Speed up do_format_decimal (#4630)

Author: user202729

include/fmt/format.h

@@ -1041,6 +1041,22 @@ inline auto digits2(size_t value) noexcept -> const char* {
   return &data[value * 2];
 }
 
+// Given i in [0, 100), let x be the first 7 digits after
+// the decimal point of i / 100 in base 2, the first 2 bytes
+// after digits2_i(x) is the string representation of i.
+inline auto digits2_i(size_t value) -> const char* {
+  alignas(2) static const char data[] =
+      "00010203  0405060707080910  1112"
+      "131414151617  18192021  222324  "
+      "25262728  2930313232333435  3637"
+      "383939404142  43444546  474849  "
+      "50515253  5455565757585960  6162"
+      "636464656667  68697071  727374  "
+      "75767778  7980818282838485  8687"
+      "888989909192  93949596  979899  ";
+  return &data[value * 2];
+}
+
 template <typename Char> constexpr auto getsign(sign s) -> Char {
   return static_cast<char>(((' ' << 24) | ('+' << 16) | ('-' << 8)) >>
                            (static_cast<int>(s) * 8));
@@ -1209,6 +1225,16 @@ FMT_CONSTEXPR20 FMT_INLINE void write2digits(Char* out, size_t value) {
   *out = static_cast<Char>('0' + value % 10);
 }
 
+template <typename Char>
+FMT_INLINE void write2digits_i(Char* out, size_t value) {
+  if (std::is_same<Char, char>::value && !FMT_OPTIMIZE_SIZE) {
+    memcpy(out, digits2_i(value), 2);
+    return;
+  }
+  *out++ = static_cast<Char>(digits2_i(value)[0]);
+  *out = static_cast<Char>(digits2_i(value)[1]);
+}
+
 // Formats a decimal unsigned integer value writing to out pointing to a buffer
 // of specified size. The caller must ensure that the buffer is large enough.
 template <typename Char, typename UInt>
@@ -1217,12 +1243,19 @@ FMT_CONSTEXPR20 auto do_format_decimal(Char* out, UInt value, int size)
   FMT_ASSERT(size >= count_digits(value), "invalid digit count");
   unsigned n = to_unsigned(size);
   while (value >= 100) {
-    // Integer division is slow so do it for a group of two digits instead
-    // of for every digit. The idea comes from the talk by Alexandrescu
-    // "Three Optimization Tips for C++". See speed-test for a comparison.
     n -= 2;
-    write2digits(out + n, static_cast<unsigned>(value % 100));
-    value /= 100;
+    if (!is_constant_evaluated() && sizeof(UInt) == 4) {
+      auto p = value * static_cast<uint64_t>((1ull << 39) / 100 + 1);
+      write2digits_i(out + n, p >> (39 - 7) & ((1 << 7) - 1));
+      value = static_cast<UInt>(p >> 39) +
+              (static_cast<UInt>(value >= (100u << 25)) << 25);
+    } else {
+      // Integer division is slow so do it for a group of two digits instead
+      // of for every digit. The idea comes from the talk by Alexandrescu
+      // "Three Optimization Tips for C++". See speed-test for a comparison.
+      write2digits(out + n, static_cast<unsigned>(value % 100));
+      value /= 100;
+    }
   }
   if (value >= 10) {
     n -= 2;