what is "ab_x2_high32" in <func::SaturatingRoundingDoublingHighMul> stand for?

[jiaheni1127]

Hi,
In

inline std::int32_t SaturatingRoundingDoublingHighMul(std::int32_t a,
                                                      std::int32_t b) {
  bool overflow = a == b && a == std::numeric_limits<std::int32_t>::min();
  std::int64_t a_64(a);
  std::int64_t b_64(b);
  std::int64_t ab_64 = a_64 * b_64;
  std::int32_t nudge = ab_64 >= 0 ? (1 << 30) : (1 - (1 << 30));
  std::int32_t ab_x2_high32 =
      static_cast<std::int32_t>((ab_64 + nudge) / (1ll << 31));
  return overflow ? std::numeric_limits<std::int32_t>::max() : ab_x2_high32;
}

it seemed this function is computing a * b
i wondered what is the relationship between ab_x2_high32 and ab_64. Could you explain how is ab_x2_high32 computed?

Thank you!