Math-Ryu

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      if (vpDiv10 <= vmDiv10) {
        break;
      }
      const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10);
      const uint64_t vrDiv10 = div10(vr);
      const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
      vmIsTrailingZeros &= vmMod10 == 0;
      vrIsTrailingZeros &= lastRemovedDigit == 0;
      lastRemovedDigit = (uint8_t) vrMod10;
      vr = vrDiv10;
      vp = vpDiv10;
      vm = vmDiv10;
      ++removed;
    }
#ifdef RYU_DEBUG
    printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
    printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false");
#endif
    if (vmIsTrailingZeros) {
      for (;;) {
        const uint64_t vmDiv10 = div10(vm);
        const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10);
        if (vmMod10 != 0) {
          break;
        }
        const uint64_t vpDiv10 = div10(vp);
        const uint64_t vrDiv10 = div10(vr);
        const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
        vrIsTrailingZeros &= lastRemovedDigit == 0;
        lastRemovedDigit = (uint8_t) vrMod10;
        vr = vrDiv10;
        vp = vpDiv10;
        vm = vmDiv10;
        ++removed;
      }
    }
#ifdef RYU_DEBUG
    printf("%" PRIu64 " %d\n", vr, lastRemovedDigit);
    printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
#endif
    if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0) {
      // Round even if the exact number is .....50..0.
      lastRemovedDigit = 4;
    }
    // We need to take vr + 1 if vr is outside bounds or we need to round up.
    output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
  } else {
    // Specialized for the common case (~99.3%). Percentages below are relative to this.
    bool roundUp = false;
    const uint64_t vpDiv100 = div100(vp);
    const uint64_t vmDiv100 = div100(vm);
    if (vpDiv100 > vmDiv100) { // Optimization: remove two digits at a time (~86.2%).
      const uint64_t vrDiv100 = div100(vr);
      const uint32_t vrMod100 = ((uint32_t) vr) - 100 * ((uint32_t) vrDiv100);
      roundUp = vrMod100 >= 50;
      vr = vrDiv100;
      vp = vpDiv100;
      vm = vmDiv100;
      removed += 2;
    }
    // Loop iterations below (approximately), without optimization above:
    // 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
    // Loop iterations below (approximately), with optimization above:
    // 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
    for (;;) {
      const uint64_t vpDiv10 = div10(vp);
      const uint64_t vmDiv10 = div10(vm);
      if (vpDiv10 <= vmDiv10) {
        break;
      }
      const uint64_t vrDiv10 = div10(vr);
      const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
      roundUp = vrMod10 >= 5;
      vr = vrDiv10;
      vp = vpDiv10;
      vm = vmDiv10;
      ++removed;
    }
#ifdef RYU_DEBUG
    printf("%" PRIu64 " roundUp=%s\n", vr, roundUp ? "true" : "false");
    printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
#endif
    // We need to take vr + 1 if vr is outside bounds or we need to round up.
    output = vr + (vr == vm || roundUp);
  }
  const int32_t exp = e10 + removed;

#ifdef RYU_DEBUG
  printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
  printf("O=%" PRIu64 "\n", output);
  printf("EXP=%d\n", exp);
#endif

  floating_decimal_64 fd;
  fd.exponent = exp;
  fd.mantissa = output;
  return fd;
}

static inline int to_chars(const floating_decimal_64 v, const bool sign, char* const result) {
  // Step 5: Print the decimal representation.
  int index = 0;
  if (sign) {
    result[index++] = '-';
  }

  uint64_t output = v.mantissa;
  const uint32_t olength = decimalLength17(output);

#ifdef RYU_DEBUG
  printf("DIGITS=%" PRIu64 "\n", v.mantissa);
  printf("OLEN=%u\n", olength);
  printf("EXP=%u\n", v.exponent + olength);
#endif

  // Print the decimal digits.
  // The following code is equivalent to:
  // for (uint32_t i = 0; i < olength - 1; ++i) {
  //   const uint32_t c = output % 10; output /= 10;
  //   result[index + olength - i] = (char) ('0' + c);
  // }
  // result[index] = '0' + output % 10;



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