| 1 | // Formatting library for C++ - implementation |
| 2 | // |
| 3 | // Copyright (c) 2012 - 2016, Victor Zverovich |
| 4 | // All rights reserved. |
| 5 | // |
| 6 | // For the license information refer to format.h. |
| 7 | |
| 8 | #ifndef FMT_FORMAT_INL_H_ |
| 9 | #define FMT_FORMAT_INL_H_ |
| 10 | |
| 11 | #include <algorithm> |
| 12 | #include <cctype> |
| 13 | #include <cerrno> // errno |
| 14 | #include <climits> |
| 15 | #include <cmath> |
| 16 | #include <cstdarg> |
| 17 | #include <cstring> // std::memmove |
| 18 | #include <cwchar> |
| 19 | #include <exception> |
| 20 | |
| 21 | #ifndef FMT_STATIC_THOUSANDS_SEPARATOR |
| 22 | # include <locale> |
| 23 | #endif |
| 24 | |
| 25 | #ifdef _WIN32 |
| 26 | # include <io.h> // _isatty |
| 27 | #endif |
| 28 | |
| 29 | #include "format.h" |
| 30 | |
| 31 | FMT_BEGIN_NAMESPACE |
| 32 | namespace detail { |
| 33 | |
| 34 | FMT_FUNC void assert_fail(const char* file, int line, const char* message) { |
| 35 | // Use unchecked std::fprintf to avoid triggering another assertion when |
| 36 | // writing to stderr fails |
| 37 | std::fprintf(stderr, "%s:%d: assertion failed: %s", file, line, message); |
| 38 | // Chosen instead of std::abort to satisfy Clang in CUDA mode during device |
| 39 | // code pass. |
| 40 | std::terminate(); |
| 41 | } |
| 42 | |
| 43 | FMT_FUNC void throw_format_error(const char* message) { |
| 44 | FMT_THROW(format_error(message)); |
| 45 | } |
| 46 | |
| 47 | #ifndef _MSC_VER |
| 48 | # define FMT_SNPRINTF snprintf |
| 49 | #else // _MSC_VER |
| 50 | inline int fmt_snprintf(char* buffer, size_t size, const char* format, ...) { |
| 51 | va_list args; |
| 52 | va_start(args, format); |
| 53 | int result = vsnprintf_s(buffer, size, _TRUNCATE, format, args); |
| 54 | va_end(args); |
| 55 | return result; |
| 56 | } |
| 57 | # define FMT_SNPRINTF fmt_snprintf |
| 58 | #endif // _MSC_VER |
| 59 | |
| 60 | FMT_FUNC void format_error_code(detail::buffer<char>& out, int error_code, |
| 61 | string_view message) FMT_NOEXCEPT { |
| 62 | // Report error code making sure that the output fits into |
| 63 | // inline_buffer_size to avoid dynamic memory allocation and potential |
| 64 | // bad_alloc. |
| 65 | out.try_resize(0); |
| 66 | static const char SEP[] = ": "; |
| 67 | static const char ERROR_STR[] = "error "; |
| 68 | // Subtract 2 to account for terminating null characters in SEP and ERROR_STR. |
| 69 | size_t error_code_size = sizeof(SEP) + sizeof(ERROR_STR) - 2; |
| 70 | auto abs_value = static_cast<uint32_or_64_or_128_t<int>>(error_code); |
| 71 | if (detail::is_negative(error_code)) { |
| 72 | abs_value = 0 - abs_value; |
| 73 | ++error_code_size; |
| 74 | } |
| 75 | error_code_size += detail::to_unsigned(detail::count_digits(abs_value)); |
| 76 | auto it = buffer_appender<char>(out); |
| 77 | if (message.size() <= inline_buffer_size - error_code_size) |
| 78 | format_to(it, FMT_STRING("{}{}"), message, SEP); |
| 79 | format_to(it, FMT_STRING("{}{}"), ERROR_STR, error_code); |
| 80 | FMT_ASSERT(out.size() <= inline_buffer_size, ""); |
| 81 | } |
| 82 | |
| 83 | FMT_FUNC void report_error(format_func func, int error_code, |
| 84 | const char* message) FMT_NOEXCEPT { |
| 85 | memory_buffer full_message; |
| 86 | func(full_message, error_code, message); |
| 87 | // Don't use fwrite_fully because the latter may throw. |
| 88 | if (std::fwrite(full_message.data(), full_message.size(), 1, stderr) > 0) |
| 89 | std::fputc('\n', stderr); |
| 90 | } |
| 91 | |
| 92 | // A wrapper around fwrite that throws on error. |
| 93 | inline void fwrite_fully(const void* ptr, size_t size, size_t count, |
| 94 | FILE* stream) { |
| 95 | size_t written = std::fwrite(ptr, size, count, stream); |
| 96 | if (written < count) FMT_THROW(system_error(errno, "cannot write to file")); |
| 97 | } |
| 98 | |
| 99 | #ifndef FMT_STATIC_THOUSANDS_SEPARATOR |
| 100 | template <typename Locale> |
| 101 | locale_ref::locale_ref(const Locale& loc) : locale_(&loc) { |
| 102 | static_assert(std::is_same<Locale, std::locale>::value, ""); |
| 103 | } |
| 104 | |
| 105 | template <typename Locale> Locale locale_ref::get() const { |
| 106 | static_assert(std::is_same<Locale, std::locale>::value, ""); |
| 107 | return locale_ ? *static_cast<const std::locale*>(locale_) : std::locale(); |
| 108 | } |
| 109 | |
| 110 | template <typename Char> |
| 111 | FMT_FUNC auto thousands_sep_impl(locale_ref loc) -> thousands_sep_result<Char> { |
| 112 | auto& facet = std::use_facet<std::numpunct<Char>>(loc.get<std::locale>()); |
| 113 | auto grouping = facet.grouping(); |
| 114 | auto thousands_sep = grouping.empty() ? Char() : facet.thousands_sep(); |
| 115 | return {std::move(grouping), thousands_sep}; |
| 116 | } |
| 117 | template <typename Char> FMT_FUNC Char decimal_point_impl(locale_ref loc) { |
| 118 | return std::use_facet<std::numpunct<Char>>(loc.get<std::locale>()) |
| 119 | .decimal_point(); |
| 120 | } |
| 121 | #else |
| 122 | template <typename Char> |
| 123 | FMT_FUNC auto thousands_sep_impl(locale_ref) -> thousands_sep_result<Char> { |
| 124 | return {"\03", FMT_STATIC_THOUSANDS_SEPARATOR}; |
| 125 | } |
| 126 | template <typename Char> FMT_FUNC Char decimal_point_impl(locale_ref) { |
| 127 | return '.'; |
| 128 | } |
| 129 | #endif |
| 130 | } // namespace detail |
| 131 | |
| 132 | #if !FMT_MSC_VER |
| 133 | FMT_API FMT_FUNC format_error::~format_error() FMT_NOEXCEPT = default; |
| 134 | #endif |
| 135 | |
| 136 | FMT_FUNC std::system_error vsystem_error(int error_code, string_view format_str, |
| 137 | format_args args) { |
| 138 | auto ec = std::error_code(error_code, std::generic_category()); |
| 139 | return std::system_error(ec, vformat(format_str, args)); |
| 140 | } |
| 141 | |
| 142 | namespace detail { |
| 143 | |
| 144 | template <> FMT_FUNC int count_digits<4>(detail::fallback_uintptr n) { |
| 145 | // fallback_uintptr is always stored in little endian. |
| 146 | int i = static_cast<int>(sizeof(void*)) - 1; |
| 147 | while (i > 0 && n.value[i] == 0) --i; |
| 148 | auto char_digits = std::numeric_limits<unsigned char>::digits / 4; |
| 149 | return i >= 0 ? i * char_digits + count_digits<4, unsigned>(n.value[i]) : 1; |
| 150 | } |
| 151 | |
| 152 | // log10(2) = 0x0.4d104d427de7fbcc... |
| 153 | static constexpr uint64_t log10_2_significand = 0x4d104d427de7fbcc; |
| 154 | |
| 155 | template <typename T = void> struct basic_impl_data { |
| 156 | // Normalized 64-bit significands of pow(10, k), for k = -348, -340, ..., 340. |
| 157 | // These are generated by support/compute-powers.py. |
| 158 | static constexpr uint64_t pow10_significands[87] = { |
| 159 | 0xfa8fd5a0081c0288, 0xbaaee17fa23ebf76, 0x8b16fb203055ac76, |
| 160 | 0xcf42894a5dce35ea, 0x9a6bb0aa55653b2d, 0xe61acf033d1a45df, |
| 161 | 0xab70fe17c79ac6ca, 0xff77b1fcbebcdc4f, 0xbe5691ef416bd60c, |
| 162 | 0x8dd01fad907ffc3c, 0xd3515c2831559a83, 0x9d71ac8fada6c9b5, |
| 163 | 0xea9c227723ee8bcb, 0xaecc49914078536d, 0x823c12795db6ce57, |
| 164 | 0xc21094364dfb5637, 0x9096ea6f3848984f, 0xd77485cb25823ac7, |
| 165 | 0xa086cfcd97bf97f4, 0xef340a98172aace5, 0xb23867fb2a35b28e, |
| 166 | 0x84c8d4dfd2c63f3b, 0xc5dd44271ad3cdba, 0x936b9fcebb25c996, |
| 167 | 0xdbac6c247d62a584, 0xa3ab66580d5fdaf6, 0xf3e2f893dec3f126, |
| 168 | 0xb5b5ada8aaff80b8, 0x87625f056c7c4a8b, 0xc9bcff6034c13053, |
| 169 | 0x964e858c91ba2655, 0xdff9772470297ebd, 0xa6dfbd9fb8e5b88f, |
| 170 | 0xf8a95fcf88747d94, 0xb94470938fa89bcf, 0x8a08f0f8bf0f156b, |
| 171 | 0xcdb02555653131b6, 0x993fe2c6d07b7fac, 0xe45c10c42a2b3b06, |
| 172 | 0xaa242499697392d3, 0xfd87b5f28300ca0e, 0xbce5086492111aeb, |
| 173 | 0x8cbccc096f5088cc, 0xd1b71758e219652c, 0x9c40000000000000, |
| 174 | 0xe8d4a51000000000, 0xad78ebc5ac620000, 0x813f3978f8940984, |
| 175 | 0xc097ce7bc90715b3, 0x8f7e32ce7bea5c70, 0xd5d238a4abe98068, |
| 176 | 0x9f4f2726179a2245, 0xed63a231d4c4fb27, 0xb0de65388cc8ada8, |
| 177 | 0x83c7088e1aab65db, 0xc45d1df942711d9a, 0x924d692ca61be758, |
| 178 | 0xda01ee641a708dea, 0xa26da3999aef774a, 0xf209787bb47d6b85, |
| 179 | 0xb454e4a179dd1877, 0x865b86925b9bc5c2, 0xc83553c5c8965d3d, |
| 180 | 0x952ab45cfa97a0b3, 0xde469fbd99a05fe3, 0xa59bc234db398c25, |
| 181 | 0xf6c69a72a3989f5c, 0xb7dcbf5354e9bece, 0x88fcf317f22241e2, |
| 182 | 0xcc20ce9bd35c78a5, 0x98165af37b2153df, 0xe2a0b5dc971f303a, |
| 183 | 0xa8d9d1535ce3b396, 0xfb9b7cd9a4a7443c, 0xbb764c4ca7a44410, |
| 184 | 0x8bab8eefb6409c1a, 0xd01fef10a657842c, 0x9b10a4e5e9913129, |
| 185 | 0xe7109bfba19c0c9d, 0xac2820d9623bf429, 0x80444b5e7aa7cf85, |
| 186 | 0xbf21e44003acdd2d, 0x8e679c2f5e44ff8f, 0xd433179d9c8cb841, |
| 187 | 0x9e19db92b4e31ba9, 0xeb96bf6ebadf77d9, 0xaf87023b9bf0ee6b, |
| 188 | }; |
| 189 | |
| 190 | #if FMT_GCC_VERSION && FMT_GCC_VERSION < 409 |
| 191 | # pragma GCC diagnostic push |
| 192 | # pragma GCC diagnostic ignored "-Wnarrowing" |
| 193 | #endif |
| 194 | // Binary exponents of pow(10, k), for k = -348, -340, ..., 340, corresponding |
| 195 | // to significands above. |
| 196 | static constexpr int16_t pow10_exponents[87] = { |
| 197 | -1220, -1193, -1166, -1140, -1113, -1087, -1060, -1034, -1007, -980, -954, |
| 198 | -927, -901, -874, -847, -821, -794, -768, -741, -715, -688, -661, |
| 199 | -635, -608, -582, -555, -529, -502, -475, -449, -422, -396, -369, |
| 200 | -343, -316, -289, -263, -236, -210, -183, -157, -130, -103, -77, |
| 201 | -50, -24, 3, 30, 56, 83, 109, 136, 162, 189, 216, |
| 202 | 242, 269, 295, 322, 348, 375, 402, 428, 455, 481, 508, |
| 203 | 534, 561, 588, 614, 641, 667, 694, 720, 747, 774, 800, |
| 204 | 827, 853, 880, 907, 933, 960, 986, 1013, 1039, 1066}; |
| 205 | #if FMT_GCC_VERSION && FMT_GCC_VERSION < 409 |
| 206 | # pragma GCC diagnostic pop |
| 207 | #endif |
| 208 | |
| 209 | static constexpr uint64_t power_of_10_64[20] = { |
| 210 | 1, FMT_POWERS_OF_10(1ULL), FMT_POWERS_OF_10(1000000000ULL), |
| 211 | 10000000000000000000ULL}; |
| 212 | }; |
| 213 | |
| 214 | // This is a struct rather than an alias to avoid shadowing warnings in gcc. |
| 215 | struct impl_data : basic_impl_data<> {}; |
| 216 | |
| 217 | #if __cplusplus < 201703L |
| 218 | template <typename T> |
| 219 | constexpr uint64_t basic_impl_data<T>::pow10_significands[]; |
| 220 | template <typename T> constexpr int16_t basic_impl_data<T>::pow10_exponents[]; |
| 221 | template <typename T> constexpr uint64_t basic_impl_data<T>::power_of_10_64[]; |
| 222 | #endif |
| 223 | |
| 224 | template <typename T> struct bits { |
| 225 | static FMT_CONSTEXPR_DECL const int value = |
| 226 | static_cast<int>(sizeof(T) * std::numeric_limits<unsigned char>::digits); |
| 227 | }; |
| 228 | |
| 229 | // Returns the number of significand bits in Float excluding the implicit bit. |
| 230 | template <typename Float> constexpr int num_significand_bits() { |
| 231 | // Subtract 1 to account for an implicit most significant bit in the |
| 232 | // normalized form. |
| 233 | return std::numeric_limits<Float>::digits - 1; |
| 234 | } |
| 235 | |
| 236 | // A floating-point number f * pow(2, e). |
| 237 | struct fp { |
| 238 | uint64_t f; |
| 239 | int e; |
| 240 | |
| 241 | static constexpr const int num_significand_bits = bits<decltype(f)>::value; |
| 242 | |
| 243 | constexpr fp() : f(0), e(0) {} |
| 244 | constexpr fp(uint64_t f_val, int e_val) : f(f_val), e(e_val) {} |
| 245 | |
| 246 | // Constructs fp from an IEEE754 floating-point number. It is a template to |
| 247 | // prevent compile errors on systems where n is not IEEE754. |
| 248 | template <typename Float> explicit FMT_CONSTEXPR fp(Float n) { assign(n); } |
| 249 | |
| 250 | template <typename Float> |
| 251 | using is_supported = bool_constant<sizeof(Float) == sizeof(uint64_t) || |
| 252 | sizeof(Float) == sizeof(uint32_t)>; |
| 253 | |
| 254 | // Assigns d to this and return true iff predecessor is closer than successor. |
| 255 | template <typename Float, FMT_ENABLE_IF(is_supported<Float>::value)> |
| 256 | FMT_CONSTEXPR bool assign(Float n) { |
| 257 | // Assume float is in the format [sign][exponent][significand]. |
| 258 | const int num_float_significand_bits = |
| 259 | detail::num_significand_bits<Float>(); |
| 260 | const uint64_t implicit_bit = 1ULL << num_float_significand_bits; |
| 261 | const uint64_t significand_mask = implicit_bit - 1; |
| 262 | constexpr bool is_double = sizeof(Float) == sizeof(uint64_t); |
| 263 | auto u = bit_cast<conditional_t<is_double, uint64_t, uint32_t>>(n); |
| 264 | f = u & significand_mask; |
| 265 | const uint64_t exponent_mask = (~0ULL >> 1) & ~significand_mask; |
| 266 | int biased_e = |
| 267 | static_cast<int>((u & exponent_mask) >> num_float_significand_bits); |
| 268 | // The predecessor is closer if n is a normalized power of 2 (f == 0) other |
| 269 | // than the smallest normalized number (biased_e > 1). |
| 270 | bool is_predecessor_closer = f == 0 && biased_e > 1; |
| 271 | if (biased_e != 0) |
| 272 | f += implicit_bit; |
| 273 | else |
| 274 | biased_e = 1; // Subnormals use biased exponent 1 (min exponent). |
| 275 | const int exponent_bias = std::numeric_limits<Float>::max_exponent - 1; |
| 276 | e = biased_e - exponent_bias - num_float_significand_bits; |
| 277 | return is_predecessor_closer; |
| 278 | } |
| 279 | |
| 280 | template <typename Float, FMT_ENABLE_IF(!is_supported<Float>::value)> |
| 281 | bool assign(Float) { |
| 282 | FMT_ASSERT(false, ""); |
| 283 | return false; |
| 284 | } |
| 285 | }; |
| 286 | |
| 287 | // Normalizes the value converted from double and multiplied by (1 << SHIFT). |
| 288 | template <int SHIFT = 0> FMT_CONSTEXPR fp normalize(fp value) { |
| 289 | // Handle subnormals. |
| 290 | const uint64_t implicit_bit = 1ULL << num_significand_bits<double>(); |
| 291 | const auto shifted_implicit_bit = implicit_bit << SHIFT; |
| 292 | while ((value.f & shifted_implicit_bit) == 0) { |
| 293 | value.f <<= 1; |
| 294 | --value.e; |
| 295 | } |
| 296 | // Subtract 1 to account for hidden bit. |
| 297 | const auto offset = |
| 298 | fp::num_significand_bits - num_significand_bits<double>() - SHIFT - 1; |
| 299 | value.f <<= offset; |
| 300 | value.e -= offset; |
| 301 | return value; |
| 302 | } |
| 303 | |
| 304 | inline bool operator==(fp x, fp y) { return x.f == y.f && x.e == y.e; } |
| 305 | |
| 306 | // Computes lhs * rhs / pow(2, 64) rounded to nearest with half-up tie breaking. |
| 307 | FMT_CONSTEXPR inline uint64_t multiply(uint64_t lhs, uint64_t rhs) { |
| 308 | #if FMT_USE_INT128 |
| 309 | auto product = static_cast<__uint128_t>(lhs) * rhs; |
| 310 | auto f = static_cast<uint64_t>(product >> 64); |
| 311 | return (static_cast<uint64_t>(product) & (1ULL << 63)) != 0 ? f + 1 : f; |
| 312 | #else |
| 313 | // Multiply 32-bit parts of significands. |
| 314 | uint64_t mask = (1ULL << 32) - 1; |
| 315 | uint64_t a = lhs >> 32, b = lhs & mask; |
| 316 | uint64_t c = rhs >> 32, d = rhs & mask; |
| 317 | uint64_t ac = a * c, bc = b * c, ad = a * d, bd = b * d; |
| 318 | // Compute mid 64-bit of result and round. |
| 319 | uint64_t mid = (bd >> 32) + (ad & mask) + (bc & mask) + (1U << 31); |
| 320 | return ac + (ad >> 32) + (bc >> 32) + (mid >> 32); |
| 321 | #endif |
| 322 | } |
| 323 | |
| 324 | FMT_CONSTEXPR inline fp operator*(fp x, fp y) { |
| 325 | return {multiply(x.f, y.f), x.e + y.e + 64}; |
| 326 | } |
| 327 | |
| 328 | // Returns a cached power of 10 `c_k = c_k.f * pow(2, c_k.e)` such that its |
| 329 | // (binary) exponent satisfies `min_exponent <= c_k.e <= min_exponent + 28`. |
| 330 | FMT_CONSTEXPR inline fp get_cached_power(int min_exponent, |
| 331 | int& pow10_exponent) { |
| 332 | const int shift = 32; |
| 333 | const auto significand = static_cast<int64_t>(log10_2_significand); |
| 334 | int index = static_cast<int>( |
| 335 | ((min_exponent + fp::num_significand_bits - 1) * (significand >> shift) + |
| 336 | ((int64_t(1) << shift) - 1)) // ceil |
| 337 | >> 32 // arithmetic shift |
| 338 | ); |
| 339 | // Decimal exponent of the first (smallest) cached power of 10. |
| 340 | const int first_dec_exp = -348; |
| 341 | // Difference between 2 consecutive decimal exponents in cached powers of 10. |
| 342 | const int dec_exp_step = 8; |
| 343 | index = (index - first_dec_exp - 1) / dec_exp_step + 1; |
| 344 | pow10_exponent = first_dec_exp + index * dec_exp_step; |
| 345 | return {impl_data::pow10_significands[index], |
| 346 | impl_data::pow10_exponents[index]}; |
| 347 | } |
| 348 | |
| 349 | // A simple accumulator to hold the sums of terms in bigint::square if uint128_t |
| 350 | // is not available. |
| 351 | struct accumulator { |
| 352 | uint64_t lower; |
| 353 | uint64_t upper; |
| 354 | |
| 355 | constexpr accumulator() : lower(0), upper(0) {} |
| 356 | constexpr explicit operator uint32_t() const { |
| 357 | return static_cast<uint32_t>(lower); |
| 358 | } |
| 359 | |
| 360 | FMT_CONSTEXPR void operator+=(uint64_t n) { |
| 361 | lower += n; |
| 362 | if (lower < n) ++upper; |
| 363 | } |
| 364 | FMT_CONSTEXPR void operator>>=(int shift) { |
| 365 | FMT_ASSERT(shift == 32, ""); |
| 366 | (void)shift; |
| 367 | lower = (upper << 32) | (lower >> 32); |
| 368 | upper >>= 32; |
| 369 | } |
| 370 | }; |
| 371 | |
| 372 | class bigint { |
| 373 | private: |
| 374 | // A bigint is stored as an array of bigits (big digits), with bigit at index |
| 375 | // 0 being the least significant one. |
| 376 | using bigit = uint32_t; |
| 377 | using double_bigit = uint64_t; |
| 378 | enum { bigits_capacity = 32 }; |
| 379 | basic_memory_buffer<bigit, bigits_capacity> bigits_; |
| 380 | int exp_; |
| 381 | |
| 382 | FMT_CONSTEXPR20 bigit operator[](int index) const { |
| 383 | return bigits_[to_unsigned(index)]; |
| 384 | } |
| 385 | FMT_CONSTEXPR20 bigit& operator[](int index) { |
| 386 | return bigits_[to_unsigned(index)]; |
| 387 | } |
| 388 | |
| 389 | static FMT_CONSTEXPR_DECL const int bigit_bits = bits<bigit>::value; |
| 390 | |
| 391 | friend struct formatter<bigint>; |
| 392 | |
| 393 | FMT_CONSTEXPR20 void subtract_bigits(int index, bigit other, bigit& borrow) { |
| 394 | auto result = static_cast<double_bigit>((*this)[index]) - other - borrow; |
| 395 | (*this)[index] = static_cast<bigit>(result); |
| 396 | borrow = static_cast<bigit>(result >> (bigit_bits * 2 - 1)); |
| 397 | } |
| 398 | |
| 399 | FMT_CONSTEXPR20 void remove_leading_zeros() { |
| 400 | int num_bigits = static_cast<int>(bigits_.size()) - 1; |
| 401 | while (num_bigits > 0 && (*this)[num_bigits] == 0) --num_bigits; |
| 402 | bigits_.resize(to_unsigned(num_bigits + 1)); |
| 403 | } |
| 404 | |
| 405 | // Computes *this -= other assuming aligned bigints and *this >= other. |
| 406 | FMT_CONSTEXPR20 void subtract_aligned(const bigint& other) { |
| 407 | FMT_ASSERT(other.exp_ >= exp_, "unaligned bigints"); |
| 408 | FMT_ASSERT(compare(*this, other) >= 0, ""); |
| 409 | bigit borrow = 0; |
| 410 | int i = other.exp_ - exp_; |
| 411 | for (size_t j = 0, n = other.bigits_.size(); j != n; ++i, ++j) |
| 412 | subtract_bigits(i, other.bigits_[j], borrow); |
| 413 | while (borrow > 0) subtract_bigits(i, 0, borrow); |
| 414 | remove_leading_zeros(); |
| 415 | } |
| 416 | |
| 417 | FMT_CONSTEXPR20 void multiply(uint32_t value) { |
| 418 | const double_bigit wide_value = value; |
| 419 | bigit carry = 0; |
| 420 | for (size_t i = 0, n = bigits_.size(); i < n; ++i) { |
| 421 | double_bigit result = bigits_[i] * wide_value + carry; |
| 422 | bigits_[i] = static_cast<bigit>(result); |
| 423 | carry = static_cast<bigit>(result >> bigit_bits); |
| 424 | } |
| 425 | if (carry != 0) bigits_.push_back(carry); |
| 426 | } |
| 427 | |
| 428 | FMT_CONSTEXPR20 void multiply(uint64_t value) { |
| 429 | const bigit mask = ~bigit(0); |
| 430 | const double_bigit lower = value & mask; |
| 431 | const double_bigit upper = value >> bigit_bits; |
| 432 | double_bigit carry = 0; |
| 433 | for (size_t i = 0, n = bigits_.size(); i < n; ++i) { |
| 434 | double_bigit result = bigits_[i] * lower + (carry & mask); |
| 435 | carry = |
| 436 | bigits_[i] * upper + (result >> bigit_bits) + (carry >> bigit_bits); |
| 437 | bigits_[i] = static_cast<bigit>(result); |
| 438 | } |
| 439 | while (carry != 0) { |
| 440 | bigits_.push_back(carry & mask); |
| 441 | carry >>= bigit_bits; |
| 442 | } |
| 443 | } |
| 444 | |
| 445 | public: |
| 446 | FMT_CONSTEXPR20 bigint() : exp_(0) {} |
| 447 | explicit bigint(uint64_t n) { assign(n); } |
| 448 | FMT_CONSTEXPR20 ~bigint() { |
| 449 | FMT_ASSERT(bigits_.capacity() <= bigits_capacity, ""); |
| 450 | } |
| 451 | |
| 452 | bigint(const bigint&) = delete; |
| 453 | void operator=(const bigint&) = delete; |
| 454 | |
| 455 | FMT_CONSTEXPR20 void assign(const bigint& other) { |
| 456 | auto size = other.bigits_.size(); |
| 457 | bigits_.resize(size); |
| 458 | auto data = other.bigits_.data(); |
| 459 | std::copy(data, data + size, make_checked(bigits_.data(), size)); |
| 460 | exp_ = other.exp_; |
| 461 | } |
| 462 | |
| 463 | FMT_CONSTEXPR20 void assign(uint64_t n) { |
| 464 | size_t num_bigits = 0; |
| 465 | do { |
| 466 | bigits_[num_bigits++] = n & ~bigit(0); |
| 467 | n >>= bigit_bits; |
| 468 | } while (n != 0); |
| 469 | bigits_.resize(num_bigits); |
| 470 | exp_ = 0; |
| 471 | } |
| 472 | |
| 473 | FMT_CONSTEXPR20 int num_bigits() const { |
| 474 | return static_cast<int>(bigits_.size()) + exp_; |
| 475 | } |
| 476 | |
| 477 | FMT_NOINLINE FMT_CONSTEXPR20 bigint& operator<<=(int shift) { |
| 478 | FMT_ASSERT(shift >= 0, ""); |
| 479 | exp_ += shift / bigit_bits; |
| 480 | shift %= bigit_bits; |
| 481 | if (shift == 0) return *this; |
| 482 | bigit carry = 0; |
| 483 | for (size_t i = 0, n = bigits_.size(); i < n; ++i) { |
| 484 | bigit c = bigits_[i] >> (bigit_bits - shift); |
| 485 | bigits_[i] = (bigits_[i] << shift) + carry; |
| 486 | carry = c; |
| 487 | } |
| 488 | if (carry != 0) bigits_.push_back(carry); |
| 489 | return *this; |
| 490 | } |
| 491 | |
| 492 | template <typename Int> FMT_CONSTEXPR20 bigint& operator*=(Int value) { |
| 493 | FMT_ASSERT(value > 0, ""); |
| 494 | multiply(uint32_or_64_or_128_t<Int>(value)); |
| 495 | return *this; |
| 496 | } |
| 497 | |
| 498 | friend FMT_CONSTEXPR20 int compare(const bigint& lhs, const bigint& rhs) { |
| 499 | int num_lhs_bigits = lhs.num_bigits(), num_rhs_bigits = rhs.num_bigits(); |
| 500 | if (num_lhs_bigits != num_rhs_bigits) |
| 501 | return num_lhs_bigits > num_rhs_bigits ? 1 : -1; |
| 502 | int i = static_cast<int>(lhs.bigits_.size()) - 1; |
| 503 | int j = static_cast<int>(rhs.bigits_.size()) - 1; |
| 504 | int end = i - j; |
| 505 | if (end < 0) end = 0; |
| 506 | for (; i >= end; --i, --j) { |
| 507 | bigit lhs_bigit = lhs[i], rhs_bigit = rhs[j]; |
| 508 | if (lhs_bigit != rhs_bigit) return lhs_bigit > rhs_bigit ? 1 : -1; |
| 509 | } |
| 510 | if (i != j) return i > j ? 1 : -1; |
| 511 | return 0; |
| 512 | } |
| 513 | |
| 514 | // Returns compare(lhs1 + lhs2, rhs). |
| 515 | friend FMT_CONSTEXPR20 int add_compare(const bigint& lhs1, const bigint& lhs2, |
| 516 | const bigint& rhs) { |
| 517 | int max_lhs_bigits = (std::max)(lhs1.num_bigits(), lhs2.num_bigits()); |
| 518 | int num_rhs_bigits = rhs.num_bigits(); |
| 519 | if (max_lhs_bigits + 1 < num_rhs_bigits) return -1; |
| 520 | if (max_lhs_bigits > num_rhs_bigits) return 1; |
| 521 | auto get_bigit = [](const bigint& n, int i) -> bigit { |
| 522 | return i >= n.exp_ && i < n.num_bigits() ? n[i - n.exp_] : 0; |
| 523 | }; |
| 524 | double_bigit borrow = 0; |
| 525 | int min_exp = (std::min)((std::min)(lhs1.exp_, lhs2.exp_), rhs.exp_); |
| 526 | for (int i = num_rhs_bigits - 1; i >= min_exp; --i) { |
| 527 | double_bigit sum = |
| 528 | static_cast<double_bigit>(get_bigit(lhs1, i)) + get_bigit(lhs2, i); |
| 529 | bigit rhs_bigit = get_bigit(rhs, i); |
| 530 | if (sum > rhs_bigit + borrow) return 1; |
| 531 | borrow = rhs_bigit + borrow - sum; |
| 532 | if (borrow > 1) return -1; |
| 533 | borrow <<= bigit_bits; |
| 534 | } |
| 535 | return borrow != 0 ? -1 : 0; |
| 536 | } |
| 537 | |
| 538 | // Assigns pow(10, exp) to this bigint. |
| 539 | FMT_CONSTEXPR20 void assign_pow10(int exp) { |
| 540 | FMT_ASSERT(exp >= 0, ""); |
| 541 | if (exp == 0) return assign(1); |
| 542 | // Find the top bit. |
| 543 | int bitmask = 1; |
| 544 | while (exp >= bitmask) bitmask <<= 1; |
| 545 | bitmask >>= 1; |
| 546 | // pow(10, exp) = pow(5, exp) * pow(2, exp). First compute pow(5, exp) by |
| 547 | // repeated squaring and multiplication. |
| 548 | assign(5); |
| 549 | bitmask >>= 1; |
| 550 | while (bitmask != 0) { |
| 551 | square(); |
| 552 | if ((exp & bitmask) != 0) *this *= 5; |
| 553 | bitmask >>= 1; |
| 554 | } |
| 555 | *this <<= exp; // Multiply by pow(2, exp) by shifting. |
| 556 | } |
| 557 | |
| 558 | FMT_CONSTEXPR20 void square() { |
| 559 | int num_bigits = static_cast<int>(bigits_.size()); |
| 560 | int num_result_bigits = 2 * num_bigits; |
| 561 | basic_memory_buffer<bigit, bigits_capacity> n(std::move(bigits_)); |
| 562 | bigits_.resize(to_unsigned(num_result_bigits)); |
| 563 | using accumulator_t = conditional_t<FMT_USE_INT128, uint128_t, accumulator>; |
| 564 | auto sum = accumulator_t(); |
| 565 | for (int bigit_index = 0; bigit_index < num_bigits; ++bigit_index) { |
| 566 | // Compute bigit at position bigit_index of the result by adding |
| 567 | // cross-product terms n[i] * n[j] such that i + j == bigit_index. |
| 568 | for (int i = 0, j = bigit_index; j >= 0; ++i, --j) { |
| 569 | // Most terms are multiplied twice which can be optimized in the future. |
| 570 | sum += static_cast<double_bigit>(n[i]) * n[j]; |
| 571 | } |
| 572 | (*this)[bigit_index] = static_cast<bigit>(sum); |
| 573 | sum >>= bits<bigit>::value; // Compute the carry. |
| 574 | } |
| 575 | // Do the same for the top half. |
| 576 | for (int bigit_index = num_bigits; bigit_index < num_result_bigits; |
| 577 | ++bigit_index) { |
| 578 | for (int j = num_bigits - 1, i = bigit_index - j; i < num_bigits;) |
| 579 | sum += static_cast<double_bigit>(n[i++]) * n[j--]; |
| 580 | (*this)[bigit_index] = static_cast<bigit>(sum); |
| 581 | sum >>= bits<bigit>::value; |
| 582 | } |
| 583 | remove_leading_zeros(); |
| 584 | exp_ *= 2; |
| 585 | } |
| 586 | |
| 587 | // If this bigint has a bigger exponent than other, adds trailing zero to make |
| 588 | // exponents equal. This simplifies some operations such as subtraction. |
| 589 | FMT_CONSTEXPR20 void align(const bigint& other) { |
| 590 | int exp_difference = exp_ - other.exp_; |
| 591 | if (exp_difference <= 0) return; |
| 592 | int num_bigits = static_cast<int>(bigits_.size()); |
| 593 | bigits_.resize(to_unsigned(num_bigits + exp_difference)); |
| 594 | for (int i = num_bigits - 1, j = i + exp_difference; i >= 0; --i, --j) |
| 595 | bigits_[j] = bigits_[i]; |
| 596 | std::uninitialized_fill_n(bigits_.data(), exp_difference, 0); |
| 597 | exp_ -= exp_difference; |
| 598 | } |
| 599 | |
| 600 | // Divides this bignum by divisor, assigning the remainder to this and |
| 601 | // returning the quotient. |
| 602 | FMT_CONSTEXPR20 int divmod_assign(const bigint& divisor) { |
| 603 | FMT_ASSERT(this != &divisor, ""); |
| 604 | if (compare(*this, divisor) < 0) return 0; |
| 605 | FMT_ASSERT(divisor.bigits_[divisor.bigits_.size() - 1u] != 0, ""); |
| 606 | align(divisor); |
| 607 | int quotient = 0; |
| 608 | do { |
| 609 | subtract_aligned(divisor); |
| 610 | ++quotient; |
| 611 | } while (compare(*this, divisor) >= 0); |
| 612 | return quotient; |
| 613 | } |
| 614 | }; |
| 615 | |
| 616 | enum class round_direction { unknown, up, down }; |
| 617 | |
| 618 | // Given the divisor (normally a power of 10), the remainder = v % divisor for |
| 619 | // some number v and the error, returns whether v should be rounded up, down, or |
| 620 | // whether the rounding direction can't be determined due to error. |
| 621 | // error should be less than divisor / 2. |
| 622 | FMT_CONSTEXPR inline round_direction get_round_direction(uint64_t divisor, |
| 623 | uint64_t remainder, |
| 624 | uint64_t error) { |
| 625 | FMT_ASSERT(remainder < divisor, ""); // divisor - remainder won't overflow. |
| 626 | FMT_ASSERT(error < divisor, ""); // divisor - error won't overflow. |
| 627 | FMT_ASSERT(error < divisor - error, ""); // error * 2 won't overflow. |
| 628 | // Round down if (remainder + error) * 2 <= divisor. |
| 629 | if (remainder <= divisor - remainder && error * 2 <= divisor - remainder * 2) |
| 630 | return round_direction::down; |
| 631 | // Round up if (remainder - error) * 2 >= divisor. |
| 632 | if (remainder >= error && |
| 633 | remainder - error >= divisor - (remainder - error)) { |
| 634 | return round_direction::up; |
| 635 | } |
| 636 | return round_direction::unknown; |
| 637 | } |
| 638 | |
| 639 | namespace digits { |
| 640 | enum result { |
| 641 | more, // Generate more digits. |
| 642 | done, // Done generating digits. |
| 643 | error // Digit generation cancelled due to an error. |
| 644 | }; |
| 645 | } |
| 646 | |
| 647 | struct gen_digits_handler { |
| 648 | char* buf; |
| 649 | int size; |
| 650 | int precision; |
| 651 | int exp10; |
| 652 | bool fixed; |
| 653 | |
| 654 | FMT_CONSTEXPR digits::result on_digit(char digit, uint64_t divisor, |
| 655 | uint64_t remainder, uint64_t error, |
| 656 | bool integral) { |
| 657 | FMT_ASSERT(remainder < divisor, ""); |
| 658 | buf[size++] = digit; |
| 659 | if (!integral && error >= remainder) return digits::error; |
| 660 | if (size < precision) return digits::more; |
| 661 | if (!integral) { |
| 662 | // Check if error * 2 < divisor with overflow prevention. |
| 663 | // The check is not needed for the integral part because error = 1 |
| 664 | // and divisor > (1 << 32) there. |
| 665 | if (error >= divisor || error >= divisor - error) return digits::error; |
| 666 | } else { |
| 667 | FMT_ASSERT(error == 1 && divisor > 2, ""); |
| 668 | } |
| 669 | auto dir = get_round_direction(divisor, remainder, error); |
| 670 | if (dir != round_direction::up) |
| 671 | return dir == round_direction::down ? digits::done : digits::error; |
| 672 | ++buf[size - 1]; |
| 673 | for (int i = size - 1; i > 0 && buf[i] > '9'; --i) { |
| 674 | buf[i] = '0'; |
| 675 | ++buf[i - 1]; |
| 676 | } |
| 677 | if (buf[0] > '9') { |
| 678 | buf[0] = '1'; |
| 679 | if (fixed) |
| 680 | buf[size++] = '0'; |
| 681 | else |
| 682 | ++exp10; |
| 683 | } |
| 684 | return digits::done; |
| 685 | } |
| 686 | }; |
| 687 | |
| 688 | // Generates output using the Grisu digit-gen algorithm. |
| 689 | // error: the size of the region (lower, upper) outside of which numbers |
| 690 | // definitely do not round to value (Delta in Grisu3). |
| 691 | FMT_INLINE FMT_CONSTEXPR20 digits::result grisu_gen_digits( |
| 692 | fp value, uint64_t error, int& exp, gen_digits_handler& handler) { |
| 693 | const fp one(1ULL << -value.e, value.e); |
| 694 | // The integral part of scaled value (p1 in Grisu) = value / one. It cannot be |
| 695 | // zero because it contains a product of two 64-bit numbers with MSB set (due |
| 696 | // to normalization) - 1, shifted right by at most 60 bits. |
| 697 | auto integral = static_cast<uint32_t>(value.f >> -one.e); |
| 698 | FMT_ASSERT(integral != 0, ""); |
| 699 | FMT_ASSERT(integral == value.f >> -one.e, ""); |
| 700 | // The fractional part of scaled value (p2 in Grisu) c = value % one. |
| 701 | uint64_t fractional = value.f & (one.f - 1); |
| 702 | exp = count_digits(integral); // kappa in Grisu. |
| 703 | // Non-fixed formats require at least one digit and no precision adjustment. |
| 704 | if (handler.fixed) { |
| 705 | // Adjust fixed precision by exponent because it is relative to decimal |
| 706 | // point. |
| 707 | int precision_offset = exp + handler.exp10; |
| 708 | if (precision_offset > 0 && |
| 709 | handler.precision > max_value<int>() - precision_offset) { |
| 710 | FMT_THROW(format_error("number is too big")); |
| 711 | } |
| 712 | handler.precision += precision_offset; |
| 713 | // Check if precision is satisfied just by leading zeros, e.g. |
| 714 | // format("{:.2f}", 0.001) gives "0.00" without generating any digits. |
| 715 | if (handler.precision <= 0) { |
| 716 | if (handler.precision < 0) return digits::done; |
| 717 | // Divide by 10 to prevent overflow. |
| 718 | uint64_t divisor = impl_data::power_of_10_64[exp - 1] << -one.e; |
| 719 | auto dir = get_round_direction(divisor, value.f / 10, error * 10); |
| 720 | if (dir == round_direction::unknown) return digits::error; |
| 721 | handler.buf[handler.size++] = dir == round_direction::up ? '1' : '0'; |
| 722 | return digits::done; |
| 723 | } |
| 724 | } |
| 725 | // Generate digits for the integral part. This can produce up to 10 digits. |
| 726 | do { |
| 727 | uint32_t digit = 0; |
| 728 | auto divmod_integral = [&](uint32_t divisor) { |
| 729 | digit = integral / divisor; |
| 730 | integral %= divisor; |
| 731 | }; |
| 732 | // This optimization by Milo Yip reduces the number of integer divisions by |
| 733 | // one per iteration. |
| 734 | switch (exp) { |
| 735 | case 10: |
| 736 | divmod_integral(1000000000); |
| 737 | break; |
| 738 | case 9: |
| 739 | divmod_integral(100000000); |
| 740 | break; |
| 741 | case 8: |
| 742 | divmod_integral(10000000); |
| 743 | break; |
| 744 | case 7: |
| 745 | divmod_integral(1000000); |
| 746 | break; |
| 747 | case 6: |
| 748 | divmod_integral(100000); |
| 749 | break; |
| 750 | case 5: |
| 751 | divmod_integral(10000); |
| 752 | break; |
| 753 | case 4: |
| 754 | divmod_integral(1000); |
| 755 | break; |
| 756 | case 3: |
| 757 | divmod_integral(100); |
| 758 | break; |
| 759 | case 2: |
| 760 | divmod_integral(10); |
| 761 | break; |
| 762 | case 1: |
| 763 | digit = integral; |
| 764 | integral = 0; |
| 765 | break; |
| 766 | default: |
| 767 | FMT_ASSERT(false, "invalid number of digits"); |
| 768 | } |
| 769 | --exp; |
| 770 | auto remainder = (static_cast<uint64_t>(integral) << -one.e) + fractional; |
| 771 | auto result = handler.on_digit(static_cast<char>('0' + digit), |
| 772 | impl_data::power_of_10_64[exp] << -one.e, |
| 773 | remainder, error, true); |
| 774 | if (result != digits::more) return result; |
| 775 | } while (exp > 0); |
| 776 | // Generate digits for the fractional part. |
| 777 | for (;;) { |
| 778 | fractional *= 10; |
| 779 | error *= 10; |
| 780 | char digit = static_cast<char>('0' + (fractional >> -one.e)); |
| 781 | fractional &= one.f - 1; |
| 782 | --exp; |
| 783 | auto result = handler.on_digit(digit, one.f, fractional, error, false); |
| 784 | if (result != digits::more) return result; |
| 785 | } |
| 786 | } |
| 787 | |
| 788 | // A 128-bit integer type used internally, |
| 789 | struct uint128_wrapper { |
| 790 | uint128_wrapper() = default; |
| 791 | |
| 792 | #if FMT_USE_INT128 |
| 793 | uint128_t internal_; |
| 794 | |
| 795 | constexpr uint128_wrapper(uint64_t high, uint64_t low) FMT_NOEXCEPT |
| 796 | : internal_{static_cast<uint128_t>(low) | |
| 797 | (static_cast<uint128_t>(high) << 64)} {} |
| 798 | |
| 799 | constexpr uint128_wrapper(uint128_t u) : internal_{u} {} |
| 800 | |
| 801 | constexpr uint64_t high() const FMT_NOEXCEPT { |
| 802 | return uint64_t(internal_ >> 64); |
| 803 | } |
| 804 | constexpr uint64_t low() const FMT_NOEXCEPT { return uint64_t(internal_); } |
| 805 | |
| 806 | uint128_wrapper& operator+=(uint64_t n) FMT_NOEXCEPT { |
| 807 | internal_ += n; |
| 808 | return *this; |
| 809 | } |
| 810 | #else |
| 811 | uint64_t high_; |
| 812 | uint64_t low_; |
| 813 | |
| 814 | constexpr uint128_wrapper(uint64_t high, uint64_t low) FMT_NOEXCEPT |
| 815 | : high_{high}, |
| 816 | low_{low} {} |
| 817 | |
| 818 | constexpr uint64_t high() const FMT_NOEXCEPT { return high_; } |
| 819 | constexpr uint64_t low() const FMT_NOEXCEPT { return low_; } |
| 820 | |
| 821 | uint128_wrapper& operator+=(uint64_t n) FMT_NOEXCEPT { |
| 822 | # if defined(_MSC_VER) && defined(_M_X64) |
| 823 | unsigned char carry = _addcarry_u64(0, low_, n, &low_); |
| 824 | _addcarry_u64(carry, high_, 0, &high_); |
| 825 | return *this; |
| 826 | # else |
| 827 | uint64_t sum = low_ + n; |
| 828 | high_ += (sum < low_ ? 1 : 0); |
| 829 | low_ = sum; |
| 830 | return *this; |
| 831 | # endif |
| 832 | } |
| 833 | #endif |
| 834 | }; |
| 835 | |
| 836 | // Implementation of Dragonbox algorithm: https://github.com/jk-jeon/dragonbox. |
| 837 | namespace dragonbox { |
| 838 | // Computes 128-bit result of multiplication of two 64-bit unsigned integers. |
| 839 | inline uint128_wrapper umul128(uint64_t x, uint64_t y) FMT_NOEXCEPT { |
| 840 | #if FMT_USE_INT128 |
| 841 | return static_cast<uint128_t>(x) * static_cast<uint128_t>(y); |
| 842 | #elif defined(_MSC_VER) && defined(_M_X64) |
| 843 | uint128_wrapper result; |
| 844 | result.low_ = _umul128(x, y, &result.high_); |
| 845 | return result; |
| 846 | #else |
| 847 | const uint64_t mask = (uint64_t(1) << 32) - uint64_t(1); |
| 848 | |
| 849 | uint64_t a = x >> 32; |
| 850 | uint64_t b = x & mask; |
| 851 | uint64_t c = y >> 32; |
| 852 | uint64_t d = y & mask; |
| 853 | |
| 854 | uint64_t ac = a * c; |
| 855 | uint64_t bc = b * c; |
| 856 | uint64_t ad = a * d; |
| 857 | uint64_t bd = b * d; |
| 858 | |
| 859 | uint64_t intermediate = (bd >> 32) + (ad & mask) + (bc & mask); |
| 860 | |
| 861 | return {ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32), |
| 862 | (intermediate << 32) + (bd & mask)}; |
| 863 | #endif |
| 864 | } |
| 865 | |
| 866 | // Computes upper 64 bits of multiplication of two 64-bit unsigned integers. |
| 867 | inline uint64_t umul128_upper64(uint64_t x, uint64_t y) FMT_NOEXCEPT { |
| 868 | #if FMT_USE_INT128 |
| 869 | auto p = static_cast<uint128_t>(x) * static_cast<uint128_t>(y); |
| 870 | return static_cast<uint64_t>(p >> 64); |
| 871 | #elif defined(_MSC_VER) && defined(_M_X64) |
| 872 | return __umulh(x, y); |
| 873 | #else |
| 874 | return umul128(x, y).high(); |
| 875 | #endif |
| 876 | } |
| 877 | |
| 878 | // Computes upper 64 bits of multiplication of a 64-bit unsigned integer and a |
| 879 | // 128-bit unsigned integer. |
| 880 | inline uint64_t umul192_upper64(uint64_t x, uint128_wrapper y) FMT_NOEXCEPT { |
| 881 | uint128_wrapper g0 = umul128(x, y.high()); |
| 882 | g0 += umul128_upper64(x, y.low()); |
| 883 | return g0.high(); |
| 884 | } |
| 885 | |
| 886 | // Computes upper 32 bits of multiplication of a 32-bit unsigned integer and a |
| 887 | // 64-bit unsigned integer. |
| 888 | inline uint32_t umul96_upper32(uint32_t x, uint64_t y) FMT_NOEXCEPT { |
| 889 | return static_cast<uint32_t>(umul128_upper64(x, y)); |
| 890 | } |
| 891 | |
| 892 | // Computes middle 64 bits of multiplication of a 64-bit unsigned integer and a |
| 893 | // 128-bit unsigned integer. |
| 894 | inline uint64_t umul192_middle64(uint64_t x, uint128_wrapper y) FMT_NOEXCEPT { |
| 895 | uint64_t g01 = x * y.high(); |
| 896 | uint64_t g10 = umul128_upper64(x, y.low()); |
| 897 | return g01 + g10; |
| 898 | } |
| 899 | |
| 900 | // Computes lower 64 bits of multiplication of a 32-bit unsigned integer and a |
| 901 | // 64-bit unsigned integer. |
| 902 | inline uint64_t umul96_lower64(uint32_t x, uint64_t y) FMT_NOEXCEPT { |
| 903 | return x * y; |
| 904 | } |
| 905 | |
| 906 | // Computes floor(log10(pow(2, e))) for e in [-1700, 1700] using the method from |
| 907 | // https://fmt.dev/papers/Grisu-Exact.pdf#page=5, section 3.4. |
| 908 | inline int floor_log10_pow2(int e) FMT_NOEXCEPT { |
| 909 | FMT_ASSERT(e <= 1700 && e >= -1700, "too large exponent"); |
| 910 | const int shift = 22; |
| 911 | return (e * static_cast<int>(log10_2_significand >> (64 - shift))) >> shift; |
| 912 | } |
| 913 | |
| 914 | // Various fast log computations. |
| 915 | inline int floor_log2_pow10(int e) FMT_NOEXCEPT { |
| 916 | FMT_ASSERT(e <= 1233 && e >= -1233, "too large exponent"); |
| 917 | const uint64_t log2_10_integer_part = 3; |
| 918 | const uint64_t log2_10_fractional_digits = 0x5269e12f346e2bf9; |
| 919 | const int shift_amount = 19; |
| 920 | return (e * static_cast<int>( |
| 921 | (log2_10_integer_part << shift_amount) | |
| 922 | (log2_10_fractional_digits >> (64 - shift_amount)))) >> |
| 923 | shift_amount; |
| 924 | } |
| 925 | inline int floor_log10_pow2_minus_log10_4_over_3(int e) FMT_NOEXCEPT { |
| 926 | FMT_ASSERT(e <= 1700 && e >= -1700, "too large exponent"); |
| 927 | const uint64_t log10_4_over_3_fractional_digits = 0x1ffbfc2bbc780375; |
| 928 | const int shift_amount = 22; |
| 929 | return (e * static_cast<int>(log10_2_significand >> (64 - shift_amount)) - |
| 930 | static_cast<int>(log10_4_over_3_fractional_digits >> |
| 931 | (64 - shift_amount))) >> |
| 932 | shift_amount; |
| 933 | } |
| 934 | |
| 935 | // Returns true iff x is divisible by pow(2, exp). |
| 936 | inline bool divisible_by_power_of_2(uint32_t x, int exp) FMT_NOEXCEPT { |
| 937 | FMT_ASSERT(exp >= 1, ""); |
| 938 | FMT_ASSERT(x != 0, ""); |
| 939 | #ifdef FMT_BUILTIN_CTZ |
| 940 | return FMT_BUILTIN_CTZ(x) >= exp; |
| 941 | #else |
| 942 | return exp < num_bits<uint32_t>() && x == ((x >> exp) << exp); |
| 943 | #endif |
| 944 | } |
| 945 | inline bool divisible_by_power_of_2(uint64_t x, int exp) FMT_NOEXCEPT { |
| 946 | FMT_ASSERT(exp >= 1, ""); |
| 947 | FMT_ASSERT(x != 0, ""); |
| 948 | #ifdef FMT_BUILTIN_CTZLL |
| 949 | return FMT_BUILTIN_CTZLL(x) >= exp; |
| 950 | #else |
| 951 | return exp < num_bits<uint64_t>() && x == ((x >> exp) << exp); |
| 952 | #endif |
| 953 | } |
| 954 | |
| 955 | // Table entry type for divisibility test. |
| 956 | template <typename T> struct divtest_table_entry { |
| 957 | T mod_inv; |
| 958 | T max_quotient; |
| 959 | }; |
| 960 | |
| 961 | // Returns true iff x is divisible by pow(5, exp). |
| 962 | inline bool divisible_by_power_of_5(uint32_t x, int exp) FMT_NOEXCEPT { |
| 963 | FMT_ASSERT(exp <= 10, "too large exponent"); |
| 964 | static constexpr const divtest_table_entry<uint32_t> divtest_table[] = { |
| 965 | {0x00000001, 0xffffffff}, {0xcccccccd, 0x33333333}, |
| 966 | {0xc28f5c29, 0x0a3d70a3}, {0x26e978d5, 0x020c49ba}, |
| 967 | {0x3afb7e91, 0x0068db8b}, {0x0bcbe61d, 0x0014f8b5}, |
| 968 | {0x68c26139, 0x000431bd}, {0xae8d46a5, 0x0000d6bf}, |
| 969 | {0x22e90e21, 0x00002af3}, {0x3a2e9c6d, 0x00000897}, |
| 970 | {0x3ed61f49, 0x000001b7}}; |
| 971 | return x * divtest_table[exp].mod_inv <= divtest_table[exp].max_quotient; |
| 972 | } |
| 973 | inline bool divisible_by_power_of_5(uint64_t x, int exp) FMT_NOEXCEPT { |
| 974 | FMT_ASSERT(exp <= 23, "too large exponent"); |
| 975 | static constexpr const divtest_table_entry<uint64_t> divtest_table[] = { |
| 976 | {0x0000000000000001, 0xffffffffffffffff}, |
| 977 | {0xcccccccccccccccd, 0x3333333333333333}, |
| 978 | {0x8f5c28f5c28f5c29, 0x0a3d70a3d70a3d70}, |
| 979 | {0x1cac083126e978d5, 0x020c49ba5e353f7c}, |
| 980 | {0xd288ce703afb7e91, 0x0068db8bac710cb2}, |
| 981 | {0x5d4e8fb00bcbe61d, 0x0014f8b588e368f0}, |
| 982 | {0x790fb65668c26139, 0x000431bde82d7b63}, |
| 983 | {0xe5032477ae8d46a5, 0x0000d6bf94d5e57a}, |
| 984 | {0xc767074b22e90e21, 0x00002af31dc46118}, |
| 985 | {0x8e47ce423a2e9c6d, 0x0000089705f4136b}, |
| 986 | {0x4fa7f60d3ed61f49, 0x000001b7cdfd9d7b}, |
| 987 | {0x0fee64690c913975, 0x00000057f5ff85e5}, |
| 988 | {0x3662e0e1cf503eb1, 0x000000119799812d}, |
| 989 | {0xa47a2cf9f6433fbd, 0x0000000384b84d09}, |
| 990 | {0x54186f653140a659, 0x00000000b424dc35}, |
| 991 | {0x7738164770402145, 0x0000000024075f3d}, |
| 992 | {0xe4a4d1417cd9a041, 0x000000000734aca5}, |
| 993 | {0xc75429d9e5c5200d, 0x000000000170ef54}, |
| 994 | {0xc1773b91fac10669, 0x000000000049c977}, |
| 995 | {0x26b172506559ce15, 0x00000000000ec1e4}, |
| 996 | {0xd489e3a9addec2d1, 0x000000000002f394}, |
| 997 | {0x90e860bb892c8d5d, 0x000000000000971d}, |
| 998 | {0x502e79bf1b6f4f79, 0x0000000000001e39}, |
| 999 | {0xdcd618596be30fe5, 0x000000000000060b}}; |
| 1000 | return x * divtest_table[exp].mod_inv <= divtest_table[exp].max_quotient; |
| 1001 | } |
| 1002 | |
| 1003 | // Replaces n by floor(n / pow(5, N)) returning true if and only if n is |
| 1004 | // divisible by pow(5, N). |
| 1005 | // Precondition: n <= 2 * pow(5, N + 1). |
| 1006 | template <int N> |
| 1007 | bool check_divisibility_and_divide_by_pow5(uint32_t& n) FMT_NOEXCEPT { |
| 1008 | static constexpr struct { |
| 1009 | uint32_t magic_number; |
| 1010 | int bits_for_comparison; |
| 1011 | uint32_t threshold; |
| 1012 | int shift_amount; |
| 1013 | } infos[] = {{0xcccd, 16, 0x3333, 18}, {0xa429, 8, 0x0a, 20}}; |
| 1014 | constexpr auto info = infos[N - 1]; |
| 1015 | n *= info.magic_number; |
| 1016 | const uint32_t comparison_mask = (1u << info.bits_for_comparison) - 1; |
| 1017 | bool result = (n & comparison_mask) <= info.threshold; |
| 1018 | n >>= info.shift_amount; |
| 1019 | return result; |
| 1020 | } |
| 1021 | |
| 1022 | // Computes floor(n / pow(10, N)) for small n and N. |
| 1023 | // Precondition: n <= pow(10, N + 1). |
| 1024 | template <int N> uint32_t small_division_by_pow10(uint32_t n) FMT_NOEXCEPT { |
| 1025 | static constexpr struct { |
| 1026 | uint32_t magic_number; |
| 1027 | int shift_amount; |
| 1028 | uint32_t divisor_times_10; |
| 1029 | } infos[] = {{0xcccd, 19, 100}, {0xa3d8, 22, 1000}}; |
| 1030 | constexpr auto info = infos[N - 1]; |
| 1031 | FMT_ASSERT(n <= info.divisor_times_10, "n is too large"); |
| 1032 | return n * info.magic_number >> info.shift_amount; |
| 1033 | } |
| 1034 | |
| 1035 | // Computes floor(n / 10^(kappa + 1)) (float) |
| 1036 | inline uint32_t divide_by_10_to_kappa_plus_1(uint32_t n) FMT_NOEXCEPT { |
| 1037 | return n / float_info<float>::big_divisor; |
| 1038 | } |
| 1039 | // Computes floor(n / 10^(kappa + 1)) (double) |
| 1040 | inline uint64_t divide_by_10_to_kappa_plus_1(uint64_t n) FMT_NOEXCEPT { |
| 1041 | return umul128_upper64(n, 0x83126e978d4fdf3c) >> 9; |
| 1042 | } |
| 1043 | |
| 1044 | // Various subroutines using pow10 cache |
| 1045 | template <class T> struct cache_accessor; |
| 1046 | |
| 1047 | template <> struct cache_accessor<float> { |
| 1048 | using carrier_uint = float_info<float>::carrier_uint; |
| 1049 | using cache_entry_type = uint64_t; |
| 1050 | |
| 1051 | static uint64_t get_cached_power(int k) FMT_NOEXCEPT { |
| 1052 | FMT_ASSERT(k >= float_info<float>::min_k && k <= float_info<float>::max_k, |
| 1053 | "k is out of range"); |
| 1054 | static constexpr const uint64_t pow10_significands[] = { |
| 1055 | 0x81ceb32c4b43fcf5, 0xa2425ff75e14fc32, 0xcad2f7f5359a3b3f, |
| 1056 | 0xfd87b5f28300ca0e, 0x9e74d1b791e07e49, 0xc612062576589ddb, |
| 1057 | 0xf79687aed3eec552, 0x9abe14cd44753b53, 0xc16d9a0095928a28, |
| 1058 | 0xf1c90080baf72cb2, 0x971da05074da7bef, 0xbce5086492111aeb, |
| 1059 | 0xec1e4a7db69561a6, 0x9392ee8e921d5d08, 0xb877aa3236a4b44a, |
| 1060 | 0xe69594bec44de15c, 0x901d7cf73ab0acda, 0xb424dc35095cd810, |
| 1061 | 0xe12e13424bb40e14, 0x8cbccc096f5088cc, 0xafebff0bcb24aaff, |
| 1062 | 0xdbe6fecebdedd5bf, 0x89705f4136b4a598, 0xabcc77118461cefd, |
| 1063 | 0xd6bf94d5e57a42bd, 0x8637bd05af6c69b6, 0xa7c5ac471b478424, |
| 1064 | 0xd1b71758e219652c, 0x83126e978d4fdf3c, 0xa3d70a3d70a3d70b, |
| 1065 | 0xcccccccccccccccd, 0x8000000000000000, 0xa000000000000000, |
| 1066 | 0xc800000000000000, 0xfa00000000000000, 0x9c40000000000000, |
| 1067 | 0xc350000000000000, 0xf424000000000000, 0x9896800000000000, |
| 1068 | 0xbebc200000000000, 0xee6b280000000000, 0x9502f90000000000, |
| 1069 | 0xba43b74000000000, 0xe8d4a51000000000, 0x9184e72a00000000, |
| 1070 | 0xb5e620f480000000, 0xe35fa931a0000000, 0x8e1bc9bf04000000, |
| 1071 | 0xb1a2bc2ec5000000, 0xde0b6b3a76400000, 0x8ac7230489e80000, |
| 1072 | 0xad78ebc5ac620000, 0xd8d726b7177a8000, 0x878678326eac9000, |
| 1073 | 0xa968163f0a57b400, 0xd3c21bcecceda100, 0x84595161401484a0, |
| 1074 | 0xa56fa5b99019a5c8, 0xcecb8f27f4200f3a, 0x813f3978f8940984, |
| 1075 | 0xa18f07d736b90be5, 0xc9f2c9cd04674ede, 0xfc6f7c4045812296, |
| 1076 | 0x9dc5ada82b70b59d, 0xc5371912364ce305, 0xf684df56c3e01bc6, |
| 1077 | 0x9a130b963a6c115c, 0xc097ce7bc90715b3, 0xf0bdc21abb48db20, |
| 1078 | 0x96769950b50d88f4, 0xbc143fa4e250eb31, 0xeb194f8e1ae525fd, |
| 1079 | 0x92efd1b8d0cf37be, 0xb7abc627050305ad, 0xe596b7b0c643c719, |
| 1080 | 0x8f7e32ce7bea5c6f, 0xb35dbf821ae4f38b, 0xe0352f62a19e306e}; |
| 1081 | return pow10_significands[k - float_info<float>::min_k]; |
| 1082 | } |
| 1083 | |
| 1084 | static carrier_uint compute_mul(carrier_uint u, |
| 1085 | const cache_entry_type& cache) FMT_NOEXCEPT { |
| 1086 | return umul96_upper32(u, cache); |
| 1087 | } |
| 1088 | |
| 1089 | static uint32_t compute_delta(const cache_entry_type& cache, |
| 1090 | int beta_minus_1) FMT_NOEXCEPT { |
| 1091 | return static_cast<uint32_t>(cache >> (64 - 1 - beta_minus_1)); |
| 1092 | } |
| 1093 | |
| 1094 | static bool compute_mul_parity(carrier_uint two_f, |
| 1095 | const cache_entry_type& cache, |
| 1096 | int beta_minus_1) FMT_NOEXCEPT { |
| 1097 | FMT_ASSERT(beta_minus_1 >= 1, ""); |
| 1098 | FMT_ASSERT(beta_minus_1 < 64, ""); |
| 1099 | |
| 1100 | return ((umul96_lower64(two_f, cache) >> (64 - beta_minus_1)) & 1) != 0; |
| 1101 | } |
| 1102 | |
| 1103 | static carrier_uint compute_left_endpoint_for_shorter_interval_case( |
| 1104 | const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT { |
| 1105 | return static_cast<carrier_uint>( |
| 1106 | (cache - (cache >> (float_info<float>::significand_bits + 2))) >> |
| 1107 | (64 - float_info<float>::significand_bits - 1 - beta_minus_1)); |
| 1108 | } |
| 1109 | |
| 1110 | static carrier_uint compute_right_endpoint_for_shorter_interval_case( |
| 1111 | const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT { |
| 1112 | return static_cast<carrier_uint>( |
| 1113 | (cache + (cache >> (float_info<float>::significand_bits + 1))) >> |
| 1114 | (64 - float_info<float>::significand_bits - 1 - beta_minus_1)); |
| 1115 | } |
| 1116 | |
| 1117 | static carrier_uint compute_round_up_for_shorter_interval_case( |
| 1118 | const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT { |
| 1119 | return (static_cast<carrier_uint>( |
| 1120 | cache >> |
| 1121 | (64 - float_info<float>::significand_bits - 2 - beta_minus_1)) + |
| 1122 | 1) / |
| 1123 | 2; |
| 1124 | } |
| 1125 | }; |
| 1126 | |
| 1127 | template <> struct cache_accessor<double> { |
| 1128 | using carrier_uint = float_info<double>::carrier_uint; |
| 1129 | using cache_entry_type = uint128_wrapper; |
| 1130 | |
| 1131 | static uint128_wrapper get_cached_power(int k) FMT_NOEXCEPT { |
| 1132 | FMT_ASSERT(k >= float_info<double>::min_k && k <= float_info<double>::max_k, |
| 1133 | "k is out of range"); |
| 1134 | |
| 1135 | static constexpr const uint128_wrapper pow10_significands[] = { |
| 1136 | #if FMT_USE_FULL_CACHE_DRAGONBOX |
| 1137 | {0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7b}, |
| 1138 | {0x9faacf3df73609b1, 0x77b191618c54e9ad}, |
| 1139 | {0xc795830d75038c1d, 0xd59df5b9ef6a2418}, |
| 1140 | {0xf97ae3d0d2446f25, 0x4b0573286b44ad1e}, |
| 1141 | {0x9becce62836ac577, 0x4ee367f9430aec33}, |
| 1142 | {0xc2e801fb244576d5, 0x229c41f793cda740}, |
| 1143 | {0xf3a20279ed56d48a, 0x6b43527578c11110}, |
| 1144 | {0x9845418c345644d6, 0x830a13896b78aaaa}, |
| 1145 | {0xbe5691ef416bd60c, 0x23cc986bc656d554}, |
| 1146 | {0xedec366b11c6cb8f, 0x2cbfbe86b7ec8aa9}, |
| 1147 | {0x94b3a202eb1c3f39, 0x7bf7d71432f3d6aa}, |
| 1148 | {0xb9e08a83a5e34f07, 0xdaf5ccd93fb0cc54}, |
| 1149 | {0xe858ad248f5c22c9, 0xd1b3400f8f9cff69}, |
| 1150 | {0x91376c36d99995be, 0x23100809b9c21fa2}, |
| 1151 | {0xb58547448ffffb2d, 0xabd40a0c2832a78b}, |
| 1152 | {0xe2e69915b3fff9f9, 0x16c90c8f323f516d}, |
| 1153 | {0x8dd01fad907ffc3b, 0xae3da7d97f6792e4}, |
| 1154 | {0xb1442798f49ffb4a, 0x99cd11cfdf41779d}, |
| 1155 | {0xdd95317f31c7fa1d, 0x40405643d711d584}, |
| 1156 | {0x8a7d3eef7f1cfc52, 0x482835ea666b2573}, |
| 1157 | {0xad1c8eab5ee43b66, 0xda3243650005eed0}, |
| 1158 | {0xd863b256369d4a40, 0x90bed43e40076a83}, |
| 1159 | {0x873e4f75e2224e68, 0x5a7744a6e804a292}, |
| 1160 | {0xa90de3535aaae202, 0x711515d0a205cb37}, |
| 1161 | {0xd3515c2831559a83, 0x0d5a5b44ca873e04}, |
| 1162 | {0x8412d9991ed58091, 0xe858790afe9486c3}, |
| 1163 | {0xa5178fff668ae0b6, 0x626e974dbe39a873}, |
| 1164 | {0xce5d73ff402d98e3, 0xfb0a3d212dc81290}, |
| 1165 | {0x80fa687f881c7f8e, 0x7ce66634bc9d0b9a}, |
| 1166 | {0xa139029f6a239f72, 0x1c1fffc1ebc44e81}, |
| 1167 | {0xc987434744ac874e, 0xa327ffb266b56221}, |
| 1168 | {0xfbe9141915d7a922, 0x4bf1ff9f0062baa9}, |
| 1169 | {0x9d71ac8fada6c9b5, 0x6f773fc3603db4aa}, |
| 1170 | {0xc4ce17b399107c22, 0xcb550fb4384d21d4}, |
| 1171 | {0xf6019da07f549b2b, 0x7e2a53a146606a49}, |
| 1172 | {0x99c102844f94e0fb, 0x2eda7444cbfc426e}, |
| 1173 | {0xc0314325637a1939, 0xfa911155fefb5309}, |
| 1174 | {0xf03d93eebc589f88, 0x793555ab7eba27cb}, |
| 1175 | {0x96267c7535b763b5, 0x4bc1558b2f3458df}, |
| 1176 | {0xbbb01b9283253ca2, 0x9eb1aaedfb016f17}, |
| 1177 | {0xea9c227723ee8bcb, 0x465e15a979c1cadd}, |
| 1178 | {0x92a1958a7675175f, 0x0bfacd89ec191eca}, |
| 1179 | {0xb749faed14125d36, 0xcef980ec671f667c}, |
| 1180 | {0xe51c79a85916f484, 0x82b7e12780e7401b}, |
| 1181 | {0x8f31cc0937ae58d2, 0xd1b2ecb8b0908811}, |
| 1182 | {0xb2fe3f0b8599ef07, 0x861fa7e6dcb4aa16}, |
| 1183 | {0xdfbdcece67006ac9, 0x67a791e093e1d49b}, |
| 1184 | {0x8bd6a141006042bd, 0xe0c8bb2c5c6d24e1}, |
| 1185 | {0xaecc49914078536d, 0x58fae9f773886e19}, |
| 1186 | {0xda7f5bf590966848, 0xaf39a475506a899f}, |
| 1187 | {0x888f99797a5e012d, 0x6d8406c952429604}, |
| 1188 | {0xaab37fd7d8f58178, 0xc8e5087ba6d33b84}, |
| 1189 | {0xd5605fcdcf32e1d6, 0xfb1e4a9a90880a65}, |
| 1190 | {0x855c3be0a17fcd26, 0x5cf2eea09a550680}, |
| 1191 | {0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481f}, |
| 1192 | {0xd0601d8efc57b08b, 0xf13b94daf124da27}, |
| 1193 | {0x823c12795db6ce57, 0x76c53d08d6b70859}, |
| 1194 | {0xa2cb1717b52481ed, 0x54768c4b0c64ca6f}, |
| 1195 | {0xcb7ddcdda26da268, 0xa9942f5dcf7dfd0a}, |
| 1196 | {0xfe5d54150b090b02, 0xd3f93b35435d7c4d}, |
| 1197 | {0x9efa548d26e5a6e1, 0xc47bc5014a1a6db0}, |
| 1198 | {0xc6b8e9b0709f109a, 0x359ab6419ca1091c}, |
| 1199 | {0xf867241c8cc6d4c0, 0xc30163d203c94b63}, |
| 1200 | {0x9b407691d7fc44f8, 0x79e0de63425dcf1e}, |
| 1201 | {0xc21094364dfb5636, 0x985915fc12f542e5}, |
| 1202 | {0xf294b943e17a2bc4, 0x3e6f5b7b17b2939e}, |
| 1203 | {0x979cf3ca6cec5b5a, 0xa705992ceecf9c43}, |
| 1204 | {0xbd8430bd08277231, 0x50c6ff782a838354}, |
| 1205 | {0xece53cec4a314ebd, 0xa4f8bf5635246429}, |
| 1206 | {0x940f4613ae5ed136, 0x871b7795e136be9a}, |
| 1207 | {0xb913179899f68584, 0x28e2557b59846e40}, |
| 1208 | {0xe757dd7ec07426e5, 0x331aeada2fe589d0}, |
| 1209 | {0x9096ea6f3848984f, 0x3ff0d2c85def7622}, |
| 1210 | {0xb4bca50b065abe63, 0x0fed077a756b53aa}, |
| 1211 | {0xe1ebce4dc7f16dfb, 0xd3e8495912c62895}, |
| 1212 | {0x8d3360f09cf6e4bd, 0x64712dd7abbbd95d}, |
| 1213 | {0xb080392cc4349dec, 0xbd8d794d96aacfb4}, |
| 1214 | {0xdca04777f541c567, 0xecf0d7a0fc5583a1}, |
| 1215 | {0x89e42caaf9491b60, 0xf41686c49db57245}, |
| 1216 | {0xac5d37d5b79b6239, 0x311c2875c522ced6}, |
| 1217 | {0xd77485cb25823ac7, 0x7d633293366b828c}, |
| 1218 | {0x86a8d39ef77164bc, 0xae5dff9c02033198}, |
| 1219 | {0xa8530886b54dbdeb, 0xd9f57f830283fdfd}, |
| 1220 | {0xd267caa862a12d66, 0xd072df63c324fd7c}, |
| 1221 | {0x8380dea93da4bc60, 0x4247cb9e59f71e6e}, |
| 1222 | {0xa46116538d0deb78, 0x52d9be85f074e609}, |
| 1223 | {0xcd795be870516656, 0x67902e276c921f8c}, |
| 1224 | {0x806bd9714632dff6, 0x00ba1cd8a3db53b7}, |
| 1225 | {0xa086cfcd97bf97f3, 0x80e8a40eccd228a5}, |
| 1226 | {0xc8a883c0fdaf7df0, 0x6122cd128006b2ce}, |
| 1227 | {0xfad2a4b13d1b5d6c, 0x796b805720085f82}, |
| 1228 | {0x9cc3a6eec6311a63, 0xcbe3303674053bb1}, |
| 1229 | {0xc3f490aa77bd60fc, 0xbedbfc4411068a9d}, |
| 1230 | {0xf4f1b4d515acb93b, 0xee92fb5515482d45}, |
| 1231 | {0x991711052d8bf3c5, 0x751bdd152d4d1c4b}, |
| 1232 | {0xbf5cd54678eef0b6, 0xd262d45a78a0635e}, |
| 1233 | {0xef340a98172aace4, 0x86fb897116c87c35}, |
| 1234 | {0x9580869f0e7aac0e, 0xd45d35e6ae3d4da1}, |
| 1235 | {0xbae0a846d2195712, 0x8974836059cca10a}, |
| 1236 | {0xe998d258869facd7, 0x2bd1a438703fc94c}, |
| 1237 | {0x91ff83775423cc06, 0x7b6306a34627ddd0}, |
| 1238 | {0xb67f6455292cbf08, 0x1a3bc84c17b1d543}, |
| 1239 | {0xe41f3d6a7377eeca, 0x20caba5f1d9e4a94}, |
| 1240 | {0x8e938662882af53e, 0x547eb47b7282ee9d}, |
| 1241 | {0xb23867fb2a35b28d, 0xe99e619a4f23aa44}, |
| 1242 | {0xdec681f9f4c31f31, 0x6405fa00e2ec94d5}, |
| 1243 | {0x8b3c113c38f9f37e, 0xde83bc408dd3dd05}, |
| 1244 | {0xae0b158b4738705e, 0x9624ab50b148d446}, |
| 1245 | {0xd98ddaee19068c76, 0x3badd624dd9b0958}, |
| 1246 | {0x87f8a8d4cfa417c9, 0xe54ca5d70a80e5d7}, |
| 1247 | {0xa9f6d30a038d1dbc, 0x5e9fcf4ccd211f4d}, |
| 1248 | {0xd47487cc8470652b, 0x7647c32000696720}, |
| 1249 | {0x84c8d4dfd2c63f3b, 0x29ecd9f40041e074}, |
| 1250 | {0xa5fb0a17c777cf09, 0xf468107100525891}, |
| 1251 | {0xcf79cc9db955c2cc, 0x7182148d4066eeb5}, |
| 1252 | {0x81ac1fe293d599bf, 0xc6f14cd848405531}, |
| 1253 | {0xa21727db38cb002f, 0xb8ada00e5a506a7d}, |
| 1254 | {0xca9cf1d206fdc03b, 0xa6d90811f0e4851d}, |
| 1255 | {0xfd442e4688bd304a, 0x908f4a166d1da664}, |
| 1256 | {0x9e4a9cec15763e2e, 0x9a598e4e043287ff}, |
| 1257 | {0xc5dd44271ad3cdba, 0x40eff1e1853f29fe}, |
| 1258 | {0xf7549530e188c128, 0xd12bee59e68ef47d}, |
| 1259 | {0x9a94dd3e8cf578b9, 0x82bb74f8301958cf}, |
| 1260 | {0xc13a148e3032d6e7, 0xe36a52363c1faf02}, |
| 1261 | {0xf18899b1bc3f8ca1, 0xdc44e6c3cb279ac2}, |
| 1262 | {0x96f5600f15a7b7e5, 0x29ab103a5ef8c0ba}, |
| 1263 | {0xbcb2b812db11a5de, 0x7415d448f6b6f0e8}, |
| 1264 | {0xebdf661791d60f56, 0x111b495b3464ad22}, |
| 1265 | {0x936b9fcebb25c995, 0xcab10dd900beec35}, |
| 1266 | {0xb84687c269ef3bfb, 0x3d5d514f40eea743}, |
| 1267 | {0xe65829b3046b0afa, 0x0cb4a5a3112a5113}, |
| 1268 | {0x8ff71a0fe2c2e6dc, 0x47f0e785eaba72ac}, |
| 1269 | {0xb3f4e093db73a093, 0x59ed216765690f57}, |
| 1270 | {0xe0f218b8d25088b8, 0x306869c13ec3532d}, |
| 1271 | {0x8c974f7383725573, 0x1e414218c73a13fc}, |
| 1272 | {0xafbd2350644eeacf, 0xe5d1929ef90898fb}, |
| 1273 | {0xdbac6c247d62a583, 0xdf45f746b74abf3a}, |
| 1274 | {0x894bc396ce5da772, 0x6b8bba8c328eb784}, |
| 1275 | {0xab9eb47c81f5114f, 0x066ea92f3f326565}, |
| 1276 | {0xd686619ba27255a2, 0xc80a537b0efefebe}, |
| 1277 | {0x8613fd0145877585, 0xbd06742ce95f5f37}, |
| 1278 | {0xa798fc4196e952e7, 0x2c48113823b73705}, |
| 1279 | {0xd17f3b51fca3a7a0, 0xf75a15862ca504c6}, |
| 1280 | {0x82ef85133de648c4, 0x9a984d73dbe722fc}, |
| 1281 | {0xa3ab66580d5fdaf5, 0xc13e60d0d2e0ebbb}, |
| 1282 | {0xcc963fee10b7d1b3, 0x318df905079926a9}, |
| 1283 | {0xffbbcfe994e5c61f, 0xfdf17746497f7053}, |
| 1284 | {0x9fd561f1fd0f9bd3, 0xfeb6ea8bedefa634}, |
| 1285 | {0xc7caba6e7c5382c8, 0xfe64a52ee96b8fc1}, |
| 1286 | {0xf9bd690a1b68637b, 0x3dfdce7aa3c673b1}, |
| 1287 | {0x9c1661a651213e2d, 0x06bea10ca65c084f}, |
| 1288 | {0xc31bfa0fe5698db8, 0x486e494fcff30a63}, |
| 1289 | {0xf3e2f893dec3f126, 0x5a89dba3c3efccfb}, |
| 1290 | {0x986ddb5c6b3a76b7, 0xf89629465a75e01d}, |
| 1291 | {0xbe89523386091465, 0xf6bbb397f1135824}, |
| 1292 | {0xee2ba6c0678b597f, 0x746aa07ded582e2d}, |
| 1293 | {0x94db483840b717ef, 0xa8c2a44eb4571cdd}, |
| 1294 | {0xba121a4650e4ddeb, 0x92f34d62616ce414}, |
| 1295 | {0xe896a0d7e51e1566, 0x77b020baf9c81d18}, |
| 1296 | {0x915e2486ef32cd60, 0x0ace1474dc1d122f}, |
| 1297 | {0xb5b5ada8aaff80b8, 0x0d819992132456bb}, |
| 1298 | {0xe3231912d5bf60e6, 0x10e1fff697ed6c6a}, |
| 1299 | {0x8df5efabc5979c8f, 0xca8d3ffa1ef463c2}, |
| 1300 | {0xb1736b96b6fd83b3, 0xbd308ff8a6b17cb3}, |
| 1301 | {0xddd0467c64bce4a0, 0xac7cb3f6d05ddbdf}, |
| 1302 | {0x8aa22c0dbef60ee4, 0x6bcdf07a423aa96c}, |
| 1303 | {0xad4ab7112eb3929d, 0x86c16c98d2c953c7}, |
| 1304 | {0xd89d64d57a607744, 0xe871c7bf077ba8b8}, |
| 1305 | {0x87625f056c7c4a8b, 0x11471cd764ad4973}, |
| 1306 | {0xa93af6c6c79b5d2d, 0xd598e40d3dd89bd0}, |
| 1307 | {0xd389b47879823479, 0x4aff1d108d4ec2c4}, |
| 1308 | {0x843610cb4bf160cb, 0xcedf722a585139bb}, |
| 1309 | {0xa54394fe1eedb8fe, 0xc2974eb4ee658829}, |
| 1310 | {0xce947a3da6a9273e, 0x733d226229feea33}, |
| 1311 | {0x811ccc668829b887, 0x0806357d5a3f5260}, |
| 1312 | {0xa163ff802a3426a8, 0xca07c2dcb0cf26f8}, |
| 1313 | {0xc9bcff6034c13052, 0xfc89b393dd02f0b6}, |
| 1314 | {0xfc2c3f3841f17c67, 0xbbac2078d443ace3}, |
| 1315 | {0x9d9ba7832936edc0, 0xd54b944b84aa4c0e}, |
| 1316 | {0xc5029163f384a931, 0x0a9e795e65d4df12}, |
| 1317 | {0xf64335bcf065d37d, 0x4d4617b5ff4a16d6}, |
| 1318 | {0x99ea0196163fa42e, 0x504bced1bf8e4e46}, |
| 1319 | {0xc06481fb9bcf8d39, 0xe45ec2862f71e1d7}, |
| 1320 | {0xf07da27a82c37088, 0x5d767327bb4e5a4d}, |
| 1321 | {0x964e858c91ba2655, 0x3a6a07f8d510f870}, |
| 1322 | {0xbbe226efb628afea, 0x890489f70a55368c}, |
| 1323 | {0xeadab0aba3b2dbe5, 0x2b45ac74ccea842f}, |
| 1324 | {0x92c8ae6b464fc96f, 0x3b0b8bc90012929e}, |
| 1325 | {0xb77ada0617e3bbcb, 0x09ce6ebb40173745}, |
| 1326 | {0xe55990879ddcaabd, 0xcc420a6a101d0516}, |
| 1327 | {0x8f57fa54c2a9eab6, 0x9fa946824a12232e}, |
| 1328 | {0xb32df8e9f3546564, 0x47939822dc96abfa}, |
| 1329 | {0xdff9772470297ebd, 0x59787e2b93bc56f8}, |
| 1330 | {0x8bfbea76c619ef36, 0x57eb4edb3c55b65b}, |
| 1331 | {0xaefae51477a06b03, 0xede622920b6b23f2}, |
| 1332 | {0xdab99e59958885c4, 0xe95fab368e45ecee}, |
| 1333 | {0x88b402f7fd75539b, 0x11dbcb0218ebb415}, |
| 1334 | {0xaae103b5fcd2a881, 0xd652bdc29f26a11a}, |
| 1335 | {0xd59944a37c0752a2, 0x4be76d3346f04960}, |
| 1336 | {0x857fcae62d8493a5, 0x6f70a4400c562ddc}, |
| 1337 | {0xa6dfbd9fb8e5b88e, 0xcb4ccd500f6bb953}, |
| 1338 | {0xd097ad07a71f26b2, 0x7e2000a41346a7a8}, |
| 1339 | {0x825ecc24c873782f, 0x8ed400668c0c28c9}, |
| 1340 | {0xa2f67f2dfa90563b, 0x728900802f0f32fb}, |
| 1341 | {0xcbb41ef979346bca, 0x4f2b40a03ad2ffba}, |
| 1342 | {0xfea126b7d78186bc, 0xe2f610c84987bfa9}, |
| 1343 | {0x9f24b832e6b0f436, 0x0dd9ca7d2df4d7ca}, |
| 1344 | {0xc6ede63fa05d3143, 0x91503d1c79720dbc}, |
| 1345 | {0xf8a95fcf88747d94, 0x75a44c6397ce912b}, |
| 1346 | {0x9b69dbe1b548ce7c, 0xc986afbe3ee11abb}, |
| 1347 | {0xc24452da229b021b, 0xfbe85badce996169}, |
| 1348 | {0xf2d56790ab41c2a2, 0xfae27299423fb9c4}, |
| 1349 | {0x97c560ba6b0919a5, 0xdccd879fc967d41b}, |
| 1350 | {0xbdb6b8e905cb600f, 0x5400e987bbc1c921}, |
| 1351 | {0xed246723473e3813, 0x290123e9aab23b69}, |
| 1352 | {0x9436c0760c86e30b, 0xf9a0b6720aaf6522}, |
| 1353 | {0xb94470938fa89bce, 0xf808e40e8d5b3e6a}, |
| 1354 | {0xe7958cb87392c2c2, 0xb60b1d1230b20e05}, |
| 1355 | {0x90bd77f3483bb9b9, 0xb1c6f22b5e6f48c3}, |
| 1356 | {0xb4ecd5f01a4aa828, 0x1e38aeb6360b1af4}, |
| 1357 | {0xe2280b6c20dd5232, 0x25c6da63c38de1b1}, |
| 1358 | {0x8d590723948a535f, 0x579c487e5a38ad0f}, |
| 1359 | {0xb0af48ec79ace837, 0x2d835a9df0c6d852}, |
| 1360 | {0xdcdb1b2798182244, 0xf8e431456cf88e66}, |
| 1361 | {0x8a08f0f8bf0f156b, 0x1b8e9ecb641b5900}, |
| 1362 | {0xac8b2d36eed2dac5, 0xe272467e3d222f40}, |
| 1363 | {0xd7adf884aa879177, 0x5b0ed81dcc6abb10}, |
| 1364 | {0x86ccbb52ea94baea, 0x98e947129fc2b4ea}, |
| 1365 | {0xa87fea27a539e9a5, 0x3f2398d747b36225}, |
| 1366 | {0xd29fe4b18e88640e, 0x8eec7f0d19a03aae}, |
| 1367 | {0x83a3eeeef9153e89, 0x1953cf68300424ad}, |
| 1368 | {0xa48ceaaab75a8e2b, 0x5fa8c3423c052dd8}, |
| 1369 | {0xcdb02555653131b6, 0x3792f412cb06794e}, |
| 1370 | {0x808e17555f3ebf11, 0xe2bbd88bbee40bd1}, |
| 1371 | {0xa0b19d2ab70e6ed6, 0x5b6aceaeae9d0ec5}, |
| 1372 | {0xc8de047564d20a8b, 0xf245825a5a445276}, |
| 1373 | {0xfb158592be068d2e, 0xeed6e2f0f0d56713}, |
| 1374 | {0x9ced737bb6c4183d, 0x55464dd69685606c}, |
| 1375 | {0xc428d05aa4751e4c, 0xaa97e14c3c26b887}, |
| 1376 | {0xf53304714d9265df, 0xd53dd99f4b3066a9}, |
| 1377 | {0x993fe2c6d07b7fab, 0xe546a8038efe402a}, |
| 1378 | {0xbf8fdb78849a5f96, 0xde98520472bdd034}, |
| 1379 | {0xef73d256a5c0f77c, 0x963e66858f6d4441}, |
| 1380 | {0x95a8637627989aad, 0xdde7001379a44aa9}, |
| 1381 | {0xbb127c53b17ec159, 0x5560c018580d5d53}, |
| 1382 | {0xe9d71b689dde71af, 0xaab8f01e6e10b4a7}, |
| 1383 | {0x9226712162ab070d, 0xcab3961304ca70e9}, |
| 1384 | {0xb6b00d69bb55c8d1, 0x3d607b97c5fd0d23}, |
| 1385 | {0xe45c10c42a2b3b05, 0x8cb89a7db77c506b}, |
| 1386 | {0x8eb98a7a9a5b04e3, 0x77f3608e92adb243}, |
| 1387 | {0xb267ed1940f1c61c, 0x55f038b237591ed4}, |
| 1388 | {0xdf01e85f912e37a3, 0x6b6c46dec52f6689}, |
| 1389 | {0x8b61313bbabce2c6, 0x2323ac4b3b3da016}, |
| 1390 | {0xae397d8aa96c1b77, 0xabec975e0a0d081b}, |
| 1391 | {0xd9c7dced53c72255, 0x96e7bd358c904a22}, |
| 1392 | {0x881cea14545c7575, 0x7e50d64177da2e55}, |
| 1393 | {0xaa242499697392d2, 0xdde50bd1d5d0b9ea}, |
| 1394 | {0xd4ad2dbfc3d07787, 0x955e4ec64b44e865}, |
| 1395 | {0x84ec3c97da624ab4, 0xbd5af13bef0b113f}, |
| 1396 | {0xa6274bbdd0fadd61, 0xecb1ad8aeacdd58f}, |
| 1397 | {0xcfb11ead453994ba, 0x67de18eda5814af3}, |
| 1398 | {0x81ceb32c4b43fcf4, 0x80eacf948770ced8}, |
| 1399 | {0xa2425ff75e14fc31, 0xa1258379a94d028e}, |
| 1400 | {0xcad2f7f5359a3b3e, 0x096ee45813a04331}, |
| 1401 | {0xfd87b5f28300ca0d, 0x8bca9d6e188853fd}, |
| 1402 | {0x9e74d1b791e07e48, 0x775ea264cf55347e}, |
| 1403 | {0xc612062576589dda, 0x95364afe032a819e}, |
| 1404 | {0xf79687aed3eec551, 0x3a83ddbd83f52205}, |
| 1405 | {0x9abe14cd44753b52, 0xc4926a9672793543}, |
| 1406 | {0xc16d9a0095928a27, 0x75b7053c0f178294}, |
| 1407 | {0xf1c90080baf72cb1, 0x5324c68b12dd6339}, |
| 1408 | {0x971da05074da7bee, 0xd3f6fc16ebca5e04}, |
| 1409 | {0xbce5086492111aea, 0x88f4bb1ca6bcf585}, |
| 1410 | {0xec1e4a7db69561a5, 0x2b31e9e3d06c32e6}, |
| 1411 | {0x9392ee8e921d5d07, 0x3aff322e62439fd0}, |
| 1412 | {0xb877aa3236a4b449, 0x09befeb9fad487c3}, |
| 1413 | {0xe69594bec44de15b, 0x4c2ebe687989a9b4}, |
| 1414 | {0x901d7cf73ab0acd9, 0x0f9d37014bf60a11}, |
| 1415 | {0xb424dc35095cd80f, 0x538484c19ef38c95}, |
| 1416 | {0xe12e13424bb40e13, 0x2865a5f206b06fba}, |
| 1417 | {0x8cbccc096f5088cb, 0xf93f87b7442e45d4}, |
| 1418 | {0xafebff0bcb24aafe, 0xf78f69a51539d749}, |
| 1419 | {0xdbe6fecebdedd5be, 0xb573440e5a884d1c}, |
| 1420 | {0x89705f4136b4a597, 0x31680a88f8953031}, |
| 1421 | {0xabcc77118461cefc, 0xfdc20d2b36ba7c3e}, |
| 1422 | {0xd6bf94d5e57a42bc, 0x3d32907604691b4d}, |
| 1423 | {0x8637bd05af6c69b5, 0xa63f9a49c2c1b110}, |
| 1424 | {0xa7c5ac471b478423, 0x0fcf80dc33721d54}, |
| 1425 | {0xd1b71758e219652b, 0xd3c36113404ea4a9}, |
| 1426 | {0x83126e978d4fdf3b, 0x645a1cac083126ea}, |
| 1427 | {0xa3d70a3d70a3d70a, 0x3d70a3d70a3d70a4}, |
| 1428 | {0xcccccccccccccccc, 0xcccccccccccccccd}, |
| 1429 | {0x8000000000000000, 0x0000000000000000}, |
| 1430 | {0xa000000000000000, 0x0000000000000000}, |
| 1431 | {0xc800000000000000, 0x0000000000000000}, |
| 1432 | {0xfa00000000000000, 0x0000000000000000}, |
| 1433 | {0x9c40000000000000, 0x0000000000000000}, |
| 1434 | {0xc350000000000000, 0x0000000000000000}, |
| 1435 | {0xf424000000000000, 0x0000000000000000}, |
| 1436 | {0x9896800000000000, 0x0000000000000000}, |
| 1437 | {0xbebc200000000000, 0x0000000000000000}, |
| 1438 | {0xee6b280000000000, 0x0000000000000000}, |
| 1439 | {0x9502f90000000000, 0x0000000000000000}, |
| 1440 | {0xba43b74000000000, 0x0000000000000000}, |
| 1441 | {0xe8d4a51000000000, 0x0000000000000000}, |
| 1442 | {0x9184e72a00000000, 0x0000000000000000}, |
| 1443 | {0xb5e620f480000000, 0x0000000000000000}, |
| 1444 | {0xe35fa931a0000000, 0x0000000000000000}, |
| 1445 | {0x8e1bc9bf04000000, 0x0000000000000000}, |
| 1446 | {0xb1a2bc2ec5000000, 0x0000000000000000}, |
| 1447 | {0xde0b6b3a76400000, 0x0000000000000000}, |
| 1448 | {0x8ac7230489e80000, 0x0000000000000000}, |
| 1449 | {0xad78ebc5ac620000, 0x0000000000000000}, |
| 1450 | {0xd8d726b7177a8000, 0x0000000000000000}, |
| 1451 | {0x878678326eac9000, 0x0000000000000000}, |
| 1452 | {0xa968163f0a57b400, 0x0000000000000000}, |
| 1453 | {0xd3c21bcecceda100, 0x0000000000000000}, |
| 1454 | {0x84595161401484a0, 0x0000000000000000}, |
| 1455 | {0xa56fa5b99019a5c8, 0x0000000000000000}, |
| 1456 | {0xcecb8f27f4200f3a, 0x0000000000000000}, |
| 1457 | {0x813f3978f8940984, 0x4000000000000000}, |
| 1458 | {0xa18f07d736b90be5, 0x5000000000000000}, |
| 1459 | {0xc9f2c9cd04674ede, 0xa400000000000000}, |
| 1460 | {0xfc6f7c4045812296, 0x4d00000000000000}, |
| 1461 | {0x9dc5ada82b70b59d, 0xf020000000000000}, |
| 1462 | {0xc5371912364ce305, 0x6c28000000000000}, |
| 1463 | {0xf684df56c3e01bc6, 0xc732000000000000}, |
| 1464 | {0x9a130b963a6c115c, 0x3c7f400000000000}, |
| 1465 | {0xc097ce7bc90715b3, 0x4b9f100000000000}, |
| 1466 | {0xf0bdc21abb48db20, 0x1e86d40000000000}, |
| 1467 | {0x96769950b50d88f4, 0x1314448000000000}, |
| 1468 | {0xbc143fa4e250eb31, 0x17d955a000000000}, |
| 1469 | {0xeb194f8e1ae525fd, 0x5dcfab0800000000}, |
| 1470 | {0x92efd1b8d0cf37be, 0x5aa1cae500000000}, |
| 1471 | {0xb7abc627050305ad, 0xf14a3d9e40000000}, |
| 1472 | {0xe596b7b0c643c719, 0x6d9ccd05d0000000}, |
| 1473 | {0x8f7e32ce7bea5c6f, 0xe4820023a2000000}, |
| 1474 | {0xb35dbf821ae4f38b, 0xdda2802c8a800000}, |
| 1475 | {0xe0352f62a19e306e, 0xd50b2037ad200000}, |
| 1476 | {0x8c213d9da502de45, 0x4526f422cc340000}, |
| 1477 | {0xaf298d050e4395d6, 0x9670b12b7f410000}, |
| 1478 | {0xdaf3f04651d47b4c, 0x3c0cdd765f114000}, |
| 1479 | {0x88d8762bf324cd0f, 0xa5880a69fb6ac800}, |
| 1480 | {0xab0e93b6efee0053, 0x8eea0d047a457a00}, |
| 1481 | {0xd5d238a4abe98068, 0x72a4904598d6d880}, |
| 1482 | {0x85a36366eb71f041, 0x47a6da2b7f864750}, |
| 1483 | {0xa70c3c40a64e6c51, 0x999090b65f67d924}, |
| 1484 | {0xd0cf4b50cfe20765, 0xfff4b4e3f741cf6d}, |
| 1485 | {0x82818f1281ed449f, 0xbff8f10e7a8921a4}, |
| 1486 | {0xa321f2d7226895c7, 0xaff72d52192b6a0d}, |
| 1487 | {0xcbea6f8ceb02bb39, 0x9bf4f8a69f764490}, |
| 1488 | {0xfee50b7025c36a08, 0x02f236d04753d5b4}, |
| 1489 | {0x9f4f2726179a2245, 0x01d762422c946590}, |
| 1490 | {0xc722f0ef9d80aad6, 0x424d3ad2b7b97ef5}, |
| 1491 | {0xf8ebad2b84e0d58b, 0xd2e0898765a7deb2}, |
| 1492 | {0x9b934c3b330c8577, 0x63cc55f49f88eb2f}, |
| 1493 | {0xc2781f49ffcfa6d5, 0x3cbf6b71c76b25fb}, |
| 1494 | {0xf316271c7fc3908a, 0x8bef464e3945ef7a}, |
| 1495 | {0x97edd871cfda3a56, 0x97758bf0e3cbb5ac}, |
| 1496 | {0xbde94e8e43d0c8ec, 0x3d52eeed1cbea317}, |
| 1497 | {0xed63a231d4c4fb27, 0x4ca7aaa863ee4bdd}, |
| 1498 | {0x945e455f24fb1cf8, 0x8fe8caa93e74ef6a}, |
| 1499 | {0xb975d6b6ee39e436, 0xb3e2fd538e122b44}, |
| 1500 | {0xe7d34c64a9c85d44, 0x60dbbca87196b616}, |
| 1501 | {0x90e40fbeea1d3a4a, 0xbc8955e946fe31cd}, |
| 1502 | {0xb51d13aea4a488dd, 0x6babab6398bdbe41}, |
| 1503 | {0xe264589a4dcdab14, 0xc696963c7eed2dd1}, |
| 1504 | {0x8d7eb76070a08aec, 0xfc1e1de5cf543ca2}, |
| 1505 | {0xb0de65388cc8ada8, 0x3b25a55f43294bcb}, |
| 1506 | {0xdd15fe86affad912, 0x49ef0eb713f39ebe}, |
| 1507 | {0x8a2dbf142dfcc7ab, 0x6e3569326c784337}, |
| 1508 | {0xacb92ed9397bf996, 0x49c2c37f07965404}, |
| 1509 | {0xd7e77a8f87daf7fb, 0xdc33745ec97be906}, |
| 1510 | {0x86f0ac99b4e8dafd, 0x69a028bb3ded71a3}, |
| 1511 | {0xa8acd7c0222311bc, 0xc40832ea0d68ce0c}, |
| 1512 | {0xd2d80db02aabd62b, 0xf50a3fa490c30190}, |
| 1513 | {0x83c7088e1aab65db, 0x792667c6da79e0fa}, |
| 1514 | {0xa4b8cab1a1563f52, 0x577001b891185938}, |
| 1515 | {0xcde6fd5e09abcf26, 0xed4c0226b55e6f86}, |
| 1516 | {0x80b05e5ac60b6178, 0x544f8158315b05b4}, |
| 1517 | {0xa0dc75f1778e39d6, 0x696361ae3db1c721}, |
| 1518 | {0xc913936dd571c84c, 0x03bc3a19cd1e38e9}, |
| 1519 | {0xfb5878494ace3a5f, 0x04ab48a04065c723}, |
| 1520 | {0x9d174b2dcec0e47b, 0x62eb0d64283f9c76}, |
| 1521 | {0xc45d1df942711d9a, 0x3ba5d0bd324f8394}, |
| 1522 | {0xf5746577930d6500, 0xca8f44ec7ee36479}, |
| 1523 | {0x9968bf6abbe85f20, 0x7e998b13cf4e1ecb}, |
| 1524 | {0xbfc2ef456ae276e8, 0x9e3fedd8c321a67e}, |
| 1525 | {0xefb3ab16c59b14a2, 0xc5cfe94ef3ea101e}, |
| 1526 | {0x95d04aee3b80ece5, 0xbba1f1d158724a12}, |
| 1527 | {0xbb445da9ca61281f, 0x2a8a6e45ae8edc97}, |
| 1528 | {0xea1575143cf97226, 0xf52d09d71a3293bd}, |
| 1529 | {0x924d692ca61be758, 0x593c2626705f9c56}, |
| 1530 | {0xb6e0c377cfa2e12e, 0x6f8b2fb00c77836c}, |
| 1531 | {0xe498f455c38b997a, 0x0b6dfb9c0f956447}, |
| 1532 | {0x8edf98b59a373fec, 0x4724bd4189bd5eac}, |
| 1533 | {0xb2977ee300c50fe7, 0x58edec91ec2cb657}, |
| 1534 | {0xdf3d5e9bc0f653e1, 0x2f2967b66737e3ed}, |
| 1535 | {0x8b865b215899f46c, 0xbd79e0d20082ee74}, |
| 1536 | {0xae67f1e9aec07187, 0xecd8590680a3aa11}, |
| 1537 | {0xda01ee641a708de9, 0xe80e6f4820cc9495}, |
| 1538 | {0x884134fe908658b2, 0x3109058d147fdcdd}, |
| 1539 | {0xaa51823e34a7eede, 0xbd4b46f0599fd415}, |
| 1540 | {0xd4e5e2cdc1d1ea96, 0x6c9e18ac7007c91a}, |
| 1541 | {0x850fadc09923329e, 0x03e2cf6bc604ddb0}, |
| 1542 | {0xa6539930bf6bff45, 0x84db8346b786151c}, |
| 1543 | {0xcfe87f7cef46ff16, 0xe612641865679a63}, |
| 1544 | {0x81f14fae158c5f6e, 0x4fcb7e8f3f60c07e}, |
| 1545 | {0xa26da3999aef7749, 0xe3be5e330f38f09d}, |
| 1546 | {0xcb090c8001ab551c, 0x5cadf5bfd3072cc5}, |
| 1547 | {0xfdcb4fa002162a63, 0x73d9732fc7c8f7f6}, |
| 1548 | {0x9e9f11c4014dda7e, 0x2867e7fddcdd9afa}, |
| 1549 | {0xc646d63501a1511d, 0xb281e1fd541501b8}, |
| 1550 | {0xf7d88bc24209a565, 0x1f225a7ca91a4226}, |
| 1551 | {0x9ae757596946075f, 0x3375788de9b06958}, |
| 1552 | {0xc1a12d2fc3978937, 0x0052d6b1641c83ae}, |
| 1553 | {0xf209787bb47d6b84, 0xc0678c5dbd23a49a}, |
| 1554 | {0x9745eb4d50ce6332, 0xf840b7ba963646e0}, |
| 1555 | {0xbd176620a501fbff, 0xb650e5a93bc3d898}, |
| 1556 | {0xec5d3fa8ce427aff, 0xa3e51f138ab4cebe}, |
| 1557 | {0x93ba47c980e98cdf, 0xc66f336c36b10137}, |
| 1558 | {0xb8a8d9bbe123f017, 0xb80b0047445d4184}, |
| 1559 | {0xe6d3102ad96cec1d, 0xa60dc059157491e5}, |
| 1560 | {0x9043ea1ac7e41392, 0x87c89837ad68db2f}, |
| 1561 | {0xb454e4a179dd1877, 0x29babe4598c311fb}, |
| 1562 | {0xe16a1dc9d8545e94, 0xf4296dd6fef3d67a}, |
| 1563 | {0x8ce2529e2734bb1d, 0x1899e4a65f58660c}, |
| 1564 | {0xb01ae745b101e9e4, 0x5ec05dcff72e7f8f}, |
| 1565 | {0xdc21a1171d42645d, 0x76707543f4fa1f73}, |
| 1566 | {0x899504ae72497eba, 0x6a06494a791c53a8}, |
| 1567 | {0xabfa45da0edbde69, 0x0487db9d17636892}, |
| 1568 | {0xd6f8d7509292d603, 0x45a9d2845d3c42b6}, |
| 1569 | {0x865b86925b9bc5c2, 0x0b8a2392ba45a9b2}, |
| 1570 | {0xa7f26836f282b732, 0x8e6cac7768d7141e}, |
| 1571 | {0xd1ef0244af2364ff, 0x3207d795430cd926}, |
| 1572 | {0x8335616aed761f1f, 0x7f44e6bd49e807b8}, |
| 1573 | {0xa402b9c5a8d3a6e7, 0x5f16206c9c6209a6}, |
| 1574 | {0xcd036837130890a1, 0x36dba887c37a8c0f}, |
| 1575 | {0x802221226be55a64, 0xc2494954da2c9789}, |
| 1576 | {0xa02aa96b06deb0fd, 0xf2db9baa10b7bd6c}, |
| 1577 | {0xc83553c5c8965d3d, 0x6f92829494e5acc7}, |
| 1578 | {0xfa42a8b73abbf48c, 0xcb772339ba1f17f9}, |
| 1579 | {0x9c69a97284b578d7, 0xff2a760414536efb}, |
| 1580 | {0xc38413cf25e2d70d, 0xfef5138519684aba}, |
| 1581 | {0xf46518c2ef5b8cd1, 0x7eb258665fc25d69}, |
| 1582 | {0x98bf2f79d5993802, 0xef2f773ffbd97a61}, |
| 1583 | {0xbeeefb584aff8603, 0xaafb550ffacfd8fa}, |
| 1584 | {0xeeaaba2e5dbf6784, 0x95ba2a53f983cf38}, |
| 1585 | {0x952ab45cfa97a0b2, 0xdd945a747bf26183}, |
| 1586 | {0xba756174393d88df, 0x94f971119aeef9e4}, |
| 1587 | {0xe912b9d1478ceb17, 0x7a37cd5601aab85d}, |
| 1588 | {0x91abb422ccb812ee, 0xac62e055c10ab33a}, |
| 1589 | {0xb616a12b7fe617aa, 0x577b986b314d6009}, |
| 1590 | {0xe39c49765fdf9d94, 0xed5a7e85fda0b80b}, |
| 1591 | {0x8e41ade9fbebc27d, 0x14588f13be847307}, |
| 1592 | {0xb1d219647ae6b31c, 0x596eb2d8ae258fc8}, |
| 1593 | {0xde469fbd99a05fe3, 0x6fca5f8ed9aef3bb}, |
| 1594 | {0x8aec23d680043bee, 0x25de7bb9480d5854}, |
| 1595 | {0xada72ccc20054ae9, 0xaf561aa79a10ae6a}, |
| 1596 | {0xd910f7ff28069da4, 0x1b2ba1518094da04}, |
| 1597 | {0x87aa9aff79042286, 0x90fb44d2f05d0842}, |
| 1598 | {0xa99541bf57452b28, 0x353a1607ac744a53}, |
| 1599 | {0xd3fa922f2d1675f2, 0x42889b8997915ce8}, |
| 1600 | {0x847c9b5d7c2e09b7, 0x69956135febada11}, |
| 1601 | {0xa59bc234db398c25, 0x43fab9837e699095}, |
| 1602 | {0xcf02b2c21207ef2e, 0x94f967e45e03f4bb}, |
| 1603 | {0x8161afb94b44f57d, 0x1d1be0eebac278f5}, |
| 1604 | {0xa1ba1ba79e1632dc, 0x6462d92a69731732}, |
| 1605 | {0xca28a291859bbf93, 0x7d7b8f7503cfdcfe}, |
| 1606 | {0xfcb2cb35e702af78, 0x5cda735244c3d43e}, |
| 1607 | {0x9defbf01b061adab, 0x3a0888136afa64a7}, |
| 1608 | {0xc56baec21c7a1916, 0x088aaa1845b8fdd0}, |
| 1609 | {0xf6c69a72a3989f5b, 0x8aad549e57273d45}, |
| 1610 | {0x9a3c2087a63f6399, 0x36ac54e2f678864b}, |
| 1611 | {0xc0cb28a98fcf3c7f, 0x84576a1bb416a7dd}, |
| 1612 | {0xf0fdf2d3f3c30b9f, 0x656d44a2a11c51d5}, |
| 1613 | {0x969eb7c47859e743, 0x9f644ae5a4b1b325}, |
| 1614 | {0xbc4665b596706114, 0x873d5d9f0dde1fee}, |
| 1615 | {0xeb57ff22fc0c7959, 0xa90cb506d155a7ea}, |
| 1616 | {0x9316ff75dd87cbd8, 0x09a7f12442d588f2}, |
| 1617 | {0xb7dcbf5354e9bece, 0x0c11ed6d538aeb2f}, |
| 1618 | {0xe5d3ef282a242e81, 0x8f1668c8a86da5fa}, |
| 1619 | {0x8fa475791a569d10, 0xf96e017d694487bc}, |
| 1620 | {0xb38d92d760ec4455, 0x37c981dcc395a9ac}, |
| 1621 | {0xe070f78d3927556a, 0x85bbe253f47b1417}, |
| 1622 | {0x8c469ab843b89562, 0x93956d7478ccec8e}, |
| 1623 | {0xaf58416654a6babb, 0x387ac8d1970027b2}, |
| 1624 | {0xdb2e51bfe9d0696a, 0x06997b05fcc0319e}, |
| 1625 | {0x88fcf317f22241e2, 0x441fece3bdf81f03}, |
| 1626 | {0xab3c2fddeeaad25a, 0xd527e81cad7626c3}, |
| 1627 | {0xd60b3bd56a5586f1, 0x8a71e223d8d3b074}, |
| 1628 | {0x85c7056562757456, 0xf6872d5667844e49}, |
| 1629 | {0xa738c6bebb12d16c, 0xb428f8ac016561db}, |
| 1630 | {0xd106f86e69d785c7, 0xe13336d701beba52}, |
| 1631 | {0x82a45b450226b39c, 0xecc0024661173473}, |
| 1632 | {0xa34d721642b06084, 0x27f002d7f95d0190}, |
| 1633 | {0xcc20ce9bd35c78a5, 0x31ec038df7b441f4}, |
| 1634 | {0xff290242c83396ce, 0x7e67047175a15271}, |
| 1635 | {0x9f79a169bd203e41, 0x0f0062c6e984d386}, |
| 1636 | {0xc75809c42c684dd1, 0x52c07b78a3e60868}, |
| 1637 | {0xf92e0c3537826145, 0xa7709a56ccdf8a82}, |
| 1638 | {0x9bbcc7a142b17ccb, 0x88a66076400bb691}, |
| 1639 | {0xc2abf989935ddbfe, 0x6acff893d00ea435}, |
| 1640 | {0xf356f7ebf83552fe, 0x0583f6b8c4124d43}, |
| 1641 | {0x98165af37b2153de, 0xc3727a337a8b704a}, |
| 1642 | {0xbe1bf1b059e9a8d6, 0x744f18c0592e4c5c}, |
| 1643 | {0xeda2ee1c7064130c, 0x1162def06f79df73}, |
| 1644 | {0x9485d4d1c63e8be7, 0x8addcb5645ac2ba8}, |
| 1645 | {0xb9a74a0637ce2ee1, 0x6d953e2bd7173692}, |
| 1646 | {0xe8111c87c5c1ba99, 0xc8fa8db6ccdd0437}, |
| 1647 | {0x910ab1d4db9914a0, 0x1d9c9892400a22a2}, |
| 1648 | {0xb54d5e4a127f59c8, 0x2503beb6d00cab4b}, |
| 1649 | {0xe2a0b5dc971f303a, 0x2e44ae64840fd61d}, |
| 1650 | {0x8da471a9de737e24, 0x5ceaecfed289e5d2}, |
| 1651 | {0xb10d8e1456105dad, 0x7425a83e872c5f47}, |
| 1652 | {0xdd50f1996b947518, 0xd12f124e28f77719}, |
| 1653 | {0x8a5296ffe33cc92f, 0x82bd6b70d99aaa6f}, |
| 1654 | {0xace73cbfdc0bfb7b, 0x636cc64d1001550b}, |
| 1655 | {0xd8210befd30efa5a, 0x3c47f7e05401aa4e}, |
| 1656 | {0x8714a775e3e95c78, 0x65acfaec34810a71}, |
| 1657 | {0xa8d9d1535ce3b396, 0x7f1839a741a14d0d}, |
| 1658 | {0xd31045a8341ca07c, 0x1ede48111209a050}, |
| 1659 | {0x83ea2b892091e44d, 0x934aed0aab460432}, |
| 1660 | {0xa4e4b66b68b65d60, 0xf81da84d5617853f}, |
| 1661 | {0xce1de40642e3f4b9, 0x36251260ab9d668e}, |
| 1662 | {0x80d2ae83e9ce78f3, 0xc1d72b7c6b426019}, |
| 1663 | {0xa1075a24e4421730, 0xb24cf65b8612f81f}, |
| 1664 | {0xc94930ae1d529cfc, 0xdee033f26797b627}, |
| 1665 | {0xfb9b7cd9a4a7443c, 0x169840ef017da3b1}, |
| 1666 | {0x9d412e0806e88aa5, 0x8e1f289560ee864e}, |
| 1667 | {0xc491798a08a2ad4e, 0xf1a6f2bab92a27e2}, |
| 1668 | {0xf5b5d7ec8acb58a2, 0xae10af696774b1db}, |
| 1669 | {0x9991a6f3d6bf1765, 0xacca6da1e0a8ef29}, |
| 1670 | {0xbff610b0cc6edd3f, 0x17fd090a58d32af3}, |
| 1671 | {0xeff394dcff8a948e, 0xddfc4b4cef07f5b0}, |
| 1672 | {0x95f83d0a1fb69cd9, 0x4abdaf101564f98e}, |
| 1673 | {0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f1}, |
| 1674 | {0xea53df5fd18d5513, 0x84c86189216dc5ed}, |
| 1675 | {0x92746b9be2f8552c, 0x32fd3cf5b4e49bb4}, |
| 1676 | {0xb7118682dbb66a77, 0x3fbc8c33221dc2a1}, |
| 1677 | {0xe4d5e82392a40515, 0x0fabaf3feaa5334a}, |
| 1678 | {0x8f05b1163ba6832d, 0x29cb4d87f2a7400e}, |
| 1679 | {0xb2c71d5bca9023f8, 0x743e20e9ef511012}, |
| 1680 | {0xdf78e4b2bd342cf6, 0x914da9246b255416}, |
| 1681 | {0x8bab8eefb6409c1a, 0x1ad089b6c2f7548e}, |
| 1682 | {0xae9672aba3d0c320, 0xa184ac2473b529b1}, |
| 1683 | {0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741e}, |
| 1684 | {0x8865899617fb1871, 0x7e2fa67c7a658892}, |
| 1685 | {0xaa7eebfb9df9de8d, 0xddbb901b98feeab7}, |
| 1686 | {0xd51ea6fa85785631, 0x552a74227f3ea565}, |
| 1687 | {0x8533285c936b35de, 0xd53a88958f87275f}, |
| 1688 | {0xa67ff273b8460356, 0x8a892abaf368f137}, |
| 1689 | {0xd01fef10a657842c, 0x2d2b7569b0432d85}, |
| 1690 | {0x8213f56a67f6b29b, 0x9c3b29620e29fc73}, |
| 1691 | {0xa298f2c501f45f42, 0x8349f3ba91b47b8f}, |
| 1692 | {0xcb3f2f7642717713, 0x241c70a936219a73}, |
| 1693 | {0xfe0efb53d30dd4d7, 0xed238cd383aa0110}, |
| 1694 | {0x9ec95d1463e8a506, 0xf4363804324a40aa}, |
| 1695 | {0xc67bb4597ce2ce48, 0xb143c6053edcd0d5}, |
| 1696 | {0xf81aa16fdc1b81da, 0xdd94b7868e94050a}, |
| 1697 | {0x9b10a4e5e9913128, 0xca7cf2b4191c8326}, |
| 1698 | {0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f0}, |
| 1699 | {0xf24a01a73cf2dccf, 0xbc633b39673c8cec}, |
| 1700 | {0x976e41088617ca01, 0xd5be0503e085d813}, |
| 1701 | {0xbd49d14aa79dbc82, 0x4b2d8644d8a74e18}, |
| 1702 | {0xec9c459d51852ba2, 0xddf8e7d60ed1219e}, |
| 1703 | {0x93e1ab8252f33b45, 0xcabb90e5c942b503}, |
| 1704 | {0xb8da1662e7b00a17, 0x3d6a751f3b936243}, |
| 1705 | {0xe7109bfba19c0c9d, 0x0cc512670a783ad4}, |
| 1706 | {0x906a617d450187e2, 0x27fb2b80668b24c5}, |
| 1707 | {0xb484f9dc9641e9da, 0xb1f9f660802dedf6}, |
| 1708 | {0xe1a63853bbd26451, 0x5e7873f8a0396973}, |
| 1709 | {0x8d07e33455637eb2, 0xdb0b487b6423e1e8}, |
| 1710 | {0xb049dc016abc5e5f, 0x91ce1a9a3d2cda62}, |
| 1711 | {0xdc5c5301c56b75f7, 0x7641a140cc7810fb}, |
| 1712 | {0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9d}, |
| 1713 | {0xac2820d9623bf429, 0x546345fa9fbdcd44}, |
| 1714 | {0xd732290fbacaf133, 0xa97c177947ad4095}, |
| 1715 | {0x867f59a9d4bed6c0, 0x49ed8eabcccc485d}, |
| 1716 | {0xa81f301449ee8c70, 0x5c68f256bfff5a74}, |
| 1717 | {0xd226fc195c6a2f8c, 0x73832eec6fff3111}, |
| 1718 | {0x83585d8fd9c25db7, 0xc831fd53c5ff7eab}, |
| 1719 | {0xa42e74f3d032f525, 0xba3e7ca8b77f5e55}, |
| 1720 | {0xcd3a1230c43fb26f, 0x28ce1bd2e55f35eb}, |
| 1721 | {0x80444b5e7aa7cf85, 0x7980d163cf5b81b3}, |
| 1722 | {0xa0555e361951c366, 0xd7e105bcc332621f}, |
| 1723 | {0xc86ab5c39fa63440, 0x8dd9472bf3fefaa7}, |
| 1724 | {0xfa856334878fc150, 0xb14f98f6f0feb951}, |
| 1725 | {0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d3}, |
| 1726 | {0xc3b8358109e84f07, 0x0a862f80ec4700c8}, |
| 1727 | {0xf4a642e14c6262c8, 0xcd27bb612758c0fa}, |
| 1728 | {0x98e7e9cccfbd7dbd, 0x8038d51cb897789c}, |
| 1729 | {0xbf21e44003acdd2c, 0xe0470a63e6bd56c3}, |
| 1730 | {0xeeea5d5004981478, 0x1858ccfce06cac74}, |
| 1731 | {0x95527a5202df0ccb, 0x0f37801e0c43ebc8}, |
| 1732 | {0xbaa718e68396cffd, 0xd30560258f54e6ba}, |
| 1733 | {0xe950df20247c83fd, 0x47c6b82ef32a2069}, |
| 1734 | {0x91d28b7416cdd27e, 0x4cdc331d57fa5441}, |
| 1735 | {0xb6472e511c81471d, 0xe0133fe4adf8e952}, |
| 1736 | {0xe3d8f9e563a198e5, 0x58180fddd97723a6}, |
| 1737 | {0x8e679c2f5e44ff8f, 0x570f09eaa7ea7648}, |
| 1738 | {0xb201833b35d63f73, 0x2cd2cc6551e513da}, |
| 1739 | {0xde81e40a034bcf4f, 0xf8077f7ea65e58d1}, |
| 1740 | {0x8b112e86420f6191, 0xfb04afaf27faf782}, |
| 1741 | {0xadd57a27d29339f6, 0x79c5db9af1f9b563}, |
| 1742 | {0xd94ad8b1c7380874, 0x18375281ae7822bc}, |
| 1743 | {0x87cec76f1c830548, 0x8f2293910d0b15b5}, |
| 1744 | {0xa9c2794ae3a3c69a, 0xb2eb3875504ddb22}, |
| 1745 | {0xd433179d9c8cb841, 0x5fa60692a46151eb}, |
| 1746 | {0x849feec281d7f328, 0xdbc7c41ba6bcd333}, |
| 1747 | {0xa5c7ea73224deff3, 0x12b9b522906c0800}, |
| 1748 | {0xcf39e50feae16bef, 0xd768226b34870a00}, |
| 1749 | {0x81842f29f2cce375, 0xe6a1158300d46640}, |
| 1750 | {0xa1e53af46f801c53, 0x60495ae3c1097fd0}, |
| 1751 | {0xca5e89b18b602368, 0x385bb19cb14bdfc4}, |
| 1752 | {0xfcf62c1dee382c42, 0x46729e03dd9ed7b5}, |
| 1753 | {0x9e19db92b4e31ba9, 0x6c07a2c26a8346d1}, |
| 1754 | {0xc5a05277621be293, 0xc7098b7305241885}, |
| 1755 | { 0xf70867153aa2db38, |
| 1756 | 0xb8cbee4fc66d1ea7 } |
| 1757 | #else |
| 1758 | {0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7b}, |
| 1759 | {0xce5d73ff402d98e3, 0xfb0a3d212dc81290}, |
| 1760 | {0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481f}, |
| 1761 | {0x86a8d39ef77164bc, 0xae5dff9c02033198}, |
| 1762 | {0xd98ddaee19068c76, 0x3badd624dd9b0958}, |
| 1763 | {0xafbd2350644eeacf, 0xe5d1929ef90898fb}, |
| 1764 | {0x8df5efabc5979c8f, 0xca8d3ffa1ef463c2}, |
| 1765 | {0xe55990879ddcaabd, 0xcc420a6a101d0516}, |
| 1766 | {0xb94470938fa89bce, 0xf808e40e8d5b3e6a}, |
| 1767 | {0x95a8637627989aad, 0xdde7001379a44aa9}, |
| 1768 | {0xf1c90080baf72cb1, 0x5324c68b12dd6339}, |
| 1769 | {0xc350000000000000, 0x0000000000000000}, |
| 1770 | {0x9dc5ada82b70b59d, 0xf020000000000000}, |
| 1771 | {0xfee50b7025c36a08, 0x02f236d04753d5b4}, |
| 1772 | {0xcde6fd5e09abcf26, 0xed4c0226b55e6f86}, |
| 1773 | {0xa6539930bf6bff45, 0x84db8346b786151c}, |
| 1774 | {0x865b86925b9bc5c2, 0x0b8a2392ba45a9b2}, |
| 1775 | {0xd910f7ff28069da4, 0x1b2ba1518094da04}, |
| 1776 | {0xaf58416654a6babb, 0x387ac8d1970027b2}, |
| 1777 | {0x8da471a9de737e24, 0x5ceaecfed289e5d2}, |
| 1778 | {0xe4d5e82392a40515, 0x0fabaf3feaa5334a}, |
| 1779 | {0xb8da1662e7b00a17, 0x3d6a751f3b936243}, |
| 1780 | { 0x95527a5202df0ccb, |
| 1781 | 0x0f37801e0c43ebc8 } |
| 1782 | #endif |
| 1783 | }; |
| 1784 | |
| 1785 | #if FMT_USE_FULL_CACHE_DRAGONBOX |
| 1786 | return pow10_significands[k - float_info<double>::min_k]; |
| 1787 | #else |
| 1788 | static constexpr const uint64_t powers_of_5_64[] = { |
| 1789 | 0x0000000000000001, 0x0000000000000005, 0x0000000000000019, |
| 1790 | 0x000000000000007d, 0x0000000000000271, 0x0000000000000c35, |
| 1791 | 0x0000000000003d09, 0x000000000001312d, 0x000000000005f5e1, |
| 1792 | 0x00000000001dcd65, 0x00000000009502f9, 0x0000000002e90edd, |
| 1793 | 0x000000000e8d4a51, 0x0000000048c27395, 0x000000016bcc41e9, |
| 1794 | 0x000000071afd498d, 0x0000002386f26fc1, 0x000000b1a2bc2ec5, |
| 1795 | 0x000003782dace9d9, 0x00001158e460913d, 0x000056bc75e2d631, |
| 1796 | 0x0001b1ae4d6e2ef5, 0x000878678326eac9, 0x002a5a058fc295ed, |
| 1797 | 0x00d3c21bcecceda1, 0x0422ca8b0a00a425, 0x14adf4b7320334b9}; |
| 1798 | |
| 1799 | static constexpr const uint32_t pow10_recovery_errors[] = { |
| 1800 | 0x50001400, 0x54044100, 0x54014555, 0x55954415, 0x54115555, 0x00000001, |
| 1801 | 0x50000000, 0x00104000, 0x54010004, 0x05004001, 0x55555544, 0x41545555, |
| 1802 | 0x54040551, 0x15445545, 0x51555514, 0x10000015, 0x00101100, 0x01100015, |
| 1803 | 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x04450514, 0x45414110, |
| 1804 | 0x55555145, 0x50544050, 0x15040155, 0x11054140, 0x50111514, 0x11451454, |
| 1805 | 0x00400541, 0x00000000, 0x55555450, 0x10056551, 0x10054011, 0x55551014, |
| 1806 | 0x69514555, 0x05151109, 0x00155555}; |
| 1807 | |
| 1808 | static const int compression_ratio = 27; |
| 1809 | |
| 1810 | // Compute base index. |
| 1811 | int cache_index = (k - float_info<double>::min_k) / compression_ratio; |
| 1812 | int kb = cache_index * compression_ratio + float_info<double>::min_k; |
| 1813 | int offset = k - kb; |
| 1814 | |
| 1815 | // Get base cache. |
| 1816 | uint128_wrapper base_cache = pow10_significands[cache_index]; |
| 1817 | if (offset == 0) return base_cache; |
| 1818 | |
| 1819 | // Compute the required amount of bit-shift. |
| 1820 | int alpha = floor_log2_pow10(kb + offset) - floor_log2_pow10(kb) - offset; |
| 1821 | FMT_ASSERT(alpha > 0 && alpha < 64, "shifting error detected"); |
| 1822 | |
| 1823 | // Try to recover the real cache. |
| 1824 | uint64_t pow5 = powers_of_5_64[offset]; |
| 1825 | uint128_wrapper recovered_cache = umul128(base_cache.high(), pow5); |
| 1826 | uint128_wrapper middle_low = |
| 1827 | umul128(base_cache.low() - (kb < 0 ? 1u : 0u), pow5); |
| 1828 | |
| 1829 | recovered_cache += middle_low.high(); |
| 1830 | |
| 1831 | uint64_t high_to_middle = recovered_cache.high() << (64 - alpha); |
| 1832 | uint64_t middle_to_low = recovered_cache.low() << (64 - alpha); |
| 1833 | |
| 1834 | recovered_cache = |
| 1835 | uint128_wrapper{(recovered_cache.low() >> alpha) | high_to_middle, |
| 1836 | ((middle_low.low() >> alpha) | middle_to_low)}; |
| 1837 | |
| 1838 | if (kb < 0) recovered_cache += 1; |
| 1839 | |
| 1840 | // Get error. |
| 1841 | int error_idx = (k - float_info<double>::min_k) / 16; |
| 1842 | uint32_t error = (pow10_recovery_errors[error_idx] >> |
| 1843 | ((k - float_info<double>::min_k) % 16) * 2) & |
| 1844 | 0x3; |
| 1845 | |
| 1846 | // Add the error back. |
| 1847 | FMT_ASSERT(recovered_cache.low() + error >= recovered_cache.low(), ""); |
| 1848 | return {recovered_cache.high(), recovered_cache.low() + error}; |
| 1849 | #endif |
| 1850 | } |
| 1851 | |
| 1852 | static carrier_uint compute_mul(carrier_uint u, |
| 1853 | const cache_entry_type& cache) FMT_NOEXCEPT { |
| 1854 | return umul192_upper64(u, cache); |
| 1855 | } |
| 1856 | |
| 1857 | static uint32_t compute_delta(cache_entry_type const& cache, |
| 1858 | int beta_minus_1) FMT_NOEXCEPT { |
| 1859 | return static_cast<uint32_t>(cache.high() >> (64 - 1 - beta_minus_1)); |
| 1860 | } |
| 1861 | |
| 1862 | static bool compute_mul_parity(carrier_uint two_f, |
| 1863 | const cache_entry_type& cache, |
| 1864 | int beta_minus_1) FMT_NOEXCEPT { |
| 1865 | FMT_ASSERT(beta_minus_1 >= 1, ""); |
| 1866 | FMT_ASSERT(beta_minus_1 < 64, ""); |
| 1867 | |
| 1868 | return ((umul192_middle64(two_f, cache) >> (64 - beta_minus_1)) & 1) != 0; |
| 1869 | } |
| 1870 | |
| 1871 | static carrier_uint compute_left_endpoint_for_shorter_interval_case( |
| 1872 | const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT { |
| 1873 | return (cache.high() - |
| 1874 | (cache.high() >> (float_info<double>::significand_bits + 2))) >> |
| 1875 | (64 - float_info<double>::significand_bits - 1 - beta_minus_1); |
| 1876 | } |
| 1877 | |
| 1878 | static carrier_uint compute_right_endpoint_for_shorter_interval_case( |
| 1879 | const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT { |
| 1880 | return (cache.high() + |
| 1881 | (cache.high() >> (float_info<double>::significand_bits + 1))) >> |
| 1882 | (64 - float_info<double>::significand_bits - 1 - beta_minus_1); |
| 1883 | } |
| 1884 | |
| 1885 | static carrier_uint compute_round_up_for_shorter_interval_case( |
| 1886 | const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT { |
| 1887 | return ((cache.high() >> |
| 1888 | (64 - float_info<double>::significand_bits - 2 - beta_minus_1)) + |
| 1889 | 1) / |
| 1890 | 2; |
| 1891 | } |
| 1892 | }; |
| 1893 | |
| 1894 | // Various integer checks |
| 1895 | template <class T> |
| 1896 | bool is_left_endpoint_integer_shorter_interval(int exponent) FMT_NOEXCEPT { |
| 1897 | return exponent >= |
| 1898 | float_info< |
| 1899 | T>::case_shorter_interval_left_endpoint_lower_threshold && |
| 1900 | exponent <= |
| 1901 | float_info<T>::case_shorter_interval_left_endpoint_upper_threshold; |
| 1902 | } |
| 1903 | template <class T> |
| 1904 | bool is_endpoint_integer(typename float_info<T>::carrier_uint two_f, |
| 1905 | int exponent, int minus_k) FMT_NOEXCEPT { |
| 1906 | if (exponent < float_info<T>::case_fc_pm_half_lower_threshold) return false; |
| 1907 | // For k >= 0. |
| 1908 | if (exponent <= float_info<T>::case_fc_pm_half_upper_threshold) return true; |
| 1909 | // For k < 0. |
| 1910 | if (exponent > float_info<T>::divisibility_check_by_5_threshold) return false; |
| 1911 | return divisible_by_power_of_5(two_f, minus_k); |
| 1912 | } |
| 1913 | |
| 1914 | template <class T> |
| 1915 | bool is_center_integer(typename float_info<T>::carrier_uint two_f, int exponent, |
| 1916 | int minus_k) FMT_NOEXCEPT { |
| 1917 | // Exponent for 5 is negative. |
| 1918 | if (exponent > float_info<T>::divisibility_check_by_5_threshold) return false; |
| 1919 | if (exponent > float_info<T>::case_fc_upper_threshold) |
| 1920 | return divisible_by_power_of_5(two_f, minus_k); |
| 1921 | // Both exponents are nonnegative. |
| 1922 | if (exponent >= float_info<T>::case_fc_lower_threshold) return true; |
| 1923 | // Exponent for 2 is negative. |
| 1924 | return divisible_by_power_of_2(two_f, minus_k - exponent + 1); |
| 1925 | } |
| 1926 | |
| 1927 | // Remove trailing zeros from n and return the number of zeros removed (float) |
| 1928 | FMT_INLINE int remove_trailing_zeros(uint32_t& n) FMT_NOEXCEPT { |
| 1929 | #ifdef FMT_BUILTIN_CTZ |
| 1930 | int t = FMT_BUILTIN_CTZ(n); |
| 1931 | #else |
| 1932 | int t = ctz(n); |
| 1933 | #endif |
| 1934 | if (t > float_info<float>::max_trailing_zeros) |
| 1935 | t = float_info<float>::max_trailing_zeros; |
| 1936 | |
| 1937 | const uint32_t mod_inv1 = 0xcccccccd; |
| 1938 | const uint32_t max_quotient1 = 0x33333333; |
| 1939 | const uint32_t mod_inv2 = 0xc28f5c29; |
| 1940 | const uint32_t max_quotient2 = 0x0a3d70a3; |
| 1941 | |
| 1942 | int s = 0; |
| 1943 | for (; s < t - 1; s += 2) { |
| 1944 | if (n * mod_inv2 > max_quotient2) break; |
| 1945 | n *= mod_inv2; |
| 1946 | } |
| 1947 | if (s < t && n * mod_inv1 <= max_quotient1) { |
| 1948 | n *= mod_inv1; |
| 1949 | ++s; |
| 1950 | } |
| 1951 | n >>= s; |
| 1952 | return s; |
| 1953 | } |
| 1954 | |
| 1955 | // Removes trailing zeros and returns the number of zeros removed (double) |
| 1956 | FMT_INLINE int remove_trailing_zeros(uint64_t& n) FMT_NOEXCEPT { |
| 1957 | #ifdef FMT_BUILTIN_CTZLL |
| 1958 | int t = FMT_BUILTIN_CTZLL(n); |
| 1959 | #else |
| 1960 | int t = ctzll(n); |
| 1961 | #endif |
| 1962 | if (t > float_info<double>::max_trailing_zeros) |
| 1963 | t = float_info<double>::max_trailing_zeros; |
| 1964 | // Divide by 10^8 and reduce to 32-bits |
| 1965 | // Since ret_value.significand <= (2^64 - 1) / 1000 < 10^17, |
| 1966 | // both of the quotient and the r should fit in 32-bits |
| 1967 | |
| 1968 | const uint32_t mod_inv1 = 0xcccccccd; |
| 1969 | const uint32_t max_quotient1 = 0x33333333; |
| 1970 | const uint64_t mod_inv8 = 0xc767074b22e90e21; |
| 1971 | const uint64_t max_quotient8 = 0x00002af31dc46118; |
| 1972 | |
| 1973 | // If the number is divisible by 1'0000'0000, work with the quotient |
| 1974 | if (t >= 8) { |
| 1975 | auto quotient_candidate = n * mod_inv8; |
| 1976 | |
| 1977 | if (quotient_candidate <= max_quotient8) { |
| 1978 | auto quotient = static_cast<uint32_t>(quotient_candidate >> 8); |
| 1979 | |
| 1980 | int s = 8; |
| 1981 | for (; s < t; ++s) { |
| 1982 | if (quotient * mod_inv1 > max_quotient1) break; |
| 1983 | quotient *= mod_inv1; |
| 1984 | } |
| 1985 | quotient >>= (s - 8); |
| 1986 | n = quotient; |
| 1987 | return s; |
| 1988 | } |
| 1989 | } |
| 1990 | |
| 1991 | // Otherwise, work with the remainder |
| 1992 | auto quotient = static_cast<uint32_t>(n / 100000000); |
| 1993 | auto remainder = static_cast<uint32_t>(n - 100000000 * quotient); |
| 1994 | |
| 1995 | if (t == 0 || remainder * mod_inv1 > max_quotient1) { |
| 1996 | return 0; |
| 1997 | } |
| 1998 | remainder *= mod_inv1; |
| 1999 | |
| 2000 | if (t == 1 || remainder * mod_inv1 > max_quotient1) { |
| 2001 | n = (remainder >> 1) + quotient * 10000000ull; |
| 2002 | return 1; |
| 2003 | } |
| 2004 | remainder *= mod_inv1; |
| 2005 | |
| 2006 | if (t == 2 || remainder * mod_inv1 > max_quotient1) { |
| 2007 | n = (remainder >> 2) + quotient * 1000000ull; |
| 2008 | return 2; |
| 2009 | } |
| 2010 | remainder *= mod_inv1; |
| 2011 | |
| 2012 | if (t == 3 || remainder * mod_inv1 > max_quotient1) { |
| 2013 | n = (remainder >> 3) + quotient * 100000ull; |
| 2014 | return 3; |
| 2015 | } |
| 2016 | remainder *= mod_inv1; |
| 2017 | |
| 2018 | if (t == 4 || remainder * mod_inv1 > max_quotient1) { |
| 2019 | n = (remainder >> 4) + quotient * 10000ull; |
| 2020 | return 4; |
| 2021 | } |
| 2022 | remainder *= mod_inv1; |
| 2023 | |
| 2024 | if (t == 5 || remainder * mod_inv1 > max_quotient1) { |
| 2025 | n = (remainder >> 5) + quotient * 1000ull; |
| 2026 | return 5; |
| 2027 | } |
| 2028 | remainder *= mod_inv1; |
| 2029 | |
| 2030 | if (t == 6 || remainder * mod_inv1 > max_quotient1) { |
| 2031 | n = (remainder >> 6) + quotient * 100ull; |
| 2032 | return 6; |
| 2033 | } |
| 2034 | remainder *= mod_inv1; |
| 2035 | |
| 2036 | n = (remainder >> 7) + quotient * 10ull; |
| 2037 | return 7; |
| 2038 | } |
| 2039 | |
| 2040 | // The main algorithm for shorter interval case |
| 2041 | template <class T> |
| 2042 | FMT_INLINE decimal_fp<T> shorter_interval_case(int exponent) FMT_NOEXCEPT { |
| 2043 | decimal_fp<T> ret_value; |
| 2044 | // Compute k and beta |
| 2045 | const int minus_k = floor_log10_pow2_minus_log10_4_over_3(exponent); |
| 2046 | const int beta_minus_1 = exponent + floor_log2_pow10(-minus_k); |
| 2047 | |
| 2048 | // Compute xi and zi |
| 2049 | using cache_entry_type = typename cache_accessor<T>::cache_entry_type; |
| 2050 | const cache_entry_type cache = cache_accessor<T>::get_cached_power(-minus_k); |
| 2051 | |
| 2052 | auto xi = cache_accessor<T>::compute_left_endpoint_for_shorter_interval_case( |
| 2053 | cache, beta_minus_1); |
| 2054 | auto zi = cache_accessor<T>::compute_right_endpoint_for_shorter_interval_case( |
| 2055 | cache, beta_minus_1); |
| 2056 | |
| 2057 | // If the left endpoint is not an integer, increase it |
| 2058 | if (!is_left_endpoint_integer_shorter_interval<T>(exponent)) ++xi; |
| 2059 | |
| 2060 | // Try bigger divisor |
| 2061 | ret_value.significand = zi / 10; |
| 2062 | |
| 2063 | // If succeed, remove trailing zeros if necessary and return |
| 2064 | if (ret_value.significand * 10 >= xi) { |
| 2065 | ret_value.exponent = minus_k + 1; |
| 2066 | ret_value.exponent += remove_trailing_zeros(ret_value.significand); |
| 2067 | return ret_value; |
| 2068 | } |
| 2069 | |
| 2070 | // Otherwise, compute the round-up of y |
| 2071 | ret_value.significand = |
| 2072 | cache_accessor<T>::compute_round_up_for_shorter_interval_case( |
| 2073 | cache, beta_minus_1); |
| 2074 | ret_value.exponent = minus_k; |
| 2075 | |
| 2076 | // When tie occurs, choose one of them according to the rule |
| 2077 | if (exponent >= float_info<T>::shorter_interval_tie_lower_threshold && |
| 2078 | exponent <= float_info<T>::shorter_interval_tie_upper_threshold) { |
| 2079 | ret_value.significand = ret_value.significand % 2 == 0 |
| 2080 | ? ret_value.significand |
| 2081 | : ret_value.significand - 1; |
| 2082 | } else if (ret_value.significand < xi) { |
| 2083 | ++ret_value.significand; |
| 2084 | } |
| 2085 | return ret_value; |
| 2086 | } |
| 2087 | |
| 2088 | template <typename T> decimal_fp<T> to_decimal(T x) FMT_NOEXCEPT { |
| 2089 | // Step 1: integer promotion & Schubfach multiplier calculation. |
| 2090 | |
| 2091 | using carrier_uint = typename float_info<T>::carrier_uint; |
| 2092 | using cache_entry_type = typename cache_accessor<T>::cache_entry_type; |
| 2093 | auto br = bit_cast<carrier_uint>(x); |
| 2094 | |
| 2095 | // Extract significand bits and exponent bits. |
| 2096 | const carrier_uint significand_mask = |
| 2097 | (static_cast<carrier_uint>(1) << float_info<T>::significand_bits) - 1; |
| 2098 | carrier_uint significand = (br & significand_mask); |
| 2099 | int exponent = static_cast<int>((br & exponent_mask<T>()) >> |
| 2100 | float_info<T>::significand_bits); |
| 2101 | |
| 2102 | if (exponent != 0) { // Check if normal. |
| 2103 | exponent += float_info<T>::exponent_bias - float_info<T>::significand_bits; |
| 2104 | |
| 2105 | // Shorter interval case; proceed like Schubfach. |
| 2106 | if (significand == 0) return shorter_interval_case<T>(exponent); |
| 2107 | |
| 2108 | significand |= |
| 2109 | (static_cast<carrier_uint>(1) << float_info<T>::significand_bits); |
| 2110 | } else { |
| 2111 | // Subnormal case; the interval is always regular. |
| 2112 | if (significand == 0) return {0, 0}; |
| 2113 | exponent = float_info<T>::min_exponent - float_info<T>::significand_bits; |
| 2114 | } |
| 2115 | |
| 2116 | const bool include_left_endpoint = (significand % 2 == 0); |
| 2117 | const bool include_right_endpoint = include_left_endpoint; |
| 2118 | |
| 2119 | // Compute k and beta. |
| 2120 | const int minus_k = floor_log10_pow2(exponent) - float_info<T>::kappa; |
| 2121 | const cache_entry_type cache = cache_accessor<T>::get_cached_power(-minus_k); |
| 2122 | const int beta_minus_1 = exponent + floor_log2_pow10(-minus_k); |
| 2123 | |
| 2124 | // Compute zi and deltai |
| 2125 | // 10^kappa <= deltai < 10^(kappa + 1) |
| 2126 | const uint32_t deltai = cache_accessor<T>::compute_delta(cache, beta_minus_1); |
| 2127 | const carrier_uint two_fc = significand << 1; |
| 2128 | const carrier_uint two_fr = two_fc | 1; |
| 2129 | const carrier_uint zi = |
| 2130 | cache_accessor<T>::compute_mul(two_fr << beta_minus_1, cache); |
| 2131 | |
| 2132 | // Step 2: Try larger divisor; remove trailing zeros if necessary |
| 2133 | |
| 2134 | // Using an upper bound on zi, we might be able to optimize the division |
| 2135 | // better than the compiler; we are computing zi / big_divisor here |
| 2136 | decimal_fp<T> ret_value; |
| 2137 | ret_value.significand = divide_by_10_to_kappa_plus_1(zi); |
| 2138 | uint32_t r = static_cast<uint32_t>(zi - float_info<T>::big_divisor * |
| 2139 | ret_value.significand); |
| 2140 | |
| 2141 | if (r > deltai) { |
| 2142 | goto small_divisor_case_label; |
| 2143 | } else if (r < deltai) { |
| 2144 | // Exclude the right endpoint if necessary |
| 2145 | if (r == 0 && !include_right_endpoint && |
| 2146 | is_endpoint_integer<T>(two_fr, exponent, minus_k)) { |
| 2147 | --ret_value.significand; |
| 2148 | r = float_info<T>::big_divisor; |
| 2149 | goto small_divisor_case_label; |
| 2150 | } |
| 2151 | } else { |
| 2152 | // r == deltai; compare fractional parts |
| 2153 | // Check conditions in the order different from the paper |
| 2154 | // to take advantage of short-circuiting |
| 2155 | const carrier_uint two_fl = two_fc - 1; |
| 2156 | if ((!include_left_endpoint || |
| 2157 | !is_endpoint_integer<T>(two_fl, exponent, minus_k)) && |
| 2158 | !cache_accessor<T>::compute_mul_parity(two_fl, cache, beta_minus_1)) { |
| 2159 | goto small_divisor_case_label; |
| 2160 | } |
| 2161 | } |
| 2162 | ret_value.exponent = minus_k + float_info<T>::kappa + 1; |
| 2163 | |
| 2164 | // We may need to remove trailing zeros |
| 2165 | ret_value.exponent += remove_trailing_zeros(ret_value.significand); |
| 2166 | return ret_value; |
| 2167 | |
| 2168 | // Step 3: Find the significand with the smaller divisor |
| 2169 | |
| 2170 | small_divisor_case_label: |
| 2171 | ret_value.significand *= 10; |
| 2172 | ret_value.exponent = minus_k + float_info<T>::kappa; |
| 2173 | |
| 2174 | const uint32_t mask = (1u << float_info<T>::kappa) - 1; |
| 2175 | auto dist = r - (deltai / 2) + (float_info<T>::small_divisor / 2); |
| 2176 | |
| 2177 | // Is dist divisible by 2^kappa? |
| 2178 | if ((dist & mask) == 0) { |
| 2179 | const bool approx_y_parity = |
| 2180 | ((dist ^ (float_info<T>::small_divisor / 2)) & 1) != 0; |
| 2181 | dist >>= float_info<T>::kappa; |
| 2182 | |
| 2183 | // Is dist divisible by 5^kappa? |
| 2184 | if (check_divisibility_and_divide_by_pow5<float_info<T>::kappa>(dist)) { |
| 2185 | ret_value.significand += dist; |
| 2186 | |
| 2187 | // Check z^(f) >= epsilon^(f) |
| 2188 | // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1, |
| 2189 | // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f) |
| 2190 | // Since there are only 2 possibilities, we only need to care about the |
| 2191 | // parity. Also, zi and r should have the same parity since the divisor |
| 2192 | // is an even number |
| 2193 | if (cache_accessor<T>::compute_mul_parity(two_fc, cache, beta_minus_1) != |
| 2194 | approx_y_parity) { |
| 2195 | --ret_value.significand; |
| 2196 | } else { |
| 2197 | // If z^(f) >= epsilon^(f), we might have a tie |
| 2198 | // when z^(f) == epsilon^(f), or equivalently, when y is an integer |
| 2199 | if (is_center_integer<T>(two_fc, exponent, minus_k)) { |
| 2200 | ret_value.significand = ret_value.significand % 2 == 0 |
| 2201 | ? ret_value.significand |
| 2202 | : ret_value.significand - 1; |
| 2203 | } |
| 2204 | } |
| 2205 | } |
| 2206 | // Is dist not divisible by 5^kappa? |
| 2207 | else { |
| 2208 | ret_value.significand += dist; |
| 2209 | } |
| 2210 | } |
| 2211 | // Is dist not divisible by 2^kappa? |
| 2212 | else { |
| 2213 | // Since we know dist is small, we might be able to optimize the division |
| 2214 | // better than the compiler; we are computing dist / small_divisor here |
| 2215 | ret_value.significand += |
| 2216 | small_division_by_pow10<float_info<T>::kappa>(dist); |
| 2217 | } |
| 2218 | return ret_value; |
| 2219 | } |
| 2220 | } // namespace dragonbox |
| 2221 | |
| 2222 | // Formats a floating-point number using a variation of the Fixed-Precision |
| 2223 | // Positive Floating-Point Printout ((FPP)^2) algorithm by Steele & White: |
| 2224 | // https://fmt.dev/papers/p372-steele.pdf. |
| 2225 | FMT_CONSTEXPR20 inline void format_dragon(fp value, bool is_predecessor_closer, |
| 2226 | int num_digits, buffer<char>& buf, |
| 2227 | int& exp10) { |
| 2228 | bigint numerator; // 2 * R in (FPP)^2. |
| 2229 | bigint denominator; // 2 * S in (FPP)^2. |
| 2230 | // lower and upper are differences between value and corresponding boundaries. |
| 2231 | bigint lower; // (M^- in (FPP)^2). |
| 2232 | bigint upper_store; // upper's value if different from lower. |
| 2233 | bigint* upper = nullptr; // (M^+ in (FPP)^2). |
| 2234 | // Shift numerator and denominator by an extra bit or two (if lower boundary |
| 2235 | // is closer) to make lower and upper integers. This eliminates multiplication |
| 2236 | // by 2 during later computations. |
| 2237 | int shift = is_predecessor_closer ? 2 : 1; |
| 2238 | uint64_t significand = value.f << shift; |
| 2239 | if (value.e >= 0) { |
| 2240 | numerator.assign(significand); |
| 2241 | numerator <<= value.e; |
| 2242 | lower.assign(1); |
| 2243 | lower <<= value.e; |
| 2244 | if (shift != 1) { |
| 2245 | upper_store.assign(1); |
| 2246 | upper_store <<= value.e + 1; |
| 2247 | upper = &upper_store; |
| 2248 | } |
| 2249 | denominator.assign_pow10(exp10); |
| 2250 | denominator <<= shift; |
| 2251 | } else if (exp10 < 0) { |
| 2252 | numerator.assign_pow10(-exp10); |
| 2253 | lower.assign(numerator); |
| 2254 | if (shift != 1) { |
| 2255 | upper_store.assign(numerator); |
| 2256 | upper_store <<= 1; |
| 2257 | upper = &upper_store; |
| 2258 | } |
| 2259 | numerator *= significand; |
| 2260 | denominator.assign(1); |
| 2261 | denominator <<= shift - value.e; |
| 2262 | } else { |
| 2263 | numerator.assign(significand); |
| 2264 | denominator.assign_pow10(exp10); |
| 2265 | denominator <<= shift - value.e; |
| 2266 | lower.assign(1); |
| 2267 | if (shift != 1) { |
| 2268 | upper_store.assign(1ULL << 1); |
| 2269 | upper = &upper_store; |
| 2270 | } |
| 2271 | } |
| 2272 | // Invariant: value == (numerator / denominator) * pow(10, exp10). |
| 2273 | if (num_digits < 0) { |
| 2274 | // Generate the shortest representation. |
| 2275 | if (!upper) upper = &lower; |
| 2276 | bool even = (value.f & 1) == 0; |
| 2277 | num_digits = 0; |
| 2278 | char* data = buf.data(); |
| 2279 | for (;;) { |
| 2280 | int digit = numerator.divmod_assign(denominator); |
| 2281 | bool low = compare(numerator, lower) - even < 0; // numerator <[=] lower. |
| 2282 | // numerator + upper >[=] pow10: |
| 2283 | bool high = add_compare(numerator, *upper, denominator) + even > 0; |
| 2284 | data[num_digits++] = static_cast<char>('0' + digit); |
| 2285 | if (low || high) { |
| 2286 | if (!low) { |
| 2287 | ++data[num_digits - 1]; |
| 2288 | } else if (high) { |
| 2289 | int result = add_compare(numerator, numerator, denominator); |
| 2290 | // Round half to even. |
| 2291 | if (result > 0 || (result == 0 && (digit % 2) != 0)) |
| 2292 | ++data[num_digits - 1]; |
| 2293 | } |
| 2294 | buf.try_resize(to_unsigned(num_digits)); |
| 2295 | exp10 -= num_digits - 1; |
| 2296 | return; |
| 2297 | } |
| 2298 | numerator *= 10; |
| 2299 | lower *= 10; |
| 2300 | if (upper != &lower) *upper *= 10; |
| 2301 | } |
| 2302 | } |
| 2303 | // Generate the given number of digits. |
| 2304 | exp10 -= num_digits - 1; |
| 2305 | if (num_digits == 0) { |
| 2306 | denominator *= 10; |
| 2307 | auto digit = add_compare(numerator, numerator, denominator) > 0 ? '1' : '0'; |
| 2308 | buf.push_back(digit); |
| 2309 | return; |
| 2310 | } |
| 2311 | buf.try_resize(to_unsigned(num_digits)); |
| 2312 | for (int i = 0; i < num_digits - 1; ++i) { |
| 2313 | int digit = numerator.divmod_assign(denominator); |
| 2314 | buf[i] = static_cast<char>('0' + digit); |
| 2315 | numerator *= 10; |
| 2316 | } |
| 2317 | int digit = numerator.divmod_assign(denominator); |
| 2318 | auto result = add_compare(numerator, numerator, denominator); |
| 2319 | if (result > 0 || (result == 0 && (digit % 2) != 0)) { |
| 2320 | if (digit == 9) { |
| 2321 | const auto overflow = '0' + 10; |
| 2322 | buf[num_digits - 1] = overflow; |
| 2323 | // Propagate the carry. |
| 2324 | for (int i = num_digits - 1; i > 0 && buf[i] == overflow; --i) { |
| 2325 | buf[i] = '0'; |
| 2326 | ++buf[i - 1]; |
| 2327 | } |
| 2328 | if (buf[0] == overflow) { |
| 2329 | buf[0] = '1'; |
| 2330 | ++exp10; |
| 2331 | } |
| 2332 | return; |
| 2333 | } |
| 2334 | ++digit; |
| 2335 | } |
| 2336 | buf[num_digits - 1] = static_cast<char>('0' + digit); |
| 2337 | } |
| 2338 | |
| 2339 | template <typename Float> |
| 2340 | FMT_HEADER_ONLY_CONSTEXPR20 int format_float(Float value, int precision, |
| 2341 | float_specs specs, |
| 2342 | buffer<char>& buf) { |
| 2343 | // float is passed as double to reduce the number of instantiations. |
| 2344 | static_assert(!std::is_same<Float, float>::value, ""); |
| 2345 | FMT_ASSERT(value >= 0, "value is negative"); |
| 2346 | |
| 2347 | const bool fixed = specs.format == float_format::fixed; |
| 2348 | if (value <= 0) { // <= instead of == to silence a warning. |
| 2349 | if (precision <= 0 || !fixed) { |
| 2350 | buf.push_back('0'); |
| 2351 | return 0; |
| 2352 | } |
| 2353 | buf.try_resize(to_unsigned(precision)); |
| 2354 | fill_n(buf.data(), precision, '0'); |
| 2355 | return -precision; |
| 2356 | } |
| 2357 | |
| 2358 | if (specs.fallback) return snprintf_float(value, precision, specs, buf); |
| 2359 | |
| 2360 | if (!is_constant_evaluated() && precision < 0) { |
| 2361 | // Use Dragonbox for the shortest format. |
| 2362 | if (specs.binary32) { |
| 2363 | auto dec = dragonbox::to_decimal(static_cast<float>(value)); |
| 2364 | write<char>(buffer_appender<char>(buf), dec.significand); |
| 2365 | return dec.exponent; |
| 2366 | } |
| 2367 | auto dec = dragonbox::to_decimal(static_cast<double>(value)); |
| 2368 | write<char>(buffer_appender<char>(buf), dec.significand); |
| 2369 | return dec.exponent; |
| 2370 | } |
| 2371 | |
| 2372 | int exp = 0; |
| 2373 | bool use_dragon = true; |
| 2374 | if (is_fast_float<Float>()) { |
| 2375 | // Use Grisu + Dragon4 for the given precision: |
| 2376 | // https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf. |
| 2377 | const int min_exp = -60; // alpha in Grisu. |
| 2378 | int cached_exp10 = 0; // K in Grisu. |
| 2379 | fp normalized = normalize(fp(value)); |
| 2380 | const auto cached_pow = get_cached_power( |
| 2381 | min_exp - (normalized.e + fp::num_significand_bits), cached_exp10); |
| 2382 | normalized = normalized * cached_pow; |
| 2383 | gen_digits_handler handler{buf.data(), 0, precision, -cached_exp10, fixed}; |
| 2384 | if (grisu_gen_digits(normalized, 1, exp, handler) != digits::error && |
| 2385 | !is_constant_evaluated()) { |
| 2386 | exp += handler.exp10; |
| 2387 | buf.try_resize(to_unsigned(handler.size)); |
| 2388 | use_dragon = false; |
| 2389 | } else { |
| 2390 | exp += handler.size - cached_exp10 - 1; |
| 2391 | precision = handler.precision; |
| 2392 | } |
| 2393 | } |
| 2394 | if (use_dragon) { |
| 2395 | auto f = fp(); |
| 2396 | bool is_predecessor_closer = |
| 2397 | specs.binary32 ? f.assign(static_cast<float>(value)) : f.assign(value); |
| 2398 | // Limit precision to the maximum possible number of significant digits in |
| 2399 | // an IEEE754 double because we don't need to generate zeros. |
| 2400 | const int max_double_digits = 767; |
| 2401 | if (precision > max_double_digits) precision = max_double_digits; |
| 2402 | format_dragon(f, is_predecessor_closer, precision, buf, exp); |
| 2403 | } |
| 2404 | if (!fixed && !specs.showpoint) { |
| 2405 | // Remove trailing zeros. |
| 2406 | auto num_digits = buf.size(); |
| 2407 | while (num_digits > 0 && buf[num_digits - 1] == '0') { |
| 2408 | --num_digits; |
| 2409 | ++exp; |
| 2410 | } |
| 2411 | buf.try_resize(num_digits); |
| 2412 | } |
| 2413 | return exp; |
| 2414 | } |
| 2415 | |
| 2416 | template <typename T> |
| 2417 | int snprintf_float(T value, int precision, float_specs specs, |
| 2418 | buffer<char>& buf) { |
| 2419 | // Buffer capacity must be non-zero, otherwise MSVC's vsnprintf_s will fail. |
| 2420 | FMT_ASSERT(buf.capacity() > buf.size(), "empty buffer"); |
| 2421 | static_assert(!std::is_same<T, float>::value, ""); |
| 2422 | |
| 2423 | // Subtract 1 to account for the difference in precision since we use %e for |
| 2424 | // both general and exponent format. |
| 2425 | if (specs.format == float_format::general || |
| 2426 | specs.format == float_format::exp) |
| 2427 | precision = (precision >= 0 ? precision : 6) - 1; |
| 2428 | |
| 2429 | // Build the format string. |
| 2430 | enum { max_format_size = 7 }; // The longest format is "%#.*Le". |
| 2431 | char format[max_format_size]; |
| 2432 | char* format_ptr = format; |
| 2433 | *format_ptr++ = '%'; |
| 2434 | if (specs.showpoint && specs.format == float_format::hex) *format_ptr++ = '#'; |
| 2435 | if (precision >= 0) { |
| 2436 | *format_ptr++ = '.'; |
| 2437 | *format_ptr++ = '*'; |
| 2438 | } |
| 2439 | if (std::is_same<T, long double>()) *format_ptr++ = 'L'; |
| 2440 | *format_ptr++ = specs.format != float_format::hex |
| 2441 | ? (specs.format == float_format::fixed ? 'f' : 'e') |
| 2442 | : (specs.upper ? 'A' : 'a'); |
| 2443 | *format_ptr = '\0'; |
| 2444 | |
| 2445 | // Format using snprintf. |
| 2446 | auto offset = buf.size(); |
| 2447 | for (;;) { |
| 2448 | auto begin = buf.data() + offset; |
| 2449 | auto capacity = buf.capacity() - offset; |
| 2450 | #ifdef FMT_FUZZ |
| 2451 | if (precision > 100000) |
| 2452 | throw std::runtime_error( |
| 2453 | "fuzz mode - avoid large allocation inside snprintf"); |
| 2454 | #endif |
| 2455 | // Suppress the warning about a nonliteral format string. |
| 2456 | // Cannot use auto because of a bug in MinGW (#1532). |
| 2457 | int (*snprintf_ptr)(char*, size_t, const char*, ...) = FMT_SNPRINTF; |
| 2458 | int result = precision >= 0 |
| 2459 | ? snprintf_ptr(begin, capacity, format, precision, value) |
| 2460 | : snprintf_ptr(begin, capacity, format, value); |
| 2461 | if (result < 0) { |
| 2462 | // The buffer will grow exponentially. |
| 2463 | buf.try_reserve(buf.capacity() + 1); |
| 2464 | continue; |
| 2465 | } |
| 2466 | auto size = to_unsigned(result); |
| 2467 | // Size equal to capacity means that the last character was truncated. |
| 2468 | if (size >= capacity) { |
| 2469 | buf.try_reserve(size + offset + 1); // Add 1 for the terminating '\0'. |
| 2470 | continue; |
| 2471 | } |
| 2472 | auto is_digit = [](char c) { return c >= '0' && c <= '9'; }; |
| 2473 | if (specs.format == float_format::fixed) { |
| 2474 | if (precision == 0) { |
| 2475 | buf.try_resize(size); |
| 2476 | return 0; |
| 2477 | } |
| 2478 | // Find and remove the decimal point. |
| 2479 | auto end = begin + size, p = end; |
| 2480 | do { |
| 2481 | --p; |
| 2482 | } while (is_digit(*p)); |
| 2483 | int fraction_size = static_cast<int>(end - p - 1); |
| 2484 | std::memmove(p, p + 1, to_unsigned(fraction_size)); |
| 2485 | buf.try_resize(size - 1); |
| 2486 | return -fraction_size; |
| 2487 | } |
| 2488 | if (specs.format == float_format::hex) { |
| 2489 | buf.try_resize(size + offset); |
| 2490 | return 0; |
| 2491 | } |
| 2492 | // Find and parse the exponent. |
| 2493 | auto end = begin + size, exp_pos = end; |
| 2494 | do { |
| 2495 | --exp_pos; |
| 2496 | } while (*exp_pos != 'e'); |
| 2497 | char sign = exp_pos[1]; |
| 2498 | FMT_ASSERT(sign == '+' || sign == '-', ""); |
| 2499 | int exp = 0; |
| 2500 | auto p = exp_pos + 2; // Skip 'e' and sign. |
| 2501 | do { |
| 2502 | FMT_ASSERT(is_digit(*p), ""); |
| 2503 | exp = exp * 10 + (*p++ - '0'); |
| 2504 | } while (p != end); |
| 2505 | if (sign == '-') exp = -exp; |
| 2506 | int fraction_size = 0; |
| 2507 | if (exp_pos != begin + 1) { |
| 2508 | // Remove trailing zeros. |
| 2509 | auto fraction_end = exp_pos - 1; |
| 2510 | while (*fraction_end == '0') --fraction_end; |
| 2511 | // Move the fractional part left to get rid of the decimal point. |
| 2512 | fraction_size = static_cast<int>(fraction_end - begin - 1); |
| 2513 | std::memmove(begin + 1, begin + 2, to_unsigned(fraction_size)); |
| 2514 | } |
| 2515 | buf.try_resize(to_unsigned(fraction_size) + offset + 1); |
| 2516 | return exp - fraction_size; |
| 2517 | } |
| 2518 | } |
| 2519 | } // namespace detail |
| 2520 | |
| 2521 | template <> struct formatter<detail::bigint> { |
| 2522 | FMT_CONSTEXPR format_parse_context::iterator parse( |
| 2523 | format_parse_context& ctx) { |
| 2524 | return ctx.begin(); |
| 2525 | } |
| 2526 | |
| 2527 | format_context::iterator format(const detail::bigint& n, |
| 2528 | format_context& ctx) { |
| 2529 | auto out = ctx.out(); |
| 2530 | bool first = true; |
| 2531 | for (auto i = n.bigits_.size(); i > 0; --i) { |
| 2532 | auto value = n.bigits_[i - 1u]; |
| 2533 | if (first) { |
| 2534 | out = format_to(out, FMT_STRING("{:x}"), value); |
| 2535 | first = false; |
| 2536 | continue; |
| 2537 | } |
| 2538 | out = format_to(out, FMT_STRING("{:08x}"), value); |
| 2539 | } |
| 2540 | if (n.exp_ > 0) |
| 2541 | out = format_to(out, FMT_STRING("p{}"), |
| 2542 | n.exp_ * detail::bigint::bigit_bits); |
| 2543 | return out; |
| 2544 | } |
| 2545 | }; |
| 2546 | |
| 2547 | FMT_FUNC detail::utf8_to_utf16::utf8_to_utf16(string_view s) { |
| 2548 | for_each_codepoint(s, [this](uint32_t cp, string_view) { |
| 2549 | if (cp == invalid_code_point) FMT_THROW(std::runtime_error("invalid utf8")); |
| 2550 | if (cp <= 0xFFFF) { |
| 2551 | buffer_.push_back(static_cast<wchar_t>(cp)); |
| 2552 | } else { |
| 2553 | cp -= 0x10000; |
| 2554 | buffer_.push_back(static_cast<wchar_t>(0xD800 + (cp >> 10))); |
| 2555 | buffer_.push_back(static_cast<wchar_t>(0xDC00 + (cp & 0x3FF))); |
| 2556 | } |
| 2557 | return true; |
| 2558 | }); |
| 2559 | buffer_.push_back(0); |
| 2560 | } |
| 2561 | |
| 2562 | FMT_FUNC void format_system_error(detail::buffer<char>& out, int error_code, |
| 2563 | const char* message) FMT_NOEXCEPT { |
| 2564 | FMT_TRY { |
| 2565 | auto ec = std::error_code(error_code, std::generic_category()); |
| 2566 | write(std::back_inserter(out), std::system_error(ec, message).what()); |
| 2567 | return; |
| 2568 | } |
| 2569 | FMT_CATCH(...) {} |
| 2570 | format_error_code(out, error_code, message); |
| 2571 | } |
| 2572 | |
| 2573 | FMT_FUNC void report_system_error(int error_code, |
| 2574 | const char* message) FMT_NOEXCEPT { |
| 2575 | report_error(format_system_error, error_code, message); |
| 2576 | } |
| 2577 | |
| 2578 | // DEPRECATED! |
| 2579 | // This function is defined here and not inline for ABI compatiblity. |
| 2580 | FMT_FUNC void detail::error_handler::on_error(const char* message) { |
| 2581 | throw_format_error(message); |
| 2582 | } |
| 2583 | |
| 2584 | FMT_FUNC std::string vformat(string_view fmt, format_args args) { |
| 2585 | // Don't optimize the "{}" case to keep the binary size small and because it |
| 2586 | // can be better optimized in fmt::format anyway. |
| 2587 | auto buffer = memory_buffer(); |
| 2588 | detail::vformat_to(buffer, fmt, args); |
| 2589 | return to_string(buffer); |
| 2590 | } |
| 2591 | |
| 2592 | #ifdef _WIN32 |
| 2593 | namespace detail { |
| 2594 | using dword = conditional_t<sizeof(long) == 4, unsigned long, unsigned>; |
| 2595 | extern "C" __declspec(dllimport) int __stdcall WriteConsoleW( // |
| 2596 | void*, const void*, dword, dword*, void*); |
| 2597 | } // namespace detail |
| 2598 | #endif |
| 2599 | |
| 2600 | namespace detail { |
| 2601 | FMT_FUNC void print(std::FILE* f, string_view text) { |
| 2602 | #ifdef _WIN32 |
| 2603 | auto fd = _fileno(f); |
| 2604 | if (_isatty(fd)) { |
| 2605 | detail::utf8_to_utf16 u16(string_view(text.data(), text.size())); |
| 2606 | auto written = detail::dword(); |
| 2607 | if (detail::WriteConsoleW(reinterpret_cast<void*>(_get_osfhandle(fd)), |
| 2608 | u16.c_str(), static_cast<uint32_t>(u16.size()), |
| 2609 | &written, nullptr)) { |
| 2610 | return; |
| 2611 | } |
| 2612 | // Fallback to fwrite on failure. It can happen if the output has been |
| 2613 | // redirected to NUL. |
| 2614 | } |
| 2615 | #endif |
| 2616 | detail::fwrite_fully(text.data(), 1, text.size(), f); |
| 2617 | } |
| 2618 | } // namespace detail |
| 2619 | |
| 2620 | FMT_FUNC void vprint(std::FILE* f, string_view format_str, format_args args) { |
| 2621 | memory_buffer buffer; |
| 2622 | detail::vformat_to(buffer, format_str, args); |
| 2623 | detail::print(f, {buffer.data(), buffer.size()}); |
| 2624 | } |
| 2625 | |
| 2626 | #ifdef _WIN32 |
| 2627 | // Print assuming legacy (non-Unicode) encoding. |
| 2628 | FMT_FUNC void detail::vprint_mojibake(std::FILE* f, string_view format_str, |
| 2629 | format_args args) { |
| 2630 | memory_buffer buffer; |
| 2631 | detail::vformat_to(buffer, format_str, |
| 2632 | basic_format_args<buffer_context<char>>(args)); |
| 2633 | fwrite_fully(buffer.data(), 1, buffer.size(), f); |
| 2634 | } |
| 2635 | #endif |
| 2636 | |
| 2637 | FMT_FUNC void vprint(string_view format_str, format_args args) { |
| 2638 | vprint(stdout, format_str, args); |
| 2639 | } |
| 2640 | |
| 2641 | FMT_END_NAMESPACE |
| 2642 | |
| 2643 | #endif // FMT_FORMAT_INL_H_ |