// fast_float by Daniel Lemire // fast_float by João Paulo Magalhaes // // // with contributions from Eugene Golushkov // with contributions from Maksim Kita // with contributions from Marcin Wojdyr // with contributions from Neal Richardson // with contributions from Tim Paine // with contributions from Fabio Pellacini // with contributions from Lénárd Szolnoki // with contributions from Jan Pharago // with contributions from Maya Warrier // // // Licensed under the Apache License, Version 2.0, or the // MIT License or the Boost License. This file may not be copied, // modified, or distributed except according to those terms. // // MIT License Notice // // MIT License // // Copyright (c) 2021 The fast_float authors // // Permission is hereby granted, free of charge, to any // person obtaining a copy of this software and associated // documentation files (the "Software"), to deal in the // Software without restriction, including without // limitation the rights to use, copy, modify, merge, // publish, distribute, sublicense, and/or sell copies of // the Software, and to permit persons to whom the Software // is furnished to do so, subject to the following // conditions: // // The above copyright notice and this permission notice // shall be included in all copies or substantial portions // of the Software. // // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF // ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED // TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A // PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT // SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY // CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION // OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR // IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER // DEALINGS IN THE SOFTWARE. // // Apache License (Version 2.0) Notice // // Copyright 2021 The fast_float authors // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // // BOOST License Notice // // Boost Software License - Version 1.0 - August 17th, 2003 // // Permission is hereby granted, free of charge, to any person or organization // obtaining a copy of the software and accompanying documentation covered by // this license (the "Software") to use, reproduce, display, distribute, // execute, and transmit the Software, and to prepare derivative works of the // Software, and to permit third-parties to whom the Software is furnished to // do so, all subject to the following: // // The copyright notices in the Software and this entire statement, including // the above license grant, this restriction and the following disclaimer, // must be included in all copies of the Software, in whole or in part, and // all derivative works of the Software, unless such copies or derivative // works are solely in the form of machine-executable object code generated by // a source language processor. // // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, // FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT // SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE // FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, // ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER // DEALINGS IN THE SOFTWARE. // #ifndef FASTFLOAT_CONSTEXPR_FEATURE_DETECT_H #define FASTFLOAT_CONSTEXPR_FEATURE_DETECT_H #ifdef __has_include #if __has_include() #include #endif #endif // Testing for https://wg21.link/N3652, adopted in C++14 #if __cpp_constexpr >= 201304 #define FASTFLOAT_CONSTEXPR14 constexpr #else #define FASTFLOAT_CONSTEXPR14 #endif #if defined(__cpp_lib_bit_cast) && __cpp_lib_bit_cast >= 201806L #define FASTFLOAT_HAS_BIT_CAST 1 #else #define FASTFLOAT_HAS_BIT_CAST 0 #endif #if defined(__cpp_lib_is_constant_evaluated) && __cpp_lib_is_constant_evaluated >= 201811L #define FASTFLOAT_HAS_IS_CONSTANT_EVALUATED 1 #else #define FASTFLOAT_HAS_IS_CONSTANT_EVALUATED 0 #endif // Testing for relevant C++20 constexpr library features #if FASTFLOAT_HAS_IS_CONSTANT_EVALUATED \ && FASTFLOAT_HAS_BIT_CAST \ && __cpp_lib_constexpr_algorithms >= 201806L /*For std::copy and std::fill*/ #define FASTFLOAT_CONSTEXPR20 constexpr #define FASTFLOAT_IS_CONSTEXPR 1 #else #define FASTFLOAT_CONSTEXPR20 #define FASTFLOAT_IS_CONSTEXPR 0 #endif #endif // FASTFLOAT_CONSTEXPR_FEATURE_DETECT_H #ifndef FASTFLOAT_FLOAT_COMMON_H #define FASTFLOAT_FLOAT_COMMON_H #include #include #include #include #include #include namespace fast_float { #define FASTFLOAT_JSONFMT (1 << 5) #define FASTFLOAT_FORTRANFMT (1 << 6) enum chars_format { scientific = 1 << 0, fixed = 1 << 2, hex = 1 << 3, no_infnan = 1 << 4, // RFC 8259: https://datatracker.ietf.org/doc/html/rfc8259#section-6 json = FASTFLOAT_JSONFMT | fixed | scientific | no_infnan, // Extension of RFC 8259 where, e.g., "inf" and "nan" are allowed. json_or_infnan = FASTFLOAT_JSONFMT | fixed | scientific, fortran = FASTFLOAT_FORTRANFMT | fixed | scientific, general = fixed | scientific }; template struct from_chars_result_t { UC const* ptr; std::errc ec; }; using from_chars_result = from_chars_result_t; template struct parse_options_t { constexpr explicit parse_options_t(chars_format fmt = chars_format::general, UC dot = UC('.')) : format(fmt), decimal_point(dot) {} /** Which number formats are accepted */ chars_format format; /** The character used as decimal point */ UC decimal_point; }; using parse_options = parse_options_t; } #if FASTFLOAT_HAS_BIT_CAST #include #endif #if (defined(__x86_64) || defined(__x86_64__) || defined(_M_X64) \ || defined(__amd64) || defined(__aarch64__) || defined(_M_ARM64) \ || defined(__MINGW64__) \ || defined(__s390x__) \ || (defined(__ppc64__) || defined(__PPC64__) || defined(__ppc64le__) || defined(__PPC64LE__)) \ || defined(__loongarch64) ) #define FASTFLOAT_64BIT 1 #elif (defined(__i386) || defined(__i386__) || defined(_M_IX86) \ || defined(__arm__) || defined(_M_ARM) || defined(__ppc__) \ || defined(__MINGW32__) || defined(__EMSCRIPTEN__)) #define FASTFLOAT_32BIT 1 #else // Need to check incrementally, since SIZE_MAX is a size_t, avoid overflow. // We can never tell the register width, but the SIZE_MAX is a good approximation. // UINTPTR_MAX and INTPTR_MAX are optional, so avoid them for max portability. #if SIZE_MAX == 0xffff #error Unknown platform (16-bit, unsupported) #elif SIZE_MAX == 0xffffffff #define FASTFLOAT_32BIT 1 #elif SIZE_MAX == 0xffffffffffffffff #define FASTFLOAT_64BIT 1 #else #error Unknown platform (not 32-bit, not 64-bit?) #endif #endif #if ((defined(_WIN32) || defined(_WIN64)) && !defined(__clang__)) #include #endif #if defined(_MSC_VER) && !defined(__clang__) #define FASTFLOAT_VISUAL_STUDIO 1 #endif #if defined __BYTE_ORDER__ && defined __ORDER_BIG_ENDIAN__ #define FASTFLOAT_IS_BIG_ENDIAN (__BYTE_ORDER__ == __ORDER_BIG_ENDIAN__) #elif defined _WIN32 #define FASTFLOAT_IS_BIG_ENDIAN 0 #else #if defined(__APPLE__) || defined(__FreeBSD__) #include #elif defined(sun) || defined(__sun) #include #elif defined(__MVS__) #include #else #ifdef __has_include #if __has_include() #include #endif //__has_include() #endif //__has_include #endif # #ifndef __BYTE_ORDER__ // safe choice #define FASTFLOAT_IS_BIG_ENDIAN 0 #endif # #ifndef __ORDER_LITTLE_ENDIAN__ // safe choice #define FASTFLOAT_IS_BIG_ENDIAN 0 #endif # #if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ #define FASTFLOAT_IS_BIG_ENDIAN 0 #else #define FASTFLOAT_IS_BIG_ENDIAN 1 #endif #endif #if defined(__SSE2__) || \ (defined(FASTFLOAT_VISUAL_STUDIO) && \ (defined(_M_AMD64) || defined(_M_X64) || (defined(_M_IX86_FP) && _M_IX86_FP == 2))) #define FASTFLOAT_SSE2 1 #endif #if defined(__aarch64__) || defined(_M_ARM64) #define FASTFLOAT_NEON 1 #endif #if defined(FASTFLOAT_SSE2) || defined(FASTFLOAT_NEON) #define FASTFLOAT_HAS_SIMD 1 #endif #if defined(__GNUC__) // disable -Wcast-align=strict (GCC only) #define FASTFLOAT_SIMD_DISABLE_WARNINGS \ _Pragma("GCC diagnostic push") \ _Pragma("GCC diagnostic ignored \"-Wcast-align\"") #else #define FASTFLOAT_SIMD_DISABLE_WARNINGS #endif #if defined(__GNUC__) #define FASTFLOAT_SIMD_RESTORE_WARNINGS \ _Pragma("GCC diagnostic pop") #else #define FASTFLOAT_SIMD_RESTORE_WARNINGS #endif #ifdef FASTFLOAT_VISUAL_STUDIO #define fastfloat_really_inline __forceinline #else #define fastfloat_really_inline inline __attribute__((always_inline)) #endif #ifndef FASTFLOAT_ASSERT #define FASTFLOAT_ASSERT(x) { ((void)(x)); } #endif #ifndef FASTFLOAT_DEBUG_ASSERT #define FASTFLOAT_DEBUG_ASSERT(x) { ((void)(x)); } #endif // rust style `try!()` macro, or `?` operator #define FASTFLOAT_TRY(x) { if (!(x)) return false; } #define FASTFLOAT_ENABLE_IF(...) typename std::enable_if<(__VA_ARGS__), int>::type namespace fast_float { fastfloat_really_inline constexpr bool cpp20_and_in_constexpr() { #if FASTFLOAT_HAS_IS_CONSTANT_EVALUATED return std::is_constant_evaluated(); #else return false; #endif } template fastfloat_really_inline constexpr bool is_supported_float_type() { return std::is_same::value || std::is_same::value; } template fastfloat_really_inline constexpr bool is_supported_char_type() { return std::is_same::value || std::is_same::value || std::is_same::value || std::is_same::value; } // Compares two ASCII strings in a case insensitive manner. template inline FASTFLOAT_CONSTEXPR14 bool fastfloat_strncasecmp(UC const * input1, UC const * input2, size_t length) { char running_diff{0}; for (size_t i = 0; i < length; ++i) { running_diff |= (char(input1[i]) ^ char(input2[i])); } return (running_diff == 0) || (running_diff == 32); } #ifndef FLT_EVAL_METHOD #error "FLT_EVAL_METHOD should be defined, please include cfloat." #endif // a pointer and a length to a contiguous block of memory template struct span { const T* ptr; size_t length; constexpr span(const T* _ptr, size_t _length) : ptr(_ptr), length(_length) {} constexpr span() : ptr(nullptr), length(0) {} constexpr size_t len() const noexcept { return length; } FASTFLOAT_CONSTEXPR14 const T& operator[](size_t index) const noexcept { FASTFLOAT_DEBUG_ASSERT(index < length); return ptr[index]; } }; struct value128 { uint64_t low; uint64_t high; constexpr value128(uint64_t _low, uint64_t _high) : low(_low), high(_high) {} constexpr value128() : low(0), high(0) {} }; /* Helper C++14 constexpr generic implementation of leading_zeroes */ fastfloat_really_inline FASTFLOAT_CONSTEXPR14 int leading_zeroes_generic(uint64_t input_num, int last_bit = 0) { if(input_num & uint64_t(0xffffffff00000000)) { input_num >>= 32; last_bit |= 32; } if(input_num & uint64_t( 0xffff0000)) { input_num >>= 16; last_bit |= 16; } if(input_num & uint64_t( 0xff00)) { input_num >>= 8; last_bit |= 8; } if(input_num & uint64_t( 0xf0)) { input_num >>= 4; last_bit |= 4; } if(input_num & uint64_t( 0xc)) { input_num >>= 2; last_bit |= 2; } if(input_num & uint64_t( 0x2)) { /* input_num >>= 1; */ last_bit |= 1; } return 63 - last_bit; } /* result might be undefined when input_num is zero */ fastfloat_really_inline FASTFLOAT_CONSTEXPR20 int leading_zeroes(uint64_t input_num) { assert(input_num > 0); if (cpp20_and_in_constexpr()) { return leading_zeroes_generic(input_num); } #ifdef FASTFLOAT_VISUAL_STUDIO #if defined(_M_X64) || defined(_M_ARM64) unsigned long leading_zero = 0; // Search the mask data from most significant bit (MSB) // to least significant bit (LSB) for a set bit (1). _BitScanReverse64(&leading_zero, input_num); return (int)(63 - leading_zero); #else return leading_zeroes_generic(input_num); #endif #else return __builtin_clzll(input_num); #endif } // slow emulation routine for 32-bit fastfloat_really_inline constexpr uint64_t emulu(uint32_t x, uint32_t y) { return x * (uint64_t)y; } fastfloat_really_inline FASTFLOAT_CONSTEXPR14 uint64_t umul128_generic(uint64_t ab, uint64_t cd, uint64_t *hi) { uint64_t ad = emulu((uint32_t)(ab >> 32), (uint32_t)cd); uint64_t bd = emulu((uint32_t)ab, (uint32_t)cd); uint64_t adbc = ad + emulu((uint32_t)ab, (uint32_t)(cd >> 32)); uint64_t adbc_carry = !!(adbc < ad); uint64_t lo = bd + (adbc << 32); *hi = emulu((uint32_t)(ab >> 32), (uint32_t)(cd >> 32)) + (adbc >> 32) + (adbc_carry << 32) + !!(lo < bd); return lo; } #ifdef FASTFLOAT_32BIT // slow emulation routine for 32-bit #if !defined(__MINGW64__) fastfloat_really_inline FASTFLOAT_CONSTEXPR14 uint64_t _umul128(uint64_t ab, uint64_t cd, uint64_t *hi) { return umul128_generic(ab, cd, hi); } #endif // !__MINGW64__ #endif // FASTFLOAT_32BIT // compute 64-bit a*b fastfloat_really_inline FASTFLOAT_CONSTEXPR20 value128 full_multiplication(uint64_t a, uint64_t b) { if (cpp20_and_in_constexpr()) { value128 answer; answer.low = umul128_generic(a, b, &answer.high); return answer; } value128 answer; #if defined(_M_ARM64) && !defined(__MINGW32__) // ARM64 has native support for 64-bit multiplications, no need to emulate // But MinGW on ARM64 doesn't have native support for 64-bit multiplications answer.high = __umulh(a, b); answer.low = a * b; #elif defined(FASTFLOAT_32BIT) || (defined(_WIN64) && !defined(__clang__)) answer.low = _umul128(a, b, &answer.high); // _umul128 not available on ARM64 #elif defined(FASTFLOAT_64BIT) __uint128_t r = ((__uint128_t)a) * b; answer.low = uint64_t(r); answer.high = uint64_t(r >> 64); #else answer.low = umul128_generic(a, b, &answer.high); #endif return answer; } struct adjusted_mantissa { uint64_t mantissa{0}; int32_t power2{0}; // a negative value indicates an invalid result adjusted_mantissa() = default; constexpr bool operator==(const adjusted_mantissa &o) const { return mantissa == o.mantissa && power2 == o.power2; } constexpr bool operator!=(const adjusted_mantissa &o) const { return mantissa != o.mantissa || power2 != o.power2; } }; // Bias so we can get the real exponent with an invalid adjusted_mantissa. constexpr static int32_t invalid_am_bias = -0x8000; // used for binary_format_lookup_tables::max_mantissa constexpr uint64_t constant_55555 = 5 * 5 * 5 * 5 * 5; template struct binary_format_lookup_tables; template struct binary_format : binary_format_lookup_tables { using equiv_uint = typename std::conditional::type; static inline constexpr int mantissa_explicit_bits(); static inline constexpr int minimum_exponent(); static inline constexpr int infinite_power(); static inline constexpr int sign_index(); static inline constexpr int min_exponent_fast_path(); // used when fegetround() == FE_TONEAREST static inline constexpr int max_exponent_fast_path(); static inline constexpr int max_exponent_round_to_even(); static inline constexpr int min_exponent_round_to_even(); static inline constexpr uint64_t max_mantissa_fast_path(int64_t power); static inline constexpr uint64_t max_mantissa_fast_path(); // used when fegetround() == FE_TONEAREST static inline constexpr int largest_power_of_ten(); static inline constexpr int smallest_power_of_ten(); static inline constexpr T exact_power_of_ten(int64_t power); static inline constexpr size_t max_digits(); static inline constexpr equiv_uint exponent_mask(); static inline constexpr equiv_uint mantissa_mask(); static inline constexpr equiv_uint hidden_bit_mask(); }; template struct binary_format_lookup_tables { static constexpr double powers_of_ten[] = { 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22}; // Largest integer value v so that (5**index * v) <= 1<<53. // 0x10000000000000 == 1 << 53 static constexpr uint64_t max_mantissa[] = { 0x10000000000000, 0x10000000000000 / 5, 0x10000000000000 / (5 * 5), 0x10000000000000 / (5 * 5 * 5), 0x10000000000000 / (5 * 5 * 5 * 5), 0x10000000000000 / (constant_55555), 0x10000000000000 / (constant_55555 * 5), 0x10000000000000 / (constant_55555 * 5 * 5), 0x10000000000000 / (constant_55555 * 5 * 5 * 5), 0x10000000000000 / (constant_55555 * 5 * 5 * 5 * 5), 0x10000000000000 / (constant_55555 * constant_55555), 0x10000000000000 / (constant_55555 * constant_55555 * 5), 0x10000000000000 / (constant_55555 * constant_55555 * 5 * 5), 0x10000000000000 / (constant_55555 * constant_55555 * 5 * 5 * 5), 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555), 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5), 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5 * 5), 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5), 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5 * 5), 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555), 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5), 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5 * 5), 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5), 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5 * 5)}; }; template constexpr double binary_format_lookup_tables::powers_of_ten[]; template constexpr uint64_t binary_format_lookup_tables::max_mantissa[]; template struct binary_format_lookup_tables { static constexpr float powers_of_ten[] = {1e0f, 1e1f, 1e2f, 1e3f, 1e4f, 1e5f, 1e6f, 1e7f, 1e8f, 1e9f, 1e10f}; // Largest integer value v so that (5**index * v) <= 1<<24. // 0x1000000 == 1<<24 static constexpr uint64_t max_mantissa[] = { 0x1000000, 0x1000000 / 5, 0x1000000 / (5 * 5), 0x1000000 / (5 * 5 * 5), 0x1000000 / (5 * 5 * 5 * 5), 0x1000000 / (constant_55555), 0x1000000 / (constant_55555 * 5), 0x1000000 / (constant_55555 * 5 * 5), 0x1000000 / (constant_55555 * 5 * 5 * 5), 0x1000000 / (constant_55555 * 5 * 5 * 5 * 5), 0x1000000 / (constant_55555 * constant_55555), 0x1000000 / (constant_55555 * constant_55555 * 5)}; }; template constexpr float binary_format_lookup_tables::powers_of_ten[]; template constexpr uint64_t binary_format_lookup_tables::max_mantissa[]; template <> inline constexpr int binary_format::min_exponent_fast_path() { #if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0) return 0; #else return -22; #endif } template <> inline constexpr int binary_format::min_exponent_fast_path() { #if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0) return 0; #else return -10; #endif } template <> inline constexpr int binary_format::mantissa_explicit_bits() { return 52; } template <> inline constexpr int binary_format::mantissa_explicit_bits() { return 23; } template <> inline constexpr int binary_format::max_exponent_round_to_even() { return 23; } template <> inline constexpr int binary_format::max_exponent_round_to_even() { return 10; } template <> inline constexpr int binary_format::min_exponent_round_to_even() { return -4; } template <> inline constexpr int binary_format::min_exponent_round_to_even() { return -17; } template <> inline constexpr int binary_format::minimum_exponent() { return -1023; } template <> inline constexpr int binary_format::minimum_exponent() { return -127; } template <> inline constexpr int binary_format::infinite_power() { return 0x7FF; } template <> inline constexpr int binary_format::infinite_power() { return 0xFF; } template <> inline constexpr int binary_format::sign_index() { return 63; } template <> inline constexpr int binary_format::sign_index() { return 31; } template <> inline constexpr int binary_format::max_exponent_fast_path() { return 22; } template <> inline constexpr int binary_format::max_exponent_fast_path() { return 10; } template <> inline constexpr uint64_t binary_format::max_mantissa_fast_path() { return uint64_t(2) << mantissa_explicit_bits(); } template <> inline constexpr uint64_t binary_format::max_mantissa_fast_path(int64_t power) { // caller is responsible to ensure that // power >= 0 && power <= 22 // // Work around clang bug https://godbolt.org/z/zedh7rrhc return (void)max_mantissa[0], max_mantissa[power]; } template <> inline constexpr uint64_t binary_format::max_mantissa_fast_path() { return uint64_t(2) << mantissa_explicit_bits(); } template <> inline constexpr uint64_t binary_format::max_mantissa_fast_path(int64_t power) { // caller is responsible to ensure that // power >= 0 && power <= 10 // // Work around clang bug https://godbolt.org/z/zedh7rrhc return (void)max_mantissa[0], max_mantissa[power]; } template <> inline constexpr double binary_format::exact_power_of_ten(int64_t power) { // Work around clang bug https://godbolt.org/z/zedh7rrhc return (void)powers_of_ten[0], powers_of_ten[power]; } template <> inline constexpr float binary_format::exact_power_of_ten(int64_t power) { // Work around clang bug https://godbolt.org/z/zedh7rrhc return (void)powers_of_ten[0], powers_of_ten[power]; } template <> inline constexpr int binary_format::largest_power_of_ten() { return 308; } template <> inline constexpr int binary_format::largest_power_of_ten() { return 38; } template <> inline constexpr int binary_format::smallest_power_of_ten() { return -342; } template <> inline constexpr int binary_format::smallest_power_of_ten() { return -65; } template <> inline constexpr size_t binary_format::max_digits() { return 769; } template <> inline constexpr size_t binary_format::max_digits() { return 114; } template <> inline constexpr binary_format::equiv_uint binary_format::exponent_mask() { return 0x7F800000; } template <> inline constexpr binary_format::equiv_uint binary_format::exponent_mask() { return 0x7FF0000000000000; } template <> inline constexpr binary_format::equiv_uint binary_format::mantissa_mask() { return 0x007FFFFF; } template <> inline constexpr binary_format::equiv_uint binary_format::mantissa_mask() { return 0x000FFFFFFFFFFFFF; } template <> inline constexpr binary_format::equiv_uint binary_format::hidden_bit_mask() { return 0x00800000; } template <> inline constexpr binary_format::equiv_uint binary_format::hidden_bit_mask() { return 0x0010000000000000; } template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 void to_float(bool negative, adjusted_mantissa am, T &value) { using fastfloat_uint = typename binary_format::equiv_uint; fastfloat_uint word = (fastfloat_uint)am.mantissa; word |= fastfloat_uint(am.power2) << binary_format::mantissa_explicit_bits(); word |= fastfloat_uint(negative) << binary_format::sign_index(); #if FASTFLOAT_HAS_BIT_CAST value = std::bit_cast(word); #else ::memcpy(&value, &word, sizeof(T)); #endif } #ifdef FASTFLOAT_SKIP_WHITE_SPACE // disabled by default template struct space_lut { static constexpr bool value[] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; }; template constexpr bool space_lut::value[]; inline constexpr bool is_space(uint8_t c) { return space_lut<>::value[c]; } #endif template static constexpr uint64_t int_cmp_zeros() { static_assert((sizeof(UC) == 1) || (sizeof(UC) == 2) || (sizeof(UC) == 4), "Unsupported character size"); return (sizeof(UC) == 1) ? 0x3030303030303030 : (sizeof(UC) == 2) ? (uint64_t(UC('0')) << 48 | uint64_t(UC('0')) << 32 | uint64_t(UC('0')) << 16 | UC('0')) : (uint64_t(UC('0')) << 32 | UC('0')); } template static constexpr int int_cmp_len() { return sizeof(uint64_t) / sizeof(UC); } template static constexpr UC const * str_const_nan() { return nullptr; } template<> constexpr char const * str_const_nan() { return "nan"; } template<> constexpr wchar_t const * str_const_nan() { return L"nan"; } template<> constexpr char16_t const * str_const_nan() { return u"nan"; } template<> constexpr char32_t const * str_const_nan() { return U"nan"; } template static constexpr UC const * str_const_inf() { return nullptr; } template<> constexpr char const * str_const_inf() { return "infinity"; } template<> constexpr wchar_t const * str_const_inf() { return L"infinity"; } template<> constexpr char16_t const * str_const_inf() { return u"infinity"; } template<> constexpr char32_t const * str_const_inf() { return U"infinity"; } template struct int_luts { static constexpr uint8_t chdigit[] = { 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 255, 255, 255, 255, 255, 255, 255, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 255, 255, 255, 255, 255, 255, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255 }; static constexpr size_t maxdigits_u64[] = { 64, 41, 32, 28, 25, 23, 22, 21, 20, 19, 18, 18, 17, 17, 16, 16, 16, 16, 15, 15, 15, 15, 14, 14, 14, 14, 14, 14, 14, 13, 13, 13, 13, 13, 13 }; static constexpr uint64_t min_safe_u64[] = { 9223372036854775808ull, 12157665459056928801ull, 4611686018427387904, 7450580596923828125, 4738381338321616896, 3909821048582988049, 9223372036854775808ull, 12157665459056928801ull, 10000000000000000000ull, 5559917313492231481, 2218611106740436992, 8650415919381337933, 2177953337809371136, 6568408355712890625, 1152921504606846976, 2862423051509815793, 6746640616477458432, 15181127029874798299ull, 1638400000000000000, 3243919932521508681, 6221821273427820544, 11592836324538749809ull, 876488338465357824, 1490116119384765625, 2481152873203736576, 4052555153018976267, 6502111422497947648, 10260628712958602189ull, 15943230000000000000ull, 787662783788549761, 1152921504606846976, 1667889514952984961, 2386420683693101056, 3379220508056640625, 4738381338321616896 }; }; template constexpr uint8_t int_luts::chdigit[]; template constexpr size_t int_luts::maxdigits_u64[]; template constexpr uint64_t int_luts::min_safe_u64[]; template fastfloat_really_inline constexpr uint8_t ch_to_digit(UC c) { return int_luts<>::chdigit[static_cast(c)]; } fastfloat_really_inline constexpr size_t max_digits_u64(int base) { return int_luts<>::maxdigits_u64[base - 2]; } // If a u64 is exactly max_digits_u64() in length, this is // the value below which it has definitely overflowed. fastfloat_really_inline constexpr uint64_t min_safe_u64(int base) { return int_luts<>::min_safe_u64[base - 2]; } } // namespace fast_float #endif #ifndef FASTFLOAT_FAST_FLOAT_H #define FASTFLOAT_FAST_FLOAT_H namespace fast_float { /** * This function parses the character sequence [first,last) for a number. It parses floating-point numbers expecting * a locale-indepent format equivalent to what is used by std::strtod in the default ("C") locale. * The resulting floating-point value is the closest floating-point values (using either float or double), * using the "round to even" convention for values that would otherwise fall right in-between two values. * That is, we provide exact parsing according to the IEEE standard. * * Given a successful parse, the pointer (`ptr`) in the returned value is set to point right after the * parsed number, and the `value` referenced is set to the parsed value. In case of error, the returned * `ec` contains a representative error, otherwise the default (`std::errc()`) value is stored. * * The implementation does not throw and does not allocate memory (e.g., with `new` or `malloc`). * * Like the C++17 standard, the `fast_float::from_chars` functions take an optional last argument of * the type `fast_float::chars_format`. It is a bitset value: we check whether * `fmt & fast_float::chars_format::fixed` and `fmt & fast_float::chars_format::scientific` are set * to determine whether we allow the fixed point and scientific notation respectively. * The default is `fast_float::chars_format::general` which allows both `fixed` and `scientific`. */ template())> FASTFLOAT_CONSTEXPR20 from_chars_result_t from_chars(UC const * first, UC const * last, T &value, chars_format fmt = chars_format::general) noexcept; /** * Like from_chars, but accepts an `options` argument to govern number parsing. */ template FASTFLOAT_CONSTEXPR20 from_chars_result_t from_chars_advanced(UC const * first, UC const * last, T &value, parse_options_t options) noexcept; /** * from_chars for integer types. */ template ())> FASTFLOAT_CONSTEXPR20 from_chars_result_t from_chars(UC const * first, UC const * last, T& value, int base = 10) noexcept; } // namespace fast_float #endif // FASTFLOAT_FAST_FLOAT_H #ifndef FASTFLOAT_ASCII_NUMBER_H #define FASTFLOAT_ASCII_NUMBER_H #include #include #include #include #include #include #ifdef FASTFLOAT_SSE2 #include #endif #ifdef FASTFLOAT_NEON #include #endif namespace fast_float { template fastfloat_really_inline constexpr bool has_simd_opt() { #ifdef FASTFLOAT_HAS_SIMD return std::is_same::value; #else return false; #endif } // Next function can be micro-optimized, but compilers are entirely // able to optimize it well. template fastfloat_really_inline constexpr bool is_integer(UC c) noexcept { return !(c > UC('9') || c < UC('0')); } fastfloat_really_inline constexpr uint64_t byteswap(uint64_t val) { return (val & 0xFF00000000000000) >> 56 | (val & 0x00FF000000000000) >> 40 | (val & 0x0000FF0000000000) >> 24 | (val & 0x000000FF00000000) >> 8 | (val & 0x00000000FF000000) << 8 | (val & 0x0000000000FF0000) << 24 | (val & 0x000000000000FF00) << 40 | (val & 0x00000000000000FF) << 56; } // Read 8 UC into a u64. Truncates UC if not char. template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 uint64_t read8_to_u64(const UC *chars) { if (cpp20_and_in_constexpr() || !std::is_same::value) { uint64_t val = 0; for(int i = 0; i < 8; ++i) { val |= uint64_t(uint8_t(*chars)) << (i*8); ++chars; } return val; } uint64_t val; ::memcpy(&val, chars, sizeof(uint64_t)); #if FASTFLOAT_IS_BIG_ENDIAN == 1 // Need to read as-if the number was in little-endian order. val = byteswap(val); #endif return val; } #ifdef FASTFLOAT_SSE2 fastfloat_really_inline uint64_t simd_read8_to_u64(const __m128i data) { FASTFLOAT_SIMD_DISABLE_WARNINGS const __m128i packed = _mm_packus_epi16(data, data); #ifdef FASTFLOAT_64BIT return uint64_t(_mm_cvtsi128_si64(packed)); #else uint64_t value; // Visual Studio + older versions of GCC don't support _mm_storeu_si64 _mm_storel_epi64(reinterpret_cast<__m128i*>(&value), packed); return value; #endif FASTFLOAT_SIMD_RESTORE_WARNINGS } fastfloat_really_inline uint64_t simd_read8_to_u64(const char16_t* chars) { FASTFLOAT_SIMD_DISABLE_WARNINGS return simd_read8_to_u64(_mm_loadu_si128(reinterpret_cast(chars))); FASTFLOAT_SIMD_RESTORE_WARNINGS } #elif defined(FASTFLOAT_NEON) fastfloat_really_inline uint64_t simd_read8_to_u64(const uint16x8_t data) { FASTFLOAT_SIMD_DISABLE_WARNINGS uint8x8_t utf8_packed = vmovn_u16(data); return vget_lane_u64(vreinterpret_u64_u8(utf8_packed), 0); FASTFLOAT_SIMD_RESTORE_WARNINGS } fastfloat_really_inline uint64_t simd_read8_to_u64(const char16_t* chars) { FASTFLOAT_SIMD_DISABLE_WARNINGS return simd_read8_to_u64(vld1q_u16(reinterpret_cast(chars))); FASTFLOAT_SIMD_RESTORE_WARNINGS } #endif // FASTFLOAT_SSE2 // MSVC SFINAE is broken pre-VS2017 #if defined(_MSC_VER) && _MSC_VER <= 1900 template #else template ()) = 0> #endif // dummy for compile uint64_t simd_read8_to_u64(UC const*) { return 0; } fastfloat_really_inline FASTFLOAT_CONSTEXPR20 void write_u64(uint8_t *chars, uint64_t val) { if (cpp20_and_in_constexpr()) { for(int i = 0; i < 8; ++i) { *chars = uint8_t(val); val >>= 8; ++chars; } return; } #if FASTFLOAT_IS_BIG_ENDIAN == 1 // Need to read as-if the number was in little-endian order. val = byteswap(val); #endif ::memcpy(chars, &val, sizeof(uint64_t)); } // credit @aqrit fastfloat_really_inline FASTFLOAT_CONSTEXPR14 uint32_t parse_eight_digits_unrolled(uint64_t val) { const uint64_t mask = 0x000000FF000000FF; const uint64_t mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32) const uint64_t mul2 = 0x0000271000000001; // 1 + (10000ULL << 32) val -= 0x3030303030303030; val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8; val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32; return uint32_t(val); } // Call this if chars are definitely 8 digits. template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 uint32_t parse_eight_digits_unrolled(UC const * chars) noexcept { if (cpp20_and_in_constexpr() || !has_simd_opt()) { return parse_eight_digits_unrolled(read8_to_u64(chars)); // truncation okay } return parse_eight_digits_unrolled(simd_read8_to_u64(chars)); } // credit @aqrit fastfloat_really_inline constexpr bool is_made_of_eight_digits_fast(uint64_t val) noexcept { return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) & 0x8080808080808080)); } #ifdef FASTFLOAT_HAS_SIMD // Call this if chars might not be 8 digits. // Using this style (instead of is_made_of_eight_digits_fast() then parse_eight_digits_unrolled()) // ensures we don't load SIMD registers twice. fastfloat_really_inline FASTFLOAT_CONSTEXPR20 bool simd_parse_if_eight_digits_unrolled(const char16_t* chars, uint64_t& i) noexcept { if (cpp20_and_in_constexpr()) { return false; } #ifdef FASTFLOAT_SSE2 FASTFLOAT_SIMD_DISABLE_WARNINGS const __m128i data = _mm_loadu_si128(reinterpret_cast(chars)); // (x - '0') <= 9 // http://0x80.pl/articles/simd-parsing-int-sequences.html const __m128i t0 = _mm_add_epi16(data, _mm_set1_epi16(32720)); const __m128i t1 = _mm_cmpgt_epi16(t0, _mm_set1_epi16(-32759)); if (_mm_movemask_epi8(t1) == 0) { i = i * 100000000 + parse_eight_digits_unrolled(simd_read8_to_u64(data)); return true; } else return false; FASTFLOAT_SIMD_RESTORE_WARNINGS #elif defined(FASTFLOAT_NEON) FASTFLOAT_SIMD_DISABLE_WARNINGS const uint16x8_t data = vld1q_u16(reinterpret_cast(chars)); // (x - '0') <= 9 // http://0x80.pl/articles/simd-parsing-int-sequences.html const uint16x8_t t0 = vsubq_u16(data, vmovq_n_u16('0')); const uint16x8_t mask = vcltq_u16(t0, vmovq_n_u16('9' - '0' + 1)); if (vminvq_u16(mask) == 0xFFFF) { i = i * 100000000 + parse_eight_digits_unrolled(simd_read8_to_u64(data)); return true; } else return false; FASTFLOAT_SIMD_RESTORE_WARNINGS #else (void)chars; (void)i; return false; #endif // FASTFLOAT_SSE2 } #endif // FASTFLOAT_HAS_SIMD // MSVC SFINAE is broken pre-VS2017 #if defined(_MSC_VER) && _MSC_VER <= 1900 template #else template ()) = 0> #endif // dummy for compile bool simd_parse_if_eight_digits_unrolled(UC const*, uint64_t&) { return 0; } template ::value) = 0> fastfloat_really_inline FASTFLOAT_CONSTEXPR20 void loop_parse_if_eight_digits(const UC*& p, const UC* const pend, uint64_t& i) { if (!has_simd_opt()) { return; } while ((std::distance(p, pend) >= 8) && simd_parse_if_eight_digits_unrolled(p, i)) { // in rare cases, this will overflow, but that's ok p += 8; } } fastfloat_really_inline FASTFLOAT_CONSTEXPR20 void loop_parse_if_eight_digits(const char*& p, const char* const pend, uint64_t& i) { // optimizes better than parse_if_eight_digits_unrolled() for UC = char. while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(read8_to_u64(p))) { i = i * 100000000 + parse_eight_digits_unrolled(read8_to_u64(p)); // in rare cases, this will overflow, but that's ok p += 8; } } template struct parsed_number_string_t { int64_t exponent{0}; uint64_t mantissa{0}; UC const * lastmatch{nullptr}; bool negative{false}; bool valid{false}; bool too_many_digits{false}; // contains the range of the significant digits span integer{}; // non-nullable span fraction{}; // nullable }; using byte_span = span; using parsed_number_string = parsed_number_string_t; // Assuming that you use no more than 19 digits, this will // parse an ASCII string. template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 parsed_number_string_t parse_number_string(UC const *p, UC const * pend, parse_options_t options) noexcept { chars_format const fmt = options.format; UC const decimal_point = options.decimal_point; parsed_number_string_t answer; answer.valid = false; answer.too_many_digits = false; answer.negative = (*p == UC('-')); #ifdef FASTFLOAT_ALLOWS_LEADING_PLUS // disabled by default if ((*p == UC('-')) || (!(fmt & FASTFLOAT_JSONFMT) && *p == UC('+'))) { #else if (*p == UC('-')) { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here #endif ++p; if (p == pend) { return answer; } if (fmt & FASTFLOAT_JSONFMT) { if (!is_integer(*p)) { // a sign must be followed by an integer return answer; } } else { if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot return answer; } } } UC const * const start_digits = p; uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad) while ((p != pend) && is_integer(*p)) { // a multiplication by 10 is cheaper than an arbitrary integer // multiplication i = 10 * i + uint64_t(*p - UC('0')); // might overflow, we will handle the overflow later ++p; } UC const * const end_of_integer_part = p; int64_t digit_count = int64_t(end_of_integer_part - start_digits); answer.integer = span(start_digits, size_t(digit_count)); if (fmt & FASTFLOAT_JSONFMT) { // at least 1 digit in integer part, without leading zeros if (digit_count == 0 || (start_digits[0] == UC('0') && digit_count > 1)) { return answer; } } int64_t exponent = 0; const bool has_decimal_point = (p != pend) && (*p == decimal_point); if (has_decimal_point) { ++p; UC const * before = p; // can occur at most twice without overflowing, but let it occur more, since // for integers with many digits, digit parsing is the primary bottleneck. loop_parse_if_eight_digits(p, pend, i); while ((p != pend) && is_integer(*p)) { uint8_t digit = uint8_t(*p - UC('0')); ++p; i = i * 10 + digit; // in rare cases, this will overflow, but that's ok } exponent = before - p; answer.fraction = span(before, size_t(p - before)); digit_count -= exponent; } if (fmt & FASTFLOAT_JSONFMT) { // at least 1 digit in fractional part if (has_decimal_point && exponent == 0) { return answer; } } else if (digit_count == 0) { // we must have encountered at least one integer! return answer; } int64_t exp_number = 0; // explicit exponential part if ( ((fmt & chars_format::scientific) && (p != pend) && ((UC('e') == *p) || (UC('E') == *p))) || ((fmt & FASTFLOAT_FORTRANFMT) && (p != pend) && ((UC('+') == *p) || (UC('-') == *p) || (UC('d') == *p) || (UC('D') == *p)))) { UC const * location_of_e = p; if ((UC('e') == *p) || (UC('E') == *p) || (UC('d') == *p) || (UC('D') == *p)) { ++p; } bool neg_exp = false; if ((p != pend) && (UC('-') == *p)) { neg_exp = true; ++p; } else if ((p != pend) && (UC('+') == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1) ++p; } if ((p == pend) || !is_integer(*p)) { if(!(fmt & chars_format::fixed)) { // We are in error. return answer; } // Otherwise, we will be ignoring the 'e'. p = location_of_e; } else { while ((p != pend) && is_integer(*p)) { uint8_t digit = uint8_t(*p - UC('0')); if (exp_number < 0x10000000) { exp_number = 10 * exp_number + digit; } ++p; } if(neg_exp) { exp_number = - exp_number; } exponent += exp_number; } } else { // If it scientific and not fixed, we have to bail out. if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; } } answer.lastmatch = p; answer.valid = true; // If we frequently had to deal with long strings of digits, // we could extend our code by using a 128-bit integer instead // of a 64-bit integer. However, this is uncommon. // // We can deal with up to 19 digits. if (digit_count > 19) { // this is uncommon // It is possible that the integer had an overflow. // We have to handle the case where we have 0.0000somenumber. // We need to be mindful of the case where we only have zeroes... // E.g., 0.000000000...000. UC const * start = start_digits; while ((start != pend) && (*start == UC('0') || *start == decimal_point)) { if(*start == UC('0')) { digit_count --; } start++; } if (digit_count > 19) { answer.too_many_digits = true; // Let us start again, this time, avoiding overflows. // We don't need to check if is_integer, since we use the // pre-tokenized spans from above. i = 0; p = answer.integer.ptr; UC const* int_end = p + answer.integer.len(); const uint64_t minimal_nineteen_digit_integer{ 1000000000000000000 }; while ((i < minimal_nineteen_digit_integer) && (p != int_end)) { i = i * 10 + uint64_t(*p - UC('0')); ++p; } if (i >= minimal_nineteen_digit_integer) { // We have a big integers exponent = end_of_integer_part - p + exp_number; } else { // We have a value with a fractional component. p = answer.fraction.ptr; UC const* frac_end = p + answer.fraction.len(); while ((i < minimal_nineteen_digit_integer) && (p != frac_end)) { i = i * 10 + uint64_t(*p - UC('0')); ++p; } exponent = answer.fraction.ptr - p + exp_number; } // We have now corrected both exponent and i, to a truncated value } } answer.exponent = exponent; answer.mantissa = i; return answer; } template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 from_chars_result_t parse_int_string(UC const* p, UC const* pend, T& value, int base) { from_chars_result_t answer; UC const* const first = p; bool negative = (*p == UC('-')); if (!std::is_signed::value && negative) { answer.ec = std::errc::invalid_argument; answer.ptr = first; return answer; } #ifdef FASTFLOAT_ALLOWS_LEADING_PLUS // disabled by default if ((*p == UC('-')) || (*p == UC('+'))) { #else if (*p == UC('-')) { #endif ++p; } UC const* const start_num = p; while (*p == UC('0')) { ++p; } const bool has_leading_zeros = p > start_num; UC const* const start_digits = p; uint64_t i = 0; if (base == 10) { loop_parse_if_eight_digits(p, pend, i); // use SIMD if possible } while (p != pend) { uint8_t digit = ch_to_digit(*p); if (digit >= base) { break; } i = uint64_t(base) * i + digit; // might overflow, check this later p++; } size_t digit_count = size_t(p - start_digits); if (digit_count == 0) { if (has_leading_zeros) { value = 0; answer.ec = std::errc(); answer.ptr = p; } else { answer.ec = std::errc::invalid_argument; answer.ptr = first; } return answer; } answer.ptr = p; // check u64 overflow size_t max_digits = max_digits_u64(base); if (digit_count > max_digits) { answer.ec = std::errc::result_out_of_range; return answer; } // this check can be eliminated for all other types, but they will all require a max_digits(base) equivalent if (digit_count == max_digits && i < min_safe_u64(base)) { answer.ec = std::errc::result_out_of_range; return answer; } // check other types overflow if (!std::is_same::value) { if (i > uint64_t(std::numeric_limits::max()) + uint64_t(negative)) { answer.ec = std::errc::result_out_of_range; return answer; } } if (negative) { #ifdef FASTFLOAT_VISUAL_STUDIO #pragma warning(push) #pragma warning(disable: 4146) #endif // this weird workaround is required because: // - converting unsigned to signed when its value is greater than signed max is UB pre-C++23. // - reinterpret_casting (~i + 1) would work, but it is not constexpr // this is always optimized into a neg instruction. value = T(-std::numeric_limits::max() - T(i - std::numeric_limits::max())); #ifdef FASTFLOAT_VISUAL_STUDIO #pragma warning(pop) #endif } else { value = T(i); } answer.ec = std::errc(); return answer; } } // namespace fast_float #endif #ifndef FASTFLOAT_FAST_TABLE_H #define FASTFLOAT_FAST_TABLE_H #include namespace fast_float { /** * When mapping numbers from decimal to binary, * we go from w * 10^q to m * 2^p but we have * 10^q = 5^q * 2^q, so effectively * we are trying to match * w * 2^q * 5^q to m * 2^p. Thus the powers of two * are not a concern since they can be represented * exactly using the binary notation, only the powers of five * affect the binary significand. */ /** * The smallest non-zero float (binary64) is 2^-1074. * We take as input numbers of the form w x 10^q where w < 2^64. * We have that w * 10^-343 < 2^(64-344) 5^-343 < 2^-1076. * However, we have that * (2^64-1) * 10^-342 = (2^64-1) * 2^-342 * 5^-342 > 2^-1074. * Thus it is possible for a number of the form w * 10^-342 where * w is a 64-bit value to be a non-zero floating-point number. ********* * Any number of form w * 10^309 where w>= 1 is going to be * infinite in binary64 so we never need to worry about powers * of 5 greater than 308. */ template struct powers_template { constexpr static int smallest_power_of_five = binary_format::smallest_power_of_ten(); constexpr static int largest_power_of_five = binary_format::largest_power_of_ten(); constexpr static int number_of_entries = 2 * (largest_power_of_five - smallest_power_of_five + 1); // Powers of five from 5^-342 all the way to 5^308 rounded toward one. constexpr static uint64_t power_of_five_128[number_of_entries] = { 0xeef453d6923bd65a,0x113faa2906a13b3f, 0x9558b4661b6565f8,0x4ac7ca59a424c507, 0xbaaee17fa23ebf76,0x5d79bcf00d2df649, 0xe95a99df8ace6f53,0xf4d82c2c107973dc, 0x91d8a02bb6c10594,0x79071b9b8a4be869, 0xb64ec836a47146f9,0x9748e2826cdee284, 0xe3e27a444d8d98b7,0xfd1b1b2308169b25, 0x8e6d8c6ab0787f72,0xfe30f0f5e50e20f7, 0xb208ef855c969f4f,0xbdbd2d335e51a935, 0xde8b2b66b3bc4723,0xad2c788035e61382, 0x8b16fb203055ac76,0x4c3bcb5021afcc31, 0xaddcb9e83c6b1793,0xdf4abe242a1bbf3d, 0xd953e8624b85dd78,0xd71d6dad34a2af0d, 0x87d4713d6f33aa6b,0x8672648c40e5ad68, 0xa9c98d8ccb009506,0x680efdaf511f18c2, 0xd43bf0effdc0ba48,0x212bd1b2566def2, 0x84a57695fe98746d,0x14bb630f7604b57, 0xa5ced43b7e3e9188,0x419ea3bd35385e2d, 0xcf42894a5dce35ea,0x52064cac828675b9, 0x818995ce7aa0e1b2,0x7343efebd1940993, 0xa1ebfb4219491a1f,0x1014ebe6c5f90bf8, 0xca66fa129f9b60a6,0xd41a26e077774ef6, 0xfd00b897478238d0,0x8920b098955522b4, 0x9e20735e8cb16382,0x55b46e5f5d5535b0, 0xc5a890362fddbc62,0xeb2189f734aa831d, 0xf712b443bbd52b7b,0xa5e9ec7501d523e4, 0x9a6bb0aa55653b2d,0x47b233c92125366e, 0xc1069cd4eabe89f8,0x999ec0bb696e840a, 0xf148440a256e2c76,0xc00670ea43ca250d, 0x96cd2a865764dbca,0x380406926a5e5728, 0xbc807527ed3e12bc,0xc605083704f5ecf2, 0xeba09271e88d976b,0xf7864a44c633682e, 0x93445b8731587ea3,0x7ab3ee6afbe0211d, 0xb8157268fdae9e4c,0x5960ea05bad82964, 0xe61acf033d1a45df,0x6fb92487298e33bd, 0x8fd0c16206306bab,0xa5d3b6d479f8e056, 0xb3c4f1ba87bc8696,0x8f48a4899877186c, 0xe0b62e2929aba83c,0x331acdabfe94de87, 0x8c71dcd9ba0b4925,0x9ff0c08b7f1d0b14, 0xaf8e5410288e1b6f,0x7ecf0ae5ee44dd9, 0xdb71e91432b1a24a,0xc9e82cd9f69d6150, 0x892731ac9faf056e,0xbe311c083a225cd2, 0xab70fe17c79ac6ca,0x6dbd630a48aaf406, 0xd64d3d9db981787d,0x92cbbccdad5b108, 0x85f0468293f0eb4e,0x25bbf56008c58ea5, 0xa76c582338ed2621,0xaf2af2b80af6f24e, 0xd1476e2c07286faa,0x1af5af660db4aee1, 0x82cca4db847945ca,0x50d98d9fc890ed4d, 0xa37fce126597973c,0xe50ff107bab528a0, 0xcc5fc196fefd7d0c,0x1e53ed49a96272c8, 0xff77b1fcbebcdc4f,0x25e8e89c13bb0f7a, 0x9faacf3df73609b1,0x77b191618c54e9ac, 0xc795830d75038c1d,0xd59df5b9ef6a2417, 0xf97ae3d0d2446f25,0x4b0573286b44ad1d, 0x9becce62836ac577,0x4ee367f9430aec32, 0xc2e801fb244576d5,0x229c41f793cda73f, 0xf3a20279ed56d48a,0x6b43527578c1110f, 0x9845418c345644d6,0x830a13896b78aaa9, 0xbe5691ef416bd60c,0x23cc986bc656d553, 0xedec366b11c6cb8f,0x2cbfbe86b7ec8aa8, 0x94b3a202eb1c3f39,0x7bf7d71432f3d6a9, 0xb9e08a83a5e34f07,0xdaf5ccd93fb0cc53, 0xe858ad248f5c22c9,0xd1b3400f8f9cff68, 0x91376c36d99995be,0x23100809b9c21fa1, 0xb58547448ffffb2d,0xabd40a0c2832a78a, 0xe2e69915b3fff9f9,0x16c90c8f323f516c, 0x8dd01fad907ffc3b,0xae3da7d97f6792e3, 0xb1442798f49ffb4a,0x99cd11cfdf41779c, 0xdd95317f31c7fa1d,0x40405643d711d583, 0x8a7d3eef7f1cfc52,0x482835ea666b2572, 0xad1c8eab5ee43b66,0xda3243650005eecf, 0xd863b256369d4a40,0x90bed43e40076a82, 0x873e4f75e2224e68,0x5a7744a6e804a291, 0xa90de3535aaae202,0x711515d0a205cb36, 0xd3515c2831559a83,0xd5a5b44ca873e03, 0x8412d9991ed58091,0xe858790afe9486c2, 0xa5178fff668ae0b6,0x626e974dbe39a872, 0xce5d73ff402d98e3,0xfb0a3d212dc8128f, 0x80fa687f881c7f8e,0x7ce66634bc9d0b99, 0xa139029f6a239f72,0x1c1fffc1ebc44e80, 0xc987434744ac874e,0xa327ffb266b56220, 0xfbe9141915d7a922,0x4bf1ff9f0062baa8, 0x9d71ac8fada6c9b5,0x6f773fc3603db4a9, 0xc4ce17b399107c22,0xcb550fb4384d21d3, 0xf6019da07f549b2b,0x7e2a53a146606a48, 0x99c102844f94e0fb,0x2eda7444cbfc426d, 0xc0314325637a1939,0xfa911155fefb5308, 0xf03d93eebc589f88,0x793555ab7eba27ca, 0x96267c7535b763b5,0x4bc1558b2f3458de, 0xbbb01b9283253ca2,0x9eb1aaedfb016f16, 0xea9c227723ee8bcb,0x465e15a979c1cadc, 0x92a1958a7675175f,0xbfacd89ec191ec9, 0xb749faed14125d36,0xcef980ec671f667b, 0xe51c79a85916f484,0x82b7e12780e7401a, 0x8f31cc0937ae58d2,0xd1b2ecb8b0908810, 0xb2fe3f0b8599ef07,0x861fa7e6dcb4aa15, 0xdfbdcece67006ac9,0x67a791e093e1d49a, 0x8bd6a141006042bd,0xe0c8bb2c5c6d24e0, 0xaecc49914078536d,0x58fae9f773886e18, 0xda7f5bf590966848,0xaf39a475506a899e, 0x888f99797a5e012d,0x6d8406c952429603, 0xaab37fd7d8f58178,0xc8e5087ba6d33b83, 0xd5605fcdcf32e1d6,0xfb1e4a9a90880a64, 0x855c3be0a17fcd26,0x5cf2eea09a55067f, 0xa6b34ad8c9dfc06f,0xf42faa48c0ea481e, 0xd0601d8efc57b08b,0xf13b94daf124da26, 0x823c12795db6ce57,0x76c53d08d6b70858, 0xa2cb1717b52481ed,0x54768c4b0c64ca6e, 0xcb7ddcdda26da268,0xa9942f5dcf7dfd09, 0xfe5d54150b090b02,0xd3f93b35435d7c4c, 0x9efa548d26e5a6e1,0xc47bc5014a1a6daf, 0xc6b8e9b0709f109a,0x359ab6419ca1091b, 0xf867241c8cc6d4c0,0xc30163d203c94b62, 0x9b407691d7fc44f8,0x79e0de63425dcf1d, 0xc21094364dfb5636,0x985915fc12f542e4, 0xf294b943e17a2bc4,0x3e6f5b7b17b2939d, 0x979cf3ca6cec5b5a,0xa705992ceecf9c42, 0xbd8430bd08277231,0x50c6ff782a838353, 0xece53cec4a314ebd,0xa4f8bf5635246428, 0x940f4613ae5ed136,0x871b7795e136be99, 0xb913179899f68584,0x28e2557b59846e3f, 0xe757dd7ec07426e5,0x331aeada2fe589cf, 0x9096ea6f3848984f,0x3ff0d2c85def7621, 0xb4bca50b065abe63,0xfed077a756b53a9, 0xe1ebce4dc7f16dfb,0xd3e8495912c62894, 0x8d3360f09cf6e4bd,0x64712dd7abbbd95c, 0xb080392cc4349dec,0xbd8d794d96aacfb3, 0xdca04777f541c567,0xecf0d7a0fc5583a0, 0x89e42caaf9491b60,0xf41686c49db57244, 0xac5d37d5b79b6239,0x311c2875c522ced5, 0xd77485cb25823ac7,0x7d633293366b828b, 0x86a8d39ef77164bc,0xae5dff9c02033197, 0xa8530886b54dbdeb,0xd9f57f830283fdfc, 0xd267caa862a12d66,0xd072df63c324fd7b, 0x8380dea93da4bc60,0x4247cb9e59f71e6d, 0xa46116538d0deb78,0x52d9be85f074e608, 0xcd795be870516656,0x67902e276c921f8b, 0x806bd9714632dff6,0xba1cd8a3db53b6, 0xa086cfcd97bf97f3,0x80e8a40eccd228a4, 0xc8a883c0fdaf7df0,0x6122cd128006b2cd, 0xfad2a4b13d1b5d6c,0x796b805720085f81, 0x9cc3a6eec6311a63,0xcbe3303674053bb0, 0xc3f490aa77bd60fc,0xbedbfc4411068a9c, 0xf4f1b4d515acb93b,0xee92fb5515482d44, 0x991711052d8bf3c5,0x751bdd152d4d1c4a, 0xbf5cd54678eef0b6,0xd262d45a78a0635d, 0xef340a98172aace4,0x86fb897116c87c34, 0x9580869f0e7aac0e,0xd45d35e6ae3d4da0, 0xbae0a846d2195712,0x8974836059cca109, 0xe998d258869facd7,0x2bd1a438703fc94b, 0x91ff83775423cc06,0x7b6306a34627ddcf, 0xb67f6455292cbf08,0x1a3bc84c17b1d542, 0xe41f3d6a7377eeca,0x20caba5f1d9e4a93, 0x8e938662882af53e,0x547eb47b7282ee9c, 0xb23867fb2a35b28d,0xe99e619a4f23aa43, 0xdec681f9f4c31f31,0x6405fa00e2ec94d4, 0x8b3c113c38f9f37e,0xde83bc408dd3dd04, 0xae0b158b4738705e,0x9624ab50b148d445, 0xd98ddaee19068c76,0x3badd624dd9b0957, 0x87f8a8d4cfa417c9,0xe54ca5d70a80e5d6, 0xa9f6d30a038d1dbc,0x5e9fcf4ccd211f4c, 0xd47487cc8470652b,0x7647c3200069671f, 0x84c8d4dfd2c63f3b,0x29ecd9f40041e073, 0xa5fb0a17c777cf09,0xf468107100525890, 0xcf79cc9db955c2cc,0x7182148d4066eeb4, 0x81ac1fe293d599bf,0xc6f14cd848405530, 0xa21727db38cb002f,0xb8ada00e5a506a7c, 0xca9cf1d206fdc03b,0xa6d90811f0e4851c, 0xfd442e4688bd304a,0x908f4a166d1da663, 0x9e4a9cec15763e2e,0x9a598e4e043287fe, 0xc5dd44271ad3cdba,0x40eff1e1853f29fd, 0xf7549530e188c128,0xd12bee59e68ef47c, 0x9a94dd3e8cf578b9,0x82bb74f8301958ce, 0xc13a148e3032d6e7,0xe36a52363c1faf01, 0xf18899b1bc3f8ca1,0xdc44e6c3cb279ac1, 0x96f5600f15a7b7e5,0x29ab103a5ef8c0b9, 0xbcb2b812db11a5de,0x7415d448f6b6f0e7, 0xebdf661791d60f56,0x111b495b3464ad21, 0x936b9fcebb25c995,0xcab10dd900beec34, 0xb84687c269ef3bfb,0x3d5d514f40eea742, 0xe65829b3046b0afa,0xcb4a5a3112a5112, 0x8ff71a0fe2c2e6dc,0x47f0e785eaba72ab, 0xb3f4e093db73a093,0x59ed216765690f56, 0xe0f218b8d25088b8,0x306869c13ec3532c, 0x8c974f7383725573,0x1e414218c73a13fb, 0xafbd2350644eeacf,0xe5d1929ef90898fa, 0xdbac6c247d62a583,0xdf45f746b74abf39, 0x894bc396ce5da772,0x6b8bba8c328eb783, 0xab9eb47c81f5114f,0x66ea92f3f326564, 0xd686619ba27255a2,0xc80a537b0efefebd, 0x8613fd0145877585,0xbd06742ce95f5f36, 0xa798fc4196e952e7,0x2c48113823b73704, 0xd17f3b51fca3a7a0,0xf75a15862ca504c5, 0x82ef85133de648c4,0x9a984d73dbe722fb, 0xa3ab66580d5fdaf5,0xc13e60d0d2e0ebba, 0xcc963fee10b7d1b3,0x318df905079926a8, 0xffbbcfe994e5c61f,0xfdf17746497f7052, 0x9fd561f1fd0f9bd3,0xfeb6ea8bedefa633, 0xc7caba6e7c5382c8,0xfe64a52ee96b8fc0, 0xf9bd690a1b68637b,0x3dfdce7aa3c673b0, 0x9c1661a651213e2d,0x6bea10ca65c084e, 0xc31bfa0fe5698db8,0x486e494fcff30a62, 0xf3e2f893dec3f126,0x5a89dba3c3efccfa, 0x986ddb5c6b3a76b7,0xf89629465a75e01c, 0xbe89523386091465,0xf6bbb397f1135823, 0xee2ba6c0678b597f,0x746aa07ded582e2c, 0x94db483840b717ef,0xa8c2a44eb4571cdc, 0xba121a4650e4ddeb,0x92f34d62616ce413, 0xe896a0d7e51e1566,0x77b020baf9c81d17, 0x915e2486ef32cd60,0xace1474dc1d122e, 0xb5b5ada8aaff80b8,0xd819992132456ba, 0xe3231912d5bf60e6,0x10e1fff697ed6c69, 0x8df5efabc5979c8f,0xca8d3ffa1ef463c1, 0xb1736b96b6fd83b3,0xbd308ff8a6b17cb2, 0xddd0467c64bce4a0,0xac7cb3f6d05ddbde, 0x8aa22c0dbef60ee4,0x6bcdf07a423aa96b, 0xad4ab7112eb3929d,0x86c16c98d2c953c6, 0xd89d64d57a607744,0xe871c7bf077ba8b7, 0x87625f056c7c4a8b,0x11471cd764ad4972, 0xa93af6c6c79b5d2d,0xd598e40d3dd89bcf, 0xd389b47879823479,0x4aff1d108d4ec2c3, 0x843610cb4bf160cb,0xcedf722a585139ba, 0xa54394fe1eedb8fe,0xc2974eb4ee658828, 0xce947a3da6a9273e,0x733d226229feea32, 0x811ccc668829b887,0x806357d5a3f525f, 0xa163ff802a3426a8,0xca07c2dcb0cf26f7, 0xc9bcff6034c13052,0xfc89b393dd02f0b5, 0xfc2c3f3841f17c67,0xbbac2078d443ace2, 0x9d9ba7832936edc0,0xd54b944b84aa4c0d, 0xc5029163f384a931,0xa9e795e65d4df11, 0xf64335bcf065d37d,0x4d4617b5ff4a16d5, 0x99ea0196163fa42e,0x504bced1bf8e4e45, 0xc06481fb9bcf8d39,0xe45ec2862f71e1d6, 0xf07da27a82c37088,0x5d767327bb4e5a4c, 0x964e858c91ba2655,0x3a6a07f8d510f86f, 0xbbe226efb628afea,0x890489f70a55368b, 0xeadab0aba3b2dbe5,0x2b45ac74ccea842e, 0x92c8ae6b464fc96f,0x3b0b8bc90012929d, 0xb77ada0617e3bbcb,0x9ce6ebb40173744, 0xe55990879ddcaabd,0xcc420a6a101d0515, 0x8f57fa54c2a9eab6,0x9fa946824a12232d, 0xb32df8e9f3546564,0x47939822dc96abf9, 0xdff9772470297ebd,0x59787e2b93bc56f7, 0x8bfbea76c619ef36,0x57eb4edb3c55b65a, 0xaefae51477a06b03,0xede622920b6b23f1, 0xdab99e59958885c4,0xe95fab368e45eced, 0x88b402f7fd75539b,0x11dbcb0218ebb414, 0xaae103b5fcd2a881,0xd652bdc29f26a119, 0xd59944a37c0752a2,0x4be76d3346f0495f, 0x857fcae62d8493a5,0x6f70a4400c562ddb, 0xa6dfbd9fb8e5b88e,0xcb4ccd500f6bb952, 0xd097ad07a71f26b2,0x7e2000a41346a7a7, 0x825ecc24c873782f,0x8ed400668c0c28c8, 0xa2f67f2dfa90563b,0x728900802f0f32fa, 0xcbb41ef979346bca,0x4f2b40a03ad2ffb9, 0xfea126b7d78186bc,0xe2f610c84987bfa8, 0x9f24b832e6b0f436,0xdd9ca7d2df4d7c9, 0xc6ede63fa05d3143,0x91503d1c79720dbb, 0xf8a95fcf88747d94,0x75a44c6397ce912a, 0x9b69dbe1b548ce7c,0xc986afbe3ee11aba, 0xc24452da229b021b,0xfbe85badce996168, 0xf2d56790ab41c2a2,0xfae27299423fb9c3, 0x97c560ba6b0919a5,0xdccd879fc967d41a, 0xbdb6b8e905cb600f,0x5400e987bbc1c920, 0xed246723473e3813,0x290123e9aab23b68, 0x9436c0760c86e30b,0xf9a0b6720aaf6521, 0xb94470938fa89bce,0xf808e40e8d5b3e69, 0xe7958cb87392c2c2,0xb60b1d1230b20e04, 0x90bd77f3483bb9b9,0xb1c6f22b5e6f48c2, 0xb4ecd5f01a4aa828,0x1e38aeb6360b1af3, 0xe2280b6c20dd5232,0x25c6da63c38de1b0, 0x8d590723948a535f,0x579c487e5a38ad0e, 0xb0af48ec79ace837,0x2d835a9df0c6d851, 0xdcdb1b2798182244,0xf8e431456cf88e65, 0x8a08f0f8bf0f156b,0x1b8e9ecb641b58ff, 0xac8b2d36eed2dac5,0xe272467e3d222f3f, 0xd7adf884aa879177,0x5b0ed81dcc6abb0f, 0x86ccbb52ea94baea,0x98e947129fc2b4e9, 0xa87fea27a539e9a5,0x3f2398d747b36224, 0xd29fe4b18e88640e,0x8eec7f0d19a03aad, 0x83a3eeeef9153e89,0x1953cf68300424ac, 0xa48ceaaab75a8e2b,0x5fa8c3423c052dd7, 0xcdb02555653131b6,0x3792f412cb06794d, 0x808e17555f3ebf11,0xe2bbd88bbee40bd0, 0xa0b19d2ab70e6ed6,0x5b6aceaeae9d0ec4, 0xc8de047564d20a8b,0xf245825a5a445275, 0xfb158592be068d2e,0xeed6e2f0f0d56712, 0x9ced737bb6c4183d,0x55464dd69685606b, 0xc428d05aa4751e4c,0xaa97e14c3c26b886, 0xf53304714d9265df,0xd53dd99f4b3066a8, 0x993fe2c6d07b7fab,0xe546a8038efe4029, 0xbf8fdb78849a5f96,0xde98520472bdd033, 0xef73d256a5c0f77c,0x963e66858f6d4440, 0x95a8637627989aad,0xdde7001379a44aa8, 0xbb127c53b17ec159,0x5560c018580d5d52, 0xe9d71b689dde71af,0xaab8f01e6e10b4a6, 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0x971da05074da7bee,0xd3f6fc16ebca5e04, 0xbce5086492111aea,0x88f4bb1ca6bcf585, 0xec1e4a7db69561a5,0x2b31e9e3d06c32e6, 0x9392ee8e921d5d07,0x3aff322e62439fd0, 0xb877aa3236a4b449,0x9befeb9fad487c3, 0xe69594bec44de15b,0x4c2ebe687989a9b4, 0x901d7cf73ab0acd9,0xf9d37014bf60a11, 0xb424dc35095cd80f,0x538484c19ef38c95, 0xe12e13424bb40e13,0x2865a5f206b06fba, 0x8cbccc096f5088cb,0xf93f87b7442e45d4, 0xafebff0bcb24aafe,0xf78f69a51539d749, 0xdbe6fecebdedd5be,0xb573440e5a884d1c, 0x89705f4136b4a597,0x31680a88f8953031, 0xabcc77118461cefc,0xfdc20d2b36ba7c3e, 0xd6bf94d5e57a42bc,0x3d32907604691b4d, 0x8637bd05af6c69b5,0xa63f9a49c2c1b110, 0xa7c5ac471b478423,0xfcf80dc33721d54, 0xd1b71758e219652b,0xd3c36113404ea4a9, 0x83126e978d4fdf3b,0x645a1cac083126ea, 0xa3d70a3d70a3d70a,0x3d70a3d70a3d70a4, 0xcccccccccccccccc,0xcccccccccccccccd, 0x8000000000000000,0x0, 0xa000000000000000,0x0, 0xc800000000000000,0x0, 0xfa00000000000000,0x0, 0x9c40000000000000,0x0, 0xc350000000000000,0x0, 0xf424000000000000,0x0, 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0xeb194f8e1ae525fd,0x5dcfab0800000000, 0x92efd1b8d0cf37be,0x5aa1cae500000000, 0xb7abc627050305ad,0xf14a3d9e40000000, 0xe596b7b0c643c719,0x6d9ccd05d0000000, 0x8f7e32ce7bea5c6f,0xe4820023a2000000, 0xb35dbf821ae4f38b,0xdda2802c8a800000, 0xe0352f62a19e306e,0xd50b2037ad200000, 0x8c213d9da502de45,0x4526f422cc340000, 0xaf298d050e4395d6,0x9670b12b7f410000, 0xdaf3f04651d47b4c,0x3c0cdd765f114000, 0x88d8762bf324cd0f,0xa5880a69fb6ac800, 0xab0e93b6efee0053,0x8eea0d047a457a00, 0xd5d238a4abe98068,0x72a4904598d6d880, 0x85a36366eb71f041,0x47a6da2b7f864750, 0xa70c3c40a64e6c51,0x999090b65f67d924, 0xd0cf4b50cfe20765,0xfff4b4e3f741cf6d, 0x82818f1281ed449f,0xbff8f10e7a8921a4, 0xa321f2d7226895c7,0xaff72d52192b6a0d, 0xcbea6f8ceb02bb39,0x9bf4f8a69f764490, 0xfee50b7025c36a08,0x2f236d04753d5b4, 0x9f4f2726179a2245,0x1d762422c946590, 0xc722f0ef9d80aad6,0x424d3ad2b7b97ef5, 0xf8ebad2b84e0d58b,0xd2e0898765a7deb2, 0x9b934c3b330c8577,0x63cc55f49f88eb2f, 0xc2781f49ffcfa6d5,0x3cbf6b71c76b25fb, 0xf316271c7fc3908a,0x8bef464e3945ef7a, 0x97edd871cfda3a56,0x97758bf0e3cbb5ac, 0xbde94e8e43d0c8ec,0x3d52eeed1cbea317, 0xed63a231d4c4fb27,0x4ca7aaa863ee4bdd, 0x945e455f24fb1cf8,0x8fe8caa93e74ef6a, 0xb975d6b6ee39e436,0xb3e2fd538e122b44, 0xe7d34c64a9c85d44,0x60dbbca87196b616, 0x90e40fbeea1d3a4a,0xbc8955e946fe31cd, 0xb51d13aea4a488dd,0x6babab6398bdbe41, 0xe264589a4dcdab14,0xc696963c7eed2dd1, 0x8d7eb76070a08aec,0xfc1e1de5cf543ca2, 0xb0de65388cc8ada8,0x3b25a55f43294bcb, 0xdd15fe86affad912,0x49ef0eb713f39ebe, 0x8a2dbf142dfcc7ab,0x6e3569326c784337, 0xacb92ed9397bf996,0x49c2c37f07965404, 0xd7e77a8f87daf7fb,0xdc33745ec97be906, 0x86f0ac99b4e8dafd,0x69a028bb3ded71a3, 0xa8acd7c0222311bc,0xc40832ea0d68ce0c, 0xd2d80db02aabd62b,0xf50a3fa490c30190, 0x83c7088e1aab65db,0x792667c6da79e0fa, 0xa4b8cab1a1563f52,0x577001b891185938, 0xcde6fd5e09abcf26,0xed4c0226b55e6f86, 0x80b05e5ac60b6178,0x544f8158315b05b4, 0xa0dc75f1778e39d6,0x696361ae3db1c721, 0xc913936dd571c84c,0x3bc3a19cd1e38e9, 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0x865b86925b9bc5c2,0xb8a2392ba45a9b2, 0xa7f26836f282b732,0x8e6cac7768d7141e, 0xd1ef0244af2364ff,0x3207d795430cd926, 0x8335616aed761f1f,0x7f44e6bd49e807b8, 0xa402b9c5a8d3a6e7,0x5f16206c9c6209a6, 0xcd036837130890a1,0x36dba887c37a8c0f, 0x802221226be55a64,0xc2494954da2c9789, 0xa02aa96b06deb0fd,0xf2db9baa10b7bd6c, 0xc83553c5c8965d3d,0x6f92829494e5acc7, 0xfa42a8b73abbf48c,0xcb772339ba1f17f9, 0x9c69a97284b578d7,0xff2a760414536efb, 0xc38413cf25e2d70d,0xfef5138519684aba, 0xf46518c2ef5b8cd1,0x7eb258665fc25d69, 0x98bf2f79d5993802,0xef2f773ffbd97a61, 0xbeeefb584aff8603,0xaafb550ffacfd8fa, 0xeeaaba2e5dbf6784,0x95ba2a53f983cf38, 0x952ab45cfa97a0b2,0xdd945a747bf26183, 0xba756174393d88df,0x94f971119aeef9e4, 0xe912b9d1478ceb17,0x7a37cd5601aab85d, 0x91abb422ccb812ee,0xac62e055c10ab33a, 0xb616a12b7fe617aa,0x577b986b314d6009, 0xe39c49765fdf9d94,0xed5a7e85fda0b80b, 0x8e41ade9fbebc27d,0x14588f13be847307, 0xb1d219647ae6b31c,0x596eb2d8ae258fc8, 0xde469fbd99a05fe3,0x6fca5f8ed9aef3bb, 0x8aec23d680043bee,0x25de7bb9480d5854, 0xada72ccc20054ae9,0xaf561aa79a10ae6a, 0xd910f7ff28069da4,0x1b2ba1518094da04, 0x87aa9aff79042286,0x90fb44d2f05d0842, 0xa99541bf57452b28,0x353a1607ac744a53, 0xd3fa922f2d1675f2,0x42889b8997915ce8, 0x847c9b5d7c2e09b7,0x69956135febada11, 0xa59bc234db398c25,0x43fab9837e699095, 0xcf02b2c21207ef2e,0x94f967e45e03f4bb, 0x8161afb94b44f57d,0x1d1be0eebac278f5, 0xa1ba1ba79e1632dc,0x6462d92a69731732, 0xca28a291859bbf93,0x7d7b8f7503cfdcfe, 0xfcb2cb35e702af78,0x5cda735244c3d43e, 0x9defbf01b061adab,0x3a0888136afa64a7, 0xc56baec21c7a1916,0x88aaa1845b8fdd0, 0xf6c69a72a3989f5b,0x8aad549e57273d45, 0x9a3c2087a63f6399,0x36ac54e2f678864b, 0xc0cb28a98fcf3c7f,0x84576a1bb416a7dd, 0xf0fdf2d3f3c30b9f,0x656d44a2a11c51d5, 0x969eb7c47859e743,0x9f644ae5a4b1b325, 0xbc4665b596706114,0x873d5d9f0dde1fee, 0xeb57ff22fc0c7959,0xa90cb506d155a7ea, 0x9316ff75dd87cbd8,0x9a7f12442d588f2, 0xb7dcbf5354e9bece,0xc11ed6d538aeb2f, 0xe5d3ef282a242e81,0x8f1668c8a86da5fa, 0x8fa475791a569d10,0xf96e017d694487bc, 0xb38d92d760ec4455,0x37c981dcc395a9ac, 0xe070f78d3927556a,0x85bbe253f47b1417, 0x8c469ab843b89562,0x93956d7478ccec8e, 0xaf58416654a6babb,0x387ac8d1970027b2, 0xdb2e51bfe9d0696a,0x6997b05fcc0319e, 0x88fcf317f22241e2,0x441fece3bdf81f03, 0xab3c2fddeeaad25a,0xd527e81cad7626c3, 0xd60b3bd56a5586f1,0x8a71e223d8d3b074, 0x85c7056562757456,0xf6872d5667844e49, 0xa738c6bebb12d16c,0xb428f8ac016561db, 0xd106f86e69d785c7,0xe13336d701beba52, 0x82a45b450226b39c,0xecc0024661173473, 0xa34d721642b06084,0x27f002d7f95d0190, 0xcc20ce9bd35c78a5,0x31ec038df7b441f4, 0xff290242c83396ce,0x7e67047175a15271, 0x9f79a169bd203e41,0xf0062c6e984d386, 0xc75809c42c684dd1,0x52c07b78a3e60868, 0xf92e0c3537826145,0xa7709a56ccdf8a82, 0x9bbcc7a142b17ccb,0x88a66076400bb691, 0xc2abf989935ddbfe,0x6acff893d00ea435, 0xf356f7ebf83552fe,0x583f6b8c4124d43, 0x98165af37b2153de,0xc3727a337a8b704a, 0xbe1bf1b059e9a8d6,0x744f18c0592e4c5c, 0xeda2ee1c7064130c,0x1162def06f79df73, 0x9485d4d1c63e8be7,0x8addcb5645ac2ba8, 0xb9a74a0637ce2ee1,0x6d953e2bd7173692, 0xe8111c87c5c1ba99,0xc8fa8db6ccdd0437, 0x910ab1d4db9914a0,0x1d9c9892400a22a2, 0xb54d5e4a127f59c8,0x2503beb6d00cab4b, 0xe2a0b5dc971f303a,0x2e44ae64840fd61d, 0x8da471a9de737e24,0x5ceaecfed289e5d2, 0xb10d8e1456105dad,0x7425a83e872c5f47, 0xdd50f1996b947518,0xd12f124e28f77719, 0x8a5296ffe33cc92f,0x82bd6b70d99aaa6f, 0xace73cbfdc0bfb7b,0x636cc64d1001550b, 0xd8210befd30efa5a,0x3c47f7e05401aa4e, 0x8714a775e3e95c78,0x65acfaec34810a71, 0xa8d9d1535ce3b396,0x7f1839a741a14d0d, 0xd31045a8341ca07c,0x1ede48111209a050, 0x83ea2b892091e44d,0x934aed0aab460432, 0xa4e4b66b68b65d60,0xf81da84d5617853f, 0xce1de40642e3f4b9,0x36251260ab9d668e, 0x80d2ae83e9ce78f3,0xc1d72b7c6b426019, 0xa1075a24e4421730,0xb24cf65b8612f81f, 0xc94930ae1d529cfc,0xdee033f26797b627, 0xfb9b7cd9a4a7443c,0x169840ef017da3b1, 0x9d412e0806e88aa5,0x8e1f289560ee864e, 0xc491798a08a2ad4e,0xf1a6f2bab92a27e2, 0xf5b5d7ec8acb58a2,0xae10af696774b1db, 0x9991a6f3d6bf1765,0xacca6da1e0a8ef29, 0xbff610b0cc6edd3f,0x17fd090a58d32af3, 0xeff394dcff8a948e,0xddfc4b4cef07f5b0, 0x95f83d0a1fb69cd9,0x4abdaf101564f98e, 0xbb764c4ca7a4440f,0x9d6d1ad41abe37f1, 0xea53df5fd18d5513,0x84c86189216dc5ed, 0x92746b9be2f8552c,0x32fd3cf5b4e49bb4, 0xb7118682dbb66a77,0x3fbc8c33221dc2a1, 0xe4d5e82392a40515,0xfabaf3feaa5334a, 0x8f05b1163ba6832d,0x29cb4d87f2a7400e, 0xb2c71d5bca9023f8,0x743e20e9ef511012, 0xdf78e4b2bd342cf6,0x914da9246b255416, 0x8bab8eefb6409c1a,0x1ad089b6c2f7548e, 0xae9672aba3d0c320,0xa184ac2473b529b1, 0xda3c0f568cc4f3e8,0xc9e5d72d90a2741e, 0x8865899617fb1871,0x7e2fa67c7a658892, 0xaa7eebfb9df9de8d,0xddbb901b98feeab7, 0xd51ea6fa85785631,0x552a74227f3ea565, 0x8533285c936b35de,0xd53a88958f87275f, 0xa67ff273b8460356,0x8a892abaf368f137, 0xd01fef10a657842c,0x2d2b7569b0432d85, 0x8213f56a67f6b29b,0x9c3b29620e29fc73, 0xa298f2c501f45f42,0x8349f3ba91b47b8f, 0xcb3f2f7642717713,0x241c70a936219a73, 0xfe0efb53d30dd4d7,0xed238cd383aa0110, 0x9ec95d1463e8a506,0xf4363804324a40aa, 0xc67bb4597ce2ce48,0xb143c6053edcd0d5, 0xf81aa16fdc1b81da,0xdd94b7868e94050a, 0x9b10a4e5e9913128,0xca7cf2b4191c8326, 0xc1d4ce1f63f57d72,0xfd1c2f611f63a3f0, 0xf24a01a73cf2dccf,0xbc633b39673c8cec, 0x976e41088617ca01,0xd5be0503e085d813, 0xbd49d14aa79dbc82,0x4b2d8644d8a74e18, 0xec9c459d51852ba2,0xddf8e7d60ed1219e, 0x93e1ab8252f33b45,0xcabb90e5c942b503, 0xb8da1662e7b00a17,0x3d6a751f3b936243, 0xe7109bfba19c0c9d,0xcc512670a783ad4, 0x906a617d450187e2,0x27fb2b80668b24c5, 0xb484f9dc9641e9da,0xb1f9f660802dedf6, 0xe1a63853bbd26451,0x5e7873f8a0396973, 0x8d07e33455637eb2,0xdb0b487b6423e1e8, 0xb049dc016abc5e5f,0x91ce1a9a3d2cda62, 0xdc5c5301c56b75f7,0x7641a140cc7810fb, 0x89b9b3e11b6329ba,0xa9e904c87fcb0a9d, 0xac2820d9623bf429,0x546345fa9fbdcd44, 0xd732290fbacaf133,0xa97c177947ad4095, 0x867f59a9d4bed6c0,0x49ed8eabcccc485d, 0xa81f301449ee8c70,0x5c68f256bfff5a74, 0xd226fc195c6a2f8c,0x73832eec6fff3111, 0x83585d8fd9c25db7,0xc831fd53c5ff7eab, 0xa42e74f3d032f525,0xba3e7ca8b77f5e55, 0xcd3a1230c43fb26f,0x28ce1bd2e55f35eb, 0x80444b5e7aa7cf85,0x7980d163cf5b81b3, 0xa0555e361951c366,0xd7e105bcc332621f, 0xc86ab5c39fa63440,0x8dd9472bf3fefaa7, 0xfa856334878fc150,0xb14f98f6f0feb951, 0x9c935e00d4b9d8d2,0x6ed1bf9a569f33d3, 0xc3b8358109e84f07,0xa862f80ec4700c8, 0xf4a642e14c6262c8,0xcd27bb612758c0fa, 0x98e7e9cccfbd7dbd,0x8038d51cb897789c, 0xbf21e44003acdd2c,0xe0470a63e6bd56c3, 0xeeea5d5004981478,0x1858ccfce06cac74, 0x95527a5202df0ccb,0xf37801e0c43ebc8, 0xbaa718e68396cffd,0xd30560258f54e6ba, 0xe950df20247c83fd,0x47c6b82ef32a2069, 0x91d28b7416cdd27e,0x4cdc331d57fa5441, 0xb6472e511c81471d,0xe0133fe4adf8e952, 0xe3d8f9e563a198e5,0x58180fddd97723a6, 0x8e679c2f5e44ff8f,0x570f09eaa7ea7648,}; }; template constexpr uint64_t powers_template::power_of_five_128[number_of_entries]; using powers = powers_template<>; } // namespace fast_float #endif #ifndef FASTFLOAT_DECIMAL_TO_BINARY_H #define FASTFLOAT_DECIMAL_TO_BINARY_H #include #include #include #include #include #include namespace fast_float { // This will compute or rather approximate w * 5**q and return a pair of 64-bit words approximating // the result, with the "high" part corresponding to the most significant bits and the // low part corresponding to the least significant bits. // template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 value128 compute_product_approximation(int64_t q, uint64_t w) { const int index = 2 * int(q - powers::smallest_power_of_five); // For small values of q, e.g., q in [0,27], the answer is always exact because // The line value128 firstproduct = full_multiplication(w, power_of_five_128[index]); // gives the exact answer. value128 firstproduct = full_multiplication(w, powers::power_of_five_128[index]); static_assert((bit_precision >= 0) && (bit_precision <= 64), " precision should be in (0,64]"); constexpr uint64_t precision_mask = (bit_precision < 64) ? (uint64_t(0xFFFFFFFFFFFFFFFF) >> bit_precision) : uint64_t(0xFFFFFFFFFFFFFFFF); if((firstproduct.high & precision_mask) == precision_mask) { // could further guard with (lower + w < lower) // regarding the second product, we only need secondproduct.high, but our expectation is that the compiler will optimize this extra work away if needed. value128 secondproduct = full_multiplication(w, powers::power_of_five_128[index + 1]); firstproduct.low += secondproduct.high; if(secondproduct.high > firstproduct.low) { firstproduct.high++; } } return firstproduct; } namespace detail { /** * For q in (0,350), we have that * f = (((152170 + 65536) * q ) >> 16); * is equal to * floor(p) + q * where * p = log(5**q)/log(2) = q * log(5)/log(2) * * For negative values of q in (-400,0), we have that * f = (((152170 + 65536) * q ) >> 16); * is equal to * -ceil(p) + q * where * p = log(5**-q)/log(2) = -q * log(5)/log(2) */ constexpr fastfloat_really_inline int32_t power(int32_t q) noexcept { return (((152170 + 65536) * q) >> 16) + 63; } } // namespace detail // create an adjusted mantissa, biased by the invalid power2 // for significant digits already multiplied by 10 ** q. template fastfloat_really_inline FASTFLOAT_CONSTEXPR14 adjusted_mantissa compute_error_scaled(int64_t q, uint64_t w, int lz) noexcept { int hilz = int(w >> 63) ^ 1; adjusted_mantissa answer; answer.mantissa = w << hilz; int bias = binary::mantissa_explicit_bits() - binary::minimum_exponent(); answer.power2 = int32_t(detail::power(int32_t(q)) + bias - hilz - lz - 62 + invalid_am_bias); return answer; } // w * 10 ** q, without rounding the representation up. // the power2 in the exponent will be adjusted by invalid_am_bias. template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 adjusted_mantissa compute_error(int64_t q, uint64_t w) noexcept { int lz = leading_zeroes(w); w <<= lz; value128 product = compute_product_approximation(q, w); return compute_error_scaled(q, product.high, lz); } // w * 10 ** q // The returned value should be a valid ieee64 number that simply need to be packed. // However, in some very rare cases, the computation will fail. In such cases, we // return an adjusted_mantissa with a negative power of 2: the caller should recompute // in such cases. template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 adjusted_mantissa compute_float(int64_t q, uint64_t w) noexcept { adjusted_mantissa answer; if ((w == 0) || (q < binary::smallest_power_of_ten())) { answer.power2 = 0; answer.mantissa = 0; // result should be zero return answer; } if (q > binary::largest_power_of_ten()) { // we want to get infinity: answer.power2 = binary::infinite_power(); answer.mantissa = 0; return answer; } // At this point in time q is in [powers::smallest_power_of_five, powers::largest_power_of_five]. // We want the most significant bit of i to be 1. Shift if needed. int lz = leading_zeroes(w); w <<= lz; // The required precision is binary::mantissa_explicit_bits() + 3 because // 1. We need the implicit bit // 2. We need an extra bit for rounding purposes // 3. We might lose a bit due to the "upperbit" routine (result too small, requiring a shift) value128 product = compute_product_approximation(q, w); // The computed 'product' is always sufficient. // Mathematical proof: // Noble Mushtak and Daniel Lemire, Fast Number Parsing Without Fallback (to appear) // See script/mushtak_lemire.py // The "compute_product_approximation" function can be slightly slower than a branchless approach: // value128 product = compute_product(q, w); // but in practice, we can win big with the compute_product_approximation if its additional branch // is easily predicted. Which is best is data specific. int upperbit = int(product.high >> 63); answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3); answer.power2 = int32_t(detail::power(int32_t(q)) + upperbit - lz - binary::minimum_exponent()); if (answer.power2 <= 0) { // we have a subnormal? // Here have that answer.power2 <= 0 so -answer.power2 >= 0 if(-answer.power2 + 1 >= 64) { // if we have more than 64 bits below the minimum exponent, you have a zero for sure. answer.power2 = 0; answer.mantissa = 0; // result should be zero return answer; } // next line is safe because -answer.power2 + 1 < 64 answer.mantissa >>= -answer.power2 + 1; // Thankfully, we can't have both "round-to-even" and subnormals because // "round-to-even" only occurs for powers close to 0. answer.mantissa += (answer.mantissa & 1); // round up answer.mantissa >>= 1; // There is a weird scenario where we don't have a subnormal but just. // Suppose we start with 2.2250738585072013e-308, we end up // with 0x3fffffffffffff x 2^-1023-53 which is technically subnormal // whereas 0x40000000000000 x 2^-1023-53 is normal. Now, we need to round // up 0x3fffffffffffff x 2^-1023-53 and once we do, we are no longer // subnormal, but we can only know this after rounding. // So we only declare a subnormal if we are smaller than the threshold. answer.power2 = (answer.mantissa < (uint64_t(1) << binary::mantissa_explicit_bits())) ? 0 : 1; return answer; } // usually, we round *up*, but if we fall right in between and and we have an // even basis, we need to round down // We are only concerned with the cases where 5**q fits in single 64-bit word. if ((product.low <= 1) && (q >= binary::min_exponent_round_to_even()) && (q <= binary::max_exponent_round_to_even()) && ((answer.mantissa & 3) == 1) ) { // we may fall between two floats! // To be in-between two floats we need that in doing // answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3); // ... we dropped out only zeroes. But if this happened, then we can go back!!! if((answer.mantissa << (upperbit + 64 - binary::mantissa_explicit_bits() - 3)) == product.high) { answer.mantissa &= ~uint64_t(1); // flip it so that we do not round up } } answer.mantissa += (answer.mantissa & 1); // round up answer.mantissa >>= 1; if (answer.mantissa >= (uint64_t(2) << binary::mantissa_explicit_bits())) { answer.mantissa = (uint64_t(1) << binary::mantissa_explicit_bits()); answer.power2++; // undo previous addition } answer.mantissa &= ~(uint64_t(1) << binary::mantissa_explicit_bits()); if (answer.power2 >= binary::infinite_power()) { // infinity answer.power2 = binary::infinite_power(); answer.mantissa = 0; } return answer; } } // namespace fast_float #endif #ifndef FASTFLOAT_BIGINT_H #define FASTFLOAT_BIGINT_H #include #include #include #include namespace fast_float { // the limb width: we want efficient multiplication of double the bits in // limb, or for 64-bit limbs, at least 64-bit multiplication where we can // extract the high and low parts efficiently. this is every 64-bit // architecture except for sparc, which emulates 128-bit multiplication. // we might have platforms where `CHAR_BIT` is not 8, so let's avoid // doing `8 * sizeof(limb)`. #if defined(FASTFLOAT_64BIT) && !defined(__sparc) #define FASTFLOAT_64BIT_LIMB 1 typedef uint64_t limb; constexpr size_t limb_bits = 64; #else #define FASTFLOAT_32BIT_LIMB typedef uint32_t limb; constexpr size_t limb_bits = 32; #endif typedef span limb_span; // number of bits in a bigint. this needs to be at least the number // of bits required to store the largest bigint, which is // `log2(10**(digits + max_exp))`, or `log2(10**(767 + 342))`, or // ~3600 bits, so we round to 4000. constexpr size_t bigint_bits = 4000; constexpr size_t bigint_limbs = bigint_bits / limb_bits; // vector-like type that is allocated on the stack. the entire // buffer is pre-allocated, and only the length changes. template struct stackvec { limb data[size]; // we never need more than 150 limbs uint16_t length{0}; stackvec() = default; stackvec(const stackvec &) = delete; stackvec &operator=(const stackvec &) = delete; stackvec(stackvec &&) = delete; stackvec &operator=(stackvec &&other) = delete; // create stack vector from existing limb span. FASTFLOAT_CONSTEXPR20 stackvec(limb_span s) { FASTFLOAT_ASSERT(try_extend(s)); } FASTFLOAT_CONSTEXPR14 limb& operator[](size_t index) noexcept { FASTFLOAT_DEBUG_ASSERT(index < length); return data[index]; } FASTFLOAT_CONSTEXPR14 const limb& operator[](size_t index) const noexcept { FASTFLOAT_DEBUG_ASSERT(index < length); return data[index]; } // index from the end of the container FASTFLOAT_CONSTEXPR14 const limb& rindex(size_t index) const noexcept { FASTFLOAT_DEBUG_ASSERT(index < length); size_t rindex = length - index - 1; return data[rindex]; } // set the length, without bounds checking. FASTFLOAT_CONSTEXPR14 void set_len(size_t len) noexcept { length = uint16_t(len); } constexpr size_t len() const noexcept { return length; } constexpr bool is_empty() const noexcept { return length == 0; } constexpr size_t capacity() const noexcept { return size; } // append item to vector, without bounds checking FASTFLOAT_CONSTEXPR14 void push_unchecked(limb value) noexcept { data[length] = value; length++; } // append item to vector, returning if item was added FASTFLOAT_CONSTEXPR14 bool try_push(limb value) noexcept { if (len() < capacity()) { push_unchecked(value); return true; } else { return false; } } // add items to the vector, from a span, without bounds checking FASTFLOAT_CONSTEXPR20 void extend_unchecked(limb_span s) noexcept { limb* ptr = data + length; std::copy_n(s.ptr, s.len(), ptr); set_len(len() + s.len()); } // try to add items to the vector, returning if items were added FASTFLOAT_CONSTEXPR20 bool try_extend(limb_span s) noexcept { if (len() + s.len() <= capacity()) { extend_unchecked(s); return true; } else { return false; } } // resize the vector, without bounds checking // if the new size is longer than the vector, assign value to each // appended item. FASTFLOAT_CONSTEXPR20 void resize_unchecked(size_t new_len, limb value) noexcept { if (new_len > len()) { size_t count = new_len - len(); limb* first = data + len(); limb* last = first + count; ::std::fill(first, last, value); set_len(new_len); } else { set_len(new_len); } } // try to resize the vector, returning if the vector was resized. FASTFLOAT_CONSTEXPR20 bool try_resize(size_t new_len, limb value) noexcept { if (new_len > capacity()) { return false; } else { resize_unchecked(new_len, value); return true; } } // check if any limbs are non-zero after the given index. // this needs to be done in reverse order, since the index // is relative to the most significant limbs. FASTFLOAT_CONSTEXPR14 bool nonzero(size_t index) const noexcept { while (index < len()) { if (rindex(index) != 0) { return true; } index++; } return false; } // normalize the big integer, so most-significant zero limbs are removed. FASTFLOAT_CONSTEXPR14 void normalize() noexcept { while (len() > 0 && rindex(0) == 0) { length--; } } }; fastfloat_really_inline FASTFLOAT_CONSTEXPR14 uint64_t empty_hi64(bool& truncated) noexcept { truncated = false; return 0; } fastfloat_really_inline FASTFLOAT_CONSTEXPR20 uint64_t uint64_hi64(uint64_t r0, bool& truncated) noexcept { truncated = false; int shl = leading_zeroes(r0); return r0 << shl; } fastfloat_really_inline FASTFLOAT_CONSTEXPR20 uint64_t uint64_hi64(uint64_t r0, uint64_t r1, bool& truncated) noexcept { int shl = leading_zeroes(r0); if (shl == 0) { truncated = r1 != 0; return r0; } else { int shr = 64 - shl; truncated = (r1 << shl) != 0; return (r0 << shl) | (r1 >> shr); } } fastfloat_really_inline FASTFLOAT_CONSTEXPR20 uint64_t uint32_hi64(uint32_t r0, bool& truncated) noexcept { return uint64_hi64(r0, truncated); } fastfloat_really_inline FASTFLOAT_CONSTEXPR20 uint64_t uint32_hi64(uint32_t r0, uint32_t r1, bool& truncated) noexcept { uint64_t x0 = r0; uint64_t x1 = r1; return uint64_hi64((x0 << 32) | x1, truncated); } fastfloat_really_inline FASTFLOAT_CONSTEXPR20 uint64_t uint32_hi64(uint32_t r0, uint32_t r1, uint32_t r2, bool& truncated) noexcept { uint64_t x0 = r0; uint64_t x1 = r1; uint64_t x2 = r2; return uint64_hi64(x0, (x1 << 32) | x2, truncated); } // add two small integers, checking for overflow. // we want an efficient operation. for msvc, where // we don't have built-in intrinsics, this is still // pretty fast. fastfloat_really_inline FASTFLOAT_CONSTEXPR20 limb scalar_add(limb x, limb y, bool& overflow) noexcept { limb z; // gcc and clang #if defined(__has_builtin) #if __has_builtin(__builtin_add_overflow) if (!cpp20_and_in_constexpr()) { overflow = __builtin_add_overflow(x, y, &z); return z; } #endif #endif // generic, this still optimizes correctly on MSVC. z = x + y; overflow = z < x; return z; } // multiply two small integers, getting both the high and low bits. fastfloat_really_inline FASTFLOAT_CONSTEXPR20 limb scalar_mul(limb x, limb y, limb& carry) noexcept { #ifdef FASTFLOAT_64BIT_LIMB #if defined(__SIZEOF_INT128__) // GCC and clang both define it as an extension. __uint128_t z = __uint128_t(x) * __uint128_t(y) + __uint128_t(carry); carry = limb(z >> limb_bits); return limb(z); #else // fallback, no native 128-bit integer multiplication with carry. // on msvc, this optimizes identically, somehow. value128 z = full_multiplication(x, y); bool overflow; z.low = scalar_add(z.low, carry, overflow); z.high += uint64_t(overflow); // cannot overflow carry = z.high; return z.low; #endif #else uint64_t z = uint64_t(x) * uint64_t(y) + uint64_t(carry); carry = limb(z >> limb_bits); return limb(z); #endif } // add scalar value to bigint starting from offset. // used in grade school multiplication template inline FASTFLOAT_CONSTEXPR20 bool small_add_from(stackvec& vec, limb y, size_t start) noexcept { size_t index = start; limb carry = y; bool overflow; while (carry != 0 && index < vec.len()) { vec[index] = scalar_add(vec[index], carry, overflow); carry = limb(overflow); index += 1; } if (carry != 0) { FASTFLOAT_TRY(vec.try_push(carry)); } return true; } // add scalar value to bigint. template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 bool small_add(stackvec& vec, limb y) noexcept { return small_add_from(vec, y, 0); } // multiply bigint by scalar value. template inline FASTFLOAT_CONSTEXPR20 bool small_mul(stackvec& vec, limb y) noexcept { limb carry = 0; for (size_t index = 0; index < vec.len(); index++) { vec[index] = scalar_mul(vec[index], y, carry); } if (carry != 0) { FASTFLOAT_TRY(vec.try_push(carry)); } return true; } // add bigint to bigint starting from index. // used in grade school multiplication template FASTFLOAT_CONSTEXPR20 bool large_add_from(stackvec& x, limb_span y, size_t start) noexcept { // the effective x buffer is from `xstart..x.len()`, so exit early // if we can't get that current range. if (x.len() < start || y.len() > x.len() - start) { FASTFLOAT_TRY(x.try_resize(y.len() + start, 0)); } bool carry = false; for (size_t index = 0; index < y.len(); index++) { limb xi = x[index + start]; limb yi = y[index]; bool c1 = false; bool c2 = false; xi = scalar_add(xi, yi, c1); if (carry) { xi = scalar_add(xi, 1, c2); } x[index + start] = xi; carry = c1 | c2; } // handle overflow if (carry) { FASTFLOAT_TRY(small_add_from(x, 1, y.len() + start)); } return true; } // add bigint to bigint. template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 bool large_add_from(stackvec& x, limb_span y) noexcept { return large_add_from(x, y, 0); } // grade-school multiplication algorithm template FASTFLOAT_CONSTEXPR20 bool long_mul(stackvec& x, limb_span y) noexcept { limb_span xs = limb_span(x.data, x.len()); stackvec z(xs); limb_span zs = limb_span(z.data, z.len()); if (y.len() != 0) { limb y0 = y[0]; FASTFLOAT_TRY(small_mul(x, y0)); for (size_t index = 1; index < y.len(); index++) { limb yi = y[index]; stackvec zi; if (yi != 0) { // re-use the same buffer throughout zi.set_len(0); FASTFLOAT_TRY(zi.try_extend(zs)); FASTFLOAT_TRY(small_mul(zi, yi)); limb_span zis = limb_span(zi.data, zi.len()); FASTFLOAT_TRY(large_add_from(x, zis, index)); } } } x.normalize(); return true; } // grade-school multiplication algorithm template FASTFLOAT_CONSTEXPR20 bool large_mul(stackvec& x, limb_span y) noexcept { if (y.len() == 1) { FASTFLOAT_TRY(small_mul(x, y[0])); } else { FASTFLOAT_TRY(long_mul(x, y)); } return true; } template struct pow5_tables { static constexpr uint32_t large_step = 135; static constexpr uint64_t small_power_of_5[] = { 1UL, 5UL, 25UL, 125UL, 625UL, 3125UL, 15625UL, 78125UL, 390625UL, 1953125UL, 9765625UL, 48828125UL, 244140625UL, 1220703125UL, 6103515625UL, 30517578125UL, 152587890625UL, 762939453125UL, 3814697265625UL, 19073486328125UL, 95367431640625UL, 476837158203125UL, 2384185791015625UL, 11920928955078125UL, 59604644775390625UL, 298023223876953125UL, 1490116119384765625UL, 7450580596923828125UL, }; #ifdef FASTFLOAT_64BIT_LIMB constexpr static limb large_power_of_5[] = { 1414648277510068013UL, 9180637584431281687UL, 4539964771860779200UL, 10482974169319127550UL, 198276706040285095UL}; #else constexpr static limb large_power_of_5[] = { 4279965485U, 329373468U, 4020270615U, 2137533757U, 4287402176U, 1057042919U, 1071430142U, 2440757623U, 381945767U, 46164893U}; #endif }; template constexpr uint32_t pow5_tables::large_step; template constexpr uint64_t pow5_tables::small_power_of_5[]; template constexpr limb pow5_tables::large_power_of_5[]; // big integer type. implements a small subset of big integer // arithmetic, using simple algorithms since asymptotically // faster algorithms are slower for a small number of limbs. // all operations assume the big-integer is normalized. struct bigint : pow5_tables<> { // storage of the limbs, in little-endian order. stackvec vec; FASTFLOAT_CONSTEXPR20 bigint(): vec() {} bigint(const bigint &) = delete; bigint &operator=(const bigint &) = delete; bigint(bigint &&) = delete; bigint &operator=(bigint &&other) = delete; FASTFLOAT_CONSTEXPR20 bigint(uint64_t value): vec() { #ifdef FASTFLOAT_64BIT_LIMB vec.push_unchecked(value); #else vec.push_unchecked(uint32_t(value)); vec.push_unchecked(uint32_t(value >> 32)); #endif vec.normalize(); } // get the high 64 bits from the vector, and if bits were truncated. // this is to get the significant digits for the float. FASTFLOAT_CONSTEXPR20 uint64_t hi64(bool& truncated) const noexcept { #ifdef FASTFLOAT_64BIT_LIMB if (vec.len() == 0) { return empty_hi64(truncated); } else if (vec.len() == 1) { return uint64_hi64(vec.rindex(0), truncated); } else { uint64_t result = uint64_hi64(vec.rindex(0), vec.rindex(1), truncated); truncated |= vec.nonzero(2); return result; } #else if (vec.len() == 0) { return empty_hi64(truncated); } else if (vec.len() == 1) { return uint32_hi64(vec.rindex(0), truncated); } else if (vec.len() == 2) { return uint32_hi64(vec.rindex(0), vec.rindex(1), truncated); } else { uint64_t result = uint32_hi64(vec.rindex(0), vec.rindex(1), vec.rindex(2), truncated); truncated |= vec.nonzero(3); return result; } #endif } // compare two big integers, returning the large value. // assumes both are normalized. if the return value is // negative, other is larger, if the return value is // positive, this is larger, otherwise they are equal. // the limbs are stored in little-endian order, so we // must compare the limbs in ever order. FASTFLOAT_CONSTEXPR20 int compare(const bigint& other) const noexcept { if (vec.len() > other.vec.len()) { return 1; } else if (vec.len() < other.vec.len()) { return -1; } else { for (size_t index = vec.len(); index > 0; index--) { limb xi = vec[index - 1]; limb yi = other.vec[index - 1]; if (xi > yi) { return 1; } else if (xi < yi) { return -1; } } return 0; } } // shift left each limb n bits, carrying over to the new limb // returns true if we were able to shift all the digits. FASTFLOAT_CONSTEXPR20 bool shl_bits(size_t n) noexcept { // Internally, for each item, we shift left by n, and add the previous // right shifted limb-bits. // For example, we transform (for u8) shifted left 2, to: // b10100100 b01000010 // b10 b10010001 b00001000 FASTFLOAT_DEBUG_ASSERT(n != 0); FASTFLOAT_DEBUG_ASSERT(n < sizeof(limb) * 8); size_t shl = n; size_t shr = limb_bits - shl; limb prev = 0; for (size_t index = 0; index < vec.len(); index++) { limb xi = vec[index]; vec[index] = (xi << shl) | (prev >> shr); prev = xi; } limb carry = prev >> shr; if (carry != 0) { return vec.try_push(carry); } return true; } // move the limbs left by `n` limbs. FASTFLOAT_CONSTEXPR20 bool shl_limbs(size_t n) noexcept { FASTFLOAT_DEBUG_ASSERT(n != 0); if (n + vec.len() > vec.capacity()) { return false; } else if (!vec.is_empty()) { // move limbs limb* dst = vec.data + n; const limb* src = vec.data; std::copy_backward(src, src + vec.len(), dst + vec.len()); // fill in empty limbs limb* first = vec.data; limb* last = first + n; ::std::fill(first, last, 0); vec.set_len(n + vec.len()); return true; } else { return true; } } // move the limbs left by `n` bits. FASTFLOAT_CONSTEXPR20 bool shl(size_t n) noexcept { size_t rem = n % limb_bits; size_t div = n / limb_bits; if (rem != 0) { FASTFLOAT_TRY(shl_bits(rem)); } if (div != 0) { FASTFLOAT_TRY(shl_limbs(div)); } return true; } // get the number of leading zeros in the bigint. FASTFLOAT_CONSTEXPR20 int ctlz() const noexcept { if (vec.is_empty()) { return 0; } else { #ifdef FASTFLOAT_64BIT_LIMB return leading_zeroes(vec.rindex(0)); #else // no use defining a specialized leading_zeroes for a 32-bit type. uint64_t r0 = vec.rindex(0); return leading_zeroes(r0 << 32); #endif } } // get the number of bits in the bigint. FASTFLOAT_CONSTEXPR20 int bit_length() const noexcept { int lz = ctlz(); return int(limb_bits * vec.len()) - lz; } FASTFLOAT_CONSTEXPR20 bool mul(limb y) noexcept { return small_mul(vec, y); } FASTFLOAT_CONSTEXPR20 bool add(limb y) noexcept { return small_add(vec, y); } // multiply as if by 2 raised to a power. FASTFLOAT_CONSTEXPR20 bool pow2(uint32_t exp) noexcept { return shl(exp); } // multiply as if by 5 raised to a power. FASTFLOAT_CONSTEXPR20 bool pow5(uint32_t exp) noexcept { // multiply by a power of 5 size_t large_length = sizeof(large_power_of_5) / sizeof(limb); limb_span large = limb_span(large_power_of_5, large_length); while (exp >= large_step) { FASTFLOAT_TRY(large_mul(vec, large)); exp -= large_step; } #ifdef FASTFLOAT_64BIT_LIMB uint32_t small_step = 27; limb max_native = 7450580596923828125UL; #else uint32_t small_step = 13; limb max_native = 1220703125U; #endif while (exp >= small_step) { FASTFLOAT_TRY(small_mul(vec, max_native)); exp -= small_step; } if (exp != 0) { // Work around clang bug https://godbolt.org/z/zedh7rrhc // This is similar to https://github.com/llvm/llvm-project/issues/47746, // except the workaround described there don't work here FASTFLOAT_TRY( small_mul(vec, limb(((void)small_power_of_5[0], small_power_of_5[exp]))) ); } return true; } // multiply as if by 10 raised to a power. FASTFLOAT_CONSTEXPR20 bool pow10(uint32_t exp) noexcept { FASTFLOAT_TRY(pow5(exp)); return pow2(exp); } }; } // namespace fast_float #endif #ifndef FASTFLOAT_DIGIT_COMPARISON_H #define FASTFLOAT_DIGIT_COMPARISON_H #include #include #include #include namespace fast_float { // 1e0 to 1e19 constexpr static uint64_t powers_of_ten_uint64[] = { 1UL, 10UL, 100UL, 1000UL, 10000UL, 100000UL, 1000000UL, 10000000UL, 100000000UL, 1000000000UL, 10000000000UL, 100000000000UL, 1000000000000UL, 10000000000000UL, 100000000000000UL, 1000000000000000UL, 10000000000000000UL, 100000000000000000UL, 1000000000000000000UL, 10000000000000000000UL}; // calculate the exponent, in scientific notation, of the number. // this algorithm is not even close to optimized, but it has no practical // effect on performance: in order to have a faster algorithm, we'd need // to slow down performance for faster algorithms, and this is still fast. template fastfloat_really_inline FASTFLOAT_CONSTEXPR14 int32_t scientific_exponent(parsed_number_string_t & num) noexcept { uint64_t mantissa = num.mantissa; int32_t exponent = int32_t(num.exponent); while (mantissa >= 10000) { mantissa /= 10000; exponent += 4; } while (mantissa >= 100) { mantissa /= 100; exponent += 2; } while (mantissa >= 10) { mantissa /= 10; exponent += 1; } return exponent; } // this converts a native floating-point number to an extended-precision float. template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 adjusted_mantissa to_extended(T value) noexcept { using equiv_uint = typename binary_format::equiv_uint; constexpr equiv_uint exponent_mask = binary_format::exponent_mask(); constexpr equiv_uint mantissa_mask = binary_format::mantissa_mask(); constexpr equiv_uint hidden_bit_mask = binary_format::hidden_bit_mask(); adjusted_mantissa am; int32_t bias = binary_format::mantissa_explicit_bits() - binary_format::minimum_exponent(); equiv_uint bits; #if FASTFLOAT_HAS_BIT_CAST bits = std::bit_cast(value); #else ::memcpy(&bits, &value, sizeof(T)); #endif if ((bits & exponent_mask) == 0) { // denormal am.power2 = 1 - bias; am.mantissa = bits & mantissa_mask; } else { // normal am.power2 = int32_t((bits & exponent_mask) >> binary_format::mantissa_explicit_bits()); am.power2 -= bias; am.mantissa = (bits & mantissa_mask) | hidden_bit_mask; } return am; } // get the extended precision value of the halfway point between b and b+u. // we are given a native float that represents b, so we need to adjust it // halfway between b and b+u. template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 adjusted_mantissa to_extended_halfway(T value) noexcept { adjusted_mantissa am = to_extended(value); am.mantissa <<= 1; am.mantissa += 1; am.power2 -= 1; return am; } // round an extended-precision float to the nearest machine float. template fastfloat_really_inline FASTFLOAT_CONSTEXPR14 void round(adjusted_mantissa& am, callback cb) noexcept { int32_t mantissa_shift = 64 - binary_format::mantissa_explicit_bits() - 1; if (-am.power2 >= mantissa_shift) { // have a denormal float int32_t shift = -am.power2 + 1; cb(am, std::min(shift, 64)); // check for round-up: if rounding-nearest carried us to the hidden bit. am.power2 = (am.mantissa < (uint64_t(1) << binary_format::mantissa_explicit_bits())) ? 0 : 1; return; } // have a normal float, use the default shift. cb(am, mantissa_shift); // check for carry if (am.mantissa >= (uint64_t(2) << binary_format::mantissa_explicit_bits())) { am.mantissa = (uint64_t(1) << binary_format::mantissa_explicit_bits()); am.power2++; } // check for infinite: we could have carried to an infinite power am.mantissa &= ~(uint64_t(1) << binary_format::mantissa_explicit_bits()); if (am.power2 >= binary_format::infinite_power()) { am.power2 = binary_format::infinite_power(); am.mantissa = 0; } } template fastfloat_really_inline FASTFLOAT_CONSTEXPR14 void round_nearest_tie_even(adjusted_mantissa& am, int32_t shift, callback cb) noexcept { const uint64_t mask = (shift == 64) ? UINT64_MAX : (uint64_t(1) << shift) - 1; const uint64_t halfway = (shift == 0) ? 0 : uint64_t(1) << (shift - 1); uint64_t truncated_bits = am.mantissa & mask; bool is_above = truncated_bits > halfway; bool is_halfway = truncated_bits == halfway; // shift digits into position if (shift == 64) { am.mantissa = 0; } else { am.mantissa >>= shift; } am.power2 += shift; bool is_odd = (am.mantissa & 1) == 1; am.mantissa += uint64_t(cb(is_odd, is_halfway, is_above)); } fastfloat_really_inline FASTFLOAT_CONSTEXPR14 void round_down(adjusted_mantissa& am, int32_t shift) noexcept { if (shift == 64) { am.mantissa = 0; } else { am.mantissa >>= shift; } am.power2 += shift; } template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 void skip_zeros(UC const * & first, UC const * last) noexcept { uint64_t val; while (!cpp20_and_in_constexpr() && std::distance(first, last) >= int_cmp_len()) { ::memcpy(&val, first, sizeof(uint64_t)); if (val != int_cmp_zeros()) { break; } first += int_cmp_len(); } while (first != last) { if (*first != UC('0')) { break; } first++; } } // determine if any non-zero digits were truncated. // all characters must be valid digits. template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 bool is_truncated(UC const * first, UC const * last) noexcept { // do 8-bit optimizations, can just compare to 8 literal 0s. uint64_t val; while (!cpp20_and_in_constexpr() && std::distance(first, last) >= int_cmp_len()) { ::memcpy(&val, first, sizeof(uint64_t)); if (val != int_cmp_zeros()) { return true; } first += int_cmp_len(); } while (first != last) { if (*first != UC('0')) { return true; } ++first; } return false; } template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 bool is_truncated(span s) noexcept { return is_truncated(s.ptr, s.ptr + s.len()); } template fastfloat_really_inline FASTFLOAT_CONSTEXPR20 void parse_eight_digits(const UC*& p, limb& value, size_t& counter, size_t& count) noexcept { value = value * 100000000 + parse_eight_digits_unrolled(p); p += 8; counter += 8; count += 8; } template fastfloat_really_inline FASTFLOAT_CONSTEXPR14 void parse_one_digit(UC const *& p, limb& value, size_t& counter, size_t& count) noexcept { value = value * 10 + limb(*p - UC('0')); p++; counter++; count++; } fastfloat_really_inline FASTFLOAT_CONSTEXPR20 void add_native(bigint& big, limb power, limb value) noexcept { big.mul(power); big.add(value); } fastfloat_really_inline FASTFLOAT_CONSTEXPR20 void round_up_bigint(bigint& big, size_t& count) noexcept { // need to round-up the digits, but need to avoid rounding // ....9999 to ...10000, which could cause a false halfway point. add_native(big, 10, 1); count++; } // parse the significant digits into a big integer template inline FASTFLOAT_CONSTEXPR20 void parse_mantissa(bigint& result, parsed_number_string_t& num, size_t max_digits, size_t& digits) noexcept { // try to minimize the number of big integer and scalar multiplication. // therefore, try to parse 8 digits at a time, and multiply by the largest // scalar value (9 or 19 digits) for each step. size_t counter = 0; digits = 0; limb value = 0; #ifdef FASTFLOAT_64BIT_LIMB size_t step = 19; #else size_t step = 9; #endif // process all integer digits. UC const * p = num.integer.ptr; UC const * pend = p + num.integer.len(); skip_zeros(p, pend); // process all digits, in increments of step per loop while (p != pend) { while ((std::distance(p, pend) >= 8) && (step - counter >= 8) && (max_digits - digits >= 8)) { parse_eight_digits(p, value, counter, digits); } while (counter < step && p != pend && digits < max_digits) { parse_one_digit(p, value, counter, digits); } if (digits == max_digits) { // add the temporary value, then check if we've truncated any digits add_native(result, limb(powers_of_ten_uint64[counter]), value); bool truncated = is_truncated(p, pend); if (num.fraction.ptr != nullptr) { truncated |= is_truncated(num.fraction); } if (truncated) { round_up_bigint(result, digits); } return; } else { add_native(result, limb(powers_of_ten_uint64[counter]), value); counter = 0; value = 0; } } // add our fraction digits, if they're available. if (num.fraction.ptr != nullptr) { p = num.fraction.ptr; pend = p + num.fraction.len(); if (digits == 0) { skip_zeros(p, pend); } // process all digits, in increments of step per loop while (p != pend) { while ((std::distance(p, pend) >= 8) && (step - counter >= 8) && (max_digits - digits >= 8)) { parse_eight_digits(p, value, counter, digits); } while (counter < step && p != pend && digits < max_digits) { parse_one_digit(p, value, counter, digits); } if (digits == max_digits) { // add the temporary value, then check if we've truncated any digits add_native(result, limb(powers_of_ten_uint64[counter]), value); bool truncated = is_truncated(p, pend); if (truncated) { round_up_bigint(result, digits); } return; } else { add_native(result, limb(powers_of_ten_uint64[counter]), value); counter = 0; value = 0; } } } if (counter != 0) { add_native(result, limb(powers_of_ten_uint64[counter]), value); } } template inline FASTFLOAT_CONSTEXPR20 adjusted_mantissa positive_digit_comp(bigint& bigmant, int32_t exponent) noexcept { FASTFLOAT_ASSERT(bigmant.pow10(uint32_t(exponent))); adjusted_mantissa answer; bool truncated; answer.mantissa = bigmant.hi64(truncated); int bias = binary_format::mantissa_explicit_bits() - binary_format::minimum_exponent(); answer.power2 = bigmant.bit_length() - 64 + bias; round(answer, [truncated](adjusted_mantissa& a, int32_t shift) { round_nearest_tie_even(a, shift, [truncated](bool is_odd, bool is_halfway, bool is_above) -> bool { return is_above || (is_halfway && truncated) || (is_odd && is_halfway); }); }); return answer; } // the scaling here is quite simple: we have, for the real digits `m * 10^e`, // and for the theoretical digits `n * 2^f`. Since `e` is always negative, // to scale them identically, we do `n * 2^f * 5^-f`, so we now have `m * 2^e`. // we then need to scale by `2^(f- e)`, and then the two significant digits // are of the same magnitude. template inline FASTFLOAT_CONSTEXPR20 adjusted_mantissa negative_digit_comp(bigint& bigmant, adjusted_mantissa am, int32_t exponent) noexcept { bigint& real_digits = bigmant; int32_t real_exp = exponent; // get the value of `b`, rounded down, and get a bigint representation of b+h adjusted_mantissa am_b = am; // gcc7 buf: use a lambda to remove the noexcept qualifier bug with -Wnoexcept-type. round(am_b, [](adjusted_mantissa&a, int32_t shift) { round_down(a, shift); }); T b; to_float(false, am_b, b); adjusted_mantissa theor = to_extended_halfway(b); bigint theor_digits(theor.mantissa); int32_t theor_exp = theor.power2; // scale real digits and theor digits to be same power. int32_t pow2_exp = theor_exp - real_exp; uint32_t pow5_exp = uint32_t(-real_exp); if (pow5_exp != 0) { FASTFLOAT_ASSERT(theor_digits.pow5(pow5_exp)); } if (pow2_exp > 0) { FASTFLOAT_ASSERT(theor_digits.pow2(uint32_t(pow2_exp))); } else if (pow2_exp < 0) { FASTFLOAT_ASSERT(real_digits.pow2(uint32_t(-pow2_exp))); } // compare digits, and use it to director rounding int ord = real_digits.compare(theor_digits); adjusted_mantissa answer = am; round(answer, [ord](adjusted_mantissa& a, int32_t shift) { round_nearest_tie_even(a, shift, [ord](bool is_odd, bool _, bool __) -> bool { (void)_; // not needed, since we've done our comparison (void)__; // not needed, since we've done our comparison if (ord > 0) { return true; } else if (ord < 0) { return false; } else { return is_odd; } }); }); return answer; } // parse the significant digits as a big integer to unambiguously round the // the significant digits. here, we are trying to determine how to round // an extended float representation close to `b+h`, halfway between `b` // (the float rounded-down) and `b+u`, the next positive float. this // algorithm is always correct, and uses one of two approaches. when // the exponent is positive relative to the significant digits (such as // 1234), we create a big-integer representation, get the high 64-bits, // determine if any lower bits are truncated, and use that to direct // rounding. in case of a negative exponent relative to the significant // digits (such as 1.2345), we create a theoretical representation of // `b` as a big-integer type, scaled to the same binary exponent as // the actual digits. we then compare the big integer representations // of both, and use that to direct rounding. template inline FASTFLOAT_CONSTEXPR20 adjusted_mantissa digit_comp(parsed_number_string_t& num, adjusted_mantissa am) noexcept { // remove the invalid exponent bias am.power2 -= invalid_am_bias; int32_t sci_exp = scientific_exponent(num); size_t max_digits = binary_format::max_digits(); size_t digits = 0; bigint bigmant; parse_mantissa(bigmant, num, max_digits, digits); // can't underflow, since digits is at most max_digits. int32_t exponent = sci_exp + 1 - int32_t(digits); if (exponent >= 0) { return positive_digit_comp(bigmant, exponent); } else { return negative_digit_comp(bigmant, am, exponent); } } } // namespace fast_float #endif #ifndef FASTFLOAT_PARSE_NUMBER_H #define FASTFLOAT_PARSE_NUMBER_H #include #include #include #include namespace fast_float { namespace detail { /** * Special case +inf, -inf, nan, infinity, -infinity. * The case comparisons could be made much faster given that we know that the * strings a null-free and fixed. **/ template from_chars_result_t FASTFLOAT_CONSTEXPR14 parse_infnan(UC const * first, UC const * last, T &value) noexcept { from_chars_result_t answer{}; answer.ptr = first; answer.ec = std::errc(); // be optimistic bool minusSign = false; if (*first == UC('-')) { // assume first < last, so dereference without checks; C++17 20.19.3.(7.1) explicitly forbids '+' here minusSign = true; ++first; } #ifdef FASTFLOAT_ALLOWS_LEADING_PLUS // disabled by default if (*first == UC('+')) { ++first; } #endif if (last - first >= 3) { if (fastfloat_strncasecmp(first, str_const_nan(), 3)) { answer.ptr = (first += 3); value = minusSign ? -std::numeric_limits::quiet_NaN() : std::numeric_limits::quiet_NaN(); // Check for possible nan(n-char-seq-opt), C++17 20.19.3.7, C11 7.20.1.3.3. At least MSVC produces nan(ind) and nan(snan). if(first != last && *first == UC('(')) { for(UC const * ptr = first + 1; ptr != last; ++ptr) { if (*ptr == UC(')')) { answer.ptr = ptr + 1; // valid nan(n-char-seq-opt) break; } else if(!((UC('a') <= *ptr && *ptr <= UC('z')) || (UC('A') <= *ptr && *ptr <= UC('Z')) || (UC('0') <= *ptr && *ptr <= UC('9')) || *ptr == UC('_'))) break; // forbidden char, not nan(n-char-seq-opt) } } return answer; } if (fastfloat_strncasecmp(first, str_const_inf(), 3)) { if ((last - first >= 8) && fastfloat_strncasecmp(first + 3, str_const_inf() + 3, 5)) { answer.ptr = first + 8; } else { answer.ptr = first + 3; } value = minusSign ? -std::numeric_limits::infinity() : std::numeric_limits::infinity(); return answer; } } answer.ec = std::errc::invalid_argument; return answer; } /** * Returns true if the floating-pointing rounding mode is to 'nearest'. * It is the default on most system. This function is meant to be inexpensive. * Credit : @mwalcott3 */ fastfloat_really_inline bool rounds_to_nearest() noexcept { // https://lemire.me/blog/2020/06/26/gcc-not-nearest/ #if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0) return false; #endif // See // A fast function to check your floating-point rounding mode // https://lemire.me/blog/2022/11/16/a-fast-function-to-check-your-floating-point-rounding-mode/ // // This function is meant to be equivalent to : // prior: #include // return fegetround() == FE_TONEAREST; // However, it is expected to be much faster than the fegetround() // function call. // // The volatile keywoard prevents the compiler from computing the function // at compile-time. // There might be other ways to prevent compile-time optimizations (e.g., asm). // The value does not need to be std::numeric_limits::min(), any small // value so that 1 + x should round to 1 would do (after accounting for excess // precision, as in 387 instructions). static volatile float fmin = std::numeric_limits::min(); float fmini = fmin; // we copy it so that it gets loaded at most once. // // Explanation: // Only when fegetround() == FE_TONEAREST do we have that // fmin + 1.0f == 1.0f - fmin. // // FE_UPWARD: // fmin + 1.0f > 1 // 1.0f - fmin == 1 // // FE_DOWNWARD or FE_TOWARDZERO: // fmin + 1.0f == 1 // 1.0f - fmin < 1 // // Note: This may fail to be accurate if fast-math has been // enabled, as rounding conventions may not apply. #ifdef FASTFLOAT_VISUAL_STUDIO # pragma warning(push) // todo: is there a VS warning? // see https://stackoverflow.com/questions/46079446/is-there-a-warning-for-floating-point-equality-checking-in-visual-studio-2013 #elif defined(__clang__) # pragma clang diagnostic push # pragma clang diagnostic ignored "-Wfloat-equal" #elif defined(__GNUC__) # pragma GCC diagnostic push # pragma GCC diagnostic ignored "-Wfloat-equal" #endif return (fmini + 1.0f == 1.0f - fmini); #ifdef FASTFLOAT_VISUAL_STUDIO # pragma warning(pop) #elif defined(__clang__) # pragma clang diagnostic pop #elif defined(__GNUC__) # pragma GCC diagnostic pop #endif } } // namespace detail template FASTFLOAT_CONSTEXPR20 from_chars_result_t from_chars(UC const * first, UC const * last, T &value, chars_format fmt /*= chars_format::general*/) noexcept { return from_chars_advanced(first, last, value, parse_options_t{fmt}); } template FASTFLOAT_CONSTEXPR20 from_chars_result_t from_chars_advanced(UC const * first, UC const * last, T &value, parse_options_t options) noexcept { static_assert (is_supported_float_type(), "only float and double are supported"); static_assert (is_supported_char_type(), "only char, wchar_t, char16_t and char32_t are supported"); from_chars_result_t answer; #ifdef FASTFLOAT_SKIP_WHITE_SPACE // disabled by default while ((first != last) && fast_float::is_space(uint8_t(*first))) { first++; } #endif if (first == last) { answer.ec = std::errc::invalid_argument; answer.ptr = first; return answer; } parsed_number_string_t pns = parse_number_string(first, last, options); if (!pns.valid) { if (options.format & chars_format::no_infnan) { answer.ec = std::errc::invalid_argument; answer.ptr = first; return answer; } else { return detail::parse_infnan(first, last, value); } } answer.ec = std::errc(); // be optimistic answer.ptr = pns.lastmatch; // The implementation of the Clinger's fast path is convoluted because // we want round-to-nearest in all cases, irrespective of the rounding mode // selected on the thread. // We proceed optimistically, assuming that detail::rounds_to_nearest() returns // true. if (binary_format::min_exponent_fast_path() <= pns.exponent && pns.exponent <= binary_format::max_exponent_fast_path() && !pns.too_many_digits) { // Unfortunately, the conventional Clinger's fast path is only possible // when the system rounds to the nearest float. // // We expect the next branch to almost always be selected. // We could check it first (before the previous branch), but // there might be performance advantages at having the check // be last. if(!cpp20_and_in_constexpr() && detail::rounds_to_nearest()) { // We have that fegetround() == FE_TONEAREST. // Next is Clinger's fast path. if (pns.mantissa <=binary_format::max_mantissa_fast_path()) { value = T(pns.mantissa); if (pns.exponent < 0) { value = value / binary_format::exact_power_of_ten(-pns.exponent); } else { value = value * binary_format::exact_power_of_ten(pns.exponent); } if (pns.negative) { value = -value; } return answer; } } else { // We do not have that fegetround() == FE_TONEAREST. // Next is a modified Clinger's fast path, inspired by Jakub Jelínek's proposal if (pns.exponent >= 0 && pns.mantissa <=binary_format::max_mantissa_fast_path(pns.exponent)) { #if defined(__clang__) || defined(FASTFLOAT_32BIT) // Clang may map 0 to -0.0 when fegetround() == FE_DOWNWARD if(pns.mantissa == 0) { value = pns.negative ? T(-0.) : T(0.); return answer; } #endif value = T(pns.mantissa) * binary_format::exact_power_of_ten(pns.exponent); if (pns.negative) { value = -value; } return answer; } } } adjusted_mantissa am = compute_float>(pns.exponent, pns.mantissa); if(pns.too_many_digits && am.power2 >= 0) { if(am != compute_float>(pns.exponent, pns.mantissa + 1)) { am = compute_error>(pns.exponent, pns.mantissa); } } // If we called compute_float>(pns.exponent, pns.mantissa) and we have an invalid power (am.power2 < 0), // then we need to go the long way around again. This is very uncommon. if(am.power2 < 0) { am = digit_comp(pns, am); } to_float(pns.negative, am, value); // Test for over/underflow. if ((pns.mantissa != 0 && am.mantissa == 0 && am.power2 == 0) || am.power2 == binary_format::infinite_power()) { answer.ec = std::errc::result_out_of_range; } return answer; } template FASTFLOAT_CONSTEXPR20 from_chars_result_t from_chars(UC const* first, UC const* last, T& value, int base) noexcept { static_assert (is_supported_char_type(), "only char, wchar_t, char16_t and char32_t are supported"); from_chars_result_t answer; #ifdef FASTFLOAT_SKIP_WHITE_SPACE // disabled by default while ((first != last) && fast_float::is_space(uint8_t(*first))) { first++; } #endif if (first == last || base < 2 || base > 36) { answer.ec = std::errc::invalid_argument; answer.ptr = first; return answer; } return parse_int_string(first, last, value, base); } } // namespace fast_float #endif