From 81383afc501ea575261e347d699e83ba134eab56 Mon Sep 17 00:00:00 2001 From: Connor McLaughlin Date: Sun, 15 Jan 2023 13:12:40 +1000 Subject: [PATCH] dep: Add fast_float --- dep/CMakeLists.txt | 1 + dep/fast_float/AUTHORS | 2 + dep/fast_float/CMakeLists.txt | 3 + dep/fast_float/CONTRIBUTORS | 6 + dep/fast_float/LICENSE-APACHE | 190 +++++ dep/fast_float/LICENSE-MIT | 27 + dep/fast_float/README.md | 247 +++++++ .../include/fast_float/ascii_number.h | 227 ++++++ dep/fast_float/include/fast_float/bigint.h | 590 +++++++++++++++ .../include/fast_float/decimal_to_binary.h | 194 +++++ .../include/fast_float/digit_comparison.h | 407 ++++++++++ .../include/fast_float/fast_float.h | 63 ++ .../include/fast_float/fast_table.h | 699 ++++++++++++++++++ .../include/fast_float/float_common.h | 458 ++++++++++++ .../include/fast_float/parse_number.h | 205 +++++ .../fast_float/simple_decimal_conversion.h | 360 +++++++++ 16 files changed, 3679 insertions(+) create mode 100644 dep/fast_float/AUTHORS create mode 100644 dep/fast_float/CMakeLists.txt create mode 100644 dep/fast_float/CONTRIBUTORS create mode 100644 dep/fast_float/LICENSE-APACHE create mode 100644 dep/fast_float/LICENSE-MIT create mode 100644 dep/fast_float/README.md create mode 100644 dep/fast_float/include/fast_float/ascii_number.h create mode 100644 dep/fast_float/include/fast_float/bigint.h create mode 100644 dep/fast_float/include/fast_float/decimal_to_binary.h create mode 100644 dep/fast_float/include/fast_float/digit_comparison.h create mode 100644 dep/fast_float/include/fast_float/fast_float.h create mode 100644 dep/fast_float/include/fast_float/fast_table.h create mode 100644 dep/fast_float/include/fast_float/float_common.h create mode 100644 dep/fast_float/include/fast_float/parse_number.h create mode 100644 dep/fast_float/include/fast_float/simple_decimal_conversion.h diff --git a/dep/CMakeLists.txt b/dep/CMakeLists.txt index 181d113d5..2dcbc331b 100644 --- a/dep/CMakeLists.txt +++ b/dep/CMakeLists.txt @@ -17,6 +17,7 @@ add_subdirectory(soundtouch) add_subdirectory(tinyxml2) add_subdirectory(googletest) add_subdirectory(cpuinfo) +add_subdirectory(fast_float) if(ENABLE_CUBEB) add_subdirectory(cubeb) diff --git a/dep/fast_float/AUTHORS b/dep/fast_float/AUTHORS new file mode 100644 index 000000000..60c942582 --- /dev/null +++ b/dep/fast_float/AUTHORS @@ -0,0 +1,2 @@ +Daniel Lemire +João Paulo Magalhaes diff --git a/dep/fast_float/CMakeLists.txt b/dep/fast_float/CMakeLists.txt new file mode 100644 index 000000000..589d3cbbe --- /dev/null +++ b/dep/fast_float/CMakeLists.txt @@ -0,0 +1,3 @@ +add_library(fast_float INTERFACE) +target_include_directories(fast_float INTERFACE "${CMAKE_CURRENT_SOURCE_DIR}/include") + diff --git a/dep/fast_float/CONTRIBUTORS b/dep/fast_float/CONTRIBUTORS new file mode 100644 index 000000000..58a037cc5 --- /dev/null +++ b/dep/fast_float/CONTRIBUTORS @@ -0,0 +1,6 @@ +Eugene Golushkov +Maksim Kita +Marcin Wojdyr +Neal Richardson +Tim Paine +Fabio Pellacini diff --git a/dep/fast_float/LICENSE-APACHE b/dep/fast_float/LICENSE-APACHE new file mode 100644 index 000000000..26f4398f2 --- /dev/null +++ b/dep/fast_float/LICENSE-APACHE @@ -0,0 +1,190 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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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. diff --git a/dep/fast_float/README.md b/dep/fast_float/README.md new file mode 100644 index 000000000..7b3166abd --- /dev/null +++ b/dep/fast_float/README.md @@ -0,0 +1,247 @@ +## fast_float number parsing library: 4x faster than strtod + +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 + +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. + +We assume that the rounding mode is set to nearest (`std::fegetround() == FE_TONEAREST`). + +## 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 + +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; +} +``` + +You can parse delimited numbers: +```C++ + const std::string input = "234532.3426362,7869234.9823,324562.645"; + double result; + auto answer = fast_float::from_chars(input.data(), input.data()+input.size(), result); + if(answer.ec != std::errc()) { + // check error + } + // we have result == 234532.3426362. + if(answer.ptr[0] != ',') { + // unexpected delimiter + } + answer = fast_float::from_chars(answer.ptr + 1, input.data()+input.size(), result); + if(answer.ec != std::errc()) { + // check error + } + // we have result == 7869234.9823. + if(answer.ptr[0] != ',') { + // unexpected delimiter + } + answer = fast_float::from_chars(answer.ptr + 1, input.data()+input.size(), result); + if(answer.ec != std::errc()) { + // check error + } + // we have result == 324562.645. +``` + + +## Relation With Other Work + +The fast_float library is part of: + +- GCC (as of version 12): the `from_chars` function in GCC relies on fast_float. +- [WebKit](https://github.com/WebKit/WebKit), the engine behind Safari (Apple's web browser) + + +The fastfloat algorithm is part of the [LLVM standard libraries](https://github.com/llvm/llvm-project/commit/87c016078ad72c46505461e4ff8bfa04819fe7ba). + +There is a [derived implementation part of AdaCore](https://github.com/AdaCore/VSS). + + +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). + +## Reference + +- Daniel Lemire, [Number Parsing at a Gigabyte per Second](https://arxiv.org/abs/2101.11408), Software: Practice 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`. It used for important systems such as [Jackson](https://github.com/FasterXML/jackson-core). +- [There is a C# port of the fast_float library](https://github.com/CarlVerret/csFastFloat) called `csFastFloat`. + + +## Users + +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. + + + +``` +$ ./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 + +[![Go Systems 2020](http://img.youtube.com/vi/AVXgvlMeIm4/0.jpg)](http://www.youtube.com/watch?v=AVXgvlMeIm4)
+ +## 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/v3.4.0/fast_float.h + +## Credit + +Though this work is inspired by many different people, this work benefited especially from exchanges with +Michael Eisel, who motivated the original research with his key insights, and with Nigel Tao who provided +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 + + +Licensed under either of Apache License, Version +2.0 or MIT license at your option. + + +
+ + +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. + diff --git a/dep/fast_float/include/fast_float/ascii_number.h b/dep/fast_float/include/fast_float/ascii_number.h new file mode 100644 index 000000000..1783bd4ab --- /dev/null +++ b/dep/fast_float/include/fast_float/ascii_number.h @@ -0,0 +1,227 @@ +#ifndef FASTFLOAT_ASCII_NUMBER_H +#define FASTFLOAT_ASCII_NUMBER_H + +#include +#include +#include +#include + +#include "float_common.h" + +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 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 ((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 diff --git a/dep/fast_float/include/fast_float/bigint.h b/dep/fast_float/include/fast_float/bigint.h new file mode 100644 index 000000000..220e0572a --- /dev/null +++ b/dep/fast_float/include/fast_float/bigint.h @@ -0,0 +1,590 @@ +#ifndef FASTFLOAT_BIGINT_H +#define FASTFLOAT_BIGINT_H + +#include +#include +#include +#include + +#include "float_common.h" + +namespace fast_float { + +// the limb width: we want efficient multiplication of double the bits in +// limb, or for 64-bit limbs, at least 64-bit multiplication where we can +// extract the high and low parts efficiently. this is every 64-bit +// architecture except for sparc, which emulates 128-bit multiplication. +// we might have platforms where `CHAR_BIT` is not 8, so let's avoid +// doing `8 * sizeof(limb)`. +#if defined(FASTFLOAT_64BIT) && !defined(__sparc) +#define FASTFLOAT_64BIT_LIMB 1 +typedef uint64_t limb; +constexpr size_t limb_bits = 64; +#else +#define FASTFLOAT_32BIT_LIMB +typedef uint32_t limb; +constexpr size_t limb_bits = 32; +#endif + +typedef span limb_span; + +// number of bits in a bigint. this needs to be at least the number +// of bits required to store the largest bigint, which is +// `log2(10**(digits + max_exp))`, or `log2(10**(767 + 342))`, or +// ~3600 bits, so we round to 4000. +constexpr size_t bigint_bits = 4000; +constexpr size_t bigint_limbs = bigint_bits / limb_bits; + +// vector-like type that is allocated on the stack. the entire +// buffer is pre-allocated, and only the length changes. +template +struct stackvec { + limb data[size]; + // we never need more than 150 limbs + uint16_t length{0}; + + stackvec() = default; + stackvec(const stackvec &) = delete; + stackvec &operator=(const stackvec &) = delete; + stackvec(stackvec &&) = delete; + stackvec &operator=(stackvec &&other) = delete; + + // create stack vector from existing limb span. + 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 +inline bool small_add_from(stackvec& vec, limb y, size_t start) noexcept { + size_t index = start; + limb carry = y; + bool overflow; + while (carry != 0 && index < vec.len()) { + vec[index] = scalar_add(vec[index], carry, overflow); + carry = limb(overflow); + index += 1; + } + if (carry != 0) { + FASTFLOAT_TRY(vec.try_push(carry)); + } + return true; +} + +// add scalar value to bigint. +template +fastfloat_really_inline bool small_add(stackvec& vec, limb y) noexcept { + return small_add_from(vec, y, 0); +} + +// multiply bigint by scalar value. +template +inline bool small_mul(stackvec& vec, limb y) noexcept { + 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 +bool large_add_from(stackvec& x, limb_span y, size_t start) noexcept { + // the effective x buffer is from `xstart..x.len()`, so exit early + // if we can't get that current range. + if (x.len() < start || y.len() > x.len() - start) { + FASTFLOAT_TRY(x.try_resize(y.len() + start, 0)); + } + + bool carry = false; + for (size_t index = 0; index < y.len(); index++) { + limb xi = x[index + start]; + limb yi = y[index]; + bool c1 = false; + bool c2 = false; + xi = scalar_add(xi, yi, c1); + if (carry) { + xi = scalar_add(xi, 1, c2); + } + x[index + start] = xi; + carry = c1 | c2; + } + + // handle overflow + if (carry) { + FASTFLOAT_TRY(small_add_from(x, 1, y.len() + start)); + } + return true; +} + +// add bigint to bigint. +template +fastfloat_really_inline bool large_add_from(stackvec& x, limb_span y) noexcept { + return large_add_from(x, y, 0); +} + +// grade-school multiplication algorithm +template +bool long_mul(stackvec& x, limb_span y) noexcept { + limb_span xs = limb_span(x.data, x.len()); + stackvec z(xs); + limb_span zs = limb_span(z.data, z.len()); + + if (y.len() != 0) { + limb y0 = y[0]; + FASTFLOAT_TRY(small_mul(x, y0)); + for (size_t index = 1; index < y.len(); index++) { + limb yi = y[index]; + stackvec zi; + if (yi != 0) { + // re-use the same buffer throughout + zi.set_len(0); + FASTFLOAT_TRY(zi.try_extend(zs)); + FASTFLOAT_TRY(small_mul(zi, yi)); + limb_span zis = limb_span(zi.data, zi.len()); + FASTFLOAT_TRY(large_add_from(x, zis, index)); + } + } + } + + x.normalize(); + return true; +} + +// grade-school multiplication algorithm +template +bool large_mul(stackvec& x, limb_span y) noexcept { + if (y.len() == 1) { + FASTFLOAT_TRY(small_mul(x, y[0])); + } else { + FASTFLOAT_TRY(long_mul(x, y)); + } + return true; +} + +// 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 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 diff --git a/dep/fast_float/include/fast_float/decimal_to_binary.h b/dep/fast_float/include/fast_float/decimal_to_binary.h new file mode 100644 index 000000000..6da6c66a3 --- /dev/null +++ b/dep/fast_float/include/fast_float/decimal_to_binary.h @@ -0,0 +1,194 @@ +#ifndef FASTFLOAT_DECIMAL_TO_BINARY_H +#define FASTFLOAT_DECIMAL_TO_BINARY_H + +#include "float_common.h" +#include "fast_table.h" +#include +#include +#include +#include +#include +#include + +namespace fast_float { + +// This will compute or rather approximate w * 5**q and return a pair of 64-bit words approximating +// the result, with the "high" part corresponding to the most significant bits and the +// low part corresponding to the least significant bits. +// +template +fastfloat_really_inline +value128 compute_product_approximation(int64_t q, uint64_t w) { + const int index = 2 * int(q - powers::smallest_power_of_five); + // For small values of q, e.g., q in [0,27], the answer is always exact because + // The line value128 firstproduct = full_multiplication(w, power_of_five_128[index]); + // gives the exact answer. + value128 firstproduct = full_multiplication(w, powers::power_of_five_128[index]); + static_assert((bit_precision >= 0) && (bit_precision <= 64), " precision should be in (0,64]"); + constexpr uint64_t precision_mask = (bit_precision < 64) ? + (uint64_t(0xFFFFFFFFFFFFFFFF) >> bit_precision) + : uint64_t(0xFFFFFFFFFFFFFFFF); + if((firstproduct.high & precision_mask) == precision_mask) { // could further guard with (lower + w < lower) + // regarding the second product, we only need secondproduct.high, but our expectation is that the compiler will optimize this extra work away if needed. + value128 secondproduct = full_multiplication(w, powers::power_of_five_128[index + 1]); + firstproduct.low += secondproduct.high; + if(secondproduct.high > firstproduct.low) { + firstproduct.high++; + } + } + return firstproduct; +} + +namespace detail { +/** + * For q in (0,350), we have that + * f = (((152170 + 65536) * q ) >> 16); + * is equal to + * floor(p) + q + * where + * p = log(5**q)/log(2) = q * log(5)/log(2) + * + * For negative values of q in (-400,0), we have that + * f = (((152170 + 65536) * q ) >> 16); + * is equal to + * -ceil(p) + q + * where + * p = log(5**-q)/log(2) = -q * log(5)/log(2) + */ + constexpr fastfloat_really_inline int32_t power(int32_t q) noexcept { + return (((152170 + 65536) * q) >> 16) + 63; + } +} // namespace detail + +// create an adjusted mantissa, biased by the invalid power2 +// for significant digits already multiplied by 10 ** q. +template +fastfloat_really_inline +adjusted_mantissa compute_error_scaled(int64_t q, uint64_t w, int lz) noexcept { + int hilz = int(w >> 63) ^ 1; + adjusted_mantissa answer; + answer.mantissa = w << hilz; + int bias = binary::mantissa_explicit_bits() - binary::minimum_exponent(); + answer.power2 = int32_t(detail::power(int32_t(q)) + bias - hilz - lz - 62 + invalid_am_bias); + return answer; +} + +// w * 10 ** q, without rounding the representation up. +// the power2 in the exponent will be adjusted by invalid_am_bias. +template +fastfloat_really_inline +adjusted_mantissa compute_error(int64_t q, uint64_t w) noexcept { + int lz = leading_zeroes(w); + w <<= lz; + value128 product = compute_product_approximation(q, w); + return compute_error_scaled(q, product.high, lz); +} + +// w * 10 ** q +// The returned value should be a valid ieee64 number that simply need to be packed. +// However, in some very rare cases, the computation will fail. In such cases, we +// return an adjusted_mantissa with a negative power of 2: the caller should recompute +// in such cases. +template +fastfloat_really_inline +adjusted_mantissa compute_float(int64_t q, uint64_t w) noexcept { + adjusted_mantissa answer; + if ((w == 0) || (q < binary::smallest_power_of_ten())) { + answer.power2 = 0; + answer.mantissa = 0; + // result should be zero + return answer; + } + if (q > binary::largest_power_of_ten()) { + // we want to get infinity: + answer.power2 = binary::infinite_power(); + answer.mantissa = 0; + return answer; + } + // At this point in time q is in [powers::smallest_power_of_five, powers::largest_power_of_five]. + + // We want the most significant bit of i to be 1. Shift if needed. + int lz = leading_zeroes(w); + w <<= lz; + + // The required precision is binary::mantissa_explicit_bits() + 3 because + // 1. We need the implicit bit + // 2. We need an extra bit for rounding purposes + // 3. We might lose a bit due to the "upperbit" routine (result too small, requiring a shift) + + value128 product = compute_product_approximation(q, w); + if(product.low == 0xFFFFFFFFFFFFFFFF) { // could guard it further + // In some very rare cases, this could happen, in which case we might need a more accurate + // computation that what we can provide cheaply. This is very, very unlikely. + // + const bool inside_safe_exponent = (q >= -27) && (q <= 55); // always good because 5**q <2**128 when q>=0, + // and otherwise, for q<0, we have 5**-q<2**64 and the 128-bit reciprocal allows for exact computation. + if(!inside_safe_exponent) { + return compute_error_scaled(q, product.high, lz); + } + } + // The "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 diff --git a/dep/fast_float/include/fast_float/digit_comparison.h b/dep/fast_float/include/fast_float/digit_comparison.h new file mode 100644 index 000000000..4c4343396 --- /dev/null +++ b/dep/fast_float/include/fast_float/digit_comparison.h @@ -0,0 +1,407 @@ +#ifndef FASTFLOAT_DIGIT_COMPARISON_H +#define FASTFLOAT_DIGIT_COMPARISON_H + +#include +#include +#include +#include + +#include "float_common.h" +#include "bigint.h" +#include "ascii_number.h" + +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 +fastfloat_really_inline adjusted_mantissa to_extended(T value) noexcept { + using equiv_uint = typename binary_format::equiv_uint; + constexpr equiv_uint exponent_mask = binary_format::exponent_mask(); + constexpr equiv_uint mantissa_mask = binary_format::mantissa_mask(); + constexpr equiv_uint hidden_bit_mask = binary_format::hidden_bit_mask(); + + adjusted_mantissa am; + int32_t bias = binary_format::mantissa_explicit_bits() - binary_format::minimum_exponent(); + equiv_uint bits; + ::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::mantissa_explicit_bits()); + am.power2 -= bias; + am.mantissa = (bits & mantissa_mask) | hidden_bit_mask; + } + + return am; +} + +// get the extended precision value of the halfway point between b and b+u. +// we are given a native float that represents b, so we need to adjust it +// halfway between b and b+u. +template +fastfloat_really_inline adjusted_mantissa to_extended_halfway(T value) noexcept { + adjusted_mantissa am = to_extended(value); + am.mantissa <<= 1; + am.mantissa += 1; + am.power2 -= 1; + return am; +} + +// round an extended-precision float to the nearest machine float. +template +fastfloat_really_inline void round(adjusted_mantissa& am, callback cb) noexcept { + int32_t mantissa_shift = 64 - binary_format::mantissa_explicit_bits() - 1; + if (-am.power2 >= mantissa_shift) { + // have a denormal float + int32_t shift = -am.power2 + 1; + cb(am, std::min(shift, 64)); + // check for round-up: if rounding-nearest carried us to the hidden bit. + am.power2 = (am.mantissa < (uint64_t(1) << binary_format::mantissa_explicit_bits())) ? 0 : 1; + return; + } + + // have a normal float, use the default shift. + cb(am, mantissa_shift); + + // check for carry + if (am.mantissa >= (uint64_t(2) << binary_format::mantissa_explicit_bits())) { + am.mantissa = (uint64_t(1) << binary_format::mantissa_explicit_bits()); + am.power2++; + } + + // check for infinite: we could have carried to an infinite power + am.mantissa &= ~(uint64_t(1) << binary_format::mantissa_explicit_bits()); + if (am.power2 >= binary_format::infinite_power()) { + am.power2 = binary_format::infinite_power(); + am.mantissa = 0; + } +} + +template +fastfloat_really_inline +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; + bool is_above = truncated_bits > halfway; + bool is_halfway = truncated_bits == halfway; + + // shift digits into position + if (shift == 64) { + am.mantissa = 0; + } else { + am.mantissa >>= shift; + } + am.power2 += shift; + + bool is_odd = (am.mantissa & 1) == 1; + am.mantissa += uint64_t(cb(is_odd, is_halfway, is_above)); +} + +fastfloat_really_inline 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 +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::mantissa_explicit_bits() - binary_format::minimum_exponent(); + answer.power2 = bigmant.bit_length() - 64 + bias; + + round(answer, [truncated](adjusted_mantissa& a, int32_t shift) { + round_nearest_tie_even(a, shift, [truncated](bool is_odd, bool is_halfway, bool is_above) -> bool { + return is_above || (is_halfway && truncated) || (is_odd && is_halfway); + }); + }); + + return answer; +} + +// the scaling here is quite simple: we have, for the real digits `m * 10^e`, +// and for the theoretical digits `n * 2^f`. Since `e` is always negative, +// to scale them identically, we do `n * 2^f * 5^-f`, so we now have `m * 2^e`. +// we then need to scale by `2^(f- e)`, and then the two significant digits +// are of the same magnitude. +template +inline adjusted_mantissa negative_digit_comp(bigint& bigmant, adjusted_mantissa am, int32_t exponent) noexcept { + bigint& real_digits = bigmant; + int32_t real_exp = exponent; + + // get the value of `b`, rounded down, and get a bigint representation of b+h + adjusted_mantissa am_b = am; + // gcc7 buf: use a lambda to remove the noexcept qualifier bug with -Wnoexcept-type. + round(am_b, [](adjusted_mantissa&a, int32_t shift) { round_down(a, shift); }); + T b; + to_float(false, am_b, b); + adjusted_mantissa theor = to_extended_halfway(b); + bigint theor_digits(theor.mantissa); + int32_t theor_exp = theor.power2; + + // scale real digits and theor digits to be same power. + int32_t pow2_exp = theor_exp - real_exp; + uint32_t pow5_exp = uint32_t(-real_exp); + if (pow5_exp != 0) { + FASTFLOAT_ASSERT(theor_digits.pow5(pow5_exp)); + } + if (pow2_exp > 0) { + FASTFLOAT_ASSERT(theor_digits.pow2(uint32_t(pow2_exp))); + } else if (pow2_exp < 0) { + FASTFLOAT_ASSERT(real_digits.pow2(uint32_t(-pow2_exp))); + } + + // compare digits, and use it to director rounding + int ord = real_digits.compare(theor_digits); + adjusted_mantissa answer = am; + round(answer, [ord](adjusted_mantissa& a, int32_t shift) { + round_nearest_tie_even(a, shift, [ord](bool is_odd, bool _, bool __) -> bool { + (void)_; // not needed, since we've done our comparison + (void)__; // not needed, since we've done our comparison + if (ord > 0) { + return true; + } else if (ord < 0) { + return false; + } else { + return is_odd; + } + }); + }); + + return answer; +} + +// parse the significant digits as a big integer to unambiguously round the +// the significant digits. here, we are trying to determine how to round +// an extended float representation close to `b+h`, halfway between `b` +// (the float rounded-down) and `b+u`, the next positive float. this +// algorithm is always correct, and uses one of two approaches. when +// the exponent is positive relative to the significant digits (such as +// 1234), we create a big-integer representation, get the high 64-bits, +// determine if any lower bits are truncated, and use that to direct +// rounding. in case of a negative exponent relative to the significant +// digits (such as 1.2345), we create a theoretical representation of +// `b` as a big-integer type, scaled to the same binary exponent as +// the actual digits. we then compare the big integer representations +// of both, and use that to direct rounding. +template +inline 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::max_digits(); + size_t digits = 0; + bigint bigmant; + parse_mantissa(bigmant, num, max_digits, digits); + // can't underflow, since digits is at most max_digits. + int32_t exponent = sci_exp + 1 - int32_t(digits); + if (exponent >= 0) { + return positive_digit_comp(bigmant, exponent); + } else { + return negative_digit_comp(bigmant, am, exponent); + } +} + +} // namespace fast_float + +#endif diff --git a/dep/fast_float/include/fast_float/fast_float.h b/dep/fast_float/include/fast_float/fast_float.h new file mode 100644 index 000000000..d3497fd6b --- /dev/null +++ b/dep/fast_float/include/fast_float/fast_float.h @@ -0,0 +1,63 @@ +#ifndef FASTFLOAT_FAST_FLOAT_H +#define FASTFLOAT_FAST_FLOAT_H + +#include + +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 allow the fixed point and scientific notation respectively. + * The default is `fast_float::chars_format::general` which allows both `fixed` and `scientific`. + */ +template +from_chars_result from_chars(const char *first, const char *last, + T &value, chars_format fmt = chars_format::general) noexcept; + +/** + * Like from_chars, but accepts an `options` argument to govern number parsing. + */ +template +from_chars_result from_chars_advanced(const char *first, const char *last, + T &value, parse_options options) noexcept; + +} // namespace fast_float +#include "parse_number.h" +#endif // FASTFLOAT_FAST_FLOAT_H diff --git a/dep/fast_float/include/fast_float/fast_table.h b/dep/fast_float/include/fast_float/fast_table.h new file mode 100644 index 000000000..aa7804b2e --- /dev/null +++ b/dep/fast_float/include/fast_float/fast_table.h @@ -0,0 +1,699 @@ +#ifndef FASTFLOAT_FAST_TABLE_H +#define FASTFLOAT_FAST_TABLE_H + +#include + +namespace fast_float { + +/** + * When mapping numbers from decimal to binary, + * we go from w * 10^q to m * 2^p but we have + * 10^q = 5^q * 2^q, so effectively + * we are trying to match + * w * 2^q * 5^q to m * 2^p. Thus the powers of two + * are not a concern since they can be represented + * exactly using the binary notation, only the powers of five + * affect the binary significand. + */ + +/** + * The smallest non-zero float (binary64) is 2^-1074. + * We take as input numbers of the form w x 10^q where w < 2^64. + * We have that w * 10^-343 < 2^(64-344) 5^-343 < 2^-1076. + * However, we have that + * (2^64-1) * 10^-342 = (2^64-1) * 2^-342 * 5^-342 > 2^-1074. + * Thus it is possible for a number of the form w * 10^-342 where + * w is a 64-bit value to be a non-zero floating-point number. + ********* + * Any number of form w * 10^309 where w>= 1 is going to be + * infinite in binary64 so we never need to worry about powers + * of 5 greater than 308. + */ +template +struct powers_template { + +constexpr static int smallest_power_of_five = binary_format::smallest_power_of_ten(); +constexpr static int largest_power_of_five = binary_format::largest_power_of_ten(); +constexpr static int number_of_entries = 2 * (largest_power_of_five - smallest_power_of_five + 1); +// Powers of five from 5^-342 all the way to 5^308 rounded toward one. +static const uint64_t power_of_five_128[number_of_entries]; +}; + +template +const uint64_t powers_template::power_of_five_128[number_of_entries] = { + 0xeef453d6923bd65a,0x113faa2906a13b3f, + 0x9558b4661b6565f8,0x4ac7ca59a424c507, + 0xbaaee17fa23ebf76,0x5d79bcf00d2df649, + 0xe95a99df8ace6f53,0xf4d82c2c107973dc, + 0x91d8a02bb6c10594,0x79071b9b8a4be869, + 0xb64ec836a47146f9,0x9748e2826cdee284, + 0xe3e27a444d8d98b7,0xfd1b1b2308169b25, + 0x8e6d8c6ab0787f72,0xfe30f0f5e50e20f7, + 0xb208ef855c969f4f,0xbdbd2d335e51a935, + 0xde8b2b66b3bc4723,0xad2c788035e61382, + 0x8b16fb203055ac76,0x4c3bcb5021afcc31, + 0xaddcb9e83c6b1793,0xdf4abe242a1bbf3d, + 0xd953e8624b85dd78,0xd71d6dad34a2af0d, + 0x87d4713d6f33aa6b,0x8672648c40e5ad68, + 0xa9c98d8ccb009506,0x680efdaf511f18c2, + 0xd43bf0effdc0ba48,0x212bd1b2566def2, + 0x84a57695fe98746d,0x14bb630f7604b57, + 0xa5ced43b7e3e9188,0x419ea3bd35385e2d, + 0xcf42894a5dce35ea,0x52064cac828675b9, + 0x818995ce7aa0e1b2,0x7343efebd1940993, + 0xa1ebfb4219491a1f,0x1014ebe6c5f90bf8, + 0xca66fa129f9b60a6,0xd41a26e077774ef6, + 0xfd00b897478238d0,0x8920b098955522b4, + 0x9e20735e8cb16382,0x55b46e5f5d5535b0, + 0xc5a890362fddbc62,0xeb2189f734aa831d, + 0xf712b443bbd52b7b,0xa5e9ec7501d523e4, + 0x9a6bb0aa55653b2d,0x47b233c92125366e, + 0xc1069cd4eabe89f8,0x999ec0bb696e840a, + 0xf148440a256e2c76,0xc00670ea43ca250d, + 0x96cd2a865764dbca,0x380406926a5e5728, + 0xbc807527ed3e12bc,0xc605083704f5ecf2, + 0xeba09271e88d976b,0xf7864a44c633682e, + 0x93445b8731587ea3,0x7ab3ee6afbe0211d, + 0xb8157268fdae9e4c,0x5960ea05bad82964, + 0xe61acf033d1a45df,0x6fb92487298e33bd, + 0x8fd0c16206306bab,0xa5d3b6d479f8e056, + 0xb3c4f1ba87bc8696,0x8f48a4899877186c, + 0xe0b62e2929aba83c,0x331acdabfe94de87, + 0x8c71dcd9ba0b4925,0x9ff0c08b7f1d0b14, + 0xaf8e5410288e1b6f,0x7ecf0ae5ee44dd9, + 0xdb71e91432b1a24a,0xc9e82cd9f69d6150, + 0x892731ac9faf056e,0xbe311c083a225cd2, + 0xab70fe17c79ac6ca,0x6dbd630a48aaf406, + 0xd64d3d9db981787d,0x92cbbccdad5b108, + 0x85f0468293f0eb4e,0x25bbf56008c58ea5, + 0xa76c582338ed2621,0xaf2af2b80af6f24e, + 0xd1476e2c07286faa,0x1af5af660db4aee1, + 0x82cca4db847945ca,0x50d98d9fc890ed4d, + 0xa37fce126597973c,0xe50ff107bab528a0, + 0xcc5fc196fefd7d0c,0x1e53ed49a96272c8, + 0xff77b1fcbebcdc4f,0x25e8e89c13bb0f7a, + 0x9faacf3df73609b1,0x77b191618c54e9ac, + 0xc795830d75038c1d,0xd59df5b9ef6a2417, + 0xf97ae3d0d2446f25,0x4b0573286b44ad1d, + 0x9becce62836ac577,0x4ee367f9430aec32, + 0xc2e801fb244576d5,0x229c41f793cda73f, + 0xf3a20279ed56d48a,0x6b43527578c1110f, + 0x9845418c345644d6,0x830a13896b78aaa9, + 0xbe5691ef416bd60c,0x23cc986bc656d553, + 0xedec366b11c6cb8f,0x2cbfbe86b7ec8aa8, + 0x94b3a202eb1c3f39,0x7bf7d71432f3d6a9, + 0xb9e08a83a5e34f07,0xdaf5ccd93fb0cc53, + 0xe858ad248f5c22c9,0xd1b3400f8f9cff68, + 0x91376c36d99995be,0x23100809b9c21fa1, + 0xb58547448ffffb2d,0xabd40a0c2832a78a, + 0xe2e69915b3fff9f9,0x16c90c8f323f516c, + 0x8dd01fad907ffc3b,0xae3da7d97f6792e3, + 0xb1442798f49ffb4a,0x99cd11cfdf41779c, + 0xdd95317f31c7fa1d,0x40405643d711d583, + 0x8a7d3eef7f1cfc52,0x482835ea666b2572, + 0xad1c8eab5ee43b66,0xda3243650005eecf, + 0xd863b256369d4a40,0x90bed43e40076a82, + 0x873e4f75e2224e68,0x5a7744a6e804a291, + 0xa90de3535aaae202,0x711515d0a205cb36, + 0xd3515c2831559a83,0xd5a5b44ca873e03, + 0x8412d9991ed58091,0xe858790afe9486c2, + 0xa5178fff668ae0b6,0x626e974dbe39a872, + 0xce5d73ff402d98e3,0xfb0a3d212dc8128f, + 0x80fa687f881c7f8e,0x7ce66634bc9d0b99, + 0xa139029f6a239f72,0x1c1fffc1ebc44e80, + 0xc987434744ac874e,0xa327ffb266b56220, + 0xfbe9141915d7a922,0x4bf1ff9f0062baa8, + 0x9d71ac8fada6c9b5,0x6f773fc3603db4a9, + 0xc4ce17b399107c22,0xcb550fb4384d21d3, + 0xf6019da07f549b2b,0x7e2a53a146606a48, + 0x99c102844f94e0fb,0x2eda7444cbfc426d, + 0xc0314325637a1939,0xfa911155fefb5308, + 0xf03d93eebc589f88,0x793555ab7eba27ca, + 0x96267c7535b763b5,0x4bc1558b2f3458de, + 0xbbb01b9283253ca2,0x9eb1aaedfb016f16, + 0xea9c227723ee8bcb,0x465e15a979c1cadc, + 0x92a1958a7675175f,0xbfacd89ec191ec9, + 0xb749faed14125d36,0xcef980ec671f667b, + 0xe51c79a85916f484,0x82b7e12780e7401a, + 0x8f31cc0937ae58d2,0xd1b2ecb8b0908810, + 0xb2fe3f0b8599ef07,0x861fa7e6dcb4aa15, + 0xdfbdcece67006ac9,0x67a791e093e1d49a, + 0x8bd6a141006042bd,0xe0c8bb2c5c6d24e0, + 0xaecc49914078536d,0x58fae9f773886e18, + 0xda7f5bf590966848,0xaf39a475506a899e, + 0x888f99797a5e012d,0x6d8406c952429603, + 0xaab37fd7d8f58178,0xc8e5087ba6d33b83, + 0xd5605fcdcf32e1d6,0xfb1e4a9a90880a64, + 0x855c3be0a17fcd26,0x5cf2eea09a55067f, + 0xa6b34ad8c9dfc06f,0xf42faa48c0ea481e, + 0xd0601d8efc57b08b,0xf13b94daf124da26, + 0x823c12795db6ce57,0x76c53d08d6b70858, + 0xa2cb1717b52481ed,0x54768c4b0c64ca6e, + 0xcb7ddcdda26da268,0xa9942f5dcf7dfd09, + 0xfe5d54150b090b02,0xd3f93b35435d7c4c, + 0x9efa548d26e5a6e1,0xc47bc5014a1a6daf, + 0xc6b8e9b0709f109a,0x359ab6419ca1091b, + 0xf867241c8cc6d4c0,0xc30163d203c94b62, + 0x9b407691d7fc44f8,0x79e0de63425dcf1d, + 0xc21094364dfb5636,0x985915fc12f542e4, + 0xf294b943e17a2bc4,0x3e6f5b7b17b2939d, + 0x979cf3ca6cec5b5a,0xa705992ceecf9c42, + 0xbd8430bd08277231,0x50c6ff782a838353, + 0xece53cec4a314ebd,0xa4f8bf5635246428, + 0x940f4613ae5ed136,0x871b7795e136be99, + 0xb913179899f68584,0x28e2557b59846e3f, + 0xe757dd7ec07426e5,0x331aeada2fe589cf, + 0x9096ea6f3848984f,0x3ff0d2c85def7621, + 0xb4bca50b065abe63,0xfed077a756b53a9, + 0xe1ebce4dc7f16dfb,0xd3e8495912c62894, + 0x8d3360f09cf6e4bd,0x64712dd7abbbd95c, + 0xb080392cc4349dec,0xbd8d794d96aacfb3, + 0xdca04777f541c567,0xecf0d7a0fc5583a0, + 0x89e42caaf9491b60,0xf41686c49db57244, + 0xac5d37d5b79b6239,0x311c2875c522ced5, + 0xd77485cb25823ac7,0x7d633293366b828b, + 0x86a8d39ef77164bc,0xae5dff9c02033197, + 0xa8530886b54dbdeb,0xd9f57f830283fdfc, + 0xd267caa862a12d66,0xd072df63c324fd7b, + 0x8380dea93da4bc60,0x4247cb9e59f71e6d, + 0xa46116538d0deb78,0x52d9be85f074e608, + 0xcd795be870516656,0x67902e276c921f8b, + 0x806bd9714632dff6,0xba1cd8a3db53b6, + 0xa086cfcd97bf97f3,0x80e8a40eccd228a4, + 0xc8a883c0fdaf7df0,0x6122cd128006b2cd, + 0xfad2a4b13d1b5d6c,0x796b805720085f81, + 0x9cc3a6eec6311a63,0xcbe3303674053bb0, + 0xc3f490aa77bd60fc,0xbedbfc4411068a9c, + 0xf4f1b4d515acb93b,0xee92fb5515482d44, + 0x991711052d8bf3c5,0x751bdd152d4d1c4a, + 0xbf5cd54678eef0b6,0xd262d45a78a0635d, + 0xef340a98172aace4,0x86fb897116c87c34, + 0x9580869f0e7aac0e,0xd45d35e6ae3d4da0, + 0xbae0a846d2195712,0x8974836059cca109, + 0xe998d258869facd7,0x2bd1a438703fc94b, + 0x91ff83775423cc06,0x7b6306a34627ddcf, + 0xb67f6455292cbf08,0x1a3bc84c17b1d542, + 0xe41f3d6a7377eeca,0x20caba5f1d9e4a93, + 0x8e938662882af53e,0x547eb47b7282ee9c, + 0xb23867fb2a35b28d,0xe99e619a4f23aa43, + 0xdec681f9f4c31f31,0x6405fa00e2ec94d4, + 0x8b3c113c38f9f37e,0xde83bc408dd3dd04, + 0xae0b158b4738705e,0x9624ab50b148d445, + 0xd98ddaee19068c76,0x3badd624dd9b0957, + 0x87f8a8d4cfa417c9,0xe54ca5d70a80e5d6, + 0xa9f6d30a038d1dbc,0x5e9fcf4ccd211f4c, + 0xd47487cc8470652b,0x7647c3200069671f, + 0x84c8d4dfd2c63f3b,0x29ecd9f40041e073, + 0xa5fb0a17c777cf09,0xf468107100525890, + 0xcf79cc9db955c2cc,0x7182148d4066eeb4, + 0x81ac1fe293d599bf,0xc6f14cd848405530, + 0xa21727db38cb002f,0xb8ada00e5a506a7c, + 0xca9cf1d206fdc03b,0xa6d90811f0e4851c, + 0xfd442e4688bd304a,0x908f4a166d1da663, + 0x9e4a9cec15763e2e,0x9a598e4e043287fe, + 0xc5dd44271ad3cdba,0x40eff1e1853f29fd, + 0xf7549530e188c128,0xd12bee59e68ef47c, + 0x9a94dd3e8cf578b9,0x82bb74f8301958ce, + 0xc13a148e3032d6e7,0xe36a52363c1faf01, + 0xf18899b1bc3f8ca1,0xdc44e6c3cb279ac1, + 0x96f5600f15a7b7e5,0x29ab103a5ef8c0b9, + 0xbcb2b812db11a5de,0x7415d448f6b6f0e7, + 0xebdf661791d60f56,0x111b495b3464ad21, + 0x936b9fcebb25c995,0xcab10dd900beec34, + 0xb84687c269ef3bfb,0x3d5d514f40eea742, + 0xe65829b3046b0afa,0xcb4a5a3112a5112, + 0x8ff71a0fe2c2e6dc,0x47f0e785eaba72ab, + 0xb3f4e093db73a093,0x59ed216765690f56, + 0xe0f218b8d25088b8,0x306869c13ec3532c, + 0x8c974f7383725573,0x1e414218c73a13fb, + 0xafbd2350644eeacf,0xe5d1929ef90898fa, + 0xdbac6c247d62a583,0xdf45f746b74abf39, + 0x894bc396ce5da772,0x6b8bba8c328eb783, + 0xab9eb47c81f5114f,0x66ea92f3f326564, + 0xd686619ba27255a2,0xc80a537b0efefebd, + 0x8613fd0145877585,0xbd06742ce95f5f36, + 0xa798fc4196e952e7,0x2c48113823b73704, + 0xd17f3b51fca3a7a0,0xf75a15862ca504c5, + 0x82ef85133de648c4,0x9a984d73dbe722fb, + 0xa3ab66580d5fdaf5,0xc13e60d0d2e0ebba, + 0xcc963fee10b7d1b3,0x318df905079926a8, + 0xffbbcfe994e5c61f,0xfdf17746497f7052, + 0x9fd561f1fd0f9bd3,0xfeb6ea8bedefa633, + 0xc7caba6e7c5382c8,0xfe64a52ee96b8fc0, + 0xf9bd690a1b68637b,0x3dfdce7aa3c673b0, + 0x9c1661a651213e2d,0x6bea10ca65c084e, + 0xc31bfa0fe5698db8,0x486e494fcff30a62, + 0xf3e2f893dec3f126,0x5a89dba3c3efccfa, + 0x986ddb5c6b3a76b7,0xf89629465a75e01c, + 0xbe89523386091465,0xf6bbb397f1135823, + 0xee2ba6c0678b597f,0x746aa07ded582e2c, + 0x94db483840b717ef,0xa8c2a44eb4571cdc, + 0xba121a4650e4ddeb,0x92f34d62616ce413, + 0xe896a0d7e51e1566,0x77b020baf9c81d17, + 0x915e2486ef32cd60,0xace1474dc1d122e, + 0xb5b5ada8aaff80b8,0xd819992132456ba, + 0xe3231912d5bf60e6,0x10e1fff697ed6c69, + 0x8df5efabc5979c8f,0xca8d3ffa1ef463c1, + 0xb1736b96b6fd83b3,0xbd308ff8a6b17cb2, + 0xddd0467c64bce4a0,0xac7cb3f6d05ddbde, + 0x8aa22c0dbef60ee4,0x6bcdf07a423aa96b, + 0xad4ab7112eb3929d,0x86c16c98d2c953c6, + 0xd89d64d57a607744,0xe871c7bf077ba8b7, + 0x87625f056c7c4a8b,0x11471cd764ad4972, + 0xa93af6c6c79b5d2d,0xd598e40d3dd89bcf, + 0xd389b47879823479,0x4aff1d108d4ec2c3, + 0x843610cb4bf160cb,0xcedf722a585139ba, + 0xa54394fe1eedb8fe,0xc2974eb4ee658828, + 0xce947a3da6a9273e,0x733d226229feea32, + 0x811ccc668829b887,0x806357d5a3f525f, + 0xa163ff802a3426a8,0xca07c2dcb0cf26f7, + 0xc9bcff6034c13052,0xfc89b393dd02f0b5, + 0xfc2c3f3841f17c67,0xbbac2078d443ace2, + 0x9d9ba7832936edc0,0xd54b944b84aa4c0d, + 0xc5029163f384a931,0xa9e795e65d4df11, + 0xf64335bcf065d37d,0x4d4617b5ff4a16d5, + 0x99ea0196163fa42e,0x504bced1bf8e4e45, + 0xc06481fb9bcf8d39,0xe45ec2862f71e1d6, + 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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<>; + +} // namespace fast_float + +#endif diff --git a/dep/fast_float/include/fast_float/float_common.h b/dep/fast_float/include/fast_float/float_common.h new file mode 100644 index 000000000..ad0854d33 --- /dev/null +++ b/dep/fast_float/include/fast_float/float_common.h @@ -0,0 +1,458 @@ +#ifndef FASTFLOAT_FLOAT_COMMON_H +#define FASTFLOAT_FLOAT_COMMON_H + +#include +#include +#include +#include +#include + +#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__)) ) +#define FASTFLOAT_64BIT 1 +#elif (defined(__i386) || defined(__i386__) || defined(_M_IX86) \ + || defined(__arm__) || defined(_M_ARM) \ + || defined(__MINGW32__) || defined(__EMSCRIPTEN__)) +#define FASTFLOAT_32BIT 1 +#else + // Need to check incrementally, since SIZE_MAX is a size_t, avoid overflow. + // We can never tell the register width, but the SIZE_MAX is a good approximation. + // UINTPTR_MAX and INTPTR_MAX are optional, so avoid them for max portability. + #if SIZE_MAX == 0xffff + #error Unknown platform (16-bit, unsupported) + #elif SIZE_MAX == 0xffffffff + #define FASTFLOAT_32BIT 1 + #elif SIZE_MAX == 0xffffffffffffffff + #define FASTFLOAT_64BIT 1 + #else + #error Unknown platform (not 32-bit, not 64-bit?) + #endif +#endif + +#if ((defined(_WIN32) || defined(_WIN64)) && !defined(__clang__)) +#include +#endif + +#if defined(_MSC_VER) && !defined(__clang__) +#define FASTFLOAT_VISUAL_STUDIO 1 +#endif + +#if defined __BYTE_ORDER__ && defined __ORDER_BIG_ENDIAN__ +#define FASTFLOAT_IS_BIG_ENDIAN (__BYTE_ORDER__ == __ORDER_BIG_ENDIAN__) +#elif defined _WIN32 +#define FASTFLOAT_IS_BIG_ENDIAN 0 +#else +#if defined(__APPLE__) || defined(__FreeBSD__) +#include +#elif defined(sun) || defined(__sun) +#include +#else +#ifdef __has_include +#if __has_include() +#include +#endif //__has_include() +#endif //__has_include +#endif +# +#ifndef __BYTE_ORDER__ +// safe choice +#define FASTFLOAT_IS_BIG_ENDIAN 0 +#endif +# +#ifndef __ORDER_LITTLE_ENDIAN__ +// safe choice +#define FASTFLOAT_IS_BIG_ENDIAN 0 +#endif +# +#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ +#define FASTFLOAT_IS_BIG_ENDIAN 0 +#else +#define FASTFLOAT_IS_BIG_ENDIAN 1 +#endif +#endif + +#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 +#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 +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; +#if defined(_M_ARM64) && !defined(__MINGW32__) + // ARM64 has native support for 64-bit multiplications, no need to emulate + // But MinGW on ARM64 doesn't have native support for 64-bit multiplications + answer.high = __umulh(a, b); + answer.low = a * b; +#elif defined(FASTFLOAT_32BIT) || (defined(_WIN64) && !defined(__clang__)) + answer.low = _umul128(a, b, &answer.high); // _umul128 not available on ARM64 +#elif defined(FASTFLOAT_64BIT) + __uint128_t r = ((__uint128_t)a) * b; + answer.low = uint64_t(r); + answer.high = uint64_t(r >> 64); +#else + #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[] = {1e0f, 1e1f, 1e2f, 1e3f, 1e4f, 1e5f, + 1e6f, 1e7f, 1e8f, 1e9f, 1e10f}; +// used for max_mantissa_double and max_mantissa_float +constexpr uint64_t constant_55555 = 5 * 5 * 5 * 5 * 5; +// Largest integer value v so that (5**index * v) <= 1<<53. +// 0x10000000000000 == 1 << 53 +constexpr static uint64_t max_mantissa_double[] = { + 0x10000000000000, + 0x10000000000000 / 5, + 0x10000000000000 / (5 * 5), + 0x10000000000000 / (5 * 5 * 5), + 0x10000000000000 / (5 * 5 * 5 * 5), + 0x10000000000000 / (constant_55555), + 0x10000000000000 / (constant_55555 * 5), + 0x10000000000000 / (constant_55555 * 5 * 5), + 0x10000000000000 / (constant_55555 * 5 * 5 * 5), + 0x10000000000000 / (constant_55555 * 5 * 5 * 5 * 5), + 0x10000000000000 / (constant_55555 * constant_55555), + 0x10000000000000 / (constant_55555 * constant_55555 * 5), + 0x10000000000000 / (constant_55555 * constant_55555 * 5 * 5), + 0x10000000000000 / (constant_55555 * constant_55555 * 5 * 5 * 5), + 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555), + 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5), + 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5 * 5), + 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5), + 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5 * 5), + 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555), + 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5), + 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5 * 5), + 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5), + 0x10000000000000 / (constant_55555 * constant_55555 * constant_55555 * constant_55555 * 5 * 5 * 5 * 5)}; + // Largest integer value v so that (5**index * v) <= 1<<24. + // 0x1000000 == 1<<24 + constexpr static uint64_t max_mantissa_float[] = { + 0x1000000, + 0x1000000 / 5, + 0x1000000 / (5 * 5), + 0x1000000 / (5 * 5 * 5), + 0x1000000 / (5 * 5 * 5 * 5), + 0x1000000 / (constant_55555), + 0x1000000 / (constant_55555 * 5), + 0x1000000 / (constant_55555 * 5 * 5), + 0x1000000 / (constant_55555 * 5 * 5 * 5), + 0x1000000 / (constant_55555 * 5 * 5 * 5 * 5), + 0x1000000 / (constant_55555 * constant_55555), + 0x1000000 / (constant_55555 * constant_55555 * 5)}; + +template struct binary_format { + using equiv_uint = typename std::conditional::type; + + static inline constexpr int mantissa_explicit_bits(); + static inline constexpr int minimum_exponent(); + static inline constexpr int infinite_power(); + static inline constexpr int sign_index(); + static inline constexpr int min_exponent_fast_path(); // used when fegetround() == FE_TONEAREST + static inline constexpr int max_exponent_fast_path(); + static inline constexpr int max_exponent_round_to_even(); + static inline constexpr int min_exponent_round_to_even(); + static inline constexpr uint64_t max_mantissa_fast_path(int64_t power); + static inline constexpr uint64_t max_mantissa_fast_path(); // used when fegetround() == FE_TONEAREST + static inline constexpr int largest_power_of_ten(); + static inline constexpr int smallest_power_of_ten(); + static inline constexpr T exact_power_of_ten(int64_t power); + static inline constexpr size_t max_digits(); + static inline constexpr equiv_uint exponent_mask(); + static inline constexpr equiv_uint mantissa_mask(); + static inline constexpr equiv_uint hidden_bit_mask(); +}; + +template <> inline constexpr int binary_format::min_exponent_fast_path() { +#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0) + return 0; +#else + return -22; +#endif +} + +template <> inline constexpr int binary_format::min_exponent_fast_path() { +#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0) + return 0; +#else + return -10; +#endif +} + +template <> inline constexpr int binary_format::mantissa_explicit_bits() { + return 52; +} +template <> inline constexpr int binary_format::mantissa_explicit_bits() { + return 23; +} + +template <> inline constexpr int binary_format::max_exponent_round_to_even() { + return 23; +} + +template <> inline constexpr int binary_format::max_exponent_round_to_even() { + return 10; +} + +template <> inline constexpr int binary_format::min_exponent_round_to_even() { + return -4; +} + +template <> inline constexpr int binary_format::min_exponent_round_to_even() { + return -17; +} + +template <> inline constexpr int binary_format::minimum_exponent() { + return -1023; +} +template <> inline constexpr int binary_format::minimum_exponent() { + return -127; +} + +template <> inline constexpr int binary_format::infinite_power() { + return 0x7FF; +} +template <> inline constexpr int binary_format::infinite_power() { + return 0xFF; +} + +template <> inline constexpr int binary_format::sign_index() { return 63; } +template <> inline constexpr int binary_format::sign_index() { return 31; } + +template <> inline constexpr int binary_format::max_exponent_fast_path() { + return 22; +} +template <> inline constexpr int binary_format::max_exponent_fast_path() { + return 10; +} +template <> inline constexpr uint64_t binary_format::max_mantissa_fast_path() { + return uint64_t(2) << mantissa_explicit_bits(); +} +template <> inline constexpr uint64_t binary_format::max_mantissa_fast_path(int64_t power) { + // caller is responsible to ensure that + // power >= 0 && power <= 22 + // + return max_mantissa_double[power]; +} +template <> inline constexpr uint64_t binary_format::max_mantissa_fast_path() { + return uint64_t(2) << mantissa_explicit_bits(); +} +template <> inline constexpr uint64_t binary_format::max_mantissa_fast_path(int64_t power) { + // caller is responsible to ensure that + // power >= 0 && power <= 10 + // + return max_mantissa_float[power]; +} + +template <> +inline constexpr double binary_format::exact_power_of_ten(int64_t power) { + return powers_of_ten_double[power]; +} +template <> +inline constexpr float binary_format::exact_power_of_ten(int64_t power) { + + return powers_of_ten_float[power]; +} + + +template <> +inline constexpr int binary_format::largest_power_of_ten() { + return 308; +} +template <> +inline constexpr int binary_format::largest_power_of_ten() { + return 38; +} + +template <> +inline constexpr int binary_format::smallest_power_of_ten() { + return -342; +} +template <> +inline constexpr int binary_format::smallest_power_of_ten() { + return -65; +} + +template <> inline constexpr size_t binary_format::max_digits() { + return 769; +} +template <> inline constexpr size_t binary_format::max_digits() { + return 114; +} + +template <> inline constexpr binary_format::equiv_uint + binary_format::exponent_mask() { + return 0x7F800000; +} +template <> inline constexpr binary_format::equiv_uint + binary_format::exponent_mask() { + return 0x7FF0000000000000; +} + +template <> inline constexpr binary_format::equiv_uint + binary_format::mantissa_mask() { + return 0x007FFFFF; +} +template <> inline constexpr binary_format::equiv_uint + binary_format::mantissa_mask() { + return 0x000FFFFFFFFFFFFF; +} + +template <> inline constexpr binary_format::equiv_uint + binary_format::hidden_bit_mask() { + return 0x00800000; +} +template <> inline constexpr binary_format::equiv_uint + binary_format::hidden_bit_mask() { + return 0x0010000000000000; +} + +template +fastfloat_really_inline void to_float(bool negative, adjusted_mantissa am, T &value) { + uint64_t word = am.mantissa; + word |= uint64_t(am.power2) << binary_format::mantissa_explicit_bits(); + word = negative + ? word | (uint64_t(1) << binary_format::sign_index()) : word; +#if FASTFLOAT_IS_BIG_ENDIAN == 1 + if (std::is_same::value) { + ::memcpy(&value, (char *)&word + 4, sizeof(T)); // extract value at offset 4-7 if float on big-endian + } else { + ::memcpy(&value, &word, sizeof(T)); + } +#else + // For little-endian systems: + ::memcpy(&value, &word, sizeof(T)); +#endif +} + +} // namespace fast_float + +#endif diff --git a/dep/fast_float/include/fast_float/parse_number.h b/dep/fast_float/include/fast_float/parse_number.h new file mode 100644 index 000000000..4e646cac4 --- /dev/null +++ b/dep/fast_float/include/fast_float/parse_number.h @@ -0,0 +1,205 @@ +#ifndef FASTFLOAT_PARSE_NUMBER_H +#define FASTFLOAT_PARSE_NUMBER_H + +#include "ascii_number.h" +#include "decimal_to_binary.h" +#include "digit_comparison.h" + +#include +#include +#include +#include + +namespace fast_float { + + +namespace detail { +/** + * Special case +inf, -inf, nan, infinity, -infinity. + * The case comparisons could be made much faster given that we know that the + * strings a null-free and fixed. + **/ +template +from_chars_result 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::quiet_NaN() : std::numeric_limits::quiet_NaN(); + // Check for possible nan(n-char-seq-opt), C++17 20.19.3.7, C11 7.20.1.3.3. At least MSVC produces nan(ind) and nan(snan). + if(first != last && *first == '(') { + for(const char* ptr = first + 1; ptr != last; ++ptr) { + if (*ptr == ')') { + 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::infinity() : std::numeric_limits::infinity(); + return answer; + } + } + answer.ec = std::errc::invalid_argument; + return answer; +} + +/** + * Returns true if the floating-pointing rounding mode is to 'nearest'. + * It is the default on most system. This function is meant to be inexpensive. + * Credit : @mwalcott3 + */ +fastfloat_really_inline bool rounds_to_nearest() noexcept { + // See + // A fast function to check your floating-point rounding mode + // https://lemire.me/blog/2022/11/16/a-fast-function-to-check-your-floating-point-rounding-mode/ + // + // This function is meant to be equivalent to : + // prior: #include + // return fegetround() == FE_TONEAREST; + // However, it is expected to be much faster than the fegetround() + // function call. + // + // The volatile keywoard prevents the compiler from computing the function + // at compile-time. + // There might be other ways to prevent compile-time optimizations (e.g., asm). + // The value does not need to be std::numeric_limits::min(), any small + // value so that 1 + x should round to 1 would do (after accounting for excess + // precision, as in 387 instructions). + static volatile float fmin = std::numeric_limits::min(); + float fmini = fmin; // we copy it so that it gets loaded at most once. + // + // Explanation: + // Only when fegetround() == FE_TONEAREST do we have that + // fmin + 1.0f == 1.0f - fmin. + // + // FE_UPWARD: + // fmin + 1.0f > 1 + // 1.0f - fmin == 1 + // + // FE_DOWNWARD or FE_TOWARDZERO: + // fmin + 1.0f == 1 + // 1.0f - fmin < 1 + // + // Note: This may fail to be accurate if fast-math has been + // enabled, as rounding conventions may not apply. + #if FASTFLOAT_VISUAL_STUDIO + # pragma warning(push) + // todo: is there a VS warning? + // see https://stackoverflow.com/questions/46079446/is-there-a-warning-for-floating-point-equality-checking-in-visual-studio-2013 + #elif defined(__clang__) + # pragma clang diagnostic push + # pragma clang diagnostic ignored "-Wfloat-equal" + #elif defined(__GNUC__) + # pragma GCC diagnostic push + # pragma GCC diagnostic ignored "-Wfloat-equal" + #endif + return (fmini + 1.0f == 1.0f - fmini); + #if FASTFLOAT_VISUAL_STUDIO + # pragma warning(pop) + #elif defined(__clang__) + # pragma clang diagnostic pop + #elif defined(__GNUC__) + # pragma GCC diagnostic pop + #endif +} + +} // namespace detail + +template +from_chars_result from_chars(const char *first, const char *last, + T &value, chars_format fmt /*= chars_format::general*/) noexcept { + return from_chars_advanced(first, last, value, parse_options{fmt}); +} + +template +from_chars_result from_chars_advanced(const char *first, const char *last, + T &value, parse_options options) noexcept { + + static_assert (std::is_same::value || std::is_same::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; + // The implementation of the Clinger's fast path is convoluted because + // we want round-to-nearest in all cases, irrespective of the rounding mode + // selected on the thread. + // We proceed optimistically, assuming that detail::rounds_to_nearest() returns + // true. + if (binary_format::min_exponent_fast_path() <= pns.exponent && pns.exponent <= binary_format::max_exponent_fast_path() && !pns.too_many_digits) { + // Unfortunately, the conventional Clinger's fast path is only possible + // when the system rounds to the nearest float. + // + // We expect the next branch to almost always be selected. + // We could check it first (before the previous branch), but + // there might be performance advantages at having the check + // be last. + if(detail::rounds_to_nearest()) { + // We have that fegetround() == FE_TONEAREST. + // Next is Clinger's fast path. + if (pns.mantissa <=binary_format::max_mantissa_fast_path()) { + value = T(pns.mantissa); + if (pns.exponent < 0) { value = value / binary_format::exact_power_of_ten(-pns.exponent); } + else { value = value * binary_format::exact_power_of_ten(pns.exponent); } + if (pns.negative) { value = -value; } + return answer; + } + } else { + // We do not have that fegetround() == FE_TONEAREST. + // Next is a modified Clinger's fast path, inspired by Jakub Jelínek's proposal + if (pns.exponent >= 0 && pns.mantissa <=binary_format::max_mantissa_fast_path(pns.exponent)) { +#if defined(__clang__) + // Clang may map 0 to -0.0 when fegetround() == FE_DOWNWARD + if(pns.mantissa == 0) { + value = 0; + return answer; + } +#endif + value = T(pns.mantissa) * binary_format::exact_power_of_ten(pns.exponent); + if (pns.negative) { value = -value; } + return answer; + } + } + } + adjusted_mantissa am = compute_float>(pns.exponent, pns.mantissa); + if(pns.too_many_digits && am.power2 >= 0) { + if(am != compute_float>(pns.exponent, pns.mantissa + 1)) { + am = compute_error>(pns.exponent, pns.mantissa); + } + } + // If we called compute_float>(pns.exponent, pns.mantissa) and we have an invalid power (am.power2 < 0), + // then we need to go the long way around again. This is very uncommon. + if(am.power2 < 0) { am = digit_comp(pns, am); } + to_float(pns.negative, am, value); + return answer; +} + +} // namespace fast_float + +#endif diff --git a/dep/fast_float/include/fast_float/simple_decimal_conversion.h b/dep/fast_float/include/fast_float/simple_decimal_conversion.h new file mode 100644 index 000000000..0484d7462 --- /dev/null +++ b/dep/fast_float/include/fast_float/simple_decimal_conversion.h @@ -0,0 +1,360 @@ +#ifndef FASTFLOAT_GENERIC_DECIMAL_TO_BINARY_H +#define FASTFLOAT_GENERIC_DECIMAL_TO_BINARY_H + +/** + * This code is meant to handle the case where we have more than 19 digits. + * + * It is based on work by Nigel Tao (at https://github.com/google/wuffs/) + * who credits Ken Thompson for the design (via a reference to the Go source + * code). + * + * Rob Pike suggested that this algorithm be called "Simple Decimal Conversion". + * + * It is probably not very fast but it is a fallback that should almost never + * be used in real life. Though it is not fast, it is "easily" understood and debugged. + **/ +#include "ascii_number.h" +#include "decimal_to_binary.h" +#include + +namespace fast_float { + +namespace detail { + +// remove all final zeroes +inline void trim(decimal &h) { + while ((h.num_digits > 0) && (h.digits[h.num_digits - 1] == 0)) { + h.num_digits--; + } +} + + + +inline uint32_t number_of_digits_decimal_left_shift(const decimal &h, uint32_t shift) { + shift &= 63; + constexpr uint16_t number_of_digits_decimal_left_shift_table[65] = { + 0x0000, 0x0800, 0x0801, 0x0803, 0x1006, 0x1009, 0x100D, 0x1812, 0x1817, + 0x181D, 0x2024, 0x202B, 0x2033, 0x203C, 0x2846, 0x2850, 0x285B, 0x3067, + 0x3073, 0x3080, 0x388E, 0x389C, 0x38AB, 0x38BB, 0x40CC, 0x40DD, 0x40EF, + 0x4902, 0x4915, 0x4929, 0x513E, 0x5153, 0x5169, 0x5180, 0x5998, 0x59B0, + 0x59C9, 0x61E3, 0x61FD, 0x6218, 0x6A34, 0x6A50, 0x6A6D, 0x6A8B, 0x72AA, + 0x72C9, 0x72E9, 0x7B0A, 0x7B2B, 0x7B4D, 0x8370, 0x8393, 0x83B7, 0x83DC, + 0x8C02, 0x8C28, 0x8C4F, 0x9477, 0x949F, 0x94C8, 0x9CF2, 0x051C, 0x051C, + 0x051C, 0x051C, + }; + uint32_t x_a = number_of_digits_decimal_left_shift_table[shift]; + uint32_t x_b = number_of_digits_decimal_left_shift_table[shift + 1]; + uint32_t num_new_digits = x_a >> 11; + uint32_t pow5_a = 0x7FF & x_a; + uint32_t pow5_b = 0x7FF & x_b; + constexpr uint8_t + number_of_digits_decimal_left_shift_table_powers_of_5[0x051C] = { + 5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5, 3, + 9, 0, 6, 2, 5, 1, 9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8, 2, 8, + 1, 2, 5, 2, 4, 4, 1, 4, 0, 6, 2, 5, 1, 2, 2, 0, 7, 0, 3, 1, 2, 5, 6, 1, + 0, 3, 5, 1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2, 5, 1, 5, 2, 5, 8, + 7, 8, 9, 0, 6, 2, 5, 7, 6, 2, 9, 3, 9, 4, 5, 3, 1, 2, 5, 3, 8, 1, 4, 6, + 9, 7, 2, 6, 5, 6, 2, 5, 1, 9, 0, 7, 3, 4, 8, 6, 3, 2, 8, 1, 2, 5, 9, 5, + 3, 6, 7, 4, 3, 1, 6, 4, 0, 6, 2, 5, 4, 7, 6, 8, 3, 7, 1, 5, 8, 2, 0, 3, + 1, 2, 5, 2, 3, 8, 4, 1, 8, 5, 7, 9, 1, 0, 1, 5, 6, 2, 5, 1, 1, 9, 2, 0, + 9, 2, 8, 9, 5, 5, 0, 7, 8, 1, 2, 5, 5, 9, 6, 0, 4, 6, 4, 4, 7, 7, 5, 3, + 9, 0, 6, 2, 5, 2, 9, 8, 0, 2, 3, 2, 2, 3, 8, 7, 6, 9, 5, 3, 1, 2, 5, 1, + 4, 9, 0, 1, 1, 6, 1, 1, 9, 3, 8, 4, 7, 6, 5, 6, 2, 5, 7, 4, 5, 0, 5, 8, + 0, 5, 9, 6, 9, 2, 3, 8, 2, 8, 1, 2, 5, 3, 7, 2, 5, 2, 9, 0, 2, 9, 8, 4, + 6, 1, 9, 1, 4, 0, 6, 2, 5, 1, 8, 6, 2, 6, 4, 5, 1, 4, 9, 2, 3, 0, 9, 5, + 7, 0, 3, 1, 2, 5, 9, 3, 1, 3, 2, 2, 5, 7, 4, 6, 1, 5, 4, 7, 8, 5, 1, 5, + 6, 2, 5, 4, 6, 5, 6, 6, 1, 2, 8, 7, 3, 0, 7, 7, 3, 9, 2, 5, 7, 8, 1, 2, + 5, 2, 3, 2, 8, 3, 0, 6, 4, 3, 6, 5, 3, 8, 6, 9, 6, 2, 8, 9, 0, 6, 2, 5, + 1, 1, 6, 4, 1, 5, 3, 2, 1, 8, 2, 6, 9, 3, 4, 8, 1, 4, 4, 5, 3, 1, 2, 5, + 5, 8, 2, 0, 7, 6, 6, 0, 9, 1, 3, 4, 6, 7, 4, 0, 7, 2, 2, 6, 5, 6, 2, 5, + 2, 9, 1, 0, 3, 8, 3, 0, 4, 5, 6, 7, 3, 3, 7, 0, 3, 6, 1, 3, 2, 8, 1, 2, + 5, 1, 4, 5, 5, 1, 9, 1, 5, 2, 2, 8, 3, 6, 6, 8, 5, 1, 8, 0, 6, 6, 4, 0, + 6, 2, 5, 7, 2, 7, 5, 9, 5, 7, 6, 1, 4, 1, 8, 3, 4, 2, 5, 9, 0, 3, 3, 2, + 0, 3, 1, 2, 5, 3, 6, 3, 7, 9, 7, 8, 8, 0, 7, 0, 9, 1, 7, 1, 2, 9, 5, 1, + 6, 6, 0, 1, 5, 6, 2, 5, 1, 8, 1, 8, 9, 8, 9, 4, 0, 3, 5, 4, 5, 8, 5, 6, + 4, 7, 5, 8, 3, 0, 0, 7, 8, 1, 2, 5, 9, 0, 9, 4, 9, 4, 7, 0, 1, 7, 7, 2, + 9, 2, 8, 2, 3, 7, 9, 1, 5, 0, 3, 9, 0, 6, 2, 5, 4, 5, 4, 7, 4, 7, 3, 5, + 0, 8, 8, 6, 4, 6, 4, 1, 1, 8, 9, 5, 7, 5, 1, 9, 5, 3, 1, 2, 5, 2, 2, 7, + 3, 7, 3, 6, 7, 5, 4, 4, 3, 2, 3, 2, 0, 5, 9, 4, 7, 8, 7, 5, 9, 7, 6, 5, + 6, 2, 5, 1, 1, 3, 6, 8, 6, 8, 3, 7, 7, 2, 1, 6, 1, 6, 0, 2, 9, 7, 3, 9, + 3, 7, 9, 8, 8, 2, 8, 1, 2, 5, 5, 6, 8, 4, 3, 4, 1, 8, 8, 6, 0, 8, 0, 8, + 0, 1, 4, 8, 6, 9, 6, 8, 9, 9, 4, 1, 4, 0, 6, 2, 5, 2, 8, 4, 2, 1, 7, 0, + 9, 4, 3, 0, 4, 0, 4, 0, 0, 7, 4, 3, 4, 8, 4, 4, 9, 7, 0, 7, 0, 3, 1, 2, + 5, 1, 4, 2, 1, 0, 8, 5, 4, 7, 1, 5, 2, 0, 2, 0, 0, 3, 7, 1, 7, 4, 2, 2, + 4, 8, 5, 3, 5, 1, 5, 6, 2, 5, 7, 1, 0, 5, 4, 2, 7, 3, 5, 7, 6, 0, 1, 0, + 0, 1, 8, 5, 8, 7, 1, 1, 2, 4, 2, 6, 7, 5, 7, 8, 1, 2, 5, 3, 5, 5, 2, 7, + 1, 3, 6, 7, 8, 8, 0, 0, 5, 0, 0, 9, 2, 9, 3, 5, 5, 6, 2, 1, 3, 3, 7, 8, + 9, 0, 6, 2, 5, 1, 7, 7, 6, 3, 5, 6, 8, 3, 9, 4, 0, 0, 2, 5, 0, 4, 6, 4, + 6, 7, 7, 8, 1, 0, 6, 6, 8, 9, 4, 5, 3, 1, 2, 5, 8, 8, 8, 1, 7, 8, 4, 1, + 9, 7, 0, 0, 1, 2, 5, 2, 3, 2, 3, 3, 8, 9, 0, 5, 3, 3, 4, 4, 7, 2, 6, 5, + 6, 2, 5, 4, 4, 4, 0, 8, 9, 2, 0, 9, 8, 5, 0, 0, 6, 2, 6, 1, 6, 1, 6, 9, + 4, 5, 2, 6, 6, 7, 2, 3, 6, 3, 2, 8, 1, 2, 5, 2, 2, 2, 0, 4, 4, 6, 0, 4, + 9, 2, 5, 0, 3, 1, 3, 0, 8, 0, 8, 4, 7, 2, 6, 3, 3, 3, 6, 1, 8, 1, 6, 4, + 0, 6, 2, 5, 1, 1, 1, 0, 2, 2, 3, 0, 2, 4, 6, 2, 5, 1, 5, 6, 5, 4, 0, 4, + 2, 3, 6, 3, 1, 6, 6, 8, 0, 9, 0, 8, 2, 0, 3, 1, 2, 5, 5, 5, 5, 1, 1, 1, + 5, 1, 2, 3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 1, 1, 8, 1, 5, 8, 3, 4, 0, 4, 5, + 4, 1, 0, 1, 5, 6, 2, 5, 2, 7, 7, 5, 5, 5, 7, 5, 6, 1, 5, 6, 2, 8, 9, 1, + 3, 5, 1, 0, 5, 9, 0, 7, 9, 1, 7, 0, 2, 2, 7, 0, 5, 0, 7, 8, 1, 2, 5, 1, + 3, 8, 7, 7, 7, 8, 7, 8, 0, 7, 8, 1, 4, 4, 5, 6, 7, 5, 5, 2, 9, 5, 3, 9, + 5, 8, 5, 1, 1, 3, 5, 2, 5, 3, 9, 0, 6, 2, 5, 6, 9, 3, 8, 8, 9, 3, 9, 0, + 3, 9, 0, 7, 2, 2, 8, 3, 7, 7, 6, 4, 7, 6, 9, 7, 9, 2, 5, 5, 6, 7, 6, 2, + 6, 9, 5, 3, 1, 2, 5, 3, 4, 6, 9, 4, 4, 6, 9, 5, 1, 9, 5, 3, 6, 1, 4, 1, + 8, 8, 8, 2, 3, 8, 4, 8, 9, 6, 2, 7, 8, 3, 8, 1, 3, 4, 7, 6, 5, 6, 2, 5, + 1, 7, 3, 4, 7, 2, 3, 4, 7, 5, 9, 7, 6, 8, 0, 7, 0, 9, 4, 4, 1, 1, 9, 2, + 4, 4, 8, 1, 3, 9, 1, 9, 0, 6, 7, 3, 8, 2, 8, 1, 2, 5, 8, 6, 7, 3, 6, 1, + 7, 3, 7, 9, 8, 8, 4, 0, 3, 5, 4, 7, 2, 0, 5, 9, 6, 2, 2, 4, 0, 6, 9, 5, + 9, 5, 3, 3, 6, 9, 1, 4, 0, 6, 2, 5, + }; + const uint8_t *pow5 = + &number_of_digits_decimal_left_shift_table_powers_of_5[pow5_a]; + uint32_t i = 0; + uint32_t n = pow5_b - pow5_a; + for (; i < n; i++) { + if (i >= h.num_digits) { + return num_new_digits - 1; + } else if (h.digits[i] == pow5[i]) { + continue; + } else if (h.digits[i] < pow5[i]) { + return num_new_digits - 1; + } else { + return num_new_digits; + } + } + return num_new_digits; +} + +inline uint64_t round(decimal &h) { + if ((h.num_digits == 0) || (h.decimal_point < 0)) { + return 0; + } else if (h.decimal_point > 18) { + return UINT64_MAX; + } + // at this point, we know that h.decimal_point >= 0 + uint32_t dp = uint32_t(h.decimal_point); + uint64_t n = 0; + for (uint32_t i = 0; i < dp; i++) { + n = (10 * n) + ((i < h.num_digits) ? h.digits[i] : 0); + } + bool round_up = false; + if (dp < h.num_digits) { + round_up = h.digits[dp] >= 5; // normally, we round up + // but we may need to round to even! + if ((h.digits[dp] == 5) && (dp + 1 == h.num_digits)) { + round_up = h.truncated || ((dp > 0) && (1 & h.digits[dp - 1])); + } + } + if (round_up) { + n++; + } + return n; +} + +// computes h * 2^-shift +inline void decimal_left_shift(decimal &h, uint32_t shift) { + if (h.num_digits == 0) { + return; + } + uint32_t num_new_digits = number_of_digits_decimal_left_shift(h, shift); + int32_t read_index = int32_t(h.num_digits - 1); + uint32_t write_index = h.num_digits - 1 + num_new_digits; + uint64_t n = 0; + + while (read_index >= 0) { + n += uint64_t(h.digits[read_index]) << shift; + uint64_t quotient = n / 10; + uint64_t remainder = n - (10 * quotient); + if (write_index < max_digits) { + h.digits[write_index] = uint8_t(remainder); + } else if (remainder > 0) { + h.truncated = true; + } + n = quotient; + write_index--; + read_index--; + } + while (n > 0) { + uint64_t quotient = n / 10; + uint64_t remainder = n - (10 * quotient); + if (write_index < max_digits) { + h.digits[write_index] = uint8_t(remainder); + } else if (remainder > 0) { + h.truncated = true; + } + n = quotient; + write_index--; + } + h.num_digits += num_new_digits; + if (h.num_digits > max_digits) { + h.num_digits = max_digits; + } + h.decimal_point += int32_t(num_new_digits); + trim(h); +} + +// computes h * 2^shift +inline void decimal_right_shift(decimal &h, uint32_t shift) { + uint32_t read_index = 0; + uint32_t write_index = 0; + + uint64_t n = 0; + + while ((n >> shift) == 0) { + if (read_index < h.num_digits) { + n = (10 * n) + h.digits[read_index++]; + } else if (n == 0) { + return; + } else { + while ((n >> shift) == 0) { + n = 10 * n; + read_index++; + } + break; + } + } + h.decimal_point -= int32_t(read_index - 1); + if (h.decimal_point < -decimal_point_range) { // it is zero + h.num_digits = 0; + h.decimal_point = 0; + h.negative = false; + h.truncated = false; + return; + } + uint64_t mask = (uint64_t(1) << shift) - 1; + while (read_index < h.num_digits) { + uint8_t new_digit = uint8_t(n >> shift); + n = (10 * (n & mask)) + h.digits[read_index++]; + h.digits[write_index++] = new_digit; + } + while (n > 0) { + uint8_t new_digit = uint8_t(n >> shift); + n = 10 * (n & mask); + if (write_index < max_digits) { + h.digits[write_index++] = new_digit; + } else if (new_digit > 0) { + h.truncated = true; + } + } + h.num_digits = write_index; + trim(h); +} + +} // namespace detail + +template +adjusted_mantissa compute_float(decimal &d) { + adjusted_mantissa answer; + if (d.num_digits == 0) { + // should be zero + answer.power2 = 0; + answer.mantissa = 0; + return answer; + } + // At this point, going further, we can assume that d.num_digits > 0. + // + // We want to guard against excessive decimal point values because + // they can result in long running times. Indeed, we do + // shifts by at most 60 bits. We have that log(10**400)/log(2**60) ~= 22 + // which is fine, but log(10**299995)/log(2**60) ~= 16609 which is not + // fine (runs for a long time). + // + if(d.decimal_point < -324) { + // We have something smaller than 1e-324 which is always zero + // in binary64 and binary32. + // It should be zero. + answer.power2 = 0; + answer.mantissa = 0; + return answer; + } else if(d.decimal_point >= 310) { + // We have something at least as large as 0.1e310 which is + // always infinite. + answer.power2 = binary::infinite_power(); + answer.mantissa = 0; + return answer; + } + constexpr uint32_t max_shift = 60; + constexpr uint32_t num_powers = 19; + constexpr uint8_t decimal_powers[19] = { + 0, 3, 6, 9, 13, 16, 19, 23, 26, 29, // + 33, 36, 39, 43, 46, 49, 53, 56, 59, // + }; + int32_t exp2 = 0; + while (d.decimal_point > 0) { + uint32_t n = uint32_t(d.decimal_point); + uint32_t shift = (n < num_powers) ? decimal_powers[n] : max_shift; + detail::decimal_right_shift(d, shift); + if (d.decimal_point < -decimal_point_range) { + // should be zero + answer.power2 = 0; + answer.mantissa = 0; + return answer; + } + exp2 += int32_t(shift); + } + // We shift left toward [1/2 ... 1]. + while (d.decimal_point <= 0) { + uint32_t shift; + if (d.decimal_point == 0) { + if (d.digits[0] >= 5) { + break; + } + shift = (d.digits[0] < 2) ? 2 : 1; + } else { + uint32_t n = uint32_t(-d.decimal_point); + shift = (n < num_powers) ? decimal_powers[n] : max_shift; + } + detail::decimal_left_shift(d, shift); + if (d.decimal_point > decimal_point_range) { + // we want to get infinity: + answer.power2 = binary::infinite_power(); + answer.mantissa = 0; + return answer; + } + exp2 -= int32_t(shift); + } + // We are now in the range [1/2 ... 1] but the binary format uses [1 ... 2]. + exp2--; + constexpr int32_t minimum_exponent = binary::minimum_exponent(); + while ((minimum_exponent + 1) > exp2) { + uint32_t n = uint32_t((minimum_exponent + 1) - exp2); + if (n > max_shift) { + n = max_shift; + } + detail::decimal_right_shift(d, n); + exp2 += int32_t(n); + } + if ((exp2 - minimum_exponent) >= binary::infinite_power()) { + answer.power2 = binary::infinite_power(); + answer.mantissa = 0; + return answer; + } + + const int mantissa_size_in_bits = binary::mantissa_explicit_bits() + 1; + detail::decimal_left_shift(d, mantissa_size_in_bits); + + uint64_t mantissa = detail::round(d); + // It is possible that we have an overflow, in which case we need + // to shift back. + if(mantissa >= (uint64_t(1) << mantissa_size_in_bits)) { + detail::decimal_right_shift(d, 1); + exp2 += 1; + mantissa = detail::round(d); + if ((exp2 - minimum_exponent) >= binary::infinite_power()) { + answer.power2 = binary::infinite_power(); + answer.mantissa = 0; + return answer; + } + } + answer.power2 = exp2 - binary::minimum_exponent(); + if(mantissa < (uint64_t(1) << binary::mantissa_explicit_bits())) { answer.power2--; } + answer.mantissa = mantissa & ((uint64_t(1) << binary::mantissa_explicit_bits()) - 1); + return answer; +} + +template +adjusted_mantissa parse_long_mantissa(const char *first, const char* last, parse_options options) { + decimal d = parse_decimal(first, last, options); + return compute_float(d); +} + +} // namespace fast_float +#endif