+ return std::signbit(static_cast<double>(value));
+}
+
+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;
+}
+
+namespace digits {
+enum result {
+ more, // Generate more digits.
+ done, // Done generating digits.
+ error // Digit generation cancelled due to an error.
+};
+}
+
+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;
+ }
+};
+
+inline FMT_CONSTEXPR20 void adjust_precision(int& precision, int exp10) {
+ // Adjust fixed precision by exponent because it is relative to decimal
+ // point.
+ if (exp10 > 0 && precision > max_value<int>() - exp10)
+ FMT_THROW(format_error("number is too big"));
+ precision += exp10;
+}
+
+// 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 auto grisu_gen_digits(fp value, uint64_t error,
+ int& exp,
+ gen_digits_handler& handler)
+ -> digits::result {
+ 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_precision(handler.precision, exp + handler.exp10);
+ // 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 = 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),
+ 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;
+ }
+}
+
+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 constexpr const int bigit_bits = num_bits<bigit>();
+
+ 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);
+ }
+
+ template <typename UInt, FMT_ENABLE_IF(std::is_same<UInt, uint64_t>::value ||
+ std::is_same<UInt, uint128_t>::value)>
+ FMT_CONSTEXPR20 void multiply(UInt value) {
+ using half_uint =
+ conditional_t<std::is_same<UInt, uint128_t>::value, uint64_t, uint32_t>;
+ const int shift = num_bits<half_uint>() - bigit_bits;
+ const UInt lower = static_cast<half_uint>(value);
+ const UInt upper = value >> num_bits<half_uint>();
+ UInt carry = 0;
+ for (size_t i = 0, n = bigits_.size(); i < n; ++i) {
+ UInt result = lower * bigits_[i] + static_cast<bigit>(carry);
+ carry = (upper * bigits_[i] << shift) + (result >> bigit_bits) +
+ (carry >> bigit_bits);
+ bigits_[i] = static_cast<bigit>(result);
+ }
+ while (carry != 0) {
+ bigits_.push_back(static_cast<bigit>(carry));
+ carry >>= bigit_bits;
+ }
+ }
+
+ template <typename UInt, FMT_ENABLE_IF(std::is_same<UInt, uint64_t>::value ||
+ std::is_same<UInt, uint128_t>::value)>
+ FMT_CONSTEXPR20 void assign(UInt n) {
+ size_t num_bigits = 0;
+ do {
+ bigits_[num_bigits++] = static_cast<bigit>(n);
+ n >>= bigit_bits;
+ } while (n != 0);
+ bigits_.resize(num_bigits);
+ exp_ = 0;
+ }
+
+ public:
+ FMT_CONSTEXPR20 bigint() : exp_(0) {}
+ explicit bigint(uint64_t n) { assign(n); }
+
+ 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_;
+ }
+
+ template <typename Int> FMT_CONSTEXPR20 void operator=(Int n) {
+ FMT_ASSERT(n > 0, "");
+ assign(uint64_or_128_t<Int>(n));
+ }
+
+ 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) {
+ auto minimum = [](int a, int b) { return a < b ? a : b; };
+ auto maximum = [](int a, int b) { return a > b ? a : b; };
+ int max_lhs_bigits = maximum(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 = minimum(minimum(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 *this = 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.
+ *this = 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));
+ auto sum = uint128_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 >>= num_bits<bigit>(); // 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 >>= num_bits<bigit>();
+ }
+ 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;
+ }
+};
+
+// format_dragon flags.
+enum dragon {
+ predecessor_closer = 1,
+ fixup = 2, // Run fixup to correct exp10 which can be off by one.
+ fixed = 4,
+};
+
+// 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(basic_fp<uint128_t> value,
+ unsigned flags, 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.
+ bool is_predecessor_closer = (flags & dragon::predecessor_closer) != 0;
+ int shift = is_predecessor_closer ? 2 : 1;
+ if (value.e >= 0) {
+ numerator = value.f;
+ numerator <<= value.e + shift;
+ lower = 1;
+ lower <<= value.e;
+ if (is_predecessor_closer) {
+ upper_store = 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 (is_predecessor_closer) {
+ upper_store.assign(numerator);
+ upper_store <<= 1;
+ upper = &upper_store;
+ }
+ numerator *= value.f;
+ numerator <<= shift;
+ denominator = 1;
+ denominator <<= shift - value.e;
+ } else {
+ numerator = value.f;
+ numerator <<= shift;
+ denominator.assign_pow10(exp10);
+ denominator <<= shift - value.e;
+ lower = 1;
+ if (is_predecessor_closer) {
+ upper_store = 1ULL << 1;
+ upper = &upper_store;
+ }
+ }
+ int even = static_cast<int>((value.f & 1) == 0);
+ if (!upper) upper = &lower;
+ if ((flags & dragon::fixup) != 0) {
+ if (add_compare(numerator, *upper, denominator) + even <= 0) {
+ --exp10;
+ numerator *= 10;
+ if (num_digits < 0) {
+ lower *= 10;
+ if (upper != &lower) *upper *= 10;
+ }
+ }
+ if ((flags & dragon::fixed) != 0) adjust_precision(num_digits, exp10 + 1);
+ }
+ // Invariant: value == (numerator / denominator) * pow(10, exp10).
+ if (num_digits < 0) {
+ // Generate the shortest representation.
+ 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_CONSTEXPR20 auto format_float(Float value, int precision, float_specs specs,
+ buffer<char>& buf) -> int {
+ // 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");
+ auto converted_value = convert_float(value);
+
+ 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;
+ }
+
+ int exp = 0;
+ bool use_dragon = true;
+ unsigned dragon_flags = 0;
+ if (!is_fast_float<Float>()) {
+ const auto inv_log2_10 = 0.3010299956639812; // 1 / log2(10)
+ using info = dragonbox::float_info<decltype(converted_value)>;
+ const auto f = basic_fp<typename info::carrier_uint>(converted_value);
+ // Compute exp, an approximate power of 10, such that
+ // 10^(exp - 1) <= value < 10^exp or 10^exp <= value < 10^(exp + 1).
+ // This is based on log10(value) == log2(value) / log2(10) and approximation
+ // of log2(value) by e + num_fraction_bits idea from double-conversion.
+ exp = static_cast<int>(
+ std::ceil((f.e + count_digits<1>(f.f) - 1) * inv_log2_10 - 1e-10));
+ dragon_flags = dragon::fixup;
+ } else 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;
+ } else {
+ // 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(converted_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 = basic_fp<uint128_t>();
+ bool is_predecessor_closer = specs.binary32
+ ? f.assign(static_cast<float>(value))
+ : f.assign(converted_value);
+ if (is_predecessor_closer) dragon_flags |= dragon::predecessor_closer;
+ if (fixed) dragon_flags |= dragon::fixed;
+ // 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, dragon_flags, 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;