[gcc r12-6646] libstdc++: Import the fast_float library
Patrick Palka
ppalka@gcc.gnu.org
Mon Jan 17 19:33:34 GMT 2022
https://gcc.gnu.org/g:2800bc08e4ab4c116f556f17791936c889191fbf
commit r12-6646-g2800bc08e4ab4c116f556f17791936c889191fbf
Author: Patrick Palka <ppalka@redhat.com>
Date: Mon Jan 17 14:32:16 2022 -0500
libstdc++: Import the fast_float library
We're going to use the fast_float library[1] in our (compiled-in)
floating-point std::from_chars implementation for faster and more
portable parsing of binary32/64 decimal strings.
The single file fast_float.h is an amalgamation of the entire library,
which can be (re)generated with the amalgamate.py script (from the
fast_float repository) via the command
python3 ./script/amalgamate.py --license=MIT \
> $GCC_SRC/libstdc++-v3/c++17/fast_float/fast_float.h
The code has a GPL-compatible license.
[1]: https://github.com/fastfloat/fast_float
libstdc++-v3/ChangeLog:
* src/c++17/fast_float/LOCAL_PATCHES: New file.
* src/c++17/fast_float/MERGE: New file.
* src/c++17/fast_float/README.md: New file, copied from the
fast_float repository.
* src/c++17/fast_float/fast_float.h: New file, an amalgamation
of the fast_float library.
Signed-off-by: Patrick Palka <ppalka@redhat.com>
Diff:
---
libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES | 0
libstdc++-v3/src/c++17/fast_float/MERGE | 4 +
libstdc++-v3/src/c++17/fast_float/README.md | 218 ++
libstdc++-v3/src/c++17/fast_float/fast_float.h | 2944 +++++++++++++++++++++++
4 files changed, 3166 insertions(+)
diff --git a/libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES b/libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES
new file mode 100644
index 00000000000..e69de29bb2d
diff --git a/libstdc++-v3/src/c++17/fast_float/MERGE b/libstdc++-v3/src/c++17/fast_float/MERGE
new file mode 100644
index 00000000000..43bdc3981c8
--- /dev/null
+++ b/libstdc++-v3/src/c++17/fast_float/MERGE
@@ -0,0 +1,4 @@
+d35368cae610b4edeec61cd41e4d2367a4d33f58
+
+The first line of this file holds the git revision number of the
+last merge done from the master library sources.
diff --git a/libstdc++-v3/src/c++17/fast_float/README.md b/libstdc++-v3/src/c++17/fast_float/README.md
new file mode 100644
index 00000000000..1e1c06d0a3e
--- /dev/null
+++ b/libstdc++-v3/src/c++17/fast_float/README.md
@@ -0,0 +1,218 @@
+## fast_float number parsing library: 4x faster than strtod
+
+/badge.svg)
+/badge.svg)
+
+
+
+[](https://github.com/fastfloat/fast_float/actions/workflows/vs16-ci.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
+decimal values (e.g., `1.3e10`) into binary types. We provide exact rounding (including
+round to even). In our experience, these `fast_float` functions many times faster than comparable number-parsing functions from existing C++ standard libraries.
+
+Specifically, `fast_float` provides the following two functions with a C++17-like syntax (the library itself only requires C++11):
+
+```C++
+from_chars_result from_chars(const char* first, const char* last, float& value, ...);
+from_chars_result from_chars(const char* first, const char* last, double& value, ...);
+```
+
+The return type (`from_chars_result`) is defined as the struct:
+```C++
+struct from_chars_result {
+ const char* ptr;
+ std::errc ec;
+};
+```
+
+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),
+using the "round to even" convention for values that would otherwise fall right in-between two values.
+That is, we provide exact parsing according to the IEEE standard.
+
+
+Given a successful parse, the pointer (`ptr`) in the returned value is set to point right after the
+parsed number, and the `value` referenced is set to the parsed value. In case of error, the returned
+`ec` contains a representative error, otherwise the default (`std::errc()`) value is stored.
+
+The implementation does not throw and does not allocate memory (e.g., with `new` or `malloc`).
+
+It will parse infinity and nan values.
+
+Example:
+
+``` C++
+#include "fast_float/fast_float.h"
+#include <iostream>
+
+int main() {
+ const std::string input = "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;
+}
+```
+
+
+Like the C++17 standard, the `fast_float::from_chars` functions take an optional last argument of
+the type `fast_float::chars_format`. It is a bitset value: we check whether
+`fmt & fast_float::chars_format::fixed` and `fmt & fast_float::chars_format::scientific` are set
+to determine whether we allow the fixed point and scientific notation respectively.
+The default is `fast_float::chars_format::general` which allows both `fixed` and `scientific`.
+
+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.
+
+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.
+
+We support Visual Studio, macOS, Linux, freeBSD. We support big and little endian. We support 32-bit and 64-bit systems.
+
+
+
+## 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
+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.,
+the comma). You may use it as follows.
+
+```C++
+#include "fast_float/fast_float.h"
+#include <iostream>
+
+int main() {
+ const std::string input = "3,1416 xyz ";
+ double result;
+ fast_float::parse_options options{fast_float::chars_format::general, ','};
+ auto answer = fast_float::from_chars_advanced(input.data(), input.data()+input.size(), result, options);
+ if((answer.ec != std::errc()) || ((result != 3.1416))) { std::cerr << "parsing failure\n"; return EXIT_FAILURE; }
+ std::cout << "parsed the number " << result << std::endl;
+ return EXIT_SUCCESS;
+}
+```
+
+
+## Reference
+
+- Daniel Lemire, [Number Parsing at a Gigabyte per Second](https://arxiv.org/abs/2101.11408), Software: Pratice and Experience 51 (8), 2021.
+
+## 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`.
+- [There is a C# port of the fast_float library](https://github.com/CarlVerret/csFastFloat) called `csFastFloat`.
+
+
+## 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 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).
+
+## Users
+
+The fast_float library is used by [Apache Arrow](https://github.com/apache/arrow/pull/8494) where it multiplied the number parsing speed by two or three times. It is also used by [Yandex ClickHouse](https://github.com/ClickHouse/ClickHouse) and by [Google Jsonnet](https://github.com/google/jsonnet).
+
+
+## How fast is it?
+
+It can parse random floating-point numbers at a speed of 1 GB/s on some systems. We find that it is often twice as fast as the best available competitor, and many times faster than many standard-library implementations.
+
+<img src="http://lemire.me/blog/wp-content/uploads/2020/11/fastfloat_speed.png" width="400">
+
+```
+$ ./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
+```
+
+See https://github.com/lemire/simple_fastfloat_benchmark for our benchmarking code.
+
+
+## Video
+
+[](http://www.youtube.com/watch?v=AVXgvlMeIm4)<br />
+
+## Using as a CMake dependency
+
+This library is header-only by design. The CMake file provides the `fast_float` target
+which is merely a pointer to the `include` directory.
+
+If you drop the `fast_float` repository in your CMake project, you should be able to use
+it in this manner:
+
+```cmake
+add_subdirectory(fast_float)
+target_link_libraries(myprogram PUBLIC fast_float)
+```
+
+Or you may want to retrieve the dependency automatically if you have a sufficiently recent version of CMake (3.11 or better at least):
+
+```cmake
+FetchContent_Declare(
+ fast_float
+ GIT_REPOSITORY https://github.com/lemire/fast_float.git
+ GIT_TAG tags/v1.1.2
+ GIT_SHALLOW TRUE)
+
+FetchContent_MakeAvailable(fast_float)
+target_link_libraries(myprogram PUBLIC fast_float)
+
+```
+
+You should change the `GIT_TAG` line so that you recover the version you wish to use.
+
+## Using as 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.
+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/v1.1.2/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
+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
+under the Apache 2.0 license.
+
+## License
+
+<sup>
+Licensed under either of <a href="LICENSE-APACHE">Apache License, Version
+2.0</a> or <a href="LICENSE-MIT">MIT license</a> at your option.
+</sup>
+
+<br>
+
+<sub>
+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.
+</sub>
diff --git a/libstdc++-v3/src/c++17/fast_float/fast_float.h b/libstdc++-v3/src/c++17/fast_float/fast_float.h
new file mode 100644
index 00000000000..8a45ebca8a8
--- /dev/null
+++ b/libstdc++-v3/src/c++17/fast_float/fast_float.h
@@ -0,0 +1,2944 @@
+// fast_float by Daniel Lemire
+// fast_float by João Paulo Magalhaes
+//
+// with contributions from Eugene Golushkov
+// with contributions from Maksim Kita
+// with contributions from Marcin Wojdyr
+// with contributions from Neal Richardson
+// with contributions from Tim Paine
+// with contributions from Fabio Pellacini
+//
+// MIT License Notice
+//
+// MIT License
+//
+// Copyright (c) 2021 The fast_float authors
+//
+// Permission is hereby granted, free of charge, to any
+// person obtaining a copy of this software and associated
+// documentation files (the "Software"), to deal in the
+// Software without restriction, including without
+// limitation the rights to use, copy, modify, merge,
+// publish, distribute, sublicense, and/or sell copies of
+// the Software, and to permit persons to whom the Software
+// is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice
+// shall be included in all copies or substantial portions
+// of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF
+// ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
+// TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
+// PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT
+// SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
+// CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
+// OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
+// IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+// DEALINGS IN THE SOFTWARE.
+//
+
+#ifndef FASTFLOAT_FAST_FLOAT_H
+#define FASTFLOAT_FAST_FLOAT_H
+
+#include <system_error>
+
+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.
+ * The resulting floating-point value is the closest floating-point values (using either float or double),
+ * using the "round to even" convention for values that would otherwise fall right in-between two values.
+ * That is, we provide exact parsing according to the IEEE standard.
+ *
+ * Given a successful parse, the pointer (`ptr`) in the returned value is set to point right after the
+ * parsed number, and the `value` referenced is set to the parsed value. In case of error, the returned
+ * `ec` contains a representative error, otherwise the default (`std::errc()`) value is stored.
+ *
+ * The implementation does not throw and does not allocate memory (e.g., with `new` or `malloc`).
+ *
+ * Like the C++17 standard, the `fast_float::from_chars` functions take an optional last argument of
+ * the type `fast_float::chars_format`. It is a bitset value: we check whether
+ * `fmt & fast_float::chars_format::fixed` and `fmt & fast_float::chars_format::scientific` are set
+ * to determine whether we allowe the fixed point and scientific notation respectively.
+ * The default is `fast_float::chars_format::general` which allows both `fixed` and `scientific`.
+ */
+template<typename T>
+from_chars_result from_chars(const char *first, const char *last,
+ T &value, chars_format fmt = chars_format::general) noexcept;
+
+/**
+ * Like from_chars, but accepts an `options` argument to govern number parsing.
+ */
+template<typename T>
+from_chars_result from_chars_advanced(const char *first, const char *last,
+ T &value, parse_options options) noexcept;
+
+}
+#endif // FASTFLOAT_FAST_FLOAT_H
+
+#ifndef FASTFLOAT_FLOAT_COMMON_H
+#define FASTFLOAT_FLOAT_COMMON_H
+
+#include <cfloat>
+#include <cstdint>
+#include <cassert>
+#include <cstring>
+
+#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
+#elif (defined(__i386) || defined(__i386__) || defined(_M_IX86) \
+ || defined(__arm__) || defined(_M_ARM) \
+ || defined(__MINGW32__))
+#define FASTFLOAT_32BIT
+#else
+ // Need to check incrementally, since SIZE_MAX is a size_t, avoid overflow.
+ // We can never tell the register width, but the SIZE_MAX is a good approximation.
+ // UINTPTR_MAX and INTPTR_MAX are optional, so avoid them for max portability.
+ #if SIZE_MAX == 0xffff
+ #error Unknown platform (16-bit, unsupported)
+ #elif SIZE_MAX == 0xffffffff
+ #define FASTFLOAT_32BIT
+ #elif SIZE_MAX == 0xffffffffffffffff
+ #define FASTFLOAT_64BIT
+ #else
+ #error Unknown platform (not 32-bit, not 64-bit?)
+ #endif
+#endif
+
+#if ((defined(_WIN32) || defined(_WIN64)) && !defined(__clang__))
+#include <intrin.h>
+#endif
+
+#if defined(_MSC_VER) && !defined(__clang__)
+#define FASTFLOAT_VISUAL_STUDIO 1
+#endif
+
+#ifdef _WIN32
+#define FASTFLOAT_IS_BIG_ENDIAN 0
+#else
+#if defined(__APPLE__) || defined(__FreeBSD__)
+#include <machine/endian.h>
+#elif defined(sun) || defined(__sun)
+#include <sys/byteorder.h>
+#else
+#include <endian.h>
+#endif
+#
+#ifndef __BYTE_ORDER__
+// safe choice
+#define FASTFLOAT_IS_BIG_ENDIAN 0
+#endif
+#
+#ifndef __ORDER_LITTLE_ENDIAN__
+// safe choice
+#define FASTFLOAT_IS_BIG_ENDIAN 0
+#endif
+#
+#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
+#define FASTFLOAT_IS_BIG_ENDIAN 0
+#else
+#define FASTFLOAT_IS_BIG_ENDIAN 1
+#endif
+#endif
+
+#ifdef FASTFLOAT_VISUAL_STUDIO
+#define fastfloat_really_inline __forceinline
+#else
+#define fastfloat_really_inline inline __attribute__((always_inline))
+#endif
+
+#ifndef FASTFLOAT_ASSERT
+#define FASTFLOAT_ASSERT(x) { if (!(x)) abort(); }
+#endif
+
+#ifndef FASTFLOAT_DEBUG_ASSERT
+#include <cassert>
+#define FASTFLOAT_DEBUG_ASSERT(x) assert(x)
+#endif
+
+// rust style `try!()` macro, or `?` operator
+#define FASTFLOAT_TRY(x) { if (!(x)) return false; }
+
+namespace fast_float {
+
+// Compares two ASCII strings in a case insensitive manner.
+inline bool fastfloat_strncasecmp(const char *input1, const char *input2,
+ size_t length) {
+ char running_diff{0};
+ for (size_t i = 0; i < length; i++) {
+ running_diff |= (input1[i] ^ input2[i]);
+ }
+ return (running_diff == 0) || (running_diff == 32);
+}
+
+#ifndef FLT_EVAL_METHOD
+#error "FLT_EVAL_METHOD should be defined, please include cfloat."
+#endif
+
+// a pointer and a length to a contiguous block of memory
+template <typename T>
+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 size_t len() const noexcept {
+ return length;
+ }
+
+ const T& operator[](size_t index) const noexcept {
+ FASTFLOAT_DEBUG_ASSERT(index < length);
+ return ptr[index];
+ }
+};
+
+struct value128 {
+ uint64_t low;
+ uint64_t high;
+ value128(uint64_t _low, uint64_t _high) : low(_low), high(_high) {}
+ value128() : low(0), high(0) {}
+};
+
+/* result might be undefined when input_num is zero */
+fastfloat_really_inline int leading_zeroes(uint64_t input_num) {
+ assert(input_num > 0);
+#ifdef FASTFLOAT_VISUAL_STUDIO
+ #if defined(_M_X64) || defined(_M_ARM64)
+ unsigned long leading_zero = 0;
+ // Search the mask data from most significant bit (MSB)
+ // to least significant bit (LSB) for a set bit (1).
+ _BitScanReverse64(&leading_zero, input_num);
+ return (int)(63 - leading_zero);
+ #else
+ 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;
+ #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) {
+ 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) {
+ uint64_t ad = emulu((uint32_t)(ab >> 32), (uint32_t)cd);
+ uint64_t bd = emulu((uint32_t)ab, (uint32_t)cd);
+ uint64_t adbc = ad + emulu((uint32_t)ab, (uint32_t)(cd >> 32));
+ uint64_t adbc_carry = !!(adbc < ad);
+ uint64_t lo = bd + (adbc << 32);
+ *hi = emulu((uint32_t)(ab >> 32), (uint32_t)(cd >> 32)) + (adbc >> 32) +
+ (adbc_carry << 32) + !!(lo < bd);
+ return lo;
+}
+#endif // !__MINGW64__
+
+#endif // FASTFLOAT_32BIT
+
+
+// compute 64-bit a*b
+fastfloat_really_inline value128 full_multiplication(uint64_t a,
+ uint64_t b) {
+ value128 answer;
+#ifdef _M_ARM64
+ // ARM64 has native support for 64-bit multiplications, no need to emulate
+ answer.high = __umulh(a, b);
+ answer.low = a * b;
+#elif defined(FASTFLOAT_32BIT) || (defined(_WIN64) && !defined(__clang__))
+ answer.low = _umul128(a, b, &answer.high); // _umul128 not available on ARM64
+#elif defined(FASTFLOAT_64BIT)
+ __uint128_t r = ((__uint128_t)a) * b;
+ answer.low = uint64_t(r);
+ answer.high = uint64_t(r >> 64);
+#else
+ #error Not implemented
+#endif
+ return answer;
+}
+
+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 {
+ return mantissa == o.mantissa && power2 == o.power2;
+ }
+ bool operator!=(const adjusted_mantissa &o) const {
+ return mantissa != o.mantissa || power2 != o.power2;
+ }
+};
+
+// Bias so we can get the real exponent with an invalid adjusted_mantissa.
+constexpr static int32_t invalid_am_bias = -0x8000;
+
+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};
+
+template <typename T> struct binary_format {
+ 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 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 int largest_power_of_ten();
+ static inline constexpr int smallest_power_of_ten();
+ static inline constexpr T exact_power_of_ten(int64_t power);
+ static inline constexpr size_t max_digits();
+};
+
+template <> inline constexpr int binary_format<double>::mantissa_explicit_bits() {
+ return 52;
+}
+template <> inline constexpr int binary_format<float>::mantissa_explicit_bits() {
+ return 23;
+}
+
+template <> inline constexpr int binary_format<double>::max_exponent_round_to_even() {
+ return 23;
+}
+
+template <> inline constexpr int binary_format<float>::max_exponent_round_to_even() {
+ return 10;
+}
+
+template <> inline constexpr int binary_format<double>::min_exponent_round_to_even() {
+ return -4;
+}
+
+template <> inline constexpr int binary_format<float>::min_exponent_round_to_even() {
+ return -17;
+}
+
+template <> inline constexpr int binary_format<double>::minimum_exponent() {
+ return -1023;
+}
+template <> inline constexpr int binary_format<float>::minimum_exponent() {
+ return -127;
+}
+
+template <> inline constexpr int binary_format<double>::infinite_power() {
+ return 0x7FF;
+}
+template <> inline constexpr int binary_format<float>::infinite_power() {
+ return 0xFF;
+}
+
+template <> inline constexpr int binary_format<double>::sign_index() { return 63; }
+template <> inline constexpr int binary_format<float>::sign_index() { return 31; }
+
+template <> inline constexpr int binary_format<double>::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<float>::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<double>::max_exponent_fast_path() {
+ return 22;
+}
+template <> inline constexpr int binary_format<float>::max_exponent_fast_path() {
+ return 10;
+}
+
+template <> inline constexpr uint64_t binary_format<double>::max_mantissa_fast_path() {
+ return uint64_t(2) << mantissa_explicit_bits();
+}
+template <> inline constexpr uint64_t binary_format<float>::max_mantissa_fast_path() {
+ return uint64_t(2) << mantissa_explicit_bits();
+}
+
+template <>
+inline constexpr double binary_format<double>::exact_power_of_ten(int64_t power) {
+ return powers_of_ten_double[power];
+}
+template <>
+inline constexpr float binary_format<float>::exact_power_of_ten(int64_t power) {
+
+ return powers_of_ten_float[power];
+}
+
+
+template <>
+inline constexpr int binary_format<double>::largest_power_of_ten() {
+ return 308;
+}
+template <>
+inline constexpr int binary_format<float>::largest_power_of_ten() {
+ return 38;
+}
+
+template <>
+inline constexpr int binary_format<double>::smallest_power_of_ten() {
+ return -342;
+}
+template <>
+inline constexpr int binary_format<float>::smallest_power_of_ten() {
+ return -65;
+}
+
+template <> inline constexpr size_t binary_format<double>::max_digits() {
+ return 769;
+}
+template <> inline constexpr size_t binary_format<float>::max_digits() {
+ return 114;
+}
+
+template<typename T>
+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<T>::mantissa_explicit_bits();
+ word = negative
+ ? word | (uint64_t(1) << binary_format<T>::sign_index()) : word;
+#if FASTFLOAT_IS_BIG_ENDIAN == 1
+ if (std::is_same<T, float>::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));
+ }
+#else
+ // For little-endian systems:
+ ::memcpy(&value, &word, sizeof(T));
+#endif
+}
+
+} // namespace fast_float
+
+#endif
+
+#ifndef FASTFLOAT_ASCII_NUMBER_H
+#define FASTFLOAT_ASCII_NUMBER_H
+
+#include <cctype>
+#include <cstdint>
+#include <cstring>
+#include <iterator>
+
+
+namespace fast_float {
+
+// Next function can be micro-optimized, but compilers are entirely
+// able to optimize it well.
+fastfloat_really_inline bool is_integer(char c) noexcept { return c >= '0' && c <= '9'; }
+
+fastfloat_really_inline uint64_t byteswap(uint64_t val) {
+ return (val & 0xFF00000000000000) >> 56
+ | (val & 0x00FF000000000000) >> 40
+ | (val & 0x0000FF0000000000) >> 24
+ | (val & 0x000000FF00000000) >> 8
+ | (val & 0x00000000FF000000) << 8
+ | (val & 0x0000000000FF0000) << 24
+ | (val & 0x000000000000FF00) << 40
+ | (val & 0x00000000000000FF) << 56;
+}
+
+fastfloat_really_inline uint64_t read_u64(const char *chars) {
+ uint64_t val;
+ ::memcpy(&val, chars, sizeof(uint64_t));
+#if FASTFLOAT_IS_BIG_ENDIAN == 1
+ // Need to read as-if the number was in little-endian order.
+ val = byteswap(val);
+#endif
+ return val;
+}
+
+fastfloat_really_inline void write_u64(uint8_t *chars, uint64_t val) {
+#if FASTFLOAT_IS_BIG_ENDIAN == 1
+ // Need to read as-if the number was in little-endian order.
+ val = byteswap(val);
+#endif
+ ::memcpy(chars, &val, sizeof(uint64_t));
+}
+
+// credit @aqrit
+fastfloat_really_inline uint32_t parse_eight_digits_unrolled(uint64_t val) {
+ const uint64_t mask = 0x000000FF000000FF;
+ const uint64_t mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32)
+ const uint64_t mul2 = 0x0000271000000001; // 1 + (10000ULL << 32)
+ val -= 0x3030303030303030;
+ val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8;
+ val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32;
+ return uint32_t(val);
+}
+
+fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars) noexcept {
+ return parse_eight_digits_unrolled(read_u64(chars));
+}
+
+// credit @aqrit
+fastfloat_really_inline 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));
+}
+
+typedef span<const char> byte_span;
+
+struct parsed_number_string {
+ int64_t exponent{0};
+ uint64_t mantissa{0};
+ const char *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
+};
+
+// 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;
+
+ parsed_number_string 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
+ ++p;
+ if (p == pend) {
+ return answer;
+ }
+ if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot
+ return answer;
+ }
+ }
+ const char *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
+ ++p;
+ }
+ const char *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));
+ int64_t exponent = 0;
+ if ((p != pend) && (*p == decimal_point)) {
+ ++p;
+ const char* 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;
+ }
+ while ((p != pend) && is_integer(*p)) {
+ uint8_t digit = uint8_t(*p - '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));
+ digit_count -= exponent;
+ }
+ // we must have encountered at least one integer!
+ if (digit_count == 0) {
+ 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;
+ ++p;
+ bool neg_exp = false;
+ if ((p != pend) && ('-' == *p)) {
+ neg_exp = true;
+ ++p;
+ } else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
+ ++p;
+ }
+ if ((p == pend) || !is_integer(*p)) {
+ if(!(fmt & chars_format::fixed)) {
+ // We are in error.
+ return answer;
+ }
+ // Otherwise, we will be ignoring the 'e'.
+ p = location_of_e;
+ } else {
+ while ((p != pend) && is_integer(*p)) {
+ uint8_t digit = uint8_t(*p - '0');
+ if (exp_number < 0x10000000) {
+ exp_number = 10 * exp_number + digit;
+ }
+ ++p;
+ }
+ if(neg_exp) { exp_number = - exp_number; }
+ exponent += exp_number;
+ }
+ } else {
+ // If it scientific and not fixed, we have to bail out.
+ if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; }
+ }
+ answer.lastmatch = p;
+ answer.valid = true;
+
+ // If we frequently had to deal with long strings of digits,
+ // we could extend our code by using a 128-bit integer instead
+ // of a 64-bit integer. However, this is uncommon.
+ //
+ // We can deal with up to 19 digits.
+ if (digit_count > 19) { // this is uncommon
+ // It is possible that the integer had an overflow.
+ // We have to handle the case where we have 0.0000somenumber.
+ // We need to be mindful of the case where we only have zeroes...
+ // E.g., 0.000000000...000.
+ const char *start = start_digits;
+ while ((start != pend) && (*start == '0' || *start == decimal_point)) {
+ if(*start == '0') { digit_count --; }
+ start++;
+ }
+ if (digit_count > 19) {
+ answer.too_many_digits = true;
+ // Let us start again, this time, avoiding overflows.
+ // We don't need to check if is_integer, since we use the
+ // pre-tokenized spans from above.
+ i = 0;
+ p = answer.integer.ptr;
+ 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');
+ ++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;
+ }
+ // We have now corrected both exponent and i, to a truncated value
+ }
+ }
+ answer.exponent = exponent;
+ answer.mantissa = i;
+ return answer;
+}
+
+} // namespace fast_float
+
+#endif
+
+#ifndef FASTFLOAT_FAST_TABLE_H
+#define FASTFLOAT_FAST_TABLE_H
+
+#include <cstdint>
+
+namespace fast_float {
+
+/**
+ * When mapping numbers from decimal to binary,
+ * we go from w * 10^q to m * 2^p but we have
+ * 10^q = 5^q * 2^q, so effectively
+ * we are trying to match
+ * w * 2^q * 5^q to m * 2^p. Thus the powers of two
+ * are not a concern since they can be represented
+ * exactly using the binary notation, only the powers of five
+ * affect the binary significand.
+ */
+
+/**
+ * The smallest non-zero float (binary64) is 2^−1074.
+ * We take as input numbers of the form w x 10^q where w < 2^64.
+ * We have that w * 10^-343 < 2^(64-344) 5^-343 < 2^-1076.
+ * However, we have that
+ * (2^64-1) * 10^-342 = (2^64-1) * 2^-342 * 5^-342 > 2^−1074.
+ * Thus it is possible for a number of the form w * 10^-342 where
+ * w is a 64-bit value to be a non-zero floating-point number.
+ *********
+ * Any number of form w * 10^309 where w>= 1 is going to be
+ * infinite in binary64 so we never need to worry about powers
+ * of 5 greater than 308.
+ */
+template <class unused = void>
+struct powers_template {
+
+constexpr static int smallest_power_of_five = binary_format<double>::smallest_power_of_ten();
+constexpr static int largest_power_of_five = binary_format<double>::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];
+};
+
+template <class unused>
+const uint64_t powers_template<unused>::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,};
+using powers = powers_template<>;
+
+}
+
+#endif
+
+#ifndef FASTFLOAT_DECIMAL_TO_BINARY_H
+#define FASTFLOAT_DECIMAL_TO_BINARY_H
+
+#include <cfloat>
+#include <cinttypes>
+#include <cmath>
+#include <cstdint>
+#include <cstdlib>
+#include <cstring>
+
+namespace fast_float {
+
+// This will compute or rather approximate w * 5**q and return a pair of 64-bit words approximating
+// the result, with the "high" part corresponding to the most significant bits and the
+// low part corresponding to the least significant bits.
+//
+template <int bit_precision>
+fastfloat_really_inline
+value128 compute_product_approximation(int64_t q, uint64_t w) {
+ const int index = 2 * int(q - powers::smallest_power_of_five);
+ // For small values of q, e.g., q in [0,27], the answer is always exact because
+ // The line value128 firstproduct = full_multiplication(w, power_of_five_128[index]);
+ // gives the exact answer.
+ value128 firstproduct = full_multiplication(w, powers::power_of_five_128[index]);
+ static_assert((bit_precision >= 0) && (bit_precision <= 64), " precision should be in (0,64]");
+ constexpr uint64_t precision_mask = (bit_precision < 64) ?
+ (uint64_t(0xFFFFFFFFFFFFFFFF) >> bit_precision)
+ : uint64_t(0xFFFFFFFFFFFFFFFF);
+ if((firstproduct.high & precision_mask) == precision_mask) { // could further guard with (lower + w < lower)
+ // regarding the second product, we only need secondproduct.high, but our expectation is that the compiler will optimize this extra work away if needed.
+ value128 secondproduct = full_multiplication(w, powers::power_of_five_128[index + 1]);
+ firstproduct.low += secondproduct.high;
+ if(secondproduct.high > firstproduct.low) {
+ firstproduct.high++;
+ }
+ }
+ return firstproduct;
+}
+
+namespace detail {
+/**
+ * For q in (0,350), we have that
+ * f = (((152170 + 65536) * q ) >> 16);
+ * is equal to
+ * floor(p) + q
+ * where
+ * p = log(5**q)/log(2) = q * log(5)/log(2)
+ *
+ * For negative values of q in (-400,0), we have that
+ * f = (((152170 + 65536) * q ) >> 16);
+ * is equal to
+ * -ceil(p) + q
+ * where
+ * p = log(5**-q)/log(2) = -q * log(5)/log(2)
+ */
+ constexpr fastfloat_really_inline int32_t power(int32_t q) noexcept {
+ return (((152170 + 65536) * q) >> 16) + 63;
+ }
+} // namespace detail
+
+// create an adjusted mantissa, biased by the invalid power2
+// for significant digits already multiplied by 10 ** q.
+template <typename binary>
+fastfloat_really_inline
+adjusted_mantissa compute_error_scaled(int64_t q, uint64_t w, int lz) noexcept {
+ int hilz = int(w >> 63) ^ 1;
+ adjusted_mantissa answer;
+ answer.mantissa = w << hilz;
+ int bias = binary::mantissa_explicit_bits() - binary::minimum_exponent();
+ answer.power2 = int32_t(detail::power(int32_t(q)) + bias - hilz - lz - 62 + invalid_am_bias);
+ return answer;
+}
+
+// w * 10 ** q, without rounding the representation up.
+// the power2 in the exponent will be adjusted by invalid_am_bias.
+template <typename binary>
+fastfloat_really_inline
+adjusted_mantissa compute_error(int64_t q, uint64_t w) noexcept {
+ int lz = leading_zeroes(w);
+ w <<= lz;
+ value128 product = compute_product_approximation<binary::mantissa_explicit_bits() + 3>(q, w);
+ return compute_error_scaled<binary>(q, product.high, lz);
+}
+
+// w * 10 ** q
+// The returned value should be a valid ieee64 number that simply need to be packed.
+// However, in some very rare cases, the computation will fail. In such cases, we
+// return an adjusted_mantissa with a negative power of 2: the caller should recompute
+// in such cases.
+template <typename binary>
+fastfloat_really_inline
+adjusted_mantissa compute_float(int64_t q, uint64_t w) noexcept {
+ adjusted_mantissa answer;
+ if ((w == 0) || (q < binary::smallest_power_of_ten())) {
+ answer.power2 = 0;
+ answer.mantissa = 0;
+ // result should be zero
+ return answer;
+ }
+ if (q > binary::largest_power_of_ten()) {
+ // we want to get infinity:
+ answer.power2 = binary::infinite_power();
+ answer.mantissa = 0;
+ return answer;
+ }
+ // At this point in time q is in [powers::smallest_power_of_five, powers::largest_power_of_five].
+
+ // We want the most significant bit of i to be 1. Shift if needed.
+ int lz = leading_zeroes(w);
+ w <<= lz;
+
+ // The required precision is binary::mantissa_explicit_bits() + 3 because
+ // 1. We need the implicit bit
+ // 2. We need an extra bit for rounding purposes
+ // 3. We might lose a bit due to the "upperbit" routine (result too small, requiring a shift)
+
+ value128 product = compute_product_approximation<binary::mantissa_explicit_bits() + 3>(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<binary>(q, product.high, lz);
+ }
+ }
+ // The "compute_product_approximation" function can be slightly slower than a branchless approach:
+ // value128 product = compute_product(q, w);
+ // but in practice, we can win big with the compute_product_approximation if its additional branch
+ // is easily predicted. Which is best is data specific.
+ int upperbit = int(product.high >> 63);
+
+ answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3);
+
+ answer.power2 = int32_t(detail::power(int32_t(q)) + upperbit - lz - binary::minimum_exponent());
+ if (answer.power2 <= 0) { // we have a subnormal?
+ // Here have that answer.power2 <= 0 so -answer.power2 >= 0
+ if(-answer.power2 + 1 >= 64) { // if we have more than 64 bits below the minimum exponent, you have a zero for sure.
+ answer.power2 = 0;
+ answer.mantissa = 0;
+ // result should be zero
+ return answer;
+ }
+ // next line is safe because -answer.power2 + 1 < 64
+ answer.mantissa >>= -answer.power2 + 1;
+ // Thankfully, we can't have both "round-to-even" and subnormals because
+ // "round-to-even" only occurs for powers close to 0.
+ answer.mantissa += (answer.mantissa & 1); // round up
+ answer.mantissa >>= 1;
+ // There is a weird scenario where we don't have a subnormal but just.
+ // Suppose we start with 2.2250738585072013e-308, we end up
+ // with 0x3fffffffffffff x 2^-1023-53 which is technically subnormal
+ // whereas 0x40000000000000 x 2^-1023-53 is normal. Now, we need to round
+ // up 0x3fffffffffffff x 2^-1023-53 and once we do, we are no longer
+ // subnormal, but we can only know this after rounding.
+ // So we only declare a subnormal if we are smaller than the threshold.
+ answer.power2 = (answer.mantissa < (uint64_t(1) << binary::mantissa_explicit_bits())) ? 0 : 1;
+ return answer;
+ }
+
+ // usually, we round *up*, but if we fall right in between and and we have an
+ // even basis, we need to round down
+ // We are only concerned with the cases where 5**q fits in single 64-bit word.
+ if ((product.low <= 1) && (q >= binary::min_exponent_round_to_even()) && (q <= binary::max_exponent_round_to_even()) &&
+ ((answer.mantissa & 3) == 1) ) { // we may fall between two floats!
+ // To be in-between two floats we need that in doing
+ // answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3);
+ // ... we dropped out only zeroes. But if this happened, then we can go back!!!
+ if((answer.mantissa << (upperbit + 64 - binary::mantissa_explicit_bits() - 3)) == product.high) {
+ answer.mantissa &= ~uint64_t(1); // flip it so that we do not round up
+ }
+ }
+
+ answer.mantissa += (answer.mantissa & 1); // round up
+ answer.mantissa >>= 1;
+ if (answer.mantissa >= (uint64_t(2) << binary::mantissa_explicit_bits())) {
+ answer.mantissa = (uint64_t(1) << binary::mantissa_explicit_bits());
+ answer.power2++; // undo previous addition
+ }
+
+ answer.mantissa &= ~(uint64_t(1) << binary::mantissa_explicit_bits());
+ if (answer.power2 >= binary::infinite_power()) { // infinity
+ answer.power2 = binary::infinite_power();
+ answer.mantissa = 0;
+ }
+ return answer;
+}
+
+} // namespace fast_float
+
+#endif
+
+#ifndef FASTFLOAT_BIGINT_H
+#define FASTFLOAT_BIGINT_H
+
+#include <algorithm>
+#include <cstdint>
+#include <climits>
+#include <cstring>
+
+
+namespace fast_float {
+
+// the limb width: we want efficient multiplication of double the bits in
+// limb, or for 64-bit limbs, at least 64-bit multiplication where we can
+// extract the high and low parts efficiently. this is every 64-bit
+// architecture except for sparc, which emulates 128-bit multiplication.
+// we might have platforms where `CHAR_BIT` is not 8, so let's avoid
+// doing `8 * sizeof(limb)`.
+#if defined(FASTFLOAT_64BIT) && !defined(__sparc)
+#define FASTFLOAT_64BIT_LIMB
+typedef uint64_t limb;
+constexpr size_t limb_bits = 64;
+#else
+#define FASTFLOAT_32BIT_LIMB
+typedef uint32_t limb;
+constexpr size_t limb_bits = 32;
+#endif
+
+typedef span<limb> limb_span;
+
+// number of bits in a bigint. this needs to be at least the number
+// of bits required to store the largest bigint, which is
+// `log2(10**(digits + max_exp))`, or `log2(10**(767 + 342))`, or
+// ~3600 bits, so we round to 4000.
+constexpr size_t bigint_bits = 4000;
+constexpr size_t bigint_limbs = bigint_bits / limb_bits;
+
+// vector-like type that is allocated on the stack. the entire
+// buffer is pre-allocated, and only the length changes.
+template <uint16_t size>
+struct stackvec {
+ limb data[size];
+ // we never need more than 150 limbs
+ uint16_t length{0};
+
+ stackvec() = default;
+ stackvec(const stackvec &) = delete;
+ stackvec &operator=(const stackvec &) = delete;
+ stackvec(stackvec &&) = delete;
+ stackvec &operator=(stackvec &&other) = delete;
+
+ // create stack vector from existing limb span.
+ stackvec(limb_span s) {
+ FASTFLOAT_ASSERT(try_extend(s));
+ }
+
+ limb& operator[](size_t index) noexcept {
+ FASTFLOAT_DEBUG_ASSERT(index < length);
+ return data[index];
+ }
+ 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_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 {
+ length = uint16_t(len);
+ }
+ constexpr size_t len() const noexcept {
+ return length;
+ }
+ constexpr bool is_empty() const noexcept {
+ return length == 0;
+ }
+ constexpr size_t capacity() const noexcept {
+ return size;
+ }
+ // append item to vector, without bounds checking
+ 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 {
+ if (len() < capacity()) {
+ push_unchecked(value);
+ return true;
+ } else {
+ return false;
+ }
+ }
+ // add items to the vector, from a span, without bounds checking
+ void extend_unchecked(limb_span s) noexcept {
+ limb* ptr = data + length;
+ ::memcpy((void*)ptr, (const void*)s.ptr, sizeof(limb) * s.len());
+ set_len(len() + s.len());
+ }
+ // try to add items to the vector, returning if items were added
+ bool try_extend(limb_span s) noexcept {
+ if (len() + s.len() <= capacity()) {
+ extend_unchecked(s);
+ return true;
+ } else {
+ return false;
+ }
+ }
+ // resize the vector, without bounds checking
+ // if the new size is longer than the vector, assign value to each
+ // appended item.
+ void resize_unchecked(size_t new_len, limb value) noexcept {
+ if (new_len > len()) {
+ size_t count = new_len - len();
+ limb* first = data + len();
+ limb* last = first + count;
+ ::std::fill(first, last, value);
+ set_len(new_len);
+ } else {
+ set_len(new_len);
+ }
+ }
+ // try to resize the vector, returning if the vector was resized.
+ bool try_resize(size_t new_len, limb value) noexcept {
+ if (new_len > capacity()) {
+ return false;
+ } else {
+ resize_unchecked(new_len, value);
+ return true;
+ }
+ }
+ // check if any limbs are non-zero after the given index.
+ // this needs to be done in reverse order, since the index
+ // is relative to the most significant limbs.
+ bool nonzero(size_t index) const noexcept {
+ while (index < len()) {
+ if (rindex(index) != 0) {
+ return true;
+ }
+ index++;
+ }
+ return false;
+ }
+ // normalize the big integer, so most-significant zero limbs are removed.
+ void normalize() noexcept {
+ while (len() > 0 && rindex(0) == 0) {
+ length--;
+ }
+ }
+};
+
+fastfloat_really_inline
+uint64_t empty_hi64(bool& truncated) noexcept {
+ truncated = false;
+ return 0;
+}
+
+fastfloat_really_inline
+uint64_t uint64_hi64(uint64_t r0, bool& truncated) noexcept {
+ truncated = false;
+ int shl = leading_zeroes(r0);
+ return r0 << shl;
+}
+
+fastfloat_really_inline
+uint64_t uint64_hi64(uint64_t r0, uint64_t r1, bool& truncated) noexcept {
+ int shl = leading_zeroes(r0);
+ if (shl == 0) {
+ truncated = r1 != 0;
+ return r0;
+ } else {
+ int shr = 64 - shl;
+ truncated = (r1 << shl) != 0;
+ return (r0 << shl) | (r1 >> shr);
+ }
+}
+
+fastfloat_really_inline
+uint64_t uint32_hi64(uint32_t r0, bool& truncated) noexcept {
+ return uint64_hi64(r0, truncated);
+}
+
+fastfloat_really_inline
+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
+uint64_t uint32_hi64(uint32_t r0, uint32_t r1, uint32_t r2, bool& truncated) noexcept {
+ uint64_t x0 = r0;
+ uint64_t x1 = r1;
+ uint64_t x2 = r2;
+ return uint64_hi64(x0, (x1 << 32) | x2, truncated);
+}
+
+// add two small integers, checking for overflow.
+// we want an efficient operation. for msvc, where
+// we don't have built-in intrinsics, this is still
+// pretty fast.
+fastfloat_really_inline
+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;
+ #endif
+#endif
+
+ // generic, this still optimizes correctly on MSVC.
+ z = x + y;
+ overflow = z < x;
+ return z;
+}
+
+// multiply two small integers, getting both the high and low bits.
+fastfloat_really_inline
+limb scalar_mul(limb x, limb y, limb& carry) noexcept {
+#ifdef FASTFLOAT_64BIT_LIMB
+ #if defined(__SIZEOF_INT128__)
+ // GCC and clang both define it as an extension.
+ __uint128_t z = __uint128_t(x) * __uint128_t(y) + __uint128_t(carry);
+ carry = limb(z >> limb_bits);
+ return limb(z);
+ #else
+ // fallback, no native 128-bit integer multiplication with carry.
+ // on msvc, this optimizes identically, somehow.
+ value128 z = full_multiplication(x, y);
+ bool overflow;
+ z.low = scalar_add(z.low, carry, overflow);
+ z.high += uint64_t(overflow); // cannot overflow
+ carry = z.high;
+ return z.low;
+ #endif
+#else
+ uint64_t z = uint64_t(x) * uint64_t(y) + uint64_t(carry);
+ carry = limb(z >> limb_bits);
+ return limb(z);
+#endif
+}
+
+// add scalar value to bigint starting from offset.
+// used in grade school multiplication
+template <uint16_t size>
+inline bool small_add_from(stackvec<size>& vec, limb y, size_t start) noexcept {
+ size_t index = start;
+ limb carry = y;
+ bool overflow;
+ while (carry != 0 && index < vec.len()) {
+ vec[index] = scalar_add(vec[index], carry, overflow);
+ carry = limb(overflow);
+ index += 1;
+ }
+ if (carry != 0) {
+ FASTFLOAT_TRY(vec.try_push(carry));
+ }
+ return true;
+}
+
+// add scalar value to bigint.
+template <uint16_t size>
+fastfloat_really_inline bool small_add(stackvec<size>& vec, limb y) noexcept {
+ return small_add_from(vec, y, 0);
+}
+
+// multiply bigint by scalar value.
+template <uint16_t size>
+inline bool small_mul(stackvec<size>& vec, limb y) noexcept {
+ limb carry = 0;
+ for (size_t index = 0; index < vec.len(); index++) {
+ vec[index] = scalar_mul(vec[index], y, carry);
+ }
+ if (carry != 0) {
+ FASTFLOAT_TRY(vec.try_push(carry));
+ }
+ return true;
+}
+
+// add bigint to bigint starting from index.
+// used in grade school multiplication
+template <uint16_t size>
+bool large_add_from(stackvec<size>& x, limb_span y, size_t start) noexcept {
+ // the effective x buffer is from `xstart..x.len()`, so exit early
+ // if we can't get that current range.
+ if (x.len() < start || y.len() > x.len() - start) {
+ FASTFLOAT_TRY(x.try_resize(y.len() + start, 0));
+ }
+
+ bool carry = false;
+ for (size_t index = 0; index < y.len(); index++) {
+ limb xi = x[index + start];
+ limb yi = y[index];
+ bool c1 = false;
+ bool c2 = false;
+ xi = scalar_add(xi, yi, c1);
+ if (carry) {
+ xi = scalar_add(xi, 1, c2);
+ }
+ x[index + start] = xi;
+ carry = c1 | c2;
+ }
+
+ // handle overflow
+ if (carry) {
+ FASTFLOAT_TRY(small_add_from(x, 1, y.len() + start));
+ }
+ return true;
+}
+
+// add bigint to bigint.
+template <uint16_t size>
+fastfloat_really_inline bool large_add_from(stackvec<size>& x, limb_span y) noexcept {
+ return large_add_from(x, y, 0);
+}
+
+// grade-school multiplication algorithm
+template <uint16_t size>
+bool long_mul(stackvec<size>& x, limb_span y) noexcept {
+ limb_span xs = limb_span(x.data, x.len());
+ stackvec<size> z(xs);
+ limb_span zs = limb_span(z.data, z.len());
+
+ if (y.len() != 0) {
+ limb y0 = y[0];
+ FASTFLOAT_TRY(small_mul(x, y0));
+ for (size_t index = 1; index < y.len(); index++) {
+ limb yi = y[index];
+ stackvec<size> zi;
+ if (yi != 0) {
+ // re-use the same buffer throughout
+ zi.set_len(0);
+ FASTFLOAT_TRY(zi.try_extend(zs));
+ FASTFLOAT_TRY(small_mul(zi, yi));
+ limb_span zis = limb_span(zi.data, zi.len());
+ FASTFLOAT_TRY(large_add_from(x, zis, index));
+ }
+ }
+ }
+
+ x.normalize();
+ return true;
+}
+
+// grade-school multiplication algorithm
+template <uint16_t size>
+bool large_mul(stackvec<size>& x, limb_span y) noexcept {
+ if (y.len() == 1) {
+ FASTFLOAT_TRY(small_mul(x, y[0]));
+ } else {
+ FASTFLOAT_TRY(long_mul(x, y));
+ }
+ return true;
+}
+
+// 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 {
+ // storage of the limbs, in little-endian order.
+ stackvec<bigint_limbs> vec;
+
+ bigint(): vec() {}
+ bigint(const bigint &) = delete;
+ bigint &operator=(const bigint &) = delete;
+ bigint(bigint &&) = delete;
+ bigint &operator=(bigint &&other) = delete;
+
+ bigint(uint64_t value): vec() {
+#ifdef FASTFLOAT_64BIT_LIMB
+ vec.push_unchecked(value);
+#else
+ vec.push_unchecked(uint32_t(value));
+ vec.push_unchecked(uint32_t(value >> 32));
+#endif
+ vec.normalize();
+ }
+
+ // get the high 64 bits from the vector, and if bits were truncated.
+ // this is to get the significant digits for the float.
+ uint64_t hi64(bool& truncated) const noexcept {
+#ifdef FASTFLOAT_64BIT_LIMB
+ if (vec.len() == 0) {
+ return empty_hi64(truncated);
+ } else if (vec.len() == 1) {
+ return uint64_hi64(vec.rindex(0), truncated);
+ } else {
+ uint64_t result = uint64_hi64(vec.rindex(0), vec.rindex(1), truncated);
+ truncated |= vec.nonzero(2);
+ return result;
+ }
+#else
+ if (vec.len() == 0) {
+ return empty_hi64(truncated);
+ } else if (vec.len() == 1) {
+ return uint32_hi64(vec.rindex(0), truncated);
+ } else if (vec.len() == 2) {
+ return uint32_hi64(vec.rindex(0), vec.rindex(1), truncated);
+ } else {
+ uint64_t result = uint32_hi64(vec.rindex(0), vec.rindex(1), vec.rindex(2), truncated);
+ truncated |= vec.nonzero(3);
+ return result;
+ }
+#endif
+ }
+
+ // compare two big integers, returning the large value.
+ // assumes both are normalized. if the return value is
+ // negative, other is larger, if the return value is
+ // positive, this is larger, otherwise they are equal.
+ // the limbs are stored in little-endian order, so we
+ // must compare the limbs in ever order.
+ int compare(const bigint& other) const noexcept {
+ if (vec.len() > other.vec.len()) {
+ return 1;
+ } else if (vec.len() < other.vec.len()) {
+ return -1;
+ } else {
+ for (size_t index = vec.len(); index > 0; index--) {
+ limb xi = vec[index - 1];
+ limb yi = other.vec[index - 1];
+ if (xi > yi) {
+ return 1;
+ } else if (xi < yi) {
+ return -1;
+ }
+ }
+ return 0;
+ }
+ }
+
+ // shift left each limb n bits, carrying over to the new limb
+ // returns true if we were able to shift all the digits.
+ bool shl_bits(size_t n) noexcept {
+ // Internally, for each item, we shift left by n, and add the previous
+ // right shifted limb-bits.
+ // For example, we transform (for u8) shifted left 2, to:
+ // b10100100 b01000010
+ // b10 b10010001 b00001000
+ FASTFLOAT_DEBUG_ASSERT(n != 0);
+ FASTFLOAT_DEBUG_ASSERT(n < sizeof(limb) * 8);
+
+ size_t shl = n;
+ size_t shr = limb_bits - shl;
+ limb prev = 0;
+ for (size_t index = 0; index < vec.len(); index++) {
+ limb xi = vec[index];
+ vec[index] = (xi << shl) | (prev >> shr);
+ prev = xi;
+ }
+
+ limb carry = prev >> shr;
+ if (carry != 0) {
+ return vec.try_push(carry);
+ }
+ return true;
+ }
+
+ // move the limbs left by `n` limbs.
+ bool shl_limbs(size_t n) noexcept {
+ FASTFLOAT_DEBUG_ASSERT(n != 0);
+ if (n + vec.len() > vec.capacity()) {
+ return false;
+ } else if (!vec.is_empty()) {
+ // move limbs
+ limb* dst = vec.data + n;
+ const limb* src = vec.data;
+ ::memmove(dst, src, sizeof(limb) * vec.len());
+ // fill in empty limbs
+ limb* first = vec.data;
+ limb* last = first + n;
+ ::std::fill(first, last, 0);
+ vec.set_len(n + vec.len());
+ return true;
+ } else {
+ return true;
+ }
+ }
+
+ // move the limbs left by `n` bits.
+ bool shl(size_t n) noexcept {
+ size_t rem = n % limb_bits;
+ size_t div = n / limb_bits;
+ if (rem != 0) {
+ FASTFLOAT_TRY(shl_bits(rem));
+ }
+ if (div != 0) {
+ FASTFLOAT_TRY(shl_limbs(div));
+ }
+ return true;
+ }
+
+ // get the number of leading zeros in the bigint.
+ int ctlz() const noexcept {
+ if (vec.is_empty()) {
+ return 0;
+ } else {
+#ifdef FASTFLOAT_64BIT_LIMB
+ return leading_zeroes(vec.rindex(0));
+#else
+ // no use defining a specialized leading_zeroes for a 32-bit type.
+ uint64_t r0 = vec.rindex(0);
+ return leading_zeroes(r0 << 32);
+#endif
+ }
+ }
+
+ // get the number of bits in the bigint.
+ int bit_length() const noexcept {
+ int lz = ctlz();
+ return int(limb_bits * vec.len()) - lz;
+ }
+
+ bool mul(limb y) noexcept {
+ return small_mul(vec, y);
+ }
+
+ 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 {
+ return shl(exp);
+ }
+
+ // multiply as if by 5 raised to a power.
+ 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) {
+ FASTFLOAT_TRY(large_mul(vec, large));
+ exp -= large_step;
+ }
+#ifdef FASTFLOAT_64BIT_LIMB
+ uint32_t small_step = 27;
+ limb max_native = 7450580596923828125UL;
+#else
+ uint32_t small_step = 13;
+ limb max_native = 1220703125U;
+#endif
+ while (exp >= small_step) {
+ FASTFLOAT_TRY(small_mul(vec, max_native));
+ exp -= small_step;
+ }
+ if (exp != 0) {
+ FASTFLOAT_TRY(small_mul(vec, limb(small_power_of_5[exp])));
+ }
+
+ return true;
+ }
+
+ // multiply as if by 10 raised to a power.
+ bool pow10(uint32_t exp) noexcept {
+ FASTFLOAT_TRY(pow5(exp));
+ return pow2(exp);
+ }
+};
+
+} // namespace fast_float
+
+#endif
+
+#ifndef FASTFLOAT_ASCII_NUMBER_H
+#define FASTFLOAT_ASCII_NUMBER_H
+
+#include <cctype>
+#include <cstdint>
+#include <cstring>
+#include <iterator>
+
+
+namespace fast_float {
+
+// Next function can be micro-optimized, but compilers are entirely
+// able to optimize it well.
+fastfloat_really_inline bool is_integer(char c) noexcept { return c >= '0' && c <= '9'; }
+
+fastfloat_really_inline uint64_t byteswap(uint64_t val) {
+ return (val & 0xFF00000000000000) >> 56
+ | (val & 0x00FF000000000000) >> 40
+ | (val & 0x0000FF0000000000) >> 24
+ | (val & 0x000000FF00000000) >> 8
+ | (val & 0x00000000FF000000) << 8
+ | (val & 0x0000000000FF0000) << 24
+ | (val & 0x000000000000FF00) << 40
+ | (val & 0x00000000000000FF) << 56;
+}
+
+fastfloat_really_inline uint64_t read_u64(const char *chars) {
+ uint64_t val;
+ ::memcpy(&val, chars, sizeof(uint64_t));
+#if FASTFLOAT_IS_BIG_ENDIAN == 1
+ // Need to read as-if the number was in little-endian order.
+ val = byteswap(val);
+#endif
+ return val;
+}
+
+fastfloat_really_inline void write_u64(uint8_t *chars, uint64_t val) {
+#if FASTFLOAT_IS_BIG_ENDIAN == 1
+ // Need to read as-if the number was in little-endian order.
+ val = byteswap(val);
+#endif
+ ::memcpy(chars, &val, sizeof(uint64_t));
+}
+
+// credit @aqrit
+fastfloat_really_inline uint32_t parse_eight_digits_unrolled(uint64_t val) {
+ const uint64_t mask = 0x000000FF000000FF;
+ const uint64_t mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32)
+ const uint64_t mul2 = 0x0000271000000001; // 1 + (10000ULL << 32)
+ val -= 0x3030303030303030;
+ val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8;
+ val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32;
+ return uint32_t(val);
+}
+
+fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars) noexcept {
+ return parse_eight_digits_unrolled(read_u64(chars));
+}
+
+// credit @aqrit
+fastfloat_really_inline 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));
+}
+
+typedef span<const char> byte_span;
+
+struct parsed_number_string {
+ int64_t exponent{0};
+ uint64_t mantissa{0};
+ const char *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
+};
+
+// 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;
+
+ parsed_number_string 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
+ ++p;
+ if (p == pend) {
+ return answer;
+ }
+ if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot
+ return answer;
+ }
+ }
+ const char *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
+ ++p;
+ }
+ const char *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));
+ int64_t exponent = 0;
+ if ((p != pend) && (*p == decimal_point)) {
+ ++p;
+ const char* 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;
+ }
+ while ((p != pend) && is_integer(*p)) {
+ uint8_t digit = uint8_t(*p - '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));
+ digit_count -= exponent;
+ }
+ // we must have encountered at least one integer!
+ if (digit_count == 0) {
+ 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;
+ ++p;
+ bool neg_exp = false;
+ if ((p != pend) && ('-' == *p)) {
+ neg_exp = true;
+ ++p;
+ } else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
+ ++p;
+ }
+ if ((p == pend) || !is_integer(*p)) {
+ if(!(fmt & chars_format::fixed)) {
+ // We are in error.
+ return answer;
+ }
+ // Otherwise, we will be ignoring the 'e'.
+ p = location_of_e;
+ } else {
+ while ((p != pend) && is_integer(*p)) {
+ uint8_t digit = uint8_t(*p - '0');
+ if (exp_number < 0x10000000) {
+ exp_number = 10 * exp_number + digit;
+ }
+ ++p;
+ }
+ if(neg_exp) { exp_number = - exp_number; }
+ exponent += exp_number;
+ }
+ } else {
+ // If it scientific and not fixed, we have to bail out.
+ if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; }
+ }
+ answer.lastmatch = p;
+ answer.valid = true;
+
+ // If we frequently had to deal with long strings of digits,
+ // we could extend our code by using a 128-bit integer instead
+ // of a 64-bit integer. However, this is uncommon.
+ //
+ // We can deal with up to 19 digits.
+ if (digit_count > 19) { // this is uncommon
+ // It is possible that the integer had an overflow.
+ // We have to handle the case where we have 0.0000somenumber.
+ // We need to be mindful of the case where we only have zeroes...
+ // E.g., 0.000000000...000.
+ const char *start = start_digits;
+ while ((start != pend) && (*start == '0' || *start == decimal_point)) {
+ if(*start == '0') { digit_count --; }
+ start++;
+ }
+ if (digit_count > 19) {
+ answer.too_many_digits = true;
+ // Let us start again, this time, avoiding overflows.
+ // We don't need to check if is_integer, since we use the
+ // pre-tokenized spans from above.
+ i = 0;
+ p = answer.integer.ptr;
+ 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');
+ ++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;
+ }
+ // We have now corrected both exponent and i, to a truncated value
+ }
+ }
+ answer.exponent = exponent;
+ answer.mantissa = i;
+ return answer;
+}
+
+} // namespace fast_float
+
+#endif
+
+#ifndef FASTFLOAT_DIGIT_COMPARISON_H
+#define FASTFLOAT_DIGIT_COMPARISON_H
+
+#include <algorithm>
+#include <cstdint>
+#include <cstring>
+#include <iterator>
+
+
+namespace fast_float {
+
+// 1e0 to 1e19
+constexpr static uint64_t powers_of_ten_uint64[] = {
+ 1UL, 10UL, 100UL, 1000UL, 10000UL, 100000UL, 1000000UL, 10000000UL, 100000000UL,
+ 1000000000UL, 10000000000UL, 100000000000UL, 1000000000000UL, 10000000000000UL,
+ 100000000000000UL, 1000000000000000UL, 10000000000000000UL, 100000000000000000UL,
+ 1000000000000000000UL, 10000000000000000000UL};
+
+// calculate the exponent, in scientific notation, of the number.
+// this algorithm is not even close to optimized, but it has no practical
+// effect on performance: in order to have a faster algorithm, we'd need
+// to slow down performance for faster algorithms, and this is still fast.
+fastfloat_really_inline int32_t scientific_exponent(parsed_number_string& num) noexcept {
+ uint64_t mantissa = num.mantissa;
+ int32_t exponent = int32_t(num.exponent);
+ while (mantissa >= 10000) {
+ mantissa /= 10000;
+ exponent += 4;
+ }
+ while (mantissa >= 100) {
+ mantissa /= 100;
+ exponent += 2;
+ }
+ while (mantissa >= 10) {
+ mantissa /= 10;
+ exponent += 1;
+ }
+ return exponent;
+}
+
+// this converts a native floating-point number to an extended-precision float.
+template <typename T>
+fastfloat_really_inline adjusted_mantissa to_extended(T value) noexcept {
+ adjusted_mantissa am;
+ int32_t bias = binary_format<T>::mantissa_explicit_bits() - binary_format<T>::minimum_exponent();
+ if (std::is_same<T, float>::value) {
+ constexpr uint32_t exponent_mask = 0x7F800000;
+ constexpr uint32_t mantissa_mask = 0x007FFFFF;
+ constexpr uint64_t hidden_bit_mask = 0x00800000;
+ uint32_t bits;
+ ::memcpy(&bits, &value, sizeof(T));
+ if ((bits & exponent_mask) == 0) {
+ // denormal
+ am.power2 = 1 - bias;
+ am.mantissa = bits & mantissa_mask;
+ } else {
+ // normal
+ am.power2 = int32_t((bits & exponent_mask) >> binary_format<T>::mantissa_explicit_bits());
+ am.power2 -= bias;
+ am.mantissa = (bits & mantissa_mask) | hidden_bit_mask;
+ }
+ } else {
+ constexpr uint64_t exponent_mask = 0x7FF0000000000000;
+ constexpr uint64_t mantissa_mask = 0x000FFFFFFFFFFFFF;
+ constexpr uint64_t hidden_bit_mask = 0x0010000000000000;
+ uint64_t bits;
+ ::memcpy(&bits, &value, sizeof(T));
+ if ((bits & exponent_mask) == 0) {
+ // denormal
+ am.power2 = 1 - bias;
+ am.mantissa = bits & mantissa_mask;
+ } else {
+ // normal
+ am.power2 = int32_t((bits & exponent_mask) >> binary_format<T>::mantissa_explicit_bits());
+ am.power2 -= bias;
+ am.mantissa = (bits & mantissa_mask) | hidden_bit_mask;
+ }
+ }
+
+ return am;
+}
+
+// get the extended precision value of the halfway point between b and b+u.
+// we are given a native float that represents b, so we need to adjust it
+// halfway between b and b+u.
+template <typename T>
+fastfloat_really_inline adjusted_mantissa to_extended_halfway(T value) noexcept {
+ adjusted_mantissa am = to_extended(value);
+ am.mantissa <<= 1;
+ am.mantissa += 1;
+ am.power2 -= 1;
+ return am;
+}
+
+// round an extended-precision float to the nearest machine float.
+template <typename T, typename callback>
+fastfloat_really_inline void round(adjusted_mantissa& am, callback cb) noexcept {
+ int32_t mantissa_shift = 64 - binary_format<T>::mantissa_explicit_bits() - 1;
+ if (-am.power2 >= mantissa_shift) {
+ // have a denormal float
+ int32_t shift = -am.power2 + 1;
+ cb(am, std::min(shift, 64));
+ // check for round-up: if rounding-nearest carried us to the hidden bit.
+ am.power2 = (am.mantissa < (uint64_t(1) << binary_format<T>::mantissa_explicit_bits())) ? 0 : 1;
+ return;
+ }
+
+ // have a normal float, use the default shift.
+ cb(am, mantissa_shift);
+
+ // check for carry
+ if (am.mantissa >= (uint64_t(2) << binary_format<T>::mantissa_explicit_bits())) {
+ am.mantissa = (uint64_t(1) << binary_format<T>::mantissa_explicit_bits());
+ am.power2++;
+ }
+
+ // check for infinite: we could have carried to an infinite power
+ am.mantissa &= ~(uint64_t(1) << binary_format<T>::mantissa_explicit_bits());
+ if (am.power2 >= binary_format<T>::infinite_power()) {
+ am.power2 = binary_format<T>::infinite_power();
+ am.mantissa = 0;
+ }
+}
+
+template <typename callback>
+fastfloat_really_inline
+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);
+ }
+ uint64_t truncated_bits = am.mantissa & mask;
+ uint64_t is_above = truncated_bits > halfway;
+ uint64_t is_halfway = truncated_bits == halfway;
+
+ // shift digits into position
+ if (shift == 64) {
+ am.mantissa = 0;
+ } else {
+ am.mantissa >>= shift;
+ }
+ am.power2 += shift;
+
+ bool is_odd = (am.mantissa & 1) == 1;
+ am.mantissa += uint64_t(cb(is_odd, is_halfway, is_above));
+}
+
+fastfloat_really_inline void round_down(adjusted_mantissa& am, int32_t shift) noexcept {
+ if (shift == 64) {
+ am.mantissa = 0;
+ } else {
+ am.mantissa >>= shift;
+ }
+ am.power2 += shift;
+}
+
+fastfloat_really_inline void skip_zeros(const char*& first, const char* last) noexcept {
+ uint64_t val;
+ while (std::distance(first, last) >= 8) {
+ ::memcpy(&val, first, sizeof(uint64_t));
+ if (val != 0x3030303030303030) {
+ break;
+ }
+ first += 8;
+ }
+ while (first != last) {
+ if (*first != '0') {
+ break;
+ }
+ first++;
+ }
+}
+
+// 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 {
+ // do 8-bit optimizations, can just compare to 8 literal 0s.
+ uint64_t val;
+ while (std::distance(first, last) >= 8) {
+ ::memcpy(&val, first, sizeof(uint64_t));
+ if (val != 0x3030303030303030) {
+ return true;
+ }
+ first += 8;
+ }
+ while (first != last) {
+ if (*first != '0') {
+ return true;
+ }
+ first++;
+ }
+ return false;
+}
+
+fastfloat_really_inline bool is_truncated(byte_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 {
+ 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');
+ p++;
+ counter++;
+ count++;
+}
+
+fastfloat_really_inline
+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 {
+ // need to round-up the digits, but need to avoid rounding
+ // ....9999 to ...10000, which could cause a false halfway point.
+ add_native(big, 10, 1);
+ count++;
+}
+
+// parse the significant digits into a big integer
+inline void parse_mantissa(bigint& result, parsed_number_string& num, size_t max_digits, size_t& digits) noexcept {
+ // try to minimize the number of big integer and scalar multiplication.
+ // therefore, try to parse 8 digits at a time, and multiply by the largest
+ // scalar value (9 or 19 digits) for each step.
+ size_t counter = 0;
+ digits = 0;
+ limb value = 0;
+#ifdef FASTFLOAT_64BIT_LIMB
+ size_t step = 19;
+#else
+ size_t step = 9;
+#endif
+
+ // process all integer digits.
+ const char* p = num.integer.ptr;
+ const char* pend = p + num.integer.len();
+ skip_zeros(p, pend);
+ // process all digits, in increments of step per loop
+ while (p != pend) {
+ while ((std::distance(p, pend) >= 8) && (step - counter >= 8) && (max_digits - digits >= 8)) {
+ parse_eight_digits(p, value, counter, digits);
+ }
+ while (counter < step && p != pend && digits < max_digits) {
+ parse_one_digit(p, value, counter, digits);
+ }
+ if (digits == max_digits) {
+ // add the temporary value, then check if we've truncated any digits
+ add_native(result, limb(powers_of_ten_uint64[counter]), value);
+ bool truncated = is_truncated(p, pend);
+ if (num.fraction.ptr != nullptr) {
+ truncated |= is_truncated(num.fraction);
+ }
+ if (truncated) {
+ round_up_bigint(result, digits);
+ }
+ return;
+ } else {
+ add_native(result, limb(powers_of_ten_uint64[counter]), value);
+ counter = 0;
+ value = 0;
+ }
+ }
+
+ // add our fraction digits, if they're available.
+ if (num.fraction.ptr != nullptr) {
+ p = num.fraction.ptr;
+ pend = p + num.fraction.len();
+ if (digits == 0) {
+ skip_zeros(p, pend);
+ }
+ // process all digits, in increments of step per loop
+ while (p != pend) {
+ while ((std::distance(p, pend) >= 8) && (step - counter >= 8) && (max_digits - digits >= 8)) {
+ parse_eight_digits(p, value, counter, digits);
+ }
+ while (counter < step && p != pend && digits < max_digits) {
+ parse_one_digit(p, value, counter, digits);
+ }
+ if (digits == max_digits) {
+ // add the temporary value, then check if we've truncated any digits
+ add_native(result, limb(powers_of_ten_uint64[counter]), value);
+ bool truncated = is_truncated(p, pend);
+ if (truncated) {
+ round_up_bigint(result, digits);
+ }
+ return;
+ } else {
+ add_native(result, limb(powers_of_ten_uint64[counter]), value);
+ counter = 0;
+ value = 0;
+ }
+ }
+ }
+
+ if (counter != 0) {
+ add_native(result, limb(powers_of_ten_uint64[counter]), value);
+ }
+}
+
+template <typename T>
+inline adjusted_mantissa positive_digit_comp(bigint& bigmant, int32_t exponent) noexcept {
+ FASTFLOAT_ASSERT(bigmant.pow10(uint32_t(exponent)));
+ adjusted_mantissa answer;
+ bool truncated;
+ answer.mantissa = bigmant.hi64(truncated);
+ int bias = binary_format<T>::mantissa_explicit_bits() - binary_format<T>::minimum_exponent();
+ answer.power2 = bigmant.bit_length() - 64 + bias;
+
+ round<T>(answer, [truncated](adjusted_mantissa& a, int32_t shift) {
+ round_nearest_tie_even(a, shift, [truncated](bool is_odd, bool is_halfway, bool is_above) -> bool {
+ return is_above || (is_halfway && truncated) || (is_odd && is_halfway);
+ });
+ });
+
+ return answer;
+}
+
+// the scaling here is quite simple: we have, for the real digits `m * 10^e`,
+// and for the theoretical digits `n * 2^f`. Since `e` is always negative,
+// to scale them identically, we do `n * 2^f * 5^-f`, so we now have `m * 2^e`.
+// we then need to scale by `2^(f- e)`, and then the two significant digits
+// are of the same magnitude.
+template <typename T>
+inline adjusted_mantissa negative_digit_comp(bigint& bigmant, adjusted_mantissa am, int32_t exponent) noexcept {
+ bigint& real_digits = bigmant;
+ int32_t real_exp = exponent;
+
+ // get the value of `b`, rounded down, and get a bigint representation of b+h
+ adjusted_mantissa am_b = am;
+ // gcc7 buf: use a lambda to remove the noexcept qualifier bug with -Wnoexcept-type.
+ round<T>(am_b, [](adjusted_mantissa&a, int32_t shift) { round_down(a, shift); });
+ T b;
+ to_float(false, am_b, b);
+ adjusted_mantissa theor = to_extended_halfway(b);
+ bigint theor_digits(theor.mantissa);
+ int32_t theor_exp = theor.power2;
+
+ // scale real digits and theor digits to be same power.
+ int32_t pow2_exp = theor_exp - real_exp;
+ uint32_t pow5_exp = uint32_t(-real_exp);
+ if (pow5_exp != 0) {
+ FASTFLOAT_ASSERT(theor_digits.pow5(pow5_exp));
+ }
+ if (pow2_exp > 0) {
+ FASTFLOAT_ASSERT(theor_digits.pow2(uint32_t(pow2_exp)));
+ } else if (pow2_exp < 0) {
+ FASTFLOAT_ASSERT(real_digits.pow2(uint32_t(-pow2_exp)));
+ }
+
+ // compare digits, and use it to director rounding
+ int ord = real_digits.compare(theor_digits);
+ adjusted_mantissa answer = am;
+ round<T>(answer, [ord](adjusted_mantissa& a, int32_t shift) {
+ round_nearest_tie_even(a, shift, [ord](bool is_odd, bool _, bool __) -> bool {
+ (void)_; // not needed, since we've done our comparison
+ (void)__; // not needed, since we've done our comparison
+ if (ord > 0) {
+ return true;
+ } else if (ord < 0) {
+ return false;
+ } else {
+ return is_odd;
+ }
+ });
+ });
+
+ return answer;
+}
+
+// parse the significant digits as a big integer to unambiguously round the
+// the significant digits. here, we are trying to determine how to round
+// an extended float representation close to `b+h`, halfway between `b`
+// (the float rounded-down) and `b+u`, the next positive float. this
+// algorithm is always correct, and uses one of two approaches. when
+// the exponent is positive relative to the significant digits (such as
+// 1234), we create a big-integer representation, get the high 64-bits,
+// determine if any lower bits are truncated, and use that to direct
+// rounding. in case of a negative exponent relative to the significant
+// digits (such as 1.2345), we create a theoretical representation of
+// `b` as a big-integer type, scaled to the same binary exponent as
+// the actual digits. we then compare the big integer representations
+// of both, and use that to direct rounding.
+template <typename T>
+inline adjusted_mantissa digit_comp(parsed_number_string& num, adjusted_mantissa am) noexcept {
+ // remove the invalid exponent bias
+ am.power2 -= invalid_am_bias;
+
+ int32_t sci_exp = scientific_exponent(num);
+ size_t max_digits = binary_format<T>::max_digits();
+ size_t digits = 0;
+ bigint bigmant;
+ parse_mantissa(bigmant, num, max_digits, digits);
+ // can't underflow, since digits is at most max_digits.
+ int32_t exponent = sci_exp + 1 - int32_t(digits);
+ if (exponent >= 0) {
+ return positive_digit_comp<T>(bigmant, exponent);
+ } else {
+ return negative_digit_comp<T>(bigmant, am, exponent);
+ }
+}
+
+} // namespace fast_float
+
+#endif
+
+#ifndef FASTFLOAT_PARSE_NUMBER_H
+#define FASTFLOAT_PARSE_NUMBER_H
+
+
+#include <cmath>
+#include <cstring>
+#include <limits>
+#include <system_error>
+
+namespace fast_float {
+
+
+namespace detail {
+/**
+ * Special case +inf, -inf, nan, infinity, -infinity.
+ * The case comparisons could be made much faster given that we know that the
+ * strings a null-free and fixed.
+ **/
+template <typename T>
+from_chars_result parse_infnan(const char *first, const char *last, T &value) noexcept {
+ from_chars_result 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
+ minusSign = true;
+ ++first;
+ }
+ if (last - first >= 3) {
+ if (fastfloat_strncasecmp(first, "nan", 3)) {
+ answer.ptr = (first += 3);
+ value = minusSign ? -std::numeric_limits<T>::quiet_NaN() : std::numeric_limits<T>::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 == ')') {
+ 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 == '_'))
+ 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)) {
+ answer.ptr = first + 8;
+ } else {
+ answer.ptr = first + 3;
+ }
+ value = minusSign ? -std::numeric_limits<T>::infinity() : std::numeric_limits<T>::infinity();
+ return answer;
+ }
+ }
+ answer.ec = std::errc::invalid_argument;
+ return answer;
+}
+
+} // namespace detail
+
+template<typename T>
+from_chars_result from_chars(const char *first, const char *last,
+ T &value, chars_format fmt /*= chars_format::general*/) noexcept {
+ return from_chars_advanced(first, last, value, parse_options{fmt});
+}
+
+template<typename T>
+from_chars_result from_chars_advanced(const char *first, const char *last,
+ T &value, parse_options options) noexcept {
+
+ static_assert (std::is_same<T, double>::value || std::is_same<T, float>::value, "only float and double are supported");
+
+
+ from_chars_result answer;
+ if (first == last) {
+ answer.ec = std::errc::invalid_argument;
+ answer.ptr = first;
+ return answer;
+ }
+ parsed_number_string 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<T>::min_exponent_fast_path() <= pns.exponent && pns.exponent <= binary_format<T>::max_exponent_fast_path() && pns.mantissa <=binary_format<T>::max_mantissa_fast_path() && !pns.too_many_digits) {
+ value = T(pns.mantissa);
+ if (pns.exponent < 0) { value = value / binary_format<T>::exact_power_of_ten(-pns.exponent); }
+ else { value = value * binary_format<T>::exact_power_of_ten(pns.exponent); }
+ if (pns.negative) { value = -value; }
+ return answer;
+ }
+ adjusted_mantissa am = compute_float<binary_format<T>>(pns.exponent, pns.mantissa);
+ if(pns.too_many_digits && am.power2 >= 0) {
+ if(am != compute_float<binary_format<T>>(pns.exponent, pns.mantissa + 1)) {
+ am = compute_error<binary_format<T>>(pns.exponent, pns.mantissa);
+ }
+ }
+ // If we called compute_float<binary_format<T>>(pns.exponent, pns.mantissa) and we have an invalid power (am.power2 < 0),
+ // then we need to go the long way around again. This is very uncommon.
+ if(am.power2 < 0) { am = digit_comp<T>(pns, am); }
+ to_float(pns.negative, am, value);
+ return answer;
+}
+
+} // namespace fast_float
+
+#endif
+
More information about the Libstdc++-cvs
mailing list