2450 lines
92 KiB
C++
2450 lines
92 KiB
C++
// fast_float by Daniel Lemire
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// fast_float by João Paulo Magalhaes
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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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// 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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#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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explicit parse_options(chars_format fmt = chars_format::general,
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char dot = '.')
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: format(fmt), decimal_point(dot) {}
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/** Which number formats are accepted */
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chars_format format;
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/** The character used as decimal point */
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char decimal_point;
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};
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/**
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* This function parses the character sequence [first,last) for a number. It parses floating-point numbers expecting
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* a locale-indepent format equivalent to what is used by std::strtod in the default ("C") locale.
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* The resulting floating-point value is the closest floating-point values (using either float or double),
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* using the "round to even" convention for values that would otherwise fall right in-between two values.
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* That is, we provide exact parsing according to the IEEE standard.
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*
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* Given a successful parse, the pointer (`ptr`) in the returned value is set to point right after the
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* parsed number, and the `value` referenced is set to the parsed value. In case of error, the returned
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* `ec` contains a representative error, otherwise the default (`std::errc()`) value is stored.
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*
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* The implementation does not throw and does not allocate memory (e.g., with `new` or `malloc`).
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*
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* Like the C++17 standard, the `fast_float::from_chars` functions take an optional last argument of
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* the type `fast_float::chars_format`. It is a bitset value: we check whether
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* `fmt & fast_float::chars_format::fixed` and `fmt & fast_float::chars_format::scientific` are set
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* to determine whether we allowe the fixed point and scientific notation respectively.
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* The default is `fast_float::chars_format::general` which allows both `fixed` and `scientific`.
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*/
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template<typename T>
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from_chars_result from_chars(const char *first, const char *last,
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T &value, chars_format fmt = chars_format::general) noexcept;
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/**
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* Like from_chars, but accepts an `options` argument to govern number parsing.
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*/
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template<typename T>
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from_chars_result from_chars_advanced(const char *first, const char *last,
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T &value, parse_options options) noexcept;
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}
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#endif // FASTFLOAT_FAST_FLOAT_H
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#ifndef FASTFLOAT_FLOAT_COMMON_H
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#define FASTFLOAT_FLOAT_COMMON_H
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#include <cfloat>
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#include <cstdint>
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#include <cassert>
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#if (defined(__x86_64) || defined(__x86_64__) || defined(_M_X64) \
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|| defined(__amd64) || defined(__aarch64__) || defined(_M_ARM64) \
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|| defined(__MINGW64__) \
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|| defined(__s390x__) \
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|| (defined(__ppc64__) || defined(__PPC64__) || defined(__ppc64le__) || defined(__PPC64LE__)) \
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|| defined(__EMSCRIPTEN__))
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#define FASTFLOAT_64BIT
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#elif (defined(__i386) || defined(__i386__) || defined(_M_IX86) \
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|| defined(__arm__) || defined(_M_ARM) \
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|| defined(__MINGW32__))
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#define FASTFLOAT_32BIT
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#else
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// Need to check incrementally, since SIZE_MAX is a size_t, avoid overflow.
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// We can never tell the register width, but the SIZE_MAX is a good approximation.
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// UINTPTR_MAX and INTPTR_MAX are optional, so avoid them for max portability.
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#if SIZE_MAX == 0xffff
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#error Unknown platform (16-bit, unsupported)
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#elif SIZE_MAX == 0xffffffff
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#define FASTFLOAT_32BIT
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#elif SIZE_MAX == 0xffffffffffffffff
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#define FASTFLOAT_64BIT
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#else
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#error Unknown platform (not 32-bit, not 64-bit?)
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#endif
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#endif
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#if ((defined(_WIN32) || defined(_WIN64)) && !defined(__clang__))
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#include <intrin.h>
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#endif
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#if defined(_MSC_VER) && !defined(__clang__)
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#define FASTFLOAT_VISUAL_STUDIO 1
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#endif
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#ifdef _WIN32
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#define FASTFLOAT_IS_BIG_ENDIAN 0
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#else
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#if defined(__APPLE__) || defined(__FreeBSD__)
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#include <machine/endian.h>
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#elif defined(sun) || defined(__sun)
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#include <sys/byteorder.h>
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#else
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#include <endian.h>
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#endif
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#
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#ifndef __BYTE_ORDER__
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// safe choice
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#define FASTFLOAT_IS_BIG_ENDIAN 0
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#endif
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#
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#ifndef __ORDER_LITTLE_ENDIAN__
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// safe choice
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#define FASTFLOAT_IS_BIG_ENDIAN 0
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#endif
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#
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#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
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#define FASTFLOAT_IS_BIG_ENDIAN 0
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#else
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#define FASTFLOAT_IS_BIG_ENDIAN 1
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#endif
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#endif
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#ifdef FASTFLOAT_VISUAL_STUDIO
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#define fastfloat_really_inline __forceinline
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#else
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#define fastfloat_really_inline inline __attribute__((always_inline))
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#endif
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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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namespace {
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constexpr uint32_t max_digits = 768;
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constexpr uint32_t max_digit_without_overflow = 19;
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constexpr int32_t decimal_point_range = 2047;
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} // namespace
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struct value128 {
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uint64_t low;
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uint64_t high;
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value128(uint64_t _low, uint64_t _high) : low(_low), high(_high) {}
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value128() : low(0), high(0) {}
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};
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/* result might be undefined when input_num is zero */
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fastfloat_really_inline int leading_zeroes(uint64_t input_num) {
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assert(input_num > 0);
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#ifdef FASTFLOAT_VISUAL_STUDIO
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#if defined(_M_X64) || defined(_M_ARM64)
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unsigned long leading_zero = 0;
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// Search the mask data from most significant bit (MSB)
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// to least significant bit (LSB) for a set bit (1).
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_BitScanReverse64(&leading_zero, input_num);
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return (int)(63 - leading_zero);
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#else
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int last_bit = 0;
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if(input_num & uint64_t(0xffffffff00000000)) input_num >>= 32, last_bit |= 32;
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if(input_num & uint64_t( 0xffff0000)) input_num >>= 16, last_bit |= 16;
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if(input_num & uint64_t( 0xff00)) input_num >>= 8, last_bit |= 8;
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if(input_num & uint64_t( 0xf0)) input_num >>= 4, last_bit |= 4;
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if(input_num & uint64_t( 0xc)) input_num >>= 2, last_bit |= 2;
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if(input_num & uint64_t( 0x2)) input_num >>= 1, last_bit |= 1;
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return 63 - last_bit;
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#endif
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#else
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return __builtin_clzll(input_num);
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#endif
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}
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#ifdef FASTFLOAT_32BIT
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// slow emulation routine for 32-bit
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fastfloat_really_inline uint64_t emulu(uint32_t x, uint32_t y) {
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return x * (uint64_t)y;
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}
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// slow emulation routine for 32-bit
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#if !defined(__MINGW64__)
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fastfloat_really_inline uint64_t _umul128(uint64_t ab, uint64_t cd,
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uint64_t *hi) {
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uint64_t ad = emulu((uint32_t)(ab >> 32), (uint32_t)cd);
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uint64_t bd = emulu((uint32_t)ab, (uint32_t)cd);
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uint64_t adbc = ad + emulu((uint32_t)ab, (uint32_t)(cd >> 32));
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uint64_t adbc_carry = !!(adbc < ad);
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uint64_t lo = bd + (adbc << 32);
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*hi = emulu((uint32_t)(ab >> 32), (uint32_t)(cd >> 32)) + (adbc >> 32) +
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(adbc_carry << 32) + !!(lo < bd);
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return lo;
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}
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#endif // !__MINGW64__
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#endif // FASTFLOAT_32BIT
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// compute 64-bit a*b
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fastfloat_really_inline value128 full_multiplication(uint64_t a,
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uint64_t b) {
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value128 answer;
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#ifdef _M_ARM64
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// ARM64 has native support for 64-bit multiplications, no need to emulate
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answer.high = __umulh(a, b);
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answer.low = a * b;
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#elif defined(FASTFLOAT_32BIT) || (defined(_WIN64) && !defined(__clang__))
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answer.low = _umul128(a, b, &answer.high); // _umul128 not available on ARM64
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#elif defined(FASTFLOAT_64BIT)
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__uint128_t r = ((__uint128_t)a) * b;
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answer.low = uint64_t(r);
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answer.high = uint64_t(r >> 64);
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#else
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#error Not implemented
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#endif
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return answer;
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}
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struct adjusted_mantissa {
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uint64_t mantissa{0};
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int 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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struct decimal {
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uint32_t num_digits{0};
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int32_t decimal_point{0};
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bool negative{false};
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bool truncated{false};
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uint8_t digits[max_digits];
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decimal() = default;
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// Copies are not allowed since this is a fat object.
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decimal(const decimal &) = delete;
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// Copies are not allowed since this is a fat object.
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decimal &operator=(const decimal &) = delete;
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// Moves are allowed:
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decimal(decimal &&) = default;
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decimal &operator=(decimal &&other) = default;
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};
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constexpr static double powers_of_ten_double[] = {
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1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11,
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1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22};
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constexpr static float powers_of_ten_float[] = {1e0, 1e1, 1e2, 1e3, 1e4, 1e5,
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1e6, 1e7, 1e8, 1e9, 1e10};
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template <typename T> struct binary_format {
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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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};
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template <> inline constexpr int binary_format<double>::mantissa_explicit_bits() {
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return 52;
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}
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template <> inline constexpr int binary_format<float>::mantissa_explicit_bits() {
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return 23;
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}
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template <> inline constexpr int binary_format<double>::max_exponent_round_to_even() {
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return 23;
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}
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template <> inline constexpr int binary_format<float>::max_exponent_round_to_even() {
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return 10;
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}
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template <> inline constexpr int binary_format<double>::min_exponent_round_to_even() {
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return -4;
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}
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template <> inline constexpr int binary_format<float>::min_exponent_round_to_even() {
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return -17;
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}
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template <> inline constexpr int binary_format<double>::minimum_exponent() {
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return -1023;
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}
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template <> inline constexpr int binary_format<float>::minimum_exponent() {
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return -127;
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}
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template <> inline constexpr int binary_format<double>::infinite_power() {
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return 0x7FF;
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}
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template <> inline constexpr int binary_format<float>::infinite_power() {
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return 0xFF;
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}
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template <> inline constexpr int binary_format<double>::sign_index() { return 63; }
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template <> inline constexpr int binary_format<float>::sign_index() { return 31; }
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template <> inline constexpr int binary_format<double>::min_exponent_fast_path() {
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#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
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return 0;
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#else
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return -22;
|
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#endif
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}
|
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template <> inline constexpr int binary_format<float>::min_exponent_fast_path() {
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#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
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return 0;
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#else
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return -10;
|
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#endif
|
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}
|
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|
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template <> inline constexpr int binary_format<double>::max_exponent_fast_path() {
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return 22;
|
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}
|
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template <> inline constexpr int binary_format<float>::max_exponent_fast_path() {
|
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return 10;
|
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}
|
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|
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template <> inline constexpr uint64_t binary_format<double>::max_mantissa_fast_path() {
|
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return uint64_t(2) << mantissa_explicit_bits();
|
||
}
|
||
template <> inline constexpr uint64_t binary_format<float>::max_mantissa_fast_path() {
|
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return uint64_t(2) << mantissa_explicit_bits();
|
||
}
|
||
|
||
template <>
|
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inline constexpr double binary_format<double>::exact_power_of_ten(int64_t power) {
|
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return powers_of_ten_double[power];
|
||
}
|
||
template <>
|
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inline constexpr float binary_format<float>::exact_power_of_ten(int64_t power) {
|
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|
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return powers_of_ten_float[power];
|
||
}
|
||
|
||
|
||
template <>
|
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inline constexpr int binary_format<double>::largest_power_of_ten() {
|
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return 308;
|
||
}
|
||
template <>
|
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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;
|
||
}
|
||
|
||
} // namespace fast_float
|
||
|
||
// for convenience:
|
||
template<class OStream>
|
||
inline OStream& operator<<(OStream &out, const fast_float::decimal &d) {
|
||
out << "0.";
|
||
for (size_t i = 0; i < d.num_digits; i++) {
|
||
out << int32_t(d.digits[i]);
|
||
}
|
||
out << " * 10 ** " << d.decimal_point;
|
||
return out;
|
||
}
|
||
|
||
#endif
|
||
|
||
|
||
#ifndef FASTFLOAT_ASCII_NUMBER_H
|
||
#define FASTFLOAT_ASCII_NUMBER_H
|
||
|
||
#include <cstdio>
|
||
#include <cctype>
|
||
#include <cstdint>
|
||
#include <cstring>
|
||
|
||
|
||
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));
|
||
}
|
||
|
||
struct parsed_number_string {
|
||
int64_t exponent;
|
||
uint64_t mantissa;
|
||
const char *lastmatch;
|
||
bool negative;
|
||
bool valid;
|
||
bool too_many_digits;
|
||
};
|
||
|
||
|
||
// Assuming that you use no more than 19 digits, this will
|
||
// parse an ASCII string.
|
||
fastfloat_really_inline
|
||
parsed_number_string parse_number_string(const char *p, const char *pend, parse_options options) noexcept {
|
||
const chars_format fmt = options.format;
|
||
const char decimal_point = options.decimal_point;
|
||
|
||
parsed_number_string answer;
|
||
answer.valid = false;
|
||
answer.too_many_digits = false;
|
||
answer.negative = (*p == '-');
|
||
if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
|
||
++p;
|
||
if (p == pend) {
|
||
return answer;
|
||
}
|
||
if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot
|
||
return answer;
|
||
}
|
||
}
|
||
const char *const start_digits = p;
|
||
|
||
uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad)
|
||
|
||
while ((p != pend) && is_integer(*p)) {
|
||
// a multiplication by 10 is cheaper than an arbitrary integer
|
||
// multiplication
|
||
i = 10 * i +
|
||
uint64_t(*p - '0'); // might overflow, we will handle the overflow later
|
||
++p;
|
||
}
|
||
const char *const end_of_integer_part = p;
|
||
int64_t digit_count = int64_t(end_of_integer_part - start_digits);
|
||
int64_t exponent = 0;
|
||
if ((p != pend) && (*p == decimal_point)) {
|
||
++p;
|
||
// Fast approach only tested under little endian systems
|
||
if ((p + 8 <= pend) && 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;
|
||
if ((p + 8 <= pend) && 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 = end_of_integer_part + 1 - p;
|
||
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 < 0x10000) {
|
||
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.
|
||
i = 0;
|
||
p = start_digits;
|
||
const uint64_t minimal_nineteen_digit_integer{1000000000000000000};
|
||
while((i < minimal_nineteen_digit_integer) && (p != pend) && is_integer(*p)) {
|
||
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++; // skip the dot
|
||
const char *first_after_period = p;
|
||
while((i < minimal_nineteen_digit_integer) && (p != pend) && is_integer(*p)) {
|
||
i = i * 10 + uint64_t(*p - '0');
|
||
++p;
|
||
}
|
||
exponent = first_after_period - p + exp_number;
|
||
}
|
||
// We have now corrected both exponent and i, to a truncated value
|
||
}
|
||
}
|
||
answer.exponent = exponent;
|
||
answer.mantissa = i;
|
||
return answer;
|
||
}
|
||
|
||
|
||
// This should always succeed since it follows a call to parse_number_string
|
||
// This function could be optimized. In particular, we could stop after 19 digits
|
||
// and try to bail out. Furthermore, we should be able to recover the computed
|
||
// exponent from the pass in parse_number_string.
|
||
fastfloat_really_inline decimal parse_decimal(const char *p, const char *pend, parse_options options) noexcept {
|
||
const char decimal_point = options.decimal_point;
|
||
|
||
decimal answer;
|
||
answer.num_digits = 0;
|
||
answer.decimal_point = 0;
|
||
answer.truncated = false;
|
||
answer.negative = (*p == '-');
|
||
if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
|
||
++p;
|
||
}
|
||
// skip leading zeroes
|
||
while ((p != pend) && (*p == '0')) {
|
||
++p;
|
||
}
|
||
while ((p != pend) && is_integer(*p)) {
|
||
if (answer.num_digits < max_digits) {
|
||
answer.digits[answer.num_digits] = uint8_t(*p - '0');
|
||
}
|
||
answer.num_digits++;
|
||
++p;
|
||
}
|
||
if ((p != pend) && (*p == decimal_point)) {
|
||
++p;
|
||
const char *first_after_period = p;
|
||
// if we have not yet encountered a zero, we have to skip it as well
|
||
if(answer.num_digits == 0) {
|
||
// skip zeros
|
||
while ((p != pend) && (*p == '0')) {
|
||
++p;
|
||
}
|
||
}
|
||
// We expect that this loop will often take the bulk of the running time
|
||
// because when a value has lots of digits, these digits often
|
||
while ((p + 8 <= pend) && (answer.num_digits + 8 < max_digits)) {
|
||
uint64_t val = read_u64(p);
|
||
if(! is_made_of_eight_digits_fast(val)) { break; }
|
||
// We have eight digits, process them in one go!
|
||
val -= 0x3030303030303030;
|
||
write_u64(answer.digits + answer.num_digits, val);
|
||
answer.num_digits += 8;
|
||
p += 8;
|
||
}
|
||
while ((p != pend) && is_integer(*p)) {
|
||
if (answer.num_digits < max_digits) {
|
||
answer.digits[answer.num_digits] = uint8_t(*p - '0');
|
||
}
|
||
answer.num_digits++;
|
||
++p;
|
||
}
|
||
answer.decimal_point = int32_t(first_after_period - p);
|
||
}
|
||
// We want num_digits to be the number of significant digits, excluding
|
||
// leading *and* trailing zeros! Otherwise the truncated flag later is
|
||
// going to be misleading.
|
||
if(answer.num_digits > 0) {
|
||
// We potentially need the answer.num_digits > 0 guard because we
|
||
// prune leading zeros. So with answer.num_digits > 0, we know that
|
||
// we have at least one non-zero digit.
|
||
const char *preverse = p - 1;
|
||
int32_t trailing_zeros = 0;
|
||
while ((*preverse == '0') || (*preverse == decimal_point)) {
|
||
if(*preverse == '0') { trailing_zeros++; };
|
||
--preverse;
|
||
}
|
||
answer.decimal_point += int32_t(answer.num_digits);
|
||
answer.num_digits -= uint32_t(trailing_zeros);
|
||
}
|
||
if(answer.num_digits > max_digits) {
|
||
answer.truncated = true;
|
||
answer.num_digits = max_digits;
|
||
}
|
||
if ((p != pend) && (('e' == *p) || ('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;
|
||
}
|
||
int32_t exp_number = 0; // exponential part
|
||
while ((p != pend) && is_integer(*p)) {
|
||
uint8_t digit = uint8_t(*p - '0');
|
||
if (exp_number < 0x10000) {
|
||
exp_number = 10 * exp_number + digit;
|
||
}
|
||
++p;
|
||
}
|
||
answer.decimal_point += (neg_exp ? -exp_number : exp_number);
|
||
}
|
||
// In very rare cases, we may have fewer than 19 digits, we want to be able to reliably
|
||
// assume that all digits up to max_digit_without_overflow have been initialized.
|
||
for(uint32_t i = answer.num_digits; i < max_digit_without_overflow; i++) { answer.digits[i] = 0; }
|
||
|
||
return answer;
|
||
}
|
||
} // namespace fast_float
|
||
|
||
#endif
|
||
|
||
|
||
#ifndef FASTFLOAT_FAST_TABLE_H
|
||
#define FASTFLOAT_FAST_TABLE_H
|
||
#include <cstdint>
|
||
|
||
namespace fast_float {
|
||
|
||
/**
|
||
* When mapping numbers from decimal to binary,
|
||
* we go from w * 10^q to m * 2^p but we have
|
||
* 10^q = 5^q * 2^q, so effectively
|
||
* we are trying to match
|
||
* w * 2^q * 5^q to m * 2^p. Thus the powers of two
|
||
* are not a concern since they can be represented
|
||
* exactly using the binary notation, only the powers of five
|
||
* affect the binary significand.
|
||
*/
|
||
|
||
/**
|
||
* The smallest non-zero float (binary64) is 2^−1074.
|
||
* We take as input numbers of the form w x 10^q where w < 2^64.
|
||
* We have that w * 10^-343 < 2^(64-344) 5^-343 < 2^-1076.
|
||
* However, we have that
|
||
* (2^64-1) * 10^-342 = (2^64-1) * 2^-342 * 5^-342 > 2^−1074.
|
||
* Thus it is possible for a number of the form w * 10^-342 where
|
||
* w is a 64-bit value to be a non-zero floating-point number.
|
||
*********
|
||
* Any number of form w * 10^309 where w>= 1 is going to be
|
||
* infinite in binary64 so we never need to worry about powers
|
||
* of 5 greater than 308.
|
||
*/
|
||
template <class unused = void>
|
||
struct powers_template {
|
||
|
||
constexpr static int smallest_power_of_five = binary_format<double>::smallest_power_of_ten();
|
||
constexpr static int largest_power_of_five = binary_format<double>::largest_power_of_ten();
|
||
constexpr static int number_of_entries = 2 * (largest_power_of_five - smallest_power_of_five + 1);
|
||
// Powers of five from 5^-342 all the way to 5^308 rounded toward one.
|
||
static const uint64_t power_of_five_128[number_of_entries];
|
||
};
|
||
|
||
template <class unused>
|
||
const uint64_t powers_template<unused>::power_of_five_128[number_of_entries] = {
|
||
0xeef453d6923bd65a,0x113faa2906a13b3f,
|
||
0x9558b4661b6565f8,0x4ac7ca59a424c507,
|
||
0xbaaee17fa23ebf76,0x5d79bcf00d2df649,
|
||
0xe95a99df8ace6f53,0xf4d82c2c107973dc,
|
||
0x91d8a02bb6c10594,0x79071b9b8a4be869,
|
||
0xb64ec836a47146f9,0x9748e2826cdee284,
|
||
0xe3e27a444d8d98b7,0xfd1b1b2308169b25,
|
||
0x8e6d8c6ab0787f72,0xfe30f0f5e50e20f7,
|
||
0xb208ef855c969f4f,0xbdbd2d335e51a935,
|
||
0xde8b2b66b3bc4723,0xad2c788035e61382,
|
||
0x8b16fb203055ac76,0x4c3bcb5021afcc31,
|
||
0xaddcb9e83c6b1793,0xdf4abe242a1bbf3d,
|
||
0xd953e8624b85dd78,0xd71d6dad34a2af0d,
|
||
0x87d4713d6f33aa6b,0x8672648c40e5ad68,
|
||
0xa9c98d8ccb009506,0x680efdaf511f18c2,
|
||
0xd43bf0effdc0ba48,0x212bd1b2566def2,
|
||
0x84a57695fe98746d,0x14bb630f7604b57,
|
||
0xa5ced43b7e3e9188,0x419ea3bd35385e2d,
|
||
0xcf42894a5dce35ea,0x52064cac828675b9,
|
||
0x818995ce7aa0e1b2,0x7343efebd1940993,
|
||
0xa1ebfb4219491a1f,0x1014ebe6c5f90bf8,
|
||
0xca66fa129f9b60a6,0xd41a26e077774ef6,
|
||
0xfd00b897478238d0,0x8920b098955522b4,
|
||
0x9e20735e8cb16382,0x55b46e5f5d5535b0,
|
||
0xc5a890362fddbc62,0xeb2189f734aa831d,
|
||
0xf712b443bbd52b7b,0xa5e9ec7501d523e4,
|
||
0x9a6bb0aa55653b2d,0x47b233c92125366e,
|
||
0xc1069cd4eabe89f8,0x999ec0bb696e840a,
|
||
0xf148440a256e2c76,0xc00670ea43ca250d,
|
||
0x96cd2a865764dbca,0x380406926a5e5728,
|
||
0xbc807527ed3e12bc,0xc605083704f5ecf2,
|
||
0xeba09271e88d976b,0xf7864a44c633682e,
|
||
0x93445b8731587ea3,0x7ab3ee6afbe0211d,
|
||
0xb8157268fdae9e4c,0x5960ea05bad82964,
|
||
0xe61acf033d1a45df,0x6fb92487298e33bd,
|
||
0x8fd0c16206306bab,0xa5d3b6d479f8e056,
|
||
0xb3c4f1ba87bc8696,0x8f48a4899877186c,
|
||
0xe0b62e2929aba83c,0x331acdabfe94de87,
|
||
0x8c71dcd9ba0b4925,0x9ff0c08b7f1d0b14,
|
||
0xaf8e5410288e1b6f,0x7ecf0ae5ee44dd9,
|
||
0xdb71e91432b1a24a,0xc9e82cd9f69d6150,
|
||
0x892731ac9faf056e,0xbe311c083a225cd2,
|
||
0xab70fe17c79ac6ca,0x6dbd630a48aaf406,
|
||
0xd64d3d9db981787d,0x92cbbccdad5b108,
|
||
0x85f0468293f0eb4e,0x25bbf56008c58ea5,
|
||
0xa76c582338ed2621,0xaf2af2b80af6f24e,
|
||
0xd1476e2c07286faa,0x1af5af660db4aee1,
|
||
0x82cca4db847945ca,0x50d98d9fc890ed4d,
|
||
0xa37fce126597973c,0xe50ff107bab528a0,
|
||
0xcc5fc196fefd7d0c,0x1e53ed49a96272c8,
|
||
0xff77b1fcbebcdc4f,0x25e8e89c13bb0f7a,
|
||
0x9faacf3df73609b1,0x77b191618c54e9ac,
|
||
0xc795830d75038c1d,0xd59df5b9ef6a2417,
|
||
0xf97ae3d0d2446f25,0x4b0573286b44ad1d,
|
||
0x9becce62836ac577,0x4ee367f9430aec32,
|
||
0xc2e801fb244576d5,0x229c41f793cda73f,
|
||
0xf3a20279ed56d48a,0x6b43527578c1110f,
|
||
0x9845418c345644d6,0x830a13896b78aaa9,
|
||
0xbe5691ef416bd60c,0x23cc986bc656d553,
|
||
0xedec366b11c6cb8f,0x2cbfbe86b7ec8aa8,
|
||
0x94b3a202eb1c3f39,0x7bf7d71432f3d6a9,
|
||
0xb9e08a83a5e34f07,0xdaf5ccd93fb0cc53,
|
||
0xe858ad248f5c22c9,0xd1b3400f8f9cff68,
|
||
0x91376c36d99995be,0x23100809b9c21fa1,
|
||
0xb58547448ffffb2d,0xabd40a0c2832a78a,
|
||
0xe2e69915b3fff9f9,0x16c90c8f323f516c,
|
||
0x8dd01fad907ffc3b,0xae3da7d97f6792e3,
|
||
0xb1442798f49ffb4a,0x99cd11cfdf41779c,
|
||
0xdd95317f31c7fa1d,0x40405643d711d583,
|
||
0x8a7d3eef7f1cfc52,0x482835ea666b2572,
|
||
0xad1c8eab5ee43b66,0xda3243650005eecf,
|
||
0xd863b256369d4a40,0x90bed43e40076a82,
|
||
0x873e4f75e2224e68,0x5a7744a6e804a291,
|
||
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|
||
0x95f83d0a1fb69cd9,0x4abdaf101564f98e,
|
||
0xbb764c4ca7a4440f,0x9d6d1ad41abe37f1,
|
||
0xea53df5fd18d5513,0x84c86189216dc5ed,
|
||
0x92746b9be2f8552c,0x32fd3cf5b4e49bb4,
|
||
0xb7118682dbb66a77,0x3fbc8c33221dc2a1,
|
||
0xe4d5e82392a40515,0xfabaf3feaa5334a,
|
||
0x8f05b1163ba6832d,0x29cb4d87f2a7400e,
|
||
0xb2c71d5bca9023f8,0x743e20e9ef511012,
|
||
0xdf78e4b2bd342cf6,0x914da9246b255416,
|
||
0x8bab8eefb6409c1a,0x1ad089b6c2f7548e,
|
||
0xae9672aba3d0c320,0xa184ac2473b529b1,
|
||
0xda3c0f568cc4f3e8,0xc9e5d72d90a2741e,
|
||
0x8865899617fb1871,0x7e2fa67c7a658892,
|
||
0xaa7eebfb9df9de8d,0xddbb901b98feeab7,
|
||
0xd51ea6fa85785631,0x552a74227f3ea565,
|
||
0x8533285c936b35de,0xd53a88958f87275f,
|
||
0xa67ff273b8460356,0x8a892abaf368f137,
|
||
0xd01fef10a657842c,0x2d2b7569b0432d85,
|
||
0x8213f56a67f6b29b,0x9c3b29620e29fc73,
|
||
0xa298f2c501f45f42,0x8349f3ba91b47b8f,
|
||
0xcb3f2f7642717713,0x241c70a936219a73,
|
||
0xfe0efb53d30dd4d7,0xed238cd383aa0110,
|
||
0x9ec95d1463e8a506,0xf4363804324a40aa,
|
||
0xc67bb4597ce2ce48,0xb143c6053edcd0d5,
|
||
0xf81aa16fdc1b81da,0xdd94b7868e94050a,
|
||
0x9b10a4e5e9913128,0xca7cf2b4191c8326,
|
||
0xc1d4ce1f63f57d72,0xfd1c2f611f63a3f0,
|
||
0xf24a01a73cf2dccf,0xbc633b39673c8cec,
|
||
0x976e41088617ca01,0xd5be0503e085d813,
|
||
0xbd49d14aa79dbc82,0x4b2d8644d8a74e18,
|
||
0xec9c459d51852ba2,0xddf8e7d60ed1219e,
|
||
0x93e1ab8252f33b45,0xcabb90e5c942b503,
|
||
0xb8da1662e7b00a17,0x3d6a751f3b936243,
|
||
0xe7109bfba19c0c9d,0xcc512670a783ad4,
|
||
0x906a617d450187e2,0x27fb2b80668b24c5,
|
||
0xb484f9dc9641e9da,0xb1f9f660802dedf6,
|
||
0xe1a63853bbd26451,0x5e7873f8a0396973,
|
||
0x8d07e33455637eb2,0xdb0b487b6423e1e8,
|
||
0xb049dc016abc5e5f,0x91ce1a9a3d2cda62,
|
||
0xdc5c5301c56b75f7,0x7641a140cc7810fb,
|
||
0x89b9b3e11b6329ba,0xa9e904c87fcb0a9d,
|
||
0xac2820d9623bf429,0x546345fa9fbdcd44,
|
||
0xd732290fbacaf133,0xa97c177947ad4095,
|
||
0x867f59a9d4bed6c0,0x49ed8eabcccc485d,
|
||
0xa81f301449ee8c70,0x5c68f256bfff5a74,
|
||
0xd226fc195c6a2f8c,0x73832eec6fff3111,
|
||
0x83585d8fd9c25db7,0xc831fd53c5ff7eab,
|
||
0xa42e74f3d032f525,0xba3e7ca8b77f5e55,
|
||
0xcd3a1230c43fb26f,0x28ce1bd2e55f35eb,
|
||
0x80444b5e7aa7cf85,0x7980d163cf5b81b3,
|
||
0xa0555e361951c366,0xd7e105bcc332621f,
|
||
0xc86ab5c39fa63440,0x8dd9472bf3fefaa7,
|
||
0xfa856334878fc150,0xb14f98f6f0feb951,
|
||
0x9c935e00d4b9d8d2,0x6ed1bf9a569f33d3,
|
||
0xc3b8358109e84f07,0xa862f80ec4700c8,
|
||
0xf4a642e14c6262c8,0xcd27bb612758c0fa,
|
||
0x98e7e9cccfbd7dbd,0x8038d51cb897789c,
|
||
0xbf21e44003acdd2c,0xe0470a63e6bd56c3,
|
||
0xeeea5d5004981478,0x1858ccfce06cac74,
|
||
0x95527a5202df0ccb,0xf37801e0c43ebc8,
|
||
0xbaa718e68396cffd,0xd30560258f54e6ba,
|
||
0xe950df20247c83fd,0x47c6b82ef32a2069,
|
||
0x91d28b7416cdd27e,0x4cdc331d57fa5441,
|
||
0xb6472e511c81471d,0xe0133fe4adf8e952,
|
||
0xe3d8f9e563a198e5,0x58180fddd97723a6,
|
||
0x8e679c2f5e44ff8f,0x570f09eaa7ea7648,};
|
||
using powers = powers_template<>;
|
||
|
||
}
|
||
|
||
#endif
|
||
|
||
#ifndef FASTFLOAT_DECIMAL_TO_BINARY_H
|
||
#define FASTFLOAT_DECIMAL_TO_BINARY_H
|
||
|
||
#include <cfloat>
|
||
#include <cinttypes>
|
||
#include <cmath>
|
||
#include <cstdint>
|
||
#include <cstdio>
|
||
#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)
|
||
*/
|
||
fastfloat_really_inline int power(int q) noexcept {
|
||
return (((152170 + 65536) * q) >> 16) + 63;
|
||
}
|
||
} // namespace detail
|
||
|
||
|
||
// 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) {
|
||
answer.power2 = -1; // This (a negative value) indicates an error condition.
|
||
return answer;
|
||
}
|
||
}
|
||
// 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 = int(detail::power(int(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_ASCII_NUMBER_H
|
||
#define FASTFLOAT_ASCII_NUMBER_H
|
||
|
||
#include <cstdio>
|
||
#include <cctype>
|
||
#include <cstdint>
|
||
#include <cstring>
|
||
|
||
|
||
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));
|
||
}
|
||
|
||
struct parsed_number_string {
|
||
int64_t exponent;
|
||
uint64_t mantissa;
|
||
const char *lastmatch;
|
||
bool negative;
|
||
bool valid;
|
||
bool too_many_digits;
|
||
};
|
||
|
||
|
||
// Assuming that you use no more than 19 digits, this will
|
||
// parse an ASCII string.
|
||
fastfloat_really_inline
|
||
parsed_number_string parse_number_string(const char *p, const char *pend, parse_options options) noexcept {
|
||
const chars_format fmt = options.format;
|
||
const char decimal_point = options.decimal_point;
|
||
|
||
parsed_number_string answer;
|
||
answer.valid = false;
|
||
answer.too_many_digits = false;
|
||
answer.negative = (*p == '-');
|
||
if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
|
||
++p;
|
||
if (p == pend) {
|
||
return answer;
|
||
}
|
||
if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot
|
||
return answer;
|
||
}
|
||
}
|
||
const char *const start_digits = p;
|
||
|
||
uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad)
|
||
|
||
while ((p != pend) && is_integer(*p)) {
|
||
// a multiplication by 10 is cheaper than an arbitrary integer
|
||
// multiplication
|
||
i = 10 * i +
|
||
uint64_t(*p - '0'); // might overflow, we will handle the overflow later
|
||
++p;
|
||
}
|
||
const char *const end_of_integer_part = p;
|
||
int64_t digit_count = int64_t(end_of_integer_part - start_digits);
|
||
int64_t exponent = 0;
|
||
if ((p != pend) && (*p == decimal_point)) {
|
||
++p;
|
||
// Fast approach only tested under little endian systems
|
||
if ((p + 8 <= pend) && 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;
|
||
if ((p + 8 <= pend) && 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 = end_of_integer_part + 1 - p;
|
||
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 < 0x10000) {
|
||
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.
|
||
i = 0;
|
||
p = start_digits;
|
||
const uint64_t minimal_nineteen_digit_integer{1000000000000000000};
|
||
while((i < minimal_nineteen_digit_integer) && (p != pend) && is_integer(*p)) {
|
||
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++; // skip the dot
|
||
const char *first_after_period = p;
|
||
while((i < minimal_nineteen_digit_integer) && (p != pend) && is_integer(*p)) {
|
||
i = i * 10 + uint64_t(*p - '0');
|
||
++p;
|
||
}
|
||
exponent = first_after_period - p + exp_number;
|
||
}
|
||
// We have now corrected both exponent and i, to a truncated value
|
||
}
|
||
}
|
||
answer.exponent = exponent;
|
||
answer.mantissa = i;
|
||
return answer;
|
||
}
|
||
|
||
|
||
// This should always succeed since it follows a call to parse_number_string
|
||
// This function could be optimized. In particular, we could stop after 19 digits
|
||
// and try to bail out. Furthermore, we should be able to recover the computed
|
||
// exponent from the pass in parse_number_string.
|
||
fastfloat_really_inline decimal parse_decimal(const char *p, const char *pend, parse_options options) noexcept {
|
||
const char decimal_point = options.decimal_point;
|
||
|
||
decimal answer;
|
||
answer.num_digits = 0;
|
||
answer.decimal_point = 0;
|
||
answer.truncated = false;
|
||
answer.negative = (*p == '-');
|
||
if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
|
||
++p;
|
||
}
|
||
// skip leading zeroes
|
||
while ((p != pend) && (*p == '0')) {
|
||
++p;
|
||
}
|
||
while ((p != pend) && is_integer(*p)) {
|
||
if (answer.num_digits < max_digits) {
|
||
answer.digits[answer.num_digits] = uint8_t(*p - '0');
|
||
}
|
||
answer.num_digits++;
|
||
++p;
|
||
}
|
||
if ((p != pend) && (*p == decimal_point)) {
|
||
++p;
|
||
const char *first_after_period = p;
|
||
// if we have not yet encountered a zero, we have to skip it as well
|
||
if(answer.num_digits == 0) {
|
||
// skip zeros
|
||
while ((p != pend) && (*p == '0')) {
|
||
++p;
|
||
}
|
||
}
|
||
// We expect that this loop will often take the bulk of the running time
|
||
// because when a value has lots of digits, these digits often
|
||
while ((p + 8 <= pend) && (answer.num_digits + 8 < max_digits)) {
|
||
uint64_t val = read_u64(p);
|
||
if(! is_made_of_eight_digits_fast(val)) { break; }
|
||
// We have eight digits, process them in one go!
|
||
val -= 0x3030303030303030;
|
||
write_u64(answer.digits + answer.num_digits, val);
|
||
answer.num_digits += 8;
|
||
p += 8;
|
||
}
|
||
while ((p != pend) && is_integer(*p)) {
|
||
if (answer.num_digits < max_digits) {
|
||
answer.digits[answer.num_digits] = uint8_t(*p - '0');
|
||
}
|
||
answer.num_digits++;
|
||
++p;
|
||
}
|
||
answer.decimal_point = int32_t(first_after_period - p);
|
||
}
|
||
// We want num_digits to be the number of significant digits, excluding
|
||
// leading *and* trailing zeros! Otherwise the truncated flag later is
|
||
// going to be misleading.
|
||
if(answer.num_digits > 0) {
|
||
// We potentially need the answer.num_digits > 0 guard because we
|
||
// prune leading zeros. So with answer.num_digits > 0, we know that
|
||
// we have at least one non-zero digit.
|
||
const char *preverse = p - 1;
|
||
int32_t trailing_zeros = 0;
|
||
while ((*preverse == '0') || (*preverse == decimal_point)) {
|
||
if(*preverse == '0') { trailing_zeros++; };
|
||
--preverse;
|
||
}
|
||
answer.decimal_point += int32_t(answer.num_digits);
|
||
answer.num_digits -= uint32_t(trailing_zeros);
|
||
}
|
||
if(answer.num_digits > max_digits) {
|
||
answer.truncated = true;
|
||
answer.num_digits = max_digits;
|
||
}
|
||
if ((p != pend) && (('e' == *p) || ('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;
|
||
}
|
||
int32_t exp_number = 0; // exponential part
|
||
while ((p != pend) && is_integer(*p)) {
|
||
uint8_t digit = uint8_t(*p - '0');
|
||
if (exp_number < 0x10000) {
|
||
exp_number = 10 * exp_number + digit;
|
||
}
|
||
++p;
|
||
}
|
||
answer.decimal_point += (neg_exp ? -exp_number : exp_number);
|
||
}
|
||
// In very rare cases, we may have fewer than 19 digits, we want to be able to reliably
|
||
// assume that all digits up to max_digit_without_overflow have been initialized.
|
||
for(uint32_t i = answer.num_digits; i < max_digit_without_overflow; i++) { answer.digits[i] = 0; }
|
||
|
||
return answer;
|
||
}
|
||
} // namespace fast_float
|
||
|
||
#endif
|
||
|
||
|
||
#ifndef FASTFLOAT_GENERIC_DECIMAL_TO_BINARY_H
|
||
#define FASTFLOAT_GENERIC_DECIMAL_TO_BINARY_H
|
||
|
||
/**
|
||
* This code is meant to handle the case where we have more than 19 digits.
|
||
*
|
||
* It is based on work by Nigel Tao (at https://github.com/google/wuffs/)
|
||
* who credits Ken Thompson for the design (via a reference to the Go source
|
||
* code).
|
||
*
|
||
* Rob Pike suggested that this algorithm be called "Simple Decimal Conversion".
|
||
*
|
||
* It is probably not very fast but it is a fallback that should almost never
|
||
* be used in real life. Though it is not fast, it is "easily" understood and debugged.
|
||
**/
|
||
#include <cstdint>
|
||
|
||
namespace fast_float {
|
||
|
||
namespace detail {
|
||
|
||
// remove all final zeroes
|
||
inline void trim(decimal &h) {
|
||
while ((h.num_digits > 0) && (h.digits[h.num_digits - 1] == 0)) {
|
||
h.num_digits--;
|
||
}
|
||
}
|
||
|
||
|
||
|
||
inline uint32_t number_of_digits_decimal_left_shift(const decimal &h, uint32_t shift) {
|
||
shift &= 63;
|
||
const static uint16_t number_of_digits_decimal_left_shift_table[65] = {
|
||
0x0000, 0x0800, 0x0801, 0x0803, 0x1006, 0x1009, 0x100D, 0x1812, 0x1817,
|
||
0x181D, 0x2024, 0x202B, 0x2033, 0x203C, 0x2846, 0x2850, 0x285B, 0x3067,
|
||
0x3073, 0x3080, 0x388E, 0x389C, 0x38AB, 0x38BB, 0x40CC, 0x40DD, 0x40EF,
|
||
0x4902, 0x4915, 0x4929, 0x513E, 0x5153, 0x5169, 0x5180, 0x5998, 0x59B0,
|
||
0x59C9, 0x61E3, 0x61FD, 0x6218, 0x6A34, 0x6A50, 0x6A6D, 0x6A8B, 0x72AA,
|
||
0x72C9, 0x72E9, 0x7B0A, 0x7B2B, 0x7B4D, 0x8370, 0x8393, 0x83B7, 0x83DC,
|
||
0x8C02, 0x8C28, 0x8C4F, 0x9477, 0x949F, 0x94C8, 0x9CF2, 0x051C, 0x051C,
|
||
0x051C, 0x051C,
|
||
};
|
||
uint32_t x_a = number_of_digits_decimal_left_shift_table[shift];
|
||
uint32_t x_b = number_of_digits_decimal_left_shift_table[shift + 1];
|
||
uint32_t num_new_digits = x_a >> 11;
|
||
uint32_t pow5_a = 0x7FF & x_a;
|
||
uint32_t pow5_b = 0x7FF & x_b;
|
||
const static uint8_t
|
||
number_of_digits_decimal_left_shift_table_powers_of_5[0x051C] = {
|
||
5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5, 3,
|
||
9, 0, 6, 2, 5, 1, 9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8, 2, 8,
|
||
1, 2, 5, 2, 4, 4, 1, 4, 0, 6, 2, 5, 1, 2, 2, 0, 7, 0, 3, 1, 2, 5, 6, 1,
|
||
0, 3, 5, 1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2, 5, 1, 5, 2, 5, 8,
|
||
7, 8, 9, 0, 6, 2, 5, 7, 6, 2, 9, 3, 9, 4, 5, 3, 1, 2, 5, 3, 8, 1, 4, 6,
|
||
9, 7, 2, 6, 5, 6, 2, 5, 1, 9, 0, 7, 3, 4, 8, 6, 3, 2, 8, 1, 2, 5, 9, 5,
|
||
3, 6, 7, 4, 3, 1, 6, 4, 0, 6, 2, 5, 4, 7, 6, 8, 3, 7, 1, 5, 8, 2, 0, 3,
|
||
1, 2, 5, 2, 3, 8, 4, 1, 8, 5, 7, 9, 1, 0, 1, 5, 6, 2, 5, 1, 1, 9, 2, 0,
|
||
9, 2, 8, 9, 5, 5, 0, 7, 8, 1, 2, 5, 5, 9, 6, 0, 4, 6, 4, 4, 7, 7, 5, 3,
|
||
9, 0, 6, 2, 5, 2, 9, 8, 0, 2, 3, 2, 2, 3, 8, 7, 6, 9, 5, 3, 1, 2, 5, 1,
|
||
4, 9, 0, 1, 1, 6, 1, 1, 9, 3, 8, 4, 7, 6, 5, 6, 2, 5, 7, 4, 5, 0, 5, 8,
|
||
0, 5, 9, 6, 9, 2, 3, 8, 2, 8, 1, 2, 5, 3, 7, 2, 5, 2, 9, 0, 2, 9, 8, 4,
|
||
6, 1, 9, 1, 4, 0, 6, 2, 5, 1, 8, 6, 2, 6, 4, 5, 1, 4, 9, 2, 3, 0, 9, 5,
|
||
7, 0, 3, 1, 2, 5, 9, 3, 1, 3, 2, 2, 5, 7, 4, 6, 1, 5, 4, 7, 8, 5, 1, 5,
|
||
6, 2, 5, 4, 6, 5, 6, 6, 1, 2, 8, 7, 3, 0, 7, 7, 3, 9, 2, 5, 7, 8, 1, 2,
|
||
5, 2, 3, 2, 8, 3, 0, 6, 4, 3, 6, 5, 3, 8, 6, 9, 6, 2, 8, 9, 0, 6, 2, 5,
|
||
1, 1, 6, 4, 1, 5, 3, 2, 1, 8, 2, 6, 9, 3, 4, 8, 1, 4, 4, 5, 3, 1, 2, 5,
|
||
5, 8, 2, 0, 7, 6, 6, 0, 9, 1, 3, 4, 6, 7, 4, 0, 7, 2, 2, 6, 5, 6, 2, 5,
|
||
2, 9, 1, 0, 3, 8, 3, 0, 4, 5, 6, 7, 3, 3, 7, 0, 3, 6, 1, 3, 2, 8, 1, 2,
|
||
5, 1, 4, 5, 5, 1, 9, 1, 5, 2, 2, 8, 3, 6, 6, 8, 5, 1, 8, 0, 6, 6, 4, 0,
|
||
6, 2, 5, 7, 2, 7, 5, 9, 5, 7, 6, 1, 4, 1, 8, 3, 4, 2, 5, 9, 0, 3, 3, 2,
|
||
0, 3, 1, 2, 5, 3, 6, 3, 7, 9, 7, 8, 8, 0, 7, 0, 9, 1, 7, 1, 2, 9, 5, 1,
|
||
6, 6, 0, 1, 5, 6, 2, 5, 1, 8, 1, 8, 9, 8, 9, 4, 0, 3, 5, 4, 5, 8, 5, 6,
|
||
4, 7, 5, 8, 3, 0, 0, 7, 8, 1, 2, 5, 9, 0, 9, 4, 9, 4, 7, 0, 1, 7, 7, 2,
|
||
9, 2, 8, 2, 3, 7, 9, 1, 5, 0, 3, 9, 0, 6, 2, 5, 4, 5, 4, 7, 4, 7, 3, 5,
|
||
0, 8, 8, 6, 4, 6, 4, 1, 1, 8, 9, 5, 7, 5, 1, 9, 5, 3, 1, 2, 5, 2, 2, 7,
|
||
3, 7, 3, 6, 7, 5, 4, 4, 3, 2, 3, 2, 0, 5, 9, 4, 7, 8, 7, 5, 9, 7, 6, 5,
|
||
6, 2, 5, 1, 1, 3, 6, 8, 6, 8, 3, 7, 7, 2, 1, 6, 1, 6, 0, 2, 9, 7, 3, 9,
|
||
3, 7, 9, 8, 8, 2, 8, 1, 2, 5, 5, 6, 8, 4, 3, 4, 1, 8, 8, 6, 0, 8, 0, 8,
|
||
0, 1, 4, 8, 6, 9, 6, 8, 9, 9, 4, 1, 4, 0, 6, 2, 5, 2, 8, 4, 2, 1, 7, 0,
|
||
9, 4, 3, 0, 4, 0, 4, 0, 0, 7, 4, 3, 4, 8, 4, 4, 9, 7, 0, 7, 0, 3, 1, 2,
|
||
5, 1, 4, 2, 1, 0, 8, 5, 4, 7, 1, 5, 2, 0, 2, 0, 0, 3, 7, 1, 7, 4, 2, 2,
|
||
4, 8, 5, 3, 5, 1, 5, 6, 2, 5, 7, 1, 0, 5, 4, 2, 7, 3, 5, 7, 6, 0, 1, 0,
|
||
0, 1, 8, 5, 8, 7, 1, 1, 2, 4, 2, 6, 7, 5, 7, 8, 1, 2, 5, 3, 5, 5, 2, 7,
|
||
1, 3, 6, 7, 8, 8, 0, 0, 5, 0, 0, 9, 2, 9, 3, 5, 5, 6, 2, 1, 3, 3, 7, 8,
|
||
9, 0, 6, 2, 5, 1, 7, 7, 6, 3, 5, 6, 8, 3, 9, 4, 0, 0, 2, 5, 0, 4, 6, 4,
|
||
6, 7, 7, 8, 1, 0, 6, 6, 8, 9, 4, 5, 3, 1, 2, 5, 8, 8, 8, 1, 7, 8, 4, 1,
|
||
9, 7, 0, 0, 1, 2, 5, 2, 3, 2, 3, 3, 8, 9, 0, 5, 3, 3, 4, 4, 7, 2, 6, 5,
|
||
6, 2, 5, 4, 4, 4, 0, 8, 9, 2, 0, 9, 8, 5, 0, 0, 6, 2, 6, 1, 6, 1, 6, 9,
|
||
4, 5, 2, 6, 6, 7, 2, 3, 6, 3, 2, 8, 1, 2, 5, 2, 2, 2, 0, 4, 4, 6, 0, 4,
|
||
9, 2, 5, 0, 3, 1, 3, 0, 8, 0, 8, 4, 7, 2, 6, 3, 3, 3, 6, 1, 8, 1, 6, 4,
|
||
0, 6, 2, 5, 1, 1, 1, 0, 2, 2, 3, 0, 2, 4, 6, 2, 5, 1, 5, 6, 5, 4, 0, 4,
|
||
2, 3, 6, 3, 1, 6, 6, 8, 0, 9, 0, 8, 2, 0, 3, 1, 2, 5, 5, 5, 5, 1, 1, 1,
|
||
5, 1, 2, 3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 1, 1, 8, 1, 5, 8, 3, 4, 0, 4, 5,
|
||
4, 1, 0, 1, 5, 6, 2, 5, 2, 7, 7, 5, 5, 5, 7, 5, 6, 1, 5, 6, 2, 8, 9, 1,
|
||
3, 5, 1, 0, 5, 9, 0, 7, 9, 1, 7, 0, 2, 2, 7, 0, 5, 0, 7, 8, 1, 2, 5, 1,
|
||
3, 8, 7, 7, 7, 8, 7, 8, 0, 7, 8, 1, 4, 4, 5, 6, 7, 5, 5, 2, 9, 5, 3, 9,
|
||
5, 8, 5, 1, 1, 3, 5, 2, 5, 3, 9, 0, 6, 2, 5, 6, 9, 3, 8, 8, 9, 3, 9, 0,
|
||
3, 9, 0, 7, 2, 2, 8, 3, 7, 7, 6, 4, 7, 6, 9, 7, 9, 2, 5, 5, 6, 7, 6, 2,
|
||
6, 9, 5, 3, 1, 2, 5, 3, 4, 6, 9, 4, 4, 6, 9, 5, 1, 9, 5, 3, 6, 1, 4, 1,
|
||
8, 8, 8, 2, 3, 8, 4, 8, 9, 6, 2, 7, 8, 3, 8, 1, 3, 4, 7, 6, 5, 6, 2, 5,
|
||
1, 7, 3, 4, 7, 2, 3, 4, 7, 5, 9, 7, 6, 8, 0, 7, 0, 9, 4, 4, 1, 1, 9, 2,
|
||
4, 4, 8, 1, 3, 9, 1, 9, 0, 6, 7, 3, 8, 2, 8, 1, 2, 5, 8, 6, 7, 3, 6, 1,
|
||
7, 3, 7, 9, 8, 8, 4, 0, 3, 5, 4, 7, 2, 0, 5, 9, 6, 2, 2, 4, 0, 6, 9, 5,
|
||
9, 5, 3, 3, 6, 9, 1, 4, 0, 6, 2, 5,
|
||
};
|
||
const uint8_t *pow5 =
|
||
&number_of_digits_decimal_left_shift_table_powers_of_5[pow5_a];
|
||
uint32_t i = 0;
|
||
uint32_t n = pow5_b - pow5_a;
|
||
for (; i < n; i++) {
|
||
if (i >= h.num_digits) {
|
||
return num_new_digits - 1;
|
||
} else if (h.digits[i] == pow5[i]) {
|
||
continue;
|
||
} else if (h.digits[i] < pow5[i]) {
|
||
return num_new_digits - 1;
|
||
} else {
|
||
return num_new_digits;
|
||
}
|
||
}
|
||
return num_new_digits;
|
||
}
|
||
|
||
inline uint64_t round(decimal &h) {
|
||
if ((h.num_digits == 0) || (h.decimal_point < 0)) {
|
||
return 0;
|
||
} else if (h.decimal_point > 18) {
|
||
return UINT64_MAX;
|
||
}
|
||
// at this point, we know that h.decimal_point >= 0
|
||
uint32_t dp = uint32_t(h.decimal_point);
|
||
uint64_t n = 0;
|
||
for (uint32_t i = 0; i < dp; i++) {
|
||
n = (10 * n) + ((i < h.num_digits) ? h.digits[i] : 0);
|
||
}
|
||
bool round_up = false;
|
||
if (dp < h.num_digits) {
|
||
round_up = h.digits[dp] >= 5; // normally, we round up
|
||
// but we may need to round to even!
|
||
if ((h.digits[dp] == 5) && (dp + 1 == h.num_digits)) {
|
||
round_up = h.truncated || ((dp > 0) && (1 & h.digits[dp - 1]));
|
||
}
|
||
}
|
||
if (round_up) {
|
||
n++;
|
||
}
|
||
return n;
|
||
}
|
||
|
||
// computes h * 2^-shift
|
||
inline void decimal_left_shift(decimal &h, uint32_t shift) {
|
||
if (h.num_digits == 0) {
|
||
return;
|
||
}
|
||
uint32_t num_new_digits = number_of_digits_decimal_left_shift(h, shift);
|
||
int32_t read_index = int32_t(h.num_digits - 1);
|
||
uint32_t write_index = h.num_digits - 1 + num_new_digits;
|
||
uint64_t n = 0;
|
||
|
||
while (read_index >= 0) {
|
||
n += uint64_t(h.digits[read_index]) << shift;
|
||
uint64_t quotient = n / 10;
|
||
uint64_t remainder = n - (10 * quotient);
|
||
if (write_index < max_digits) {
|
||
h.digits[write_index] = uint8_t(remainder);
|
||
} else if (remainder > 0) {
|
||
h.truncated = true;
|
||
}
|
||
n = quotient;
|
||
write_index--;
|
||
read_index--;
|
||
}
|
||
while (n > 0) {
|
||
uint64_t quotient = n / 10;
|
||
uint64_t remainder = n - (10 * quotient);
|
||
if (write_index < max_digits) {
|
||
h.digits[write_index] = uint8_t(remainder);
|
||
} else if (remainder > 0) {
|
||
h.truncated = true;
|
||
}
|
||
n = quotient;
|
||
write_index--;
|
||
}
|
||
h.num_digits += num_new_digits;
|
||
if (h.num_digits > max_digits) {
|
||
h.num_digits = max_digits;
|
||
}
|
||
h.decimal_point += int32_t(num_new_digits);
|
||
trim(h);
|
||
}
|
||
|
||
// computes h * 2^shift
|
||
inline void decimal_right_shift(decimal &h, uint32_t shift) {
|
||
uint32_t read_index = 0;
|
||
uint32_t write_index = 0;
|
||
|
||
uint64_t n = 0;
|
||
|
||
while ((n >> shift) == 0) {
|
||
if (read_index < h.num_digits) {
|
||
n = (10 * n) + h.digits[read_index++];
|
||
} else if (n == 0) {
|
||
return;
|
||
} else {
|
||
while ((n >> shift) == 0) {
|
||
n = 10 * n;
|
||
read_index++;
|
||
}
|
||
break;
|
||
}
|
||
}
|
||
h.decimal_point -= int32_t(read_index - 1);
|
||
if (h.decimal_point < -decimal_point_range) { // it is zero
|
||
h.num_digits = 0;
|
||
h.decimal_point = 0;
|
||
h.negative = false;
|
||
h.truncated = false;
|
||
return;
|
||
}
|
||
uint64_t mask = (uint64_t(1) << shift) - 1;
|
||
while (read_index < h.num_digits) {
|
||
uint8_t new_digit = uint8_t(n >> shift);
|
||
n = (10 * (n & mask)) + h.digits[read_index++];
|
||
h.digits[write_index++] = new_digit;
|
||
}
|
||
while (n > 0) {
|
||
uint8_t new_digit = uint8_t(n >> shift);
|
||
n = 10 * (n & mask);
|
||
if (write_index < max_digits) {
|
||
h.digits[write_index++] = new_digit;
|
||
} else if (new_digit > 0) {
|
||
h.truncated = true;
|
||
}
|
||
}
|
||
h.num_digits = write_index;
|
||
trim(h);
|
||
}
|
||
|
||
} // namespace detail
|
||
|
||
template <typename binary>
|
||
adjusted_mantissa compute_float(decimal &d) {
|
||
adjusted_mantissa answer;
|
||
if (d.num_digits == 0) {
|
||
// should be zero
|
||
answer.power2 = 0;
|
||
answer.mantissa = 0;
|
||
return answer;
|
||
}
|
||
// At this point, going further, we can assume that d.num_digits > 0.
|
||
//
|
||
// We want to guard against excessive decimal point values because
|
||
// they can result in long running times. Indeed, we do
|
||
// shifts by at most 60 bits. We have that log(10**400)/log(2**60) ~= 22
|
||
// which is fine, but log(10**299995)/log(2**60) ~= 16609 which is not
|
||
// fine (runs for a long time).
|
||
//
|
||
if(d.decimal_point < -324) {
|
||
// We have something smaller than 1e-324 which is always zero
|
||
// in binary64 and binary32.
|
||
// It should be zero.
|
||
answer.power2 = 0;
|
||
answer.mantissa = 0;
|
||
return answer;
|
||
} else if(d.decimal_point >= 310) {
|
||
// We have something at least as large as 0.1e310 which is
|
||
// always infinite.
|
||
answer.power2 = binary::infinite_power();
|
||
answer.mantissa = 0;
|
||
return answer;
|
||
}
|
||
static const uint32_t max_shift = 60;
|
||
static const uint32_t num_powers = 19;
|
||
static const uint8_t decimal_powers[19] = {
|
||
0, 3, 6, 9, 13, 16, 19, 23, 26, 29, //
|
||
33, 36, 39, 43, 46, 49, 53, 56, 59, //
|
||
};
|
||
int32_t exp2 = 0;
|
||
while (d.decimal_point > 0) {
|
||
uint32_t n = uint32_t(d.decimal_point);
|
||
uint32_t shift = (n < num_powers) ? decimal_powers[n] : max_shift;
|
||
detail::decimal_right_shift(d, shift);
|
||
if (d.decimal_point < -decimal_point_range) {
|
||
// should be zero
|
||
answer.power2 = 0;
|
||
answer.mantissa = 0;
|
||
return answer;
|
||
}
|
||
exp2 += int32_t(shift);
|
||
}
|
||
// We shift left toward [1/2 ... 1].
|
||
while (d.decimal_point <= 0) {
|
||
uint32_t shift;
|
||
if (d.decimal_point == 0) {
|
||
if (d.digits[0] >= 5) {
|
||
break;
|
||
}
|
||
shift = (d.digits[0] < 2) ? 2 : 1;
|
||
} else {
|
||
uint32_t n = uint32_t(-d.decimal_point);
|
||
shift = (n < num_powers) ? decimal_powers[n] : max_shift;
|
||
}
|
||
detail::decimal_left_shift(d, shift);
|
||
if (d.decimal_point > decimal_point_range) {
|
||
// we want to get infinity:
|
||
answer.power2 = binary::infinite_power();
|
||
answer.mantissa = 0;
|
||
return answer;
|
||
}
|
||
exp2 -= int32_t(shift);
|
||
}
|
||
// We are now in the range [1/2 ... 1] but the binary format uses [1 ... 2].
|
||
exp2--;
|
||
constexpr int32_t minimum_exponent = binary::minimum_exponent();
|
||
while ((minimum_exponent + 1) > exp2) {
|
||
uint32_t n = uint32_t((minimum_exponent + 1) - exp2);
|
||
if (n > max_shift) {
|
||
n = max_shift;
|
||
}
|
||
detail::decimal_right_shift(d, n);
|
||
exp2 += int32_t(n);
|
||
}
|
||
if ((exp2 - minimum_exponent) >= binary::infinite_power()) {
|
||
answer.power2 = binary::infinite_power();
|
||
answer.mantissa = 0;
|
||
return answer;
|
||
}
|
||
|
||
const int mantissa_size_in_bits = binary::mantissa_explicit_bits() + 1;
|
||
detail::decimal_left_shift(d, mantissa_size_in_bits);
|
||
|
||
uint64_t mantissa = detail::round(d);
|
||
// It is possible that we have an overflow, in which case we need
|
||
// to shift back.
|
||
if(mantissa >= (uint64_t(1) << mantissa_size_in_bits)) {
|
||
detail::decimal_right_shift(d, 1);
|
||
exp2 += 1;
|
||
mantissa = detail::round(d);
|
||
if ((exp2 - minimum_exponent) >= binary::infinite_power()) {
|
||
answer.power2 = binary::infinite_power();
|
||
answer.mantissa = 0;
|
||
return answer;
|
||
}
|
||
}
|
||
answer.power2 = exp2 - binary::minimum_exponent();
|
||
if(mantissa < (uint64_t(1) << binary::mantissa_explicit_bits())) { answer.power2--; }
|
||
answer.mantissa = mantissa & ((uint64_t(1) << binary::mantissa_explicit_bits()) - 1);
|
||
return answer;
|
||
}
|
||
|
||
template <typename binary>
|
||
adjusted_mantissa parse_long_mantissa(const char *first, const char* last, parse_options options) {
|
||
decimal d = parse_decimal(first, last, options);
|
||
return compute_float<binary>(d);
|
||
}
|
||
|
||
} // namespace fast_float
|
||
#endif
|
||
|
||
|
||
#ifndef FASTFLOAT_PARSE_NUMBER_H
|
||
#define FASTFLOAT_PARSE_NUMBER_H
|
||
|
||
#include <cassert>
|
||
#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;
|
||
}
|
||
|
||
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 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) {
|
||
if(am != compute_float<binary_format<T>>(pns.exponent, pns.mantissa + 1)) {
|
||
am.power2 = -1; // value is invalid.
|
||
}
|
||
}
|
||
// 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 = parse_long_mantissa<binary_format<T>>(first, last, options); }
|
||
detail::to_float(pns.negative, am, value);
|
||
return answer;
|
||
}
|
||
|
||
} // namespace fast_float
|
||
|
||
#endif
|
||
|