Move format_float to format-inl.h

include/fmt/format-inl.h

@@ -1374,6 +1374,305 @@ template <typename T> auto to_decimal(T x) noexcept -> decimal_fp<T> {
   return ret_value;
 }
 }  // namespace dragonbox
+
+template <typename Float>
+FMT_CONSTEXPR20 auto format_float(Float value, int precision,
+                                  const format_specs& specs, bool binary32,
+                                  buffer<char>& buf) -> int {
+  // float is passed as double to reduce the number of instantiations.
+  static_assert(!std::is_same<Float, float>::value, "");
+  auto converted_value = convert_float(value);
+
+  const bool fixed = specs.type() == presentation_type::fixed;
+  if (value == 0) {
+    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>() || is_constant_evaluated()) {
+    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.
+    auto e = (f.e + count_digits<1>(f.f) - 1) * inv_log2_10 - 1e-10;
+    exp = static_cast<int>(e);
+    if (e > exp) ++exp;  // Compute ceil.
+    dragon_flags = dragon::fixup;
+  } else {
+    // Extract significand bits and exponent bits.
+    using info = dragonbox::float_info<double>;
+    auto br = bit_cast<uint64_t>(static_cast<double>(value));
+
+    const uint64_t significand_mask =
+        (static_cast<uint64_t>(1) << num_significand_bits<double>()) - 1;
+    uint64_t significand = (br & significand_mask);
+    int exponent = static_cast<int>((br & exponent_mask<double>()) >>
+                                    num_significand_bits<double>());
+
+    if (exponent != 0) {  // Check if normal.
+      exponent -= exponent_bias<double>() + num_significand_bits<double>();
+      significand |=
+          (static_cast<uint64_t>(1) << num_significand_bits<double>());
+      significand <<= 1;
+    } else {
+      // Normalize subnormal inputs.
+      FMT_ASSERT(significand != 0, "zeros should not appear here");
+      int shift = countl_zero(significand);
+      FMT_ASSERT(shift >= num_bits<uint64_t>() - num_significand_bits<double>(),
+                 "");
+      shift -= (num_bits<uint64_t>() - num_significand_bits<double>() - 2);
+      exponent = (std::numeric_limits<double>::min_exponent -
+                  num_significand_bits<double>()) -
+                 shift;
+      significand <<= shift;
+    }
+
+    // Compute the first several nonzero decimal significand digits.
+    // We call the number we get the first segment.
+    const int k = info::kappa - dragonbox::floor_log10_pow2(exponent);
+    exp = -k;
+    const int beta = exponent + dragonbox::floor_log2_pow10(k);
+    uint64_t first_segment;
+    bool has_more_segments;
+    int digits_in_the_first_segment;
+    {
+      const auto r = dragonbox::umul192_upper128(
+          significand << beta, dragonbox::get_cached_power(k));
+      first_segment = r.high();
+      has_more_segments = r.low() != 0;
+
+      // The first segment can have 18 ~ 19 digits.
+      if (first_segment >= 1000000000000000000ULL) {
+        digits_in_the_first_segment = 19;
+      } else {
+        // When it is of 18-digits, we align it to 19-digits by adding a bogus
+        // zero at the end.
+        digits_in_the_first_segment = 18;
+        first_segment *= 10;
+      }
+    }
+
+    // Compute the actual number of decimal digits to print.
+    if (fixed) adjust_precision(precision, exp + digits_in_the_first_segment);
+
+    // Use Dragon4 only when there might be not enough digits in the first
+    // segment.
+    if (digits_in_the_first_segment > precision) {
+      use_dragon = false;
+
+      if (precision <= 0) {
+        exp += digits_in_the_first_segment;
+
+        if (precision < 0) {
+          // Nothing to do, since all we have are just leading zeros.
+          buf.try_resize(0);
+        } else {
+          // We may need to round-up.
+          buf.try_resize(1);
+          if ((first_segment | static_cast<uint64_t>(has_more_segments)) >
+              5000000000000000000ULL) {
+            buf[0] = '1';
+          } else {
+            buf[0] = '0';
+          }
+        }
+      }  // precision <= 0
+      else {
+        exp += digits_in_the_first_segment - precision;
+
+        // When precision > 0, we divide the first segment into three
+        // subsegments, each with 9, 9, and 0 ~ 1 digits so that each fits
+        // in 32-bits which usually allows faster calculation than in
+        // 64-bits. Since some compiler (e.g. MSVC) doesn't know how to optimize
+        // division-by-constant for large 64-bit divisors, we do it here
+        // manually. The magic number 7922816251426433760 below is equal to
+        // ceil(2^(64+32) / 10^10).
+        const uint32_t first_subsegment = static_cast<uint32_t>(
+            dragonbox::umul128_upper64(first_segment, 7922816251426433760ULL) >>
+            32);
+        const uint64_t second_third_subsegments =
+            first_segment - first_subsegment * 10000000000ULL;
+
+        uint64_t prod;
+        uint32_t digits;
+        bool should_round_up;
+        int number_of_digits_to_print = precision > 9 ? 9 : precision;
+
+        // Print a 9-digits subsegment, either the first or the second.
+        auto print_subsegment = [&](uint32_t subsegment, char* buffer) {
+          int number_of_digits_printed = 0;
+
+          // If we want to print an odd number of digits from the subsegment,
+          if ((number_of_digits_to_print & 1) != 0) {
+            // Convert to 64-bit fixed-point fractional form with 1-digit
+            // integer part. The magic number 720575941 is a good enough
+            // approximation of 2^(32 + 24) / 10^8; see
+            // https://jk-jeon.github.io/posts/2022/12/fixed-precision-formatting/#fixed-length-case
+            // for details.
+            prod = ((subsegment * static_cast<uint64_t>(720575941)) >> 24) + 1;
+            digits = static_cast<uint32_t>(prod >> 32);
+            *buffer = static_cast<char>('0' + digits);
+            number_of_digits_printed++;
+          }
+          // If we want to print an even number of digits from the
+          // first_subsegment,
+          else {
+            // Convert to 64-bit fixed-point fractional form with 2-digits
+            // integer part. The magic number 450359963 is a good enough
+            // approximation of 2^(32 + 20) / 10^7; see
+            // https://jk-jeon.github.io/posts/2022/12/fixed-precision-formatting/#fixed-length-case
+            // for details.
+            prod = ((subsegment * static_cast<uint64_t>(450359963)) >> 20) + 1;
+            digits = static_cast<uint32_t>(prod >> 32);
+            write2digits(buffer, digits);
+            number_of_digits_printed += 2;
+          }
+
+          // Print all digit pairs.
+          while (number_of_digits_printed < number_of_digits_to_print) {
+            prod = static_cast<uint32_t>(prod) * static_cast<uint64_t>(100);
+            digits = static_cast<uint32_t>(prod >> 32);
+            write2digits(buffer + number_of_digits_printed, digits);
+            number_of_digits_printed += 2;
+          }
+        };
+
+        // Print first subsegment.
+        print_subsegment(first_subsegment, buf.data());
+
+        // Perform rounding if the first subsegment is the last subsegment to
+        // print.
+        if (precision <= 9) {
+          // Rounding inside the subsegment.
+          // We round-up if:
+          //  - either the fractional part is strictly larger than 1/2, or
+          //  - the fractional part is exactly 1/2 and the last digit is odd.
+          // We rely on the following observations:
+          //  - If fractional_part >= threshold, then the fractional part is
+          //    strictly larger than 1/2.
+          //  - If the MSB of fractional_part is set, then the fractional part
+          //    must be at least 1/2.
+          //  - When the MSB of fractional_part is set, either
+          //    second_third_subsegments being nonzero or has_more_segments
+          //    being true means there are further digits not printed, so the
+          //    fractional part is strictly larger than 1/2.
+          if (precision < 9) {
+            uint32_t fractional_part = static_cast<uint32_t>(prod);
+            should_round_up =
+                fractional_part >= fractional_part_rounding_thresholds(
+                                       8 - number_of_digits_to_print) ||
+                ((fractional_part >> 31) &
+                 ((digits & 1) | (second_third_subsegments != 0) |
+                  has_more_segments)) != 0;
+          }
+          // Rounding at the subsegment boundary.
+          // In this case, the fractional part is at least 1/2 if and only if
+          // second_third_subsegments >= 5000000000ULL, and is strictly larger
+          // than 1/2 if we further have either second_third_subsegments >
+          // 5000000000ULL or has_more_segments == true.
+          else {
+            should_round_up = second_third_subsegments > 5000000000ULL ||
+                              (second_third_subsegments == 5000000000ULL &&
+                               ((digits & 1) != 0 || has_more_segments));
+          }
+        }
+        // Otherwise, print the second subsegment.
+        else {
+          // Compilers are not aware of how to leverage the maximum value of
+          // second_third_subsegments to find out a better magic number which
+          // allows us to eliminate an additional shift. 1844674407370955162 =
+          // ceil(2^64/10) < ceil(2^64*(10^9/(10^10 - 1))).
+          const uint32_t second_subsegment =
+              static_cast<uint32_t>(dragonbox::umul128_upper64(
+                  second_third_subsegments, 1844674407370955162ULL));
+          const uint32_t third_subsegment =
+              static_cast<uint32_t>(second_third_subsegments) -
+              second_subsegment * 10;
+
+          number_of_digits_to_print = precision - 9;
+          print_subsegment(second_subsegment, buf.data() + 9);
+
+          // Rounding inside the subsegment.
+          if (precision < 18) {
+            // The condition third_subsegment != 0 implies that the segment was
+            // of 19 digits, so in this case the third segment should be
+            // consisting of a genuine digit from the input.
+            uint32_t fractional_part = static_cast<uint32_t>(prod);
+            should_round_up =
+                fractional_part >= fractional_part_rounding_thresholds(
+                                       8 - number_of_digits_to_print) ||
+                ((fractional_part >> 31) &
+                 ((digits & 1) | (third_subsegment != 0) |
+                  has_more_segments)) != 0;
+          }
+          // Rounding at the subsegment boundary.
+          else {
+            // In this case, the segment must be of 19 digits, thus
+            // the third subsegment should be consisting of a genuine digit from
+            // the input.
+            should_round_up = third_subsegment > 5 ||
+                              (third_subsegment == 5 &&
+                               ((digits & 1) != 0 || has_more_segments));
+          }
+        }
+
+        // Round-up if necessary.
+        if (should_round_up) {
+          ++buf[precision - 1];
+          for (int i = precision - 1; i > 0 && buf[i] > '9'; --i) {
+            buf[i] = '0';
+            ++buf[i - 1];
+          }
+          if (buf[0] > '9') {
+            buf[0] = '1';
+            if (fixed)
+              buf[precision++] = '0';
+            else
+              ++exp;
+          }
+        }
+        buf.try_resize(to_unsigned(precision));
+      }
+    }  // if (digits_in_the_first_segment > precision)
+    else {
+      // Adjust the exponent for its use in Dragon4.
+      exp += digits_in_the_first_segment - 1;
+    }
+  }
+  if (use_dragon) {
+    auto f = basic_fp<uint128_t>();
+    bool is_predecessor_closer = 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.alt()) {
+    // 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;
+}
 }  // namespace detail
 
 template <> struct formatter<detail::bigint> {