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Add bit_cast for half/bfloat to/from uint16_t, fix TensorRandom

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The existing `TensorRandom.h` implementation makes the assumption that
`half` (`bfloat16`) has a `uint16_t` member `x` (`value`), which is not
always true. This currently fails on arm64, where `x` has type `__fp16`.
Added `bit_cast` specializations to allow casting to/from `uint16_t`
for both `half` and `bfloat16`.  Also added tests in
`half_float`, `bfloat16_float`, and `cxx11_tensor_random` to catch
these errors in the future.
This commit is contained in:
Antonio Sanchez
2020-11-17 15:32:44 -08:00
committed by Antonio Sánchez
parent 41d5d5334b
commit 17268b155d
6 changed files with 196 additions and 150 deletions
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101
test/bfloat16_float.cpp
View File

@@ -13,6 +13,9 @@
#include <Eigen/src/Core/arch/Default/BFloat16.h>
#define VERIFY_BFLOAT16_BITS_EQUAL(h, bits) \
VERIFY_IS_EQUAL((numext::bit_cast<numext::uint16_t>(h)), (static_cast<numext::uint16_t>(bits)))
// Make sure it's possible to forward declare Eigen::bfloat16
namespace Eigen {
struct bfloat16;
@@ -58,31 +61,45 @@ void test_conversion()
{
using Eigen::bfloat16_impl::__bfloat16_raw;
// Round-trip casts
VERIFY_IS_EQUAL(
numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(1.0f))),
bfloat16(1.0f));
VERIFY_IS_EQUAL(
numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(0.5f))),
bfloat16(0.5f));
VERIFY_IS_EQUAL(
numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(-0.33333f))),
bfloat16(-0.33333f));
VERIFY_IS_EQUAL(
numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(0.0f))),
bfloat16(0.0f));
// Conversion from float.
VERIFY_IS_EQUAL(bfloat16(1.0f).value, 0x3f80);
VERIFY_IS_EQUAL(bfloat16(0.5f).value, 0x3f00);
VERIFY_IS_EQUAL(bfloat16(0.33333f).value, 0x3eab);
VERIFY_IS_EQUAL(bfloat16(3.38e38f).value, 0x7f7e);
VERIFY_IS_EQUAL(bfloat16(3.40e38f).value, 0x7f80); // Becomes infinity.
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(1.0f), 0x3f80);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f), 0x3f00);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.33333f), 0x3eab);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3.38e38f), 0x7f7e);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3.40e38f), 0x7f80); // Becomes infinity.
// Verify round-to-nearest-even behavior.
float val1 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c00)));
float val2 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c01)));
float val3 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c02)));
VERIFY_IS_EQUAL(bfloat16(0.5f * (val1 + val2)).value, 0x3c00);
VERIFY_IS_EQUAL(bfloat16(0.5f * (val2 + val3)).value, 0x3c02);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f * (val1 + val2)), 0x3c00);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f * (val2 + val3)), 0x3c02);
// Conversion from int.
VERIFY_IS_EQUAL(bfloat16(-1).value, 0xbf80);
VERIFY_IS_EQUAL(bfloat16(0).value, 0x0000);
VERIFY_IS_EQUAL(bfloat16(1).value, 0x3f80);
VERIFY_IS_EQUAL(bfloat16(2).value, 0x4000);
VERIFY_IS_EQUAL(bfloat16(3).value, 0x4040);
VERIFY_IS_EQUAL(bfloat16(12).value, 0x4140);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(-1), 0xbf80);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0), 0x0000);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(1), 0x3f80);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(2), 0x4000);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3), 0x4040);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(12), 0x4140);
// Conversion from bool.
VERIFY_IS_EQUAL(bfloat16(false).value, 0x0000);
VERIFY_IS_EQUAL(bfloat16(true).value, 0x3f80);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(false), 0x0000);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(true), 0x3f80);
// Conversion to bool
VERIFY_IS_EQUAL(static_cast<bool>(bfloat16(3)), true);
@@ -102,8 +119,8 @@ void test_conversion()
VERIFY_IS_EQUAL(bfloat16(0.0f), bfloat16(0.0f));
VERIFY_IS_EQUAL(bfloat16(-0.0f), bfloat16(0.0f));
VERIFY_IS_EQUAL(bfloat16(-0.0f), bfloat16(-0.0f));
VERIFY_IS_EQUAL(bfloat16(0.0f).value, 0x0000);
VERIFY_IS_EQUAL(bfloat16(-0.0f).value, 0x8000);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.0f), 0x0000);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(-0.0f), 0x8000);
// Flush denormals to zero
for (float denorm = -std::numeric_limits<float>::denorm_min();
@@ -117,16 +134,16 @@ void test_conversion()
VERIFY_IS_EQUAL(bfloat16(denorm), false);
if (std::signbit(denorm)) {
VERIFY_IS_EQUAL(bf_trunc.value, 0x8000);
VERIFY_BFLOAT16_BITS_EQUAL(bf_trunc, 0x8000);
} else {
VERIFY_IS_EQUAL(bf_trunc.value, 0x0000);
VERIFY_BFLOAT16_BITS_EQUAL(bf_trunc, 0x0000);
}
bfloat16 bf_round = Eigen::bfloat16_impl::float_to_bfloat16_rtne<false>(denorm);
VERIFY_IS_EQUAL(static_cast<float>(bf_round), 0.0f);
if (std::signbit(denorm)) {
VERIFY_IS_EQUAL(bf_round.value, 0x8000);
VERIFY_BFLOAT16_BITS_EQUAL(bf_round, 0x8000);
} else {
VERIFY_IS_EQUAL(bf_round.value, 0x0000);
VERIFY_BFLOAT16_BITS_EQUAL(bf_round, 0x0000);
}
}
@@ -231,33 +248,35 @@ void test_conversion()
VERIFY((numext::isinf)(bfloat16(__bfloat16_raw(0x7f80))));
VERIFY((numext::isnan)(bfloat16(__bfloat16_raw(0x7fc0))));
VERIFY_IS_EQUAL(bfloat16(BinaryToFloat(0x0, 0xff, 0x40, 0x0)).value, 0x7fc0);
VERIFY_IS_EQUAL(bfloat16(BinaryToFloat(0x1, 0xff, 0x40, 0x0)).value, 0xffc0);
VERIFY_IS_EQUAL(Eigen::bfloat16_impl::truncate_to_bfloat16(
BinaryToFloat(0x0, 0xff, 0x40, 0x0))
.value,
0x7fc0);
VERIFY_IS_EQUAL(Eigen::bfloat16_impl::truncate_to_bfloat16(
BinaryToFloat(0x1, 0xff, 0x40, 0x0))
.value,
0xffc0);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(BinaryToFloat(0x0, 0xff, 0x40, 0x0)), 0x7fc0);
VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(BinaryToFloat(0x1, 0xff, 0x40, 0x0)), 0xffc0);
VERIFY_BFLOAT16_BITS_EQUAL(Eigen::bfloat16_impl::truncate_to_bfloat16(
BinaryToFloat(0x0, 0xff, 0x40, 0x0)),
0x7fc0);
VERIFY_BFLOAT16_BITS_EQUAL(Eigen::bfloat16_impl::truncate_to_bfloat16(
BinaryToFloat(0x1, 0xff, 0x40, 0x0)),
0xffc0);
}
void test_numtraits()
{
std::cout << "epsilon = " << NumTraits<bfloat16>::epsilon() << " (0x" << std::hex << NumTraits<bfloat16>::epsilon().value << ")" << std::endl;
std::cout << "highest = " << NumTraits<bfloat16>::highest() << " (0x" << std::hex << NumTraits<bfloat16>::highest().value << ")" << std::endl;
std::cout << "lowest = " << NumTraits<bfloat16>::lowest() << " (0x" << std::hex << NumTraits<bfloat16>::lowest().value << ")" << std::endl;
std::cout << "min = " << (std::numeric_limits<bfloat16>::min)() << " (0x" << std::hex << (std::numeric_limits<bfloat16>::min)().value << ")" << std::endl;
std::cout << "denorm min = " << (std::numeric_limits<bfloat16>::denorm_min)() << " (0x" << std::hex << (std::numeric_limits<bfloat16>::denorm_min)().value << ")" << std::endl;
std::cout << "infinity = " << NumTraits<bfloat16>::infinity() << " (0x" << std::hex << NumTraits<bfloat16>::infinity().value << ")" << std::endl;
std::cout << "quiet nan = " << NumTraits<bfloat16>::quiet_NaN() << " (0x" << std::hex << NumTraits<bfloat16>::quiet_NaN().value << ")" << std::endl;
std::cout << "signaling nan = " << std::numeric_limits<bfloat16>::signaling_NaN() << " (0x" << std::hex << std::numeric_limits<bfloat16>::signaling_NaN().value << ")" << std::endl;
std::cout << "epsilon = " << NumTraits<bfloat16>::epsilon() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::epsilon()) << ")" << std::endl;
std::cout << "highest = " << NumTraits<bfloat16>::highest() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::highest()) << ")" << std::endl;
std::cout << "lowest = " << NumTraits<bfloat16>::lowest() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::lowest()) << ")" << std::endl;
std::cout << "min = " << (std::numeric_limits<bfloat16>::min)() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>((std::numeric_limits<bfloat16>::min)()) << ")" << std::endl;
std::cout << "denorm min = " << (std::numeric_limits<bfloat16>::denorm_min)() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>((std::numeric_limits<bfloat16>::denorm_min)()) << ")" << std::endl;
std::cout << "infinity = " << NumTraits<bfloat16>::infinity() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::infinity()) << ")" << std::endl;
std::cout << "quiet nan = " << NumTraits<bfloat16>::quiet_NaN() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::quiet_NaN()) << ")" << std::endl;
std::cout << "signaling nan = " << std::numeric_limits<bfloat16>::signaling_NaN() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::signaling_NaN()) << ")" << std::endl;
VERIFY(NumTraits<bfloat16>::IsSigned);
VERIFY_IS_EQUAL( std::numeric_limits<bfloat16>::infinity().value, bfloat16(std::numeric_limits<float>::infinity()).value );
VERIFY_IS_EQUAL( std::numeric_limits<bfloat16>::quiet_NaN().value, bfloat16(std::numeric_limits<float>::quiet_NaN()).value );
VERIFY_IS_EQUAL(
numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::infinity()),
numext::bit_cast<numext::uint16_t>(bfloat16(std::numeric_limits<float>::infinity())) );
VERIFY_IS_EQUAL(
numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::quiet_NaN()),
numext::bit_cast<numext::uint16_t>(bfloat16(std::numeric_limits<float>::quiet_NaN())) );
VERIFY( (std::numeric_limits<bfloat16>::min)() > bfloat16(0.f) );
VERIFY( (std::numeric_limits<bfloat16>::denorm_min)() > bfloat16(0.f) );
VERIFY_IS_EQUAL( (std::numeric_limits<bfloat16>::denorm_min)()/bfloat16(2), bfloat16(0.f) );

124
test/half_float.cpp
View File

@@ -11,6 +11,9 @@
#include <Eigen/src/Core/arch/Default/Half.h>
#define VERIFY_HALF_BITS_EQUAL(h, bits) \
VERIFY_IS_EQUAL((numext::bit_cast<numext::uint16_t>(h)), (static_cast<numext::uint16_t>(bits)))
// Make sure it's possible to forward declare Eigen::half
namespace Eigen {
struct half;
@@ -22,75 +25,51 @@ void test_conversion()
{
using Eigen::half_impl::__half_raw;
// We don't use a uint16_t raw member x if the platform has native Arm __fp16
// support
#if !defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
// Round-trip bit-cast with uint16.
VERIFY_IS_EQUAL(
numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(1.0f))),
half(1.0f));
VERIFY_IS_EQUAL(
numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(0.5f))),
half(0.5f));
VERIFY_IS_EQUAL(
numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(-0.33333f))),
half(-0.33333f));
VERIFY_IS_EQUAL(
numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(0.0f))),
half(0.0f));
// Conversion from float.
VERIFY_IS_EQUAL(half(1.0f).x, 0x3c00);
VERIFY_IS_EQUAL(half(0.5f).x, 0x3800);
VERIFY_IS_EQUAL(half(0.33333f).x, 0x3555);
VERIFY_IS_EQUAL(half(0.0f).x, 0x0000);
VERIFY_IS_EQUAL(half(-0.0f).x, 0x8000);
VERIFY_IS_EQUAL(half(65504.0f).x, 0x7bff);
VERIFY_IS_EQUAL(half(65536.0f).x, 0x7c00); // Becomes infinity.
VERIFY_HALF_BITS_EQUAL(half(1.0f), 0x3c00);
VERIFY_HALF_BITS_EQUAL(half(0.5f), 0x3800);
VERIFY_HALF_BITS_EQUAL(half(0.33333f), 0x3555);
VERIFY_HALF_BITS_EQUAL(half(0.0f), 0x0000);
VERIFY_HALF_BITS_EQUAL(half(-0.0f), 0x8000);
VERIFY_HALF_BITS_EQUAL(half(65504.0f), 0x7bff);
VERIFY_HALF_BITS_EQUAL(half(65536.0f), 0x7c00); // Becomes infinity.
// Denormals.
VERIFY_IS_EQUAL(half(-5.96046e-08f).x, 0x8001);
VERIFY_IS_EQUAL(half(5.96046e-08f).x, 0x0001);
VERIFY_IS_EQUAL(half(1.19209e-07f).x, 0x0002);
VERIFY_HALF_BITS_EQUAL(half(-5.96046e-08f), 0x8001);
VERIFY_HALF_BITS_EQUAL(half(5.96046e-08f), 0x0001);
VERIFY_HALF_BITS_EQUAL(half(1.19209e-07f), 0x0002);
// Verify round-to-nearest-even behavior.
float val1 = float(half(__half_raw(0x3c00)));
float val2 = float(half(__half_raw(0x3c01)));
float val3 = float(half(__half_raw(0x3c02)));
VERIFY_IS_EQUAL(half(0.5f * (val1 + val2)).x, 0x3c00);
VERIFY_IS_EQUAL(half(0.5f * (val2 + val3)).x, 0x3c02);
VERIFY_HALF_BITS_EQUAL(half(0.5f * (val1 + val2)), 0x3c00);
VERIFY_HALF_BITS_EQUAL(half(0.5f * (val2 + val3)), 0x3c02);
// Conversion from int.
VERIFY_IS_EQUAL(half(-1).x, 0xbc00);
VERIFY_IS_EQUAL(half(0).x, 0x0000);
VERIFY_IS_EQUAL(half(1).x, 0x3c00);
VERIFY_IS_EQUAL(half(2).x, 0x4000);
VERIFY_IS_EQUAL(half(3).x, 0x4200);
VERIFY_HALF_BITS_EQUAL(half(-1), 0xbc00);
VERIFY_HALF_BITS_EQUAL(half(0), 0x0000);
VERIFY_HALF_BITS_EQUAL(half(1), 0x3c00);
VERIFY_HALF_BITS_EQUAL(half(2), 0x4000);
VERIFY_HALF_BITS_EQUAL(half(3), 0x4200);
// Conversion from bool.
VERIFY_IS_EQUAL(half(false).x, 0x0000);
VERIFY_IS_EQUAL(half(true).x, 0x3c00);
#endif
#if defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
// Conversion from float.
VERIFY_IS_EQUAL(half(1.0f).x, __fp16(1.0f));
VERIFY_IS_EQUAL(half(0.5f).x, __fp16(0.5f));
VERIFY_IS_EQUAL(half(0.33333f).x, __fp16(0.33333f));
VERIFY_IS_EQUAL(half(0.0f).x, __fp16(0.0f));
VERIFY_IS_EQUAL(half(-0.0f).x, __fp16(-0.0f));
VERIFY_IS_EQUAL(half(65504.0f).x, __fp16(65504.0f));
VERIFY_IS_EQUAL(half(65536.0f).x, __fp16(65536.0f)); // Becomes infinity.
// Denormals.
VERIFY_IS_EQUAL(half(-5.96046e-08f).x, __fp16(-5.96046e-08f));
VERIFY_IS_EQUAL(half(5.96046e-08f).x, __fp16(5.96046e-08f));
VERIFY_IS_EQUAL(half(1.19209e-07f).x, __fp16(1.19209e-07f));
// Verify round-to-nearest-even behavior.
float val1 = float(half(__half_raw(0x3c00)));
float val2 = float(half(__half_raw(0x3c01)));
float val3 = float(half(__half_raw(0x3c02)));
VERIFY_IS_EQUAL(half(0.5f * (val1 + val2)).x, __fp16(0.5f * (val1 + val2)));
VERIFY_IS_EQUAL(half(0.5f * (val2 + val3)).x, __fp16(0.5f * (val2 + val3)));
// Conversion from int.
VERIFY_IS_EQUAL(half(-1).x, __fp16(-1));
VERIFY_IS_EQUAL(half(0).x, __fp16(0));
VERIFY_IS_EQUAL(half(1).x, __fp16(1));
VERIFY_IS_EQUAL(half(2).x, __fp16(2));
VERIFY_IS_EQUAL(half(3).x, __fp16(3));
// Conversion from bool.
VERIFY_IS_EQUAL(half(false).x, __fp16(false));
VERIFY_IS_EQUAL(half(true).x, __fp16(true));
#endif
VERIFY_HALF_BITS_EQUAL(half(false), 0x0000);
VERIFY_HALF_BITS_EQUAL(half(true), 0x3c00);
// Conversion to float.
VERIFY_IS_EQUAL(float(half(__half_raw(0x0000))), 0.0f);
@@ -143,24 +122,27 @@ void test_conversion()
void test_numtraits()
{
std::cout << "epsilon = " << NumTraits<half>::epsilon() << " (0x" << std::hex << NumTraits<half>::epsilon().x << ")" << std::endl;
std::cout << "highest = " << NumTraits<half>::highest() << " (0x" << std::hex << NumTraits<half>::highest().x << ")" << std::endl;
std::cout << "lowest = " << NumTraits<half>::lowest() << " (0x" << std::hex << NumTraits<half>::lowest().x << ")" << std::endl;
std::cout << "min = " << (std::numeric_limits<half>::min)() << " (0x" << std::hex << half((std::numeric_limits<half>::min)()).x << ")" << std::endl;
std::cout << "denorm min = " << (std::numeric_limits<half>::denorm_min)() << " (0x" << std::hex << half((std::numeric_limits<half>::denorm_min)()).x << ")" << std::endl;
std::cout << "infinity = " << NumTraits<half>::infinity() << " (0x" << std::hex << NumTraits<half>::infinity().x << ")" << std::endl;
std::cout << "quiet nan = " << NumTraits<half>::quiet_NaN() << " (0x" << std::hex << NumTraits<half>::quiet_NaN().x << ")" << std::endl;
std::cout << "signaling nan = " << std::numeric_limits<half>::signaling_NaN() << " (0x" << std::hex << std::numeric_limits<half>::signaling_NaN().x << ")" << std::endl;
std::cout << "epsilon = " << NumTraits<half>::epsilon() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::epsilon()) << ")" << std::endl;
std::cout << "highest = " << NumTraits<half>::highest() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::highest()) << ")" << std::endl;
std::cout << "lowest = " << NumTraits<half>::lowest() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::lowest()) << ")" << std::endl;
std::cout << "min = " << (std::numeric_limits<half>::min)() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(half((std::numeric_limits<half>::min)())) << ")" << std::endl;
std::cout << "denorm min = " << (std::numeric_limits<half>::denorm_min)() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(half((std::numeric_limits<half>::denorm_min)())) << ")" << std::endl;
std::cout << "infinity = " << NumTraits<half>::infinity() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::infinity()) << ")" << std::endl;
std::cout << "quiet nan = " << NumTraits<half>::quiet_NaN() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::quiet_NaN()) << ")" << std::endl;
std::cout << "signaling nan = " << std::numeric_limits<half>::signaling_NaN() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::signaling_NaN()) << ")" << std::endl;
VERIFY(NumTraits<half>::IsSigned);
VERIFY_IS_EQUAL( std::numeric_limits<half>::infinity().x, half(std::numeric_limits<float>::infinity()).x );
VERIFY_IS_EQUAL(
numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::infinity()),
numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::infinity())) );
VERIFY_IS_EQUAL(
numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::quiet_NaN()),
numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::quiet_NaN())) );
VERIFY_IS_EQUAL(
numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::signaling_NaN()),
numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::signaling_NaN())) );
// If we have a native fp16 types this becomes a nan == nan comparision so we have to disable it
#if !defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
VERIFY_IS_EQUAL( std::numeric_limits<half>::quiet_NaN().x, half(std::numeric_limits<float>::quiet_NaN()).x );
VERIFY_IS_EQUAL( std::numeric_limits<half>::signaling_NaN().x, half(std::numeric_limits<float>::signaling_NaN()).x );
#endif
VERIFY( (std::numeric_limits<half>::min)() > half(0.f) );
VERIFY( (std::numeric_limits<half>::denorm_min)() > half(0.f) );
VERIFY( (std::numeric_limits<half>::min)()/half(2) > half(0.f) );