[C++] Complete std::numeric_limits<Float16> specialization

Author: HyukjinKwon

cpp/src/arrow/util/float16.h

@@ -185,22 +185,51 @@ static_assert(sizeof(Float16) == sizeof(uint16_t));
 }  // namespace util
 }  // namespace arrow
 
-// TODO: Not complete
 template <>
 class std::numeric_limits<arrow::util::Float16> {
   using T = arrow::util::Float16;
 
  public:
   static constexpr bool is_specialized = true;
   static constexpr bool is_signed = true;
+  static constexpr bool is_integer = false;
+  static constexpr bool is_exact = false;
   static constexpr bool has_infinity = true;
   static constexpr bool has_quiet_NaN = true;
+  static constexpr bool has_signaling_NaN = true;
+  static constexpr std::float_denorm_style has_denorm = std::denorm_present;
+  static constexpr bool has_denorm_loss = false;
+  static constexpr bool is_iec559 = true;
+  static constexpr bool is_bounded = true;
+  static constexpr bool is_modulo = false;
+  static constexpr int radix = 2;
+
+  // Float16 has 10 explicit mantissa bits + 1 implicit bit = 11 bits precision
+  static constexpr int digits = 11;
+  // Number of decimal digits that can be represented: floor(10 * log10(2))
+  static constexpr int digits10 = 3;
+  // Number of decimal digits to fully represent the type: ceil(11 * log10(2) + 1)
+  static constexpr int max_digits10 = 5;
+
+  // Exponent range: bias = 15, min subnormal exponent = -14, min normal = -13
+  static constexpr int min_exponent = -13;
+  static constexpr int min_exponent10 = -4;
+  // Max exponent before infinity: field value 30 -> 30 - 15 + 1 = 16
+  static constexpr int max_exponent = 16;
+  static constexpr int max_exponent10 = 4;
+
+  static constexpr bool traps = false;
+  static constexpr bool tinyness_before = false;
+  static constexpr std::float_round_style round_style = std::round_to_nearest;
 
   static constexpr T min() { return T::FromBits(0b0000010000000000); }
   static constexpr T max() { return T::FromBits(0b0111101111111111); }
   static constexpr T lowest() { return -max(); }
+  static constexpr T epsilon() { return T::FromBits(0b0001010000000000); }      // 2^-10
+  static constexpr T round_error() { return T::FromBits(0b0011100000000000); }  // 0.5
+  static constexpr T denorm_min() { return T::FromBits(0b0000000000000001); }
 
   static constexpr T infinity() { return T::FromBits(0b0111110000000000); }
-
   static constexpr T quiet_NaN() { return T::FromBits(0b0111111111111111); }
+  static constexpr T signaling_NaN() { return T::FromBits(0b0111110000000001); }
 };

cpp/src/arrow/util/float16_test.cc

@@ -372,5 +372,69 @@ TEST(Float16Test, FromBytes) {
   ASSERT_EQ(Float16::FromBigEndian(bytes.data()), Float16::FromBits(0x1cd0));
 }
 
+TEST(Float16Test, NumericLimits) {
+  using F16 = std::numeric_limits<Float16>;
+  using F32 = std::numeric_limits<float>;
+
+  // Boolean traits - should match standard float
+  ASSERT_EQ(F16::is_specialized, F32::is_specialized);
+  ASSERT_EQ(F16::is_signed, F32::is_signed);
+  ASSERT_EQ(F16::is_integer, F32::is_integer);
+  ASSERT_EQ(F16::is_exact, F32::is_exact);
+  ASSERT_EQ(F16::has_infinity, F32::has_infinity);
+  ASSERT_EQ(F16::has_quiet_NaN, F32::has_quiet_NaN);
+  ASSERT_EQ(F16::has_signaling_NaN, F32::has_signaling_NaN);
+  ASSERT_EQ(F16::has_denorm, F32::has_denorm);
+  ASSERT_EQ(F16::has_denorm_loss, F32::has_denorm_loss);
+  ASSERT_EQ(F16::is_iec559, F32::is_iec559);
+  ASSERT_EQ(F16::is_bounded, F32::is_bounded);
+  ASSERT_EQ(F16::is_modulo, F32::is_modulo);
+  ASSERT_EQ(F16::radix, F32::radix);
+
+  // Check if IEEE 754 is implemented correctly.
+  // Precision and exponent range
+  ASSERT_EQ(F16::digits, 11);
+  ASSERT_EQ(F16::digits10, 3);
+  ASSERT_EQ(F16::max_digits10, 5);
+  ASSERT_EQ(F16::min_exponent, -13);
+  ASSERT_EQ(F16::max_exponent, 16);
+  ASSERT_EQ(F16::min_exponent10, -4);
+  ASSERT_EQ(F16::max_exponent10, 4);
+
+  // Special values
+  ASSERT_FLOAT_EQ(F16::max().ToFloat(), 65504.0f);           // Largest finite value
+  ASSERT_EQ(F16::lowest(), -F16::max());                     // Most negative = -max
+  ASSERT_FLOAT_EQ(F16::epsilon().ToFloat(), 0.0009765625f);  // 2^-10
+  ASSERT_FLOAT_EQ(F16::round_error().ToFloat(), 0.5f);       // Round-to-nearest
+  ASSERT_TRUE(F16::infinity().is_infinity());
+  ASSERT_FALSE(F16::infinity().signbit());
+  ASSERT_TRUE((-F16::infinity()).is_infinity());
+  ASSERT_TRUE((-F16::infinity()).signbit());
+  ASSERT_TRUE(F16::quiet_NaN().is_nan());
+  ASSERT_TRUE(F16::signaling_NaN().is_nan());
+
+  // min() is smallest positive normal, denorm_min() is smallest subnormal
+  ASSERT_TRUE(F16::min().is_finite());
+  ASSERT_FALSE(F16::min().signbit());
+  ASSERT_TRUE(F16::denorm_min().is_finite());
+  ASSERT_FALSE(F16::denorm_min().signbit());
+
+  // Verify special values semantics
+  ASSERT_TRUE(F16::infinity().is_infinity());
+  ASSERT_TRUE((-F16::infinity()).is_infinity());
+  ASSERT_TRUE(F16::min() > Float16::FromBits(0));
+  ASSERT_TRUE(F16::denorm_min() > Float16::FromBits(0));
+  ASSERT_TRUE(F16::denorm_min() < F16::min());
+
+  // Verify epsilon: 1 + epsilon != 1
+  auto one = Float16(1.0f);
+  auto one_plus_epsilon = Float16(one.ToFloat() + F16::epsilon().ToFloat());
+  ASSERT_NE(one, one_plus_epsilon);
+
+  // Verify round_error is 0.5
+  ASSERT_FLOAT_EQ(F16::round_error().ToFloat(), 0.5f);
+  ASSERT_FLOAT_EQ(F32::round_error(), 0.5f);
+}
+
 }  // namespace
 }  // namespace arrow::util