1) { + upper_store.assign(1ULL << 1); + upper = &upper_store; + } + } + // Invariant: value == (numerator / denominator) * pow(10, exp10). + if (num_digits < 0) { + // Generate the shortest representation. + if (!upper) upper = &lower; + bool even = (value.f & 1) == 0; + num_digits = 0; + char* data = buf.data(); + for (;;) { + int digit = numerator.divmod_assign(denominator); + bool low = compare(numerator, lower) - even < 0; // numerator <[=] lower. + // numerator + upper >[=] pow10: + bool high = add_compare(numerator, *upper, denominator) + even > 0; + data[num_digits++] = static_cast<char>('0' + digit); + if (low || high) { + if (!low) { + ++data[num_digits - 1]; + } else if (high) { + int result = add_compare(numerator, numerator, denominator); + // Round half to even. + if (result > 0 || (result == 0 && (digit % 2) != 0)) + ++data[num_digits - 1]; + } + buf.try_resize(to_unsigned(num_digits)); + exp10 -= num_digits - 1; + return; + } + numerator *= 10; + lower *= 10; + if (upper != &lower) *upper *= 10; + } + } + // Generate the given number of digits. + exp10 -= num_digits - 1; + if (num_digits == 0) { + buf.try_resize(1); + denominator *= 10; + buf[0] = add_compare(numerator, numerator, denominator) > 0 ? '1' : '0'; + return; + } + buf.try_resize(to_unsigned(num_digits)); + for (int i = 0; i < num_digits - 1; ++i) { + int digit = numerator.divmod_assign(denominator); + buf[i] = static_cast<char>('0' + digit); + numerator *= 10; + } + int digit = numerator.divmod_assign(denominator); + auto result = add_compare(numerator, numerator, denominator); + if (result > 0 || (result == 0 && (digit % 2) != 0)) { + if (digit == 9) { + const auto overflow = '0' + 10; + buf[num_digits - 1] = overflow; + // Propagate the carry. + for (int i = num_digits - 1; i > 0 && buf[i] == overflow; --i) { + buf[i] = '0'; + ++buf[i - 1]; + } + if (buf[0] == overflow) { + buf[0] = '1'; + ++exp10; + } + return; + } + ++digit; + } + buf[num_digits - 1] = static_cast<char>('0' + digit); +} + +template <typename T> +int format_float(T value, int precision, float_specs specs, buffer<char>& buf) { + static_assert(!std::is_same<T, float>::value, ""); + FMT_ASSERT(value >= 0, "value is negative"); + + const bool fixed = specs.format == float_format::fixed; + if (value <= 0) { // <= instead of == to silence a warning. + if (precision <= 0 || !fixed) { + buf.push_back('0'); + return 0; + } + buf.try_resize(to_unsigned(precision)); + std::uninitialized_fill_n(buf.data(), precision, '0'); + return -precision; + } + + if (!specs.use_grisu) return snprintf_float(value, precision, specs, buf); + + if (precision < 0) { + // Use Dragonbox for the shortest format. + if (specs.binary32) { + auto dec = dragonbox::to_decimal(static_cast<float>(value)); + write<char>(buffer_appender<char>(buf), dec.significand); + return dec.exponent; + } + auto dec = dragonbox::to_decimal(static_cast<double>(value)); + write<char>(buffer_appender<char>(buf), dec.significand); + return dec.exponent; + } + + // Use Grisu + Dragon4 for the given precision: + // https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf. + int exp = 0; + const int min_exp = -60; // alpha in Grisu. + int cached_exp10 = 0; // K in Grisu. + fp normalized = normalize(fp(value)); + const auto cached_pow = get_cached_power( + min_exp - (normalized.e + fp::significand_size), cached_exp10); + normalized = normalized * cached_pow; + // Limit precision to the maximum possible number of significant digits in an + // IEEE754 double because we don't need to generate zeros. + const int max_double_digits = 767; + if (precision > max_double_digits) precision = max_double_digits; + fixed_handler handler{buf.data(), 0, precision, -cached_exp10, fixed}; + if (grisu_gen_digits(normalized, 1, exp, handler) == digits::error) { + exp += handler.size - cached_exp10 - 1; + fallback_format(value, handler.precision, specs.binary32, buf, exp); + } else { + exp += handler.exp10; + buf.try_resize(to_unsigned(handler.size)); + } + if (!fixed && !specs.showpoint) { + // Remove trailing zeros. + auto num_digits = buf.size(); + while (num_digits > 0 && buf[num_digits - 1] == '0') { + --num_digits; + ++exp; + } + buf.try_resize(num_digits); + } + return exp; +} // namespace detail + +template <typename T> +int snprintf_float(T value, int precision, float_specs specs, + buffer<char>& buf) { + // Buffer capacity must be non-zero, otherwise MSVC's vsnprintf_s will fail. + FMT_ASSERT(buf.capacity() > buf.size(), "empty buffer"); + static_assert(!std::is_same<T, float>::value, ""); + + // Subtract 1 to account for the difference in precision since we use %e for + // both general and exponent format. + if (specs.format == float_format::general || + specs.format == float_format::exp) + precision = (precision >= 0 ? precision : 6) - 1; + + // Build the format string. + enum { max_format_size = 7 }; // The longest format is "%#.*Le". + char format[max_format_size]; + char* format_ptr = format; + *format_ptr++ = '%'; + if (specs.showpoint && specs.format == float_format::hex) *format_ptr++ = '#'; + if (precision >= 0) { + *format_ptr++ = '.'; + *format_ptr++ = '*'; + } + if (std::is_same<T, long double>()) *format_ptr++ = 'L'; + *format_ptr++ = specs.format != float_format::hex + ? (specs.format == float_format::fixed ? 'f' : 'e') + : (specs.upper ? 'A' : 'a'); + *format_ptr = '\0'; + + // Format using snprintf. + auto offset = buf.size(); + for (;;) { + auto begin = buf.data() + offset; + auto capacity = buf.capacity() - offset; +#ifdef FMT_FUZZ + if (precision > 100000) + throw std::runtime_error( + "fuzz mode - avoid large allocation inside snprintf"); +#endif + // Suppress the warning about a nonliteral format string. + // Cannot use auto because of a bug in MinGW (#1532). + int (*snprintf_ptr)(char*, size_t, const char*, ...) = FMT_SNPRINTF; + int result = precision >= 0 + ? snprintf_ptr(begin, capacity, format, precision, value) + : snprintf_ptr(begin, capacity, format, value); + if (result < 0) { + // The buffer will grow exponentially. + buf.try_reserve(buf.capacity() + 1); + continue; + } + auto size = to_unsigned(result); + // Size equal to capacity means that the last character was truncated. + if (size >= capacity) { + buf.try_reserve(size + offset + 1); // Add 1 for the terminating '\0'. + continue; + } + auto is_digit = [](char c) { return c >= '0' && c <= '9'; }; + if (specs.format == float_format::fixed) { + if (precision == 0) { + buf.try_resize(size); + return 0; + } + // Find and remove the decimal point. + auto end = begin + size, p = end; + do { + --p; + } while (is_digit(*p)); + int fraction_size = static_cast<int>(end - p - 1); + std::memmove(p, p + 1, to_unsigned(fraction_size)); + buf.try_resize(size - 1); + return -fraction_size; + } + if (specs.format == float_format::hex) { + buf.try_resize(size + offset); + return 0; + } + // Find and parse the exponent. + auto end = begin + size, exp_pos = end; + do { + --exp_pos; + } while (*exp_pos != 'e'); + char sign = exp_pos[1]; + assert(sign == '+' || sign == '-'); + int exp = 0; + auto p = exp_pos + 2; // Skip 'e' and sign. + do { + assert(is_digit(*p)); + exp = exp * 10 + (*p++ - '0'); + } while (p != end); + if (sign == '-') exp = -exp; + int fraction_size = 0; + if (exp_pos != begin + 1) { + // Remove trailing zeros. + auto fraction_end = exp_pos - 1; + while (*fraction_end == '0') --fraction_end; + // Move the fractional part left to get rid of the decimal point. + fraction_size = static_cast<int>(fraction_end - begin - 1); + std::memmove(begin + 1, begin + 2, to_unsigned(fraction_size)); + } + buf.try_resize(to_unsigned(fraction_size) + offset + 1); + return exp - fraction_size; + } +} + +// A public domain branchless UTF-8 decoder by Christopher Wellons: +// https://github.com/skeeto/branchless-utf8 +/* Decode the next character, c, from buf, reporting errors in e. + * + * Since this is a branchless decoder, four bytes will be read from the + * buffer regardless of the actual length of the next character. This + * means the buffer _must_ have at least three bytes of zero padding + * following the end of the data stream. + * + * Errors are reported in e, which will be non-zero if the parsed + * character was somehow invalid: invalid byte sequence, non-canonical + * encoding, or a surrogate half. + * + * The function returns a pointer to the next character. When an error + * occurs, this pointer will be a guess that depends on the particular + * error, but it will always advance at least one byte. + */ +inline const char* utf8_decode(const char* buf, uint32_t* c, int* e) { + static const int masks[] = {0x00, 0x7f, 0x1f, 0x0f, 0x07}; + static const uint32_t mins[] = {4194304, 0, 128, 2048, 65536}; + static const int shiftc[] = {0, 18, 12, 6, 0}; + static const int shifte[] = {0, 6, 4, 2, 0}; + + int len = code_point_length(buf); + const char* next = buf + len; + + // Assume a four-byte character and load four bytes. Unused bits are + // shifted out. + auto s = reinterpret_cast<const unsigned char*>(buf); + *c = uint32_t(s[0] & masks[len]) << 18; + *c |= uint32_t(s[1] & 0x3f) << 12; + *c |= uint32_t(s[2] & 0x3f) << 6; + *c |= uint32_t(s[3] & 0x3f) << 0; + *c >>= shiftc[len]; + + // Accumulate the various error conditions. + *e = (*c < mins[len]) << 6; // non-canonical encoding + *e |= ((*c >> 11) == 0x1b) << 7; // surrogate half? + *e |= (*c > 0x10FFFF) << 8; // out of range? + *e |= (s[1] & 0xc0) >> 2; + *e |= (s[2] & 0xc0) >> 4; + *e |= (s[3]) >> 6; + *e ^= 0x2a; // top two bits of each tail byte correct? + *e >>= shifte[len]; + + return next; +} + +struct stringifier { + template <typename T> FMT_INLINE std::string operator()(T value) const { + return to_string(value); + } + std::string operator()(basic_format_arg<format_context>::handle h) const { + memory_buffer buf; + format_parse_context parse_ctx({}); + format_context format_ctx(buffer_appender<char>(buf), {}, {}); + h.format(parse_ctx, format_ctx); + return to_string(buf); + } +}; +} // namespace detail + +template <> struct formatter<detail::bigint> { + format_parse_context::iterator parse(format_parse_context& ctx) { + return ctx.begin(); + } + + format_context::iterator format(const detail::bigint& n, + format_context& ctx) { + auto out = ctx.out(); + bool first = true; + for (auto i = n.bigits_.size(); i > 0; --i) { + auto value = n.bigits_[i - 1u]; + if (first) { + out = format_to(out, "{:x}", value); + first = false; + continue; + } + out = format_to(out, "{:08x}", value); + } + if (n.exp_ > 0) + out = format_to(out, "p{}", n.exp_ * detail::bigint::bigit_bits); + return out; + } +}; + +FMT_FUNC detail::utf8_to_utf16::utf8_to_utf16(string_view s) { + auto transcode = [this](const char* p) { + auto cp = uint32_t(); + auto error = 0; + p = utf8_decode(p, &cp, &error); + if (error != 0) FMT_THROW(std::runtime_error("invalid utf8")); + if (cp <= 0xFFFF) { + buffer_.push_back(static_cast<wchar_t>(cp)); + } else { + cp -= 0x10000; + buffer_.push_back(static_cast<wchar_t>(0xD800 + (cp >> 10))); + buffer_.push_back(static_cast<wchar_t>(0xDC00 + (cp & 0x3FF))); + } + return p; + }; + auto p = s.data(); + const size_t block_size = 4; // utf8_decode always reads blocks of 4 chars. + if (s.size() >= block_size) { + for (auto end = p + s.size() - block_size + 1; p < end;) p = transcode(p); + } + if (auto num_chars_left = s.data() + s.size() - p) { + char buf[2 * block_size - 1] = {}; + memcpy(buf, p, to_unsigned(num_chars_left)); + p = buf; + do { + p = transcode(p); + } while (p - buf < num_chars_left); + } + buffer_.push_back(0); +} + +FMT_FUNC void format_system_error(detail::buffer<char>& out, int error_code, + string_view message) FMT_NOEXCEPT { + FMT_TRY { + memory_buffer buf; + buf.resize(inline_buffer_size); + for (;;) { + char* system_message = &buf[0]; + int result = + detail::safe_strerror(error_code, system_message, buf.size()); + if (result == 0) { + format_to(detail::buffer_appender<char>(out), "{}: {}", message, + system_message); + return; + } + if (result != ERANGE) + break; // Can't get error message, report error code instead. + buf.resize(buf.size() * 2); + } + } + FMT_CATCH(...) {} + format_error_code(out, error_code, message); +} + +FMT_FUNC void detail::error_handler::on_error(const char* message) { + FMT_THROW(format_error(message)); +} + +FMT_FUNC void report_system_error(int error_code, + fmt::string_view message) FMT_NOEXCEPT { + report_error(format_system_error, error_code, message); +} + +FMT_FUNC std::string detail::vformat(string_view format_str, format_args args) { + if (format_str.size() == 2 && equal2(format_str.data(), "{}")) { + auto arg = args.get(0); + if (!arg) error_handler().on_error("argument not found"); + return visit_format_arg(stringifier(), arg); + } + memory_buffer buffer; + detail::vformat_to(buffer, format_str, args); + return to_string(buffer); +} + +#ifdef _WIN32 +namespace detail { +using dword = conditional_t<sizeof(long) == 4, unsigned long, unsigned>; +extern "C" __declspec(dllimport) int __stdcall WriteConsoleW( // + void*, const void*, dword, dword*, void*); +} // namespace detail +#endif + +FMT_FUNC void vprint(std::FILE* f, string_view format_str, format_args args) { + memory_buffer buffer; + detail::vformat_to(buffer, format_str, + basic_format_args<buffer_context<char>>(args)); +#ifdef _WIN32 + auto fd = _fileno(f); + if (_isatty(fd)) { + detail::utf8_to_utf16 u16(string_view(buffer.data(), buffer.size())); + auto written = detail::dword(); + if (!detail::WriteConsoleW(reinterpret_cast<void*>(_get_osfhandle(fd)), + u16.c_str(), static_cast<uint32_t>(u16.size()), + &written, nullptr)) { + FMT_THROW(format_error("failed to write to console")); + } + return; + } +#endif + detail::fwrite_fully(buffer.data(), 1, buffer.size(), f); +} + +#ifdef _WIN32 +// Print assuming legacy (non-Unicode) encoding. +FMT_FUNC void detail::vprint_mojibake(std::FILE* f, string_view format_str, + format_args args) { + memory_buffer buffer; + detail::vformat_to(buffer, format_str, + basic_format_args<buffer_context<char>>(args)); + fwrite_fully(buffer.data(), 1, buffer.size(), f); +} +#endif + +FMT_FUNC void vprint(string_view format_str, format_args args) { + vprint(stdout, format_str, args); +} + +FMT_END_NAMESPACE + +#endif // FMT_FORMAT_INL_H_ |