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Diffstat (limited to 'absl/strings/charconv.cc')
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diff --git a/absl/strings/charconv.cc b/absl/strings/charconv.cc new file mode 100644 index 00000000..ab75ab49 --- /dev/null +++ b/absl/strings/charconv.cc @@ -0,0 +1,984 @@ +// Copyright 2018 The Abseil Authors. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +#include "absl/strings/charconv.h" + +#include <algorithm> +#include <cassert> +#include <cmath> +#include <cstring> + +#include "absl/base/casts.h" +#include "absl/numeric/int128.h" +#include "absl/strings/internal/bits.h" +#include "absl/strings/internal/charconv_bigint.h" +#include "absl/strings/internal/charconv_parse.h" + +// The macro ABSL_BIT_PACK_FLOATS is defined on x86-64, where IEEE floating +// point numbers have the same endianness in memory as a bitfield struct +// containing the corresponding parts. +// +// When set, we replace calls to ldexp() with manual bit packing, which is +// faster and is unaffected by floating point environment. +#ifdef ABSL_BIT_PACK_FLOATS +#error ABSL_BIT_PACK_FLOATS cannot be directly set +#elif defined(__x86_64__) || defined(_M_X64) +#define ABSL_BIT_PACK_FLOATS 1 +#endif + +// A note about subnormals: +// +// The code below talks about "normals" and "subnormals". A normal IEEE float +// has a fixed-width mantissa and power of two exponent. For example, a normal +// `double` has a 53-bit mantissa. Because the high bit is always 1, it is not +// stored in the representation. The implicit bit buys an extra bit of +// resolution in the datatype. +// +// The downside of this scheme is that there is a large gap between DBL_MIN and +// zero. (Large, at least, relative to the different between DBL_MIN and the +// next representable number). This gap is softened by the "subnormal" numbers, +// which have the same power-of-two exponent as DBL_MIN, but no implicit 53rd +// bit. An all-bits-zero exponent in the encoding represents subnormals. (Zero +// is represented as a subnormal with an all-bits-zero mantissa.) +// +// The code below, in calculations, represents the mantissa as a uint64_t. The +// end result normally has the 53rd bit set. It represents subnormals by using +// narrower mantissas. + +namespace absl { +inline namespace lts_2018_06_20 { +namespace { + +template <typename FloatType> +struct FloatTraits; + +template <> +struct FloatTraits<double> { + // The number of mantissa bits in the given float type. This includes the + // implied high bit. + static constexpr int kTargetMantissaBits = 53; + + // The largest supported IEEE exponent, in our integral mantissa + // representation. + // + // If `m` is the largest possible int kTargetMantissaBits bits wide, then + // m * 2**kMaxExponent is exactly equal to DBL_MAX. + static constexpr int kMaxExponent = 971; + + // The smallest supported IEEE normal exponent, in our integral mantissa + // representation. + // + // If `m` is the smallest possible int kTargetMantissaBits bits wide, then + // m * 2**kMinNormalExponent is exactly equal to DBL_MIN. + static constexpr int kMinNormalExponent = -1074; + + static double MakeNan(const char* tagp) { + // Support nan no matter which namespace it's in. Some platforms + // incorrectly don't put it in namespace std. + using namespace std; // NOLINT + return nan(tagp); + } + + // Builds a nonzero floating point number out of the provided parts. + // + // This is intended to do the same operation as ldexp(mantissa, exponent), + // but using purely integer math, to avoid -ffastmath and floating + // point environment issues. Using type punning is also faster. We fall back + // to ldexp on a per-platform basis for portability. + // + // `exponent` must be between kMinNormalExponent and kMaxExponent. + // + // `mantissa` must either be exactly kTargetMantissaBits wide, in which case + // a normal value is made, or it must be less narrow than that, in which case + // `exponent` must be exactly kMinNormalExponent, and a subnormal value is + // made. + static double Make(uint64_t mantissa, int exponent, bool sign) { +#ifndef ABSL_BIT_PACK_FLOATS + // Support ldexp no matter which namespace it's in. Some platforms + // incorrectly don't put it in namespace std. + using namespace std; // NOLINT + return sign ? -ldexp(mantissa, exponent) : ldexp(mantissa, exponent); +#else + constexpr uint64_t kMantissaMask = + (uint64_t(1) << (kTargetMantissaBits - 1)) - 1; + uint64_t dbl = static_cast<uint64_t>(sign) << 63; + if (mantissa > kMantissaMask) { + // Normal value. + // Adjust by 1023 for the exponent representation bias, and an additional + // 52 due to the implied decimal point in the IEEE mantissa represenation. + dbl += uint64_t{exponent + 1023u + kTargetMantissaBits - 1} << 52; + mantissa &= kMantissaMask; + } else { + // subnormal value + assert(exponent == kMinNormalExponent); + } + dbl += mantissa; + return absl::bit_cast<double>(dbl); +#endif // ABSL_BIT_PACK_FLOATS + } +}; + +// Specialization of floating point traits for the `float` type. See the +// FloatTraits<double> specialization above for meaning of each of the following +// members and methods. +template <> +struct FloatTraits<float> { + static constexpr int kTargetMantissaBits = 24; + static constexpr int kMaxExponent = 104; + static constexpr int kMinNormalExponent = -149; + static float MakeNan(const char* tagp) { + // Support nanf no matter which namespace it's in. Some platforms + // incorrectly don't put it in namespace std. + using namespace std; // NOLINT + return nanf(tagp); + } + static float Make(uint32_t mantissa, int exponent, bool sign) { +#ifndef ABSL_BIT_PACK_FLOATS + // Support ldexpf no matter which namespace it's in. Some platforms + // incorrectly don't put it in namespace std. + using namespace std; // NOLINT + return sign ? -ldexpf(mantissa, exponent) : ldexpf(mantissa, exponent); +#else + constexpr uint32_t kMantissaMask = + (uint32_t(1) << (kTargetMantissaBits - 1)) - 1; + uint32_t flt = static_cast<uint32_t>(sign) << 31; + if (mantissa > kMantissaMask) { + // Normal value. + // Adjust by 127 for the exponent representation bias, and an additional + // 23 due to the implied decimal point in the IEEE mantissa represenation. + flt += uint32_t{exponent + 127u + kTargetMantissaBits - 1} << 23; + mantissa &= kMantissaMask; + } else { + // subnormal value + assert(exponent == kMinNormalExponent); + } + flt += mantissa; + return absl::bit_cast<float>(flt); +#endif // ABSL_BIT_PACK_FLOATS + } +}; + +// Decimal-to-binary conversions require coercing powers of 10 into a mantissa +// and a power of 2. The two helper functions Power10Mantissa(n) and +// Power10Exponent(n) perform this task. Together, these represent a hand- +// rolled floating point value which is equal to or just less than 10**n. +// +// The return values satisfy two range guarantees: +// +// Power10Mantissa(n) * 2**Power10Exponent(n) <= 10**n +// < (Power10Mantissa(n) + 1) * 2**Power10Exponent(n) +// +// 2**63 <= Power10Mantissa(n) < 2**64. +// +// Lookups into the power-of-10 table must first check the Power10Overflow() and +// Power10Underflow() functions, to avoid out-of-bounds table access. +// +// Indexes into these tables are biased by -kPower10TableMin, and the table has +// values in the range [kPower10TableMin, kPower10TableMax]. +extern const uint64_t kPower10MantissaTable[]; +extern const int16_t kPower10ExponentTable[]; + +// The smallest allowed value for use with the Power10Mantissa() and +// Power10Exponent() functions below. (If a smaller exponent is needed in +// calculations, the end result is guaranteed to underflow.) +constexpr int kPower10TableMin = -342; + +// The largest allowed value for use with the Power10Mantissa() and +// Power10Exponent() functions below. (If a smaller exponent is needed in +// calculations, the end result is guaranteed to overflow.) +constexpr int kPower10TableMax = 308; + +uint64_t Power10Mantissa(int n) { + return kPower10MantissaTable[n - kPower10TableMin]; +} + +int Power10Exponent(int n) { + return kPower10ExponentTable[n - kPower10TableMin]; +} + +// Returns true if n is large enough that 10**n always results in an IEEE +// overflow. +bool Power10Overflow(int n) { return n > kPower10TableMax; } + +// Returns true if n is small enough that 10**n times a ParsedFloat mantissa +// always results in an IEEE underflow. +bool Power10Underflow(int n) { return n < kPower10TableMin; } + +// Returns true if Power10Mantissa(n) * 2**Power10Exponent(n) is exactly equal +// to 10**n numerically. Put another way, this returns true if there is no +// truncation error in Power10Mantissa(n). +bool Power10Exact(int n) { return n >= 0 && n <= 27; } + +// Sentinel exponent values for representing numbers too large or too close to +// zero to represent in a double. +constexpr int kOverflow = 99999; +constexpr int kUnderflow = -99999; + +// Struct representing the calculated conversion result of a positive (nonzero) +// floating point number. +// +// The calculated number is mantissa * 2**exponent (mantissa is treated as an +// integer.) `mantissa` is chosen to be the correct width for the IEEE float +// representation being calculated. (`mantissa` will always have the same bit +// width for normal values, and narrower bit widths for subnormals.) +// +// If the result of conversion was an underflow or overflow, exponent is set +// to kUnderflow or kOverflow. +struct CalculatedFloat { + uint64_t mantissa = 0; + int exponent = 0; +}; + +// Returns the bit width of the given uint128. (Equivalently, returns 128 +// minus the number of leading zero bits.) +int BitWidth(uint128 value) { + if (Uint128High64(value) == 0) { + return 64 - strings_internal::CountLeadingZeros64(Uint128Low64(value)); + } + return 128 - strings_internal::CountLeadingZeros64(Uint128High64(value)); +} + +// Calculates how far to the right a mantissa needs to be shifted to create a +// properly adjusted mantissa for an IEEE floating point number. +// +// `mantissa_width` is the bit width of the mantissa to be shifted, and +// `binary_exponent` is the exponent of the number before the shift. +// +// This accounts for subnormal values, and will return a larger-than-normal +// shift if binary_exponent would otherwise be too low. +template <typename FloatType> +int NormalizedShiftSize(int mantissa_width, int binary_exponent) { + const int normal_shift = + mantissa_width - FloatTraits<FloatType>::kTargetMantissaBits; + const int minimum_shift = + FloatTraits<FloatType>::kMinNormalExponent - binary_exponent; + return std::max(normal_shift, minimum_shift); +} + +// Right shifts a uint128 so that it has the requested bit width. (The +// resulting value will have 128 - bit_width leading zeroes.) The initial +// `value` must be wider than the requested bit width. +// +// Returns the number of bits shifted. +int TruncateToBitWidth(int bit_width, uint128* value) { + const int current_bit_width = BitWidth(*value); + const int shift = current_bit_width - bit_width; + *value >>= shift; + return shift; +} + +// Checks if the given ParsedFloat represents one of the edge cases that are +// not dependent on number base: zero, infinity, or NaN. If so, sets *value +// the appropriate double, and returns true. +template <typename FloatType> +bool HandleEdgeCase(const strings_internal::ParsedFloat& input, bool negative, + FloatType* value) { + if (input.type == strings_internal::FloatType::kNan) { + // A bug in both clang and gcc would cause the compiler to optimize away the + // buffer we are building below. Declaring the buffer volatile avoids the + // issue, and has no measurable performance impact in microbenchmarks. + // + // https://bugs.llvm.org/show_bug.cgi?id=37778 + // https://gcc.gnu.org/bugzilla/show_bug.cgi?id=86113 + constexpr ptrdiff_t kNanBufferSize = 128; + volatile char n_char_sequence[kNanBufferSize]; + if (input.subrange_begin == nullptr) { + n_char_sequence[0] = '\0'; + } else { + ptrdiff_t nan_size = input.subrange_end - input.subrange_begin; + nan_size = std::min(nan_size, kNanBufferSize - 1); + std::copy_n(input.subrange_begin, nan_size, n_char_sequence); + n_char_sequence[nan_size] = '\0'; + } + char* nan_argument = const_cast<char*>(n_char_sequence); + *value = negative ? -FloatTraits<FloatType>::MakeNan(nan_argument) + : FloatTraits<FloatType>::MakeNan(nan_argument); + return true; + } + if (input.type == strings_internal::FloatType::kInfinity) { + *value = negative ? -std::numeric_limits<FloatType>::infinity() + : std::numeric_limits<FloatType>::infinity(); + return true; + } + if (input.mantissa == 0) { + *value = negative ? -0.0 : 0.0; + return true; + } + return false; +} + +// Given a CalculatedFloat result of a from_chars conversion, generate the +// correct output values. +// +// CalculatedFloat can represent an underflow or overflow, in which case the +// error code in *result is set. Otherwise, the calculated floating point +// number is stored in *value. +template <typename FloatType> +void EncodeResult(const CalculatedFloat& calculated, bool negative, + absl::from_chars_result* result, FloatType* value) { + if (calculated.exponent == kOverflow) { + result->ec = std::errc::result_out_of_range; + *value = negative ? -std::numeric_limits<FloatType>::max() + : std::numeric_limits<FloatType>::max(); + return; + } else if (calculated.mantissa == 0 || calculated.exponent == kUnderflow) { + result->ec = std::errc::result_out_of_range; + *value = negative ? -0.0 : 0.0; + return; + } + *value = FloatTraits<FloatType>::Make(calculated.mantissa, + calculated.exponent, negative); +} + +// Returns the given uint128 shifted to the right by `shift` bits, and rounds +// the remaining bits using round_to_nearest logic. The value is returned as a +// uint64_t, since this is the type used by this library for storing calculated +// floating point mantissas. +// +// It is expected that the width of the input value shifted by `shift` will +// be the correct bit-width for the target mantissa, which is strictly narrower +// than a uint64_t. +// +// If `input_exact` is false, then a nonzero error epsilon is assumed. For +// rounding purposes, the true value being rounded is strictly greater than the +// input value. The error may represent a single lost carry bit. +// +// When input_exact, shifted bits of the form 1000000... represent a tie, which +// is broken by rounding to even -- the rounding direction is chosen so the low +// bit of the returned value is 0. +// +// When !input_exact, shifted bits of the form 10000000... represent a value +// strictly greater than one half (due to the error epsilon), and so ties are +// always broken by rounding up. +// +// When !input_exact, shifted bits of the form 01111111... are uncertain; +// the true value may or may not be greater than 10000000..., due to the +// possible lost carry bit. The correct rounding direction is unknown. In this +// case, the result is rounded down, and `output_exact` is set to false. +// +// Zero and negative values of `shift` are accepted, in which case the word is +// shifted left, as necessary. +uint64_t ShiftRightAndRound(uint128 value, int shift, bool input_exact, + bool* output_exact) { + if (shift <= 0) { + *output_exact = input_exact; + return static_cast<uint64_t>(value << -shift); + } + if (shift >= 128) { + // Exponent is so small that we are shifting away all significant bits. + // Answer will not be representable, even as a subnormal, so return a zero + // mantissa (which represents underflow). + *output_exact = true; + return 0; + } + + *output_exact = true; + const uint128 shift_mask = (uint128(1) << shift) - 1; + const uint128 halfway_point = uint128(1) << (shift - 1); + + const uint128 shifted_bits = value & shift_mask; + value >>= shift; + if (shifted_bits > halfway_point) { + // Shifted bits greater than 10000... require rounding up. + return static_cast<uint64_t>(value + 1); + } + if (shifted_bits == halfway_point) { + // In exact mode, shifted bits of 10000... mean we're exactly halfway + // between two numbers, and we must round to even. So only round up if + // the low bit of `value` is set. + // + // In inexact mode, the nonzero error means the actual value is greater + // than the halfway point and we must alway round up. + if ((value & 1) == 1 || !input_exact) { + ++value; + } + return static_cast<uint64_t>(value); + } + if (!input_exact && shifted_bits == halfway_point - 1) { + // Rounding direction is unclear, due to error. + *output_exact = false; + } + // Otherwise, round down. + return static_cast<uint64_t>(value); +} + +// Checks if a floating point guess needs to be rounded up, using high precision +// math. +// +// `guess_mantissa` and `guess_exponent` represent a candidate guess for the +// number represented by `parsed_decimal`. +// +// The exact number represented by `parsed_decimal` must lie between the two +// numbers: +// A = `guess_mantissa * 2**guess_exponent` +// B = `(guess_mantissa + 1) * 2**guess_exponent` +// +// This function returns false if `A` is the better guess, and true if `B` is +// the better guess, with rounding ties broken by rounding to even. +bool MustRoundUp(uint64_t guess_mantissa, int guess_exponent, + const strings_internal::ParsedFloat& parsed_decimal) { + // 768 is the number of digits needed in the worst case. We could determine a + // better limit dynamically based on the value of parsed_decimal.exponent. + // This would optimize pathological input cases only. (Sane inputs won't have + // hundreds of digits of mantissa.) + absl::strings_internal::BigUnsigned<84> exact_mantissa; + int exact_exponent = exact_mantissa.ReadFloatMantissa(parsed_decimal, 768); + + // Adjust the `guess` arguments to be halfway between A and B. + guess_mantissa = guess_mantissa * 2 + 1; + guess_exponent -= 1; + + // In our comparison: + // lhs = exact = exact_mantissa * 10**exact_exponent + // = exact_mantissa * 5**exact_exponent * 2**exact_exponent + // rhs = guess = guess_mantissa * 2**guess_exponent + // + // Because we are doing integer math, we can't directly deal with negative + // exponents. We instead move these to the other side of the inequality. + absl::strings_internal::BigUnsigned<84>& lhs = exact_mantissa; + int comparison; + if (exact_exponent >= 0) { + lhs.MultiplyByFiveToTheNth(exact_exponent); + absl::strings_internal::BigUnsigned<84> rhs(guess_mantissa); + // There are powers of 2 on both sides of the inequality; reduce this to + // a single bit-shift. + if (exact_exponent > guess_exponent) { + lhs.ShiftLeft(exact_exponent - guess_exponent); + } else { + rhs.ShiftLeft(guess_exponent - exact_exponent); + } + comparison = Compare(lhs, rhs); + } else { + // Move the power of 5 to the other side of the equation, giving us: + // lhs = exact_mantissa * 2**exact_exponent + // rhs = guess_mantissa * 5**(-exact_exponent) * 2**guess_exponent + absl::strings_internal::BigUnsigned<84> rhs = + absl::strings_internal::BigUnsigned<84>::FiveToTheNth(-exact_exponent); + rhs.MultiplyBy(guess_mantissa); + if (exact_exponent > guess_exponent) { + lhs.ShiftLeft(exact_exponent - guess_exponent); + } else { + rhs.ShiftLeft(guess_exponent - exact_exponent); + } + comparison = Compare(lhs, rhs); + } + if (comparison < 0) { + return false; + } else if (comparison > 0) { + return true; + } else { + // When lhs == rhs, the decimal input is exactly between A and B. + // Round towards even -- round up only if the low bit of the initial + // `guess_mantissa` was a 1. We shifted guess_mantissa left 1 bit at + // the beginning of this function, so test the 2nd bit here. + return (guess_mantissa & 2) == 2; + } +} + +// Constructs a CalculatedFloat from a given mantissa and exponent, but +// with the following normalizations applied: +// +// If rounding has caused mantissa to increase just past the allowed bit +// width, shift and adjust exponent. +// +// If exponent is too high, sets kOverflow. +// +// If mantissa is zero (representing a non-zero value not representable, even +// as a subnormal), sets kUnderflow. +template <typename FloatType> +CalculatedFloat CalculatedFloatFromRawValues(uint64_t mantissa, int exponent) { + CalculatedFloat result; + if (mantissa == uint64_t(1) << FloatTraits<FloatType>::kTargetMantissaBits) { + mantissa >>= 1; + exponent += 1; + } + if (exponent > FloatTraits<FloatType>::kMaxExponent) { + result.exponent = kOverflow; + } else if (mantissa == 0) { + result.exponent = kUnderflow; + } else { + result.exponent = exponent; + result.mantissa = mantissa; + } + return result; +} + +template <typename FloatType> +CalculatedFloat CalculateFromParsedHexadecimal( + const strings_internal::ParsedFloat& parsed_hex) { + uint64_t mantissa = parsed_hex.mantissa; + int exponent = parsed_hex.exponent; + int mantissa_width = 64 - strings_internal::CountLeadingZeros64(mantissa); + const int shift = NormalizedShiftSize<FloatType>(mantissa_width, exponent); + bool result_exact; + exponent += shift; + mantissa = ShiftRightAndRound(mantissa, shift, + /* input exact= */ true, &result_exact); + // ParseFloat handles rounding in the hexadecimal case, so we don't have to + // check `result_exact` here. + return CalculatedFloatFromRawValues<FloatType>(mantissa, exponent); +} + +template <typename FloatType> +CalculatedFloat CalculateFromParsedDecimal( + const strings_internal::ParsedFloat& parsed_decimal) { + CalculatedFloat result; + + // Large or small enough decimal exponents will always result in overflow + // or underflow. + if (Power10Underflow(parsed_decimal.exponent)) { + result.exponent = kUnderflow; + return result; + } else if (Power10Overflow(parsed_decimal.exponent)) { + result.exponent = kOverflow; + return result; + } + + // Otherwise convert our power of 10 into a power of 2 times an integer + // mantissa, and multiply this by our parsed decimal mantissa. + uint128 wide_binary_mantissa = parsed_decimal.mantissa; + wide_binary_mantissa *= Power10Mantissa(parsed_decimal.exponent); + int binary_exponent = Power10Exponent(parsed_decimal.exponent); + + // Discard bits that are inaccurate due to truncation error. The magic + // `mantissa_width` constants below are justified in charconv_algorithm.md. + // They represent the number of bits in `wide_binary_mantissa` that are + // guaranteed to be unaffected by error propagation. + bool mantissa_exact; + int mantissa_width; + if (parsed_decimal.subrange_begin) { + // Truncated mantissa + mantissa_width = 58; + mantissa_exact = false; + binary_exponent += + TruncateToBitWidth(mantissa_width, &wide_binary_mantissa); + } else if (!Power10Exact(parsed_decimal.exponent)) { + // Exact mantissa, truncated power of ten + mantissa_width = 63; + mantissa_exact = false; + binary_exponent += + TruncateToBitWidth(mantissa_width, &wide_binary_mantissa); + } else { + // Product is exact + mantissa_width = BitWidth(wide_binary_mantissa); + mantissa_exact = true; + } + + // Shift into an FloatType-sized mantissa, and round to nearest. + const int shift = + NormalizedShiftSize<FloatType>(mantissa_width, binary_exponent); + bool result_exact; + binary_exponent += shift; + uint64_t binary_mantissa = ShiftRightAndRound(wide_binary_mantissa, shift, + mantissa_exact, &result_exact); + if (!result_exact) { + // We could not determine the rounding direction using int128 math. Use + // full resolution math instead. + if (MustRoundUp(binary_mantissa, binary_exponent, parsed_decimal)) { + binary_mantissa += 1; + } + } + + return CalculatedFloatFromRawValues<FloatType>(binary_mantissa, + binary_exponent); +} + +template <typename FloatType> +from_chars_result FromCharsImpl(const char* first, const char* last, + FloatType& value, chars_format fmt_flags) { + from_chars_result result; + result.ptr = first; // overwritten on successful parse + result.ec = std::errc(); + + bool negative = false; + if (first != last && *first == '-') { + ++first; + negative = true; + } + // If the `hex` flag is *not* set, then we will accept a 0x prefix and try + // to parse a hexadecimal float. + if ((fmt_flags & chars_format::hex) == chars_format{} && last - first >= 2 && + *first == '0' && (first[1] == 'x' || first[1] == 'X')) { + const char* hex_first = first + 2; + strings_internal::ParsedFloat hex_parse = + strings_internal::ParseFloat<16>(hex_first, last, fmt_flags); + if (hex_parse.end == nullptr || + hex_parse.type != strings_internal::FloatType::kNumber) { + // Either we failed to parse a hex float after the "0x", or we read + // "0xinf" or "0xnan" which we don't want to match. + // + // However, a std::string that begins with "0x" also begins with "0", which + // is normally a valid match for the number zero. So we want these + // strings to match zero unless fmt_flags is `scientific`. (This flag + // means an exponent is required, which the std::string "0" does not have.) + if (fmt_flags == chars_format::scientific) { + result.ec = std::errc::invalid_argument; + } else { + result.ptr = first + 1; + value = negative ? -0.0 : 0.0; + } + return result; + } + // We matched a value. + result.ptr = hex_parse.end; + if (HandleEdgeCase(hex_parse, negative, &value)) { + return result; + } + CalculatedFloat calculated = + CalculateFromParsedHexadecimal<FloatType>(hex_parse); + EncodeResult(calculated, negative, &result, &value); + return result; + } + // Otherwise, we choose the number base based on the flags. + if ((fmt_flags & chars_format::hex) == chars_format::hex) { + strings_internal::ParsedFloat hex_parse = + strings_internal::ParseFloat<16>(first, last, fmt_flags); + if (hex_parse.end == nullptr) { + result.ec = std::errc::invalid_argument; + return result; + } + result.ptr = hex_parse.end; + if (HandleEdgeCase(hex_parse, negative, &value)) { + return result; + } + CalculatedFloat calculated = + CalculateFromParsedHexadecimal<FloatType>(hex_parse); + EncodeResult(calculated, negative, &result, &value); + return result; + } else { + strings_internal::ParsedFloat decimal_parse = + strings_internal::ParseFloat<10>(first, last, fmt_flags); + if (decimal_parse.end == nullptr) { + result.ec = std::errc::invalid_argument; + return result; + } + result.ptr = decimal_parse.end; + if (HandleEdgeCase(decimal_parse, negative, &value)) { + return result; + } + CalculatedFloat calculated = + CalculateFromParsedDecimal<FloatType>(decimal_parse); + EncodeResult(calculated, negative, &result, &value); + return result; + } + return result; +} +} // namespace + +from_chars_result from_chars(const char* first, const char* last, double& value, + chars_format fmt) { + return FromCharsImpl(first, last, value, fmt); +} + +from_chars_result from_chars(const char* first, const char* last, float& value, + chars_format fmt) { + return FromCharsImpl(first, last, value, fmt); +} + +namespace { + +// Table of powers of 10, from kPower10TableMin to kPower10TableMax. +// +// kPower10MantissaTable[i - kPower10TableMin] stores the 64-bit mantissa (high +// bit always on), and kPower10ExponentTable[i - kPower10TableMin] stores the +// power-of-two exponent. For a given number i, this gives the unique mantissa +// and exponent such that mantissa * 2**exponent <= 10**i < (mantissa + 1) * +// 2**exponent. + +const uint64_t kPower10MantissaTable[] = { + 0xeef453d6923bd65aU, 0x9558b4661b6565f8U, 0xbaaee17fa23ebf76U, + 0xe95a99df8ace6f53U, 0x91d8a02bb6c10594U, 0xb64ec836a47146f9U, + 0xe3e27a444d8d98b7U, 0x8e6d8c6ab0787f72U, 0xb208ef855c969f4fU, + 0xde8b2b66b3bc4723U, 0x8b16fb203055ac76U, 0xaddcb9e83c6b1793U, + 0xd953e8624b85dd78U, 0x87d4713d6f33aa6bU, 0xa9c98d8ccb009506U, + 0xd43bf0effdc0ba48U, 0x84a57695fe98746dU, 0xa5ced43b7e3e9188U, + 0xcf42894a5dce35eaU, 0x818995ce7aa0e1b2U, 0xa1ebfb4219491a1fU, + 0xca66fa129f9b60a6U, 0xfd00b897478238d0U, 0x9e20735e8cb16382U, + 0xc5a890362fddbc62U, 0xf712b443bbd52b7bU, 0x9a6bb0aa55653b2dU, + 0xc1069cd4eabe89f8U, 0xf148440a256e2c76U, 0x96cd2a865764dbcaU, + 0xbc807527ed3e12bcU, 0xeba09271e88d976bU, 0x93445b8731587ea3U, + 0xb8157268fdae9e4cU, 0xe61acf033d1a45dfU, 0x8fd0c16206306babU, + 0xb3c4f1ba87bc8696U, 0xe0b62e2929aba83cU, 0x8c71dcd9ba0b4925U, + 0xaf8e5410288e1b6fU, 0xdb71e91432b1a24aU, 0x892731ac9faf056eU, + 0xab70fe17c79ac6caU, 0xd64d3d9db981787dU, 0x85f0468293f0eb4eU, + 0xa76c582338ed2621U, 0xd1476e2c07286faaU, 0x82cca4db847945caU, + 0xa37fce126597973cU, 0xcc5fc196fefd7d0cU, 0xff77b1fcbebcdc4fU, + 0x9faacf3df73609b1U, 0xc795830d75038c1dU, 0xf97ae3d0d2446f25U, + 0x9becce62836ac577U, 0xc2e801fb244576d5U, 0xf3a20279ed56d48aU, + 0x9845418c345644d6U, 0xbe5691ef416bd60cU, 0xedec366b11c6cb8fU, + 0x94b3a202eb1c3f39U, 0xb9e08a83a5e34f07U, 0xe858ad248f5c22c9U, + 0x91376c36d99995beU, 0xb58547448ffffb2dU, 0xe2e69915b3fff9f9U, + 0x8dd01fad907ffc3bU, 0xb1442798f49ffb4aU, 0xdd95317f31c7fa1dU, + 0x8a7d3eef7f1cfc52U, 0xad1c8eab5ee43b66U, 0xd863b256369d4a40U, + 0x873e4f75e2224e68U, 0xa90de3535aaae202U, 0xd3515c2831559a83U, + 0x8412d9991ed58091U, 0xa5178fff668ae0b6U, 0xce5d73ff402d98e3U, + 0x80fa687f881c7f8eU, 0xa139029f6a239f72U, 0xc987434744ac874eU, + 0xfbe9141915d7a922U, 0x9d71ac8fada6c9b5U, 0xc4ce17b399107c22U, + 0xf6019da07f549b2bU, 0x99c102844f94e0fbU, 0xc0314325637a1939U, + 0xf03d93eebc589f88U, 0x96267c7535b763b5U, 0xbbb01b9283253ca2U, + 0xea9c227723ee8bcbU, 0x92a1958a7675175fU, 0xb749faed14125d36U, + 0xe51c79a85916f484U, 0x8f31cc0937ae58d2U, 0xb2fe3f0b8599ef07U, + 0xdfbdcece67006ac9U, 0x8bd6a141006042bdU, 0xaecc49914078536dU, + 0xda7f5bf590966848U, 0x888f99797a5e012dU, 0xaab37fd7d8f58178U, + 0xd5605fcdcf32e1d6U, 0x855c3be0a17fcd26U, 0xa6b34ad8c9dfc06fU, + 0xd0601d8efc57b08bU, 0x823c12795db6ce57U, 0xa2cb1717b52481edU, + 0xcb7ddcdda26da268U, 0xfe5d54150b090b02U, 0x9efa548d26e5a6e1U, + 0xc6b8e9b0709f109aU, 0xf867241c8cc6d4c0U, 0x9b407691d7fc44f8U, + 0xc21094364dfb5636U, 0xf294b943e17a2bc4U, 0x979cf3ca6cec5b5aU, + 0xbd8430bd08277231U, 0xece53cec4a314ebdU, 0x940f4613ae5ed136U, + 0xb913179899f68584U, 0xe757dd7ec07426e5U, 0x9096ea6f3848984fU, + 0xb4bca50b065abe63U, 0xe1ebce4dc7f16dfbU, 0x8d3360f09cf6e4bdU, + 0xb080392cc4349decU, 0xdca04777f541c567U, 0x89e42caaf9491b60U, + 0xac5d37d5b79b6239U, 0xd77485cb25823ac7U, 0x86a8d39ef77164bcU, + 0xa8530886b54dbdebU, 0xd267caa862a12d66U, 0x8380dea93da4bc60U, + 0xa46116538d0deb78U, 0xcd795be870516656U, 0x806bd9714632dff6U, + 0xa086cfcd97bf97f3U, 0xc8a883c0fdaf7df0U, 0xfad2a4b13d1b5d6cU, + 0x9cc3a6eec6311a63U, 0xc3f490aa77bd60fcU, 0xf4f1b4d515acb93bU, + 0x991711052d8bf3c5U, 0xbf5cd54678eef0b6U, 0xef340a98172aace4U, + 0x9580869f0e7aac0eU, 0xbae0a846d2195712U, 0xe998d258869facd7U, + 0x91ff83775423cc06U, 0xb67f6455292cbf08U, 0xe41f3d6a7377eecaU, + 0x8e938662882af53eU, 0xb23867fb2a35b28dU, 0xdec681f9f4c31f31U, + 0x8b3c113c38f9f37eU, 0xae0b158b4738705eU, 0xd98ddaee19068c76U, + 0x87f8a8d4cfa417c9U, 0xa9f6d30a038d1dbcU, 0xd47487cc8470652bU, + 0x84c8d4dfd2c63f3bU, 0xa5fb0a17c777cf09U, 0xcf79cc9db955c2ccU, + 0x81ac1fe293d599bfU, 0xa21727db38cb002fU, 0xca9cf1d206fdc03bU, + 0xfd442e4688bd304aU, 0x9e4a9cec15763e2eU, 0xc5dd44271ad3cdbaU, + 0xf7549530e188c128U, 0x9a94dd3e8cf578b9U, 0xc13a148e3032d6e7U, + 0xf18899b1bc3f8ca1U, 0x96f5600f15a7b7e5U, 0xbcb2b812db11a5deU, + 0xebdf661791d60f56U, 0x936b9fcebb25c995U, 0xb84687c269ef3bfbU, + 0xe65829b3046b0afaU, 0x8ff71a0fe2c2e6dcU, 0xb3f4e093db73a093U, + 0xe0f218b8d25088b8U, 0x8c974f7383725573U, 0xafbd2350644eeacfU, + 0xdbac6c247d62a583U, 0x894bc396ce5da772U, 0xab9eb47c81f5114fU, + 0xd686619ba27255a2U, 0x8613fd0145877585U, 0xa798fc4196e952e7U, + 0xd17f3b51fca3a7a0U, 0x82ef85133de648c4U, 0xa3ab66580d5fdaf5U, + 0xcc963fee10b7d1b3U, 0xffbbcfe994e5c61fU, 0x9fd561f1fd0f9bd3U, + 0xc7caba6e7c5382c8U, 0xf9bd690a1b68637bU, 0x9c1661a651213e2dU, + 0xc31bfa0fe5698db8U, 0xf3e2f893dec3f126U, 0x986ddb5c6b3a76b7U, + 0xbe89523386091465U, 0xee2ba6c0678b597fU, 0x94db483840b717efU, + 0xba121a4650e4ddebU, 0xe896a0d7e51e1566U, 0x915e2486ef32cd60U, + 0xb5b5ada8aaff80b8U, 0xe3231912d5bf60e6U, 0x8df5efabc5979c8fU, + 0xb1736b96b6fd83b3U, 0xddd0467c64bce4a0U, 0x8aa22c0dbef60ee4U, + 0xad4ab7112eb3929dU, 0xd89d64d57a607744U, 0x87625f056c7c4a8bU, + 0xa93af6c6c79b5d2dU, 0xd389b47879823479U, 0x843610cb4bf160cbU, + 0xa54394fe1eedb8feU, 0xce947a3da6a9273eU, 0x811ccc668829b887U, + 0xa163ff802a3426a8U, 0xc9bcff6034c13052U, 0xfc2c3f3841f17c67U, + 0x9d9ba7832936edc0U, 0xc5029163f384a931U, 0xf64335bcf065d37dU, + 0x99ea0196163fa42eU, 0xc06481fb9bcf8d39U, 0xf07da27a82c37088U, + 0x964e858c91ba2655U, 0xbbe226efb628afeaU, 0xeadab0aba3b2dbe5U, + 0x92c8ae6b464fc96fU, 0xb77ada0617e3bbcbU, 0xe55990879ddcaabdU, + 0x8f57fa54c2a9eab6U, 0xb32df8e9f3546564U, 0xdff9772470297ebdU, + 0x8bfbea76c619ef36U, 0xaefae51477a06b03U, 0xdab99e59958885c4U, + 0x88b402f7fd75539bU, 0xaae103b5fcd2a881U, 0xd59944a37c0752a2U, + 0x857fcae62d8493a5U, 0xa6dfbd9fb8e5b88eU, 0xd097ad07a71f26b2U, + 0x825ecc24c873782fU, 0xa2f67f2dfa90563bU, 0xcbb41ef979346bcaU, + 0xfea126b7d78186bcU, 0x9f24b832e6b0f436U, 0xc6ede63fa05d3143U, + 0xf8a95fcf88747d94U, 0x9b69dbe1b548ce7cU, 0xc24452da229b021bU, + 0xf2d56790ab41c2a2U, 0x97c560ba6b0919a5U, 0xbdb6b8e905cb600fU, + 0xed246723473e3813U, 0x9436c0760c86e30bU, 0xb94470938fa89bceU, + 0xe7958cb87392c2c2U, 0x90bd77f3483bb9b9U, 0xb4ecd5f01a4aa828U, + 0xe2280b6c20dd5232U, 0x8d590723948a535fU, 0xb0af48ec79ace837U, + 0xdcdb1b2798182244U, 0x8a08f0f8bf0f156bU, 0xac8b2d36eed2dac5U, + 0xd7adf884aa879177U, 0x86ccbb52ea94baeaU, 0xa87fea27a539e9a5U, + 0xd29fe4b18e88640eU, 0x83a3eeeef9153e89U, 0xa48ceaaab75a8e2bU, + 0xcdb02555653131b6U, 0x808e17555f3ebf11U, 0xa0b19d2ab70e6ed6U, + 0xc8de047564d20a8bU, 0xfb158592be068d2eU, 0x9ced737bb6c4183dU, + 0xc428d05aa4751e4cU, 0xf53304714d9265dfU, 0x993fe2c6d07b7fabU, + 0xbf8fdb78849a5f96U, 0xef73d256a5c0f77cU, 0x95a8637627989aadU, + 0xbb127c53b17ec159U, 0xe9d71b689dde71afU, 0x9226712162ab070dU, + 0xb6b00d69bb55c8d1U, 0xe45c10c42a2b3b05U, 0x8eb98a7a9a5b04e3U, + 0xb267ed1940f1c61cU, 0xdf01e85f912e37a3U, 0x8b61313bbabce2c6U, + 0xae397d8aa96c1b77U, 0xd9c7dced53c72255U, 0x881cea14545c7575U, + 0xaa242499697392d2U, 0xd4ad2dbfc3d07787U, 0x84ec3c97da624ab4U, + 0xa6274bbdd0fadd61U, 0xcfb11ead453994baU, 0x81ceb32c4b43fcf4U, + 0xa2425ff75e14fc31U, 0xcad2f7f5359a3b3eU, 0xfd87b5f28300ca0dU, + 0x9e74d1b791e07e48U, 0xc612062576589ddaU, 0xf79687aed3eec551U, + 0x9abe14cd44753b52U, 0xc16d9a0095928a27U, 0xf1c90080baf72cb1U, + 0x971da05074da7beeU, 0xbce5086492111aeaU, 0xec1e4a7db69561a5U, + 0x9392ee8e921d5d07U, 0xb877aa3236a4b449U, 0xe69594bec44de15bU, + 0x901d7cf73ab0acd9U, 0xb424dc35095cd80fU, 0xe12e13424bb40e13U, + 0x8cbccc096f5088cbU, 0xafebff0bcb24aafeU, 0xdbe6fecebdedd5beU, + 0x89705f4136b4a597U, 0xabcc77118461cefcU, 0xd6bf94d5e57a42bcU, + 0x8637bd05af6c69b5U, 0xa7c5ac471b478423U, 0xd1b71758e219652bU, + 0x83126e978d4fdf3bU, 0xa3d70a3d70a3d70aU, 0xccccccccccccccccU, + 0x8000000000000000U, 0xa000000000000000U, 0xc800000000000000U, + 0xfa00000000000000U, 0x9c40000000000000U, 0xc350000000000000U, + 0xf424000000000000U, 0x9896800000000000U, 0xbebc200000000000U, + 0xee6b280000000000U, 0x9502f90000000000U, 0xba43b74000000000U, + 0xe8d4a51000000000U, 0x9184e72a00000000U, 0xb5e620f480000000U, + 0xe35fa931a0000000U, 0x8e1bc9bf04000000U, 0xb1a2bc2ec5000000U, + 0xde0b6b3a76400000U, 0x8ac7230489e80000U, 0xad78ebc5ac620000U, + 0xd8d726b7177a8000U, 0x878678326eac9000U, 0xa968163f0a57b400U, + 0xd3c21bcecceda100U, 0x84595161401484a0U, 0xa56fa5b99019a5c8U, + 0xcecb8f27f4200f3aU, 0x813f3978f8940984U, 0xa18f07d736b90be5U, + 0xc9f2c9cd04674edeU, 0xfc6f7c4045812296U, 0x9dc5ada82b70b59dU, + 0xc5371912364ce305U, 0xf684df56c3e01bc6U, 0x9a130b963a6c115cU, + 0xc097ce7bc90715b3U, 0xf0bdc21abb48db20U, 0x96769950b50d88f4U, + 0xbc143fa4e250eb31U, 0xeb194f8e1ae525fdU, 0x92efd1b8d0cf37beU, + 0xb7abc627050305adU, 0xe596b7b0c643c719U, 0x8f7e32ce7bea5c6fU, + 0xb35dbf821ae4f38bU, 0xe0352f62a19e306eU, 0x8c213d9da502de45U, + 0xaf298d050e4395d6U, 0xdaf3f04651d47b4cU, 0x88d8762bf324cd0fU, + 0xab0e93b6efee0053U, 0xd5d238a4abe98068U, 0x85a36366eb71f041U, + 0xa70c3c40a64e6c51U, 0xd0cf4b50cfe20765U, 0x82818f1281ed449fU, + 0xa321f2d7226895c7U, 0xcbea6f8ceb02bb39U, 0xfee50b7025c36a08U, + 0x9f4f2726179a2245U, 0xc722f0ef9d80aad6U, 0xf8ebad2b84e0d58bU, + 0x9b934c3b330c8577U, 0xc2781f49ffcfa6d5U, 0xf316271c7fc3908aU, + 0x97edd871cfda3a56U, 0xbde94e8e43d0c8ecU, 0xed63a231d4c4fb27U, + 0x945e455f24fb1cf8U, 0xb975d6b6ee39e436U, 0xe7d34c64a9c85d44U, + 0x90e40fbeea1d3a4aU, 0xb51d13aea4a488ddU, 0xe264589a4dcdab14U, + 0x8d7eb76070a08aecU, 0xb0de65388cc8ada8U, 0xdd15fe86affad912U, + 0x8a2dbf142dfcc7abU, 0xacb92ed9397bf996U, 0xd7e77a8f87daf7fbU, + 0x86f0ac99b4e8dafdU, 0xa8acd7c0222311bcU, 0xd2d80db02aabd62bU, + 0x83c7088e1aab65dbU, 0xa4b8cab1a1563f52U, 0xcde6fd5e09abcf26U, + 0x80b05e5ac60b6178U, 0xa0dc75f1778e39d6U, 0xc913936dd571c84cU, + 0xfb5878494ace3a5fU, 0x9d174b2dcec0e47bU, 0xc45d1df942711d9aU, + 0xf5746577930d6500U, 0x9968bf6abbe85f20U, 0xbfc2ef456ae276e8U, + 0xefb3ab16c59b14a2U, 0x95d04aee3b80ece5U, 0xbb445da9ca61281fU, + 0xea1575143cf97226U, 0x924d692ca61be758U, 0xb6e0c377cfa2e12eU, + 0xe498f455c38b997aU, 0x8edf98b59a373fecU, 0xb2977ee300c50fe7U, + 0xdf3d5e9bc0f653e1U, 0x8b865b215899f46cU, 0xae67f1e9aec07187U, + 0xda01ee641a708de9U, 0x884134fe908658b2U, 0xaa51823e34a7eedeU, + 0xd4e5e2cdc1d1ea96U, 0x850fadc09923329eU, 0xa6539930bf6bff45U, + 0xcfe87f7cef46ff16U, 0x81f14fae158c5f6eU, 0xa26da3999aef7749U, + 0xcb090c8001ab551cU, 0xfdcb4fa002162a63U, 0x9e9f11c4014dda7eU, + 0xc646d63501a1511dU, 0xf7d88bc24209a565U, 0x9ae757596946075fU, + 0xc1a12d2fc3978937U, 0xf209787bb47d6b84U, 0x9745eb4d50ce6332U, + 0xbd176620a501fbffU, 0xec5d3fa8ce427affU, 0x93ba47c980e98cdfU, + 0xb8a8d9bbe123f017U, 0xe6d3102ad96cec1dU, 0x9043ea1ac7e41392U, + 0xb454e4a179dd1877U, 0xe16a1dc9d8545e94U, 0x8ce2529e2734bb1dU, + 0xb01ae745b101e9e4U, 0xdc21a1171d42645dU, 0x899504ae72497ebaU, + 0xabfa45da0edbde69U, 0xd6f8d7509292d603U, 0x865b86925b9bc5c2U, + 0xa7f26836f282b732U, 0xd1ef0244af2364ffU, 0x8335616aed761f1fU, + 0xa402b9c5a8d3a6e7U, 0xcd036837130890a1U, 0x802221226be55a64U, + 0xa02aa96b06deb0fdU, 0xc83553c5c8965d3dU, 0xfa42a8b73abbf48cU, + 0x9c69a97284b578d7U, 0xc38413cf25e2d70dU, 0xf46518c2ef5b8cd1U, + 0x98bf2f79d5993802U, 0xbeeefb584aff8603U, 0xeeaaba2e5dbf6784U, + 0x952ab45cfa97a0b2U, 0xba756174393d88dfU, 0xe912b9d1478ceb17U, + 0x91abb422ccb812eeU, 0xb616a12b7fe617aaU, 0xe39c49765fdf9d94U, + 0x8e41ade9fbebc27dU, 0xb1d219647ae6b31cU, 0xde469fbd99a05fe3U, + 0x8aec23d680043beeU, 0xada72ccc20054ae9U, 0xd910f7ff28069da4U, + 0x87aa9aff79042286U, 0xa99541bf57452b28U, 0xd3fa922f2d1675f2U, + 0x847c9b5d7c2e09b7U, 0xa59bc234db398c25U, 0xcf02b2c21207ef2eU, + 0x8161afb94b44f57dU, 0xa1ba1ba79e1632dcU, 0xca28a291859bbf93U, + 0xfcb2cb35e702af78U, 0x9defbf01b061adabU, 0xc56baec21c7a1916U, + 0xf6c69a72a3989f5bU, 0x9a3c2087a63f6399U, 0xc0cb28a98fcf3c7fU, + 0xf0fdf2d3f3c30b9fU, 0x969eb7c47859e743U, 0xbc4665b596706114U, + 0xeb57ff22fc0c7959U, 0x9316ff75dd87cbd8U, 0xb7dcbf5354e9beceU, + 0xe5d3ef282a242e81U, 0x8fa475791a569d10U, 0xb38d92d760ec4455U, + 0xe070f78d3927556aU, 0x8c469ab843b89562U, 0xaf58416654a6babbU, + 0xdb2e51bfe9d0696aU, 0x88fcf317f22241e2U, 0xab3c2fddeeaad25aU, + 0xd60b3bd56a5586f1U, 0x85c7056562757456U, 0xa738c6bebb12d16cU, + 0xd106f86e69d785c7U, 0x82a45b450226b39cU, 0xa34d721642b06084U, + 0xcc20ce9bd35c78a5U, 0xff290242c83396ceU, 0x9f79a169bd203e41U, + 0xc75809c42c684dd1U, 0xf92e0c3537826145U, 0x9bbcc7a142b17ccbU, + 0xc2abf989935ddbfeU, 0xf356f7ebf83552feU, 0x98165af37b2153deU, + 0xbe1bf1b059e9a8d6U, 0xeda2ee1c7064130cU, 0x9485d4d1c63e8be7U, + 0xb9a74a0637ce2ee1U, 0xe8111c87c5c1ba99U, 0x910ab1d4db9914a0U, + 0xb54d5e4a127f59c8U, 0xe2a0b5dc971f303aU, 0x8da471a9de737e24U, + 0xb10d8e1456105dadU, 0xdd50f1996b947518U, 0x8a5296ffe33cc92fU, + 0xace73cbfdc0bfb7bU, 0xd8210befd30efa5aU, 0x8714a775e3e95c78U, + 0xa8d9d1535ce3b396U, 0xd31045a8341ca07cU, 0x83ea2b892091e44dU, + 0xa4e4b66b68b65d60U, 0xce1de40642e3f4b9U, 0x80d2ae83e9ce78f3U, + 0xa1075a24e4421730U, 0xc94930ae1d529cfcU, 0xfb9b7cd9a4a7443cU, + 0x9d412e0806e88aa5U, 0xc491798a08a2ad4eU, 0xf5b5d7ec8acb58a2U, + 0x9991a6f3d6bf1765U, 0xbff610b0cc6edd3fU, 0xeff394dcff8a948eU, + 0x95f83d0a1fb69cd9U, 0xbb764c4ca7a4440fU, 0xea53df5fd18d5513U, + 0x92746b9be2f8552cU, 0xb7118682dbb66a77U, 0xe4d5e82392a40515U, + 0x8f05b1163ba6832dU, 0xb2c71d5bca9023f8U, 0xdf78e4b2bd342cf6U, + 0x8bab8eefb6409c1aU, 0xae9672aba3d0c320U, 0xda3c0f568cc4f3e8U, + 0x8865899617fb1871U, 0xaa7eebfb9df9de8dU, 0xd51ea6fa85785631U, + 0x8533285c936b35deU, 0xa67ff273b8460356U, 0xd01fef10a657842cU, + 0x8213f56a67f6b29bU, 0xa298f2c501f45f42U, 0xcb3f2f7642717713U, + 0xfe0efb53d30dd4d7U, 0x9ec95d1463e8a506U, 0xc67bb4597ce2ce48U, + 0xf81aa16fdc1b81daU, 0x9b10a4e5e9913128U, 0xc1d4ce1f63f57d72U, + 0xf24a01a73cf2dccfU, 0x976e41088617ca01U, 0xbd49d14aa79dbc82U, + 0xec9c459d51852ba2U, 0x93e1ab8252f33b45U, 0xb8da1662e7b00a17U, + 0xe7109bfba19c0c9dU, 0x906a617d450187e2U, 0xb484f9dc9641e9daU, + 0xe1a63853bbd26451U, 0x8d07e33455637eb2U, 0xb049dc016abc5e5fU, + 0xdc5c5301c56b75f7U, 0x89b9b3e11b6329baU, 0xac2820d9623bf429U, + 0xd732290fbacaf133U, 0x867f59a9d4bed6c0U, 0xa81f301449ee8c70U, + 0xd226fc195c6a2f8cU, 0x83585d8fd9c25db7U, 0xa42e74f3d032f525U, + 0xcd3a1230c43fb26fU, 0x80444b5e7aa7cf85U, 0xa0555e361951c366U, + 0xc86ab5c39fa63440U, 0xfa856334878fc150U, 0x9c935e00d4b9d8d2U, + 0xc3b8358109e84f07U, 0xf4a642e14c6262c8U, 0x98e7e9cccfbd7dbdU, + 0xbf21e44003acdd2cU, 0xeeea5d5004981478U, 0x95527a5202df0ccbU, + 0xbaa718e68396cffdU, 0xe950df20247c83fdU, 0x91d28b7416cdd27eU, + 0xb6472e511c81471dU, 0xe3d8f9e563a198e5U, 0x8e679c2f5e44ff8fU, +}; + +const int16_t kPower10ExponentTable[] = { + -1200, -1196, -1193, -1190, -1186, -1183, -1180, -1176, -1173, -1170, -1166, + -1163, -1160, -1156, -1153, -1150, -1146, -1143, -1140, -1136, -1133, -1130, + -1127, -1123, -1120, -1117, -1113, -1110, -1107, -1103, -1100, -1097, -1093, + -1090, -1087, -1083, -1080, -1077, -1073, -1070, -1067, -1063, -1060, -1057, + -1053, -1050, -1047, -1043, -1040, -1037, -1034, -1030, -1027, -1024, -1020, + -1017, -1014, -1010, -1007, -1004, -1000, -997, -994, -990, -987, -984, + -980, -977, -974, -970, -967, -964, -960, -957, -954, -950, -947, + -944, -940, -937, -934, -931, -927, -924, -921, -917, -914, -911, + -907, -904, -901, -897, -894, -891, -887, -884, -881, -877, -874, + -871, -867, -864, -861, -857, -854, -851, -847, -844, -841, -838, + -834, -831, -828, -824, -821, -818, -814, -811, -808, -804, -801, + -798, -794, -791, -788, -784, -781, -778, -774, -771, -768, -764, + -761, -758, -754, -751, -748, -744, -741, -738, -735, -731, -728, + -725, -721, -718, -715, -711, -708, -705, -701, -698, -695, -691, + -688, -685, -681, -678, -675, -671, -668, -665, -661, -658, -655, + -651, -648, -645, -642, -638, -635, -632, -628, -625, -622, -618, + -615, -612, -608, -605, -602, -598, -595, -592, -588, -585, -582, + -578, -575, -572, -568, -565, -562, -558, -555, -552, -549, -545, + -542, -539, -535, -532, -529, -525, -522, -519, -515, -512, -509, + -505, -502, -499, -495, -492, -489, -485, -482, -479, -475, -472, + -469, -465, -462, -459, -455, -452, -449, -446, -442, -439, -436, + -432, -429, -426, -422, -419, -416, -412, -409, -406, -402, -399, + -396, -392, -389, -386, -382, -379, -376, -372, -369, -366, -362, + -359, -356, -353, -349, -346, -343, -339, -336, -333, -329, -326, + -323, -319, -316, -313, -309, -306, -303, -299, -296, -293, -289, + -286, -283, -279, -276, -273, -269, -266, -263, -259, -256, -253, + -250, -246, -243, -240, -236, -233, -230, -226, -223, -220, -216, + -213, -210, -206, -203, -200, -196, -193, -190, -186, -183, -180, + -176, -173, -170, -166, -163, -160, -157, -153, -150, -147, -143, + -140, -137, -133, -130, -127, -123, -120, -117, -113, -110, -107, + -103, -100, -97, -93, -90, -87, -83, -80, -77, -73, -70, + -67, -63, -60, -57, -54, -50, -47, -44, -40, -37, -34, + -30, -27, -24, -20, -17, -14, -10, -7, -4, 0, 3, + 6, 10, 13, 16, 20, 23, 26, 30, 33, 36, 39, + 43, 46, 49, 53, 56, 59, 63, 66, 69, 73, 76, + 79, 83, 86, 89, 93, 96, 99, 103, 106, 109, 113, + 116, 119, 123, 126, 129, 132, 136, 139, 142, 146, 149, + 152, 156, 159, 162, 166, 169, 172, 176, 179, 182, 186, + 189, 192, 196, 199, 202, 206, 209, 212, 216, 219, 222, + 226, 229, 232, 235, 239, 242, 245, 249, 252, 255, 259, + 262, 265, 269, 272, 275, 279, 282, 285, 289, 292, 295, + 299, 302, 305, 309, 312, 315, 319, 322, 325, 328, 332, + 335, 338, 342, 345, 348, 352, 355, 358, 362, 365, 368, + 372, 375, 378, 382, 385, 388, 392, 395, 398, 402, 405, + 408, 412, 415, 418, 422, 425, 428, 431, 435, 438, 441, + 445, 448, 451, 455, 458, 461, 465, 468, 471, 475, 478, + 481, 485, 488, 491, 495, 498, 501, 505, 508, 511, 515, + 518, 521, 524, 528, 531, 534, 538, 541, 544, 548, 551, + 554, 558, 561, 564, 568, 571, 574, 578, 581, 584, 588, + 591, 594, 598, 601, 604, 608, 611, 614, 617, 621, 624, + 627, 631, 634, 637, 641, 644, 647, 651, 654, 657, 661, + 664, 667, 671, 674, 677, 681, 684, 687, 691, 694, 697, + 701, 704, 707, 711, 714, 717, 720, 724, 727, 730, 734, + 737, 740, 744, 747, 750, 754, 757, 760, 764, 767, 770, + 774, 777, 780, 784, 787, 790, 794, 797, 800, 804, 807, + 810, 813, 817, 820, 823, 827, 830, 833, 837, 840, 843, + 847, 850, 853, 857, 860, 863, 867, 870, 873, 877, 880, + 883, 887, 890, 893, 897, 900, 903, 907, 910, 913, 916, + 920, 923, 926, 930, 933, 936, 940, 943, 946, 950, 953, + 956, 960, +}; + +} // namespace +} // inline namespace lts_2018_06_20 +} // namespace absl |