Method format_dragon

include/fmt/format.h:2936–3068

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.

// 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;
  bool shortest = num_digits < 0;
  if ((flags & dragon::fixup) != 0) {
    if (add_compare(numerator, *upper, denominator) + even <= 0) {
      --exp10;
      numerator *= 10;
      if (num_digits < 0) {
        lower *= 10;