diff options
Diffstat (limited to 'include/spdlog/fmt/bundled/format-inl.h')
| -rw-r--r-- | include/spdlog/fmt/bundled/format-inl.h | 2801 |
1 files changed, 0 insertions, 2801 deletions
diff --git a/include/spdlog/fmt/bundled/format-inl.h b/include/spdlog/fmt/bundled/format-inl.h deleted file mode 100644 index 8f2fe735..00000000 --- a/include/spdlog/fmt/bundled/format-inl.h +++ /dev/null @@ -1,2801 +0,0 @@ -// 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}, - {0xec1e4a7db69561a5, 0x2b31e9e3d06c32e6}, - {0x9392ee8e921d5d07, 0x3aff322e62439fd0}, - {0xb877aa3236a4b449, 0x09befeb9fad487c3}, - {0xe69594bec44de15b, 0x4c2ebe687989a9b4}, - {0x901d7cf73ab0acd9, 0x0f9d37014bf60a11}, - {0xb424dc35095cd80f, 0x538484c19ef38c95}, - {0xe12e13424bb40e13, 0x2865a5f206b06fba}, - {0x8cbccc096f5088cb, 0xf93f87b7442e45d4}, - {0xafebff0bcb24aafe, 0xf78f69a51539d749}, - {0xdbe6fecebdedd5be, 0xb573440e5a884d1c}, - {0x89705f4136b4a597, 0x31680a88f8953031}, - {0xabcc77118461cefc, 0xfdc20d2b36ba7c3e}, - {0xd6bf94d5e57a42bc, 0x3d32907604691b4d}, - {0x8637bd05af6c69b5, 0xa63f9a49c2c1b110}, - {0xa7c5ac471b478423, 0x0fcf80dc33721d54}, - {0xd1b71758e219652b, 0xd3c36113404ea4a9}, - 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{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_ |