in thrift/compiler/detail/fmt/fmt/format-inl.h [2226:2338]
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);
}