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// clang-format off
#include <c10/util/BFloat16.h>
#include <c10/util/BFloat16-math.h>
#include <c10/util/irange.h>
// clang-format on
#include <gtest/gtest.h>
namespace {
float float_from_bytes(uint32_t sign, uint32_t exponent, uint32_t fraction) {
// NOLINTNEXTLINE(cppcoreguidelines-init-variables)
uint32_t bytes;
bytes = 0;
bytes |= sign;
bytes <<= 8;
bytes |= exponent;
bytes <<= 23;
bytes |= fraction;
// NOLINTNEXTLINE(cppcoreguidelines-init-variables)
float res;
std::memcpy(&res, &bytes, sizeof(res));
return res;
}
TEST(BFloat16Conversion, FloatToBFloat16AndBack) {
// NOLINTNEXTLINE(cppcoreguidelines-avoid-c-arrays,cppcoreguidelines-avoid-magic-numbers,modernize-avoid-c-arrays)
float in[100];
for (const auto i : c10::irange(100)) {
// NOLINTNEXTLINE(bugprone-narrowing-conversions,cppcoreguidelines-narrowing-conversions,cppcoreguidelines-avoid-magic-numbers)
in[i] = i + 1.25;
}
// NOLINTNEXTLINE(cppcoreguidelines-avoid-c-arrays,cppcoreguidelines-avoid-magic-numbers,modernize-avoid-c-arrays)
c10::BFloat16 bfloats[100];
// NOLINTNEXTLINE(cppcoreguidelines-avoid-c-arrays,cppcoreguidelines-avoid-magic-numbers,modernize-avoid-c-arrays)
float out[100];
for (const auto i : c10::irange(100)) {
bfloats[i].x = c10::detail::bits_from_f32(in[i]);
out[i] = c10::detail::f32_from_bits(bfloats[i].x);
// The relative error should be less than 1/(2^7) since BFloat16
// has 7 bits mantissa.
EXPECT_LE(fabs(out[i] - in[i]) / in[i], 1.0 / 128);
}
}
TEST(BFloat16Conversion, FloatToBFloat16RNEAndBack) {
// NOLINTNEXTLINE(cppcoreguidelines-avoid-c-arrays,cppcoreguidelines-avoid-magic-numbers,modernize-avoid-c-arrays)
float in[100];
for (const auto i : c10::irange(100)) {
// NOLINTNEXTLINE(bugprone-narrowing-conversions,cppcoreguidelines-narrowing-conversions,cppcoreguidelines-avoid-magic-numbers)
in[i] = i + 1.25;
}
// NOLINTNEXTLINE(cppcoreguidelines-avoid-c-arrays,cppcoreguidelines-avoid-magic-numbers,modernize-avoid-c-arrays)
c10::BFloat16 bfloats[100];
// NOLINTNEXTLINE(cppcoreguidelines-avoid-c-arrays,cppcoreguidelines-avoid-magic-numbers,modernize-avoid-c-arrays)
float out[100];
for (const auto i : c10::irange(100)) {
bfloats[i].x = c10::detail::round_to_nearest_even(in[i]);
out[i] = c10::detail::f32_from_bits(bfloats[i].x);
// The relative error should be less than 1/(2^7) since BFloat16
// has 7 bits mantissa.
EXPECT_LE(fabs(out[i] - in[i]) / in[i], 1.0 / 128);
}
}
TEST(BFloat16Conversion, NaN) {
float inNaN = float_from_bytes(0, 0xFF, 0x7FFFFF);
EXPECT_TRUE(std::isnan(inNaN));
c10::BFloat16 a = c10::BFloat16(inNaN);
float out = c10::detail::f32_from_bits(a.x);
EXPECT_TRUE(std::isnan(out));
}
TEST(BFloat16Conversion, Inf) {
float inInf = float_from_bytes(0, 0xFF, 0);
EXPECT_TRUE(std::isinf(inInf));
c10::BFloat16 a = c10::BFloat16(inInf);
float out = c10::detail::f32_from_bits(a.x);
EXPECT_TRUE(std::isinf(out));
}
TEST(BFloat16Conversion, SmallestDenormal) {
float in = std::numeric_limits<float>::denorm_min(); // The smallest non-zero
// subnormal number
c10::BFloat16 a = c10::BFloat16(in);
float out = c10::detail::f32_from_bits(a.x);
EXPECT_FLOAT_EQ(in, out);
}
TEST(BFloat16Math, Addition) {
// This test verifies that if only first 7 bits of float's mantissa are
// changed after addition, we should have no loss in precision.
// input bits
// S | Exponent | Mantissa
// 0 | 10000000 | 10010000000000000000000 = 3.125
float input = float_from_bytes(0, 0, 0x40480000);
// expected bits
// S | Exponent | Mantissa
// 0 | 10000001 | 10010000000000000000000 = 6.25
float expected = float_from_bytes(0, 0, 0x40c80000);
// NOLINTNEXTLINE(cppcoreguidelines-pro-type-member-init)
c10::BFloat16 b;
b.x = c10::detail::bits_from_f32(input);
b = b + b;
float res = c10::detail::f32_from_bits(b.x);
EXPECT_EQ(res, expected);
}
TEST(BFloat16Math, Subtraction) {
// This test verifies that if only first 7 bits of float's mantissa are
// changed after subtraction, we should have no loss in precision.
// input bits
// S | Exponent | Mantissa
// 0 | 10000001 | 11101000000000000000000 = 7.625
float input = float_from_bytes(0, 0, 0x40f40000);
// expected bits
// S | Exponent | Mantissa
// 0 | 10000000 | 01010000000000000000000 = 2.625
float expected = float_from_bytes(0, 0, 0x40280000);
// NOLINTNEXTLINE(cppcoreguidelines-pro-type-member-init)
c10::BFloat16 b;
b.x = c10::detail::bits_from_f32(input);
b = b - 5;
float res = c10::detail::f32_from_bits(b.x);
EXPECT_EQ(res, expected);
}
// NOLINTNEXTLINE(cppcoreguidelines-avoid-non-const-global-variables)
TEST(BFloat16Math, NextAfterZero) {
const c10::BFloat16 zero{0};
auto check_nextafter =
[](c10::BFloat16 from, c10::BFloat16 to, c10::BFloat16 expected) {
c10::BFloat16 actual = std::nextafter(from, to);
// Check for bitwise equality!
ASSERT_EQ(actual.x ^ expected.x, uint16_t{0});
};
check_nextafter(zero, zero, /*expected=*/zero);
check_nextafter(zero, -zero, /*expected=*/-zero);
check_nextafter(-zero, zero, /*expected=*/zero);
check_nextafter(-zero, -zero, /*expected=*/-zero);
}
float BinaryToFloat(uint32_t bytes) {
// NOLINTNEXTLINE(cppcoreguidelines-init-variables)
float res;
std::memcpy(&res, &bytes, sizeof(res));
return res;
}
struct BFloat16TestParam {
uint32_t input;
uint16_t rne;
};
class BFloat16Test : public ::testing::Test,
public ::testing::WithParamInterface<BFloat16TestParam> {};
TEST_P(BFloat16Test, BFloat16RNETest) {
float value = BinaryToFloat(GetParam().input);
uint16_t rounded = c10::detail::round_to_nearest_even(value);
EXPECT_EQ(GetParam().rne, rounded);
}
INSTANTIATE_TEST_CASE_P(
BFloat16Test_Instantiation,
BFloat16Test,
::testing::Values(
BFloat16TestParam{0x3F848000, 0x3F84},
BFloat16TestParam{0x3F848010, 0x3F85},
BFloat16TestParam{0x3F850000, 0x3F85},
BFloat16TestParam{0x3F858000, 0x3F86},
BFloat16TestParam{0x3FFF8000, 0x4000}));
} // namespace
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