diff --git a/src/ascii-parser-basetype.cc b/src/ascii-parser-basetype.cc index cb0b79d55..fd250f4da 100644 --- a/src/ascii-parser-basetype.cc +++ b/src/ascii-parser-basetype.cc @@ -142,6 +142,7 @@ int parseInt(const std::string &s, int *out_result) { } nonstd::expected ParseFloat(const std::string &s) { + // Parse with fast_float float result; auto ans = fast_float::from_chars(s.data(), s.data() + s.size(), result); @@ -154,6 +155,7 @@ nonstd::expected ParseFloat(const std::string &s) { } nonstd::expected ParseDouble(const std::string &s) { + // Parse with fast_float double result; auto ans = fast_float::from_chars(s.data(), s.data() + s.size(), result); diff --git a/src/ascii-parser.cc b/src/ascii-parser.cc index 0b14918b6..27c5d5f44 100644 --- a/src/ascii-parser.cc +++ b/src/ascii-parser.cc @@ -2597,10 +2597,9 @@ bool AsciiParser::LexFloat(std::string *result) { } _curr_cursor.col++; - ss << sc; - // sign, '.' or [0-9] if ((sc == '+') || (sc == '-')) { + ss << sc; has_sign = true; char c; @@ -2621,9 +2620,14 @@ bool AsciiParser::LexFloat(std::string *result) { } else if ((sc >= '0') && (sc <= '9')) { // ok + ss << sc; } else if (sc == '.') { - // ok + // ok but rescan again in 2. leading_decimal_dots = true; + if (!Rewind(1)) { + return false; + } + _curr_cursor.col--; } else { PUSH_ERROR_AND_RETURN("Sign or `.` or 0-9 expected."); } @@ -2689,6 +2693,7 @@ bool AsciiParser::LexFloat(std::string *result) { return true; } + if (Eof()) { (*result) = ss.str(); return true; @@ -3852,6 +3857,21 @@ bool AsciiParser::ParsePrimProps(std::map *props, std::ve &attr)) { return false; } + } else if (type_name == value::kQuath) { + if (!ParseBasicPrimAttr(array_qual, primattr_name, + &attr)) { + return false; + } + } else if (type_name == value::kQuatf) { + if (!ParseBasicPrimAttr(array_qual, primattr_name, + &attr)) { + return false; + } + } else if (type_name == value::kQuatd) { + if (!ParseBasicPrimAttr(array_qual, primattr_name, + &attr)) { + return false; + } } else if (type_name == value::kPoint3f) { if (!ParseBasicPrimAttr(array_qual, primattr_name, &attr)) { diff --git a/src/external/fast_float/LICENSE-BOOST b/src/external/fast_float/LICENSE-BOOST new file mode 100644 index 000000000..127a5bc39 --- /dev/null +++ b/src/external/fast_float/LICENSE-BOOST @@ -0,0 +1,23 @@ +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. \ No newline at end of file diff --git a/src/external/fast_float/README.md b/src/external/fast_float/README.md index 63379935c..f12dea551 100644 --- a/src/external/fast_float/README.md +++ b/src/external/fast_float/README.md @@ -1,4 +1,8 @@ + ## fast_float number parsing library: 4x faster than strtod +[![Fuzzing Status](https://oss-fuzz-build-logs.storage.googleapis.com/badges/fast_float.svg)](https://bugs.chromium.org/p/oss-fuzz/issues/list?sort=-opened&can=1&q=proj:fast_float) +[![VS17-CI](https://github.com/fastfloat/fast_float/actions/workflows/vs17-ci.yml/badge.svg)](https://github.com/fastfloat/fast_float/actions/workflows/vs17-ci.yml) +[![Ubuntu 22.04 CI (GCC 11)](https://github.com/fastfloat/fast_float/actions/workflows/ubuntu22.yml/badge.svg)](https://github.com/fastfloat/fast_float/actions/workflows/ubuntu22.yml) The fast_float library provides fast header-only implementations for the C++ from_chars functions for `float` and `double` types. These functions convert ASCII strings representing @@ -21,8 +25,8 @@ struct from_chars_result { ``` It parses the character sequence [first,last) for a number. It parses floating-point numbers expecting -a locale-independent format equivalent to the C++17 from_chars function. -The resulting floating-point value is the closest floating-point values (using either float or double), +a locale-independent format equivalent to the C++17 from_chars function. +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. @@ -40,7 +44,7 @@ Example: ``` C++ #include "fast_float/fast_float.h" #include - + int main() { const std::string input = "3.1416 xyz "; double result; @@ -53,39 +57,78 @@ int main() { 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 +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`. -The library seeks to follow the C++17 (see [20.19.3](http://eel.is/c++draft/charconv.from.chars).(7.1)) specification. +The library seeks to follow the C++17 (see [20.19.3](http://eel.is/c++draft/charconv.from.chars).(7.1)) specification. * The `from_chars` function does not skip leading white-space characters. * [A leading `+` sign](https://en.cppreference.com/w/cpp/utility/from_chars) is forbidden. -* It is generally impossible to represent a decimal value exactly as binary floating-point number (`float` and `double` types). We seek the nearest value. We round to an even mantissa when we are in-between two binary floating-point numbers. +* It is generally impossible to represent a decimal value exactly as binary floating-point number (`float` and `double` types). We seek the nearest value. We round to an even mantissa when we are in-between two binary floating-point numbers. Furthermore, we have the following restrictions: * We only support `float` and `double` types at this time. * We only support the decimal format: we do not support hexadecimal strings. -* For values that are either very large or very small (e.g., `1e9999`), we represent it using the infinity or negative infinity value. +* For values that are either very large or very small (e.g., `1e9999`), we represent it using the infinity or negative infinity value and the returned `ec` is set to `std::errc::result_out_of_range`. We support Visual Studio, macOS, Linux, freeBSD. We support big and little endian. We support 32-bit and 64-bit systems. +We assume that the rounding mode is set to nearest (`std::fegetround() == FE_TONEAREST`). + +## C++20: compile-time evaluation (constexpr) + +In C++20, you may use `fast_float::from_chars` to parse strings +at compile-time, as in the following example: + +```C++ +// consteval forces compile-time evaluation of the function in C++20. +consteval double parse(std::string_view input) { + double result; + auto answer = fast_float::from_chars(input.data(), input.data()+input.size(), result); + if(answer.ec != std::errc()) { return -1.0; } + return result; +} + +// This function should compile to a function which +// merely returns 3.1415. +constexpr double constexptest() { + return parse("3.1415 input"); +} +``` + +## Non-ASCII Inputs +We also support UTF-16 and UTF-32 inputs, as well as ASCII/UTF-8, as in the following example: + +``` C++ +#include "fast_float/fast_float.h" +#include + +int main() { + const std::u16string input = u"3.1416 xyz "; + double result; + auto answer = fast_float::from_chars(input.data(), input.data()+input.size(), result); + if(answer.ec != std::errc()) { std::cerr << "parsing failure\n"; return EXIT_FAILURE; } + std::cout << "parsed the number " << result << std::endl; + return EXIT_SUCCESS; +} +``` ## Using commas as decimal separator The C++ standard stipulate that `from_chars` has to be locale-independent. In -particular, the decimal separator has to be the period (`.`). However, -some users still want to use the `fast_float` library with in a locale-dependent +particular, the decimal separator has to be the period (`.`). However, +some users still want to use the `fast_float` library with in a locale-dependent manner. Using a separate function called `from_chars_advanced`, we allow the users -to pass a `parse_options` instance which contains a custom decimal separator (e.g., +to pass a `parse_options` instance which contains a custom decimal separator (e.g., the comma). You may use it as follows. ```C++ #include "fast_float/fast_float.h" #include - + int main() { const std::string input = "3,1416 xyz "; double result; @@ -97,28 +140,61 @@ int main() { } ``` +You can parse delimited numbers: +```C++ + const std::string input = "234532.3426362,7869234.9823,324562.645"; + double result; + auto answer = fast_float::from_chars(input.data(), input.data()+input.size(), result); + if(answer.ec != std::errc()) { + // check error + } + // we have result == 234532.3426362. + if(answer.ptr[0] != ',') { + // unexpected delimiter + } + answer = fast_float::from_chars(answer.ptr + 1, input.data()+input.size(), result); + if(answer.ec != std::errc()) { + // check error + } + // we have result == 7869234.9823. + if(answer.ptr[0] != ',') { + // unexpected delimiter + } + answer = fast_float::from_chars(answer.ptr + 1, input.data()+input.size(), result); + if(answer.ec != std::errc()) { + // check error + } + // we have result == 324562.645. +``` -## Reference -- Daniel Lemire, [Number Parsing at a Gigabyte per Second](https://arxiv.org/abs/2101.11408), Software: Pratice and Experience 51 (8), 2021. +## Relation With Other Work -## Other programming languages +The fast_float library is part of: -- [There is an R binding](https://github.com/eddelbuettel/rcppfastfloat) called `rcppfastfloat`. -- [There is a Rust port of the fast_float library](https://github.com/aldanor/fast-float-rust/) called `fast-float-rust`. -- [There is a Java port of the fast_float library](https://github.com/wrandelshofer/FastDoubleParser) called `FastDoubleParser`. -- [There is a C# port of the fast_float library](https://github.com/CarlVerret/csFastFloat) called `csFastFloat`. +- GCC (as of version 12): the `from_chars` function in GCC relies on fast_float. +- [WebKit](https://github.com/WebKit/WebKit), the engine behind Safari (Apple's web browser) -## Relation With Other Work +The fastfloat algorithm is part of the [LLVM standard libraries](https://github.com/llvm/llvm-project/commit/87c016078ad72c46505461e4ff8bfa04819fe7ba). -The fast_float library is part of GCC (as of version 12): the `from_chars` function in GCC relies on fast_float. +There is a [derived implementation part of AdaCore](https://github.com/AdaCore/VSS). -The fastfloat algorithm is part of the [LLVM standard libraries](https://github.com/llvm/llvm-project/commit/87c016078ad72c46505461e4ff8bfa04819fe7ba). The fast_float library provides a performance similar to that of the [fast_double_parser](https://github.com/lemire/fast_double_parser) library but using an updated algorithm reworked from the ground up, and while offering an API more in line with the expectations of C++ programmers. The fast_double_parser library is part of the [Microsoft LightGBM machine-learning framework](https://github.com/microsoft/LightGBM). -There is a [derived implementation part of AdaCore](https://github.com/AdaCore/VSS). +## References + +- Daniel Lemire, [Number Parsing at a Gigabyte per Second](https://arxiv.org/abs/2101.11408), Software: Practice and Experience 51 (8), 2021. +- Noble Mushtak, Daniel Lemire, [Fast Number Parsing Without Fallback](https://arxiv.org/abs/2212.06644), Software: Practice and Experience 53 (7), 2023. + +## Other programming languages + +- [There is an R binding](https://github.com/eddelbuettel/rcppfastfloat) called `rcppfastfloat`. +- [There is a Rust port of the fast_float library](https://github.com/aldanor/fast-float-rust/) called `fast-float-rust`. +- [There is a Java port of the fast_float library](https://github.com/wrandelshofer/FastDoubleParser) called `FastDoubleParser`. It used for important systems such as [Jackson](https://github.com/FasterXML/jackson-core). +- [There is a C# port of the fast_float library](https://github.com/CarlVerret/csFastFloat) called `csFastFloat`. + ## Users @@ -132,14 +208,14 @@ It can parse random floating-point numbers at a speed of 1 GB/s on some systems. ``` -$ ./build/benchmarks/benchmark +$ ./build/benchmarks/benchmark # parsing random integers in the range [0,1) -volume = 2.09808 MB -netlib : 271.18 MB/s (+/- 1.2 %) 12.93 Mfloat/s -doubleconversion : 225.35 MB/s (+/- 1.2 %) 10.74 Mfloat/s -strtod : 190.94 MB/s (+/- 1.6 %) 9.10 Mfloat/s -abseil : 430.45 MB/s (+/- 2.2 %) 20.52 Mfloat/s -fastfloat : 1042.38 MB/s (+/- 9.9 %) 49.68 Mfloat/s +volume = 2.09808 MB +netlib : 271.18 MB/s (+/- 1.2 %) 12.93 Mfloat/s +doubleconversion : 225.35 MB/s (+/- 1.2 %) 10.74 Mfloat/s +strtod : 190.94 MB/s (+/- 1.6 %) 9.10 Mfloat/s +abseil : 430.45 MB/s (+/- 2.2 %) 20.52 Mfloat/s +fastfloat : 1042.38 MB/s (+/- 9.9 %) 49.68 Mfloat/s ``` See https://github.com/lemire/simple_fastfloat_benchmark for our benchmarking code. @@ -180,30 +256,30 @@ You should change the `GIT_TAG` line so that you recover the version you wish to ## Using as single header -The script `script/amalgamate.py` may be used to generate a single header +The script `script/amalgamate.py` may be used to generate a single header version of the library if so desired. -Just run the script from the root directory of this repository. +Just run the script from the root directory of this repository. You can customize the license type and output file if desired as described in the command line help. You may directly download automatically generated single-header files: -https://github.com/fastfloat/fast_float/releases/download/v3.4.0/fast_float.h +https://github.com/fastfloat/fast_float/releases/download/v5.2.0/fast_float.h ## Credit -Though this work is inspired by many different people, this work benefited especially from exchanges with -Michael Eisel, who motivated the original research with his key insights, and with Nigel Tao who provided +Though this work is inspired by many different people, this work benefited especially from exchanges with +Michael Eisel, who motivated the original research with his key insights, and with Nigel Tao who provided invaluable feedback. Rémy Oudompheng first implemented a fast path we use in the case of long digits. -The library includes code adapted from Google Wuffs (written by Nigel Tao) which was originally published +The library includes code adapted from Google Wuffs (written by Nigel Tao) which was originally published under the Apache 2.0 license. ## License Licensed under either of Apache License, Version -2.0 or MIT license at your option. +2.0 or MIT license or BOOST license .
@@ -211,5 +287,5 @@ Licensed under either of Apache License, Version Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in this repository by you, as defined in the Apache-2.0 license, -shall be dual licensed as above, without any additional terms or conditions. +shall be triple licensed as above, without any additional terms or conditions. diff --git a/src/external/fast_float/include/fast_float/ascii_number.h b/src/external/fast_float/include/fast_float/ascii_number.h index 3e6bb3e9e..9afcdc4ec 100644 --- a/src/external/fast_float/include/fast_float/ascii_number.h +++ b/src/external/fast_float/include/fast_float/ascii_number.h @@ -5,16 +5,37 @@ #include #include #include +#include #include "float_common.h" +#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. -fastfloat_really_inline bool is_integer(char c) noexcept { return c >= '0' && c <= '9'; } +template +fastfloat_really_inline constexpr bool is_integer(UC c) noexcept { + return !(c > UC('9') || c < UC('0')); +} -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 @@ -25,7 +46,18 @@ fastfloat_really_inline uint64_t byteswap(uint64_t val) { | (val & 0x00000000000000FF) << 56; } -fastfloat_really_inline uint64_t read_u64(const char *chars) { +// 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 @@ -35,7 +67,72 @@ fastfloat_really_inline uint64_t read_u64(const char *chars) { return val; } -fastfloat_really_inline void write_u64(uint8_t *chars, uint64_t 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 ())> +#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); @@ -44,7 +141,8 @@ 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) @@ -54,46 +152,138 @@ fastfloat_really_inline uint32_t parse_eight_digits_unrolled(uint64_t val) { return uint32_t(val); } -fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars) noexcept { - return parse_eight_digits_unrolled(read_u64(chars)); + +// 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 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)); } -fastfloat_really_inline bool is_made_of_eight_digits_fast(const char *chars) noexcept { - return is_made_of_eight_digits_fast(read_u64(chars)); + +#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 ())> +#endif +// dummy for compile +bool simd_parse_if_eight_digits_unrolled(UC const*, uint64_t&) { + return 0; } -typedef span byte_span; -struct parsed_number_string { +template ::value)> +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}; - const char *lastmatch{nullptr}; + UC const * lastmatch{nullptr}; bool negative{false}; bool valid{false}; bool too_many_digits{false}; // contains the range of the significant digits - byte_span integer{}; // non-nullable - byte_span fraction{}; // nullable + 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. -fastfloat_really_inline -parsed_number_string parse_number_string(const char *p, const char *pend, parse_options options) noexcept { - const chars_format fmt = options.format; - const char decimal_point = options.decimal_point; +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 answer; + parsed_number_string_t answer; answer.valid = false; answer.too_many_digits = false; - answer.negative = (*p == '-'); - if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here + answer.negative = (*p == UC('-')); +#ifdef FASTFLOAT_ALLOWS_LEADING_PLUS // disabled by default + if ((*p == UC('-')) || (*p == UC('+'))) { +#else + if (*p == UC('-')) { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here +#endif ++p; if (p == pend) { return answer; @@ -102,41 +292,35 @@ parsed_number_string parse_number_string(const char *p, const char *pend, parse_ return answer; } } - const char *const start_digits = p; + UC const * const start_digits = p; uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad) - while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(p)) { - i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok - p += 8; - } while ((p != pend) && is_integer(*p)) { // a multiplication by 10 is cheaper than an arbitrary integer // multiplication i = 10 * i + - uint64_t(*p - '0'); // might overflow, we will handle the overflow later + uint64_t(*p - UC('0')); // might overflow, we will handle the overflow later ++p; } - const char *const end_of_integer_part = p; + UC const * const end_of_integer_part = p; int64_t digit_count = int64_t(end_of_integer_part - start_digits); - answer.integer = byte_span(start_digits, size_t(digit_count)); + answer.integer = span(start_digits, size_t(digit_count)); int64_t exponent = 0; if ((p != pend) && (*p == decimal_point)) { ++p; - const char* before = 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. - while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(p)) { - i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok - p += 8; - } + loop_parse_if_eight_digits(p, pend, i); + while ((p != pend) && is_integer(*p)) { - uint8_t digit = uint8_t(*p - '0'); + 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 = byte_span(before, size_t(p - before)); + answer.fraction = span(before, size_t(p - before)); digit_count -= exponent; } // we must have encountered at least one integer! @@ -144,14 +328,14 @@ parsed_number_string parse_number_string(const char *p, const char *pend, parse_ return answer; } int64_t exp_number = 0; // explicit exponential part - if ((fmt & chars_format::scientific) && (p != pend) && (('e' == *p) || ('E' == *p))) { - const char * location_of_e = p; + if ((fmt & chars_format::scientific) && (p != pend) && ((UC('e') == *p) || (UC('E') == *p))) { + UC const * location_of_e = p; ++p; bool neg_exp = false; - if ((p != pend) && ('-' == *p)) { + if ((p != pend) && (UC('-') == *p)) { neg_exp = true; ++p; - } else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1) + } 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)) { @@ -163,7 +347,7 @@ parsed_number_string parse_number_string(const char *p, const char *pend, parse_ p = location_of_e; } else { while ((p != pend) && is_integer(*p)) { - uint8_t digit = uint8_t(*p - '0'); + uint8_t digit = uint8_t(*p - UC('0')); if (exp_number < 0x10000000) { exp_number = 10 * exp_number + digit; } @@ -189,11 +373,12 @@ parsed_number_string parse_number_string(const char *p, const char *pend, parse_ // 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. - const char *start = start_digits; - while ((start != pend) && (*start == '0' || *start == decimal_point)) { - if(*start == '0') { digit_count --; } + 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. @@ -201,22 +386,23 @@ parsed_number_string parse_number_string(const char *p, const char *pend, parse_ // pre-tokenized spans from above. i = 0; p = answer.integer.ptr; - const char* 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 - '0'); + 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; - const char* frac_end = p + answer.fraction.len(); - while((i < minimal_nineteen_digit_integer) && (p != frac_end)) { - i = i * 10 + uint64_t(*p - '0'); - ++p; - } - exponent = answer.fraction.ptr - 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 } diff --git a/src/external/fast_float/include/fast_float/bigint.h b/src/external/fast_float/include/fast_float/bigint.h index b56cb9b03..5076b47cc 100644 --- a/src/external/fast_float/include/fast_float/bigint.h +++ b/src/external/fast_float/include/fast_float/bigint.h @@ -17,7 +17,7 @@ namespace fast_float { // 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 +#define FASTFLOAT_64BIT_LIMB 1 typedef uint64_t limb; constexpr size_t limb_bits = 64; #else @@ -50,27 +50,27 @@ 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 { @@ -83,12 +83,12 @@ 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; @@ -97,13 +97,13 @@ 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; @@ -114,6 +114,7 @@ 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(); @@ -126,7 +127,7 @@ 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 { @@ -137,7 +138,7 @@ 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; @@ -147,27 +148,27 @@ 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) { @@ -180,19 +181,19 @@ 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; @@ -204,15 +205,16 @@ 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 @@ -223,7 +225,7 @@ 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__) @@ -251,7 +253,8 @@ 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; @@ -268,13 +271,15 @@ 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); @@ -288,6 +293,7 @@ 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. @@ -318,12 +324,14 @@ 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); @@ -352,6 +360,7 @@ 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])); @@ -361,21 +370,52 @@ 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 @@ -387,7 +427,7 @@ 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); @@ -419,7 +459,7 @@ 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()) { @@ -440,7 +480,7 @@ 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: @@ -466,7 +506,7 @@ 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; @@ -474,7 +514,7 @@ struct bigint { // move limbs limb* dst = vec.data + n; const limb* src = vec.data; - ::memmove(dst, src, sizeof(limb) * vec.len()); + std::copy_backward(src, src + vec.len(), dst + vec.len()); // fill in empty limbs limb* first = vec.data; limb* last = first + n; @@ -487,7 +527,7 @@ 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) { @@ -500,7 +540,7 @@ 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 { @@ -515,45 +555,27 @@ 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) { @@ -572,14 +594,19 @@ struct bigint { exp -= small_step; } if (exp != 0) { - FASTFLOAT_TRY(small_mul(vec, limb(small_power_of_5[exp]))); + // 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. - bool pow10(uint32_t exp) noexcept { + FASTFLOAT_CONSTEXPR20 bool pow10(uint32_t exp) noexcept { FASTFLOAT_TRY(pow5(exp)); return pow2(exp); } diff --git a/src/external/fast_float/include/fast_float/constexpr_feature_detect.h b/src/external/fast_float/include/fast_float/constexpr_feature_detect.h new file mode 100644 index 000000000..ba8b65c64 --- /dev/null +++ b/src/external/fast_float/include/fast_float/constexpr_feature_detect.h @@ -0,0 +1,40 @@ +#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 diff --git a/src/external/fast_float/include/fast_float/decimal_to_binary.h b/src/external/fast_float/include/fast_float/decimal_to_binary.h index 6da6c66a3..fec916f3a 100644 --- a/src/external/fast_float/include/fast_float/decimal_to_binary.h +++ b/src/external/fast_float/include/fast_float/decimal_to_binary.h @@ -17,7 +17,7 @@ namespace fast_float { // low part corresponding to the least significant bits. // template -fastfloat_really_inline +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 @@ -48,9 +48,9 @@ namespace detail { * where * p = log(5**q)/log(2) = q * log(5)/log(2) * - * For negative values of q in (-400,0), we have that + * For negative values of q in (-400,0), we have that * f = (((152170 + 65536) * q ) >> 16); - * is equal to + * is equal to * -ceil(p) + q * where * p = log(5**-q)/log(2) = -q * log(5)/log(2) @@ -63,7 +63,7 @@ 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; @@ -76,7 +76,7 @@ adjusted_mantissa compute_error_scaled(int64_t q, uint64_t w, int lz) noexcept // 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_really_inline FASTFLOAT_CONSTEXPR20 adjusted_mantissa compute_error(int64_t q, uint64_t w) noexcept { int lz = leading_zeroes(w); w <<= lz; @@ -90,7 +90,7 @@ adjusted_mantissa compute_error(int64_t q, uint64_t w) noexcept { // return an adjusted_mantissa with a negative power of 2: the caller should recompute // in such cases. template -fastfloat_really_inline +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())) { @@ -117,16 +117,11 @@ 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 diff --git a/src/external/fast_float/include/fast_float/digit_comparison.h b/src/external/fast_float/include/fast_float/digit_comparison.h index 77c710f57..512a27f5a 100644 --- a/src/external/fast_float/include/fast_float/digit_comparison.h +++ b/src/external/fast_float/include/fast_float/digit_comparison.h @@ -23,7 +23,9 @@ 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 { +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) { @@ -43,7 +45,8 @@ fastfloat_really_inline int32_t scientific_exponent(parsed_number_string& num) n // this converts a native floating-point number to an extended-precision float. template -fastfloat_really_inline adjusted_mantissa to_extended(T value) noexcept { +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(); @@ -52,7 +55,11 @@ fastfloat_really_inline adjusted_mantissa to_extended(T value) noexcept { 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; @@ -71,7 +78,8 @@ fastfloat_really_inline adjusted_mantissa to_extended(T value) noexcept { // 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 adjusted_mantissa to_extended_halfway(T value) noexcept { +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; @@ -81,7 +89,8 @@ 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 @@ -110,23 +119,19 @@ 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; - uint64_t is_above = truncated_bits > halfway; - uint64_t is_halfway = truncated_bits == halfway; + bool is_above = truncated_bits > halfway; + bool is_halfway = truncated_bits == halfway; // shift digits into position if (shift == 64) { @@ -140,7 +145,8 @@ 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 { @@ -148,18 +154,19 @@ fastfloat_really_inline void round_down(adjusted_mantissa& am, int32_t shift) no } am.power2 += shift; } - -fastfloat_really_inline void skip_zeros(const char*& first, const char* last) noexcept { +template +fastfloat_really_inline FASTFLOAT_CONSTEXPR20 +void skip_zeros(UC const * & first, UC const * last) noexcept { uint64_t val; - while (std::distance(first, last) >= 8) { + while (!cpp20_and_in_constexpr() && std::distance(first, last) >= int_cmp_len()) { ::memcpy(&val, first, sizeof(uint64_t)); - if (val != 0x3030303030303030) { + if (val != int_cmp_zeros()) { break; } - first += 8; + first += int_cmp_len(); } while (first != last) { - if (*first != '0') { + if (*first != UC('0')) { break; } first++; @@ -168,52 +175,59 @@ fastfloat_really_inline void skip_zeros(const char*& first, const char* last) no // determine if any non-zero digits were truncated. // all characters must be valid digits. -fastfloat_really_inline bool is_truncated(const char* first, const char* last) noexcept { +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 (std::distance(first, last) >= 8) { + while (!cpp20_and_in_constexpr() && std::distance(first, last) >= int_cmp_len()) { ::memcpy(&val, first, sizeof(uint64_t)); - if (val != 0x3030303030303030) { + if (val != int_cmp_zeros()) { return true; } - first += 8; + first += int_cmp_len(); } while (first != last) { - if (*first != '0') { + if (*first != UC('0')) { return true; } - first++; + ++first; } return false; } - -fastfloat_really_inline bool is_truncated(byte_span s) noexcept { +template +fastfloat_really_inline FASTFLOAT_CONSTEXPR20 +bool is_truncated(span s) noexcept { return is_truncated(s.ptr, s.ptr + s.len()); } -fastfloat_really_inline -void parse_eight_digits(const char*& p, limb& value, size_t& counter, size_t& count) noexcept { + +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; } -fastfloat_really_inline -void parse_one_digit(const char*& p, limb& value, size_t& counter, size_t& count) noexcept { - value = value * 10 + limb(*p - '0'); +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_really_inline FASTFLOAT_CONSTEXPR20 void add_native(bigint& big, limb power, limb value) noexcept { big.mul(power); big.add(value); } -fastfloat_really_inline void round_up_bigint(bigint& big, size_t& count) noexcept { +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); @@ -221,7 +235,9 @@ fastfloat_really_inline void round_up_bigint(bigint& big, size_t& count) noexcep } // parse the significant digits into a big integer -inline void parse_mantissa(bigint& result, parsed_number_string& num, size_t max_digits, size_t& digits) noexcept { +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. @@ -235,8 +251,8 @@ inline void parse_mantissa(bigint& result, parsed_number_string& num, size_t max #endif // process all integer digits. - const char* p = num.integer.ptr; - const char* pend = p + num.integer.len(); + 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) { @@ -301,7 +317,8 @@ inline void parse_mantissa(bigint& result, parsed_number_string& num, size_t max } template -inline adjusted_mantissa positive_digit_comp(bigint& bigmant, int32_t exponent) noexcept { +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; @@ -324,7 +341,8 @@ inline adjusted_mantissa positive_digit_comp(bigint& bigmant, int32_t exponent) // we then need to scale by `2^(f- e)`, and then the two significant digits // are of the same magnitude. template -inline adjusted_mantissa negative_digit_comp(bigint& bigmant, adjusted_mantissa am, int32_t exponent) noexcept { +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; @@ -383,8 +401,9 @@ inline adjusted_mantissa negative_digit_comp(bigint& bigmant, adjusted_mantissa // `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 adjusted_mantissa digit_comp(parsed_number_string& num, adjusted_mantissa am) noexcept { +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; diff --git a/src/external/fast_float/include/fast_float/fast_float.h b/src/external/fast_float/include/fast_float/fast_float.h index 3c483803a..04efa877e 100644 --- a/src/external/fast_float/include/fast_float/fast_float.h +++ b/src/external/fast_float/include/fast_float/fast_float.h @@ -1,33 +1,10 @@ + #ifndef FASTFLOAT_FAST_FLOAT_H #define FASTFLOAT_FAST_FLOAT_H -#include +#include "float_common.h" namespace fast_float { -enum chars_format { - scientific = 1<<0, - fixed = 1<<2, - hex = 1<<3, - general = fixed | scientific -}; - - -struct from_chars_result { - const char *ptr; - std::errc ec; -}; - -struct parse_options { - constexpr explicit parse_options(chars_format fmt = chars_format::general, - char dot = '.') - : format(fmt), decimal_point(dot) {} - - /** Which number formats are accepted */ - chars_format format; - /** The character used as decimal point */ - char decimal_point; -}; - /** * 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. @@ -44,20 +21,22 @@ struct parse_options { * 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 allowe the fixed point and scientific notation respectively. + * 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 -from_chars_result from_chars(const char *first, const char *last, +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 -from_chars_result from_chars_advanced(const char *first, const char *last, - T &value, parse_options options) noexcept; +template +FASTFLOAT_CONSTEXPR20 +from_chars_result_t from_chars_advanced(UC const * first, UC const * last, + T &value, parse_options_t options) noexcept; -} +} // namespace fast_float #include "parse_number.h" #endif // FASTFLOAT_FAST_FLOAT_H diff --git a/src/external/fast_float/include/fast_float/fast_table.h b/src/external/fast_float/include/fast_float/fast_table.h index 5766274ca..d8dc56905 100644 --- a/src/external/fast_float/include/fast_float/fast_table.h +++ b/src/external/fast_float/include/fast_float/fast_table.h @@ -17,11 +17,11 @@ namespace fast_float { */ /** - * The smallest non-zero float (binary64) is 2^−1074. + * 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. + * (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. ********* @@ -36,664 +36,665 @@ 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, + 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, + 0x9226712162ab070d,0xcab3961304ca70e8, + 0xb6b00d69bb55c8d1,0x3d607b97c5fd0d22, + 0xe45c10c42a2b3b05,0x8cb89a7db77c506a, + 0x8eb98a7a9a5b04e3,0x77f3608e92adb242, + 0xb267ed1940f1c61c,0x55f038b237591ed3, + 0xdf01e85f912e37a3,0x6b6c46dec52f6688, + 0x8b61313bbabce2c6,0x2323ac4b3b3da015, + 0xae397d8aa96c1b77,0xabec975e0a0d081a, + 0xd9c7dced53c72255,0x96e7bd358c904a21, + 0x881cea14545c7575,0x7e50d64177da2e54, + 0xaa242499697392d2,0xdde50bd1d5d0b9e9, + 0xd4ad2dbfc3d07787,0x955e4ec64b44e864, + 0x84ec3c97da624ab4,0xbd5af13bef0b113e, + 0xa6274bbdd0fadd61,0xecb1ad8aeacdd58e, + 0xcfb11ead453994ba,0x67de18eda5814af2, + 0x81ceb32c4b43fcf4,0x80eacf948770ced7, + 0xa2425ff75e14fc31,0xa1258379a94d028d, + 0xcad2f7f5359a3b3e,0x96ee45813a04330, + 0xfd87b5f28300ca0d,0x8bca9d6e188853fc, + 0x9e74d1b791e07e48,0x775ea264cf55347e, + 0xc612062576589dda,0x95364afe032a819e, + 0xf79687aed3eec551,0x3a83ddbd83f52205, + 0x9abe14cd44753b52,0xc4926a9672793543, + 0xc16d9a0095928a27,0x75b7053c0f178294, + 0xf1c90080baf72cb1,0x5324c68b12dd6339, + 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, + 0x9896800000000000,0x0, + 0xbebc200000000000,0x0, + 0xee6b280000000000,0x0, + 0x9502f90000000000,0x0, + 0xba43b74000000000,0x0, + 0xe8d4a51000000000,0x0, + 0x9184e72a00000000,0x0, + 0xb5e620f480000000,0x0, + 0xe35fa931a0000000,0x0, + 0x8e1bc9bf04000000,0x0, + 0xb1a2bc2ec5000000,0x0, + 0xde0b6b3a76400000,0x0, + 0x8ac7230489e80000,0x0, + 0xad78ebc5ac620000,0x0, + 0xd8d726b7177a8000,0x0, + 0x878678326eac9000,0x0, + 0xa968163f0a57b400,0x0, + 0xd3c21bcecceda100,0x0, + 0x84595161401484a0,0x0, + 0xa56fa5b99019a5c8,0x0, + 0xcecb8f27f4200f3a,0x0, + 0x813f3978f8940984,0x4000000000000000, + 0xa18f07d736b90be5,0x5000000000000000, + 0xc9f2c9cd04674ede,0xa400000000000000, + 0xfc6f7c4045812296,0x4d00000000000000, + 0x9dc5ada82b70b59d,0xf020000000000000, + 0xc5371912364ce305,0x6c28000000000000, + 0xf684df56c3e01bc6,0xc732000000000000, + 0x9a130b963a6c115c,0x3c7f400000000000, + 0xc097ce7bc90715b3,0x4b9f100000000000, + 0xf0bdc21abb48db20,0x1e86d40000000000, + 0x96769950b50d88f4,0x1314448000000000, + 0xbc143fa4e250eb31,0x17d955a000000000, + 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, + 0xfb5878494ace3a5f,0x4ab48a04065c723, + 0x9d174b2dcec0e47b,0x62eb0d64283f9c76, + 0xc45d1df942711d9a,0x3ba5d0bd324f8394, + 0xf5746577930d6500,0xca8f44ec7ee36479, + 0x9968bf6abbe85f20,0x7e998b13cf4e1ecb, + 0xbfc2ef456ae276e8,0x9e3fedd8c321a67e, + 0xefb3ab16c59b14a2,0xc5cfe94ef3ea101e, + 0x95d04aee3b80ece5,0xbba1f1d158724a12, + 0xbb445da9ca61281f,0x2a8a6e45ae8edc97, + 0xea1575143cf97226,0xf52d09d71a3293bd, + 0x924d692ca61be758,0x593c2626705f9c56, + 0xb6e0c377cfa2e12e,0x6f8b2fb00c77836c, + 0xe498f455c38b997a,0xb6dfb9c0f956447, + 0x8edf98b59a373fec,0x4724bd4189bd5eac, + 0xb2977ee300c50fe7,0x58edec91ec2cb657, + 0xdf3d5e9bc0f653e1,0x2f2967b66737e3ed, + 0x8b865b215899f46c,0xbd79e0d20082ee74, + 0xae67f1e9aec07187,0xecd8590680a3aa11, + 0xda01ee641a708de9,0xe80e6f4820cc9495, + 0x884134fe908658b2,0x3109058d147fdcdd, + 0xaa51823e34a7eede,0xbd4b46f0599fd415, + 0xd4e5e2cdc1d1ea96,0x6c9e18ac7007c91a, + 0x850fadc09923329e,0x3e2cf6bc604ddb0, + 0xa6539930bf6bff45,0x84db8346b786151c, + 0xcfe87f7cef46ff16,0xe612641865679a63, + 0x81f14fae158c5f6e,0x4fcb7e8f3f60c07e, + 0xa26da3999aef7749,0xe3be5e330f38f09d, + 0xcb090c8001ab551c,0x5cadf5bfd3072cc5, + 0xfdcb4fa002162a63,0x73d9732fc7c8f7f6, + 0x9e9f11c4014dda7e,0x2867e7fddcdd9afa, + 0xc646d63501a1511d,0xb281e1fd541501b8, + 0xf7d88bc24209a565,0x1f225a7ca91a4226, + 0x9ae757596946075f,0x3375788de9b06958, + 0xc1a12d2fc3978937,0x52d6b1641c83ae, + 0xf209787bb47d6b84,0xc0678c5dbd23a49a, + 0x9745eb4d50ce6332,0xf840b7ba963646e0, + 0xbd176620a501fbff,0xb650e5a93bc3d898, + 0xec5d3fa8ce427aff,0xa3e51f138ab4cebe, + 0x93ba47c980e98cdf,0xc66f336c36b10137, + 0xb8a8d9bbe123f017,0xb80b0047445d4184, + 0xe6d3102ad96cec1d,0xa60dc059157491e5, + 0x9043ea1ac7e41392,0x87c89837ad68db2f, + 0xb454e4a179dd1877,0x29babe4598c311fb, + 0xe16a1dc9d8545e94,0xf4296dd6fef3d67a, + 0x8ce2529e2734bb1d,0x1899e4a65f58660c, + 0xb01ae745b101e9e4,0x5ec05dcff72e7f8f, + 0xdc21a1171d42645d,0x76707543f4fa1f73, + 0x899504ae72497eba,0x6a06494a791c53a8, + 0xabfa45da0edbde69,0x487db9d17636892, + 0xd6f8d7509292d603,0x45a9d2845d3c42b6, + 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 -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, - 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, - 0x9226712162ab070d,0xcab3961304ca70e8, - 0xb6b00d69bb55c8d1,0x3d607b97c5fd0d22, - 0xe45c10c42a2b3b05,0x8cb89a7db77c506a, - 0x8eb98a7a9a5b04e3,0x77f3608e92adb242, - 0xb267ed1940f1c61c,0x55f038b237591ed3, - 0xdf01e85f912e37a3,0x6b6c46dec52f6688, - 0x8b61313bbabce2c6,0x2323ac4b3b3da015, - 0xae397d8aa96c1b77,0xabec975e0a0d081a, - 0xd9c7dced53c72255,0x96e7bd358c904a21, - 0x881cea14545c7575,0x7e50d64177da2e54, - 0xaa242499697392d2,0xdde50bd1d5d0b9e9, - 0xd4ad2dbfc3d07787,0x955e4ec64b44e864, - 0x84ec3c97da624ab4,0xbd5af13bef0b113e, - 0xa6274bbdd0fadd61,0xecb1ad8aeacdd58e, - 0xcfb11ead453994ba,0x67de18eda5814af2, - 0x81ceb32c4b43fcf4,0x80eacf948770ced7, - 0xa2425ff75e14fc31,0xa1258379a94d028d, - 0xcad2f7f5359a3b3e,0x96ee45813a04330, - 0xfd87b5f28300ca0d,0x8bca9d6e188853fc, - 0x9e74d1b791e07e48,0x775ea264cf55347e, - 0xc612062576589dda,0x95364afe032a819e, - 0xf79687aed3eec551,0x3a83ddbd83f52205, - 0x9abe14cd44753b52,0xc4926a9672793543, - 0xc16d9a0095928a27,0x75b7053c0f178294, - 0xf1c90080baf72cb1,0x5324c68b12dd6339, - 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, - 0x9896800000000000,0x0, - 0xbebc200000000000,0x0, - 0xee6b280000000000,0x0, - 0x9502f90000000000,0x0, - 0xba43b74000000000,0x0, - 0xe8d4a51000000000,0x0, - 0x9184e72a00000000,0x0, - 0xb5e620f480000000,0x0, - 0xe35fa931a0000000,0x0, - 0x8e1bc9bf04000000,0x0, - 0xb1a2bc2ec5000000,0x0, - 0xde0b6b3a76400000,0x0, - 0x8ac7230489e80000,0x0, - 0xad78ebc5ac620000,0x0, - 0xd8d726b7177a8000,0x0, - 0x878678326eac9000,0x0, - 0xa968163f0a57b400,0x0, - 0xd3c21bcecceda100,0x0, - 0x84595161401484a0,0x0, - 0xa56fa5b99019a5c8,0x0, - 0xcecb8f27f4200f3a,0x0, - 0x813f3978f8940984,0x4000000000000000, - 0xa18f07d736b90be5,0x5000000000000000, - 0xc9f2c9cd04674ede,0xa400000000000000, - 0xfc6f7c4045812296,0x4d00000000000000, - 0x9dc5ada82b70b59d,0xf020000000000000, - 0xc5371912364ce305,0x6c28000000000000, - 0xf684df56c3e01bc6,0xc732000000000000, - 0x9a130b963a6c115c,0x3c7f400000000000, - 0xc097ce7bc90715b3,0x4b9f100000000000, - 0xf0bdc21abb48db20,0x1e86d40000000000, - 0x96769950b50d88f4,0x1314448000000000, - 0xbc143fa4e250eb31,0x17d955a000000000, - 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, - 0xfb5878494ace3a5f,0x4ab48a04065c723, - 0x9d174b2dcec0e47b,0x62eb0d64283f9c76, - 0xc45d1df942711d9a,0x3ba5d0bd324f8394, - 0xf5746577930d6500,0xca8f44ec7ee36479, - 0x9968bf6abbe85f20,0x7e998b13cf4e1ecb, - 0xbfc2ef456ae276e8,0x9e3fedd8c321a67e, - 0xefb3ab16c59b14a2,0xc5cfe94ef3ea101e, - 0x95d04aee3b80ece5,0xbba1f1d158724a12, - 0xbb445da9ca61281f,0x2a8a6e45ae8edc97, - 0xea1575143cf97226,0xf52d09d71a3293bd, - 0x924d692ca61be758,0x593c2626705f9c56, - 0xb6e0c377cfa2e12e,0x6f8b2fb00c77836c, - 0xe498f455c38b997a,0xb6dfb9c0f956447, - 0x8edf98b59a373fec,0x4724bd4189bd5eac, - 0xb2977ee300c50fe7,0x58edec91ec2cb657, - 0xdf3d5e9bc0f653e1,0x2f2967b66737e3ed, - 0x8b865b215899f46c,0xbd79e0d20082ee74, - 0xae67f1e9aec07187,0xecd8590680a3aa11, - 0xda01ee641a708de9,0xe80e6f4820cc9495, - 0x884134fe908658b2,0x3109058d147fdcdd, - 0xaa51823e34a7eede,0xbd4b46f0599fd415, - 0xd4e5e2cdc1d1ea96,0x6c9e18ac7007c91a, - 0x850fadc09923329e,0x3e2cf6bc604ddb0, - 0xa6539930bf6bff45,0x84db8346b786151c, - 0xcfe87f7cef46ff16,0xe612641865679a63, - 0x81f14fae158c5f6e,0x4fcb7e8f3f60c07e, - 0xa26da3999aef7749,0xe3be5e330f38f09d, - 0xcb090c8001ab551c,0x5cadf5bfd3072cc5, - 0xfdcb4fa002162a63,0x73d9732fc7c8f7f6, - 0x9e9f11c4014dda7e,0x2867e7fddcdd9afa, - 0xc646d63501a1511d,0xb281e1fd541501b8, - 0xf7d88bc24209a565,0x1f225a7ca91a4226, - 0x9ae757596946075f,0x3375788de9b06958, - 0xc1a12d2fc3978937,0x52d6b1641c83ae, - 0xf209787bb47d6b84,0xc0678c5dbd23a49a, - 0x9745eb4d50ce6332,0xf840b7ba963646e0, - 0xbd176620a501fbff,0xb650e5a93bc3d898, - 0xec5d3fa8ce427aff,0xa3e51f138ab4cebe, - 0x93ba47c980e98cdf,0xc66f336c36b10137, - 0xb8a8d9bbe123f017,0xb80b0047445d4184, - 0xe6d3102ad96cec1d,0xa60dc059157491e5, - 0x9043ea1ac7e41392,0x87c89837ad68db2f, - 0xb454e4a179dd1877,0x29babe4598c311fb, - 0xe16a1dc9d8545e94,0xf4296dd6fef3d67a, - 0x8ce2529e2734bb1d,0x1899e4a65f58660c, - 0xb01ae745b101e9e4,0x5ec05dcff72e7f8f, - 0xdc21a1171d42645d,0x76707543f4fa1f73, - 0x899504ae72497eba,0x6a06494a791c53a8, - 0xabfa45da0edbde69,0x487db9d17636892, - 0xd6f8d7509292d603,0x45a9d2845d3c42b6, - 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,}; +constexpr uint64_t powers_template::power_of_five_128[number_of_entries]; + using powers = powers_template<>; -} +} // namespace fast_float #endif diff --git a/src/external/fast_float/include/fast_float/float_common.h b/src/external/fast_float/include/fast_float/float_common.h index bb8580efc..4a290f489 100644 --- a/src/external/fast_float/include/fast_float/float_common.h +++ b/src/external/fast_float/include/fast_float/float_common.h @@ -6,18 +6,56 @@ #include #include #include +#include + +#include "constexpr_feature_detect.h" + +namespace fast_float { + +enum chars_format { + scientific = 1 << 0, + fixed = 1 << 2, + hex = 1 << 3, + 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(__EMSCRIPTEN__)) -#define FASTFLOAT_64BIT + || defined(__loongarch64) ) +#define FASTFLOAT_64BIT 1 #elif (defined(__i386) || defined(__i386__) || defined(_M_IX86) \ - || defined(__arm__) || defined(_M_ARM) \ - || defined(__MINGW32__)) -#define FASTFLOAT_32BIT + || 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. @@ -25,9 +63,9 @@ #if SIZE_MAX == 0xffff #error Unknown platform (16-bit, unsupported) #elif SIZE_MAX == 0xffffffff - #define FASTFLOAT_32BIT + #define FASTFLOAT_32BIT 1 #elif SIZE_MAX == 0xffffffffffffffff - #define FASTFLOAT_64BIT + #define FASTFLOAT_64BIT 1 #else #error Unknown platform (not 32-bit, not 64-bit?) #endif @@ -50,8 +88,14 @@ #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__ @@ -71,6 +115,38 @@ #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_ARM64) +#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 @@ -78,25 +154,36 @@ #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; } +#define FASTFLOAT_ENABLE_IF(...) typename std::enable_if<(__VA_ARGS__), int>::type = 0 + + 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) { +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 |= (input1[i] ^ input2[i]); + for (size_t i = 0; i < length; ++i) { + running_diff |= (char(input1[i]) ^ char(input2[i])); } return (running_diff == 0) || (running_diff == 32); } @@ -110,14 +197,14 @@ 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]; } @@ -126,13 +213,29 @@ 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++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 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; @@ -141,31 +244,20 @@ 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)); @@ -175,17 +267,32 @@ 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; -#ifdef _M_ARM64 +#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__)) @@ -195,7 +302,7 @@ 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; } @@ -204,10 +311,10 @@ 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; } }; @@ -215,24 +322,25 @@ struct adjusted_mantissa { // Bias so we can get the real exponent with an invalid adjusted_mantissa. constexpr static int32_t invalid_am_bias = -0x8000; -constexpr static double powers_of_ten_double[] = { - 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, - 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22}; -constexpr static float powers_of_ten_float[] = {1e0, 1e1, 1e2, 1e3, 1e4, 1e5, - 1e6, 1e7, 1e8, 1e9, 1e10}; +// 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 { +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(); + 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(); + 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); @@ -242,6 +350,91 @@ template struct binary_format { 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; } @@ -282,21 +475,6 @@ template <> inline constexpr int binary_format::infinite_power() { 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::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::max_exponent_fast_path() { return 22; } @@ -307,18 +485,33 @@ template <> inline constexpr int binary_format::max_exponent_fast_path() 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) { - return powers_of_ten_double[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) { - - return powers_of_ten_float[power]; + // Work around clang bug https://godbolt.org/z/zedh7rrhc + return (void)powers_of_ten[0], powers_of_ten[power]; } @@ -375,23 +568,103 @@ 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 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 - // For little-endian systems: - ::memcpy(&value, &word, sizeof(T)); + ::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"; +} } // namespace fast_float #endif diff --git a/src/external/fast_float/include/fast_float/parse_number.h b/src/external/fast_float/include/fast_float/parse_number.h index 62ae3b039..e077b9d03 100644 --- a/src/external/fast_float/include/fast_float/parse_number.h +++ b/src/external/fast_float/include/fast_float/parse_number.h @@ -4,6 +4,7 @@ #include "ascii_number.h" #include "decimal_to_binary.h" #include "digit_comparison.h" +#include "float_common.h" #include #include @@ -19,35 +20,41 @@ namespace detail { * The case comparisons could be made much faster given that we know that the * strings a null-free and fixed. **/ -template -from_chars_result parse_infnan(const char *first, const char *last, T &value) noexcept { - from_chars_result answer; +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 == '-') { // assume first < last, so dereference without checks; C++17 20.19.3.(7.1) explicitly forbids '+' here + 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, "nan", 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 == '(') { - for(const char* ptr = first + 1; ptr != last; ++ptr) { - if (*ptr == ')') { + 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(!(('a' <= *ptr && *ptr <= 'z') || ('A' <= *ptr && *ptr <= 'Z') || ('0' <= *ptr && *ptr <= '9') || *ptr == '_')) + 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, "inf", 3)) { - if ((last - first >= 8) && fastfloat_strncasecmp(first + 3, "inity", 5)) { + 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; @@ -60,40 +67,147 @@ from_chars_result parse_infnan(const char *first, const char *last, T &value) n 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 -from_chars_result from_chars(const char *first, const char *last, +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{fmt}); + return from_chars_advanced(first, last, value, parse_options_t{fmt}); } -template -from_chars_result from_chars_advanced(const char *first, const char *last, - T &value, parse_options options) noexcept { +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 (std::is_same::value || std::is_same::value, "only float and double are supported"); + static_assert (std::is_same::value || + std::is_same::value || + std::is_same::value || + std::is_same::value , "only char, wchar_t, char16_t and char32_t are supported"); - - from_chars_result answer; + 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 pns = parse_number_string(first, last, options); + parsed_number_string_t pns = parse_number_string(first, last, options); if (!pns.valid) { return detail::parse_infnan(first, last, value); } + answer.ec = std::errc(); // be optimistic answer.ptr = pns.lastmatch; - // Next is Clinger's fast path. - if (binary_format::min_exponent_fast_path() <= pns.exponent && pns.exponent <= binary_format::max_exponent_fast_path() && pns.mantissa <=binary_format::max_mantissa_fast_path() && !pns.too_many_digits) { - 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; + // 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__) + // Clang may map 0 to -0.0 when fegetround() == FE_DOWNWARD + if(pns.mantissa == 0) { + value = pns.negative ? -0. : 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) { @@ -105,6 +219,10 @@ from_chars_result from_chars_advanced(const char *first, const char *last, // 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; } diff --git a/tests/usda/floating-point-001.usda b/tests/usda/floating-point-001.usda new file mode 100644 index 000000000..bacf5cdcd --- /dev/null +++ b/tests/usda/floating-point-001.usda @@ -0,0 +1,2 @@ +#usda 1.0 +( metersPerUnit = .001 ) diff --git a/tests/usda/floating-point-002.usda b/tests/usda/floating-point-002.usda new file mode 100644 index 000000000..10d42e74a --- /dev/null +++ b/tests/usda/floating-point-002.usda @@ -0,0 +1,2 @@ +#usda 1.0 +( metersPerUnit = .001E+3 )