// 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}, 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{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_