forked from bartvdbraak/blender
213cd39b6d
Continued improvements to the new C++ based OBJ importer. Performance: about 2x faster. - Rungholt.obj (several meshes, 263MB file): Windows 12.7s -> 5.9s, Mac 7.7s -> 3.1s. - Blender 3.0 splash (24k meshes, 2.4GB file): Windows 97.3s -> 53.6s, Mac 137.3s -> 80.0s. - "Windows" is VS2022, AMD Ryzen 5950X (32 threads), "Mac" is Xcode/clang 13, M1Max (10 threads). - Slightly reduced memory usage during import as well. The performance gains are a combination of several things: - Replacing `std::stof` / `std::stoi` with C++17 `from_chars`. - Stop reading input file char-by-char using `std::getline`, and instead read in 64kb chunks, and parse from there (taking care of possibly handling lines split mid-way due to chunk boundaries). - Removing abstractions for splitting a line by some char, - Avoid tiny memory allocations: instead of storing a vector of polygon corners in each face, store all the corners in one big array, and per-face only store indices "where do corners start, and how many". Likewise, don't store full string names of material/group names for each face; only store indices into overall material/group names arrays. - Stop always doing mesh validation, which is slow. Do it just like the Alembic importer does: only do validation if found some invalid faces during import, or if requested by the user via an import setting checkbox (which defaults to off). - Stop doing "collection sync" for each object being added; instead do the collection sync right after creating all the objects. Cleanup / Robustness: This reworking of parser (see "removing abstractions" point above) means that all the functions that were in `parser_string_utils` file are gone, and replaced with different set of functions. However they are not OBJ specific, so as pointed out during review of the previous differential, they are now in `source/blender/io/common` library. Added gtest coverage for said functions as well; something that was only indirectly covered by obj tests previously. Rework of some bits of parsing made the parser actually better able to deal with invalid syntax. E.g. previously, if a face corner were a `/123` string, it would have incorrectly treated that as a vertex index (since it would get "hey that's one number" after splitting a string by a slash), instead of properly marking it as invalid syntax. Added gtest coverage for .mtl parsing; something that was not covered by any tests at all previously. Reviewed By: Howard Trickey Differential Revision: https://developer.blender.org/D14586
2980 lines
105 KiB
C++
2980 lines
105 KiB
C++
// fast_float by Daniel Lemire
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// fast_float by João Paulo Magalhaes
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//
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// with contributions from Eugene Golushkov
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// with contributions from Maksim Kita
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// with contributions from Marcin Wojdyr
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// with contributions from Neal Richardson
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// with contributions from Tim Paine
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// with contributions from Fabio Pellacini
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//
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// Licensed under the Apache License, Version 2.0, or the
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// MIT License at your option. This file may not be copied,
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// modified, or distributed except according to those terms.
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//
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// MIT License Notice
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//
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// MIT License
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//
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// Copyright (c) 2021 The fast_float authors
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//
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// Permission is hereby granted, free of charge, to any
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// person obtaining a copy of this software and associated
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// documentation files (the "Software"), to deal in the
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// Software without restriction, including without
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// limitation the rights to use, copy, modify, merge,
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// publish, distribute, sublicense, and/or sell copies of
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// the Software, and to permit persons to whom the Software
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// is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice
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// shall be included in all copies or substantial portions
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// of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF
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// ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
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// TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
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// PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT
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// SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
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// CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
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// OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
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// IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
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// DEALINGS IN THE SOFTWARE.
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//
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// Apache License (Version 2.0) Notice
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//
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// Copyright 2021 The fast_float authors
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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//
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#ifndef FASTFLOAT_FAST_FLOAT_H
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#define FASTFLOAT_FAST_FLOAT_H
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#include <system_error>
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namespace fast_float {
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enum chars_format {
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scientific = 1<<0,
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fixed = 1<<2,
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hex = 1<<3,
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general = fixed | scientific
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};
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struct from_chars_result {
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const char *ptr;
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std::errc ec;
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};
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struct parse_options {
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constexpr explicit parse_options(chars_format fmt = chars_format::general,
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char dot = '.')
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: format(fmt), decimal_point(dot) {}
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/** Which number formats are accepted */
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chars_format format;
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/** The character used as decimal point */
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char decimal_point;
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};
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/**
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* This function parses the character sequence [first,last) for a number. It parses floating-point numbers expecting
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* a locale-indepent format equivalent to what is used by std::strtod in the default ("C") locale.
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* The resulting floating-point value is the closest floating-point values (using either float or double),
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* using the "round to even" convention for values that would otherwise fall right in-between two values.
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* That is, we provide exact parsing according to the IEEE standard.
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*
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* Given a successful parse, the pointer (`ptr`) in the returned value is set to point right after the
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* parsed number, and the `value` referenced is set to the parsed value. In case of error, the returned
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* `ec` contains a representative error, otherwise the default (`std::errc()`) value is stored.
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*
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* The implementation does not throw and does not allocate memory (e.g., with `new` or `malloc`).
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*
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* Like the C++17 standard, the `fast_float::from_chars` functions take an optional last argument of
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* the type `fast_float::chars_format`. It is a bitset value: we check whether
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* `fmt & fast_float::chars_format::fixed` and `fmt & fast_float::chars_format::scientific` are set
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* to determine whether we allowe the fixed point and scientific notation respectively.
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* The default is `fast_float::chars_format::general` which allows both `fixed` and `scientific`.
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*/
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template<typename T>
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from_chars_result from_chars(const char *first, const char *last,
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T &value, chars_format fmt = chars_format::general) noexcept;
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/**
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* Like from_chars, but accepts an `options` argument to govern number parsing.
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*/
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template<typename T>
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from_chars_result from_chars_advanced(const char *first, const char *last,
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T &value, parse_options options) noexcept;
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}
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#endif // FASTFLOAT_FAST_FLOAT_H
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#ifndef FASTFLOAT_FLOAT_COMMON_H
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#define FASTFLOAT_FLOAT_COMMON_H
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#include <cfloat>
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#include <cstdint>
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#include <cassert>
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#include <cstring>
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#include <type_traits>
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#if (defined(__x86_64) || defined(__x86_64__) || defined(_M_X64) \
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|| defined(__amd64) || defined(__aarch64__) || defined(_M_ARM64) \
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|| defined(__MINGW64__) \
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|| defined(__s390x__) \
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|| (defined(__ppc64__) || defined(__PPC64__) || defined(__ppc64le__) || defined(__PPC64LE__)) \
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|| defined(__EMSCRIPTEN__))
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#define FASTFLOAT_64BIT
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#elif (defined(__i386) || defined(__i386__) || defined(_M_IX86) \
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|| defined(__arm__) || defined(_M_ARM) \
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|| defined(__MINGW32__))
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#define FASTFLOAT_32BIT
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#else
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// Need to check incrementally, since SIZE_MAX is a size_t, avoid overflow.
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// We can never tell the register width, but the SIZE_MAX is a good approximation.
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// UINTPTR_MAX and INTPTR_MAX are optional, so avoid them for max portability.
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#if SIZE_MAX == 0xffff
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#error Unknown platform (16-bit, unsupported)
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#elif SIZE_MAX == 0xffffffff
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#define FASTFLOAT_32BIT
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#elif SIZE_MAX == 0xffffffffffffffff
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#define FASTFLOAT_64BIT
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#else
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#error Unknown platform (not 32-bit, not 64-bit?)
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#endif
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#endif
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#if ((defined(_WIN32) || defined(_WIN64)) && !defined(__clang__))
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#include <intrin.h>
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#endif
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#if defined(_MSC_VER) && !defined(__clang__)
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#define FASTFLOAT_VISUAL_STUDIO 1
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#endif
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#ifdef _WIN32
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#define FASTFLOAT_IS_BIG_ENDIAN 0
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#else
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#if defined(__APPLE__) || defined(__FreeBSD__)
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#include <machine/endian.h>
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#elif defined(sun) || defined(__sun)
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#include <sys/byteorder.h>
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#else
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#include <endian.h>
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#endif
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#
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#ifndef __BYTE_ORDER__
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// safe choice
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#define FASTFLOAT_IS_BIG_ENDIAN 0
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#endif
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#
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#ifndef __ORDER_LITTLE_ENDIAN__
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// safe choice
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#define FASTFLOAT_IS_BIG_ENDIAN 0
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#endif
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#
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#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
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#define FASTFLOAT_IS_BIG_ENDIAN 0
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#else
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#define FASTFLOAT_IS_BIG_ENDIAN 1
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#endif
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#endif
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#ifdef FASTFLOAT_VISUAL_STUDIO
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#define fastfloat_really_inline __forceinline
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#else
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#define fastfloat_really_inline inline __attribute__((always_inline))
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#endif
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#ifndef FASTFLOAT_ASSERT
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#define FASTFLOAT_ASSERT(x) { if (!(x)) abort(); }
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#endif
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#ifndef FASTFLOAT_DEBUG_ASSERT
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#include <cassert>
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#define FASTFLOAT_DEBUG_ASSERT(x) assert(x)
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#endif
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// rust style `try!()` macro, or `?` operator
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#define FASTFLOAT_TRY(x) { if (!(x)) return false; }
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namespace fast_float {
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// Compares two ASCII strings in a case insensitive manner.
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inline bool fastfloat_strncasecmp(const char *input1, const char *input2,
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size_t length) {
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char running_diff{0};
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for (size_t i = 0; i < length; i++) {
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running_diff |= (input1[i] ^ input2[i]);
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}
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return (running_diff == 0) || (running_diff == 32);
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}
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#ifndef FLT_EVAL_METHOD
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#error "FLT_EVAL_METHOD should be defined, please include cfloat."
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#endif
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// a pointer and a length to a contiguous block of memory
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template <typename T>
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struct span {
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const T* ptr;
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size_t length;
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span(const T* _ptr, size_t _length) : ptr(_ptr), length(_length) {}
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span() : ptr(nullptr), length(0) {}
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constexpr size_t len() const noexcept {
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return length;
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}
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const T& operator[](size_t index) const noexcept {
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FASTFLOAT_DEBUG_ASSERT(index < length);
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return ptr[index];
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}
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};
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struct value128 {
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uint64_t low;
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uint64_t high;
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value128(uint64_t _low, uint64_t _high) : low(_low), high(_high) {}
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value128() : low(0), high(0) {}
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};
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/* result might be undefined when input_num is zero */
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fastfloat_really_inline int leading_zeroes(uint64_t input_num) {
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assert(input_num > 0);
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#ifdef FASTFLOAT_VISUAL_STUDIO
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#if defined(_M_X64) || defined(_M_ARM64)
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unsigned long leading_zero = 0;
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// Search the mask data from most significant bit (MSB)
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// to least significant bit (LSB) for a set bit (1).
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_BitScanReverse64(&leading_zero, input_num);
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return (int)(63 - leading_zero);
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#else
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int last_bit = 0;
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if(input_num & uint64_t(0xffffffff00000000)) input_num >>= 32, last_bit |= 32;
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if(input_num & uint64_t( 0xffff0000)) input_num >>= 16, last_bit |= 16;
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if(input_num & uint64_t( 0xff00)) input_num >>= 8, last_bit |= 8;
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if(input_num & uint64_t( 0xf0)) input_num >>= 4, last_bit |= 4;
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if(input_num & uint64_t( 0xc)) input_num >>= 2, last_bit |= 2;
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if(input_num & uint64_t( 0x2)) input_num >>= 1, last_bit |= 1;
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return 63 - last_bit;
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#endif
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#else
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return __builtin_clzll(input_num);
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#endif
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}
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#ifdef FASTFLOAT_32BIT
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// slow emulation routine for 32-bit
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fastfloat_really_inline uint64_t emulu(uint32_t x, uint32_t y) {
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return x * (uint64_t)y;
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}
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// slow emulation routine for 32-bit
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#if !defined(__MINGW64__)
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fastfloat_really_inline uint64_t _umul128(uint64_t ab, uint64_t cd,
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uint64_t *hi) {
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uint64_t ad = emulu((uint32_t)(ab >> 32), (uint32_t)cd);
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uint64_t bd = emulu((uint32_t)ab, (uint32_t)cd);
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uint64_t adbc = ad + emulu((uint32_t)ab, (uint32_t)(cd >> 32));
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uint64_t adbc_carry = !!(adbc < ad);
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uint64_t lo = bd + (adbc << 32);
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*hi = emulu((uint32_t)(ab >> 32), (uint32_t)(cd >> 32)) + (adbc >> 32) +
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(adbc_carry << 32) + !!(lo < bd);
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return lo;
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}
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#endif // !__MINGW64__
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#endif // FASTFLOAT_32BIT
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// compute 64-bit a*b
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fastfloat_really_inline value128 full_multiplication(uint64_t a,
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uint64_t b) {
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value128 answer;
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#ifdef _M_ARM64
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// ARM64 has native support for 64-bit multiplications, no need to emulate
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answer.high = __umulh(a, b);
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answer.low = a * b;
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#elif defined(FASTFLOAT_32BIT) || (defined(_WIN64) && !defined(__clang__))
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answer.low = _umul128(a, b, &answer.high); // _umul128 not available on ARM64
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#elif defined(FASTFLOAT_64BIT)
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__uint128_t r = ((__uint128_t)a) * b;
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answer.low = uint64_t(r);
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answer.high = uint64_t(r >> 64);
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#else
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#error Not implemented
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#endif
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return answer;
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}
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struct adjusted_mantissa {
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uint64_t mantissa{0};
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int32_t power2{0}; // a negative value indicates an invalid result
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adjusted_mantissa() = default;
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bool operator==(const adjusted_mantissa &o) const {
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return mantissa == o.mantissa && power2 == o.power2;
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}
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bool operator!=(const adjusted_mantissa &o) const {
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return mantissa != o.mantissa || power2 != o.power2;
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}
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};
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// Bias so we can get the real exponent with an invalid adjusted_mantissa.
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constexpr static int32_t invalid_am_bias = -0x8000;
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constexpr static double powers_of_ten_double[] = {
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1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11,
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1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22};
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constexpr static float powers_of_ten_float[] = {1e0, 1e1, 1e2, 1e3, 1e4, 1e5,
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1e6, 1e7, 1e8, 1e9, 1e10};
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template <typename T> struct binary_format {
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using equiv_uint = typename std::conditional<sizeof(T) == 4, uint32_t, uint64_t>::type;
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static inline constexpr int mantissa_explicit_bits();
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static inline constexpr int minimum_exponent();
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static inline constexpr int infinite_power();
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static inline constexpr int sign_index();
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static inline constexpr int min_exponent_fast_path();
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static inline constexpr int max_exponent_fast_path();
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static inline constexpr int max_exponent_round_to_even();
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static inline constexpr int min_exponent_round_to_even();
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static inline constexpr uint64_t max_mantissa_fast_path();
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static inline constexpr int largest_power_of_ten();
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static inline constexpr int smallest_power_of_ten();
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static inline constexpr T exact_power_of_ten(int64_t power);
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static inline constexpr size_t max_digits();
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static inline constexpr equiv_uint exponent_mask();
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static inline constexpr equiv_uint mantissa_mask();
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static inline constexpr equiv_uint hidden_bit_mask();
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};
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template <> inline constexpr int binary_format<double>::mantissa_explicit_bits() {
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return 52;
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}
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template <> inline constexpr int binary_format<float>::mantissa_explicit_bits() {
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return 23;
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}
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template <> inline constexpr int binary_format<double>::max_exponent_round_to_even() {
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return 23;
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}
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template <> inline constexpr int binary_format<float>::max_exponent_round_to_even() {
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return 10;
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}
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template <> inline constexpr int binary_format<double>::min_exponent_round_to_even() {
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return -4;
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}
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template <> inline constexpr int binary_format<float>::min_exponent_round_to_even() {
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return -17;
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}
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template <> inline constexpr int binary_format<double>::minimum_exponent() {
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return -1023;
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}
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template <> inline constexpr int binary_format<float>::minimum_exponent() {
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return -127;
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}
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template <> inline constexpr int binary_format<double>::infinite_power() {
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return 0x7FF;
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}
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template <> inline constexpr int binary_format<float>::infinite_power() {
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return 0xFF;
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}
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template <> inline constexpr int binary_format<double>::sign_index() { return 63; }
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template <> inline constexpr int binary_format<float>::sign_index() { return 31; }
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template <> inline constexpr int binary_format<double>::min_exponent_fast_path() {
|
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#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
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return 0;
|
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#else
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return -22;
|
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#endif
|
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}
|
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template <> inline constexpr int binary_format<float>::min_exponent_fast_path() {
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#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
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return 0;
|
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#else
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return -10;
|
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#endif
|
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}
|
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|
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template <> inline constexpr int binary_format<double>::max_exponent_fast_path() {
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return 22;
|
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}
|
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template <> inline constexpr int binary_format<float>::max_exponent_fast_path() {
|
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return 10;
|
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}
|
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|
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template <> inline constexpr uint64_t binary_format<double>::max_mantissa_fast_path() {
|
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return uint64_t(2) << mantissa_explicit_bits();
|
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}
|
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template <> inline constexpr uint64_t binary_format<float>::max_mantissa_fast_path() {
|
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return uint64_t(2) << mantissa_explicit_bits();
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}
|
||
|
||
template <>
|
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inline constexpr double binary_format<double>::exact_power_of_ten(int64_t power) {
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return powers_of_ten_double[power];
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||
}
|
||
template <>
|
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inline constexpr float binary_format<float>::exact_power_of_ten(int64_t power) {
|
||
|
||
return powers_of_ten_float[power];
|
||
}
|
||
|
||
|
||
template <>
|
||
inline constexpr int binary_format<double>::largest_power_of_ten() {
|
||
return 308;
|
||
}
|
||
template <>
|
||
inline constexpr int binary_format<float>::largest_power_of_ten() {
|
||
return 38;
|
||
}
|
||
|
||
template <>
|
||
inline constexpr int binary_format<double>::smallest_power_of_ten() {
|
||
return -342;
|
||
}
|
||
template <>
|
||
inline constexpr int binary_format<float>::smallest_power_of_ten() {
|
||
return -65;
|
||
}
|
||
|
||
template <> inline constexpr size_t binary_format<double>::max_digits() {
|
||
return 769;
|
||
}
|
||
template <> inline constexpr size_t binary_format<float>::max_digits() {
|
||
return 114;
|
||
}
|
||
|
||
template <> inline constexpr binary_format<float>::equiv_uint
|
||
binary_format<float>::exponent_mask() {
|
||
return 0x7F800000;
|
||
}
|
||
template <> inline constexpr binary_format<double>::equiv_uint
|
||
binary_format<double>::exponent_mask() {
|
||
return 0x7FF0000000000000;
|
||
}
|
||
|
||
template <> inline constexpr binary_format<float>::equiv_uint
|
||
binary_format<float>::mantissa_mask() {
|
||
return 0x007FFFFF;
|
||
}
|
||
template <> inline constexpr binary_format<double>::equiv_uint
|
||
binary_format<double>::mantissa_mask() {
|
||
return 0x000FFFFFFFFFFFFF;
|
||
}
|
||
|
||
template <> inline constexpr binary_format<float>::equiv_uint
|
||
binary_format<float>::hidden_bit_mask() {
|
||
return 0x00800000;
|
||
}
|
||
template <> inline constexpr binary_format<double>::equiv_uint
|
||
binary_format<double>::hidden_bit_mask() {
|
||
return 0x0010000000000000;
|
||
}
|
||
|
||
template<typename T>
|
||
fastfloat_really_inline void to_float(bool negative, adjusted_mantissa am, T &value) {
|
||
uint64_t word = am.mantissa;
|
||
word |= uint64_t(am.power2) << binary_format<T>::mantissa_explicit_bits();
|
||
word = negative
|
||
? word | (uint64_t(1) << binary_format<T>::sign_index()) : word;
|
||
#if FASTFLOAT_IS_BIG_ENDIAN == 1
|
||
if (std::is_same<T, float>::value) {
|
||
::memcpy(&value, (char *)&word + 4, sizeof(T)); // extract value at offset 4-7 if float on big-endian
|
||
} else {
|
||
::memcpy(&value, &word, sizeof(T));
|
||
}
|
||
#else
|
||
// For little-endian systems:
|
||
::memcpy(&value, &word, sizeof(T));
|
||
#endif
|
||
}
|
||
|
||
} // namespace fast_float
|
||
|
||
#endif
|
||
|
||
#ifndef FASTFLOAT_ASCII_NUMBER_H
|
||
#define FASTFLOAT_ASCII_NUMBER_H
|
||
|
||
#include <cctype>
|
||
#include <cstdint>
|
||
#include <cstring>
|
||
#include <iterator>
|
||
|
||
|
||
namespace fast_float {
|
||
|
||
// Next function can be micro-optimized, but compilers are entirely
|
||
// able to optimize it well.
|
||
fastfloat_really_inline bool is_integer(char c) noexcept { return c >= '0' && c <= '9'; }
|
||
|
||
fastfloat_really_inline uint64_t byteswap(uint64_t val) {
|
||
return (val & 0xFF00000000000000) >> 56
|
||
| (val & 0x00FF000000000000) >> 40
|
||
| (val & 0x0000FF0000000000) >> 24
|
||
| (val & 0x000000FF00000000) >> 8
|
||
| (val & 0x00000000FF000000) << 8
|
||
| (val & 0x0000000000FF0000) << 24
|
||
| (val & 0x000000000000FF00) << 40
|
||
| (val & 0x00000000000000FF) << 56;
|
||
}
|
||
|
||
fastfloat_really_inline uint64_t read_u64(const char *chars) {
|
||
uint64_t val;
|
||
::memcpy(&val, chars, sizeof(uint64_t));
|
||
#if FASTFLOAT_IS_BIG_ENDIAN == 1
|
||
// Need to read as-if the number was in little-endian order.
|
||
val = byteswap(val);
|
||
#endif
|
||
return val;
|
||
}
|
||
|
||
fastfloat_really_inline void write_u64(uint8_t *chars, uint64_t val) {
|
||
#if FASTFLOAT_IS_BIG_ENDIAN == 1
|
||
// Need to read as-if the number was in little-endian order.
|
||
val = byteswap(val);
|
||
#endif
|
||
::memcpy(chars, &val, sizeof(uint64_t));
|
||
}
|
||
|
||
// credit @aqrit
|
||
fastfloat_really_inline uint32_t parse_eight_digits_unrolled(uint64_t val) {
|
||
const uint64_t mask = 0x000000FF000000FF;
|
||
const uint64_t mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32)
|
||
const uint64_t mul2 = 0x0000271000000001; // 1 + (10000ULL << 32)
|
||
val -= 0x3030303030303030;
|
||
val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8;
|
||
val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32;
|
||
return uint32_t(val);
|
||
}
|
||
|
||
fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars) noexcept {
|
||
return parse_eight_digits_unrolled(read_u64(chars));
|
||
}
|
||
|
||
// credit @aqrit
|
||
fastfloat_really_inline bool is_made_of_eight_digits_fast(uint64_t val) noexcept {
|
||
return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) &
|
||
0x8080808080808080));
|
||
}
|
||
|
||
fastfloat_really_inline bool is_made_of_eight_digits_fast(const char *chars) noexcept {
|
||
return is_made_of_eight_digits_fast(read_u64(chars));
|
||
}
|
||
|
||
typedef span<const char> byte_span;
|
||
|
||
struct parsed_number_string {
|
||
int64_t exponent{0};
|
||
uint64_t mantissa{0};
|
||
const char *lastmatch{nullptr};
|
||
bool negative{false};
|
||
bool valid{false};
|
||
bool too_many_digits{false};
|
||
// contains the range of the significant digits
|
||
byte_span integer{}; // non-nullable
|
||
byte_span fraction{}; // nullable
|
||
};
|
||
|
||
// Assuming that you use no more than 19 digits, this will
|
||
// parse an ASCII string.
|
||
fastfloat_really_inline
|
||
parsed_number_string parse_number_string(const char *p, const char *pend, parse_options options) noexcept {
|
||
const chars_format fmt = options.format;
|
||
const char decimal_point = options.decimal_point;
|
||
|
||
parsed_number_string answer;
|
||
answer.valid = false;
|
||
answer.too_many_digits = false;
|
||
answer.negative = (*p == '-');
|
||
if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
|
||
++p;
|
||
if (p == pend) {
|
||
return answer;
|
||
}
|
||
if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot
|
||
return answer;
|
||
}
|
||
}
|
||
const char *const start_digits = p;
|
||
|
||
uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad)
|
||
|
||
while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(p)) {
|
||
i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
|
||
p += 8;
|
||
}
|
||
while ((p != pend) && is_integer(*p)) {
|
||
// a multiplication by 10 is cheaper than an arbitrary integer
|
||
// multiplication
|
||
i = 10 * i +
|
||
uint64_t(*p - '0'); // might overflow, we will handle the overflow later
|
||
++p;
|
||
}
|
||
const char *const end_of_integer_part = p;
|
||
int64_t digit_count = int64_t(end_of_integer_part - start_digits);
|
||
answer.integer = byte_span(start_digits, size_t(digit_count));
|
||
int64_t exponent = 0;
|
||
if ((p != pend) && (*p == decimal_point)) {
|
||
++p;
|
||
const char* before = p;
|
||
// can occur at most twice without overflowing, but let it occur more, since
|
||
// for integers with many digits, digit parsing is the primary bottleneck.
|
||
while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(p)) {
|
||
i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
|
||
p += 8;
|
||
}
|
||
while ((p != pend) && is_integer(*p)) {
|
||
uint8_t digit = uint8_t(*p - '0');
|
||
++p;
|
||
i = i * 10 + digit; // in rare cases, this will overflow, but that's ok
|
||
}
|
||
exponent = before - p;
|
||
answer.fraction = byte_span(before, size_t(p - before));
|
||
digit_count -= exponent;
|
||
}
|
||
// we must have encountered at least one integer!
|
||
if (digit_count == 0) {
|
||
return answer;
|
||
}
|
||
int64_t exp_number = 0; // explicit exponential part
|
||
if ((fmt & chars_format::scientific) && (p != pend) && (('e' == *p) || ('E' == *p))) {
|
||
const char * location_of_e = p;
|
||
++p;
|
||
bool neg_exp = false;
|
||
if ((p != pend) && ('-' == *p)) {
|
||
neg_exp = true;
|
||
++p;
|
||
} else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
|
||
++p;
|
||
}
|
||
if ((p == pend) || !is_integer(*p)) {
|
||
if(!(fmt & chars_format::fixed)) {
|
||
// We are in error.
|
||
return answer;
|
||
}
|
||
// Otherwise, we will be ignoring the 'e'.
|
||
p = location_of_e;
|
||
} else {
|
||
while ((p != pend) && is_integer(*p)) {
|
||
uint8_t digit = uint8_t(*p - '0');
|
||
if (exp_number < 0x10000000) {
|
||
exp_number = 10 * exp_number + digit;
|
||
}
|
||
++p;
|
||
}
|
||
if(neg_exp) { exp_number = - exp_number; }
|
||
exponent += exp_number;
|
||
}
|
||
} else {
|
||
// If it scientific and not fixed, we have to bail out.
|
||
if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; }
|
||
}
|
||
answer.lastmatch = p;
|
||
answer.valid = true;
|
||
|
||
// If we frequently had to deal with long strings of digits,
|
||
// we could extend our code by using a 128-bit integer instead
|
||
// of a 64-bit integer. However, this is uncommon.
|
||
//
|
||
// We can deal with up to 19 digits.
|
||
if (digit_count > 19) { // this is uncommon
|
||
// It is possible that the integer had an overflow.
|
||
// We have to handle the case where we have 0.0000somenumber.
|
||
// We need to be mindful of the case where we only have zeroes...
|
||
// E.g., 0.000000000...000.
|
||
const char *start = start_digits;
|
||
while ((start != pend) && (*start == '0' || *start == decimal_point)) {
|
||
if(*start == '0') { digit_count --; }
|
||
start++;
|
||
}
|
||
if (digit_count > 19) {
|
||
answer.too_many_digits = true;
|
||
// Let us start again, this time, avoiding overflows.
|
||
// We don't need to check if is_integer, since we use the
|
||
// pre-tokenized spans from above.
|
||
i = 0;
|
||
p = answer.integer.ptr;
|
||
const char* int_end = p + answer.integer.len();
|
||
const uint64_t minimal_nineteen_digit_integer{1000000000000000000};
|
||
while((i < minimal_nineteen_digit_integer) && (p != int_end)) {
|
||
i = i * 10 + uint64_t(*p - '0');
|
||
++p;
|
||
}
|
||
if (i >= minimal_nineteen_digit_integer) { // We have a big integers
|
||
exponent = end_of_integer_part - p + exp_number;
|
||
} else { // We have a value with a fractional component.
|
||
p = answer.fraction.ptr;
|
||
const char* frac_end = p + answer.fraction.len();
|
||
while((i < minimal_nineteen_digit_integer) && (p != frac_end)) {
|
||
i = i * 10 + uint64_t(*p - '0');
|
||
++p;
|
||
}
|
||
exponent = answer.fraction.ptr - p + exp_number;
|
||
}
|
||
// We have now corrected both exponent and i, to a truncated value
|
||
}
|
||
}
|
||
answer.exponent = exponent;
|
||
answer.mantissa = i;
|
||
return answer;
|
||
}
|
||
|
||
} // namespace fast_float
|
||
|
||
#endif
|
||
|
||
#ifndef FASTFLOAT_FAST_TABLE_H
|
||
#define FASTFLOAT_FAST_TABLE_H
|
||
|
||
#include <cstdint>
|
||
|
||
namespace fast_float {
|
||
|
||
/**
|
||
* When mapping numbers from decimal to binary,
|
||
* we go from w * 10^q to m * 2^p but we have
|
||
* 10^q = 5^q * 2^q, so effectively
|
||
* we are trying to match
|
||
* w * 2^q * 5^q to m * 2^p. Thus the powers of two
|
||
* are not a concern since they can be represented
|
||
* exactly using the binary notation, only the powers of five
|
||
* affect the binary significand.
|
||
*/
|
||
|
||
/**
|
||
* The smallest non-zero float (binary64) is 2^−1074.
|
||
* We take as input numbers of the form w x 10^q where w < 2^64.
|
||
* We have that w * 10^-343 < 2^(64-344) 5^-343 < 2^-1076.
|
||
* However, we have that
|
||
* (2^64-1) * 10^-342 = (2^64-1) * 2^-342 * 5^-342 > 2^−1074.
|
||
* Thus it is possible for a number of the form w * 10^-342 where
|
||
* w is a 64-bit value to be a non-zero floating-point number.
|
||
*********
|
||
* Any number of form w * 10^309 where w>= 1 is going to be
|
||
* infinite in binary64 so we never need to worry about powers
|
||
* of 5 greater than 308.
|
||
*/
|
||
template <class unused = void>
|
||
struct powers_template {
|
||
|
||
constexpr static int smallest_power_of_five = binary_format<double>::smallest_power_of_ten();
|
||
constexpr static int largest_power_of_five = binary_format<double>::largest_power_of_ten();
|
||
constexpr static int number_of_entries = 2 * (largest_power_of_five - smallest_power_of_five + 1);
|
||
// Powers of five from 5^-342 all the way to 5^308 rounded toward one.
|
||
static const uint64_t power_of_five_128[number_of_entries];
|
||
};
|
||
|
||
template <class unused>
|
||
const uint64_t powers_template<unused>::power_of_five_128[number_of_entries] = {
|
||
0xeef453d6923bd65a,0x113faa2906a13b3f,
|
||
0x9558b4661b6565f8,0x4ac7ca59a424c507,
|
||
0xbaaee17fa23ebf76,0x5d79bcf00d2df649,
|
||
0xe95a99df8ace6f53,0xf4d82c2c107973dc,
|
||
0x91d8a02bb6c10594,0x79071b9b8a4be869,
|
||
0xb64ec836a47146f9,0x9748e2826cdee284,
|
||
0xe3e27a444d8d98b7,0xfd1b1b2308169b25,
|
||
0x8e6d8c6ab0787f72,0xfe30f0f5e50e20f7,
|
||
0xb208ef855c969f4f,0xbdbd2d335e51a935,
|
||
0xde8b2b66b3bc4723,0xad2c788035e61382,
|
||
0x8b16fb203055ac76,0x4c3bcb5021afcc31,
|
||
0xaddcb9e83c6b1793,0xdf4abe242a1bbf3d,
|
||
0xd953e8624b85dd78,0xd71d6dad34a2af0d,
|
||
0x87d4713d6f33aa6b,0x8672648c40e5ad68,
|
||
0xa9c98d8ccb009506,0x680efdaf511f18c2,
|
||
0xd43bf0effdc0ba48,0x212bd1b2566def2,
|
||
0x84a57695fe98746d,0x14bb630f7604b57,
|
||
0xa5ced43b7e3e9188,0x419ea3bd35385e2d,
|
||
0xcf42894a5dce35ea,0x52064cac828675b9,
|
||
0x818995ce7aa0e1b2,0x7343efebd1940993,
|
||
0xa1ebfb4219491a1f,0x1014ebe6c5f90bf8,
|
||
0xca66fa129f9b60a6,0xd41a26e077774ef6,
|
||
0xfd00b897478238d0,0x8920b098955522b4,
|
||
0x9e20735e8cb16382,0x55b46e5f5d5535b0,
|
||
0xc5a890362fddbc62,0xeb2189f734aa831d,
|
||
0xf712b443bbd52b7b,0xa5e9ec7501d523e4,
|
||
0x9a6bb0aa55653b2d,0x47b233c92125366e,
|
||
0xc1069cd4eabe89f8,0x999ec0bb696e840a,
|
||
0xf148440a256e2c76,0xc00670ea43ca250d,
|
||
0x96cd2a865764dbca,0x380406926a5e5728,
|
||
0xbc807527ed3e12bc,0xc605083704f5ecf2,
|
||
0xeba09271e88d976b,0xf7864a44c633682e,
|
||
0x93445b8731587ea3,0x7ab3ee6afbe0211d,
|
||
0xb8157268fdae9e4c,0x5960ea05bad82964,
|
||
0xe61acf033d1a45df,0x6fb92487298e33bd,
|
||
0x8fd0c16206306bab,0xa5d3b6d479f8e056,
|
||
0xb3c4f1ba87bc8696,0x8f48a4899877186c,
|
||
0xe0b62e2929aba83c,0x331acdabfe94de87,
|
||
0x8c71dcd9ba0b4925,0x9ff0c08b7f1d0b14,
|
||
0xaf8e5410288e1b6f,0x7ecf0ae5ee44dd9,
|
||
0xdb71e91432b1a24a,0xc9e82cd9f69d6150,
|
||
0x892731ac9faf056e,0xbe311c083a225cd2,
|
||
0xab70fe17c79ac6ca,0x6dbd630a48aaf406,
|
||
0xd64d3d9db981787d,0x92cbbccdad5b108,
|
||
0x85f0468293f0eb4e,0x25bbf56008c58ea5,
|
||
0xa76c582338ed2621,0xaf2af2b80af6f24e,
|
||
0xd1476e2c07286faa,0x1af5af660db4aee1,
|
||
0x82cca4db847945ca,0x50d98d9fc890ed4d,
|
||
0xa37fce126597973c,0xe50ff107bab528a0,
|
||
0xcc5fc196fefd7d0c,0x1e53ed49a96272c8,
|
||
0xff77b1fcbebcdc4f,0x25e8e89c13bb0f7a,
|
||
0x9faacf3df73609b1,0x77b191618c54e9ac,
|
||
0xc795830d75038c1d,0xd59df5b9ef6a2417,
|
||
0xf97ae3d0d2446f25,0x4b0573286b44ad1d,
|
||
0x9becce62836ac577,0x4ee367f9430aec32,
|
||
0xc2e801fb244576d5,0x229c41f793cda73f,
|
||
0xf3a20279ed56d48a,0x6b43527578c1110f,
|
||
0x9845418c345644d6,0x830a13896b78aaa9,
|
||
0xbe5691ef416bd60c,0x23cc986bc656d553,
|
||
0xedec366b11c6cb8f,0x2cbfbe86b7ec8aa8,
|
||
0x94b3a202eb1c3f39,0x7bf7d71432f3d6a9,
|
||
0xb9e08a83a5e34f07,0xdaf5ccd93fb0cc53,
|
||
0xe858ad248f5c22c9,0xd1b3400f8f9cff68,
|
||
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|
||
0x80d2ae83e9ce78f3,0xc1d72b7c6b426019,
|
||
0xa1075a24e4421730,0xb24cf65b8612f81f,
|
||
0xc94930ae1d529cfc,0xdee033f26797b627,
|
||
0xfb9b7cd9a4a7443c,0x169840ef017da3b1,
|
||
0x9d412e0806e88aa5,0x8e1f289560ee864e,
|
||
0xc491798a08a2ad4e,0xf1a6f2bab92a27e2,
|
||
0xf5b5d7ec8acb58a2,0xae10af696774b1db,
|
||
0x9991a6f3d6bf1765,0xacca6da1e0a8ef29,
|
||
0xbff610b0cc6edd3f,0x17fd090a58d32af3,
|
||
0xeff394dcff8a948e,0xddfc4b4cef07f5b0,
|
||
0x95f83d0a1fb69cd9,0x4abdaf101564f98e,
|
||
0xbb764c4ca7a4440f,0x9d6d1ad41abe37f1,
|
||
0xea53df5fd18d5513,0x84c86189216dc5ed,
|
||
0x92746b9be2f8552c,0x32fd3cf5b4e49bb4,
|
||
0xb7118682dbb66a77,0x3fbc8c33221dc2a1,
|
||
0xe4d5e82392a40515,0xfabaf3feaa5334a,
|
||
0x8f05b1163ba6832d,0x29cb4d87f2a7400e,
|
||
0xb2c71d5bca9023f8,0x743e20e9ef511012,
|
||
0xdf78e4b2bd342cf6,0x914da9246b255416,
|
||
0x8bab8eefb6409c1a,0x1ad089b6c2f7548e,
|
||
0xae9672aba3d0c320,0xa184ac2473b529b1,
|
||
0xda3c0f568cc4f3e8,0xc9e5d72d90a2741e,
|
||
0x8865899617fb1871,0x7e2fa67c7a658892,
|
||
0xaa7eebfb9df9de8d,0xddbb901b98feeab7,
|
||
0xd51ea6fa85785631,0x552a74227f3ea565,
|
||
0x8533285c936b35de,0xd53a88958f87275f,
|
||
0xa67ff273b8460356,0x8a892abaf368f137,
|
||
0xd01fef10a657842c,0x2d2b7569b0432d85,
|
||
0x8213f56a67f6b29b,0x9c3b29620e29fc73,
|
||
0xa298f2c501f45f42,0x8349f3ba91b47b8f,
|
||
0xcb3f2f7642717713,0x241c70a936219a73,
|
||
0xfe0efb53d30dd4d7,0xed238cd383aa0110,
|
||
0x9ec95d1463e8a506,0xf4363804324a40aa,
|
||
0xc67bb4597ce2ce48,0xb143c6053edcd0d5,
|
||
0xf81aa16fdc1b81da,0xdd94b7868e94050a,
|
||
0x9b10a4e5e9913128,0xca7cf2b4191c8326,
|
||
0xc1d4ce1f63f57d72,0xfd1c2f611f63a3f0,
|
||
0xf24a01a73cf2dccf,0xbc633b39673c8cec,
|
||
0x976e41088617ca01,0xd5be0503e085d813,
|
||
0xbd49d14aa79dbc82,0x4b2d8644d8a74e18,
|
||
0xec9c459d51852ba2,0xddf8e7d60ed1219e,
|
||
0x93e1ab8252f33b45,0xcabb90e5c942b503,
|
||
0xb8da1662e7b00a17,0x3d6a751f3b936243,
|
||
0xe7109bfba19c0c9d,0xcc512670a783ad4,
|
||
0x906a617d450187e2,0x27fb2b80668b24c5,
|
||
0xb484f9dc9641e9da,0xb1f9f660802dedf6,
|
||
0xe1a63853bbd26451,0x5e7873f8a0396973,
|
||
0x8d07e33455637eb2,0xdb0b487b6423e1e8,
|
||
0xb049dc016abc5e5f,0x91ce1a9a3d2cda62,
|
||
0xdc5c5301c56b75f7,0x7641a140cc7810fb,
|
||
0x89b9b3e11b6329ba,0xa9e904c87fcb0a9d,
|
||
0xac2820d9623bf429,0x546345fa9fbdcd44,
|
||
0xd732290fbacaf133,0xa97c177947ad4095,
|
||
0x867f59a9d4bed6c0,0x49ed8eabcccc485d,
|
||
0xa81f301449ee8c70,0x5c68f256bfff5a74,
|
||
0xd226fc195c6a2f8c,0x73832eec6fff3111,
|
||
0x83585d8fd9c25db7,0xc831fd53c5ff7eab,
|
||
0xa42e74f3d032f525,0xba3e7ca8b77f5e55,
|
||
0xcd3a1230c43fb26f,0x28ce1bd2e55f35eb,
|
||
0x80444b5e7aa7cf85,0x7980d163cf5b81b3,
|
||
0xa0555e361951c366,0xd7e105bcc332621f,
|
||
0xc86ab5c39fa63440,0x8dd9472bf3fefaa7,
|
||
0xfa856334878fc150,0xb14f98f6f0feb951,
|
||
0x9c935e00d4b9d8d2,0x6ed1bf9a569f33d3,
|
||
0xc3b8358109e84f07,0xa862f80ec4700c8,
|
||
0xf4a642e14c6262c8,0xcd27bb612758c0fa,
|
||
0x98e7e9cccfbd7dbd,0x8038d51cb897789c,
|
||
0xbf21e44003acdd2c,0xe0470a63e6bd56c3,
|
||
0xeeea5d5004981478,0x1858ccfce06cac74,
|
||
0x95527a5202df0ccb,0xf37801e0c43ebc8,
|
||
0xbaa718e68396cffd,0xd30560258f54e6ba,
|
||
0xe950df20247c83fd,0x47c6b82ef32a2069,
|
||
0x91d28b7416cdd27e,0x4cdc331d57fa5441,
|
||
0xb6472e511c81471d,0xe0133fe4adf8e952,
|
||
0xe3d8f9e563a198e5,0x58180fddd97723a6,
|
||
0x8e679c2f5e44ff8f,0x570f09eaa7ea7648,};
|
||
using powers = powers_template<>;
|
||
|
||
}
|
||
|
||
#endif
|
||
|
||
#ifndef FASTFLOAT_DECIMAL_TO_BINARY_H
|
||
#define FASTFLOAT_DECIMAL_TO_BINARY_H
|
||
|
||
#include <cfloat>
|
||
#include <cinttypes>
|
||
#include <cmath>
|
||
#include <cstdint>
|
||
#include <cstdlib>
|
||
#include <cstring>
|
||
|
||
namespace fast_float {
|
||
|
||
// This will compute or rather approximate w * 5**q and return a pair of 64-bit words approximating
|
||
// the result, with the "high" part corresponding to the most significant bits and the
|
||
// low part corresponding to the least significant bits.
|
||
//
|
||
template <int bit_precision>
|
||
fastfloat_really_inline
|
||
value128 compute_product_approximation(int64_t q, uint64_t w) {
|
||
const int index = 2 * int(q - powers::smallest_power_of_five);
|
||
// For small values of q, e.g., q in [0,27], the answer is always exact because
|
||
// The line value128 firstproduct = full_multiplication(w, power_of_five_128[index]);
|
||
// gives the exact answer.
|
||
value128 firstproduct = full_multiplication(w, powers::power_of_five_128[index]);
|
||
static_assert((bit_precision >= 0) && (bit_precision <= 64), " precision should be in (0,64]");
|
||
constexpr uint64_t precision_mask = (bit_precision < 64) ?
|
||
(uint64_t(0xFFFFFFFFFFFFFFFF) >> bit_precision)
|
||
: uint64_t(0xFFFFFFFFFFFFFFFF);
|
||
if((firstproduct.high & precision_mask) == precision_mask) { // could further guard with (lower + w < lower)
|
||
// regarding the second product, we only need secondproduct.high, but our expectation is that the compiler will optimize this extra work away if needed.
|
||
value128 secondproduct = full_multiplication(w, powers::power_of_five_128[index + 1]);
|
||
firstproduct.low += secondproduct.high;
|
||
if(secondproduct.high > firstproduct.low) {
|
||
firstproduct.high++;
|
||
}
|
||
}
|
||
return firstproduct;
|
||
}
|
||
|
||
namespace detail {
|
||
/**
|
||
* For q in (0,350), we have that
|
||
* f = (((152170 + 65536) * q ) >> 16);
|
||
* is equal to
|
||
* floor(p) + q
|
||
* where
|
||
* p = log(5**q)/log(2) = q * log(5)/log(2)
|
||
*
|
||
* For negative values of q in (-400,0), we have that
|
||
* f = (((152170 + 65536) * q ) >> 16);
|
||
* is equal to
|
||
* -ceil(p) + q
|
||
* where
|
||
* p = log(5**-q)/log(2) = -q * log(5)/log(2)
|
||
*/
|
||
constexpr fastfloat_really_inline int32_t power(int32_t q) noexcept {
|
||
return (((152170 + 65536) * q) >> 16) + 63;
|
||
}
|
||
} // namespace detail
|
||
|
||
// create an adjusted mantissa, biased by the invalid power2
|
||
// for significant digits already multiplied by 10 ** q.
|
||
template <typename binary>
|
||
fastfloat_really_inline
|
||
adjusted_mantissa compute_error_scaled(int64_t q, uint64_t w, int lz) noexcept {
|
||
int hilz = int(w >> 63) ^ 1;
|
||
adjusted_mantissa answer;
|
||
answer.mantissa = w << hilz;
|
||
int bias = binary::mantissa_explicit_bits() - binary::minimum_exponent();
|
||
answer.power2 = int32_t(detail::power(int32_t(q)) + bias - hilz - lz - 62 + invalid_am_bias);
|
||
return answer;
|
||
}
|
||
|
||
// w * 10 ** q, without rounding the representation up.
|
||
// the power2 in the exponent will be adjusted by invalid_am_bias.
|
||
template <typename binary>
|
||
fastfloat_really_inline
|
||
adjusted_mantissa compute_error(int64_t q, uint64_t w) noexcept {
|
||
int lz = leading_zeroes(w);
|
||
w <<= lz;
|
||
value128 product = compute_product_approximation<binary::mantissa_explicit_bits() + 3>(q, w);
|
||
return compute_error_scaled<binary>(q, product.high, lz);
|
||
}
|
||
|
||
// w * 10 ** q
|
||
// The returned value should be a valid ieee64 number that simply need to be packed.
|
||
// However, in some very rare cases, the computation will fail. In such cases, we
|
||
// return an adjusted_mantissa with a negative power of 2: the caller should recompute
|
||
// in such cases.
|
||
template <typename binary>
|
||
fastfloat_really_inline
|
||
adjusted_mantissa compute_float(int64_t q, uint64_t w) noexcept {
|
||
adjusted_mantissa answer;
|
||
if ((w == 0) || (q < binary::smallest_power_of_ten())) {
|
||
answer.power2 = 0;
|
||
answer.mantissa = 0;
|
||
// result should be zero
|
||
return answer;
|
||
}
|
||
if (q > binary::largest_power_of_ten()) {
|
||
// we want to get infinity:
|
||
answer.power2 = binary::infinite_power();
|
||
answer.mantissa = 0;
|
||
return answer;
|
||
}
|
||
// At this point in time q is in [powers::smallest_power_of_five, powers::largest_power_of_five].
|
||
|
||
// We want the most significant bit of i to be 1. Shift if needed.
|
||
int lz = leading_zeroes(w);
|
||
w <<= lz;
|
||
|
||
// The required precision is binary::mantissa_explicit_bits() + 3 because
|
||
// 1. We need the implicit bit
|
||
// 2. We need an extra bit for rounding purposes
|
||
// 3. We might lose a bit due to the "upperbit" routine (result too small, requiring a shift)
|
||
|
||
value128 product = compute_product_approximation<binary::mantissa_explicit_bits() + 3>(q, w);
|
||
if(product.low == 0xFFFFFFFFFFFFFFFF) { // could guard it further
|
||
// In some very rare cases, this could happen, in which case we might need a more accurate
|
||
// computation that what we can provide cheaply. This is very, very unlikely.
|
||
//
|
||
const bool inside_safe_exponent = (q >= -27) && (q <= 55); // always good because 5**q <2**128 when q>=0,
|
||
// and otherwise, for q<0, we have 5**-q<2**64 and the 128-bit reciprocal allows for exact computation.
|
||
if(!inside_safe_exponent) {
|
||
return compute_error_scaled<binary>(q, product.high, lz);
|
||
}
|
||
}
|
||
// The "compute_product_approximation" function can be slightly slower than a branchless approach:
|
||
// value128 product = compute_product(q, w);
|
||
// but in practice, we can win big with the compute_product_approximation if its additional branch
|
||
// is easily predicted. Which is best is data specific.
|
||
int upperbit = int(product.high >> 63);
|
||
|
||
answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3);
|
||
|
||
answer.power2 = int32_t(detail::power(int32_t(q)) + upperbit - lz - binary::minimum_exponent());
|
||
if (answer.power2 <= 0) { // we have a subnormal?
|
||
// Here have that answer.power2 <= 0 so -answer.power2 >= 0
|
||
if(-answer.power2 + 1 >= 64) { // if we have more than 64 bits below the minimum exponent, you have a zero for sure.
|
||
answer.power2 = 0;
|
||
answer.mantissa = 0;
|
||
// result should be zero
|
||
return answer;
|
||
}
|
||
// next line is safe because -answer.power2 + 1 < 64
|
||
answer.mantissa >>= -answer.power2 + 1;
|
||
// Thankfully, we can't have both "round-to-even" and subnormals because
|
||
// "round-to-even" only occurs for powers close to 0.
|
||
answer.mantissa += (answer.mantissa & 1); // round up
|
||
answer.mantissa >>= 1;
|
||
// There is a weird scenario where we don't have a subnormal but just.
|
||
// Suppose we start with 2.2250738585072013e-308, we end up
|
||
// with 0x3fffffffffffff x 2^-1023-53 which is technically subnormal
|
||
// whereas 0x40000000000000 x 2^-1023-53 is normal. Now, we need to round
|
||
// up 0x3fffffffffffff x 2^-1023-53 and once we do, we are no longer
|
||
// subnormal, but we can only know this after rounding.
|
||
// So we only declare a subnormal if we are smaller than the threshold.
|
||
answer.power2 = (answer.mantissa < (uint64_t(1) << binary::mantissa_explicit_bits())) ? 0 : 1;
|
||
return answer;
|
||
}
|
||
|
||
// usually, we round *up*, but if we fall right in between and and we have an
|
||
// even basis, we need to round down
|
||
// We are only concerned with the cases where 5**q fits in single 64-bit word.
|
||
if ((product.low <= 1) && (q >= binary::min_exponent_round_to_even()) && (q <= binary::max_exponent_round_to_even()) &&
|
||
((answer.mantissa & 3) == 1) ) { // we may fall between two floats!
|
||
// To be in-between two floats we need that in doing
|
||
// answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3);
|
||
// ... we dropped out only zeroes. But if this happened, then we can go back!!!
|
||
if((answer.mantissa << (upperbit + 64 - binary::mantissa_explicit_bits() - 3)) == product.high) {
|
||
answer.mantissa &= ~uint64_t(1); // flip it so that we do not round up
|
||
}
|
||
}
|
||
|
||
answer.mantissa += (answer.mantissa & 1); // round up
|
||
answer.mantissa >>= 1;
|
||
if (answer.mantissa >= (uint64_t(2) << binary::mantissa_explicit_bits())) {
|
||
answer.mantissa = (uint64_t(1) << binary::mantissa_explicit_bits());
|
||
answer.power2++; // undo previous addition
|
||
}
|
||
|
||
answer.mantissa &= ~(uint64_t(1) << binary::mantissa_explicit_bits());
|
||
if (answer.power2 >= binary::infinite_power()) { // infinity
|
||
answer.power2 = binary::infinite_power();
|
||
answer.mantissa = 0;
|
||
}
|
||
return answer;
|
||
}
|
||
|
||
} // namespace fast_float
|
||
|
||
#endif
|
||
|
||
#ifndef FASTFLOAT_BIGINT_H
|
||
#define FASTFLOAT_BIGINT_H
|
||
|
||
#include <algorithm>
|
||
#include <cstdint>
|
||
#include <climits>
|
||
#include <cstring>
|
||
|
||
|
||
namespace fast_float {
|
||
|
||
// the limb width: we want efficient multiplication of double the bits in
|
||
// limb, or for 64-bit limbs, at least 64-bit multiplication where we can
|
||
// extract the high and low parts efficiently. this is every 64-bit
|
||
// architecture except for sparc, which emulates 128-bit multiplication.
|
||
// we might have platforms where `CHAR_BIT` is not 8, so let's avoid
|
||
// doing `8 * sizeof(limb)`.
|
||
#if defined(FASTFLOAT_64BIT) && !defined(__sparc)
|
||
#define FASTFLOAT_64BIT_LIMB
|
||
typedef uint64_t limb;
|
||
constexpr size_t limb_bits = 64;
|
||
#else
|
||
#define FASTFLOAT_32BIT_LIMB
|
||
typedef uint32_t limb;
|
||
constexpr size_t limb_bits = 32;
|
||
#endif
|
||
|
||
typedef span<limb> limb_span;
|
||
|
||
// number of bits in a bigint. this needs to be at least the number
|
||
// of bits required to store the largest bigint, which is
|
||
// `log2(10**(digits + max_exp))`, or `log2(10**(767 + 342))`, or
|
||
// ~3600 bits, so we round to 4000.
|
||
constexpr size_t bigint_bits = 4000;
|
||
constexpr size_t bigint_limbs = bigint_bits / limb_bits;
|
||
|
||
// vector-like type that is allocated on the stack. the entire
|
||
// buffer is pre-allocated, and only the length changes.
|
||
template <uint16_t size>
|
||
struct stackvec {
|
||
limb data[size];
|
||
// we never need more than 150 limbs
|
||
uint16_t length{0};
|
||
|
||
stackvec() = default;
|
||
stackvec(const stackvec &) = delete;
|
||
stackvec &operator=(const stackvec &) = delete;
|
||
stackvec(stackvec &&) = delete;
|
||
stackvec &operator=(stackvec &&other) = delete;
|
||
|
||
// create stack vector from existing limb span.
|
||
stackvec(limb_span s) {
|
||
FASTFLOAT_ASSERT(try_extend(s));
|
||
}
|
||
|
||
limb& operator[](size_t index) noexcept {
|
||
FASTFLOAT_DEBUG_ASSERT(index < length);
|
||
return data[index];
|
||
}
|
||
const limb& operator[](size_t index) const noexcept {
|
||
FASTFLOAT_DEBUG_ASSERT(index < length);
|
||
return data[index];
|
||
}
|
||
// index from the end of the container
|
||
const limb& rindex(size_t index) const noexcept {
|
||
FASTFLOAT_DEBUG_ASSERT(index < length);
|
||
size_t rindex = length - index - 1;
|
||
return data[rindex];
|
||
}
|
||
|
||
// set the length, without bounds checking.
|
||
void set_len(size_t len) noexcept {
|
||
length = uint16_t(len);
|
||
}
|
||
constexpr size_t len() const noexcept {
|
||
return length;
|
||
}
|
||
constexpr bool is_empty() const noexcept {
|
||
return length == 0;
|
||
}
|
||
constexpr size_t capacity() const noexcept {
|
||
return size;
|
||
}
|
||
// append item to vector, without bounds checking
|
||
void push_unchecked(limb value) noexcept {
|
||
data[length] = value;
|
||
length++;
|
||
}
|
||
// append item to vector, returning if item was added
|
||
bool try_push(limb value) noexcept {
|
||
if (len() < capacity()) {
|
||
push_unchecked(value);
|
||
return true;
|
||
} else {
|
||
return false;
|
||
}
|
||
}
|
||
// add items to the vector, from a span, without bounds checking
|
||
void extend_unchecked(limb_span s) noexcept {
|
||
limb* ptr = data + length;
|
||
::memcpy((void*)ptr, (const void*)s.ptr, sizeof(limb) * s.len());
|
||
set_len(len() + s.len());
|
||
}
|
||
// try to add items to the vector, returning if items were added
|
||
bool try_extend(limb_span s) noexcept {
|
||
if (len() + s.len() <= capacity()) {
|
||
extend_unchecked(s);
|
||
return true;
|
||
} else {
|
||
return false;
|
||
}
|
||
}
|
||
// resize the vector, without bounds checking
|
||
// if the new size is longer than the vector, assign value to each
|
||
// appended item.
|
||
void resize_unchecked(size_t new_len, limb value) noexcept {
|
||
if (new_len > len()) {
|
||
size_t count = new_len - len();
|
||
limb* first = data + len();
|
||
limb* last = first + count;
|
||
::std::fill(first, last, value);
|
||
set_len(new_len);
|
||
} else {
|
||
set_len(new_len);
|
||
}
|
||
}
|
||
// try to resize the vector, returning if the vector was resized.
|
||
bool try_resize(size_t new_len, limb value) noexcept {
|
||
if (new_len > capacity()) {
|
||
return false;
|
||
} else {
|
||
resize_unchecked(new_len, value);
|
||
return true;
|
||
}
|
||
}
|
||
// check if any limbs are non-zero after the given index.
|
||
// this needs to be done in reverse order, since the index
|
||
// is relative to the most significant limbs.
|
||
bool nonzero(size_t index) const noexcept {
|
||
while (index < len()) {
|
||
if (rindex(index) != 0) {
|
||
return true;
|
||
}
|
||
index++;
|
||
}
|
||
return false;
|
||
}
|
||
// normalize the big integer, so most-significant zero limbs are removed.
|
||
void normalize() noexcept {
|
||
while (len() > 0 && rindex(0) == 0) {
|
||
length--;
|
||
}
|
||
}
|
||
};
|
||
|
||
fastfloat_really_inline
|
||
uint64_t empty_hi64(bool& truncated) noexcept {
|
||
truncated = false;
|
||
return 0;
|
||
}
|
||
|
||
fastfloat_really_inline
|
||
uint64_t uint64_hi64(uint64_t r0, bool& truncated) noexcept {
|
||
truncated = false;
|
||
int shl = leading_zeroes(r0);
|
||
return r0 << shl;
|
||
}
|
||
|
||
fastfloat_really_inline
|
||
uint64_t uint64_hi64(uint64_t r0, uint64_t r1, bool& truncated) noexcept {
|
||
int shl = leading_zeroes(r0);
|
||
if (shl == 0) {
|
||
truncated = r1 != 0;
|
||
return r0;
|
||
} else {
|
||
int shr = 64 - shl;
|
||
truncated = (r1 << shl) != 0;
|
||
return (r0 << shl) | (r1 >> shr);
|
||
}
|
||
}
|
||
|
||
fastfloat_really_inline
|
||
uint64_t uint32_hi64(uint32_t r0, bool& truncated) noexcept {
|
||
return uint64_hi64(r0, truncated);
|
||
}
|
||
|
||
fastfloat_really_inline
|
||
uint64_t uint32_hi64(uint32_t r0, uint32_t r1, bool& truncated) noexcept {
|
||
uint64_t x0 = r0;
|
||
uint64_t x1 = r1;
|
||
return uint64_hi64((x0 << 32) | x1, truncated);
|
||
}
|
||
|
||
fastfloat_really_inline
|
||
uint64_t uint32_hi64(uint32_t r0, uint32_t r1, uint32_t r2, bool& truncated) noexcept {
|
||
uint64_t x0 = r0;
|
||
uint64_t x1 = r1;
|
||
uint64_t x2 = r2;
|
||
return uint64_hi64(x0, (x1 << 32) | x2, truncated);
|
||
}
|
||
|
||
// add two small integers, checking for overflow.
|
||
// we want an efficient operation. for msvc, where
|
||
// we don't have built-in intrinsics, this is still
|
||
// pretty fast.
|
||
fastfloat_really_inline
|
||
limb scalar_add(limb x, limb y, bool& overflow) noexcept {
|
||
limb z;
|
||
|
||
// gcc and clang
|
||
#if defined(__has_builtin)
|
||
#if __has_builtin(__builtin_add_overflow)
|
||
overflow = __builtin_add_overflow(x, y, &z);
|
||
return z;
|
||
#endif
|
||
#endif
|
||
|
||
// generic, this still optimizes correctly on MSVC.
|
||
z = x + y;
|
||
overflow = z < x;
|
||
return z;
|
||
}
|
||
|
||
// multiply two small integers, getting both the high and low bits.
|
||
fastfloat_really_inline
|
||
limb scalar_mul(limb x, limb y, limb& carry) noexcept {
|
||
#ifdef FASTFLOAT_64BIT_LIMB
|
||
#if defined(__SIZEOF_INT128__)
|
||
// GCC and clang both define it as an extension.
|
||
__uint128_t z = __uint128_t(x) * __uint128_t(y) + __uint128_t(carry);
|
||
carry = limb(z >> limb_bits);
|
||
return limb(z);
|
||
#else
|
||
// fallback, no native 128-bit integer multiplication with carry.
|
||
// on msvc, this optimizes identically, somehow.
|
||
value128 z = full_multiplication(x, y);
|
||
bool overflow;
|
||
z.low = scalar_add(z.low, carry, overflow);
|
||
z.high += uint64_t(overflow); // cannot overflow
|
||
carry = z.high;
|
||
return z.low;
|
||
#endif
|
||
#else
|
||
uint64_t z = uint64_t(x) * uint64_t(y) + uint64_t(carry);
|
||
carry = limb(z >> limb_bits);
|
||
return limb(z);
|
||
#endif
|
||
}
|
||
|
||
// add scalar value to bigint starting from offset.
|
||
// used in grade school multiplication
|
||
template <uint16_t size>
|
||
inline bool small_add_from(stackvec<size>& vec, limb y, size_t start) noexcept {
|
||
size_t index = start;
|
||
limb carry = y;
|
||
bool overflow;
|
||
while (carry != 0 && index < vec.len()) {
|
||
vec[index] = scalar_add(vec[index], carry, overflow);
|
||
carry = limb(overflow);
|
||
index += 1;
|
||
}
|
||
if (carry != 0) {
|
||
FASTFLOAT_TRY(vec.try_push(carry));
|
||
}
|
||
return true;
|
||
}
|
||
|
||
// add scalar value to bigint.
|
||
template <uint16_t size>
|
||
fastfloat_really_inline bool small_add(stackvec<size>& vec, limb y) noexcept {
|
||
return small_add_from(vec, y, 0);
|
||
}
|
||
|
||
// multiply bigint by scalar value.
|
||
template <uint16_t size>
|
||
inline bool small_mul(stackvec<size>& vec, limb y) noexcept {
|
||
limb carry = 0;
|
||
for (size_t index = 0; index < vec.len(); index++) {
|
||
vec[index] = scalar_mul(vec[index], y, carry);
|
||
}
|
||
if (carry != 0) {
|
||
FASTFLOAT_TRY(vec.try_push(carry));
|
||
}
|
||
return true;
|
||
}
|
||
|
||
// add bigint to bigint starting from index.
|
||
// used in grade school multiplication
|
||
template <uint16_t size>
|
||
bool large_add_from(stackvec<size>& x, limb_span y, size_t start) noexcept {
|
||
// the effective x buffer is from `xstart..x.len()`, so exit early
|
||
// if we can't get that current range.
|
||
if (x.len() < start || y.len() > x.len() - start) {
|
||
FASTFLOAT_TRY(x.try_resize(y.len() + start, 0));
|
||
}
|
||
|
||
bool carry = false;
|
||
for (size_t index = 0; index < y.len(); index++) {
|
||
limb xi = x[index + start];
|
||
limb yi = y[index];
|
||
bool c1 = false;
|
||
bool c2 = false;
|
||
xi = scalar_add(xi, yi, c1);
|
||
if (carry) {
|
||
xi = scalar_add(xi, 1, c2);
|
||
}
|
||
x[index + start] = xi;
|
||
carry = c1 | c2;
|
||
}
|
||
|
||
// handle overflow
|
||
if (carry) {
|
||
FASTFLOAT_TRY(small_add_from(x, 1, y.len() + start));
|
||
}
|
||
return true;
|
||
}
|
||
|
||
// add bigint to bigint.
|
||
template <uint16_t size>
|
||
fastfloat_really_inline bool large_add_from(stackvec<size>& x, limb_span y) noexcept {
|
||
return large_add_from(x, y, 0);
|
||
}
|
||
|
||
// grade-school multiplication algorithm
|
||
template <uint16_t size>
|
||
bool long_mul(stackvec<size>& x, limb_span y) noexcept {
|
||
limb_span xs = limb_span(x.data, x.len());
|
||
stackvec<size> z(xs);
|
||
limb_span zs = limb_span(z.data, z.len());
|
||
|
||
if (y.len() != 0) {
|
||
limb y0 = y[0];
|
||
FASTFLOAT_TRY(small_mul(x, y0));
|
||
for (size_t index = 1; index < y.len(); index++) {
|
||
limb yi = y[index];
|
||
stackvec<size> zi;
|
||
if (yi != 0) {
|
||
// re-use the same buffer throughout
|
||
zi.set_len(0);
|
||
FASTFLOAT_TRY(zi.try_extend(zs));
|
||
FASTFLOAT_TRY(small_mul(zi, yi));
|
||
limb_span zis = limb_span(zi.data, zi.len());
|
||
FASTFLOAT_TRY(large_add_from(x, zis, index));
|
||
}
|
||
}
|
||
}
|
||
|
||
x.normalize();
|
||
return true;
|
||
}
|
||
|
||
// grade-school multiplication algorithm
|
||
template <uint16_t size>
|
||
bool large_mul(stackvec<size>& x, limb_span y) noexcept {
|
||
if (y.len() == 1) {
|
||
FASTFLOAT_TRY(small_mul(x, y[0]));
|
||
} else {
|
||
FASTFLOAT_TRY(long_mul(x, y));
|
||
}
|
||
return true;
|
||
}
|
||
|
||
// big integer type. implements a small subset of big integer
|
||
// arithmetic, using simple algorithms since asymptotically
|
||
// faster algorithms are slower for a small number of limbs.
|
||
// all operations assume the big-integer is normalized.
|
||
struct bigint {
|
||
// storage of the limbs, in little-endian order.
|
||
stackvec<bigint_limbs> vec;
|
||
|
||
bigint(): vec() {}
|
||
bigint(const bigint &) = delete;
|
||
bigint &operator=(const bigint &) = delete;
|
||
bigint(bigint &&) = delete;
|
||
bigint &operator=(bigint &&other) = delete;
|
||
|
||
bigint(uint64_t value): vec() {
|
||
#ifdef FASTFLOAT_64BIT_LIMB
|
||
vec.push_unchecked(value);
|
||
#else
|
||
vec.push_unchecked(uint32_t(value));
|
||
vec.push_unchecked(uint32_t(value >> 32));
|
||
#endif
|
||
vec.normalize();
|
||
}
|
||
|
||
// get the high 64 bits from the vector, and if bits were truncated.
|
||
// this is to get the significant digits for the float.
|
||
uint64_t hi64(bool& truncated) const noexcept {
|
||
#ifdef FASTFLOAT_64BIT_LIMB
|
||
if (vec.len() == 0) {
|
||
return empty_hi64(truncated);
|
||
} else if (vec.len() == 1) {
|
||
return uint64_hi64(vec.rindex(0), truncated);
|
||
} else {
|
||
uint64_t result = uint64_hi64(vec.rindex(0), vec.rindex(1), truncated);
|
||
truncated |= vec.nonzero(2);
|
||
return result;
|
||
}
|
||
#else
|
||
if (vec.len() == 0) {
|
||
return empty_hi64(truncated);
|
||
} else if (vec.len() == 1) {
|
||
return uint32_hi64(vec.rindex(0), truncated);
|
||
} else if (vec.len() == 2) {
|
||
return uint32_hi64(vec.rindex(0), vec.rindex(1), truncated);
|
||
} else {
|
||
uint64_t result = uint32_hi64(vec.rindex(0), vec.rindex(1), vec.rindex(2), truncated);
|
||
truncated |= vec.nonzero(3);
|
||
return result;
|
||
}
|
||
#endif
|
||
}
|
||
|
||
// compare two big integers, returning the large value.
|
||
// assumes both are normalized. if the return value is
|
||
// negative, other is larger, if the return value is
|
||
// positive, this is larger, otherwise they are equal.
|
||
// the limbs are stored in little-endian order, so we
|
||
// must compare the limbs in ever order.
|
||
int compare(const bigint& other) const noexcept {
|
||
if (vec.len() > other.vec.len()) {
|
||
return 1;
|
||
} else if (vec.len() < other.vec.len()) {
|
||
return -1;
|
||
} else {
|
||
for (size_t index = vec.len(); index > 0; index--) {
|
||
limb xi = vec[index - 1];
|
||
limb yi = other.vec[index - 1];
|
||
if (xi > yi) {
|
||
return 1;
|
||
} else if (xi < yi) {
|
||
return -1;
|
||
}
|
||
}
|
||
return 0;
|
||
}
|
||
}
|
||
|
||
// shift left each limb n bits, carrying over to the new limb
|
||
// returns true if we were able to shift all the digits.
|
||
bool shl_bits(size_t n) noexcept {
|
||
// Internally, for each item, we shift left by n, and add the previous
|
||
// right shifted limb-bits.
|
||
// For example, we transform (for u8) shifted left 2, to:
|
||
// b10100100 b01000010
|
||
// b10 b10010001 b00001000
|
||
FASTFLOAT_DEBUG_ASSERT(n != 0);
|
||
FASTFLOAT_DEBUG_ASSERT(n < sizeof(limb) * 8);
|
||
|
||
size_t shl = n;
|
||
size_t shr = limb_bits - shl;
|
||
limb prev = 0;
|
||
for (size_t index = 0; index < vec.len(); index++) {
|
||
limb xi = vec[index];
|
||
vec[index] = (xi << shl) | (prev >> shr);
|
||
prev = xi;
|
||
}
|
||
|
||
limb carry = prev >> shr;
|
||
if (carry != 0) {
|
||
return vec.try_push(carry);
|
||
}
|
||
return true;
|
||
}
|
||
|
||
// move the limbs left by `n` limbs.
|
||
bool shl_limbs(size_t n) noexcept {
|
||
FASTFLOAT_DEBUG_ASSERT(n != 0);
|
||
if (n + vec.len() > vec.capacity()) {
|
||
return false;
|
||
} else if (!vec.is_empty()) {
|
||
// move limbs
|
||
limb* dst = vec.data + n;
|
||
const limb* src = vec.data;
|
||
::memmove(dst, src, sizeof(limb) * vec.len());
|
||
// fill in empty limbs
|
||
limb* first = vec.data;
|
||
limb* last = first + n;
|
||
::std::fill(first, last, 0);
|
||
vec.set_len(n + vec.len());
|
||
return true;
|
||
} else {
|
||
return true;
|
||
}
|
||
}
|
||
|
||
// move the limbs left by `n` bits.
|
||
bool shl(size_t n) noexcept {
|
||
size_t rem = n % limb_bits;
|
||
size_t div = n / limb_bits;
|
||
if (rem != 0) {
|
||
FASTFLOAT_TRY(shl_bits(rem));
|
||
}
|
||
if (div != 0) {
|
||
FASTFLOAT_TRY(shl_limbs(div));
|
||
}
|
||
return true;
|
||
}
|
||
|
||
// get the number of leading zeros in the bigint.
|
||
int ctlz() const noexcept {
|
||
if (vec.is_empty()) {
|
||
return 0;
|
||
} else {
|
||
#ifdef FASTFLOAT_64BIT_LIMB
|
||
return leading_zeroes(vec.rindex(0));
|
||
#else
|
||
// no use defining a specialized leading_zeroes for a 32-bit type.
|
||
uint64_t r0 = vec.rindex(0);
|
||
return leading_zeroes(r0 << 32);
|
||
#endif
|
||
}
|
||
}
|
||
|
||
// get the number of bits in the bigint.
|
||
int bit_length() const noexcept {
|
||
int lz = ctlz();
|
||
return int(limb_bits * vec.len()) - lz;
|
||
}
|
||
|
||
bool mul(limb y) noexcept {
|
||
return small_mul(vec, y);
|
||
}
|
||
|
||
bool add(limb y) noexcept {
|
||
return small_add(vec, y);
|
||
}
|
||
|
||
// multiply as if by 2 raised to a power.
|
||
bool pow2(uint32_t exp) noexcept {
|
||
return shl(exp);
|
||
}
|
||
|
||
// multiply as if by 5 raised to a power.
|
||
bool pow5(uint32_t exp) noexcept {
|
||
// multiply by a power of 5
|
||
static constexpr uint32_t large_step = 135;
|
||
static constexpr uint64_t small_power_of_5[] = {
|
||
1UL, 5UL, 25UL, 125UL, 625UL, 3125UL, 15625UL, 78125UL, 390625UL,
|
||
1953125UL, 9765625UL, 48828125UL, 244140625UL, 1220703125UL,
|
||
6103515625UL, 30517578125UL, 152587890625UL, 762939453125UL,
|
||
3814697265625UL, 19073486328125UL, 95367431640625UL, 476837158203125UL,
|
||
2384185791015625UL, 11920928955078125UL, 59604644775390625UL,
|
||
298023223876953125UL, 1490116119384765625UL, 7450580596923828125UL,
|
||
};
|
||
#ifdef FASTFLOAT_64BIT_LIMB
|
||
constexpr static limb large_power_of_5[] = {
|
||
1414648277510068013UL, 9180637584431281687UL, 4539964771860779200UL,
|
||
10482974169319127550UL, 198276706040285095UL};
|
||
#else
|
||
constexpr static limb large_power_of_5[] = {
|
||
4279965485U, 329373468U, 4020270615U, 2137533757U, 4287402176U,
|
||
1057042919U, 1071430142U, 2440757623U, 381945767U, 46164893U};
|
||
#endif
|
||
size_t large_length = sizeof(large_power_of_5) / sizeof(limb);
|
||
limb_span large = limb_span(large_power_of_5, large_length);
|
||
while (exp >= large_step) {
|
||
FASTFLOAT_TRY(large_mul(vec, large));
|
||
exp -= large_step;
|
||
}
|
||
#ifdef FASTFLOAT_64BIT_LIMB
|
||
uint32_t small_step = 27;
|
||
limb max_native = 7450580596923828125UL;
|
||
#else
|
||
uint32_t small_step = 13;
|
||
limb max_native = 1220703125U;
|
||
#endif
|
||
while (exp >= small_step) {
|
||
FASTFLOAT_TRY(small_mul(vec, max_native));
|
||
exp -= small_step;
|
||
}
|
||
if (exp != 0) {
|
||
FASTFLOAT_TRY(small_mul(vec, limb(small_power_of_5[exp])));
|
||
}
|
||
|
||
return true;
|
||
}
|
||
|
||
// multiply as if by 10 raised to a power.
|
||
bool pow10(uint32_t exp) noexcept {
|
||
FASTFLOAT_TRY(pow5(exp));
|
||
return pow2(exp);
|
||
}
|
||
};
|
||
|
||
} // namespace fast_float
|
||
|
||
#endif
|
||
|
||
#ifndef FASTFLOAT_ASCII_NUMBER_H
|
||
#define FASTFLOAT_ASCII_NUMBER_H
|
||
|
||
#include <cctype>
|
||
#include <cstdint>
|
||
#include <cstring>
|
||
#include <iterator>
|
||
|
||
|
||
namespace fast_float {
|
||
|
||
// Next function can be micro-optimized, but compilers are entirely
|
||
// able to optimize it well.
|
||
fastfloat_really_inline bool is_integer(char c) noexcept { return c >= '0' && c <= '9'; }
|
||
|
||
fastfloat_really_inline uint64_t byteswap(uint64_t val) {
|
||
return (val & 0xFF00000000000000) >> 56
|
||
| (val & 0x00FF000000000000) >> 40
|
||
| (val & 0x0000FF0000000000) >> 24
|
||
| (val & 0x000000FF00000000) >> 8
|
||
| (val & 0x00000000FF000000) << 8
|
||
| (val & 0x0000000000FF0000) << 24
|
||
| (val & 0x000000000000FF00) << 40
|
||
| (val & 0x00000000000000FF) << 56;
|
||
}
|
||
|
||
fastfloat_really_inline uint64_t read_u64(const char *chars) {
|
||
uint64_t val;
|
||
::memcpy(&val, chars, sizeof(uint64_t));
|
||
#if FASTFLOAT_IS_BIG_ENDIAN == 1
|
||
// Need to read as-if the number was in little-endian order.
|
||
val = byteswap(val);
|
||
#endif
|
||
return val;
|
||
}
|
||
|
||
fastfloat_really_inline void write_u64(uint8_t *chars, uint64_t val) {
|
||
#if FASTFLOAT_IS_BIG_ENDIAN == 1
|
||
// Need to read as-if the number was in little-endian order.
|
||
val = byteswap(val);
|
||
#endif
|
||
::memcpy(chars, &val, sizeof(uint64_t));
|
||
}
|
||
|
||
// credit @aqrit
|
||
fastfloat_really_inline uint32_t parse_eight_digits_unrolled(uint64_t val) {
|
||
const uint64_t mask = 0x000000FF000000FF;
|
||
const uint64_t mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32)
|
||
const uint64_t mul2 = 0x0000271000000001; // 1 + (10000ULL << 32)
|
||
val -= 0x3030303030303030;
|
||
val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8;
|
||
val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32;
|
||
return uint32_t(val);
|
||
}
|
||
|
||
fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars) noexcept {
|
||
return parse_eight_digits_unrolled(read_u64(chars));
|
||
}
|
||
|
||
// credit @aqrit
|
||
fastfloat_really_inline bool is_made_of_eight_digits_fast(uint64_t val) noexcept {
|
||
return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) &
|
||
0x8080808080808080));
|
||
}
|
||
|
||
fastfloat_really_inline bool is_made_of_eight_digits_fast(const char *chars) noexcept {
|
||
return is_made_of_eight_digits_fast(read_u64(chars));
|
||
}
|
||
|
||
typedef span<const char> byte_span;
|
||
|
||
struct parsed_number_string {
|
||
int64_t exponent{0};
|
||
uint64_t mantissa{0};
|
||
const char *lastmatch{nullptr};
|
||
bool negative{false};
|
||
bool valid{false};
|
||
bool too_many_digits{false};
|
||
// contains the range of the significant digits
|
||
byte_span integer{}; // non-nullable
|
||
byte_span fraction{}; // nullable
|
||
};
|
||
|
||
// Assuming that you use no more than 19 digits, this will
|
||
// parse an ASCII string.
|
||
fastfloat_really_inline
|
||
parsed_number_string parse_number_string(const char *p, const char *pend, parse_options options) noexcept {
|
||
const chars_format fmt = options.format;
|
||
const char decimal_point = options.decimal_point;
|
||
|
||
parsed_number_string answer;
|
||
answer.valid = false;
|
||
answer.too_many_digits = false;
|
||
answer.negative = (*p == '-');
|
||
if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
|
||
++p;
|
||
if (p == pend) {
|
||
return answer;
|
||
}
|
||
if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot
|
||
return answer;
|
||
}
|
||
}
|
||
const char *const start_digits = p;
|
||
|
||
uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad)
|
||
|
||
while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(p)) {
|
||
i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
|
||
p += 8;
|
||
}
|
||
while ((p != pend) && is_integer(*p)) {
|
||
// a multiplication by 10 is cheaper than an arbitrary integer
|
||
// multiplication
|
||
i = 10 * i +
|
||
uint64_t(*p - '0'); // might overflow, we will handle the overflow later
|
||
++p;
|
||
}
|
||
const char *const end_of_integer_part = p;
|
||
int64_t digit_count = int64_t(end_of_integer_part - start_digits);
|
||
answer.integer = byte_span(start_digits, size_t(digit_count));
|
||
int64_t exponent = 0;
|
||
if ((p != pend) && (*p == decimal_point)) {
|
||
++p;
|
||
const char* before = p;
|
||
// can occur at most twice without overflowing, but let it occur more, since
|
||
// for integers with many digits, digit parsing is the primary bottleneck.
|
||
while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(p)) {
|
||
i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
|
||
p += 8;
|
||
}
|
||
while ((p != pend) && is_integer(*p)) {
|
||
uint8_t digit = uint8_t(*p - '0');
|
||
++p;
|
||
i = i * 10 + digit; // in rare cases, this will overflow, but that's ok
|
||
}
|
||
exponent = before - p;
|
||
answer.fraction = byte_span(before, size_t(p - before));
|
||
digit_count -= exponent;
|
||
}
|
||
// we must have encountered at least one integer!
|
||
if (digit_count == 0) {
|
||
return answer;
|
||
}
|
||
int64_t exp_number = 0; // explicit exponential part
|
||
if ((fmt & chars_format::scientific) && (p != pend) && (('e' == *p) || ('E' == *p))) {
|
||
const char * location_of_e = p;
|
||
++p;
|
||
bool neg_exp = false;
|
||
if ((p != pend) && ('-' == *p)) {
|
||
neg_exp = true;
|
||
++p;
|
||
} else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
|
||
++p;
|
||
}
|
||
if ((p == pend) || !is_integer(*p)) {
|
||
if(!(fmt & chars_format::fixed)) {
|
||
// We are in error.
|
||
return answer;
|
||
}
|
||
// Otherwise, we will be ignoring the 'e'.
|
||
p = location_of_e;
|
||
} else {
|
||
while ((p != pend) && is_integer(*p)) {
|
||
uint8_t digit = uint8_t(*p - '0');
|
||
if (exp_number < 0x10000000) {
|
||
exp_number = 10 * exp_number + digit;
|
||
}
|
||
++p;
|
||
}
|
||
if(neg_exp) { exp_number = - exp_number; }
|
||
exponent += exp_number;
|
||
}
|
||
} else {
|
||
// If it scientific and not fixed, we have to bail out.
|
||
if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; }
|
||
}
|
||
answer.lastmatch = p;
|
||
answer.valid = true;
|
||
|
||
// If we frequently had to deal with long strings of digits,
|
||
// we could extend our code by using a 128-bit integer instead
|
||
// of a 64-bit integer. However, this is uncommon.
|
||
//
|
||
// We can deal with up to 19 digits.
|
||
if (digit_count > 19) { // this is uncommon
|
||
// It is possible that the integer had an overflow.
|
||
// We have to handle the case where we have 0.0000somenumber.
|
||
// We need to be mindful of the case where we only have zeroes...
|
||
// E.g., 0.000000000...000.
|
||
const char *start = start_digits;
|
||
while ((start != pend) && (*start == '0' || *start == decimal_point)) {
|
||
if(*start == '0') { digit_count --; }
|
||
start++;
|
||
}
|
||
if (digit_count > 19) {
|
||
answer.too_many_digits = true;
|
||
// Let us start again, this time, avoiding overflows.
|
||
// We don't need to check if is_integer, since we use the
|
||
// pre-tokenized spans from above.
|
||
i = 0;
|
||
p = answer.integer.ptr;
|
||
const char* int_end = p + answer.integer.len();
|
||
const uint64_t minimal_nineteen_digit_integer{1000000000000000000};
|
||
while((i < minimal_nineteen_digit_integer) && (p != int_end)) {
|
||
i = i * 10 + uint64_t(*p - '0');
|
||
++p;
|
||
}
|
||
if (i >= minimal_nineteen_digit_integer) { // We have a big integers
|
||
exponent = end_of_integer_part - p + exp_number;
|
||
} else { // We have a value with a fractional component.
|
||
p = answer.fraction.ptr;
|
||
const char* frac_end = p + answer.fraction.len();
|
||
while((i < minimal_nineteen_digit_integer) && (p != frac_end)) {
|
||
i = i * 10 + uint64_t(*p - '0');
|
||
++p;
|
||
}
|
||
exponent = answer.fraction.ptr - p + exp_number;
|
||
}
|
||
// We have now corrected both exponent and i, to a truncated value
|
||
}
|
||
}
|
||
answer.exponent = exponent;
|
||
answer.mantissa = i;
|
||
return answer;
|
||
}
|
||
|
||
} // namespace fast_float
|
||
|
||
#endif
|
||
|
||
#ifndef FASTFLOAT_DIGIT_COMPARISON_H
|
||
#define FASTFLOAT_DIGIT_COMPARISON_H
|
||
|
||
#include <algorithm>
|
||
#include <cstdint>
|
||
#include <cstring>
|
||
#include <iterator>
|
||
|
||
|
||
namespace fast_float {
|
||
|
||
// 1e0 to 1e19
|
||
constexpr static uint64_t powers_of_ten_uint64[] = {
|
||
1UL, 10UL, 100UL, 1000UL, 10000UL, 100000UL, 1000000UL, 10000000UL, 100000000UL,
|
||
1000000000UL, 10000000000UL, 100000000000UL, 1000000000000UL, 10000000000000UL,
|
||
100000000000000UL, 1000000000000000UL, 10000000000000000UL, 100000000000000000UL,
|
||
1000000000000000000UL, 10000000000000000000UL};
|
||
|
||
// calculate the exponent, in scientific notation, of the number.
|
||
// this algorithm is not even close to optimized, but it has no practical
|
||
// effect on performance: in order to have a faster algorithm, we'd need
|
||
// to slow down performance for faster algorithms, and this is still fast.
|
||
fastfloat_really_inline int32_t scientific_exponent(parsed_number_string& num) noexcept {
|
||
uint64_t mantissa = num.mantissa;
|
||
int32_t exponent = int32_t(num.exponent);
|
||
while (mantissa >= 10000) {
|
||
mantissa /= 10000;
|
||
exponent += 4;
|
||
}
|
||
while (mantissa >= 100) {
|
||
mantissa /= 100;
|
||
exponent += 2;
|
||
}
|
||
while (mantissa >= 10) {
|
||
mantissa /= 10;
|
||
exponent += 1;
|
||
}
|
||
return exponent;
|
||
}
|
||
|
||
// this converts a native floating-point number to an extended-precision float.
|
||
template <typename T>
|
||
fastfloat_really_inline adjusted_mantissa to_extended(T value) noexcept {
|
||
using equiv_uint = typename binary_format<T>::equiv_uint;
|
||
constexpr equiv_uint exponent_mask = binary_format<T>::exponent_mask();
|
||
constexpr equiv_uint mantissa_mask = binary_format<T>::mantissa_mask();
|
||
constexpr equiv_uint hidden_bit_mask = binary_format<T>::hidden_bit_mask();
|
||
|
||
adjusted_mantissa am;
|
||
int32_t bias = binary_format<T>::mantissa_explicit_bits() - binary_format<T>::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<T>::mantissa_explicit_bits());
|
||
am.power2 -= bias;
|
||
am.mantissa = (bits & mantissa_mask) | hidden_bit_mask;
|
||
}
|
||
|
||
return am;
|
||
}
|
||
|
||
// get the extended precision value of the halfway point between b and b+u.
|
||
// we are given a native float that represents b, so we need to adjust it
|
||
// halfway between b and b+u.
|
||
template <typename T>
|
||
fastfloat_really_inline adjusted_mantissa to_extended_halfway(T value) noexcept {
|
||
adjusted_mantissa am = to_extended(value);
|
||
am.mantissa <<= 1;
|
||
am.mantissa += 1;
|
||
am.power2 -= 1;
|
||
return am;
|
||
}
|
||
|
||
// round an extended-precision float to the nearest machine float.
|
||
template <typename T, typename callback>
|
||
fastfloat_really_inline void round(adjusted_mantissa& am, callback cb) noexcept {
|
||
int32_t mantissa_shift = 64 - binary_format<T>::mantissa_explicit_bits() - 1;
|
||
if (-am.power2 >= mantissa_shift) {
|
||
// have a denormal float
|
||
int32_t shift = -am.power2 + 1;
|
||
cb(am, std::min(shift, 64));
|
||
// check for round-up: if rounding-nearest carried us to the hidden bit.
|
||
am.power2 = (am.mantissa < (uint64_t(1) << binary_format<T>::mantissa_explicit_bits())) ? 0 : 1;
|
||
return;
|
||
}
|
||
|
||
// have a normal float, use the default shift.
|
||
cb(am, mantissa_shift);
|
||
|
||
// check for carry
|
||
if (am.mantissa >= (uint64_t(2) << binary_format<T>::mantissa_explicit_bits())) {
|
||
am.mantissa = (uint64_t(1) << binary_format<T>::mantissa_explicit_bits());
|
||
am.power2++;
|
||
}
|
||
|
||
// check for infinite: we could have carried to an infinite power
|
||
am.mantissa &= ~(uint64_t(1) << binary_format<T>::mantissa_explicit_bits());
|
||
if (am.power2 >= binary_format<T>::infinite_power()) {
|
||
am.power2 = binary_format<T>::infinite_power();
|
||
am.mantissa = 0;
|
||
}
|
||
}
|
||
|
||
template <typename callback>
|
||
fastfloat_really_inline
|
||
void round_nearest_tie_even(adjusted_mantissa& am, int32_t shift, callback cb) noexcept {
|
||
uint64_t mask;
|
||
uint64_t halfway;
|
||
if (shift == 64) {
|
||
mask = UINT64_MAX;
|
||
} else {
|
||
mask = (uint64_t(1) << shift) - 1;
|
||
}
|
||
if (shift == 0) {
|
||
halfway = 0;
|
||
} else {
|
||
halfway = uint64_t(1) << (shift - 1);
|
||
}
|
||
uint64_t truncated_bits = am.mantissa & mask;
|
||
uint64_t is_above = truncated_bits > halfway;
|
||
uint64_t is_halfway = truncated_bits == halfway;
|
||
|
||
// shift digits into position
|
||
if (shift == 64) {
|
||
am.mantissa = 0;
|
||
} else {
|
||
am.mantissa >>= shift;
|
||
}
|
||
am.power2 += shift;
|
||
|
||
bool is_odd = (am.mantissa & 1) == 1;
|
||
am.mantissa += uint64_t(cb(is_odd, is_halfway, is_above));
|
||
}
|
||
|
||
fastfloat_really_inline void round_down(adjusted_mantissa& am, int32_t shift) noexcept {
|
||
if (shift == 64) {
|
||
am.mantissa = 0;
|
||
} else {
|
||
am.mantissa >>= shift;
|
||
}
|
||
am.power2 += shift;
|
||
}
|
||
|
||
fastfloat_really_inline void skip_zeros(const char*& first, const char* last) noexcept {
|
||
uint64_t val;
|
||
while (std::distance(first, last) >= 8) {
|
||
::memcpy(&val, first, sizeof(uint64_t));
|
||
if (val != 0x3030303030303030) {
|
||
break;
|
||
}
|
||
first += 8;
|
||
}
|
||
while (first != last) {
|
||
if (*first != '0') {
|
||
break;
|
||
}
|
||
first++;
|
||
}
|
||
}
|
||
|
||
// determine if any non-zero digits were truncated.
|
||
// all characters must be valid digits.
|
||
fastfloat_really_inline bool is_truncated(const char* first, const char* last) noexcept {
|
||
// do 8-bit optimizations, can just compare to 8 literal 0s.
|
||
uint64_t val;
|
||
while (std::distance(first, last) >= 8) {
|
||
::memcpy(&val, first, sizeof(uint64_t));
|
||
if (val != 0x3030303030303030) {
|
||
return true;
|
||
}
|
||
first += 8;
|
||
}
|
||
while (first != last) {
|
||
if (*first != '0') {
|
||
return true;
|
||
}
|
||
first++;
|
||
}
|
||
return false;
|
||
}
|
||
|
||
fastfloat_really_inline bool is_truncated(byte_span s) noexcept {
|
||
return is_truncated(s.ptr, s.ptr + s.len());
|
||
}
|
||
|
||
fastfloat_really_inline
|
||
void parse_eight_digits(const char*& p, limb& value, size_t& counter, size_t& count) noexcept {
|
||
value = value * 100000000 + parse_eight_digits_unrolled(p);
|
||
p += 8;
|
||
counter += 8;
|
||
count += 8;
|
||
}
|
||
|
||
fastfloat_really_inline
|
||
void parse_one_digit(const char*& p, limb& value, size_t& counter, size_t& count) noexcept {
|
||
value = value * 10 + limb(*p - '0');
|
||
p++;
|
||
counter++;
|
||
count++;
|
||
}
|
||
|
||
fastfloat_really_inline
|
||
void add_native(bigint& big, limb power, limb value) noexcept {
|
||
big.mul(power);
|
||
big.add(value);
|
||
}
|
||
|
||
fastfloat_really_inline void round_up_bigint(bigint& big, size_t& count) noexcept {
|
||
// need to round-up the digits, but need to avoid rounding
|
||
// ....9999 to ...10000, which could cause a false halfway point.
|
||
add_native(big, 10, 1);
|
||
count++;
|
||
}
|
||
|
||
// parse the significant digits into a big integer
|
||
inline void parse_mantissa(bigint& result, parsed_number_string& num, size_t max_digits, size_t& digits) noexcept {
|
||
// try to minimize the number of big integer and scalar multiplication.
|
||
// therefore, try to parse 8 digits at a time, and multiply by the largest
|
||
// scalar value (9 or 19 digits) for each step.
|
||
size_t counter = 0;
|
||
digits = 0;
|
||
limb value = 0;
|
||
#ifdef FASTFLOAT_64BIT_LIMB
|
||
size_t step = 19;
|
||
#else
|
||
size_t step = 9;
|
||
#endif
|
||
|
||
// process all integer digits.
|
||
const char* p = num.integer.ptr;
|
||
const char* pend = p + num.integer.len();
|
||
skip_zeros(p, pend);
|
||
// process all digits, in increments of step per loop
|
||
while (p != pend) {
|
||
while ((std::distance(p, pend) >= 8) && (step - counter >= 8) && (max_digits - digits >= 8)) {
|
||
parse_eight_digits(p, value, counter, digits);
|
||
}
|
||
while (counter < step && p != pend && digits < max_digits) {
|
||
parse_one_digit(p, value, counter, digits);
|
||
}
|
||
if (digits == max_digits) {
|
||
// add the temporary value, then check if we've truncated any digits
|
||
add_native(result, limb(powers_of_ten_uint64[counter]), value);
|
||
bool truncated = is_truncated(p, pend);
|
||
if (num.fraction.ptr != nullptr) {
|
||
truncated |= is_truncated(num.fraction);
|
||
}
|
||
if (truncated) {
|
||
round_up_bigint(result, digits);
|
||
}
|
||
return;
|
||
} else {
|
||
add_native(result, limb(powers_of_ten_uint64[counter]), value);
|
||
counter = 0;
|
||
value = 0;
|
||
}
|
||
}
|
||
|
||
// add our fraction digits, if they're available.
|
||
if (num.fraction.ptr != nullptr) {
|
||
p = num.fraction.ptr;
|
||
pend = p + num.fraction.len();
|
||
if (digits == 0) {
|
||
skip_zeros(p, pend);
|
||
}
|
||
// process all digits, in increments of step per loop
|
||
while (p != pend) {
|
||
while ((std::distance(p, pend) >= 8) && (step - counter >= 8) && (max_digits - digits >= 8)) {
|
||
parse_eight_digits(p, value, counter, digits);
|
||
}
|
||
while (counter < step && p != pend && digits < max_digits) {
|
||
parse_one_digit(p, value, counter, digits);
|
||
}
|
||
if (digits == max_digits) {
|
||
// add the temporary value, then check if we've truncated any digits
|
||
add_native(result, limb(powers_of_ten_uint64[counter]), value);
|
||
bool truncated = is_truncated(p, pend);
|
||
if (truncated) {
|
||
round_up_bigint(result, digits);
|
||
}
|
||
return;
|
||
} else {
|
||
add_native(result, limb(powers_of_ten_uint64[counter]), value);
|
||
counter = 0;
|
||
value = 0;
|
||
}
|
||
}
|
||
}
|
||
|
||
if (counter != 0) {
|
||
add_native(result, limb(powers_of_ten_uint64[counter]), value);
|
||
}
|
||
}
|
||
|
||
template <typename T>
|
||
inline adjusted_mantissa positive_digit_comp(bigint& bigmant, int32_t exponent) noexcept {
|
||
FASTFLOAT_ASSERT(bigmant.pow10(uint32_t(exponent)));
|
||
adjusted_mantissa answer;
|
||
bool truncated;
|
||
answer.mantissa = bigmant.hi64(truncated);
|
||
int bias = binary_format<T>::mantissa_explicit_bits() - binary_format<T>::minimum_exponent();
|
||
answer.power2 = bigmant.bit_length() - 64 + bias;
|
||
|
||
round<T>(answer, [truncated](adjusted_mantissa& a, int32_t shift) {
|
||
round_nearest_tie_even(a, shift, [truncated](bool is_odd, bool is_halfway, bool is_above) -> bool {
|
||
return is_above || (is_halfway && truncated) || (is_odd && is_halfway);
|
||
});
|
||
});
|
||
|
||
return answer;
|
||
}
|
||
|
||
// the scaling here is quite simple: we have, for the real digits `m * 10^e`,
|
||
// and for the theoretical digits `n * 2^f`. Since `e` is always negative,
|
||
// to scale them identically, we do `n * 2^f * 5^-f`, so we now have `m * 2^e`.
|
||
// we then need to scale by `2^(f- e)`, and then the two significant digits
|
||
// are of the same magnitude.
|
||
template <typename T>
|
||
inline adjusted_mantissa negative_digit_comp(bigint& bigmant, adjusted_mantissa am, int32_t exponent) noexcept {
|
||
bigint& real_digits = bigmant;
|
||
int32_t real_exp = exponent;
|
||
|
||
// get the value of `b`, rounded down, and get a bigint representation of b+h
|
||
adjusted_mantissa am_b = am;
|
||
// gcc7 buf: use a lambda to remove the noexcept qualifier bug with -Wnoexcept-type.
|
||
round<T>(am_b, [](adjusted_mantissa&a, int32_t shift) { round_down(a, shift); });
|
||
T b;
|
||
to_float(false, am_b, b);
|
||
adjusted_mantissa theor = to_extended_halfway(b);
|
||
bigint theor_digits(theor.mantissa);
|
||
int32_t theor_exp = theor.power2;
|
||
|
||
// scale real digits and theor digits to be same power.
|
||
int32_t pow2_exp = theor_exp - real_exp;
|
||
uint32_t pow5_exp = uint32_t(-real_exp);
|
||
if (pow5_exp != 0) {
|
||
FASTFLOAT_ASSERT(theor_digits.pow5(pow5_exp));
|
||
}
|
||
if (pow2_exp > 0) {
|
||
FASTFLOAT_ASSERT(theor_digits.pow2(uint32_t(pow2_exp)));
|
||
} else if (pow2_exp < 0) {
|
||
FASTFLOAT_ASSERT(real_digits.pow2(uint32_t(-pow2_exp)));
|
||
}
|
||
|
||
// compare digits, and use it to director rounding
|
||
int ord = real_digits.compare(theor_digits);
|
||
adjusted_mantissa answer = am;
|
||
round<T>(answer, [ord](adjusted_mantissa& a, int32_t shift) {
|
||
round_nearest_tie_even(a, shift, [ord](bool is_odd, bool _, bool __) -> bool {
|
||
(void)_; // not needed, since we've done our comparison
|
||
(void)__; // not needed, since we've done our comparison
|
||
if (ord > 0) {
|
||
return true;
|
||
} else if (ord < 0) {
|
||
return false;
|
||
} else {
|
||
return is_odd;
|
||
}
|
||
});
|
||
});
|
||
|
||
return answer;
|
||
}
|
||
|
||
// parse the significant digits as a big integer to unambiguously round the
|
||
// the significant digits. here, we are trying to determine how to round
|
||
// an extended float representation close to `b+h`, halfway between `b`
|
||
// (the float rounded-down) and `b+u`, the next positive float. this
|
||
// algorithm is always correct, and uses one of two approaches. when
|
||
// the exponent is positive relative to the significant digits (such as
|
||
// 1234), we create a big-integer representation, get the high 64-bits,
|
||
// determine if any lower bits are truncated, and use that to direct
|
||
// rounding. in case of a negative exponent relative to the significant
|
||
// digits (such as 1.2345), we create a theoretical representation of
|
||
// `b` as a big-integer type, scaled to the same binary exponent as
|
||
// the actual digits. we then compare the big integer representations
|
||
// of both, and use that to direct rounding.
|
||
template <typename T>
|
||
inline adjusted_mantissa digit_comp(parsed_number_string& num, adjusted_mantissa am) noexcept {
|
||
// remove the invalid exponent bias
|
||
am.power2 -= invalid_am_bias;
|
||
|
||
int32_t sci_exp = scientific_exponent(num);
|
||
size_t max_digits = binary_format<T>::max_digits();
|
||
size_t digits = 0;
|
||
bigint bigmant;
|
||
parse_mantissa(bigmant, num, max_digits, digits);
|
||
// can't underflow, since digits is at most max_digits.
|
||
int32_t exponent = sci_exp + 1 - int32_t(digits);
|
||
if (exponent >= 0) {
|
||
return positive_digit_comp<T>(bigmant, exponent);
|
||
} else {
|
||
return negative_digit_comp<T>(bigmant, am, exponent);
|
||
}
|
||
}
|
||
|
||
} // namespace fast_float
|
||
|
||
#endif
|
||
|
||
#ifndef FASTFLOAT_PARSE_NUMBER_H
|
||
#define FASTFLOAT_PARSE_NUMBER_H
|
||
|
||
|
||
#include <cmath>
|
||
#include <cstring>
|
||
#include <limits>
|
||
#include <system_error>
|
||
|
||
namespace fast_float {
|
||
|
||
|
||
namespace detail {
|
||
/**
|
||
* Special case +inf, -inf, nan, infinity, -infinity.
|
||
* The case comparisons could be made much faster given that we know that the
|
||
* strings a null-free and fixed.
|
||
**/
|
||
template <typename T>
|
||
from_chars_result parse_infnan(const char *first, const char *last, T &value) noexcept {
|
||
from_chars_result answer;
|
||
answer.ptr = first;
|
||
answer.ec = std::errc(); // be optimistic
|
||
bool minusSign = false;
|
||
if (*first == '-') { // assume first < last, so dereference without checks; C++17 20.19.3.(7.1) explicitly forbids '+' here
|
||
minusSign = true;
|
||
++first;
|
||
}
|
||
if (last - first >= 3) {
|
||
if (fastfloat_strncasecmp(first, "nan", 3)) {
|
||
answer.ptr = (first += 3);
|
||
value = minusSign ? -std::numeric_limits<T>::quiet_NaN() : std::numeric_limits<T>::quiet_NaN();
|
||
// Check for possible nan(n-char-seq-opt), C++17 20.19.3.7, C11 7.20.1.3.3. At least MSVC produces nan(ind) and nan(snan).
|
||
if(first != last && *first == '(') {
|
||
for(const char* ptr = first + 1; ptr != last; ++ptr) {
|
||
if (*ptr == ')') {
|
||
answer.ptr = ptr + 1; // valid nan(n-char-seq-opt)
|
||
break;
|
||
}
|
||
else if(!(('a' <= *ptr && *ptr <= 'z') || ('A' <= *ptr && *ptr <= 'Z') || ('0' <= *ptr && *ptr <= '9') || *ptr == '_'))
|
||
break; // forbidden char, not nan(n-char-seq-opt)
|
||
}
|
||
}
|
||
return answer;
|
||
}
|
||
if (fastfloat_strncasecmp(first, "inf", 3)) {
|
||
if ((last - first >= 8) && fastfloat_strncasecmp(first + 3, "inity", 5)) {
|
||
answer.ptr = first + 8;
|
||
} else {
|
||
answer.ptr = first + 3;
|
||
}
|
||
value = minusSign ? -std::numeric_limits<T>::infinity() : std::numeric_limits<T>::infinity();
|
||
return answer;
|
||
}
|
||
}
|
||
answer.ec = std::errc::invalid_argument;
|
||
return answer;
|
||
}
|
||
|
||
} // namespace detail
|
||
|
||
template<typename T>
|
||
from_chars_result from_chars(const char *first, const char *last,
|
||
T &value, chars_format fmt /*= chars_format::general*/) noexcept {
|
||
return from_chars_advanced(first, last, value, parse_options{fmt});
|
||
}
|
||
|
||
template<typename T>
|
||
from_chars_result from_chars_advanced(const char *first, const char *last,
|
||
T &value, parse_options options) noexcept {
|
||
|
||
static_assert (std::is_same<T, double>::value || std::is_same<T, float>::value, "only float and double are supported");
|
||
|
||
|
||
from_chars_result answer;
|
||
if (first == last) {
|
||
answer.ec = std::errc::invalid_argument;
|
||
answer.ptr = first;
|
||
return answer;
|
||
}
|
||
parsed_number_string pns = parse_number_string(first, last, options);
|
||
if (!pns.valid) {
|
||
return detail::parse_infnan(first, last, value);
|
||
}
|
||
answer.ec = std::errc(); // be optimistic
|
||
answer.ptr = pns.lastmatch;
|
||
// Next is Clinger's fast path.
|
||
if (binary_format<T>::min_exponent_fast_path() <= pns.exponent && pns.exponent <= binary_format<T>::max_exponent_fast_path() && pns.mantissa <=binary_format<T>::max_mantissa_fast_path() && !pns.too_many_digits) {
|
||
value = T(pns.mantissa);
|
||
if (pns.exponent < 0) { value = value / binary_format<T>::exact_power_of_ten(-pns.exponent); }
|
||
else { value = value * binary_format<T>::exact_power_of_ten(pns.exponent); }
|
||
if (pns.negative) { value = -value; }
|
||
return answer;
|
||
}
|
||
adjusted_mantissa am = compute_float<binary_format<T>>(pns.exponent, pns.mantissa);
|
||
if(pns.too_many_digits && am.power2 >= 0) {
|
||
if(am != compute_float<binary_format<T>>(pns.exponent, pns.mantissa + 1)) {
|
||
am = compute_error<binary_format<T>>(pns.exponent, pns.mantissa);
|
||
}
|
||
}
|
||
// If we called compute_float<binary_format<T>>(pns.exponent, pns.mantissa) and we have an invalid power (am.power2 < 0),
|
||
// then we need to go the long way around again. This is very uncommon.
|
||
if(am.power2 < 0) { am = digit_comp<T>(pns, am); }
|
||
to_float(pns.negative, am, value);
|
||
return answer;
|
||
}
|
||
|
||
} // namespace fast_float
|
||
|
||
#endif
|
||
|