FMT_THROW(format_error(message));
}
-#ifndef _MSC_VER
-# define FMT_SNPRINTF snprintf
-#else // _MSC_VER
-inline int fmt_snprintf(char* buffer, size_t size, const char* format, ...) {
- va_list args;
- va_start(args, format);
- int result = vsnprintf_s(buffer, size, _TRUNCATE, format, args);
- va_end(args);
- return result;
-}
-# define FMT_SNPRINTF fmt_snprintf
-#endif // _MSC_VER
-
FMT_FUNC void format_error_code(detail::buffer<char>& out, int error_code,
- string_view message) FMT_NOEXCEPT {
+ string_view message) noexcept {
// Report error code making sure that the output fits into
// inline_buffer_size to avoid dynamic memory allocation and potential
// bad_alloc.
}
FMT_FUNC void report_error(format_func func, int error_code,
- const char* message) FMT_NOEXCEPT {
+ const char* message) noexcept {
memory_buffer full_message;
func(full_message, error_code, message);
// Don't use fwrite_fully because the latter may throw.
inline void fwrite_fully(const void* ptr, size_t size, size_t count,
FILE* stream) {
size_t written = std::fwrite(ptr, size, count, stream);
- if (written < count) FMT_THROW(system_error(errno, "cannot write to file"));
+ if (written < count)
+ FMT_THROW(system_error(errno, FMT_STRING("cannot write to file")));
}
#ifndef FMT_STATIC_THOUSANDS_SEPARATOR
#endif
} // namespace detail
-#if !FMT_MSC_VER
-FMT_API FMT_FUNC format_error::~format_error() FMT_NOEXCEPT = default;
+#if !FMT_MSC_VERSION
+FMT_API FMT_FUNC format_error::~format_error() noexcept = default;
#endif
FMT_FUNC std::system_error vsystem_error(int error_code, string_view format_str,
namespace detail {
-template <> FMT_FUNC int count_digits<4>(detail::fallback_uintptr n) {
- // fallback_uintptr is always stored in little endian.
- int i = static_cast<int>(sizeof(void*)) - 1;
- while (i > 0 && n.value[i] == 0) --i;
- auto char_digits = std::numeric_limits<unsigned char>::digits / 4;
- return i >= 0 ? i * char_digits + count_digits<4, unsigned>(n.value[i]) : 1;
-}
-
-// log10(2) = 0x0.4d104d427de7fbcc...
-static constexpr uint64_t log10_2_significand = 0x4d104d427de7fbcc;
-
-template <typename T = void> struct basic_impl_data {
- // Normalized 64-bit significands of pow(10, k), for k = -348, -340, ..., 340.
- // These are generated by support/compute-powers.py.
- static constexpr uint64_t pow10_significands[87] = {
- 0xfa8fd5a0081c0288, 0xbaaee17fa23ebf76, 0x8b16fb203055ac76,
- 0xcf42894a5dce35ea, 0x9a6bb0aa55653b2d, 0xe61acf033d1a45df,
- 0xab70fe17c79ac6ca, 0xff77b1fcbebcdc4f, 0xbe5691ef416bd60c,
- 0x8dd01fad907ffc3c, 0xd3515c2831559a83, 0x9d71ac8fada6c9b5,
- 0xea9c227723ee8bcb, 0xaecc49914078536d, 0x823c12795db6ce57,
- 0xc21094364dfb5637, 0x9096ea6f3848984f, 0xd77485cb25823ac7,
- 0xa086cfcd97bf97f4, 0xef340a98172aace5, 0xb23867fb2a35b28e,
- 0x84c8d4dfd2c63f3b, 0xc5dd44271ad3cdba, 0x936b9fcebb25c996,
- 0xdbac6c247d62a584, 0xa3ab66580d5fdaf6, 0xf3e2f893dec3f126,
- 0xb5b5ada8aaff80b8, 0x87625f056c7c4a8b, 0xc9bcff6034c13053,
- 0x964e858c91ba2655, 0xdff9772470297ebd, 0xa6dfbd9fb8e5b88f,
- 0xf8a95fcf88747d94, 0xb94470938fa89bcf, 0x8a08f0f8bf0f156b,
- 0xcdb02555653131b6, 0x993fe2c6d07b7fac, 0xe45c10c42a2b3b06,
- 0xaa242499697392d3, 0xfd87b5f28300ca0e, 0xbce5086492111aeb,
- 0x8cbccc096f5088cc, 0xd1b71758e219652c, 0x9c40000000000000,
- 0xe8d4a51000000000, 0xad78ebc5ac620000, 0x813f3978f8940984,
- 0xc097ce7bc90715b3, 0x8f7e32ce7bea5c70, 0xd5d238a4abe98068,
- 0x9f4f2726179a2245, 0xed63a231d4c4fb27, 0xb0de65388cc8ada8,
- 0x83c7088e1aab65db, 0xc45d1df942711d9a, 0x924d692ca61be758,
- 0xda01ee641a708dea, 0xa26da3999aef774a, 0xf209787bb47d6b85,
- 0xb454e4a179dd1877, 0x865b86925b9bc5c2, 0xc83553c5c8965d3d,
- 0x952ab45cfa97a0b3, 0xde469fbd99a05fe3, 0xa59bc234db398c25,
- 0xf6c69a72a3989f5c, 0xb7dcbf5354e9bece, 0x88fcf317f22241e2,
- 0xcc20ce9bd35c78a5, 0x98165af37b2153df, 0xe2a0b5dc971f303a,
- 0xa8d9d1535ce3b396, 0xfb9b7cd9a4a7443c, 0xbb764c4ca7a44410,
- 0x8bab8eefb6409c1a, 0xd01fef10a657842c, 0x9b10a4e5e9913129,
- 0xe7109bfba19c0c9d, 0xac2820d9623bf429, 0x80444b5e7aa7cf85,
- 0xbf21e44003acdd2d, 0x8e679c2f5e44ff8f, 0xd433179d9c8cb841,
- 0x9e19db92b4e31ba9, 0xeb96bf6ebadf77d9, 0xaf87023b9bf0ee6b,
- };
-
-#if FMT_GCC_VERSION && FMT_GCC_VERSION < 409
-# pragma GCC diagnostic push
-# pragma GCC diagnostic ignored "-Wnarrowing"
-#endif
- // Binary exponents of pow(10, k), for k = -348, -340, ..., 340, corresponding
- // to significands above.
- static constexpr int16_t pow10_exponents[87] = {
- -1220, -1193, -1166, -1140, -1113, -1087, -1060, -1034, -1007, -980, -954,
- -927, -901, -874, -847, -821, -794, -768, -741, -715, -688, -661,
- -635, -608, -582, -555, -529, -502, -475, -449, -422, -396, -369,
- -343, -316, -289, -263, -236, -210, -183, -157, -130, -103, -77,
- -50, -24, 3, 30, 56, 83, 109, 136, 162, 189, 216,
- 242, 269, 295, 322, 348, 375, 402, 428, 455, 481, 508,
- 534, 561, 588, 614, 641, 667, 694, 720, 747, 774, 800,
- 827, 853, 880, 907, 933, 960, 986, 1013, 1039, 1066};
-#if FMT_GCC_VERSION && FMT_GCC_VERSION < 409
-# pragma GCC diagnostic pop
-#endif
-
- static constexpr uint64_t power_of_10_64[20] = {
- 1, FMT_POWERS_OF_10(1ULL), FMT_POWERS_OF_10(1000000000ULL),
- 10000000000000000000ULL};
-};
-
-// This is a struct rather than an alias to avoid shadowing warnings in gcc.
-struct impl_data : basic_impl_data<> {};
-
-#if __cplusplus < 201703L
-template <typename T>
-constexpr uint64_t basic_impl_data<T>::pow10_significands[];
-template <typename T> constexpr int16_t basic_impl_data<T>::pow10_exponents[];
-template <typename T> constexpr uint64_t basic_impl_data<T>::power_of_10_64[];
-#endif
-
-template <typename T> struct bits {
- static FMT_CONSTEXPR_DECL const int value =
- static_cast<int>(sizeof(T) * std::numeric_limits<unsigned char>::digits);
-};
-
-// Returns the number of significand bits in Float excluding the implicit bit.
-template <typename Float> constexpr int num_significand_bits() {
- // Subtract 1 to account for an implicit most significant bit in the
- // normalized form.
- return std::numeric_limits<Float>::digits - 1;
-}
-
-// A floating-point number f * pow(2, e).
-struct fp {
- uint64_t f;
- int e;
-
- static constexpr const int num_significand_bits = bits<decltype(f)>::value;
-
- constexpr fp() : f(0), e(0) {}
- constexpr fp(uint64_t f_val, int e_val) : f(f_val), e(e_val) {}
-
- // Constructs fp from an IEEE754 floating-point number. It is a template to
- // prevent compile errors on systems where n is not IEEE754.
- template <typename Float> explicit FMT_CONSTEXPR fp(Float n) { assign(n); }
-
- template <typename Float>
- using is_supported = bool_constant<sizeof(Float) == sizeof(uint64_t) ||
- sizeof(Float) == sizeof(uint32_t)>;
-
- // Assigns d to this and return true iff predecessor is closer than successor.
- template <typename Float, FMT_ENABLE_IF(is_supported<Float>::value)>
- FMT_CONSTEXPR bool assign(Float n) {
- // Assume float is in the format [sign][exponent][significand].
- const int num_float_significand_bits =
- detail::num_significand_bits<Float>();
- const uint64_t implicit_bit = 1ULL << num_float_significand_bits;
- const uint64_t significand_mask = implicit_bit - 1;
- constexpr bool is_double = sizeof(Float) == sizeof(uint64_t);
- auto u = bit_cast<conditional_t<is_double, uint64_t, uint32_t>>(n);
- f = u & significand_mask;
- const uint64_t exponent_mask = (~0ULL >> 1) & ~significand_mask;
- int biased_e =
- static_cast<int>((u & exponent_mask) >> num_float_significand_bits);
- // The predecessor is closer if n is a normalized power of 2 (f == 0) other
- // than the smallest normalized number (biased_e > 1).
- bool is_predecessor_closer = f == 0 && biased_e > 1;
- if (biased_e != 0)
- f += implicit_bit;
- else
- biased_e = 1; // Subnormals use biased exponent 1 (min exponent).
- const int exponent_bias = std::numeric_limits<Float>::max_exponent - 1;
- e = biased_e - exponent_bias - num_float_significand_bits;
- return is_predecessor_closer;
- }
-
- template <typename Float, FMT_ENABLE_IF(!is_supported<Float>::value)>
- bool assign(Float) {
- FMT_ASSERT(false, "");
- return false;
- }
-};
-
-// Normalizes the value converted from double and multiplied by (1 << SHIFT).
-template <int SHIFT = 0> FMT_CONSTEXPR fp normalize(fp value) {
- // Handle subnormals.
- const uint64_t implicit_bit = 1ULL << num_significand_bits<double>();
- const auto shifted_implicit_bit = implicit_bit << SHIFT;
- while ((value.f & shifted_implicit_bit) == 0) {
- value.f <<= 1;
- --value.e;
- }
- // Subtract 1 to account for hidden bit.
- const auto offset =
- fp::num_significand_bits - num_significand_bits<double>() - SHIFT - 1;
- value.f <<= offset;
- value.e -= offset;
- return value;
-}
-
-inline bool operator==(fp x, fp y) { return x.f == y.f && x.e == y.e; }
-
-// Computes lhs * rhs / pow(2, 64) rounded to nearest with half-up tie breaking.
-FMT_CONSTEXPR inline uint64_t multiply(uint64_t lhs, uint64_t rhs) {
-#if FMT_USE_INT128
- auto product = static_cast<__uint128_t>(lhs) * rhs;
- auto f = static_cast<uint64_t>(product >> 64);
- return (static_cast<uint64_t>(product) & (1ULL << 63)) != 0 ? f + 1 : f;
-#else
- // Multiply 32-bit parts of significands.
- uint64_t mask = (1ULL << 32) - 1;
- uint64_t a = lhs >> 32, b = lhs & mask;
- uint64_t c = rhs >> 32, d = rhs & mask;
- uint64_t ac = a * c, bc = b * c, ad = a * d, bd = b * d;
- // Compute mid 64-bit of result and round.
- uint64_t mid = (bd >> 32) + (ad & mask) + (bc & mask) + (1U << 31);
- return ac + (ad >> 32) + (bc >> 32) + (mid >> 32);
-#endif
-}
-
-FMT_CONSTEXPR inline fp operator*(fp x, fp y) {
- return {multiply(x.f, y.f), x.e + y.e + 64};
-}
-
-// Returns a cached power of 10 `c_k = c_k.f * pow(2, c_k.e)` such that its
-// (binary) exponent satisfies `min_exponent <= c_k.e <= min_exponent + 28`.
-FMT_CONSTEXPR inline fp get_cached_power(int min_exponent,
- int& pow10_exponent) {
- const int shift = 32;
- const auto significand = static_cast<int64_t>(log10_2_significand);
- int index = static_cast<int>(
- ((min_exponent + fp::num_significand_bits - 1) * (significand >> shift) +
- ((int64_t(1) << shift) - 1)) // ceil
- >> 32 // arithmetic shift
- );
- // Decimal exponent of the first (smallest) cached power of 10.
- const int first_dec_exp = -348;
- // Difference between 2 consecutive decimal exponents in cached powers of 10.
- const int dec_exp_step = 8;
- index = (index - first_dec_exp - 1) / dec_exp_step + 1;
- pow10_exponent = first_dec_exp + index * dec_exp_step;
- return {impl_data::pow10_significands[index],
- impl_data::pow10_exponents[index]};
-}
-
-// A simple accumulator to hold the sums of terms in bigint::square if uint128_t
-// is not available.
-struct accumulator {
- uint64_t lower;
- uint64_t upper;
-
- constexpr accumulator() : lower(0), upper(0) {}
- constexpr explicit operator uint32_t() const {
- return static_cast<uint32_t>(lower);
- }
-
- FMT_CONSTEXPR void operator+=(uint64_t n) {
- lower += n;
- if (lower < n) ++upper;
- }
- FMT_CONSTEXPR void operator>>=(int shift) {
- FMT_ASSERT(shift == 32, "");
- (void)shift;
- lower = (upper << 32) | (lower >> 32);
- upper >>= 32;
- }
-};
-
-class bigint {
- private:
- // A bigint is stored as an array of bigits (big digits), with bigit at index
- // 0 being the least significant one.
- using bigit = uint32_t;
- using double_bigit = uint64_t;
- enum { bigits_capacity = 32 };
- basic_memory_buffer<bigit, bigits_capacity> bigits_;
- int exp_;
-
- FMT_CONSTEXPR20 bigit operator[](int index) const {
- return bigits_[to_unsigned(index)];
- }
- FMT_CONSTEXPR20 bigit& operator[](int index) {
- return bigits_[to_unsigned(index)];
- }
-
- static FMT_CONSTEXPR_DECL const int bigit_bits = bits<bigit>::value;
-
- friend struct formatter<bigint>;
-
- FMT_CONSTEXPR20 void subtract_bigits(int index, bigit other, bigit& borrow) {
- auto result = static_cast<double_bigit>((*this)[index]) - other - borrow;
- (*this)[index] = static_cast<bigit>(result);
- borrow = static_cast<bigit>(result >> (bigit_bits * 2 - 1));
- }
-
- FMT_CONSTEXPR20 void remove_leading_zeros() {
- int num_bigits = static_cast<int>(bigits_.size()) - 1;
- while (num_bigits > 0 && (*this)[num_bigits] == 0) --num_bigits;
- bigits_.resize(to_unsigned(num_bigits + 1));
- }
-
- // Computes *this -= other assuming aligned bigints and *this >= other.
- FMT_CONSTEXPR20 void subtract_aligned(const bigint& other) {
- FMT_ASSERT(other.exp_ >= exp_, "unaligned bigints");
- FMT_ASSERT(compare(*this, other) >= 0, "");
- bigit borrow = 0;
- int i = other.exp_ - exp_;
- for (size_t j = 0, n = other.bigits_.size(); j != n; ++i, ++j)
- subtract_bigits(i, other.bigits_[j], borrow);
- while (borrow > 0) subtract_bigits(i, 0, borrow);
- remove_leading_zeros();
- }
-
- FMT_CONSTEXPR20 void multiply(uint32_t value) {
- const double_bigit wide_value = value;
- bigit carry = 0;
- for (size_t i = 0, n = bigits_.size(); i < n; ++i) {
- double_bigit result = bigits_[i] * wide_value + carry;
- bigits_[i] = static_cast<bigit>(result);
- carry = static_cast<bigit>(result >> bigit_bits);
- }
- if (carry != 0) bigits_.push_back(carry);
- }
-
- FMT_CONSTEXPR20 void multiply(uint64_t value) {
- const bigit mask = ~bigit(0);
- const double_bigit lower = value & mask;
- const double_bigit upper = value >> bigit_bits;
- double_bigit carry = 0;
- for (size_t i = 0, n = bigits_.size(); i < n; ++i) {
- double_bigit result = bigits_[i] * lower + (carry & mask);
- carry =
- bigits_[i] * upper + (result >> bigit_bits) + (carry >> bigit_bits);
- bigits_[i] = static_cast<bigit>(result);
- }
- while (carry != 0) {
- bigits_.push_back(carry & mask);
- carry >>= bigit_bits;
- }
- }
-
- public:
- FMT_CONSTEXPR20 bigint() : exp_(0) {}
- explicit bigint(uint64_t n) { assign(n); }
- FMT_CONSTEXPR20 ~bigint() {
- FMT_ASSERT(bigits_.capacity() <= bigits_capacity, "");
- }
-
- bigint(const bigint&) = delete;
- void operator=(const bigint&) = delete;
-
- FMT_CONSTEXPR20 void assign(const bigint& other) {
- auto size = other.bigits_.size();
- bigits_.resize(size);
- auto data = other.bigits_.data();
- std::copy(data, data + size, make_checked(bigits_.data(), size));
- exp_ = other.exp_;
- }
-
- FMT_CONSTEXPR20 void assign(uint64_t n) {
- size_t num_bigits = 0;
- do {
- bigits_[num_bigits++] = n & ~bigit(0);
- n >>= bigit_bits;
- } while (n != 0);
- bigits_.resize(num_bigits);
- exp_ = 0;
- }
-
- FMT_CONSTEXPR20 int num_bigits() const {
- return static_cast<int>(bigits_.size()) + exp_;
- }
-
- FMT_NOINLINE FMT_CONSTEXPR20 bigint& operator<<=(int shift) {
- FMT_ASSERT(shift >= 0, "");
- exp_ += shift / bigit_bits;
- shift %= bigit_bits;
- if (shift == 0) return *this;
- bigit carry = 0;
- for (size_t i = 0, n = bigits_.size(); i < n; ++i) {
- bigit c = bigits_[i] >> (bigit_bits - shift);
- bigits_[i] = (bigits_[i] << shift) + carry;
- carry = c;
- }
- if (carry != 0) bigits_.push_back(carry);
- return *this;
- }
-
- template <typename Int> FMT_CONSTEXPR20 bigint& operator*=(Int value) {
- FMT_ASSERT(value > 0, "");
- multiply(uint32_or_64_or_128_t<Int>(value));
- return *this;
- }
-
- friend FMT_CONSTEXPR20 int compare(const bigint& lhs, const bigint& rhs) {
- int num_lhs_bigits = lhs.num_bigits(), num_rhs_bigits = rhs.num_bigits();
- if (num_lhs_bigits != num_rhs_bigits)
- return num_lhs_bigits > num_rhs_bigits ? 1 : -1;
- int i = static_cast<int>(lhs.bigits_.size()) - 1;
- int j = static_cast<int>(rhs.bigits_.size()) - 1;
- int end = i - j;
- if (end < 0) end = 0;
- for (; i >= end; --i, --j) {
- bigit lhs_bigit = lhs[i], rhs_bigit = rhs[j];
- if (lhs_bigit != rhs_bigit) return lhs_bigit > rhs_bigit ? 1 : -1;
- }
- if (i != j) return i > j ? 1 : -1;
- return 0;
- }
-
- // Returns compare(lhs1 + lhs2, rhs).
- friend FMT_CONSTEXPR20 int add_compare(const bigint& lhs1, const bigint& lhs2,
- const bigint& rhs) {
- int max_lhs_bigits = (std::max)(lhs1.num_bigits(), lhs2.num_bigits());
- int num_rhs_bigits = rhs.num_bigits();
- if (max_lhs_bigits + 1 < num_rhs_bigits) return -1;
- if (max_lhs_bigits > num_rhs_bigits) return 1;
- auto get_bigit = [](const bigint& n, int i) -> bigit {
- return i >= n.exp_ && i < n.num_bigits() ? n[i - n.exp_] : 0;
- };
- double_bigit borrow = 0;
- int min_exp = (std::min)((std::min)(lhs1.exp_, lhs2.exp_), rhs.exp_);
- for (int i = num_rhs_bigits - 1; i >= min_exp; --i) {
- double_bigit sum =
- static_cast<double_bigit>(get_bigit(lhs1, i)) + get_bigit(lhs2, i);
- bigit rhs_bigit = get_bigit(rhs, i);
- if (sum > rhs_bigit + borrow) return 1;
- borrow = rhs_bigit + borrow - sum;
- if (borrow > 1) return -1;
- borrow <<= bigit_bits;
- }
- return borrow != 0 ? -1 : 0;
- }
-
- // Assigns pow(10, exp) to this bigint.
- FMT_CONSTEXPR20 void assign_pow10(int exp) {
- FMT_ASSERT(exp >= 0, "");
- if (exp == 0) return assign(1);
- // Find the top bit.
- int bitmask = 1;
- while (exp >= bitmask) bitmask <<= 1;
- bitmask >>= 1;
- // pow(10, exp) = pow(5, exp) * pow(2, exp). First compute pow(5, exp) by
- // repeated squaring and multiplication.
- assign(5);
- bitmask >>= 1;
- while (bitmask != 0) {
- square();
- if ((exp & bitmask) != 0) *this *= 5;
- bitmask >>= 1;
- }
- *this <<= exp; // Multiply by pow(2, exp) by shifting.
- }
-
- FMT_CONSTEXPR20 void square() {
- int num_bigits = static_cast<int>(bigits_.size());
- int num_result_bigits = 2 * num_bigits;
- basic_memory_buffer<bigit, bigits_capacity> n(std::move(bigits_));
- bigits_.resize(to_unsigned(num_result_bigits));
- using accumulator_t = conditional_t<FMT_USE_INT128, uint128_t, accumulator>;
- auto sum = accumulator_t();
- for (int bigit_index = 0; bigit_index < num_bigits; ++bigit_index) {
- // Compute bigit at position bigit_index of the result by adding
- // cross-product terms n[i] * n[j] such that i + j == bigit_index.
- for (int i = 0, j = bigit_index; j >= 0; ++i, --j) {
- // Most terms are multiplied twice which can be optimized in the future.
- sum += static_cast<double_bigit>(n[i]) * n[j];
- }
- (*this)[bigit_index] = static_cast<bigit>(sum);
- sum >>= bits<bigit>::value; // Compute the carry.
- }
- // Do the same for the top half.
- for (int bigit_index = num_bigits; bigit_index < num_result_bigits;
- ++bigit_index) {
- for (int j = num_bigits - 1, i = bigit_index - j; i < num_bigits;)
- sum += static_cast<double_bigit>(n[i++]) * n[j--];
- (*this)[bigit_index] = static_cast<bigit>(sum);
- sum >>= bits<bigit>::value;
- }
- remove_leading_zeros();
- exp_ *= 2;
- }
-
- // If this bigint has a bigger exponent than other, adds trailing zero to make
- // exponents equal. This simplifies some operations such as subtraction.
- FMT_CONSTEXPR20 void align(const bigint& other) {
- int exp_difference = exp_ - other.exp_;
- if (exp_difference <= 0) return;
- int num_bigits = static_cast<int>(bigits_.size());
- bigits_.resize(to_unsigned(num_bigits + exp_difference));
- for (int i = num_bigits - 1, j = i + exp_difference; i >= 0; --i, --j)
- bigits_[j] = bigits_[i];
- std::uninitialized_fill_n(bigits_.data(), exp_difference, 0);
- exp_ -= exp_difference;
- }
-
- // Divides this bignum by divisor, assigning the remainder to this and
- // returning the quotient.
- FMT_CONSTEXPR20 int divmod_assign(const bigint& divisor) {
- FMT_ASSERT(this != &divisor, "");
- if (compare(*this, divisor) < 0) return 0;
- FMT_ASSERT(divisor.bigits_[divisor.bigits_.size() - 1u] != 0, "");
- align(divisor);
- int quotient = 0;
- do {
- subtract_aligned(divisor);
- ++quotient;
- } while (compare(*this, divisor) >= 0);
- return quotient;
- }
-};
-
-enum class round_direction { unknown, up, down };
-
-// Given the divisor (normally a power of 10), the remainder = v % divisor for
-// some number v and the error, returns whether v should be rounded up, down, or
-// whether the rounding direction can't be determined due to error.
-// error should be less than divisor / 2.
-FMT_CONSTEXPR inline round_direction get_round_direction(uint64_t divisor,
- uint64_t remainder,
- uint64_t error) {
- FMT_ASSERT(remainder < divisor, ""); // divisor - remainder won't overflow.
- FMT_ASSERT(error < divisor, ""); // divisor - error won't overflow.
- FMT_ASSERT(error < divisor - error, ""); // error * 2 won't overflow.
- // Round down if (remainder + error) * 2 <= divisor.
- if (remainder <= divisor - remainder && error * 2 <= divisor - remainder * 2)
- return round_direction::down;
- // Round up if (remainder - error) * 2 >= divisor.
- if (remainder >= error &&
- remainder - error >= divisor - (remainder - error)) {
- return round_direction::up;
- }
- return round_direction::unknown;
+template <typename F> inline bool operator==(basic_fp<F> x, basic_fp<F> y) {
+ return x.f == y.f && x.e == y.e;
}
-namespace digits {
-enum result {
- more, // Generate more digits.
- done, // Done generating digits.
- error // Digit generation cancelled due to an error.
-};
+// Compilers should be able to optimize this into the ror instruction.
+FMT_CONSTEXPR inline uint32_t rotr(uint32_t n, uint32_t r) noexcept {
+ r &= 31;
+ return (n >> r) | (n << (32 - r));
}
-
-struct gen_digits_handler {
- char* buf;
- int size;
- int precision;
- int exp10;
- bool fixed;
-
- FMT_CONSTEXPR digits::result on_digit(char digit, uint64_t divisor,
- uint64_t remainder, uint64_t error,
- bool integral) {
- FMT_ASSERT(remainder < divisor, "");
- buf[size++] = digit;
- if (!integral && error >= remainder) return digits::error;
- if (size < precision) return digits::more;
- if (!integral) {
- // Check if error * 2 < divisor with overflow prevention.
- // The check is not needed for the integral part because error = 1
- // and divisor > (1 << 32) there.
- if (error >= divisor || error >= divisor - error) return digits::error;
- } else {
- FMT_ASSERT(error == 1 && divisor > 2, "");
- }
- auto dir = get_round_direction(divisor, remainder, error);
- if (dir != round_direction::up)
- return dir == round_direction::down ? digits::done : digits::error;
- ++buf[size - 1];
- for (int i = size - 1; i > 0 && buf[i] > '9'; --i) {
- buf[i] = '0';
- ++buf[i - 1];
- }
- if (buf[0] > '9') {
- buf[0] = '1';
- if (fixed)
- buf[size++] = '0';
- else
- ++exp10;
- }
- return digits::done;
- }
-};
-
-// Generates output using the Grisu digit-gen algorithm.
-// error: the size of the region (lower, upper) outside of which numbers
-// definitely do not round to value (Delta in Grisu3).
-FMT_INLINE FMT_CONSTEXPR20 digits::result grisu_gen_digits(
- fp value, uint64_t error, int& exp, gen_digits_handler& handler) {
- const fp one(1ULL << -value.e, value.e);
- // The integral part of scaled value (p1 in Grisu) = value / one. It cannot be
- // zero because it contains a product of two 64-bit numbers with MSB set (due
- // to normalization) - 1, shifted right by at most 60 bits.
- auto integral = static_cast<uint32_t>(value.f >> -one.e);
- FMT_ASSERT(integral != 0, "");
- FMT_ASSERT(integral == value.f >> -one.e, "");
- // The fractional part of scaled value (p2 in Grisu) c = value % one.
- uint64_t fractional = value.f & (one.f - 1);
- exp = count_digits(integral); // kappa in Grisu.
- // Non-fixed formats require at least one digit and no precision adjustment.
- if (handler.fixed) {
- // Adjust fixed precision by exponent because it is relative to decimal
- // point.
- int precision_offset = exp + handler.exp10;
- if (precision_offset > 0 &&
- handler.precision > max_value<int>() - precision_offset) {
- FMT_THROW(format_error("number is too big"));
- }
- handler.precision += precision_offset;
- // Check if precision is satisfied just by leading zeros, e.g.
- // format("{:.2f}", 0.001) gives "0.00" without generating any digits.
- if (handler.precision <= 0) {
- if (handler.precision < 0) return digits::done;
- // Divide by 10 to prevent overflow.
- uint64_t divisor = impl_data::power_of_10_64[exp - 1] << -one.e;
- auto dir = get_round_direction(divisor, value.f / 10, error * 10);
- if (dir == round_direction::unknown) return digits::error;
- handler.buf[handler.size++] = dir == round_direction::up ? '1' : '0';
- return digits::done;
- }
- }
- // Generate digits for the integral part. This can produce up to 10 digits.
- do {
- uint32_t digit = 0;
- auto divmod_integral = [&](uint32_t divisor) {
- digit = integral / divisor;
- integral %= divisor;
- };
- // This optimization by Milo Yip reduces the number of integer divisions by
- // one per iteration.
- switch (exp) {
- case 10:
- divmod_integral(1000000000);
- break;
- case 9:
- divmod_integral(100000000);
- break;
- case 8:
- divmod_integral(10000000);
- break;
- case 7:
- divmod_integral(1000000);
- break;
- case 6:
- divmod_integral(100000);
- break;
- case 5:
- divmod_integral(10000);
- break;
- case 4:
- divmod_integral(1000);
- break;
- case 3:
- divmod_integral(100);
- break;
- case 2:
- divmod_integral(10);
- break;
- case 1:
- digit = integral;
- integral = 0;
- break;
- default:
- FMT_ASSERT(false, "invalid number of digits");
- }
- --exp;
- auto remainder = (static_cast<uint64_t>(integral) << -one.e) + fractional;
- auto result = handler.on_digit(static_cast<char>('0' + digit),
- impl_data::power_of_10_64[exp] << -one.e,
- remainder, error, true);
- if (result != digits::more) return result;
- } while (exp > 0);
- // Generate digits for the fractional part.
- for (;;) {
- fractional *= 10;
- error *= 10;
- char digit = static_cast<char>('0' + (fractional >> -one.e));
- fractional &= one.f - 1;
- --exp;
- auto result = handler.on_digit(digit, one.f, fractional, error, false);
- if (result != digits::more) return result;
- }
+FMT_CONSTEXPR inline uint64_t rotr(uint64_t n, uint32_t r) noexcept {
+ r &= 63;
+ return (n >> r) | (n << (64 - r));
}
-// A 128-bit integer type used internally,
-struct uint128_wrapper {
- uint128_wrapper() = default;
-
-#if FMT_USE_INT128
- uint128_t internal_;
-
- constexpr uint128_wrapper(uint64_t high, uint64_t low) FMT_NOEXCEPT
- : internal_{static_cast<uint128_t>(low) |
- (static_cast<uint128_t>(high) << 64)} {}
-
- constexpr uint128_wrapper(uint128_t u) : internal_{u} {}
-
- constexpr uint64_t high() const FMT_NOEXCEPT {
- return uint64_t(internal_ >> 64);
- }
- constexpr uint64_t low() const FMT_NOEXCEPT { return uint64_t(internal_); }
-
- uint128_wrapper& operator+=(uint64_t n) FMT_NOEXCEPT {
- internal_ += n;
- return *this;
- }
-#else
- uint64_t high_;
- uint64_t low_;
-
- constexpr uint128_wrapper(uint64_t high, uint64_t low) FMT_NOEXCEPT
- : high_{high},
- low_{low} {}
-
- constexpr uint64_t high() const FMT_NOEXCEPT { return high_; }
- constexpr uint64_t low() const FMT_NOEXCEPT { return low_; }
-
- uint128_wrapper& operator+=(uint64_t n) FMT_NOEXCEPT {
-# if defined(_MSC_VER) && defined(_M_X64)
- unsigned char carry = _addcarry_u64(0, low_, n, &low_);
- _addcarry_u64(carry, high_, 0, &high_);
- return *this;
-# else
- uint64_t sum = low_ + n;
- high_ += (sum < low_ ? 1 : 0);
- low_ = sum;
- return *this;
-# endif
- }
-#endif
-};
-
-// Implementation of Dragonbox algorithm: https://github.com/jk-jeon/dragonbox.
-namespace dragonbox {
// Computes 128-bit result of multiplication of two 64-bit unsigned integers.
-inline uint128_wrapper umul128(uint64_t x, uint64_t y) FMT_NOEXCEPT {
+inline uint128_fallback umul128(uint64_t x, uint64_t y) noexcept {
#if FMT_USE_INT128
- return static_cast<uint128_t>(x) * static_cast<uint128_t>(y);
+ auto p = static_cast<uint128_opt>(x) * static_cast<uint128_opt>(y);
+ return {static_cast<uint64_t>(p >> 64), static_cast<uint64_t>(p)};
#elif defined(_MSC_VER) && defined(_M_X64)
- uint128_wrapper result;
- result.low_ = _umul128(x, y, &result.high_);
+ auto result = uint128_fallback();
+ result.lo_ = _umul128(x, y, &result.hi_);
return result;
#else
- const uint64_t mask = (uint64_t(1) << 32) - uint64_t(1);
+ const uint64_t mask = static_cast<uint64_t>(max_value<uint32_t>());
uint64_t a = x >> 32;
uint64_t b = x & mask;
#endif
}
+// Implementation of Dragonbox algorithm: https://github.com/jk-jeon/dragonbox.
+namespace dragonbox {
// Computes upper 64 bits of multiplication of two 64-bit unsigned integers.
-inline uint64_t umul128_upper64(uint64_t x, uint64_t y) FMT_NOEXCEPT {
+inline uint64_t umul128_upper64(uint64_t x, uint64_t y) noexcept {
#if FMT_USE_INT128
- auto p = static_cast<uint128_t>(x) * static_cast<uint128_t>(y);
+ auto p = static_cast<uint128_opt>(x) * static_cast<uint128_opt>(y);
return static_cast<uint64_t>(p >> 64);
#elif defined(_MSC_VER) && defined(_M_X64)
return __umulh(x, y);
#endif
}
-// Computes upper 64 bits of multiplication of a 64-bit unsigned integer and a
+// Computes upper 128 bits of multiplication of a 64-bit unsigned integer and a
// 128-bit unsigned integer.
-inline uint64_t umul192_upper64(uint64_t x, uint128_wrapper y) FMT_NOEXCEPT {
- uint128_wrapper g0 = umul128(x, y.high());
- g0 += umul128_upper64(x, y.low());
- return g0.high();
+inline uint128_fallback umul192_upper128(uint64_t x,
+ uint128_fallback y) noexcept {
+ uint128_fallback r = umul128(x, y.high());
+ r += umul128_upper64(x, y.low());
+ return r;
}
-// Computes upper 32 bits of multiplication of a 32-bit unsigned integer and a
+// Computes upper 64 bits of multiplication of a 32-bit unsigned integer and a
// 64-bit unsigned integer.
-inline uint32_t umul96_upper32(uint32_t x, uint64_t y) FMT_NOEXCEPT {
- return static_cast<uint32_t>(umul128_upper64(x, y));
+inline uint64_t umul96_upper64(uint32_t x, uint64_t y) noexcept {
+ return umul128_upper64(static_cast<uint64_t>(x) << 32, y);
}
-// Computes middle 64 bits of multiplication of a 64-bit unsigned integer and a
+// Computes lower 128 bits of multiplication of a 64-bit unsigned integer and a
// 128-bit unsigned integer.
-inline uint64_t umul192_middle64(uint64_t x, uint128_wrapper y) FMT_NOEXCEPT {
- uint64_t g01 = x * y.high();
- uint64_t g10 = umul128_upper64(x, y.low());
- return g01 + g10;
+inline uint128_fallback umul192_lower128(uint64_t x,
+ uint128_fallback y) noexcept {
+ uint64_t high = x * y.high();
+ uint128_fallback high_low = umul128(x, y.low());
+ return {high + high_low.high(), high_low.low()};
}
// Computes lower 64 bits of multiplication of a 32-bit unsigned integer and a
// 64-bit unsigned integer.
-inline uint64_t umul96_lower64(uint32_t x, uint64_t y) FMT_NOEXCEPT {
+inline uint64_t umul96_lower64(uint32_t x, uint64_t y) noexcept {
return x * y;
}
-// Computes floor(log10(pow(2, e))) for e in [-1700, 1700] using the method from
-// https://fmt.dev/papers/Grisu-Exact.pdf#page=5, section 3.4.
-inline int floor_log10_pow2(int e) FMT_NOEXCEPT {
- FMT_ASSERT(e <= 1700 && e >= -1700, "too large exponent");
- const int shift = 22;
- return (e * static_cast<int>(log10_2_significand >> (64 - shift))) >> shift;
+// Computes floor(log10(pow(2, e))) for e in [-2620, 2620] using the method from
+// https://fmt.dev/papers/Dragonbox.pdf#page=28, section 6.1.
+inline int floor_log10_pow2(int e) noexcept {
+ FMT_ASSERT(e <= 2620 && e >= -2620, "too large exponent");
+ static_assert((-1 >> 1) == -1, "right shift is not arithmetic");
+ return (e * 315653) >> 20;
}
// Various fast log computations.
-inline int floor_log2_pow10(int e) FMT_NOEXCEPT {
+inline int floor_log2_pow10(int e) noexcept {
FMT_ASSERT(e <= 1233 && e >= -1233, "too large exponent");
- const uint64_t log2_10_integer_part = 3;
- const uint64_t log2_10_fractional_digits = 0x5269e12f346e2bf9;
- const int shift_amount = 19;
- return (e * static_cast<int>(
- (log2_10_integer_part << shift_amount) |
- (log2_10_fractional_digits >> (64 - shift_amount)))) >>
- shift_amount;
+ return (e * 1741647) >> 19;
}
-inline int floor_log10_pow2_minus_log10_4_over_3(int e) FMT_NOEXCEPT {
- FMT_ASSERT(e <= 1700 && e >= -1700, "too large exponent");
- const uint64_t log10_4_over_3_fractional_digits = 0x1ffbfc2bbc780375;
- const int shift_amount = 22;
- return (e * static_cast<int>(log10_2_significand >> (64 - shift_amount)) -
- static_cast<int>(log10_4_over_3_fractional_digits >>
- (64 - shift_amount))) >>
- shift_amount;
+inline int floor_log10_pow2_minus_log10_4_over_3(int e) noexcept {
+ FMT_ASSERT(e <= 2936 && e >= -2985, "too large exponent");
+ return (e * 631305 - 261663) >> 21;
}
-// Returns true iff x is divisible by pow(2, exp).
-inline bool divisible_by_power_of_2(uint32_t x, int exp) FMT_NOEXCEPT {
- FMT_ASSERT(exp >= 1, "");
- FMT_ASSERT(x != 0, "");
-#ifdef FMT_BUILTIN_CTZ
- return FMT_BUILTIN_CTZ(x) >= exp;
-#else
- return exp < num_bits<uint32_t>() && x == ((x >> exp) << exp);
-#endif
-}
-inline bool divisible_by_power_of_2(uint64_t x, int exp) FMT_NOEXCEPT {
- FMT_ASSERT(exp >= 1, "");
- FMT_ASSERT(x != 0, "");
-#ifdef FMT_BUILTIN_CTZLL
- return FMT_BUILTIN_CTZLL(x) >= exp;
-#else
- return exp < num_bits<uint64_t>() && x == ((x >> exp) << exp);
-#endif
-}
-
-// Table entry type for divisibility test.
-template <typename T> struct divtest_table_entry {
- T mod_inv;
- T max_quotient;
-};
-
-// Returns true iff x is divisible by pow(5, exp).
-inline bool divisible_by_power_of_5(uint32_t x, int exp) FMT_NOEXCEPT {
- FMT_ASSERT(exp <= 10, "too large exponent");
- static constexpr const divtest_table_entry<uint32_t> divtest_table[] = {
- {0x00000001, 0xffffffff}, {0xcccccccd, 0x33333333},
- {0xc28f5c29, 0x0a3d70a3}, {0x26e978d5, 0x020c49ba},
- {0x3afb7e91, 0x0068db8b}, {0x0bcbe61d, 0x0014f8b5},
- {0x68c26139, 0x000431bd}, {0xae8d46a5, 0x0000d6bf},
- {0x22e90e21, 0x00002af3}, {0x3a2e9c6d, 0x00000897},
- {0x3ed61f49, 0x000001b7}};
- return x * divtest_table[exp].mod_inv <= divtest_table[exp].max_quotient;
-}
-inline bool divisible_by_power_of_5(uint64_t x, int exp) FMT_NOEXCEPT {
- FMT_ASSERT(exp <= 23, "too large exponent");
- static constexpr const divtest_table_entry<uint64_t> divtest_table[] = {
- {0x0000000000000001, 0xffffffffffffffff},
- {0xcccccccccccccccd, 0x3333333333333333},
- {0x8f5c28f5c28f5c29, 0x0a3d70a3d70a3d70},
- {0x1cac083126e978d5, 0x020c49ba5e353f7c},
- {0xd288ce703afb7e91, 0x0068db8bac710cb2},
- {0x5d4e8fb00bcbe61d, 0x0014f8b588e368f0},
- {0x790fb65668c26139, 0x000431bde82d7b63},
- {0xe5032477ae8d46a5, 0x0000d6bf94d5e57a},
- {0xc767074b22e90e21, 0x00002af31dc46118},
- {0x8e47ce423a2e9c6d, 0x0000089705f4136b},
- {0x4fa7f60d3ed61f49, 0x000001b7cdfd9d7b},
- {0x0fee64690c913975, 0x00000057f5ff85e5},
- {0x3662e0e1cf503eb1, 0x000000119799812d},
- {0xa47a2cf9f6433fbd, 0x0000000384b84d09},
- {0x54186f653140a659, 0x00000000b424dc35},
- {0x7738164770402145, 0x0000000024075f3d},
- {0xe4a4d1417cd9a041, 0x000000000734aca5},
- {0xc75429d9e5c5200d, 0x000000000170ef54},
- {0xc1773b91fac10669, 0x000000000049c977},
- {0x26b172506559ce15, 0x00000000000ec1e4},
- {0xd489e3a9addec2d1, 0x000000000002f394},
- {0x90e860bb892c8d5d, 0x000000000000971d},
- {0x502e79bf1b6f4f79, 0x0000000000001e39},
- {0xdcd618596be30fe5, 0x000000000000060b}};
- return x * divtest_table[exp].mod_inv <= divtest_table[exp].max_quotient;
-}
+static constexpr struct {
+ uint32_t divisor;
+ int shift_amount;
+} div_small_pow10_infos[] = {{10, 16}, {100, 16}};
-// Replaces n by floor(n / pow(5, N)) returning true if and only if n is
-// divisible by pow(5, N).
-// Precondition: n <= 2 * pow(5, N + 1).
+// Replaces n by floor(n / pow(10, N)) returning true if and only if n is
+// divisible by pow(10, N).
+// Precondition: n <= pow(10, N + 1).
template <int N>
-bool check_divisibility_and_divide_by_pow5(uint32_t& n) FMT_NOEXCEPT {
- static constexpr struct {
- uint32_t magic_number;
- int bits_for_comparison;
- uint32_t threshold;
- int shift_amount;
- } infos[] = {{0xcccd, 16, 0x3333, 18}, {0xa429, 8, 0x0a, 20}};
- constexpr auto info = infos[N - 1];
- n *= info.magic_number;
- const uint32_t comparison_mask = (1u << info.bits_for_comparison) - 1;
- bool result = (n & comparison_mask) <= info.threshold;
+bool check_divisibility_and_divide_by_pow10(uint32_t& n) noexcept {
+ // The numbers below are chosen such that:
+ // 1. floor(n/d) = floor(nm / 2^k) where d=10 or d=100,
+ // 2. nm mod 2^k < m if and only if n is divisible by d,
+ // where m is magic_number, k is shift_amount
+ // and d is divisor.
+ //
+ // Item 1 is a common technique of replacing division by a constant with
+ // multiplication, see e.g. "Division by Invariant Integers Using
+ // Multiplication" by Granlund and Montgomery (1994). magic_number (m) is set
+ // to ceil(2^k/d) for large enough k.
+ // The idea for item 2 originates from Schubfach.
+ constexpr auto info = div_small_pow10_infos[N - 1];
+ FMT_ASSERT(n <= info.divisor * 10, "n is too large");
+ constexpr uint32_t magic_number =
+ (1u << info.shift_amount) / info.divisor + 1;
+ n *= magic_number;
+ const uint32_t comparison_mask = (1u << info.shift_amount) - 1;
+ bool result = (n & comparison_mask) < magic_number;
n >>= info.shift_amount;
return result;
}
// Computes floor(n / pow(10, N)) for small n and N.
// Precondition: n <= pow(10, N + 1).
-template <int N> uint32_t small_division_by_pow10(uint32_t n) FMT_NOEXCEPT {
- static constexpr struct {
- uint32_t magic_number;
- int shift_amount;
- uint32_t divisor_times_10;
- } infos[] = {{0xcccd, 19, 100}, {0xa3d8, 22, 1000}};
- constexpr auto info = infos[N - 1];
- FMT_ASSERT(n <= info.divisor_times_10, "n is too large");
- return n * info.magic_number >> info.shift_amount;
+template <int N> uint32_t small_division_by_pow10(uint32_t n) noexcept {
+ constexpr auto info = div_small_pow10_infos[N - 1];
+ FMT_ASSERT(n <= info.divisor * 10, "n is too large");
+ constexpr uint32_t magic_number =
+ (1u << info.shift_amount) / info.divisor + 1;
+ return (n * magic_number) >> info.shift_amount;
}
// Computes floor(n / 10^(kappa + 1)) (float)
-inline uint32_t divide_by_10_to_kappa_plus_1(uint32_t n) FMT_NOEXCEPT {
- return n / float_info<float>::big_divisor;
+inline uint32_t divide_by_10_to_kappa_plus_1(uint32_t n) noexcept {
+ // 1374389535 = ceil(2^37/100)
+ return static_cast<uint32_t>((static_cast<uint64_t>(n) * 1374389535) >> 37);
}
// Computes floor(n / 10^(kappa + 1)) (double)
-inline uint64_t divide_by_10_to_kappa_plus_1(uint64_t n) FMT_NOEXCEPT {
- return umul128_upper64(n, 0x83126e978d4fdf3c) >> 9;
+inline uint64_t divide_by_10_to_kappa_plus_1(uint64_t n) noexcept {
+ // 2361183241434822607 = ceil(2^(64+7)/1000)
+ return umul128_upper64(n, 2361183241434822607ull) >> 7;
}
// Various subroutines using pow10 cache
using carrier_uint = float_info<float>::carrier_uint;
using cache_entry_type = uint64_t;
- static uint64_t get_cached_power(int k) FMT_NOEXCEPT {
+ static uint64_t get_cached_power(int k) noexcept {
FMT_ASSERT(k >= float_info<float>::min_k && k <= float_info<float>::max_k,
"k is out of range");
static constexpr const uint64_t pow10_significands[] = {
0xb1a2bc2ec5000000, 0xde0b6b3a76400000, 0x8ac7230489e80000,
0xad78ebc5ac620000, 0xd8d726b7177a8000, 0x878678326eac9000,
0xa968163f0a57b400, 0xd3c21bcecceda100, 0x84595161401484a0,
- 0xa56fa5b99019a5c8, 0xcecb8f27f4200f3a, 0x813f3978f8940984,
- 0xa18f07d736b90be5, 0xc9f2c9cd04674ede, 0xfc6f7c4045812296,
- 0x9dc5ada82b70b59d, 0xc5371912364ce305, 0xf684df56c3e01bc6,
- 0x9a130b963a6c115c, 0xc097ce7bc90715b3, 0xf0bdc21abb48db20,
- 0x96769950b50d88f4, 0xbc143fa4e250eb31, 0xeb194f8e1ae525fd,
- 0x92efd1b8d0cf37be, 0xb7abc627050305ad, 0xe596b7b0c643c719,
- 0x8f7e32ce7bea5c6f, 0xb35dbf821ae4f38b, 0xe0352f62a19e306e};
+ 0xa56fa5b99019a5c8, 0xcecb8f27f4200f3a, 0x813f3978f8940985,
+ 0xa18f07d736b90be6, 0xc9f2c9cd04674edf, 0xfc6f7c4045812297,
+ 0x9dc5ada82b70b59e, 0xc5371912364ce306, 0xf684df56c3e01bc7,
+ 0x9a130b963a6c115d, 0xc097ce7bc90715b4, 0xf0bdc21abb48db21,
+ 0x96769950b50d88f5, 0xbc143fa4e250eb32, 0xeb194f8e1ae525fe,
+ 0x92efd1b8d0cf37bf, 0xb7abc627050305ae, 0xe596b7b0c643c71a,
+ 0x8f7e32ce7bea5c70, 0xb35dbf821ae4f38c, 0xe0352f62a19e306f};
return pow10_significands[k - float_info<float>::min_k];
}
- static carrier_uint compute_mul(carrier_uint u,
- const cache_entry_type& cache) FMT_NOEXCEPT {
- return umul96_upper32(u, cache);
+ struct compute_mul_result {
+ carrier_uint result;
+ bool is_integer;
+ };
+ struct compute_mul_parity_result {
+ bool parity;
+ bool is_integer;
+ };
+
+ static compute_mul_result compute_mul(
+ carrier_uint u, const cache_entry_type& cache) noexcept {
+ auto r = umul96_upper64(u, cache);
+ return {static_cast<carrier_uint>(r >> 32),
+ static_cast<carrier_uint>(r) == 0};
}
static uint32_t compute_delta(const cache_entry_type& cache,
- int beta_minus_1) FMT_NOEXCEPT {
- return static_cast<uint32_t>(cache >> (64 - 1 - beta_minus_1));
+ int beta) noexcept {
+ return static_cast<uint32_t>(cache >> (64 - 1 - beta));
}
- static bool compute_mul_parity(carrier_uint two_f,
- const cache_entry_type& cache,
- int beta_minus_1) FMT_NOEXCEPT {
- FMT_ASSERT(beta_minus_1 >= 1, "");
- FMT_ASSERT(beta_minus_1 < 64, "");
+ static compute_mul_parity_result compute_mul_parity(
+ carrier_uint two_f, const cache_entry_type& cache, int beta) noexcept {
+ FMT_ASSERT(beta >= 1, "");
+ FMT_ASSERT(beta < 64, "");
- return ((umul96_lower64(two_f, cache) >> (64 - beta_minus_1)) & 1) != 0;
+ auto r = umul96_lower64(two_f, cache);
+ return {((r >> (64 - beta)) & 1) != 0,
+ static_cast<uint32_t>(r >> (32 - beta)) == 0};
}
static carrier_uint compute_left_endpoint_for_shorter_interval_case(
- const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT {
+ const cache_entry_type& cache, int beta) noexcept {
return static_cast<carrier_uint>(
- (cache - (cache >> (float_info<float>::significand_bits + 2))) >>
- (64 - float_info<float>::significand_bits - 1 - beta_minus_1));
+ (cache - (cache >> (num_significand_bits<float>() + 2))) >>
+ (64 - num_significand_bits<float>() - 1 - beta));
}
static carrier_uint compute_right_endpoint_for_shorter_interval_case(
- const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT {
+ const cache_entry_type& cache, int beta) noexcept {
return static_cast<carrier_uint>(
- (cache + (cache >> (float_info<float>::significand_bits + 1))) >>
- (64 - float_info<float>::significand_bits - 1 - beta_minus_1));
+ (cache + (cache >> (num_significand_bits<float>() + 1))) >>
+ (64 - num_significand_bits<float>() - 1 - beta));
}
static carrier_uint compute_round_up_for_shorter_interval_case(
- const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT {
+ const cache_entry_type& cache, int beta) noexcept {
return (static_cast<carrier_uint>(
- cache >>
- (64 - float_info<float>::significand_bits - 2 - beta_minus_1)) +
+ cache >> (64 - num_significand_bits<float>() - 2 - beta)) +
1) /
2;
}
template <> struct cache_accessor<double> {
using carrier_uint = float_info<double>::carrier_uint;
- using cache_entry_type = uint128_wrapper;
+ using cache_entry_type = uint128_fallback;
- static uint128_wrapper get_cached_power(int k) FMT_NOEXCEPT {
+ static uint128_fallback get_cached_power(int k) noexcept {
FMT_ASSERT(k >= float_info<double>::min_k && k <= float_info<double>::max_k,
"k is out of range");
- static constexpr const uint128_wrapper pow10_significands[] = {
+ static constexpr const uint128_fallback pow10_significands[] = {
#if FMT_USE_FULL_CACHE_DRAGONBOX
{0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7b},
{0x9faacf3df73609b1, 0x77b191618c54e9ad},
{0x85a36366eb71f041, 0x47a6da2b7f864750},
{0xa70c3c40a64e6c51, 0x999090b65f67d924},
{0xd0cf4b50cfe20765, 0xfff4b4e3f741cf6d},
- {0x82818f1281ed449f, 0xbff8f10e7a8921a4},
- {0xa321f2d7226895c7, 0xaff72d52192b6a0d},
- {0xcbea6f8ceb02bb39, 0x9bf4f8a69f764490},
- {0xfee50b7025c36a08, 0x02f236d04753d5b4},
- {0x9f4f2726179a2245, 0x01d762422c946590},
- {0xc722f0ef9d80aad6, 0x424d3ad2b7b97ef5},
- {0xf8ebad2b84e0d58b, 0xd2e0898765a7deb2},
- {0x9b934c3b330c8577, 0x63cc55f49f88eb2f},
- {0xc2781f49ffcfa6d5, 0x3cbf6b71c76b25fb},
- {0xf316271c7fc3908a, 0x8bef464e3945ef7a},
- {0x97edd871cfda3a56, 0x97758bf0e3cbb5ac},
- {0xbde94e8e43d0c8ec, 0x3d52eeed1cbea317},
- {0xed63a231d4c4fb27, 0x4ca7aaa863ee4bdd},
- {0x945e455f24fb1cf8, 0x8fe8caa93e74ef6a},
- {0xb975d6b6ee39e436, 0xb3e2fd538e122b44},
- {0xe7d34c64a9c85d44, 0x60dbbca87196b616},
- {0x90e40fbeea1d3a4a, 0xbc8955e946fe31cd},
- {0xb51d13aea4a488dd, 0x6babab6398bdbe41},
- {0xe264589a4dcdab14, 0xc696963c7eed2dd1},
- {0x8d7eb76070a08aec, 0xfc1e1de5cf543ca2},
- {0xb0de65388cc8ada8, 0x3b25a55f43294bcb},
- {0xdd15fe86affad912, 0x49ef0eb713f39ebe},
- {0x8a2dbf142dfcc7ab, 0x6e3569326c784337},
- {0xacb92ed9397bf996, 0x49c2c37f07965404},
- {0xd7e77a8f87daf7fb, 0xdc33745ec97be906},
- {0x86f0ac99b4e8dafd, 0x69a028bb3ded71a3},
- {0xa8acd7c0222311bc, 0xc40832ea0d68ce0c},
- {0xd2d80db02aabd62b, 0xf50a3fa490c30190},
- {0x83c7088e1aab65db, 0x792667c6da79e0fa},
- {0xa4b8cab1a1563f52, 0x577001b891185938},
- {0xcde6fd5e09abcf26, 0xed4c0226b55e6f86},
- {0x80b05e5ac60b6178, 0x544f8158315b05b4},
- {0xa0dc75f1778e39d6, 0x696361ae3db1c721},
- {0xc913936dd571c84c, 0x03bc3a19cd1e38e9},
- {0xfb5878494ace3a5f, 0x04ab48a04065c723},
- {0x9d174b2dcec0e47b, 0x62eb0d64283f9c76},
- {0xc45d1df942711d9a, 0x3ba5d0bd324f8394},
- {0xf5746577930d6500, 0xca8f44ec7ee36479},
- {0x9968bf6abbe85f20, 0x7e998b13cf4e1ecb},
- {0xbfc2ef456ae276e8, 0x9e3fedd8c321a67e},
- {0xefb3ab16c59b14a2, 0xc5cfe94ef3ea101e},
- {0x95d04aee3b80ece5, 0xbba1f1d158724a12},
- {0xbb445da9ca61281f, 0x2a8a6e45ae8edc97},
- {0xea1575143cf97226, 0xf52d09d71a3293bd},
- {0x924d692ca61be758, 0x593c2626705f9c56},
- {0xb6e0c377cfa2e12e, 0x6f8b2fb00c77836c},
- {0xe498f455c38b997a, 0x0b6dfb9c0f956447},
- {0x8edf98b59a373fec, 0x4724bd4189bd5eac},
- {0xb2977ee300c50fe7, 0x58edec91ec2cb657},
- {0xdf3d5e9bc0f653e1, 0x2f2967b66737e3ed},
- {0x8b865b215899f46c, 0xbd79e0d20082ee74},
- {0xae67f1e9aec07187, 0xecd8590680a3aa11},
- {0xda01ee641a708de9, 0xe80e6f4820cc9495},
- {0x884134fe908658b2, 0x3109058d147fdcdd},
- {0xaa51823e34a7eede, 0xbd4b46f0599fd415},
- {0xd4e5e2cdc1d1ea96, 0x6c9e18ac7007c91a},
- {0x850fadc09923329e, 0x03e2cf6bc604ddb0},
- {0xa6539930bf6bff45, 0x84db8346b786151c},
- {0xcfe87f7cef46ff16, 0xe612641865679a63},
- {0x81f14fae158c5f6e, 0x4fcb7e8f3f60c07e},
- {0xa26da3999aef7749, 0xe3be5e330f38f09d},
- {0xcb090c8001ab551c, 0x5cadf5bfd3072cc5},
- {0xfdcb4fa002162a63, 0x73d9732fc7c8f7f6},
- {0x9e9f11c4014dda7e, 0x2867e7fddcdd9afa},
- {0xc646d63501a1511d, 0xb281e1fd541501b8},
- {0xf7d88bc24209a565, 0x1f225a7ca91a4226},
- {0x9ae757596946075f, 0x3375788de9b06958},
- {0xc1a12d2fc3978937, 0x0052d6b1641c83ae},
- {0xf209787bb47d6b84, 0xc0678c5dbd23a49a},
- {0x9745eb4d50ce6332, 0xf840b7ba963646e0},
- {0xbd176620a501fbff, 0xb650e5a93bc3d898},
- {0xec5d3fa8ce427aff, 0xa3e51f138ab4cebe},
- {0x93ba47c980e98cdf, 0xc66f336c36b10137},
- {0xb8a8d9bbe123f017, 0xb80b0047445d4184},
- {0xe6d3102ad96cec1d, 0xa60dc059157491e5},
- {0x9043ea1ac7e41392, 0x87c89837ad68db2f},
- {0xb454e4a179dd1877, 0x29babe4598c311fb},
- {0xe16a1dc9d8545e94, 0xf4296dd6fef3d67a},
- {0x8ce2529e2734bb1d, 0x1899e4a65f58660c},
- {0xb01ae745b101e9e4, 0x5ec05dcff72e7f8f},
- {0xdc21a1171d42645d, 0x76707543f4fa1f73},
- {0x899504ae72497eba, 0x6a06494a791c53a8},
- {0xabfa45da0edbde69, 0x0487db9d17636892},
- {0xd6f8d7509292d603, 0x45a9d2845d3c42b6},
- {0x865b86925b9bc5c2, 0x0b8a2392ba45a9b2},
- {0xa7f26836f282b732, 0x8e6cac7768d7141e},
- {0xd1ef0244af2364ff, 0x3207d795430cd926},
- {0x8335616aed761f1f, 0x7f44e6bd49e807b8},
- {0xa402b9c5a8d3a6e7, 0x5f16206c9c6209a6},
- {0xcd036837130890a1, 0x36dba887c37a8c0f},
- {0x802221226be55a64, 0xc2494954da2c9789},
- {0xa02aa96b06deb0fd, 0xf2db9baa10b7bd6c},
- {0xc83553c5c8965d3d, 0x6f92829494e5acc7},
- {0xfa42a8b73abbf48c, 0xcb772339ba1f17f9},
- {0x9c69a97284b578d7, 0xff2a760414536efb},
- {0xc38413cf25e2d70d, 0xfef5138519684aba},
- {0xf46518c2ef5b8cd1, 0x7eb258665fc25d69},
- {0x98bf2f79d5993802, 0xef2f773ffbd97a61},
- {0xbeeefb584aff8603, 0xaafb550ffacfd8fa},
- {0xeeaaba2e5dbf6784, 0x95ba2a53f983cf38},
- {0x952ab45cfa97a0b2, 0xdd945a747bf26183},
- {0xba756174393d88df, 0x94f971119aeef9e4},
- {0xe912b9d1478ceb17, 0x7a37cd5601aab85d},
- {0x91abb422ccb812ee, 0xac62e055c10ab33a},
- {0xb616a12b7fe617aa, 0x577b986b314d6009},
- {0xe39c49765fdf9d94, 0xed5a7e85fda0b80b},
- {0x8e41ade9fbebc27d, 0x14588f13be847307},
- {0xb1d219647ae6b31c, 0x596eb2d8ae258fc8},
- {0xde469fbd99a05fe3, 0x6fca5f8ed9aef3bb},
- {0x8aec23d680043bee, 0x25de7bb9480d5854},
- {0xada72ccc20054ae9, 0xaf561aa79a10ae6a},
- {0xd910f7ff28069da4, 0x1b2ba1518094da04},
- {0x87aa9aff79042286, 0x90fb44d2f05d0842},
- {0xa99541bf57452b28, 0x353a1607ac744a53},
- {0xd3fa922f2d1675f2, 0x42889b8997915ce8},
- {0x847c9b5d7c2e09b7, 0x69956135febada11},
- {0xa59bc234db398c25, 0x43fab9837e699095},
- {0xcf02b2c21207ef2e, 0x94f967e45e03f4bb},
- {0x8161afb94b44f57d, 0x1d1be0eebac278f5},
- {0xa1ba1ba79e1632dc, 0x6462d92a69731732},
- {0xca28a291859bbf93, 0x7d7b8f7503cfdcfe},
- {0xfcb2cb35e702af78, 0x5cda735244c3d43e},
- {0x9defbf01b061adab, 0x3a0888136afa64a7},
- {0xc56baec21c7a1916, 0x088aaa1845b8fdd0},
- {0xf6c69a72a3989f5b, 0x8aad549e57273d45},
- {0x9a3c2087a63f6399, 0x36ac54e2f678864b},
- {0xc0cb28a98fcf3c7f, 0x84576a1bb416a7dd},
- {0xf0fdf2d3f3c30b9f, 0x656d44a2a11c51d5},
- {0x969eb7c47859e743, 0x9f644ae5a4b1b325},
- {0xbc4665b596706114, 0x873d5d9f0dde1fee},
- {0xeb57ff22fc0c7959, 0xa90cb506d155a7ea},
- {0x9316ff75dd87cbd8, 0x09a7f12442d588f2},
- {0xb7dcbf5354e9bece, 0x0c11ed6d538aeb2f},
- {0xe5d3ef282a242e81, 0x8f1668c8a86da5fa},
- {0x8fa475791a569d10, 0xf96e017d694487bc},
- {0xb38d92d760ec4455, 0x37c981dcc395a9ac},
- {0xe070f78d3927556a, 0x85bbe253f47b1417},
- {0x8c469ab843b89562, 0x93956d7478ccec8e},
- {0xaf58416654a6babb, 0x387ac8d1970027b2},
- {0xdb2e51bfe9d0696a, 0x06997b05fcc0319e},
- {0x88fcf317f22241e2, 0x441fece3bdf81f03},
- {0xab3c2fddeeaad25a, 0xd527e81cad7626c3},
- {0xd60b3bd56a5586f1, 0x8a71e223d8d3b074},
- {0x85c7056562757456, 0xf6872d5667844e49},
- {0xa738c6bebb12d16c, 0xb428f8ac016561db},
- {0xd106f86e69d785c7, 0xe13336d701beba52},
- {0x82a45b450226b39c, 0xecc0024661173473},
- {0xa34d721642b06084, 0x27f002d7f95d0190},
- {0xcc20ce9bd35c78a5, 0x31ec038df7b441f4},
- {0xff290242c83396ce, 0x7e67047175a15271},
- {0x9f79a169bd203e41, 0x0f0062c6e984d386},
- {0xc75809c42c684dd1, 0x52c07b78a3e60868},
- {0xf92e0c3537826145, 0xa7709a56ccdf8a82},
- {0x9bbcc7a142b17ccb, 0x88a66076400bb691},
- {0xc2abf989935ddbfe, 0x6acff893d00ea435},
- {0xf356f7ebf83552fe, 0x0583f6b8c4124d43},
- {0x98165af37b2153de, 0xc3727a337a8b704a},
- {0xbe1bf1b059e9a8d6, 0x744f18c0592e4c5c},
- {0xeda2ee1c7064130c, 0x1162def06f79df73},
- {0x9485d4d1c63e8be7, 0x8addcb5645ac2ba8},
- {0xb9a74a0637ce2ee1, 0x6d953e2bd7173692},
- {0xe8111c87c5c1ba99, 0xc8fa8db6ccdd0437},
- {0x910ab1d4db9914a0, 0x1d9c9892400a22a2},
- {0xb54d5e4a127f59c8, 0x2503beb6d00cab4b},
- {0xe2a0b5dc971f303a, 0x2e44ae64840fd61d},
- {0x8da471a9de737e24, 0x5ceaecfed289e5d2},
- {0xb10d8e1456105dad, 0x7425a83e872c5f47},
- {0xdd50f1996b947518, 0xd12f124e28f77719},
- {0x8a5296ffe33cc92f, 0x82bd6b70d99aaa6f},
- {0xace73cbfdc0bfb7b, 0x636cc64d1001550b},
- {0xd8210befd30efa5a, 0x3c47f7e05401aa4e},
- {0x8714a775e3e95c78, 0x65acfaec34810a71},
- {0xa8d9d1535ce3b396, 0x7f1839a741a14d0d},
- {0xd31045a8341ca07c, 0x1ede48111209a050},
- {0x83ea2b892091e44d, 0x934aed0aab460432},
- {0xa4e4b66b68b65d60, 0xf81da84d5617853f},
- {0xce1de40642e3f4b9, 0x36251260ab9d668e},
- {0x80d2ae83e9ce78f3, 0xc1d72b7c6b426019},
- {0xa1075a24e4421730, 0xb24cf65b8612f81f},
- {0xc94930ae1d529cfc, 0xdee033f26797b627},
- {0xfb9b7cd9a4a7443c, 0x169840ef017da3b1},
- {0x9d412e0806e88aa5, 0x8e1f289560ee864e},
- {0xc491798a08a2ad4e, 0xf1a6f2bab92a27e2},
- {0xf5b5d7ec8acb58a2, 0xae10af696774b1db},
- {0x9991a6f3d6bf1765, 0xacca6da1e0a8ef29},
- {0xbff610b0cc6edd3f, 0x17fd090a58d32af3},
- {0xeff394dcff8a948e, 0xddfc4b4cef07f5b0},
- {0x95f83d0a1fb69cd9, 0x4abdaf101564f98e},
- {0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f1},
- {0xea53df5fd18d5513, 0x84c86189216dc5ed},
- {0x92746b9be2f8552c, 0x32fd3cf5b4e49bb4},
- {0xb7118682dbb66a77, 0x3fbc8c33221dc2a1},
- {0xe4d5e82392a40515, 0x0fabaf3feaa5334a},
- {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},
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+ {0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9e},
+ {0xac2820d9623bf429, 0x546345fa9fbdcd45},
+ {0xd732290fbacaf133, 0xa97c177947ad4096},
+ {0x867f59a9d4bed6c0, 0x49ed8eabcccc485e},
+ {0xa81f301449ee8c70, 0x5c68f256bfff5a75},
+ {0xd226fc195c6a2f8c, 0x73832eec6fff3112},
+ {0x83585d8fd9c25db7, 0xc831fd53c5ff7eac},
+ {0xa42e74f3d032f525, 0xba3e7ca8b77f5e56},
+ {0xcd3a1230c43fb26f, 0x28ce1bd2e55f35ec},
+ {0x80444b5e7aa7cf85, 0x7980d163cf5b81b4},
+ {0xa0555e361951c366, 0xd7e105bcc3326220},
+ {0xc86ab5c39fa63440, 0x8dd9472bf3fefaa8},
+ {0xfa856334878fc150, 0xb14f98f6f0feb952},
+ {0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d4},
+ {0xc3b8358109e84f07, 0x0a862f80ec4700c9},
+ {0xf4a642e14c6262c8, 0xcd27bb612758c0fb},
+ {0x98e7e9cccfbd7dbd, 0x8038d51cb897789d},
+ {0xbf21e44003acdd2c, 0xe0470a63e6bd56c4},
+ {0xeeea5d5004981478, 0x1858ccfce06cac75},
+ {0x95527a5202df0ccb, 0x0f37801e0c43ebc9},
+ {0xbaa718e68396cffd, 0xd30560258f54e6bb},
+ {0xe950df20247c83fd, 0x47c6b82ef32a206a},
+ {0x91d28b7416cdd27e, 0x4cdc331d57fa5442},
+ {0xb6472e511c81471d, 0xe0133fe4adf8e953},
+ {0xe3d8f9e563a198e5, 0x58180fddd97723a7},
+ {0x8e679c2f5e44ff8f, 0x570f09eaa7ea7649},
+ {0xb201833b35d63f73, 0x2cd2cc6551e513db},
+ {0xde81e40a034bcf4f, 0xf8077f7ea65e58d2},
+ {0x8b112e86420f6191, 0xfb04afaf27faf783},
+ {0xadd57a27d29339f6, 0x79c5db9af1f9b564},
+ {0xd94ad8b1c7380874, 0x18375281ae7822bd},
+ {0x87cec76f1c830548, 0x8f2293910d0b15b6},
+ {0xa9c2794ae3a3c69a, 0xb2eb3875504ddb23},
+ {0xd433179d9c8cb841, 0x5fa60692a46151ec},
+ {0x849feec281d7f328, 0xdbc7c41ba6bcd334},
+ {0xa5c7ea73224deff3, 0x12b9b522906c0801},
+ {0xcf39e50feae16bef, 0xd768226b34870a01},
+ {0x81842f29f2cce375, 0xe6a1158300d46641},
+ {0xa1e53af46f801c53, 0x60495ae3c1097fd1},
+ {0xca5e89b18b602368, 0x385bb19cb14bdfc5},
+ {0xfcf62c1dee382c42, 0x46729e03dd9ed7b6},
+ {0x9e19db92b4e31ba9, 0x6c07a2c26a8346d2},
+ {0xc5a05277621be293, 0xc7098b7305241886},
{ 0xf70867153aa2db38,
- 0xb8cbee4fc66d1ea7 }
+ 0xb8cbee4fc66d1ea8 }
#else
{0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7b},
{0xce5d73ff402d98e3, 0xfb0a3d212dc81290},
{0xf1c90080baf72cb1, 0x5324c68b12dd6339},
{0xc350000000000000, 0x0000000000000000},
{0x9dc5ada82b70b59d, 0xf020000000000000},
- {0xfee50b7025c36a08, 0x02f236d04753d5b4},
- {0xcde6fd5e09abcf26, 0xed4c0226b55e6f86},
- {0xa6539930bf6bff45, 0x84db8346b786151c},
- {0x865b86925b9bc5c2, 0x0b8a2392ba45a9b2},
- {0xd910f7ff28069da4, 0x1b2ba1518094da04},
- {0xaf58416654a6babb, 0x387ac8d1970027b2},
- {0x8da471a9de737e24, 0x5ceaecfed289e5d2},
- {0xe4d5e82392a40515, 0x0fabaf3feaa5334a},
- {0xb8da1662e7b00a17, 0x3d6a751f3b936243},
+ {0xfee50b7025c36a08, 0x02f236d04753d5b5},
+ {0xcde6fd5e09abcf26, 0xed4c0226b55e6f87},
+ {0xa6539930bf6bff45, 0x84db8346b786151d},
+ {0x865b86925b9bc5c2, 0x0b8a2392ba45a9b3},
+ {0xd910f7ff28069da4, 0x1b2ba1518094da05},
+ {0xaf58416654a6babb, 0x387ac8d1970027b3},
+ {0x8da471a9de737e24, 0x5ceaecfed289e5d3},
+ {0xe4d5e82392a40515, 0x0fabaf3feaa5334b},
+ {0xb8da1662e7b00a17, 0x3d6a751f3b936244},
{ 0x95527a5202df0ccb,
- 0x0f37801e0c43ebc8 }
+ 0x0f37801e0c43ebc9 }
#endif
};
0x0001b1ae4d6e2ef5, 0x000878678326eac9, 0x002a5a058fc295ed,
0x00d3c21bcecceda1, 0x0422ca8b0a00a425, 0x14adf4b7320334b9};
- static constexpr const uint32_t pow10_recovery_errors[] = {
- 0x50001400, 0x54044100, 0x54014555, 0x55954415, 0x54115555, 0x00000001,
- 0x50000000, 0x00104000, 0x54010004, 0x05004001, 0x55555544, 0x41545555,
- 0x54040551, 0x15445545, 0x51555514, 0x10000015, 0x00101100, 0x01100015,
- 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x04450514, 0x45414110,
- 0x55555145, 0x50544050, 0x15040155, 0x11054140, 0x50111514, 0x11451454,
- 0x00400541, 0x00000000, 0x55555450, 0x10056551, 0x10054011, 0x55551014,
- 0x69514555, 0x05151109, 0x00155555};
-
static const int compression_ratio = 27;
// Compute base index.
int offset = k - kb;
// Get base cache.
- uint128_wrapper base_cache = pow10_significands[cache_index];
+ uint128_fallback base_cache = pow10_significands[cache_index];
if (offset == 0) return base_cache;
// Compute the required amount of bit-shift.
// Try to recover the real cache.
uint64_t pow5 = powers_of_5_64[offset];
- uint128_wrapper recovered_cache = umul128(base_cache.high(), pow5);
- uint128_wrapper middle_low =
- umul128(base_cache.low() - (kb < 0 ? 1u : 0u), pow5);
+ uint128_fallback recovered_cache = umul128(base_cache.high(), pow5);
+ uint128_fallback middle_low = umul128(base_cache.low(), pow5);
recovered_cache += middle_low.high();
uint64_t middle_to_low = recovered_cache.low() << (64 - alpha);
recovered_cache =
- uint128_wrapper{(recovered_cache.low() >> alpha) | high_to_middle,
- ((middle_low.low() >> alpha) | middle_to_low)};
-
- if (kb < 0) recovered_cache += 1;
-
- // Get error.
- int error_idx = (k - float_info<double>::min_k) / 16;
- uint32_t error = (pow10_recovery_errors[error_idx] >>
- ((k - float_info<double>::min_k) % 16) * 2) &
- 0x3;
-
- // Add the error back.
- FMT_ASSERT(recovered_cache.low() + error >= recovered_cache.low(), "");
- return {recovered_cache.high(), recovered_cache.low() + error};
+ uint128_fallback{(recovered_cache.low() >> alpha) | high_to_middle,
+ ((middle_low.low() >> alpha) | middle_to_low)};
+ FMT_ASSERT(recovered_cache.low() + 1 != 0, "");
+ return {recovered_cache.high(), recovered_cache.low() + 1};
#endif
}
- static carrier_uint compute_mul(carrier_uint u,
- const cache_entry_type& cache) FMT_NOEXCEPT {
- return umul192_upper64(u, cache);
+ struct compute_mul_result {
+ carrier_uint result;
+ bool is_integer;
+ };
+ struct compute_mul_parity_result {
+ bool parity;
+ bool is_integer;
+ };
+
+ static compute_mul_result compute_mul(
+ carrier_uint u, const cache_entry_type& cache) noexcept {
+ auto r = umul192_upper128(u, cache);
+ return {r.high(), r.low() == 0};
}
static uint32_t compute_delta(cache_entry_type const& cache,
- int beta_minus_1) FMT_NOEXCEPT {
- return static_cast<uint32_t>(cache.high() >> (64 - 1 - beta_minus_1));
+ int beta) noexcept {
+ return static_cast<uint32_t>(cache.high() >> (64 - 1 - beta));
}
- static bool compute_mul_parity(carrier_uint two_f,
- const cache_entry_type& cache,
- int beta_minus_1) FMT_NOEXCEPT {
- FMT_ASSERT(beta_minus_1 >= 1, "");
- FMT_ASSERT(beta_minus_1 < 64, "");
+ static compute_mul_parity_result compute_mul_parity(
+ carrier_uint two_f, const cache_entry_type& cache, int beta) noexcept {
+ FMT_ASSERT(beta >= 1, "");
+ FMT_ASSERT(beta < 64, "");
- return ((umul192_middle64(two_f, cache) >> (64 - beta_minus_1)) & 1) != 0;
+ auto r = umul192_lower128(two_f, cache);
+ return {((r.high() >> (64 - beta)) & 1) != 0,
+ ((r.high() << beta) | (r.low() >> (64 - beta))) == 0};
}
static carrier_uint compute_left_endpoint_for_shorter_interval_case(
- const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT {
+ const cache_entry_type& cache, int beta) noexcept {
return (cache.high() -
- (cache.high() >> (float_info<double>::significand_bits + 2))) >>
- (64 - float_info<double>::significand_bits - 1 - beta_minus_1);
+ (cache.high() >> (num_significand_bits<double>() + 2))) >>
+ (64 - num_significand_bits<double>() - 1 - beta);
}
static carrier_uint compute_right_endpoint_for_shorter_interval_case(
- const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT {
+ const cache_entry_type& cache, int beta) noexcept {
return (cache.high() +
- (cache.high() >> (float_info<double>::significand_bits + 1))) >>
- (64 - float_info<double>::significand_bits - 1 - beta_minus_1);
+ (cache.high() >> (num_significand_bits<double>() + 1))) >>
+ (64 - num_significand_bits<double>() - 1 - beta);
}
static carrier_uint compute_round_up_for_shorter_interval_case(
- const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT {
- return ((cache.high() >>
- (64 - float_info<double>::significand_bits - 2 - beta_minus_1)) +
+ const cache_entry_type& cache, int beta) noexcept {
+ return ((cache.high() >> (64 - num_significand_bits<double>() - 2 - beta)) +
1) /
2;
}
// Various integer checks
template <class T>
-bool is_left_endpoint_integer_shorter_interval(int exponent) FMT_NOEXCEPT {
- return exponent >=
- float_info<
- T>::case_shorter_interval_left_endpoint_lower_threshold &&
- exponent <=
- float_info<T>::case_shorter_interval_left_endpoint_upper_threshold;
-}
-template <class T>
-bool is_endpoint_integer(typename float_info<T>::carrier_uint two_f,
- int exponent, int minus_k) FMT_NOEXCEPT {
- if (exponent < float_info<T>::case_fc_pm_half_lower_threshold) return false;
- // For k >= 0.
- if (exponent <= float_info<T>::case_fc_pm_half_upper_threshold) return true;
- // For k < 0.
- if (exponent > float_info<T>::divisibility_check_by_5_threshold) return false;
- return divisible_by_power_of_5(two_f, minus_k);
-}
-
-template <class T>
-bool is_center_integer(typename float_info<T>::carrier_uint two_f, int exponent,
- int minus_k) FMT_NOEXCEPT {
- // Exponent for 5 is negative.
- if (exponent > float_info<T>::divisibility_check_by_5_threshold) return false;
- if (exponent > float_info<T>::case_fc_upper_threshold)
- return divisible_by_power_of_5(two_f, minus_k);
- // Both exponents are nonnegative.
- if (exponent >= float_info<T>::case_fc_lower_threshold) return true;
- // Exponent for 2 is negative.
- return divisible_by_power_of_2(two_f, minus_k - exponent + 1);
+bool is_left_endpoint_integer_shorter_interval(int exponent) noexcept {
+ const int case_shorter_interval_left_endpoint_lower_threshold = 2;
+ const int case_shorter_interval_left_endpoint_upper_threshold = 3;
+ return exponent >= case_shorter_interval_left_endpoint_lower_threshold &&
+ exponent <= case_shorter_interval_left_endpoint_upper_threshold;
}
// Remove trailing zeros from n and return the number of zeros removed (float)
-FMT_INLINE int remove_trailing_zeros(uint32_t& n) FMT_NOEXCEPT {
-#ifdef FMT_BUILTIN_CTZ
- int t = FMT_BUILTIN_CTZ(n);
-#else
- int t = ctz(n);
-#endif
- if (t > float_info<float>::max_trailing_zeros)
- t = float_info<float>::max_trailing_zeros;
-
- const uint32_t mod_inv1 = 0xcccccccd;
- const uint32_t max_quotient1 = 0x33333333;
- const uint32_t mod_inv2 = 0xc28f5c29;
- const uint32_t max_quotient2 = 0x0a3d70a3;
+FMT_INLINE int remove_trailing_zeros(uint32_t& n) noexcept {
+ FMT_ASSERT(n != 0, "");
+ const uint32_t mod_inv_5 = 0xcccccccd;
+ const uint32_t mod_inv_25 = mod_inv_5 * mod_inv_5;
int s = 0;
- for (; s < t - 1; s += 2) {
- if (n * mod_inv2 > max_quotient2) break;
- n *= mod_inv2;
+ while (true) {
+ auto q = rotr(n * mod_inv_25, 2);
+ if (q > max_value<uint32_t>() / 100) break;
+ n = q;
+ s += 2;
}
- if (s < t && n * mod_inv1 <= max_quotient1) {
- n *= mod_inv1;
- ++s;
+ auto q = rotr(n * mod_inv_5, 1);
+ if (q <= max_value<uint32_t>() / 10) {
+ n = q;
+ s |= 1;
}
- n >>= s;
+
return s;
}
// Removes trailing zeros and returns the number of zeros removed (double)
-FMT_INLINE int remove_trailing_zeros(uint64_t& n) FMT_NOEXCEPT {
-#ifdef FMT_BUILTIN_CTZLL
- int t = FMT_BUILTIN_CTZLL(n);
-#else
- int t = ctzll(n);
-#endif
- if (t > float_info<double>::max_trailing_zeros)
- t = float_info<double>::max_trailing_zeros;
- // Divide by 10^8 and reduce to 32-bits
- // Since ret_value.significand <= (2^64 - 1) / 1000 < 10^17,
- // both of the quotient and the r should fit in 32-bits
-
- const uint32_t mod_inv1 = 0xcccccccd;
- const uint32_t max_quotient1 = 0x33333333;
- const uint64_t mod_inv8 = 0xc767074b22e90e21;
- const uint64_t max_quotient8 = 0x00002af31dc46118;
-
- // If the number is divisible by 1'0000'0000, work with the quotient
- if (t >= 8) {
- auto quotient_candidate = n * mod_inv8;
-
- if (quotient_candidate <= max_quotient8) {
- auto quotient = static_cast<uint32_t>(quotient_candidate >> 8);
-
- int s = 8;
- for (; s < t; ++s) {
- if (quotient * mod_inv1 > max_quotient1) break;
- quotient *= mod_inv1;
- }
- quotient >>= (s - 8);
- n = quotient;
- return s;
+FMT_INLINE int remove_trailing_zeros(uint64_t& n) noexcept {
+ FMT_ASSERT(n != 0, "");
+
+ // This magic number is ceil(2^90 / 10^8).
+ constexpr uint64_t magic_number = 12379400392853802749ull;
+ auto nm = umul128(n, magic_number);
+
+ // Is n is divisible by 10^8?
+ if ((nm.high() & ((1ull << (90 - 64)) - 1)) == 0 && nm.low() < magic_number) {
+ // If yes, work with the quotient.
+ auto n32 = static_cast<uint32_t>(nm.high() >> (90 - 64));
+
+ const uint32_t mod_inv_5 = 0xcccccccd;
+ const uint32_t mod_inv_25 = mod_inv_5 * mod_inv_5;
+
+ int s = 8;
+ while (true) {
+ auto q = rotr(n32 * mod_inv_25, 2);
+ if (q > max_value<uint32_t>() / 100) break;
+ n32 = q;
+ s += 2;
+ }
+ auto q = rotr(n32 * mod_inv_5, 1);
+ if (q <= max_value<uint32_t>() / 10) {
+ n32 = q;
+ s |= 1;
}
- }
-
- // Otherwise, work with the remainder
- auto quotient = static_cast<uint32_t>(n / 100000000);
- auto remainder = static_cast<uint32_t>(n - 100000000 * quotient);
-
- if (t == 0 || remainder * mod_inv1 > max_quotient1) {
- return 0;
- }
- remainder *= mod_inv1;
-
- if (t == 1 || remainder * mod_inv1 > max_quotient1) {
- n = (remainder >> 1) + quotient * 10000000ull;
- return 1;
- }
- remainder *= mod_inv1;
-
- if (t == 2 || remainder * mod_inv1 > max_quotient1) {
- n = (remainder >> 2) + quotient * 1000000ull;
- return 2;
- }
- remainder *= mod_inv1;
- if (t == 3 || remainder * mod_inv1 > max_quotient1) {
- n = (remainder >> 3) + quotient * 100000ull;
- return 3;
+ n = n32;
+ return s;
}
- remainder *= mod_inv1;
- if (t == 4 || remainder * mod_inv1 > max_quotient1) {
- n = (remainder >> 4) + quotient * 10000ull;
- return 4;
- }
- remainder *= mod_inv1;
+ // If n is not divisible by 10^8, work with n itself.
+ const uint64_t mod_inv_5 = 0xcccccccccccccccd;
+ const uint64_t mod_inv_25 = mod_inv_5 * mod_inv_5;
- if (t == 5 || remainder * mod_inv1 > max_quotient1) {
- n = (remainder >> 5) + quotient * 1000ull;
- return 5;
+ int s = 0;
+ while (true) {
+ auto q = rotr(n * mod_inv_25, 2);
+ if (q > max_value<uint64_t>() / 100) break;
+ n = q;
+ s += 2;
}
- remainder *= mod_inv1;
-
- if (t == 6 || remainder * mod_inv1 > max_quotient1) {
- n = (remainder >> 6) + quotient * 100ull;
- return 6;
+ auto q = rotr(n * mod_inv_5, 1);
+ if (q <= max_value<uint64_t>() / 10) {
+ n = q;
+ s |= 1;
}
- remainder *= mod_inv1;
- n = (remainder >> 7) + quotient * 10ull;
- return 7;
+ return s;
}
// The main algorithm for shorter interval case
template <class T>
-FMT_INLINE decimal_fp<T> shorter_interval_case(int exponent) FMT_NOEXCEPT {
+FMT_INLINE decimal_fp<T> shorter_interval_case(int exponent) noexcept {
decimal_fp<T> ret_value;
// Compute k and beta
const int minus_k = floor_log10_pow2_minus_log10_4_over_3(exponent);
- const int beta_minus_1 = exponent + floor_log2_pow10(-minus_k);
+ const int beta = exponent + floor_log2_pow10(-minus_k);
// Compute xi and zi
using cache_entry_type = typename cache_accessor<T>::cache_entry_type;
const cache_entry_type cache = cache_accessor<T>::get_cached_power(-minus_k);
auto xi = cache_accessor<T>::compute_left_endpoint_for_shorter_interval_case(
- cache, beta_minus_1);
+ cache, beta);
auto zi = cache_accessor<T>::compute_right_endpoint_for_shorter_interval_case(
- cache, beta_minus_1);
+ cache, beta);
// If the left endpoint is not an integer, increase it
if (!is_left_endpoint_integer_shorter_interval<T>(exponent)) ++xi;
// Otherwise, compute the round-up of y
ret_value.significand =
- cache_accessor<T>::compute_round_up_for_shorter_interval_case(
- cache, beta_minus_1);
+ cache_accessor<T>::compute_round_up_for_shorter_interval_case(cache,
+ beta);
ret_value.exponent = minus_k;
// When tie occurs, choose one of them according to the rule
return ret_value;
}
-template <typename T> decimal_fp<T> to_decimal(T x) FMT_NOEXCEPT {
+template <typename T> decimal_fp<T> to_decimal(T x) noexcept {
// Step 1: integer promotion & Schubfach multiplier calculation.
using carrier_uint = typename float_info<T>::carrier_uint;
// Extract significand bits and exponent bits.
const carrier_uint significand_mask =
- (static_cast<carrier_uint>(1) << float_info<T>::significand_bits) - 1;
+ (static_cast<carrier_uint>(1) << num_significand_bits<T>()) - 1;
carrier_uint significand = (br & significand_mask);
- int exponent = static_cast<int>((br & exponent_mask<T>()) >>
- float_info<T>::significand_bits);
+ int exponent =
+ static_cast<int>((br & exponent_mask<T>()) >> num_significand_bits<T>());
if (exponent != 0) { // Check if normal.
- exponent += float_info<T>::exponent_bias - float_info<T>::significand_bits;
+ exponent -= exponent_bias<T>() + num_significand_bits<T>();
// Shorter interval case; proceed like Schubfach.
+ // In fact, when exponent == 1 and significand == 0, the interval is
+ // regular. However, it can be shown that the end-results are anyway same.
if (significand == 0) return shorter_interval_case<T>(exponent);
- significand |=
- (static_cast<carrier_uint>(1) << float_info<T>::significand_bits);
+ significand |= (static_cast<carrier_uint>(1) << num_significand_bits<T>());
} else {
// Subnormal case; the interval is always regular.
if (significand == 0) return {0, 0};
- exponent = float_info<T>::min_exponent - float_info<T>::significand_bits;
+ exponent =
+ std::numeric_limits<T>::min_exponent - num_significand_bits<T>() - 1;
}
const bool include_left_endpoint = (significand % 2 == 0);
// Compute k and beta.
const int minus_k = floor_log10_pow2(exponent) - float_info<T>::kappa;
const cache_entry_type cache = cache_accessor<T>::get_cached_power(-minus_k);
- const int beta_minus_1 = exponent + floor_log2_pow10(-minus_k);
+ const int beta = exponent + floor_log2_pow10(-minus_k);
- // Compute zi and deltai
+ // Compute zi and deltai.
// 10^kappa <= deltai < 10^(kappa + 1)
- const uint32_t deltai = cache_accessor<T>::compute_delta(cache, beta_minus_1);
+ const uint32_t deltai = cache_accessor<T>::compute_delta(cache, beta);
const carrier_uint two_fc = significand << 1;
- const carrier_uint two_fr = two_fc | 1;
- const carrier_uint zi =
- cache_accessor<T>::compute_mul(two_fr << beta_minus_1, cache);
- // Step 2: Try larger divisor; remove trailing zeros if necessary
+ // For the case of binary32, the result of integer check is not correct for
+ // 29711844 * 2^-82
+ // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18
+ // and 29711844 * 2^-81
+ // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17,
+ // and they are the unique counterexamples. However, since 29711844 is even,
+ // this does not cause any problem for the endpoints calculations; it can only
+ // cause a problem when we need to perform integer check for the center.
+ // Fortunately, with these inputs, that branch is never executed, so we are
+ // fine.
+ const typename cache_accessor<T>::compute_mul_result z_mul =
+ cache_accessor<T>::compute_mul((two_fc | 1) << beta, cache);
+
+ // Step 2: Try larger divisor; remove trailing zeros if necessary.
// Using an upper bound on zi, we might be able to optimize the division
- // better than the compiler; we are computing zi / big_divisor here
+ // better than the compiler; we are computing zi / big_divisor here.
decimal_fp<T> ret_value;
- ret_value.significand = divide_by_10_to_kappa_plus_1(zi);
- uint32_t r = static_cast<uint32_t>(zi - float_info<T>::big_divisor *
- ret_value.significand);
+ ret_value.significand = divide_by_10_to_kappa_plus_1(z_mul.result);
+ uint32_t r = static_cast<uint32_t>(z_mul.result - float_info<T>::big_divisor *
+ ret_value.significand);
- if (r > deltai) {
- goto small_divisor_case_label;
- } else if (r < deltai) {
- // Exclude the right endpoint if necessary
- if (r == 0 && !include_right_endpoint &&
- is_endpoint_integer<T>(two_fr, exponent, minus_k)) {
+ if (r < deltai) {
+ // Exclude the right endpoint if necessary.
+ if (r == 0 && (z_mul.is_integer & !include_right_endpoint)) {
--ret_value.significand;
r = float_info<T>::big_divisor;
goto small_divisor_case_label;
}
+ } else if (r > deltai) {
+ goto small_divisor_case_label;
} else {
- // r == deltai; compare fractional parts
- // Check conditions in the order different from the paper
- // to take advantage of short-circuiting
- const carrier_uint two_fl = two_fc - 1;
- if ((!include_left_endpoint ||
- !is_endpoint_integer<T>(two_fl, exponent, minus_k)) &&
- !cache_accessor<T>::compute_mul_parity(two_fl, cache, beta_minus_1)) {
+ // r == deltai; compare fractional parts.
+ const typename cache_accessor<T>::compute_mul_parity_result x_mul =
+ cache_accessor<T>::compute_mul_parity(two_fc - 1, cache, beta);
+
+ if (!(x_mul.parity | (x_mul.is_integer & include_left_endpoint)))
goto small_divisor_case_label;
- }
}
ret_value.exponent = minus_k + float_info<T>::kappa + 1;
- // We may need to remove trailing zeros
+ // We may need to remove trailing zeros.
ret_value.exponent += remove_trailing_zeros(ret_value.significand);
return ret_value;
- // Step 3: Find the significand with the smaller divisor
+ // Step 3: Find the significand with the smaller divisor.
small_divisor_case_label:
ret_value.significand *= 10;
ret_value.exponent = minus_k + float_info<T>::kappa;
- const uint32_t mask = (1u << float_info<T>::kappa) - 1;
- auto dist = r - (deltai / 2) + (float_info<T>::small_divisor / 2);
-
- // Is dist divisible by 2^kappa?
- if ((dist & mask) == 0) {
- const bool approx_y_parity =
- ((dist ^ (float_info<T>::small_divisor / 2)) & 1) != 0;
- dist >>= float_info<T>::kappa;
-
- // Is dist divisible by 5^kappa?
- if (check_divisibility_and_divide_by_pow5<float_info<T>::kappa>(dist)) {
- ret_value.significand += dist;
-
- // Check z^(f) >= epsilon^(f)
- // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1,
- // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f)
- // Since there are only 2 possibilities, we only need to care about the
- // parity. Also, zi and r should have the same parity since the divisor
- // is an even number
- if (cache_accessor<T>::compute_mul_parity(two_fc, cache, beta_minus_1) !=
- approx_y_parity) {
- --ret_value.significand;
- } else {
- // If z^(f) >= epsilon^(f), we might have a tie
- // when z^(f) == epsilon^(f), or equivalently, when y is an integer
- if (is_center_integer<T>(two_fc, exponent, minus_k)) {
- ret_value.significand = ret_value.significand % 2 == 0
- ? ret_value.significand
- : ret_value.significand - 1;
- }
- }
- }
- // Is dist not divisible by 5^kappa?
- else {
- ret_value.significand += dist;
- }
- }
- // Is dist not divisible by 2^kappa?
- else {
- // Since we know dist is small, we might be able to optimize the division
- // better than the compiler; we are computing dist / small_divisor here
- ret_value.significand +=
- small_division_by_pow10<float_info<T>::kappa>(dist);
- }
+ uint32_t dist = r - (deltai / 2) + (float_info<T>::small_divisor / 2);
+ const bool approx_y_parity =
+ ((dist ^ (float_info<T>::small_divisor / 2)) & 1) != 0;
+
+ // Is dist divisible by 10^kappa?
+ const bool divisible_by_small_divisor =
+ check_divisibility_and_divide_by_pow10<float_info<T>::kappa>(dist);
+
+ // Add dist / 10^kappa to the significand.
+ ret_value.significand += dist;
+
+ if (!divisible_by_small_divisor) return ret_value;
+
+ // Check z^(f) >= epsilon^(f).
+ // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1,
+ // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f).
+ // Since there are only 2 possibilities, we only need to care about the
+ // parity. Also, zi and r should have the same parity since the divisor
+ // is an even number.
+ const auto y_mul = cache_accessor<T>::compute_mul_parity(two_fc, cache, beta);
+
+ // If z^(f) >= epsilon^(f), we might have a tie when z^(f) == epsilon^(f),
+ // or equivalently, when y is an integer.
+ if (y_mul.parity != approx_y_parity)
+ --ret_value.significand;
+ else if (y_mul.is_integer & (ret_value.significand % 2 != 0))
+ --ret_value.significand;
return ret_value;
}
} // namespace dragonbox
-// Formats a floating-point number using a variation of the Fixed-Precision
-// Positive Floating-Point Printout ((FPP)^2) algorithm by Steele & White:
-// https://fmt.dev/papers/p372-steele.pdf.
-FMT_CONSTEXPR20 inline void format_dragon(fp value, bool is_predecessor_closer,
- int num_digits, buffer<char>& buf,
- int& exp10) {
- bigint numerator; // 2 * R in (FPP)^2.
- bigint denominator; // 2 * S in (FPP)^2.
- // lower and upper are differences between value and corresponding boundaries.
- bigint lower; // (M^- in (FPP)^2).
- bigint upper_store; // upper's value if different from lower.
- bigint* upper = nullptr; // (M^+ in (FPP)^2).
- // Shift numerator and denominator by an extra bit or two (if lower boundary
- // is closer) to make lower and upper integers. This eliminates multiplication
- // by 2 during later computations.
- int shift = is_predecessor_closer ? 2 : 1;
- uint64_t significand = value.f << shift;
- if (value.e >= 0) {
- numerator.assign(significand);
- numerator <<= value.e;
- lower.assign(1);
- lower <<= value.e;
- if (shift != 1) {
- upper_store.assign(1);
- upper_store <<= value.e + 1;
- upper = &upper_store;
- }
- denominator.assign_pow10(exp10);
- denominator <<= shift;
- } else if (exp10 < 0) {
- numerator.assign_pow10(-exp10);
- lower.assign(numerator);
- if (shift != 1) {
- upper_store.assign(numerator);
- upper_store <<= 1;
- upper = &upper_store;
- }
- numerator *= significand;
- denominator.assign(1);
- denominator <<= shift - value.e;
- } else {
- numerator.assign(significand);
- denominator.assign_pow10(exp10);
- denominator <<= shift - value.e;
- lower.assign(1);
- if (shift != 1) {
- upper_store.assign(1ULL << 1);
- upper = &upper_store;
- }
- }
- // Invariant: value == (numerator / denominator) * pow(10, exp10).
- if (num_digits < 0) {
- // Generate the shortest representation.
- if (!upper) upper = &lower;
- bool even = (value.f & 1) == 0;
- num_digits = 0;
- char* data = buf.data();
- for (;;) {
- int digit = numerator.divmod_assign(denominator);
- bool low = compare(numerator, lower) - even < 0; // numerator <[=] lower.
- // numerator + upper >[=] pow10:
- bool high = add_compare(numerator, *upper, denominator) + even > 0;
- data[num_digits++] = static_cast<char>('0' + digit);
- if (low || high) {
- if (!low) {
- ++data[num_digits - 1];
- } else if (high) {
- int result = add_compare(numerator, numerator, denominator);
- // Round half to even.
- if (result > 0 || (result == 0 && (digit % 2) != 0))
- ++data[num_digits - 1];
- }
- buf.try_resize(to_unsigned(num_digits));
- exp10 -= num_digits - 1;
- return;
- }
- numerator *= 10;
- lower *= 10;
- if (upper != &lower) *upper *= 10;
- }
- }
- // Generate the given number of digits.
- exp10 -= num_digits - 1;
- if (num_digits == 0) {
- denominator *= 10;
- auto digit = add_compare(numerator, numerator, denominator) > 0 ? '1' : '0';
- buf.push_back(digit);
- return;
- }
- buf.try_resize(to_unsigned(num_digits));
- for (int i = 0; i < num_digits - 1; ++i) {
- int digit = numerator.divmod_assign(denominator);
- buf[i] = static_cast<char>('0' + digit);
- numerator *= 10;
- }
- int digit = numerator.divmod_assign(denominator);
- auto result = add_compare(numerator, numerator, denominator);
- if (result > 0 || (result == 0 && (digit % 2) != 0)) {
- if (digit == 9) {
- const auto overflow = '0' + 10;
- buf[num_digits - 1] = overflow;
- // Propagate the carry.
- for (int i = num_digits - 1; i > 0 && buf[i] == overflow; --i) {
- buf[i] = '0';
- ++buf[i - 1];
- }
- if (buf[0] == overflow) {
- buf[0] = '1';
- ++exp10;
- }
- return;
- }
- ++digit;
- }
- buf[num_digits - 1] = static_cast<char>('0' + digit);
-}
-
-template <typename Float>
-FMT_HEADER_ONLY_CONSTEXPR20 int format_float(Float value, int precision,
- float_specs specs,
- buffer<char>& buf) {
- // float is passed as double to reduce the number of instantiations.
- static_assert(!std::is_same<Float, float>::value, "");
- FMT_ASSERT(value >= 0, "value is negative");
-
- const bool fixed = specs.format == float_format::fixed;
- if (value <= 0) { // <= instead of == to silence a warning.
- if (precision <= 0 || !fixed) {
- buf.push_back('0');
- return 0;
- }
- buf.try_resize(to_unsigned(precision));
- fill_n(buf.data(), precision, '0');
- return -precision;
- }
-
- if (specs.fallback) return snprintf_float(value, precision, specs, buf);
-
- if (!is_constant_evaluated() && precision < 0) {
- // Use Dragonbox for the shortest format.
- if (specs.binary32) {
- auto dec = dragonbox::to_decimal(static_cast<float>(value));
- write<char>(buffer_appender<char>(buf), dec.significand);
- return dec.exponent;
- }
- auto dec = dragonbox::to_decimal(static_cast<double>(value));
- write<char>(buffer_appender<char>(buf), dec.significand);
- return dec.exponent;
- }
-
- int exp = 0;
- bool use_dragon = true;
- if (is_fast_float<Float>()) {
- // Use Grisu + Dragon4 for the given precision:
- // https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf.
- const int min_exp = -60; // alpha in Grisu.
- int cached_exp10 = 0; // K in Grisu.
- fp normalized = normalize(fp(value));
- const auto cached_pow = get_cached_power(
- min_exp - (normalized.e + fp::num_significand_bits), cached_exp10);
- normalized = normalized * cached_pow;
- gen_digits_handler handler{buf.data(), 0, precision, -cached_exp10, fixed};
- if (grisu_gen_digits(normalized, 1, exp, handler) != digits::error &&
- !is_constant_evaluated()) {
- exp += handler.exp10;
- buf.try_resize(to_unsigned(handler.size));
- use_dragon = false;
- } else {
- exp += handler.size - cached_exp10 - 1;
- precision = handler.precision;
- }
- }
- if (use_dragon) {
- auto f = fp();
- bool is_predecessor_closer =
- specs.binary32 ? f.assign(static_cast<float>(value)) : f.assign(value);
- // Limit precision to the maximum possible number of significant digits in
- // an IEEE754 double because we don't need to generate zeros.
- const int max_double_digits = 767;
- if (precision > max_double_digits) precision = max_double_digits;
- format_dragon(f, is_predecessor_closer, precision, buf, exp);
- }
- if (!fixed && !specs.showpoint) {
- // Remove trailing zeros.
- auto num_digits = buf.size();
- while (num_digits > 0 && buf[num_digits - 1] == '0') {
- --num_digits;
- ++exp;
- }
- buf.try_resize(num_digits);
- }
- return exp;
+#ifdef _MSC_VER
+FMT_FUNC auto fmt_snprintf(char* buf, size_t size, const char* fmt, ...)
+ -> int {
+ auto args = va_list();
+ va_start(args, fmt);
+ int result = vsnprintf_s(buf, size, _TRUNCATE, fmt, args);
+ va_end(args);
+ return result;
}
-
-template <typename T>
-int snprintf_float(T value, int precision, float_specs specs,
- buffer<char>& buf) {
- // Buffer capacity must be non-zero, otherwise MSVC's vsnprintf_s will fail.
- FMT_ASSERT(buf.capacity() > buf.size(), "empty buffer");
- static_assert(!std::is_same<T, float>::value, "");
-
- // Subtract 1 to account for the difference in precision since we use %e for
- // both general and exponent format.
- if (specs.format == float_format::general ||
- specs.format == float_format::exp)
- precision = (precision >= 0 ? precision : 6) - 1;
-
- // Build the format string.
- enum { max_format_size = 7 }; // The longest format is "%#.*Le".
- char format[max_format_size];
- char* format_ptr = format;
- *format_ptr++ = '%';
- if (specs.showpoint && specs.format == float_format::hex) *format_ptr++ = '#';
- if (precision >= 0) {
- *format_ptr++ = '.';
- *format_ptr++ = '*';
- }
- if (std::is_same<T, long double>()) *format_ptr++ = 'L';
- *format_ptr++ = specs.format != float_format::hex
- ? (specs.format == float_format::fixed ? 'f' : 'e')
- : (specs.upper ? 'A' : 'a');
- *format_ptr = '\0';
-
- // Format using snprintf.
- auto offset = buf.size();
- for (;;) {
- auto begin = buf.data() + offset;
- auto capacity = buf.capacity() - offset;
-#ifdef FMT_FUZZ
- if (precision > 100000)
- throw std::runtime_error(
- "fuzz mode - avoid large allocation inside snprintf");
#endif
- // Suppress the warning about a nonliteral format string.
- // Cannot use auto because of a bug in MinGW (#1532).
- int (*snprintf_ptr)(char*, size_t, const char*, ...) = FMT_SNPRINTF;
- int result = precision >= 0
- ? snprintf_ptr(begin, capacity, format, precision, value)
- : snprintf_ptr(begin, capacity, format, value);
- if (result < 0) {
- // The buffer will grow exponentially.
- buf.try_reserve(buf.capacity() + 1);
- continue;
- }
- auto size = to_unsigned(result);
- // Size equal to capacity means that the last character was truncated.
- if (size >= capacity) {
- buf.try_reserve(size + offset + 1); // Add 1 for the terminating '\0'.
- continue;
- }
- auto is_digit = [](char c) { return c >= '0' && c <= '9'; };
- if (specs.format == float_format::fixed) {
- if (precision == 0) {
- buf.try_resize(size);
- return 0;
- }
- // Find and remove the decimal point.
- auto end = begin + size, p = end;
- do {
- --p;
- } while (is_digit(*p));
- int fraction_size = static_cast<int>(end - p - 1);
- std::memmove(p, p + 1, to_unsigned(fraction_size));
- buf.try_resize(size - 1);
- return -fraction_size;
- }
- if (specs.format == float_format::hex) {
- buf.try_resize(size + offset);
- return 0;
- }
- // Find and parse the exponent.
- auto end = begin + size, exp_pos = end;
- do {
- --exp_pos;
- } while (*exp_pos != 'e');
- char sign = exp_pos[1];
- FMT_ASSERT(sign == '+' || sign == '-', "");
- int exp = 0;
- auto p = exp_pos + 2; // Skip 'e' and sign.
- do {
- FMT_ASSERT(is_digit(*p), "");
- exp = exp * 10 + (*p++ - '0');
- } while (p != end);
- if (sign == '-') exp = -exp;
- int fraction_size = 0;
- if (exp_pos != begin + 1) {
- // Remove trailing zeros.
- auto fraction_end = exp_pos - 1;
- while (*fraction_end == '0') --fraction_end;
- // Move the fractional part left to get rid of the decimal point.
- fraction_size = static_cast<int>(fraction_end - begin - 1);
- std::memmove(begin + 1, begin + 2, to_unsigned(fraction_size));
- }
- buf.try_resize(to_unsigned(fraction_size) + offset + 1);
- return exp - fraction_size;
- }
-}
} // namespace detail
template <> struct formatter<detail::bigint> {
- FMT_CONSTEXPR format_parse_context::iterator parse(
- format_parse_context& ctx) {
+ FMT_CONSTEXPR auto parse(format_parse_context& ctx)
+ -> format_parse_context::iterator {
return ctx.begin();
}
- format_context::iterator format(const detail::bigint& n,
- format_context& ctx) {
+ template <typename FormatContext>
+ auto format(const detail::bigint& n, FormatContext& ctx) const ->
+ typename FormatContext::iterator {
auto out = ctx.out();
bool first = true;
for (auto i = n.bigits_.size(); i > 0; --i) {
}
FMT_FUNC void format_system_error(detail::buffer<char>& out, int error_code,
- const char* message) FMT_NOEXCEPT {
+ const char* message) noexcept {
FMT_TRY {
auto ec = std::error_code(error_code, std::generic_category());
write(std::back_inserter(out), std::system_error(ec, message).what());
}
FMT_FUNC void report_system_error(int error_code,
- const char* message) FMT_NOEXCEPT {
+ const char* message) noexcept {
report_error(format_system_error, error_code, message);
}
-// DEPRECATED!
-// This function is defined here and not inline for ABI compatiblity.
-FMT_FUNC void detail::error_handler::on_error(const char* message) {
- throw_format_error(message);
-}
-
FMT_FUNC std::string vformat(string_view fmt, format_args args) {
// Don't optimize the "{}" case to keep the binary size small and because it
// can be better optimized in fmt::format anyway.
return to_string(buffer);
}
-#ifdef _WIN32
namespace detail {
+#ifdef _WIN32
using dword = conditional_t<sizeof(long) == 4, unsigned long, unsigned>;
extern "C" __declspec(dllimport) int __stdcall WriteConsoleW( //
void*, const void*, dword, dword*, void*);
-} // namespace detail
-#endif
-namespace detail {
-FMT_FUNC void print(std::FILE* f, string_view text) {
-#ifdef _WIN32
+FMT_FUNC bool write_console(std::FILE* f, string_view text) {
auto fd = _fileno(f);
if (_isatty(fd)) {
detail::utf8_to_utf16 u16(string_view(text.data(), text.size()));
if (detail::WriteConsoleW(reinterpret_cast<void*>(_get_osfhandle(fd)),
u16.c_str(), static_cast<uint32_t>(u16.size()),
&written, nullptr)) {
- return;
+ return true;
}
- // Fallback to fwrite on failure. It can happen if the output has been
- // redirected to NUL.
}
+ // We return false if the file descriptor was not TTY, or it was but
+ // SetConsoleW failed which can happen if the output has been redirected to
+ // NUL. In both cases when we return false, we should attempt to do regular
+ // write via fwrite or std::ostream::write.
+ return false;
+}
+#endif
+
+FMT_FUNC void print(std::FILE* f, string_view text) {
+#ifdef _WIN32
+ if (write_console(f, text)) return;
#endif
detail::fwrite_fully(text.data(), 1, text.size(), f);
}
vprint(stdout, format_str, args);
}
+namespace detail {
+
+struct singleton {
+ unsigned char upper;
+ unsigned char lower_count;
+};
+
+inline auto is_printable(uint16_t x, const singleton* singletons,
+ size_t singletons_size,
+ const unsigned char* singleton_lowers,
+ const unsigned char* normal, size_t normal_size)
+ -> bool {
+ auto upper = x >> 8;
+ auto lower_start = 0;
+ for (size_t i = 0; i < singletons_size; ++i) {
+ auto s = singletons[i];
+ auto lower_end = lower_start + s.lower_count;
+ if (upper < s.upper) break;
+ if (upper == s.upper) {
+ for (auto j = lower_start; j < lower_end; ++j) {
+ if (singleton_lowers[j] == (x & 0xff)) return false;
+ }
+ }
+ lower_start = lower_end;
+ }
+
+ auto xsigned = static_cast<int>(x);
+ auto current = true;
+ for (size_t i = 0; i < normal_size; ++i) {
+ auto v = static_cast<int>(normal[i]);
+ auto len = (v & 0x80) != 0 ? (v & 0x7f) << 8 | normal[++i] : v;
+ xsigned -= len;
+ if (xsigned < 0) break;
+ current = !current;
+ }
+ return current;
+}
+
+// This code is generated by support/printable.py.
+FMT_FUNC auto is_printable(uint32_t cp) -> bool {
+ static constexpr singleton singletons0[] = {
+ {0x00, 1}, {0x03, 5}, {0x05, 6}, {0x06, 3}, {0x07, 6}, {0x08, 8},
+ {0x09, 17}, {0x0a, 28}, {0x0b, 25}, {0x0c, 20}, {0x0d, 16}, {0x0e, 13},
+ {0x0f, 4}, {0x10, 3}, {0x12, 18}, {0x13, 9}, {0x16, 1}, {0x17, 5},
+ {0x18, 2}, {0x19, 3}, {0x1a, 7}, {0x1c, 2}, {0x1d, 1}, {0x1f, 22},
+ {0x20, 3}, {0x2b, 3}, {0x2c, 2}, {0x2d, 11}, {0x2e, 1}, {0x30, 3},
+ {0x31, 2}, {0x32, 1}, {0xa7, 2}, {0xa9, 2}, {0xaa, 4}, {0xab, 8},
+ {0xfa, 2}, {0xfb, 5}, {0xfd, 4}, {0xfe, 3}, {0xff, 9},
+ };
+ static constexpr unsigned char singletons0_lower[] = {
+ 0xad, 0x78, 0x79, 0x8b, 0x8d, 0xa2, 0x30, 0x57, 0x58, 0x8b, 0x8c, 0x90,
+ 0x1c, 0x1d, 0xdd, 0x0e, 0x0f, 0x4b, 0x4c, 0xfb, 0xfc, 0x2e, 0x2f, 0x3f,
+ 0x5c, 0x5d, 0x5f, 0xb5, 0xe2, 0x84, 0x8d, 0x8e, 0x91, 0x92, 0xa9, 0xb1,
+ 0xba, 0xbb, 0xc5, 0xc6, 0xc9, 0xca, 0xde, 0xe4, 0xe5, 0xff, 0x00, 0x04,
+ 0x11, 0x12, 0x29, 0x31, 0x34, 0x37, 0x3a, 0x3b, 0x3d, 0x49, 0x4a, 0x5d,
+ 0x84, 0x8e, 0x92, 0xa9, 0xb1, 0xb4, 0xba, 0xbb, 0xc6, 0xca, 0xce, 0xcf,
+ 0xe4, 0xe5, 0x00, 0x04, 0x0d, 0x0e, 0x11, 0x12, 0x29, 0x31, 0x34, 0x3a,
+ 0x3b, 0x45, 0x46, 0x49, 0x4a, 0x5e, 0x64, 0x65, 0x84, 0x91, 0x9b, 0x9d,
+ 0xc9, 0xce, 0xcf, 0x0d, 0x11, 0x29, 0x45, 0x49, 0x57, 0x64, 0x65, 0x8d,
+ 0x91, 0xa9, 0xb4, 0xba, 0xbb, 0xc5, 0xc9, 0xdf, 0xe4, 0xe5, 0xf0, 0x0d,
+ 0x11, 0x45, 0x49, 0x64, 0x65, 0x80, 0x84, 0xb2, 0xbc, 0xbe, 0xbf, 0xd5,
+ 0xd7, 0xf0, 0xf1, 0x83, 0x85, 0x8b, 0xa4, 0xa6, 0xbe, 0xbf, 0xc5, 0xc7,
+ 0xce, 0xcf, 0xda, 0xdb, 0x48, 0x98, 0xbd, 0xcd, 0xc6, 0xce, 0xcf, 0x49,
+ 0x4e, 0x4f, 0x57, 0x59, 0x5e, 0x5f, 0x89, 0x8e, 0x8f, 0xb1, 0xb6, 0xb7,
+ 0xbf, 0xc1, 0xc6, 0xc7, 0xd7, 0x11, 0x16, 0x17, 0x5b, 0x5c, 0xf6, 0xf7,
+ 0xfe, 0xff, 0x80, 0x0d, 0x6d, 0x71, 0xde, 0xdf, 0x0e, 0x0f, 0x1f, 0x6e,
+ 0x6f, 0x1c, 0x1d, 0x5f, 0x7d, 0x7e, 0xae, 0xaf, 0xbb, 0xbc, 0xfa, 0x16,
+ 0x17, 0x1e, 0x1f, 0x46, 0x47, 0x4e, 0x4f, 0x58, 0x5a, 0x5c, 0x5e, 0x7e,
+ 0x7f, 0xb5, 0xc5, 0xd4, 0xd5, 0xdc, 0xf0, 0xf1, 0xf5, 0x72, 0x73, 0x8f,
+ 0x74, 0x75, 0x96, 0x2f, 0x5f, 0x26, 0x2e, 0x2f, 0xa7, 0xaf, 0xb7, 0xbf,
+ 0xc7, 0xcf, 0xd7, 0xdf, 0x9a, 0x40, 0x97, 0x98, 0x30, 0x8f, 0x1f, 0xc0,
+ 0xc1, 0xce, 0xff, 0x4e, 0x4f, 0x5a, 0x5b, 0x07, 0x08, 0x0f, 0x10, 0x27,
+ 0x2f, 0xee, 0xef, 0x6e, 0x6f, 0x37, 0x3d, 0x3f, 0x42, 0x45, 0x90, 0x91,
+ 0xfe, 0xff, 0x53, 0x67, 0x75, 0xc8, 0xc9, 0xd0, 0xd1, 0xd8, 0xd9, 0xe7,
+ 0xfe, 0xff,
+ };
+ static constexpr singleton singletons1[] = {
+ {0x00, 6}, {0x01, 1}, {0x03, 1}, {0x04, 2}, {0x08, 8}, {0x09, 2},
+ {0x0a, 5}, {0x0b, 2}, {0x0e, 4}, {0x10, 1}, {0x11, 2}, {0x12, 5},
+ {0x13, 17}, {0x14, 1}, {0x15, 2}, {0x17, 2}, {0x19, 13}, {0x1c, 5},
+ {0x1d, 8}, {0x24, 1}, {0x6a, 3}, {0x6b, 2}, {0xbc, 2}, {0xd1, 2},
+ {0xd4, 12}, {0xd5, 9}, {0xd6, 2}, {0xd7, 2}, {0xda, 1}, {0xe0, 5},
+ {0xe1, 2}, {0xe8, 2}, {0xee, 32}, {0xf0, 4}, {0xf8, 2}, {0xf9, 2},
+ {0xfa, 2}, {0xfb, 1},
+ };
+ static constexpr unsigned char singletons1_lower[] = {
+ 0x0c, 0x27, 0x3b, 0x3e, 0x4e, 0x4f, 0x8f, 0x9e, 0x9e, 0x9f, 0x06, 0x07,
+ 0x09, 0x36, 0x3d, 0x3e, 0x56, 0xf3, 0xd0, 0xd1, 0x04, 0x14, 0x18, 0x36,
+ 0x37, 0x56, 0x57, 0x7f, 0xaa, 0xae, 0xaf, 0xbd, 0x35, 0xe0, 0x12, 0x87,
+ 0x89, 0x8e, 0x9e, 0x04, 0x0d, 0x0e, 0x11, 0x12, 0x29, 0x31, 0x34, 0x3a,
+ 0x45, 0x46, 0x49, 0x4a, 0x4e, 0x4f, 0x64, 0x65, 0x5c, 0xb6, 0xb7, 0x1b,
+ 0x1c, 0x07, 0x08, 0x0a, 0x0b, 0x14, 0x17, 0x36, 0x39, 0x3a, 0xa8, 0xa9,
+ 0xd8, 0xd9, 0x09, 0x37, 0x90, 0x91, 0xa8, 0x07, 0x0a, 0x3b, 0x3e, 0x66,
+ 0x69, 0x8f, 0x92, 0x6f, 0x5f, 0xee, 0xef, 0x5a, 0x62, 0x9a, 0x9b, 0x27,
+ 0x28, 0x55, 0x9d, 0xa0, 0xa1, 0xa3, 0xa4, 0xa7, 0xa8, 0xad, 0xba, 0xbc,
+ 0xc4, 0x06, 0x0b, 0x0c, 0x15, 0x1d, 0x3a, 0x3f, 0x45, 0x51, 0xa6, 0xa7,
+ 0xcc, 0xcd, 0xa0, 0x07, 0x19, 0x1a, 0x22, 0x25, 0x3e, 0x3f, 0xc5, 0xc6,
+ 0x04, 0x20, 0x23, 0x25, 0x26, 0x28, 0x33, 0x38, 0x3a, 0x48, 0x4a, 0x4c,
+ 0x50, 0x53, 0x55, 0x56, 0x58, 0x5a, 0x5c, 0x5e, 0x60, 0x63, 0x65, 0x66,
+ 0x6b, 0x73, 0x78, 0x7d, 0x7f, 0x8a, 0xa4, 0xaa, 0xaf, 0xb0, 0xc0, 0xd0,
+ 0xae, 0xaf, 0x79, 0xcc, 0x6e, 0x6f, 0x93,
+ };
+ static constexpr unsigned char normal0[] = {
+ 0x00, 0x20, 0x5f, 0x22, 0x82, 0xdf, 0x04, 0x82, 0x44, 0x08, 0x1b, 0x04,
+ 0x06, 0x11, 0x81, 0xac, 0x0e, 0x80, 0xab, 0x35, 0x28, 0x0b, 0x80, 0xe0,
+ 0x03, 0x19, 0x08, 0x01, 0x04, 0x2f, 0x04, 0x34, 0x04, 0x07, 0x03, 0x01,
+ 0x07, 0x06, 0x07, 0x11, 0x0a, 0x50, 0x0f, 0x12, 0x07, 0x55, 0x07, 0x03,
+ 0x04, 0x1c, 0x0a, 0x09, 0x03, 0x08, 0x03, 0x07, 0x03, 0x02, 0x03, 0x03,
+ 0x03, 0x0c, 0x04, 0x05, 0x03, 0x0b, 0x06, 0x01, 0x0e, 0x15, 0x05, 0x3a,
+ 0x03, 0x11, 0x07, 0x06, 0x05, 0x10, 0x07, 0x57, 0x07, 0x02, 0x07, 0x15,
+ 0x0d, 0x50, 0x04, 0x43, 0x03, 0x2d, 0x03, 0x01, 0x04, 0x11, 0x06, 0x0f,
+ 0x0c, 0x3a, 0x04, 0x1d, 0x25, 0x5f, 0x20, 0x6d, 0x04, 0x6a, 0x25, 0x80,
+ 0xc8, 0x05, 0x82, 0xb0, 0x03, 0x1a, 0x06, 0x82, 0xfd, 0x03, 0x59, 0x07,
+ 0x15, 0x0b, 0x17, 0x09, 0x14, 0x0c, 0x14, 0x0c, 0x6a, 0x06, 0x0a, 0x06,
+ 0x1a, 0x06, 0x59, 0x07, 0x2b, 0x05, 0x46, 0x0a, 0x2c, 0x04, 0x0c, 0x04,
+ 0x01, 0x03, 0x31, 0x0b, 0x2c, 0x04, 0x1a, 0x06, 0x0b, 0x03, 0x80, 0xac,
+ 0x06, 0x0a, 0x06, 0x21, 0x3f, 0x4c, 0x04, 0x2d, 0x03, 0x74, 0x08, 0x3c,
+ 0x03, 0x0f, 0x03, 0x3c, 0x07, 0x38, 0x08, 0x2b, 0x05, 0x82, 0xff, 0x11,
+ 0x18, 0x08, 0x2f, 0x11, 0x2d, 0x03, 0x20, 0x10, 0x21, 0x0f, 0x80, 0x8c,
+ 0x04, 0x82, 0x97, 0x19, 0x0b, 0x15, 0x88, 0x94, 0x05, 0x2f, 0x05, 0x3b,
+ 0x07, 0x02, 0x0e, 0x18, 0x09, 0x80, 0xb3, 0x2d, 0x74, 0x0c, 0x80, 0xd6,
+ 0x1a, 0x0c, 0x05, 0x80, 0xff, 0x05, 0x80, 0xdf, 0x0c, 0xee, 0x0d, 0x03,
+ 0x84, 0x8d, 0x03, 0x37, 0x09, 0x81, 0x5c, 0x14, 0x80, 0xb8, 0x08, 0x80,
+ 0xcb, 0x2a, 0x38, 0x03, 0x0a, 0x06, 0x38, 0x08, 0x46, 0x08, 0x0c, 0x06,
+ 0x74, 0x0b, 0x1e, 0x03, 0x5a, 0x04, 0x59, 0x09, 0x80, 0x83, 0x18, 0x1c,
+ 0x0a, 0x16, 0x09, 0x4c, 0x04, 0x80, 0x8a, 0x06, 0xab, 0xa4, 0x0c, 0x17,
+ 0x04, 0x31, 0xa1, 0x04, 0x81, 0xda, 0x26, 0x07, 0x0c, 0x05, 0x05, 0x80,
+ 0xa5, 0x11, 0x81, 0x6d, 0x10, 0x78, 0x28, 0x2a, 0x06, 0x4c, 0x04, 0x80,
+ 0x8d, 0x04, 0x80, 0xbe, 0x03, 0x1b, 0x03, 0x0f, 0x0d,
+ };
+ static constexpr unsigned char normal1[] = {
+ 0x5e, 0x22, 0x7b, 0x05, 0x03, 0x04, 0x2d, 0x03, 0x66, 0x03, 0x01, 0x2f,
+ 0x2e, 0x80, 0x82, 0x1d, 0x03, 0x31, 0x0f, 0x1c, 0x04, 0x24, 0x09, 0x1e,
+ 0x05, 0x2b, 0x05, 0x44, 0x04, 0x0e, 0x2a, 0x80, 0xaa, 0x06, 0x24, 0x04,
+ 0x24, 0x04, 0x28, 0x08, 0x34, 0x0b, 0x01, 0x80, 0x90, 0x81, 0x37, 0x09,
+ 0x16, 0x0a, 0x08, 0x80, 0x98, 0x39, 0x03, 0x63, 0x08, 0x09, 0x30, 0x16,
+ 0x05, 0x21, 0x03, 0x1b, 0x05, 0x01, 0x40, 0x38, 0x04, 0x4b, 0x05, 0x2f,
+ 0x04, 0x0a, 0x07, 0x09, 0x07, 0x40, 0x20, 0x27, 0x04, 0x0c, 0x09, 0x36,
+ 0x03, 0x3a, 0x05, 0x1a, 0x07, 0x04, 0x0c, 0x07, 0x50, 0x49, 0x37, 0x33,
+ 0x0d, 0x33, 0x07, 0x2e, 0x08, 0x0a, 0x81, 0x26, 0x52, 0x4e, 0x28, 0x08,
+ 0x2a, 0x56, 0x1c, 0x14, 0x17, 0x09, 0x4e, 0x04, 0x1e, 0x0f, 0x43, 0x0e,
+ 0x19, 0x07, 0x0a, 0x06, 0x48, 0x08, 0x27, 0x09, 0x75, 0x0b, 0x3f, 0x41,
+ 0x2a, 0x06, 0x3b, 0x05, 0x0a, 0x06, 0x51, 0x06, 0x01, 0x05, 0x10, 0x03,
+ 0x05, 0x80, 0x8b, 0x62, 0x1e, 0x48, 0x08, 0x0a, 0x80, 0xa6, 0x5e, 0x22,
+ 0x45, 0x0b, 0x0a, 0x06, 0x0d, 0x13, 0x39, 0x07, 0x0a, 0x36, 0x2c, 0x04,
+ 0x10, 0x80, 0xc0, 0x3c, 0x64, 0x53, 0x0c, 0x48, 0x09, 0x0a, 0x46, 0x45,
+ 0x1b, 0x48, 0x08, 0x53, 0x1d, 0x39, 0x81, 0x07, 0x46, 0x0a, 0x1d, 0x03,
+ 0x47, 0x49, 0x37, 0x03, 0x0e, 0x08, 0x0a, 0x06, 0x39, 0x07, 0x0a, 0x81,
+ 0x36, 0x19, 0x80, 0xb7, 0x01, 0x0f, 0x32, 0x0d, 0x83, 0x9b, 0x66, 0x75,
+ 0x0b, 0x80, 0xc4, 0x8a, 0xbc, 0x84, 0x2f, 0x8f, 0xd1, 0x82, 0x47, 0xa1,
+ 0xb9, 0x82, 0x39, 0x07, 0x2a, 0x04, 0x02, 0x60, 0x26, 0x0a, 0x46, 0x0a,
+ 0x28, 0x05, 0x13, 0x82, 0xb0, 0x5b, 0x65, 0x4b, 0x04, 0x39, 0x07, 0x11,
+ 0x40, 0x05, 0x0b, 0x02, 0x0e, 0x97, 0xf8, 0x08, 0x84, 0xd6, 0x2a, 0x09,
+ 0xa2, 0xf7, 0x81, 0x1f, 0x31, 0x03, 0x11, 0x04, 0x08, 0x81, 0x8c, 0x89,
+ 0x04, 0x6b, 0x05, 0x0d, 0x03, 0x09, 0x07, 0x10, 0x93, 0x60, 0x80, 0xf6,
+ 0x0a, 0x73, 0x08, 0x6e, 0x17, 0x46, 0x80, 0x9a, 0x14, 0x0c, 0x57, 0x09,
+ 0x19, 0x80, 0x87, 0x81, 0x47, 0x03, 0x85, 0x42, 0x0f, 0x15, 0x85, 0x50,
+ 0x2b, 0x80, 0xd5, 0x2d, 0x03, 0x1a, 0x04, 0x02, 0x81, 0x70, 0x3a, 0x05,
+ 0x01, 0x85, 0x00, 0x80, 0xd7, 0x29, 0x4c, 0x04, 0x0a, 0x04, 0x02, 0x83,
+ 0x11, 0x44, 0x4c, 0x3d, 0x80, 0xc2, 0x3c, 0x06, 0x01, 0x04, 0x55, 0x05,
+ 0x1b, 0x34, 0x02, 0x81, 0x0e, 0x2c, 0x04, 0x64, 0x0c, 0x56, 0x0a, 0x80,
+ 0xae, 0x38, 0x1d, 0x0d, 0x2c, 0x04, 0x09, 0x07, 0x02, 0x0e, 0x06, 0x80,
+ 0x9a, 0x83, 0xd8, 0x08, 0x0d, 0x03, 0x0d, 0x03, 0x74, 0x0c, 0x59, 0x07,
+ 0x0c, 0x14, 0x0c, 0x04, 0x38, 0x08, 0x0a, 0x06, 0x28, 0x08, 0x22, 0x4e,
+ 0x81, 0x54, 0x0c, 0x15, 0x03, 0x03, 0x05, 0x07, 0x09, 0x19, 0x07, 0x07,
+ 0x09, 0x03, 0x0d, 0x07, 0x29, 0x80, 0xcb, 0x25, 0x0a, 0x84, 0x06,
+ };
+ auto lower = static_cast<uint16_t>(cp);
+ if (cp < 0x10000) {
+ return is_printable(lower, singletons0,
+ sizeof(singletons0) / sizeof(*singletons0),
+ singletons0_lower, normal0, sizeof(normal0));
+ }
+ if (cp < 0x20000) {
+ return is_printable(lower, singletons1,
+ sizeof(singletons1) / sizeof(*singletons1),
+ singletons1_lower, normal1, sizeof(normal1));
+ }
+ if (0x2a6de <= cp && cp < 0x2a700) return false;
+ if (0x2b735 <= cp && cp < 0x2b740) return false;
+ if (0x2b81e <= cp && cp < 0x2b820) return false;
+ if (0x2cea2 <= cp && cp < 0x2ceb0) return false;
+ if (0x2ebe1 <= cp && cp < 0x2f800) return false;
+ if (0x2fa1e <= cp && cp < 0x30000) return false;
+ if (0x3134b <= cp && cp < 0xe0100) return false;
+ if (0xe01f0 <= cp && cp < 0x110000) return false;
+ return cp < 0x110000;
+}
+
+} // namespace detail
+
FMT_END_NAMESPACE
#endif // FMT_FORMAT_INL_H_
projects / lttng-tools.git / blobdiff