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GH-49123: [C++] Complete std::numeric_limits<Float16> specialization #49124

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GH-49123: [C++] Complete std::numeric_limits<Float16> specialization #49124

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33 changes: 31 additions & 2 deletions cpp/src/arrow/util/float16.h
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Original file line number Diff line number Diff line change
Expand Up @@ -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;
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@pitrou pitrou Feb 4, 2026

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This seems to be deprecated in C++23, so perhaps we shouldn't bother?

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); }
};
64 changes: 64 additions & 0 deletions cpp/src/arrow/util/float16_test.cc
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Expand Up @@ -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
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@pitrou pitrou Feb 4, 2026

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I wonder if we can also add this:

Suggested change
ASSERT_FLOAT_EQ(F16::max().ToFloat(), 65504.0f); // Largest finite value
ASSERT_FLOAT_EQ(F16::max().ToFloat(), 65504.0f); // Largest finite value
ASSERT_TRUE(Float16::FromBits(F16::max().bits() + 1U).is_infinity());

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());
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@pitrou pitrou Feb 4, 2026

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Perhaps also verify that denorm_min / 2 == 0? Am I assuming right?


// Verify epsilon: 1 + epsilon != 1
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@pitrou pitrou Feb 4, 2026

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We may also verify that 1 + (epsilon / 2) == 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
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