3197 lines
107 KiB
C++
3197 lines
107 KiB
C++
// version: 3.4.0
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// 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
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* parses floating-point numbers expecting a locale-indepent format equivalent
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* to what is used by std::strtod in the default ("C") locale. The resulting
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* floating-point value is the closest floating-point values (using either float
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* or double), using the "round to even" convention for values that would
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* otherwise fall right in-between two values. That is, we provide exact parsing
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* 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
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* point right after the parsed number, and the `value` referenced is set to the
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* parsed value. In case of error, the returned `ec` contains a representative
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* 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
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* `new` or `malloc`).
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*
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* Like the C++17 standard, the `fast_float::from_chars` functions take an
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* optional last argument of the type `fast_float::chars_format`. It is a bitset
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* value: we check whether `fmt & fast_float::chars_format::fixed` and `fmt &
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* fast_float::chars_format::scientific` are set to determine whether we allowe
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* the fixed point and scientific notation respectively. The default is
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* `fast_float::chars_format::general` which allows both `fixed` and
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* `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, T& value,
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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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} // namespace fast_float
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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 <cassert>
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#include <cfloat>
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#include <cstdint>
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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__) || defined(__s390x__) || \
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(defined(__ppc64__) || defined(__PPC64__) || defined(__ppc64le__) || \
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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) || 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
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// approximation. UINTPTR_MAX and INTPTR_MAX are optional, so avoid them for max
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// 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) \
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{ \
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if (!(x)) \
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abort(); \
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}
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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) \
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{ \
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if (!(x)) \
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return false; \
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}
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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 { return length; }
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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))
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input_num >>= 32, last_bit |= 32;
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if (input_num & uint64_t(0xffff0000))
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input_num >>= 16, last_bit |= 16;
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if (input_num & uint64_t(0xff00))
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input_num >>= 8, last_bit |= 8;
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if (input_num & uint64_t(0xf0))
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input_num >>= 4, last_bit |= 4;
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if (input_num & uint64_t(0xc))
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input_num >>= 2, last_bit |= 2;
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if (input_num & uint64_t(0x2))
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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, 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>
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struct binary_format {
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using equiv_uint =
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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 <>
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inline constexpr int binary_format<double>::mantissa_explicit_bits() {
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return 52;
|
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}
|
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template <>
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inline constexpr int binary_format<float>::mantissa_explicit_bits() {
|
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return 23;
|
||
}
|
||
|
||
template <>
|
||
inline constexpr int binary_format<double>::max_exponent_round_to_even() {
|
||
return 23;
|
||
}
|
||
|
||
template <>
|
||
inline constexpr int binary_format<float>::max_exponent_round_to_even() {
|
||
return 10;
|
||
}
|
||
|
||
template <>
|
||
inline constexpr int binary_format<double>::min_exponent_round_to_even() {
|
||
return -4;
|
||
}
|
||
|
||
template <>
|
||
inline constexpr int binary_format<float>::min_exponent_round_to_even() {
|
||
return -17;
|
||
}
|
||
|
||
template <>
|
||
inline constexpr int binary_format<double>::minimum_exponent() {
|
||
return -1023;
|
||
}
|
||
template <>
|
||
inline constexpr int binary_format<float>::minimum_exponent() {
|
||
return -127;
|
||
}
|
||
|
||
template <>
|
||
inline constexpr int binary_format<double>::infinite_power() {
|
||
return 0x7FF;
|
||
}
|
||
template <>
|
||
inline constexpr int binary_format<float>::infinite_power() {
|
||
return 0xFF;
|
||
}
|
||
|
||
template <>
|
||
inline constexpr int binary_format<double>::sign_index() {
|
||
return 63;
|
||
}
|
||
template <>
|
||
inline constexpr int binary_format<float>::sign_index() {
|
||
return 31;
|
||
}
|
||
|
||
template <>
|
||
inline constexpr int binary_format<double>::min_exponent_fast_path() {
|
||
#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
|
||
return 0;
|
||
#else
|
||
return -22;
|
||
#endif
|
||
}
|
||
template <>
|
||
inline constexpr int binary_format<float>::min_exponent_fast_path() {
|
||
#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
|
||
return 0;
|
||
#else
|
||
return -10;
|
||
#endif
|
||
}
|
||
|
||
template <>
|
||
inline constexpr int binary_format<double>::max_exponent_fast_path() {
|
||
return 22;
|
||
}
|
||
template <>
|
||
inline constexpr int binary_format<float>::max_exponent_fast_path() {
|
||
return 10;
|
||
}
|
||
|
||
template <>
|
||
inline constexpr uint64_t binary_format<double>::max_mantissa_fast_path() {
|
||
return uint64_t(2) << mantissa_explicit_bits();
|
||
}
|
||
template <>
|
||
inline constexpr uint64_t binary_format<float>::max_mantissa_fast_path() {
|
||
return uint64_t(2) << mantissa_explicit_bits();
|
||
}
|
||
|
||
template <>
|
||
inline constexpr double binary_format<double>::exact_power_of_ten(
|
||
int64_t power) {
|
||
return powers_of_ten_double[power];
|
||
}
|
||
template <>
|
||
inline constexpr float binary_format<float>::exact_power_of_ten(int64_t power) {
|
||
return powers_of_ten_float[power];
|
||
}
|
||
|
||
template <>
|
||
inline constexpr int binary_format<double>::largest_power_of_ten() {
|
||
return 308;
|
||
}
|
||
template <>
|
||
inline constexpr int binary_format<float>::largest_power_of_ten() {
|
||
return 38;
|
||
}
|
||
|
||
template <>
|
||
inline constexpr int binary_format<double>::smallest_power_of_ten() {
|
||
return -342;
|
||
}
|
||
template <>
|
||
inline constexpr int binary_format<float>::smallest_power_of_ten() {
|
||
return -65;
|
||
}
|
||
|
||
template <>
|
||
inline constexpr size_t binary_format<double>::max_digits() {
|
||
return 769;
|
||
}
|
||
template <>
|
||
inline constexpr size_t binary_format<float>::max_digits() {
|
||
return 114;
|
||
}
|
||
|
||
template <>
|
||
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,
|
||
0x91376c36d99995be, 0x23100809b9c21fa1,
|
||
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0xfd87b5f28300ca0d, 0x8bca9d6e188853fc,
|
||
0x9e74d1b791e07e48, 0x775ea264cf55347e,
|
||
0xc612062576589dda, 0x95364afe032a819e,
|
||
0xf79687aed3eec551, 0x3a83ddbd83f52205,
|
||
0x9abe14cd44753b52, 0xc4926a9672793543,
|
||
0xc16d9a0095928a27, 0x75b7053c0f178294,
|
||
0xf1c90080baf72cb1, 0x5324c68b12dd6339,
|
||
0x971da05074da7bee, 0xd3f6fc16ebca5e04,
|
||
0xbce5086492111aea, 0x88f4bb1ca6bcf585,
|
||
0xec1e4a7db69561a5, 0x2b31e9e3d06c32e6,
|
||
0x9392ee8e921d5d07, 0x3aff322e62439fd0,
|
||
0xb877aa3236a4b449, 0x9befeb9fad487c3,
|
||
0xe69594bec44de15b, 0x4c2ebe687989a9b4,
|
||
0x901d7cf73ab0acd9, 0xf9d37014bf60a11,
|
||
0xb424dc35095cd80f, 0x538484c19ef38c95,
|
||
0xe12e13424bb40e13, 0x2865a5f206b06fba,
|
||
0x8cbccc096f5088cb, 0xf93f87b7442e45d4,
|
||
0xafebff0bcb24aafe, 0xf78f69a51539d749,
|
||
0xdbe6fecebdedd5be, 0xb573440e5a884d1c,
|
||
0x89705f4136b4a597, 0x31680a88f8953031,
|
||
0xabcc77118461cefc, 0xfdc20d2b36ba7c3e,
|
||
0xd6bf94d5e57a42bc, 0x3d32907604691b4d,
|
||
0x8637bd05af6c69b5, 0xa63f9a49c2c1b110,
|
||
0xa7c5ac471b478423, 0xfcf80dc33721d54,
|
||
0xd1b71758e219652b, 0xd3c36113404ea4a9,
|
||
0x83126e978d4fdf3b, 0x645a1cac083126ea,
|
||
0xa3d70a3d70a3d70a, 0x3d70a3d70a3d70a4,
|
||
0xcccccccccccccccc, 0xcccccccccccccccd,
|
||
0x8000000000000000, 0x0,
|
||
0xa000000000000000, 0x0,
|
||
0xc800000000000000, 0x0,
|
||
0xfa00000000000000, 0x0,
|
||
0x9c40000000000000, 0x0,
|
||
0xc350000000000000, 0x0,
|
||
0xf424000000000000, 0x0,
|
||
0x9896800000000000, 0x0,
|
||
0xbebc200000000000, 0x0,
|
||
0xee6b280000000000, 0x0,
|
||
0x9502f90000000000, 0x0,
|
||
0xba43b74000000000, 0x0,
|
||
0xe8d4a51000000000, 0x0,
|
||
0x9184e72a00000000, 0x0,
|
||
0xb5e620f480000000, 0x0,
|
||
0xe35fa931a0000000, 0x0,
|
||
0x8e1bc9bf04000000, 0x0,
|
||
0xb1a2bc2ec5000000, 0x0,
|
||
0xde0b6b3a76400000, 0x0,
|
||
0x8ac7230489e80000, 0x0,
|
||
0xad78ebc5ac620000, 0x0,
|
||
0xd8d726b7177a8000, 0x0,
|
||
0x878678326eac9000, 0x0,
|
||
0xa968163f0a57b400, 0x0,
|
||
0xd3c21bcecceda100, 0x0,
|
||
0x84595161401484a0, 0x0,
|
||
0xa56fa5b99019a5c8, 0x0,
|
||
0xcecb8f27f4200f3a, 0x0,
|
||
0x813f3978f8940984, 0x4000000000000000,
|
||
0xa18f07d736b90be5, 0x5000000000000000,
|
||
0xc9f2c9cd04674ede, 0xa400000000000000,
|
||
0xfc6f7c4045812296, 0x4d00000000000000,
|
||
0x9dc5ada82b70b59d, 0xf020000000000000,
|
||
0xc5371912364ce305, 0x6c28000000000000,
|
||
0xf684df56c3e01bc6, 0xc732000000000000,
|
||
0x9a130b963a6c115c, 0x3c7f400000000000,
|
||
0xc097ce7bc90715b3, 0x4b9f100000000000,
|
||
0xf0bdc21abb48db20, 0x1e86d40000000000,
|
||
0x96769950b50d88f4, 0x1314448000000000,
|
||
0xbc143fa4e250eb31, 0x17d955a000000000,
|
||
0xeb194f8e1ae525fd, 0x5dcfab0800000000,
|
||
0x92efd1b8d0cf37be, 0x5aa1cae500000000,
|
||
0xb7abc627050305ad, 0xf14a3d9e40000000,
|
||
0xe596b7b0c643c719, 0x6d9ccd05d0000000,
|
||
0x8f7e32ce7bea5c6f, 0xe4820023a2000000,
|
||
0xb35dbf821ae4f38b, 0xdda2802c8a800000,
|
||
0xe0352f62a19e306e, 0xd50b2037ad200000,
|
||
0x8c213d9da502de45, 0x4526f422cc340000,
|
||
0xaf298d050e4395d6, 0x9670b12b7f410000,
|
||
0xdaf3f04651d47b4c, 0x3c0cdd765f114000,
|
||
0x88d8762bf324cd0f, 0xa5880a69fb6ac800,
|
||
0xab0e93b6efee0053, 0x8eea0d047a457a00,
|
||
0xd5d238a4abe98068, 0x72a4904598d6d880,
|
||
0x85a36366eb71f041, 0x47a6da2b7f864750,
|
||
0xa70c3c40a64e6c51, 0x999090b65f67d924,
|
||
0xd0cf4b50cfe20765, 0xfff4b4e3f741cf6d,
|
||
0x82818f1281ed449f, 0xbff8f10e7a8921a4,
|
||
0xa321f2d7226895c7, 0xaff72d52192b6a0d,
|
||
0xcbea6f8ceb02bb39, 0x9bf4f8a69f764490,
|
||
0xfee50b7025c36a08, 0x2f236d04753d5b4,
|
||
0x9f4f2726179a2245, 0x1d762422c946590,
|
||
0xc722f0ef9d80aad6, 0x424d3ad2b7b97ef5,
|
||
0xf8ebad2b84e0d58b, 0xd2e0898765a7deb2,
|
||
0x9b934c3b330c8577, 0x63cc55f49f88eb2f,
|
||
0xc2781f49ffcfa6d5, 0x3cbf6b71c76b25fb,
|
||
0xf316271c7fc3908a, 0x8bef464e3945ef7a,
|
||
0x97edd871cfda3a56, 0x97758bf0e3cbb5ac,
|
||
0xbde94e8e43d0c8ec, 0x3d52eeed1cbea317,
|
||
0xed63a231d4c4fb27, 0x4ca7aaa863ee4bdd,
|
||
0x945e455f24fb1cf8, 0x8fe8caa93e74ef6a,
|
||
0xb975d6b6ee39e436, 0xb3e2fd538e122b44,
|
||
0xe7d34c64a9c85d44, 0x60dbbca87196b616,
|
||
0x90e40fbeea1d3a4a, 0xbc8955e946fe31cd,
|
||
0xb51d13aea4a488dd, 0x6babab6398bdbe41,
|
||
0xe264589a4dcdab14, 0xc696963c7eed2dd1,
|
||
0x8d7eb76070a08aec, 0xfc1e1de5cf543ca2,
|
||
0xb0de65388cc8ada8, 0x3b25a55f43294bcb,
|
||
0xdd15fe86affad912, 0x49ef0eb713f39ebe,
|
||
0x8a2dbf142dfcc7ab, 0x6e3569326c784337,
|
||
0xacb92ed9397bf996, 0x49c2c37f07965404,
|
||
0xd7e77a8f87daf7fb, 0xdc33745ec97be906,
|
||
0x86f0ac99b4e8dafd, 0x69a028bb3ded71a3,
|
||
0xa8acd7c0222311bc, 0xc40832ea0d68ce0c,
|
||
0xd2d80db02aabd62b, 0xf50a3fa490c30190,
|
||
0x83c7088e1aab65db, 0x792667c6da79e0fa,
|
||
0xa4b8cab1a1563f52, 0x577001b891185938,
|
||
0xcde6fd5e09abcf26, 0xed4c0226b55e6f86,
|
||
0x80b05e5ac60b6178, 0x544f8158315b05b4,
|
||
0xa0dc75f1778e39d6, 0x696361ae3db1c721,
|
||
0xc913936dd571c84c, 0x3bc3a19cd1e38e9,
|
||
0xfb5878494ace3a5f, 0x4ab48a04065c723,
|
||
0x9d174b2dcec0e47b, 0x62eb0d64283f9c76,
|
||
0xc45d1df942711d9a, 0x3ba5d0bd324f8394,
|
||
0xf5746577930d6500, 0xca8f44ec7ee36479,
|
||
0x9968bf6abbe85f20, 0x7e998b13cf4e1ecb,
|
||
0xbfc2ef456ae276e8, 0x9e3fedd8c321a67e,
|
||
0xefb3ab16c59b14a2, 0xc5cfe94ef3ea101e,
|
||
0x95d04aee3b80ece5, 0xbba1f1d158724a12,
|
||
0xbb445da9ca61281f, 0x2a8a6e45ae8edc97,
|
||
0xea1575143cf97226, 0xf52d09d71a3293bd,
|
||
0x924d692ca61be758, 0x593c2626705f9c56,
|
||
0xb6e0c377cfa2e12e, 0x6f8b2fb00c77836c,
|
||
0xe498f455c38b997a, 0xb6dfb9c0f956447,
|
||
0x8edf98b59a373fec, 0x4724bd4189bd5eac,
|
||
0xb2977ee300c50fe7, 0x58edec91ec2cb657,
|
||
0xdf3d5e9bc0f653e1, 0x2f2967b66737e3ed,
|
||
0x8b865b215899f46c, 0xbd79e0d20082ee74,
|
||
0xae67f1e9aec07187, 0xecd8590680a3aa11,
|
||
0xda01ee641a708de9, 0xe80e6f4820cc9495,
|
||
0x884134fe908658b2, 0x3109058d147fdcdd,
|
||
0xaa51823e34a7eede, 0xbd4b46f0599fd415,
|
||
0xd4e5e2cdc1d1ea96, 0x6c9e18ac7007c91a,
|
||
0x850fadc09923329e, 0x3e2cf6bc604ddb0,
|
||
0xa6539930bf6bff45, 0x84db8346b786151c,
|
||
0xcfe87f7cef46ff16, 0xe612641865679a63,
|
||
0x81f14fae158c5f6e, 0x4fcb7e8f3f60c07e,
|
||
0xa26da3999aef7749, 0xe3be5e330f38f09d,
|
||
0xcb090c8001ab551c, 0x5cadf5bfd3072cc5,
|
||
0xfdcb4fa002162a63, 0x73d9732fc7c8f7f6,
|
||
0x9e9f11c4014dda7e, 0x2867e7fddcdd9afa,
|
||
0xc646d63501a1511d, 0xb281e1fd541501b8,
|
||
0xf7d88bc24209a565, 0x1f225a7ca91a4226,
|
||
0x9ae757596946075f, 0x3375788de9b06958,
|
||
0xc1a12d2fc3978937, 0x52d6b1641c83ae,
|
||
0xf209787bb47d6b84, 0xc0678c5dbd23a49a,
|
||
0x9745eb4d50ce6332, 0xf840b7ba963646e0,
|
||
0xbd176620a501fbff, 0xb650e5a93bc3d898,
|
||
0xec5d3fa8ce427aff, 0xa3e51f138ab4cebe,
|
||
0x93ba47c980e98cdf, 0xc66f336c36b10137,
|
||
0xb8a8d9bbe123f017, 0xb80b0047445d4184,
|
||
0xe6d3102ad96cec1d, 0xa60dc059157491e5,
|
||
0x9043ea1ac7e41392, 0x87c89837ad68db2f,
|
||
0xb454e4a179dd1877, 0x29babe4598c311fb,
|
||
0xe16a1dc9d8545e94, 0xf4296dd6fef3d67a,
|
||
0x8ce2529e2734bb1d, 0x1899e4a65f58660c,
|
||
0xb01ae745b101e9e4, 0x5ec05dcff72e7f8f,
|
||
0xdc21a1171d42645d, 0x76707543f4fa1f73,
|
||
0x899504ae72497eba, 0x6a06494a791c53a8,
|
||
0xabfa45da0edbde69, 0x487db9d17636892,
|
||
0xd6f8d7509292d603, 0x45a9d2845d3c42b6,
|
||
0x865b86925b9bc5c2, 0xb8a2392ba45a9b2,
|
||
0xa7f26836f282b732, 0x8e6cac7768d7141e,
|
||
0xd1ef0244af2364ff, 0x3207d795430cd926,
|
||
0x8335616aed761f1f, 0x7f44e6bd49e807b8,
|
||
0xa402b9c5a8d3a6e7, 0x5f16206c9c6209a6,
|
||
0xcd036837130890a1, 0x36dba887c37a8c0f,
|
||
0x802221226be55a64, 0xc2494954da2c9789,
|
||
0xa02aa96b06deb0fd, 0xf2db9baa10b7bd6c,
|
||
0xc83553c5c8965d3d, 0x6f92829494e5acc7,
|
||
0xfa42a8b73abbf48c, 0xcb772339ba1f17f9,
|
||
0x9c69a97284b578d7, 0xff2a760414536efb,
|
||
0xc38413cf25e2d70d, 0xfef5138519684aba,
|
||
0xf46518c2ef5b8cd1, 0x7eb258665fc25d69,
|
||
0x98bf2f79d5993802, 0xef2f773ffbd97a61,
|
||
0xbeeefb584aff8603, 0xaafb550ffacfd8fa,
|
||
0xeeaaba2e5dbf6784, 0x95ba2a53f983cf38,
|
||
0x952ab45cfa97a0b2, 0xdd945a747bf26183,
|
||
0xba756174393d88df, 0x94f971119aeef9e4,
|
||
0xe912b9d1478ceb17, 0x7a37cd5601aab85d,
|
||
0x91abb422ccb812ee, 0xac62e055c10ab33a,
|
||
0xb616a12b7fe617aa, 0x577b986b314d6009,
|
||
0xe39c49765fdf9d94, 0xed5a7e85fda0b80b,
|
||
0x8e41ade9fbebc27d, 0x14588f13be847307,
|
||
0xb1d219647ae6b31c, 0x596eb2d8ae258fc8,
|
||
0xde469fbd99a05fe3, 0x6fca5f8ed9aef3bb,
|
||
0x8aec23d680043bee, 0x25de7bb9480d5854,
|
||
0xada72ccc20054ae9, 0xaf561aa79a10ae6a,
|
||
0xd910f7ff28069da4, 0x1b2ba1518094da04,
|
||
0x87aa9aff79042286, 0x90fb44d2f05d0842,
|
||
0xa99541bf57452b28, 0x353a1607ac744a53,
|
||
0xd3fa922f2d1675f2, 0x42889b8997915ce8,
|
||
0x847c9b5d7c2e09b7, 0x69956135febada11,
|
||
0xa59bc234db398c25, 0x43fab9837e699095,
|
||
0xcf02b2c21207ef2e, 0x94f967e45e03f4bb,
|
||
0x8161afb94b44f57d, 0x1d1be0eebac278f5,
|
||
0xa1ba1ba79e1632dc, 0x6462d92a69731732,
|
||
0xca28a291859bbf93, 0x7d7b8f7503cfdcfe,
|
||
0xfcb2cb35e702af78, 0x5cda735244c3d43e,
|
||
0x9defbf01b061adab, 0x3a0888136afa64a7,
|
||
0xc56baec21c7a1916, 0x88aaa1845b8fdd0,
|
||
0xf6c69a72a3989f5b, 0x8aad549e57273d45,
|
||
0x9a3c2087a63f6399, 0x36ac54e2f678864b,
|
||
0xc0cb28a98fcf3c7f, 0x84576a1bb416a7dd,
|
||
0xf0fdf2d3f3c30b9f, 0x656d44a2a11c51d5,
|
||
0x969eb7c47859e743, 0x9f644ae5a4b1b325,
|
||
0xbc4665b596706114, 0x873d5d9f0dde1fee,
|
||
0xeb57ff22fc0c7959, 0xa90cb506d155a7ea,
|
||
0x9316ff75dd87cbd8, 0x9a7f12442d588f2,
|
||
0xb7dcbf5354e9bece, 0xc11ed6d538aeb2f,
|
||
0xe5d3ef282a242e81, 0x8f1668c8a86da5fa,
|
||
0x8fa475791a569d10, 0xf96e017d694487bc,
|
||
0xb38d92d760ec4455, 0x37c981dcc395a9ac,
|
||
0xe070f78d3927556a, 0x85bbe253f47b1417,
|
||
0x8c469ab843b89562, 0x93956d7478ccec8e,
|
||
0xaf58416654a6babb, 0x387ac8d1970027b2,
|
||
0xdb2e51bfe9d0696a, 0x6997b05fcc0319e,
|
||
0x88fcf317f22241e2, 0x441fece3bdf81f03,
|
||
0xab3c2fddeeaad25a, 0xd527e81cad7626c3,
|
||
0xd60b3bd56a5586f1, 0x8a71e223d8d3b074,
|
||
0x85c7056562757456, 0xf6872d5667844e49,
|
||
0xa738c6bebb12d16c, 0xb428f8ac016561db,
|
||
0xd106f86e69d785c7, 0xe13336d701beba52,
|
||
0x82a45b450226b39c, 0xecc0024661173473,
|
||
0xa34d721642b06084, 0x27f002d7f95d0190,
|
||
0xcc20ce9bd35c78a5, 0x31ec038df7b441f4,
|
||
0xff290242c83396ce, 0x7e67047175a15271,
|
||
0x9f79a169bd203e41, 0xf0062c6e984d386,
|
||
0xc75809c42c684dd1, 0x52c07b78a3e60868,
|
||
0xf92e0c3537826145, 0xa7709a56ccdf8a82,
|
||
0x9bbcc7a142b17ccb, 0x88a66076400bb691,
|
||
0xc2abf989935ddbfe, 0x6acff893d00ea435,
|
||
0xf356f7ebf83552fe, 0x583f6b8c4124d43,
|
||
0x98165af37b2153de, 0xc3727a337a8b704a,
|
||
0xbe1bf1b059e9a8d6, 0x744f18c0592e4c5c,
|
||
0xeda2ee1c7064130c, 0x1162def06f79df73,
|
||
0x9485d4d1c63e8be7, 0x8addcb5645ac2ba8,
|
||
0xb9a74a0637ce2ee1, 0x6d953e2bd7173692,
|
||
0xe8111c87c5c1ba99, 0xc8fa8db6ccdd0437,
|
||
0x910ab1d4db9914a0, 0x1d9c9892400a22a2,
|
||
0xb54d5e4a127f59c8, 0x2503beb6d00cab4b,
|
||
0xe2a0b5dc971f303a, 0x2e44ae64840fd61d,
|
||
0x8da471a9de737e24, 0x5ceaecfed289e5d2,
|
||
0xb10d8e1456105dad, 0x7425a83e872c5f47,
|
||
0xdd50f1996b947518, 0xd12f124e28f77719,
|
||
0x8a5296ffe33cc92f, 0x82bd6b70d99aaa6f,
|
||
0xace73cbfdc0bfb7b, 0x636cc64d1001550b,
|
||
0xd8210befd30efa5a, 0x3c47f7e05401aa4e,
|
||
0x8714a775e3e95c78, 0x65acfaec34810a71,
|
||
0xa8d9d1535ce3b396, 0x7f1839a741a14d0d,
|
||
0xd31045a8341ca07c, 0x1ede48111209a050,
|
||
0x83ea2b892091e44d, 0x934aed0aab460432,
|
||
0xa4e4b66b68b65d60, 0xf81da84d5617853f,
|
||
0xce1de40642e3f4b9, 0x36251260ab9d668e,
|
||
0x80d2ae83e9ce78f3, 0xc1d72b7c6b426019,
|
||
0xa1075a24e4421730, 0xb24cf65b8612f81f,
|
||
0xc94930ae1d529cfc, 0xdee033f26797b627,
|
||
0xfb9b7cd9a4a7443c, 0x169840ef017da3b1,
|
||
0x9d412e0806e88aa5, 0x8e1f289560ee864e,
|
||
0xc491798a08a2ad4e, 0xf1a6f2bab92a27e2,
|
||
0xf5b5d7ec8acb58a2, 0xae10af696774b1db,
|
||
0x9991a6f3d6bf1765, 0xacca6da1e0a8ef29,
|
||
0xbff610b0cc6edd3f, 0x17fd090a58d32af3,
|
||
0xeff394dcff8a948e, 0xddfc4b4cef07f5b0,
|
||
0x95f83d0a1fb69cd9, 0x4abdaf101564f98e,
|
||
0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f1,
|
||
0xea53df5fd18d5513, 0x84c86189216dc5ed,
|
||
0x92746b9be2f8552c, 0x32fd3cf5b4e49bb4,
|
||
0xb7118682dbb66a77, 0x3fbc8c33221dc2a1,
|
||
0xe4d5e82392a40515, 0xfabaf3feaa5334a,
|
||
0x8f05b1163ba6832d, 0x29cb4d87f2a7400e,
|
||
0xb2c71d5bca9023f8, 0x743e20e9ef511012,
|
||
0xdf78e4b2bd342cf6, 0x914da9246b255416,
|
||
0x8bab8eefb6409c1a, 0x1ad089b6c2f7548e,
|
||
0xae9672aba3d0c320, 0xa184ac2473b529b1,
|
||
0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741e,
|
||
0x8865899617fb1871, 0x7e2fa67c7a658892,
|
||
0xaa7eebfb9df9de8d, 0xddbb901b98feeab7,
|
||
0xd51ea6fa85785631, 0x552a74227f3ea565,
|
||
0x8533285c936b35de, 0xd53a88958f87275f,
|
||
0xa67ff273b8460356, 0x8a892abaf368f137,
|
||
0xd01fef10a657842c, 0x2d2b7569b0432d85,
|
||
0x8213f56a67f6b29b, 0x9c3b29620e29fc73,
|
||
0xa298f2c501f45f42, 0x8349f3ba91b47b8f,
|
||
0xcb3f2f7642717713, 0x241c70a936219a73,
|
||
0xfe0efb53d30dd4d7, 0xed238cd383aa0110,
|
||
0x9ec95d1463e8a506, 0xf4363804324a40aa,
|
||
0xc67bb4597ce2ce48, 0xb143c6053edcd0d5,
|
||
0xf81aa16fdc1b81da, 0xdd94b7868e94050a,
|
||
0x9b10a4e5e9913128, 0xca7cf2b4191c8326,
|
||
0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f0,
|
||
0xf24a01a73cf2dccf, 0xbc633b39673c8cec,
|
||
0x976e41088617ca01, 0xd5be0503e085d813,
|
||
0xbd49d14aa79dbc82, 0x4b2d8644d8a74e18,
|
||
0xec9c459d51852ba2, 0xddf8e7d60ed1219e,
|
||
0x93e1ab8252f33b45, 0xcabb90e5c942b503,
|
||
0xb8da1662e7b00a17, 0x3d6a751f3b936243,
|
||
0xe7109bfba19c0c9d, 0xcc512670a783ad4,
|
||
0x906a617d450187e2, 0x27fb2b80668b24c5,
|
||
0xb484f9dc9641e9da, 0xb1f9f660802dedf6,
|
||
0xe1a63853bbd26451, 0x5e7873f8a0396973,
|
||
0x8d07e33455637eb2, 0xdb0b487b6423e1e8,
|
||
0xb049dc016abc5e5f, 0x91ce1a9a3d2cda62,
|
||
0xdc5c5301c56b75f7, 0x7641a140cc7810fb,
|
||
0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9d,
|
||
0xac2820d9623bf429, 0x546345fa9fbdcd44,
|
||
0xd732290fbacaf133, 0xa97c177947ad4095,
|
||
0x867f59a9d4bed6c0, 0x49ed8eabcccc485d,
|
||
0xa81f301449ee8c70, 0x5c68f256bfff5a74,
|
||
0xd226fc195c6a2f8c, 0x73832eec6fff3111,
|
||
0x83585d8fd9c25db7, 0xc831fd53c5ff7eab,
|
||
0xa42e74f3d032f525, 0xba3e7ca8b77f5e55,
|
||
0xcd3a1230c43fb26f, 0x28ce1bd2e55f35eb,
|
||
0x80444b5e7aa7cf85, 0x7980d163cf5b81b3,
|
||
0xa0555e361951c366, 0xd7e105bcc332621f,
|
||
0xc86ab5c39fa63440, 0x8dd9472bf3fefaa7,
|
||
0xfa856334878fc150, 0xb14f98f6f0feb951,
|
||
0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d3,
|
||
0xc3b8358109e84f07, 0xa862f80ec4700c8,
|
||
0xf4a642e14c6262c8, 0xcd27bb612758c0fa,
|
||
0x98e7e9cccfbd7dbd, 0x8038d51cb897789c,
|
||
0xbf21e44003acdd2c, 0xe0470a63e6bd56c3,
|
||
0xeeea5d5004981478, 0x1858ccfce06cac74,
|
||
0x95527a5202df0ccb, 0xf37801e0c43ebc8,
|
||
0xbaa718e68396cffd, 0xd30560258f54e6ba,
|
||
0xe950df20247c83fd, 0x47c6b82ef32a2069,
|
||
0x91d28b7416cdd27e, 0x4cdc331d57fa5441,
|
||
0xb6472e511c81471d, 0xe0133fe4adf8e952,
|
||
0xe3d8f9e563a198e5, 0x58180fddd97723a6,
|
||
0x8e679c2f5e44ff8f, 0x570f09eaa7ea7648,
|
||
};
|
||
using powers = powers_template<>;
|
||
|
||
} // namespace fast_float
|
||
|
||
#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 <climits>
|
||
#include <cstdint>
|
||
#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
|