From c8aefe834239842de3a7dbb277f6f189d8ee546a Mon Sep 17 00:00:00 2001 From: Joao Paulo Magalhaes Date: Sat, 25 Mar 2023 19:45:07 +0000 Subject: [PATCH] [chore] update fast float --- src/c4/ext/fast_float | 2 +- src/c4/ext/fast_float_all.h | 1744 +++++++++++++++++++---------------- 2 files changed, 929 insertions(+), 817 deletions(-) diff --git a/src/c4/ext/fast_float b/src/c4/ext/fast_float index 02a61971..eb8c0012 160000 --- a/src/c4/ext/fast_float +++ b/src/c4/ext/fast_float @@ -1 +1 @@ -Subproject commit 02a61971f876c0c43e4c9ac9a07279d4e1b42fd6 +Subproject commit eb8c0012015f9404ecb8b767a57d2669032a890f diff --git a/src/c4/ext/fast_float_all.h b/src/c4/ext/fast_float_all.h index e401c175..095fbbb3 100644 --- a/src/c4/ext/fast_float_all.h +++ b/src/c4/ext/fast_float_all.h @@ -7,10 +7,7 @@ // with contributions from Neal Richardson // with contributions from Tim Paine // with contributions from Fabio Pellacini -// -// Licensed under the Apache License, Version 2.0, or the -// MIT License at your option. This file may not be copied, -// modified, or distributed except according to those terms. +// with contributions from Lénárd Szolnoki // // MIT License Notice // @@ -42,20 +39,6 @@ // 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 -// #ifndef FASTFLOAT_FAST_FLOAT_H #define FASTFLOAT_FAST_FLOAT_H @@ -129,6 +112,25 @@ from_chars_result from_chars_advanced(const char *first, const char *last, #include #include +#ifdef __has_include +#if __has_include() +#include +#endif +#endif + +#if __cpp_lib_bit_cast >= 201806L +#include +#define FASTFLOAT_HAS_BIT_CAST 1 +#else +#define FASTFLOAT_HAS_BIT_CAST 0 +#endif + +#if __cpp_lib_is_constant_evaluated >= 201811L +#define FASTFLOAT_HAS_IS_CONSTANT_EVALUATED 1 +#else +#define FASTFLOAT_HAS_IS_CONSTANT_EVALUATED 0 +#endif + #if (defined(__x86_64) || defined(__x86_64__) || defined(_M_X64) \ || defined(__amd64) || defined(__aarch64__) || defined(_M_ARM64) \ || defined(__MINGW64__) \ @@ -136,7 +138,7 @@ from_chars_result from_chars_advanced(const char *first, const char *last, || (defined(__ppc64__) || defined(__PPC64__) || defined(__ppc64le__) || defined(__PPC64LE__)) ) #define FASTFLOAT_64BIT 1 #elif (defined(__i386) || defined(__i386__) || defined(_M_IX86) \ - || defined(__arm__) || defined(_M_ARM) \ + || defined(__arm__) || defined(_M_ARM) || defined(__ppc__) \ || defined(__MINGW32__) || defined(__EMSCRIPTEN__)) #define FASTFLOAT_32BIT 1 #else @@ -172,7 +174,11 @@ from_chars_result from_chars_advanced(const char *first, const char *last, #elif defined(sun) || defined(__sun) #include #else +#ifdef __has_include +#if __has_include() #include +#endif //__has_include() +#endif //__has_include #endif # #ifndef __BYTE_ORDER__ @@ -199,22 +205,45 @@ from_chars_result from_chars_advanced(const char *first, const char *last, #endif #ifndef FASTFLOAT_ASSERT -#define FASTFLOAT_ASSERT(x) { if (!(x)) abort(); } +#define FASTFLOAT_ASSERT(x) { ((void)(x)); } #endif #ifndef FASTFLOAT_DEBUG_ASSERT -#include -#define FASTFLOAT_DEBUG_ASSERT(x) assert(x) +#define FASTFLOAT_DEBUG_ASSERT(x) { ((void)(x)); } #endif // rust style `try!()` macro, or `?` operator #define FASTFLOAT_TRY(x) { if (!(x)) return false; } +// Testing for https://wg21.link/N3652, adopted in C++14 +#if __cpp_constexpr >= 201304 +#define FASTFLOAT_CONSTEXPR14 constexpr +#else +#define FASTFLOAT_CONSTEXPR14 +#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 +#else +#define FASTFLOAT_CONSTEXPR20 +#endif + 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 +} + // Compares two ASCII strings in a case insensitive manner. -inline bool fastfloat_strncasecmp(const char *input1, const char *input2, - size_t length) { +inline FASTFLOAT_CONSTEXPR14 bool +fastfloat_strncasecmp(const char *input1, const char *input2, size_t length) { char running_diff{0}; for (size_t i = 0; i < length; i++) { running_diff |= (input1[i] ^ input2[i]); @@ -231,14 +260,14 @@ template struct span { const T* ptr; size_t length; - span(const T* _ptr, size_t _length) : ptr(_ptr), length(_length) {} - span() : ptr(nullptr), length(0) {} + 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; } - const T& operator[](size_t index) const noexcept { + FASTFLOAT_CONSTEXPR14 const T& operator[](size_t index) const noexcept { FASTFLOAT_DEBUG_ASSERT(index < length); return ptr[index]; } @@ -247,13 +276,31 @@ struct span { struct value128 { uint64_t low; uint64_t high; - value128(uint64_t _low, uint64_t _high) : low(_low), high(_high) {} - value128() : low(0), high(0) {} + constexpr value128(uint64_t _low, uint64_t _high) : low(_low), high(_high) {} + constexpr value128() : low(0), high(0) {} }; +/* Helper C++11 constexpr generic implementation of leading_zeroes */ +fastfloat_really_inline constexpr +int leading_zeroes_generic(uint64_t input_num, int last_bit = 0) { + return ( + ((input_num & uint64_t(0xffffffff00000000)) && (input_num >>= 32, last_bit |= 32)), + ((input_num & uint64_t( 0xffff0000)) && (input_num >>= 16, last_bit |= 16)), + ((input_num & uint64_t( 0xff00)) && (input_num >>= 8, last_bit |= 8)), + ((input_num & uint64_t( 0xf0)) && (input_num >>= 4, last_bit |= 4)), + ((input_num & uint64_t( 0xc)) && (input_num >>= 2, last_bit |= 2)), + ((input_num & uint64_t( 0x2)) && (input_num >>= 1, last_bit |= 1)), + 63 - last_bit + ); +} + /* result might be undefined when input_num is zero */ -fastfloat_really_inline int leading_zeroes(uint64_t input_num) { +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; @@ -262,31 +309,20 @@ fastfloat_really_inline int leading_zeroes(uint64_t input_num) { _BitScanReverse64(&leading_zero, input_num); return (int)(63 - leading_zero); #else - 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; + return leading_zeroes_generic(input_num); #endif #else return __builtin_clzll(input_num); #endif } -#ifdef FASTFLOAT_32BIT - // slow emulation routine for 32-bit -fastfloat_really_inline uint64_t emulu(uint32_t x, uint32_t y) { +fastfloat_really_inline constexpr uint64_t emulu(uint32_t x, uint32_t y) { return x * (uint64_t)y; } -// slow emulation routine for 32-bit -#if !defined(__MINGW64__) -fastfloat_really_inline uint64_t _umul128(uint64_t ab, uint64_t cd, - uint64_t *hi) { +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)); @@ -296,14 +332,28 @@ fastfloat_really_inline uint64_t _umul128(uint64_t ab, uint64_t cd, (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 value128 full_multiplication(uint64_t a, - uint64_t 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 @@ -317,7 +367,7 @@ fastfloat_really_inline value128 full_multiplication(uint64_t a, answer.low = uint64_t(r); answer.high = uint64_t(r >> 64); #else - #error Not implemented + answer.low = umul128_generic(a, b, &answer.high); #endif return answer; } @@ -326,10 +376,10 @@ struct adjusted_mantissa { uint64_t mantissa{0}; int32_t power2{0}; // a negative value indicates an invalid result adjusted_mantissa() = default; - bool operator==(const adjusted_mantissa &o) const { + constexpr bool operator==(const adjusted_mantissa &o) const { return mantissa == o.mantissa && power2 == o.power2; } - bool operator!=(const adjusted_mantissa &o) const { + constexpr bool operator!=(const adjusted_mantissa &o) const { return mantissa != o.mantissa || power2 != o.power2; } }; @@ -554,23 +604,41 @@ template <> inline constexpr binary_format::equiv_uint } template -fastfloat_really_inline void to_float(bool negative, adjusted_mantissa am, T &value) { - uint64_t word = am.mantissa; - word |= uint64_t(am.power2) << binary_format::mantissa_explicit_bits(); - word = negative - ? word | (uint64_t(1) << binary_format::sign_index()) : word; -#if FASTFLOAT_IS_BIG_ENDIAN == 1 - if (std::is_same::value) { - ::memcpy(&value, (char *)&word + 4, sizeof(T)); // extract value at offset 4-7 if float on big-endian - } else { - ::memcpy(&value, &word, sizeof(T)); - } +fastfloat_really_inline FASTFLOAT_CONSTEXPR20 +void to_float(bool negative, adjusted_mantissa am, T &value) { + using uint = typename binary_format::equiv_uint; + uint word = (uint)am.mantissa; + word |= uint(am.power2) << binary_format::mantissa_explicit_bits(); + word |= uint(negative) << binary_format::sign_index(); +#if FASTFLOAT_HAS_BIT_CAST + value = std::bit_cast(word); #else - // For little-endian systems: - ::memcpy(&value, &word, sizeof(T)); + ::memcpy(&value, &word, sizeof(T)); #endif } +#if 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 } // namespace fast_float #endif @@ -588,9 +656,11 @@ namespace fast_float { // Next function can be micro-optimized, but compilers are entirely // able to optimize it well. -fastfloat_really_inline bool is_integer(char c) noexcept { return c >= '0' && c <= '9'; } +fastfloat_really_inline constexpr bool is_integer(char c) noexcept { + return c >= '0' && c <= '9'; +} -fastfloat_really_inline uint64_t byteswap(uint64_t val) { +fastfloat_really_inline constexpr uint64_t byteswap(uint64_t val) { return (val & 0xFF00000000000000) >> 56 | (val & 0x00FF000000000000) >> 40 | (val & 0x0000FF0000000000) >> 24 @@ -620,7 +690,8 @@ fastfloat_really_inline void write_u64(uint8_t *chars, uint64_t val) { } // credit @aqrit -fastfloat_really_inline uint32_t parse_eight_digits_unrolled(uint64_t val) { +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) @@ -635,7 +706,7 @@ fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars) } // credit @aqrit -fastfloat_really_inline bool is_made_of_eight_digits_fast(uint64_t val) noexcept { +fastfloat_really_inline constexpr bool is_made_of_eight_digits_fast(uint64_t val) noexcept { return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) & 0x8080808080808080)); } @@ -669,7 +740,11 @@ parsed_number_string parse_number_string(const char *p, const char *pend, parse_ answer.valid = false; answer.too_many_digits = false; answer.negative = (*p == '-'); +#if FASTFLOAT_ALLOWS_LEADING_PLUS // disabled by default + if ((*p == '-') || (*p == '+')) { +#else if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here +#endif ++p; if (p == pend) { return answer; @@ -840,662 +915,663 @@ constexpr static int smallest_power_of_five = binary_format::smallest_po 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. -static const uint64_t power_of_five_128[number_of_entries]; +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, + 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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 -const uint64_t powers_template::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, - 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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,}; +constexpr uint64_t powers_template::power_of_five_128[number_of_entries]; + using powers = powers_template<>; } // namespace fast_float @@ -1565,7 +1641,7 @@ namespace detail { // create an adjusted mantissa, biased by the invalid power2 // for significant digits already multiplied by 10 ** q. template -fastfloat_really_inline +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; @@ -1619,16 +1695,11 @@ adjusted_mantissa compute_float(int64_t q, uint64_t w) noexcept { // 3. We might lose a bit due to the "upperbit" routine (result too small, requiring a shift) value128 product = compute_product_approximation(q, w); - if(product.low == 0xFFFFFFFFFFFFFFFF) { // could guard it further - // In some very rare cases, this could happen, in which case we might need a more accurate - // computation that what we can provide cheaply. This is very, very unlikely. - // - const bool inside_safe_exponent = (q >= -27) && (q <= 55); // always good because 5**q <2**128 when q>=0, - // and otherwise, for q<0, we have 5**-q<2**64 and the 128-bit reciprocal allows for exact computation. - if(!inside_safe_exponent) { - return compute_error_scaled(q, product.high, lz); - } - } + // 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 @@ -1746,27 +1817,27 @@ struct stackvec { stackvec &operator=(stackvec &&other) = delete; // create stack vector from existing limb span. - stackvec(limb_span s) { + FASTFLOAT_CONSTEXPR20 stackvec(limb_span s) { FASTFLOAT_ASSERT(try_extend(s)); } - limb& operator[](size_t index) noexcept { + FASTFLOAT_CONSTEXPR14 limb& operator[](size_t index) noexcept { FASTFLOAT_DEBUG_ASSERT(index < length); return data[index]; } - const limb& operator[](size_t index) const noexcept { + 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 - const limb& rindex(size_t index) const noexcept { + 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. - void set_len(size_t len) noexcept { + FASTFLOAT_CONSTEXPR14 void set_len(size_t len) noexcept { length = uint16_t(len); } constexpr size_t len() const noexcept { @@ -1779,12 +1850,12 @@ struct stackvec { return size; } // append item to vector, without bounds checking - void push_unchecked(limb value) noexcept { + FASTFLOAT_CONSTEXPR14 void push_unchecked(limb value) noexcept { data[length] = value; length++; } // append item to vector, returning if item was added - bool try_push(limb value) noexcept { + FASTFLOAT_CONSTEXPR14 bool try_push(limb value) noexcept { if (len() < capacity()) { push_unchecked(value); return true; @@ -1793,13 +1864,13 @@ struct stackvec { } } // add items to the vector, from a span, without bounds checking - void extend_unchecked(limb_span s) noexcept { + FASTFLOAT_CONSTEXPR20 void extend_unchecked(limb_span s) noexcept { limb* ptr = data + length; - ::memcpy((void*)ptr, (const void*)s.ptr, sizeof(limb) * s.len()); + 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 - bool try_extend(limb_span s) noexcept { + FASTFLOAT_CONSTEXPR20 bool try_extend(limb_span s) noexcept { if (len() + s.len() <= capacity()) { extend_unchecked(s); return true; @@ -1810,6 +1881,7 @@ struct stackvec { // 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(); @@ -1822,7 +1894,7 @@ struct stackvec { } } // try to resize the vector, returning if the vector was resized. - bool try_resize(size_t new_len, limb value) noexcept { + FASTFLOAT_CONSTEXPR20 bool try_resize(size_t new_len, limb value) noexcept { if (new_len > capacity()) { return false; } else { @@ -1833,7 +1905,7 @@ struct stackvec { // 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. - bool nonzero(size_t index) const noexcept { + FASTFLOAT_CONSTEXPR14 bool nonzero(size_t index) const noexcept { while (index < len()) { if (rindex(index) != 0) { return true; @@ -1843,27 +1915,27 @@ struct stackvec { return false; } // normalize the big integer, so most-significant zero limbs are removed. - void normalize() noexcept { + FASTFLOAT_CONSTEXPR14 void normalize() noexcept { while (len() > 0 && rindex(0) == 0) { length--; } } }; -fastfloat_really_inline +fastfloat_really_inline FASTFLOAT_CONSTEXPR14 uint64_t empty_hi64(bool& truncated) noexcept { truncated = false; return 0; } -fastfloat_really_inline +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_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) { @@ -1876,19 +1948,19 @@ uint64_t uint64_hi64(uint64_t r0, uint64_t r1, bool& truncated) noexcept { } } -fastfloat_really_inline +fastfloat_really_inline FASTFLOAT_CONSTEXPR20 uint64_t uint32_hi64(uint32_t r0, bool& truncated) noexcept { return uint64_hi64(r0, truncated); } -fastfloat_really_inline +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_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; @@ -1900,15 +1972,16 @@ uint64_t uint32_hi64(uint32_t r0, uint32_t r1, uint32_t r2, bool& truncated) noe // we want an efficient operation. for msvc, where // we don't have built-in intrinsics, this is still // pretty fast. -fastfloat_really_inline +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) - overflow = __builtin_add_overflow(x, y, &z); - return z; + if (!cpp20_and_in_constexpr()) { + overflow = __builtin_add_overflow(x, y, &z); + return z; + } #endif #endif @@ -1919,7 +1992,7 @@ limb scalar_add(limb x, limb y, bool& overflow) noexcept { } // multiply two small integers, getting both the high and low bits. -fastfloat_really_inline +fastfloat_really_inline FASTFLOAT_CONSTEXPR20 limb scalar_mul(limb x, limb y, limb& carry) noexcept { #ifdef FASTFLOAT_64BIT_LIMB #if defined(__SIZEOF_INT128__) @@ -1947,7 +2020,8 @@ limb scalar_mul(limb x, limb y, limb& carry) noexcept { // add scalar value to bigint starting from offset. // used in grade school multiplication template -inline bool small_add_from(stackvec& vec, limb y, size_t start) noexcept { +inline FASTFLOAT_CONSTEXPR20 +bool small_add_from(stackvec& vec, limb y, size_t start) noexcept { size_t index = start; limb carry = y; bool overflow; @@ -1964,13 +2038,15 @@ inline bool small_add_from(stackvec& vec, limb y, size_t start) noexcept { // add scalar value to bigint. template -fastfloat_really_inline bool small_add(stackvec& vec, limb y) noexcept { +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 bool small_mul(stackvec& vec, limb y) noexcept { +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); @@ -1984,6 +2060,7 @@ inline bool small_mul(stackvec& vec, limb y) noexcept { // 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. @@ -2014,12 +2091,14 @@ bool large_add_from(stackvec& x, limb_span y, size_t start) noexcept { // add bigint to bigint. template -fastfloat_really_inline bool large_add_from(stackvec& x, limb_span y) noexcept { +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); @@ -2048,6 +2127,7 @@ bool long_mul(stackvec& x, limb_span y) noexcept { // 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])); @@ -2057,21 +2137,52 @@ bool large_mul(stackvec& x, limb_span y) noexcept { 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 { +struct bigint : pow5_tables<> { // storage of the limbs, in little-endian order. stackvec vec; - bigint(): vec() {} + FASTFLOAT_CONSTEXPR20 bigint(): vec() {} bigint(const bigint &) = delete; bigint &operator=(const bigint &) = delete; bigint(bigint &&) = delete; bigint &operator=(bigint &&other) = delete; - bigint(uint64_t value): vec() { + FASTFLOAT_CONSTEXPR20 bigint(uint64_t value): vec() { #ifdef FASTFLOAT_64BIT_LIMB vec.push_unchecked(value); #else @@ -2083,7 +2194,7 @@ struct bigint { // get the high 64 bits from the vector, and if bits were truncated. // this is to get the significant digits for the float. - uint64_t hi64(bool& truncated) const noexcept { + FASTFLOAT_CONSTEXPR20 uint64_t hi64(bool& truncated) const noexcept { #ifdef FASTFLOAT_64BIT_LIMB if (vec.len() == 0) { return empty_hi64(truncated); @@ -2115,7 +2226,7 @@ struct bigint { // 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. - int compare(const bigint& other) const noexcept { + FASTFLOAT_CONSTEXPR20 int compare(const bigint& other) const noexcept { if (vec.len() > other.vec.len()) { return 1; } else if (vec.len() < other.vec.len()) { @@ -2136,7 +2247,7 @@ struct bigint { // shift left each limb n bits, carrying over to the new limb // returns true if we were able to shift all the digits. - bool shl_bits(size_t n) noexcept { + 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: @@ -2162,7 +2273,7 @@ struct bigint { } // move the limbs left by `n` limbs. - bool shl_limbs(size_t n) noexcept { + FASTFLOAT_CONSTEXPR20 bool shl_limbs(size_t n) noexcept { FASTFLOAT_DEBUG_ASSERT(n != 0); if (n + vec.len() > vec.capacity()) { return false; @@ -2183,7 +2294,7 @@ struct bigint { } // move the limbs left by `n` bits. - bool shl(size_t n) noexcept { + FASTFLOAT_CONSTEXPR20 bool shl(size_t n) noexcept { size_t rem = n % limb_bits; size_t div = n / limb_bits; if (rem != 0) { @@ -2196,7 +2307,7 @@ struct bigint { } // get the number of leading zeros in the bigint. - int ctlz() const noexcept { + FASTFLOAT_CONSTEXPR20 int ctlz() const noexcept { if (vec.is_empty()) { return 0; } else { @@ -2211,45 +2322,27 @@ struct bigint { } // get the number of bits in the bigint. - int bit_length() const noexcept { + FASTFLOAT_CONSTEXPR20 int bit_length() const noexcept { int lz = ctlz(); return int(limb_bits * vec.len()) - lz; } - bool mul(limb y) noexcept { + FASTFLOAT_CONSTEXPR20 bool mul(limb y) noexcept { return small_mul(vec, y); } - bool add(limb y) noexcept { + FASTFLOAT_CONSTEXPR20 bool add(limb y) noexcept { return small_add(vec, y); } // multiply as if by 2 raised to a power. - bool pow2(uint32_t exp) noexcept { + FASTFLOAT_CONSTEXPR20 bool pow2(uint32_t exp) noexcept { return shl(exp); } // multiply as if by 5 raised to a power. - bool pow5(uint32_t exp) noexcept { + FASTFLOAT_CONSTEXPR20 bool pow5(uint32_t exp) noexcept { // multiply by a power of 5 - 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 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) { @@ -2275,7 +2368,7 @@ struct bigint { } // multiply as if by 10 raised to a power. - bool pow10(uint32_t exp) noexcept { + FASTFLOAT_CONSTEXPR20 bool pow10(uint32_t exp) noexcept { FASTFLOAT_TRY(pow5(exp)); return pow2(exp); } @@ -2298,9 +2391,11 @@ namespace fast_float { // Next function can be micro-optimized, but compilers are entirely // able to optimize it well. -fastfloat_really_inline bool is_integer(char c) noexcept { return c >= '0' && c <= '9'; } +fastfloat_really_inline constexpr bool is_integer(char c) noexcept { + return c >= '0' && c <= '9'; +} -fastfloat_really_inline uint64_t byteswap(uint64_t val) { +fastfloat_really_inline constexpr uint64_t byteswap(uint64_t val) { return (val & 0xFF00000000000000) >> 56 | (val & 0x00FF000000000000) >> 40 | (val & 0x0000FF0000000000) >> 24 @@ -2330,7 +2425,8 @@ fastfloat_really_inline void write_u64(uint8_t *chars, uint64_t val) { } // credit @aqrit -fastfloat_really_inline uint32_t parse_eight_digits_unrolled(uint64_t val) { +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) @@ -2345,7 +2441,7 @@ fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars) } // credit @aqrit -fastfloat_really_inline bool is_made_of_eight_digits_fast(uint64_t val) noexcept { +fastfloat_really_inline constexpr bool is_made_of_eight_digits_fast(uint64_t val) noexcept { return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) & 0x8080808080808080)); } @@ -2379,7 +2475,11 @@ parsed_number_string parse_number_string(const char *p, const char *pend, parse_ answer.valid = false; answer.too_many_digits = false; answer.negative = (*p == '-'); +#if FASTFLOAT_ALLOWS_LEADING_PLUS // disabled by default + if ((*p == '-') || (*p == '+')) { +#else if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here +#endif ++p; if (p == pend) { return answer; @@ -2534,7 +2634,8 @@ constexpr static uint64_t powers_of_ten_uint64[] = { // 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. -fastfloat_really_inline int32_t scientific_exponent(parsed_number_string& num) noexcept { +fastfloat_really_inline FASTFLOAT_CONSTEXPR14 +int32_t scientific_exponent(parsed_number_string& num) noexcept { uint64_t mantissa = num.mantissa; int32_t exponent = int32_t(num.exponent); while (mantissa >= 10000) { @@ -2592,7 +2693,8 @@ fastfloat_really_inline adjusted_mantissa to_extended_halfway(T value) noexcept // round an extended-precision float to the nearest machine float. template -fastfloat_really_inline void round(adjusted_mantissa& am, callback cb) noexcept { +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 @@ -2621,20 +2723,16 @@ fastfloat_really_inline void round(adjusted_mantissa& am, callback cb) noexcept } template -fastfloat_really_inline +fastfloat_really_inline FASTFLOAT_CONSTEXPR14 void round_nearest_tie_even(adjusted_mantissa& am, int32_t shift, callback cb) noexcept { - uint64_t mask; - uint64_t halfway; - if (shift == 64) { - mask = UINT64_MAX; - } else { - mask = (uint64_t(1) << shift) - 1; - } - if (shift == 0) { - halfway = 0; - } else { - halfway = uint64_t(1) << (shift - 1); - } + 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; @@ -2651,7 +2749,8 @@ void round_nearest_tie_even(adjusted_mantissa& am, int32_t shift, callback cb) n am.mantissa += uint64_t(cb(is_odd, is_halfway, is_above)); } -fastfloat_really_inline void round_down(adjusted_mantissa& am, int32_t shift) noexcept { +fastfloat_really_inline FASTFLOAT_CONSTEXPR14 +void round_down(adjusted_mantissa& am, int32_t shift) noexcept { if (shift == 64) { am.mantissa = 0; } else { @@ -2710,7 +2809,7 @@ void parse_eight_digits(const char*& p, limb& value, size_t& counter, size_t& co count += 8; } -fastfloat_really_inline +fastfloat_really_inline FASTFLOAT_CONSTEXPR14 void parse_one_digit(const char*& p, limb& value, size_t& counter, size_t& count) noexcept { value = value * 10 + limb(*p - '0'); p++; @@ -2945,6 +3044,11 @@ from_chars_result parse_infnan(const char *first, const char *last, T &value) n minusSign = true; ++first; } +#if FASTFLOAT_ALLOWS_LEADING_PLUS // disabled by default + if (*first == '+') { + ++first; + } +#endif if (last - first >= 3) { if (fastfloat_strncasecmp(first, "nan", 3)) { answer.ptr = (first += 3); @@ -2982,6 +3086,10 @@ from_chars_result parse_infnan(const char *first, const char *last, T &value) n * 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/ @@ -3015,7 +3123,7 @@ fastfloat_really_inline bool rounds_to_nearest() noexcept { // // Note: This may fail to be accurate if fast-math has been // enabled, as rounding conventions may not apply. - #ifdef _MSC_VER + #if 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 @@ -3027,7 +3135,7 @@ fastfloat_really_inline bool rounds_to_nearest() noexcept { # pragma GCC diagnostic ignored "-Wfloat-equal" #endif return (fmini + 1.0f == 1.0f - fmini); - #ifdef _MSC_VER + #if FASTFLOAT_VISUAL_STUDIO # pragma warning(pop) #elif defined(__clang__) # pragma clang diagnostic pop @@ -3052,6 +3160,11 @@ from_chars_result from_chars_advanced(const char *first, const char *last, from_chars_result answer; +#if 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; @@ -3119,4 +3232,3 @@ from_chars_result from_chars_advanced(const char *first, const char *last, } // namespace fast_float #endif -