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GH-48123 [C++][Float16] Reimplement arrow::WithinUlp and Enable it for float16 #48224

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GH-48123 [C++][Float16] Reimplement arrow::WithinUlp and Enable it for float16 #48224

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bfa359c
re-implement WithinUlp and Enable float16
andishgar Nov 22, 2025
f91d298
apply pitrou suggestion
andishgar Dec 4, 2025
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88 changes: 82 additions & 6 deletions cpp/src/arrow/testing/gtest_util_test.cc
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Original file line number Diff line number Diff line change
Expand Up @@ -16,6 +16,9 @@
// under the License.

#include <cmath>
#include <memory>
#include <type_traits>
#include <vector>

#include <gtest/gtest-spi.h>
#include <gtest/gtest.h>
Expand All @@ -32,8 +35,9 @@
#include "arrow/type.h"
#include "arrow/type_traits.h"
#include "arrow/util/checked_cast.h"
#include "arrow/util/float16.h"

namespace arrow {
namespace arrow::util {

// Test basic cases for contains NaN.
class TestAssertContainsNaN : public ::testing::Test {};
Expand Down Expand Up @@ -198,8 +202,15 @@ void CheckWithinUlp(Float x, Float y, int n_ulp) {
CheckWithinUlpSingle(-y, -x, n_ulp);

for (int exp : {1, -1, 10, -10}) {
Float x_scaled = std::ldexp(x, exp);
Float y_scaled = std::ldexp(y, exp);
Float x_scaled(0);
Float y_scaled(0);
if constexpr (std::is_same_v<Float, Float16>) {
x_scaled = Float16(std::ldexp(x.ToFloat(), exp));
y_scaled = Float16(std::ldexp(y.ToFloat(), exp));
} else {
x_scaled = std::ldexp(x, exp);
y_scaled = std::ldexp(y, exp);
}
CheckWithinUlpSingle(x_scaled, y_scaled, n_ulp);
CheckWithinUlpSingle(y_scaled, x_scaled, n_ulp);
}
Expand All @@ -219,8 +230,15 @@ void CheckNotWithinUlp(Float x, Float y, int n_ulp) {
}

for (int exp : {1, -1, 10, -10}) {
Float x_scaled = std::ldexp(x, exp);
Float y_scaled = std::ldexp(y, exp);
Float x_scaled(0);
Float y_scaled(0);
if constexpr (std::is_same_v<Float, Float16>) {
x_scaled = Float16(std::ldexp(x.ToFloat(), exp));
y_scaled = Float16(std::ldexp(y.ToFloat(), exp));
} else {
x_scaled = std::ldexp(x, exp);
y_scaled = std::ldexp(y, exp);
}
CheckNotWithinUlpSingle(x_scaled, y_scaled, n_ulp);
CheckNotWithinUlpSingle(y_scaled, x_scaled, n_ulp);
}
Expand All @@ -242,6 +260,10 @@ TEST(TestWithinUlp, Double) {
CheckWithinUlp(1.0, 0.9999999999999999, 1);
CheckWithinUlp(1.0, 0.9999999999999988, 11);
CheckNotWithinUlp(1.0, 0.9999999999999988, 10);
CheckWithinUlp(1.0000000000000002, 0.9999999999999999, 2);
CheckNotWithinUlp(1.0000000000000002, 0.9999999999999999, 1);
CheckWithinUlp(0.9999999999999988, 1.0000000000000007, 14);
CheckNotWithinUlp(0.9999999999999988, 1.0000000000000007, 13);

CheckWithinUlp(123.4567, 123.45670000000015, 11);
CheckNotWithinUlp(123.4567, 123.45670000000015, 10);
Expand Down Expand Up @@ -271,6 +293,10 @@ TEST(TestWithinUlp, Float) {
CheckWithinUlp(1.0f, 0.99999994f, 1);
CheckWithinUlp(1.0f, 0.99999934f, 11);
CheckNotWithinUlp(1.0f, 0.99999934f, 10);
CheckWithinUlp(1.0000001f, 0.99999994f, 2);
CheckNotWithinUlp(1.0000001f, 0.99999994f, 1);
CheckWithinUlp(1.0000013f, 0.99999934f, 22);
CheckNotWithinUlp(1.0000013f, 0.99999934f, 21);

CheckWithinUlp(123.456f, 123.456085f, 11);
CheckNotWithinUlp(123.456f, 123.456085f, 10);
Expand All @@ -284,15 +310,65 @@ TEST(TestWithinUlp, Float) {
CheckNotWithinUlp(12.34f, -12.34f, 10);
}

std::vector<Float16> ConvertToFloat16Vector(const std::vector<float>& float_values) {
std::vector<Float16> float16_vector;
float16_vector.reserve(float_values.size());
for (auto& value : float_values) {
float16_vector.emplace_back(value);
}
return float16_vector;
}

TEST(TestWithinUlp, Float16) {
for (Float16 f : ConvertToFloat16Vector({0.0f, 1e-8f, 1.0f, 123.456f})) {
CheckWithinUlp(f, f, 0);
CheckWithinUlp(f, f, 1);
CheckWithinUlp(f, f, 42);
}
CheckWithinUlp(Float16(-0.0f), Float16(0.0f), 1);
CheckWithinUlp(Float16(1.0f), Float16(1.00097656f), 1);
CheckWithinUlp(Float16(1.0f), Float16(1.01074219f), 11);
CheckNotWithinUlp(Float16(1.0f), Float16(1.00097656f), 0);
CheckNotWithinUlp(Float16(1.0f), Float16(1.01074219f), 10);
// left and right have a different exponent but are still very close
CheckWithinUlp(Float16(1.0f), Float16(0.999511719f), 1);
CheckWithinUlp(Float16(1.0f), Float16(0.994628906f), 11);
CheckNotWithinUlp(Float16(1.0f), Float16(0.994628906f), 10);
CheckWithinUlp(Float16(1.00097656), Float16(0.999511719f), 2);
CheckNotWithinUlp(Float16(1.00097656), Float16(0.999511719f), 1);
CheckWithinUlp(Float16(1.01074219f), Float16(0.994628906f), 22);
CheckNotWithinUlp(Float16(1.01074219f), Float16(0.994628906f), 21);

CheckWithinUlp(Float16(123.456f), Float16(124.143501f), 11);
// The assertion below does not work because ldexp(Float16(124.143501f), 10)
// results in inf in Float16.
// CheckNotWithinUlp(Float16(123.456f), Float16(124.143501f), 10);

CheckWithinUlp(std::numeric_limits<Float16>::infinity(),
std::numeric_limits<Float16>::infinity(), 10);
CheckWithinUlp(-std::numeric_limits<Float16>::infinity(),
-std::numeric_limits<Float16>::infinity(), 10);
CheckWithinUlp(std::numeric_limits<Float16>::quiet_NaN(),
std::numeric_limits<Float16>::quiet_NaN(), 10);
CheckNotWithinUlp(std::numeric_limits<Float16>::infinity(),
-std::numeric_limits<Float16>::infinity(), 10);
CheckNotWithinUlp(Float16(12.34f), -std::numeric_limits<Float16>::infinity(), 10);
CheckNotWithinUlp(Float16(12.34f), std::numeric_limits<Float16>::quiet_NaN(), 10);
CheckNotWithinUlp(Float16(12.34f), Float16(-12.34f), 10);
}

TEST(AssertTestWithinUlp, Basics) {
AssertWithinUlp(123.4567, 123.45670000000015, 11);
AssertWithinUlp(123.456f, 123.456085f, 11);
AssertWithinUlp(Float16(123.456f), Float16(124.143501f), 11);
#ifndef _WIN32
// GH-47442
EXPECT_FATAL_FAILURE(AssertWithinUlp(123.4567, 123.45670000000015, 10),
"not within 10 ulps");
EXPECT_FATAL_FAILURE(AssertWithinUlp(123.456f, 123.456085f, 10), "not within 10 ulps");
EXPECT_FATAL_FAILURE(AssertWithinUlp(Float16(123.456f), Float16(124.143501f), 10),
"not within 10 ulps");
#endif
}

} // namespace arrow
} // namespace arrow::util
99 changes: 74 additions & 25 deletions cpp/src/arrow/testing/math.cc
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Original file line number Diff line number Diff line change
Expand Up @@ -17,53 +17,94 @@

#include "arrow/testing/math.h"

#include <algorithm>
#include <cmath>
#include <limits>
#include <type_traits>

#include <gtest/gtest.h>

#include "arrow/util/float16.h"
#include "arrow/util/logging_internal.h"
#include "arrow/util/ubsan.h"

namespace arrow {
namespace {

template <typename Float>
bool WithinUlpOneWay(Float left, Float right, int n_ulps) {
// The delta between 1.0 and the FP value immediately before it.
// We're using this value because `frexp` returns a mantissa between 0.5 and 1.0.
static const Float kOneUlp = Float(1.0) - std::nextafter(Float(1.0), Float(0.0));
struct FloatToUInt;

DCHECK_GE(n_ulps, 1);
template <>
struct FloatToUInt<double> {
using Type = uint64_t;
};

if (left == 0) {
return left == right;
}
if (left < 0) {
left = -left;
right = -right;
template <>
struct FloatToUInt<float> {
using Type = uint32_t;
};

template <>
struct FloatToUInt<util::Float16> {
using Type = uint16_t;
};

template <typename Float>
struct UlpDistanceUtil {
public:
using UIntType = typename FloatToUInt<Float>::Type;
static constexpr UIntType kNumberOfBits = sizeof(Float) * 8;
static constexpr UIntType kSignMask = static_cast<UIntType>(1) << (kNumberOfBits - 1);

// This implementation is inspired by:
// https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
static UIntType UlpDistance(Float left, Float right) {
auto unsigned_left = util::SafeCopy<UIntType>(left);
auto unsigned_right = util::SafeCopy<UIntType>(right);
auto biased_left = ConvertSignAndMagnitudeToBiased(unsigned_left);
auto biased_right = ConvertSignAndMagnitudeToBiased(unsigned_right);
if (biased_left > biased_right) {
std::swap(biased_left, biased_right);
}
return biased_right - biased_left;
}

int left_exp;
Float left_mant = std::frexp(left, &left_exp);
Float delta = static_cast<Float>(n_ulps) * kOneUlp;
Float lower_bound = std::ldexp(left_mant - delta, left_exp);
Float upper_bound = std::ldexp(left_mant + delta, left_exp);
return right >= lower_bound && right <= upper_bound;
}
private:
// Source reference (GoogleTest):
// https://github.com/google/googletest/blob/1b96fa13f549387b7549cc89e1a785cf143a1a50/googletest/include/gtest/internal/gtest-internal.h#L345-L368
static UIntType ConvertSignAndMagnitudeToBiased(UIntType value) {
if (value & kSignMask) {
return ~value + 1;
} else {
return value | kSignMask;
}
}
};

template <typename Float>
bool WithinUlpGeneric(Float left, Float right, int n_ulps) {
if (std::isnan(left) || std::isnan(right)) {
return std::isnan(left) == std::isnan(right);
}
if (!std::isfinite(left) || !std::isfinite(right)) {
return left == right;
if constexpr (std::is_same_v<Float, util::Float16>) {
if (left.is_nan() || right.is_nan()) {
return left.is_nan() && right.is_nan();
} else if (left.is_infinity() || right.is_infinity()) {
return left == right;
}
} else {
if (std::isnan(left) || std::isnan(right)) {
return std::isnan(left) == std::isnan(right);
}
if (!std::isfinite(left) || !std::isfinite(right)) {
return left == right;
}
}

if (n_ulps == 0) {
return left == right;
}
return (std::abs(left) <= std::abs(right)) ? WithinUlpOneWay(left, right, n_ulps)
: WithinUlpOneWay(right, left, n_ulps);

DCHECK_GE(n_ulps, 1);
return UlpDistanceUtil<Float>::UlpDistance(left, right) <=
static_cast<uint64_t>(n_ulps);
}

template <typename Float>
Expand All @@ -75,6 +116,10 @@ void AssertWithinUlpGeneric(Float left, Float right, int n_ulps) {

} // namespace

bool WithinUlp(util::Float16 left, util::Float16 right, int n_ulps) {
return WithinUlpGeneric(left, right, n_ulps);
}

bool WithinUlp(float left, float right, int n_ulps) {
return WithinUlpGeneric(left, right, n_ulps);
}
Expand All @@ -83,6 +128,10 @@ bool WithinUlp(double left, double right, int n_ulps) {
return WithinUlpGeneric(left, right, n_ulps);
}

void AssertWithinUlp(util::Float16 left, util::Float16 right, int n_ulps) {
AssertWithinUlpGeneric(left, right, n_ulps);
}

void AssertWithinUlp(float left, float right, int n_ulps) {
AssertWithinUlpGeneric(left, right, n_ulps);
}
Expand Down
5 changes: 5 additions & 0 deletions cpp/src/arrow/testing/math.h
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Original file line number Diff line number Diff line change
Expand Up @@ -18,14 +18,19 @@
#pragma once

#include "arrow/testing/visibility.h"
#include "arrow/type_fwd.h"

namespace arrow {

ARROW_TESTING_EXPORT
bool WithinUlp(util::Float16 left, util::Float16 right, int n_ulps);
ARROW_TESTING_EXPORT
bool WithinUlp(float left, float right, int n_ulps);
ARROW_TESTING_EXPORT
bool WithinUlp(double left, double right, int n_ulps);

ARROW_TESTING_EXPORT
void AssertWithinUlp(util::Float16 left, util::Float16 right, int n_ulps);
ARROW_TESTING_EXPORT
void AssertWithinUlp(float left, float right, int n_ulps);
ARROW_TESTING_EXPORT
Expand Down
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