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hex_float_test.cpp
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// Copyright (c) 2015-2016 The Khronos Group Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include <cfloat>
#include <cmath>
#include <cstdio>
#include <limits>
#include <sstream>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
#include "gmock/gmock.h"
#include "source/util/hex_float.h"
#include "test/unit_spirv.h"
namespace spvtools {
namespace utils {
namespace {
using ::testing::Eq;
// In this file "encode" means converting a number into a string,
// and "decode" means converting a string into a number.
using HexFloatTest =
::testing::TestWithParam<std::pair<FloatProxy<float>, std::string>>;
using DecodeHexFloatTest =
::testing::TestWithParam<std::pair<std::string, FloatProxy<float>>>;
using HexDoubleTest =
::testing::TestWithParam<std::pair<FloatProxy<double>, std::string>>;
using DecodeHexDoubleTest =
::testing::TestWithParam<std::pair<std::string, FloatProxy<double>>>;
using RoundTripFloatTest = ::testing::TestWithParam<float>;
using RoundTripDoubleTest = ::testing::TestWithParam<double>;
// Hex-encodes a float value.
template <typename T>
std::string EncodeViaHexFloat(const T& value) {
std::stringstream ss;
ss << HexFloat<T>(value);
return ss.str();
}
// The following two tests can't be DRY because they take different parameter
// types.
TEST_P(HexFloatTest, EncodeCorrectly) {
EXPECT_THAT(EncodeViaHexFloat(GetParam().first), Eq(GetParam().second));
}
TEST_P(HexDoubleTest, EncodeCorrectly) {
EXPECT_THAT(EncodeViaHexFloat(GetParam().first), Eq(GetParam().second));
}
// Decodes a hex-float string.
template <typename T>
FloatProxy<T> Decode(const std::string& str) {
HexFloat<FloatProxy<T>> decoded(0.f);
EXPECT_TRUE((std::stringstream(str) >> decoded).eof());
return decoded.value();
}
TEST_P(HexFloatTest, DecodeCorrectly) {
EXPECT_THAT(Decode<float>(GetParam().second), Eq(GetParam().first));
}
TEST_P(HexDoubleTest, DecodeCorrectly) {
EXPECT_THAT(Decode<double>(GetParam().second), Eq(GetParam().first));
}
INSTANTIATE_TEST_SUITE_P(
Float32Tests, HexFloatTest,
::testing::ValuesIn(std::vector<std::pair<FloatProxy<float>, std::string>>({
{0.f, "0x0p+0"},
{1.f, "0x1p+0"},
{2.f, "0x1p+1"},
{3.f, "0x1.8p+1"},
{0.5f, "0x1p-1"},
{0.25f, "0x1p-2"},
{0.75f, "0x1.8p-1"},
{-0.f, "-0x0p+0"},
{-1.f, "-0x1p+0"},
{-0.5f, "-0x1p-1"},
{-0.25f, "-0x1p-2"},
{-0.75f, "-0x1.8p-1"},
// Larger numbers
{512.f, "0x1p+9"},
{-512.f, "-0x1p+9"},
{1024.f, "0x1p+10"},
{-1024.f, "-0x1p+10"},
{1024.f + 8.f, "0x1.02p+10"},
{-1024.f - 8.f, "-0x1.02p+10"},
// Small numbers
{1.0f / 512.f, "0x1p-9"},
{1.0f / -512.f, "-0x1p-9"},
{1.0f / 1024.f, "0x1p-10"},
{1.0f / -1024.f, "-0x1p-10"},
{1.0f / 1024.f + 1.0f / 8.f, "0x1.02p-3"},
{1.0f / -1024.f - 1.0f / 8.f, "-0x1.02p-3"},
// lowest non-denorm
{float(ldexp(1.0f, -126)), "0x1p-126"},
{float(ldexp(-1.0f, -126)), "-0x1p-126"},
// Denormalized values
{float(ldexp(1.0f, -127)), "0x1p-127"},
{float(ldexp(1.0f, -127) / 2.0f), "0x1p-128"},
{float(ldexp(1.0f, -127) / 4.0f), "0x1p-129"},
{float(ldexp(1.0f, -127) / 8.0f), "0x1p-130"},
{float(ldexp(-1.0f, -127)), "-0x1p-127"},
{float(ldexp(-1.0f, -127) / 2.0f), "-0x1p-128"},
{float(ldexp(-1.0f, -127) / 4.0f), "-0x1p-129"},
{float(ldexp(-1.0f, -127) / 8.0f), "-0x1p-130"},
{float(ldexp(1.0, -127) + (ldexp(1.0, -127) / 2.0f)), "0x1.8p-127"},
{float(ldexp(1.0, -127) / 2.0 + (ldexp(1.0, -127) / 4.0f)),
"0x1.8p-128"},
})));
INSTANTIATE_TEST_SUITE_P(
Float32NanTests, HexFloatTest,
::testing::ValuesIn(std::vector<std::pair<FloatProxy<float>, std::string>>({
// Various NAN and INF cases
{uint32_t(0xFF800000), "-0x1p+128"}, // -inf
{uint32_t(0x7F800000), "0x1p+128"}, // inf
{uint32_t(0xFFC00000), "-0x1.8p+128"}, // -nan
{uint32_t(0xFF800100), "-0x1.0002p+128"}, // -nan
{uint32_t(0xFF800c00), "-0x1.0018p+128"}, // -nan
{uint32_t(0xFF80F000), "-0x1.01ep+128"}, // -nan
{uint32_t(0xFFFFFFFF), "-0x1.fffffep+128"}, // -nan
{uint32_t(0x7FC00000), "0x1.8p+128"}, // +nan
{uint32_t(0x7F800100), "0x1.0002p+128"}, // +nan
{uint32_t(0x7f800c00), "0x1.0018p+128"}, // +nan
{uint32_t(0x7F80F000), "0x1.01ep+128"}, // +nan
{uint32_t(0x7FFFFFFF), "0x1.fffffep+128"}, // +nan
})));
INSTANTIATE_TEST_SUITE_P(
Float64Tests, HexDoubleTest,
::testing::ValuesIn(
std::vector<std::pair<FloatProxy<double>, std::string>>({
{0., "0x0p+0"},
{1., "0x1p+0"},
{2., "0x1p+1"},
{3., "0x1.8p+1"},
{0.5, "0x1p-1"},
{0.25, "0x1p-2"},
{0.75, "0x1.8p-1"},
{-0., "-0x0p+0"},
{-1., "-0x1p+0"},
{-0.5, "-0x1p-1"},
{-0.25, "-0x1p-2"},
{-0.75, "-0x1.8p-1"},
// Larger numbers
{512., "0x1p+9"},
{-512., "-0x1p+9"},
{1024., "0x1p+10"},
{-1024., "-0x1p+10"},
{1024. + 8., "0x1.02p+10"},
{-1024. - 8., "-0x1.02p+10"},
// Large outside the range of normal floats
{ldexp(1.0, 128), "0x1p+128"},
{ldexp(1.0, 129), "0x1p+129"},
{ldexp(-1.0, 128), "-0x1p+128"},
{ldexp(-1.0, 129), "-0x1p+129"},
{ldexp(1.0, 128) + ldexp(1.0, 90), "0x1.0000000004p+128"},
{ldexp(1.0, 129) + ldexp(1.0, 120), "0x1.008p+129"},
{ldexp(-1.0, 128) + ldexp(1.0, 90), "-0x1.fffffffff8p+127"},
{ldexp(-1.0, 129) + ldexp(1.0, 120), "-0x1.ffp+128"},
// Small numbers
{1.0 / 512., "0x1p-9"},
{1.0 / -512., "-0x1p-9"},
{1.0 / 1024., "0x1p-10"},
{1.0 / -1024., "-0x1p-10"},
{1.0 / 1024. + 1.0 / 8., "0x1.02p-3"},
{1.0 / -1024. - 1.0 / 8., "-0x1.02p-3"},
// Small outside the range of normal floats
{ldexp(1.0, -128), "0x1p-128"},
{ldexp(1.0, -129), "0x1p-129"},
{ldexp(-1.0, -128), "-0x1p-128"},
{ldexp(-1.0, -129), "-0x1p-129"},
{ldexp(1.0, -128) + ldexp(1.0, -90), "0x1.0000000004p-90"},
{ldexp(1.0, -129) + ldexp(1.0, -120), "0x1.008p-120"},
{ldexp(-1.0, -128) + ldexp(1.0, -90), "0x1.fffffffff8p-91"},
{ldexp(-1.0, -129) + ldexp(1.0, -120), "0x1.ffp-121"},
// lowest non-denorm
{ldexp(1.0, -1022), "0x1p-1022"},
{ldexp(-1.0, -1022), "-0x1p-1022"},
// Denormalized values
{ldexp(1.0, -1023), "0x1p-1023"},
{ldexp(1.0, -1023) / 2.0, "0x1p-1024"},
{ldexp(1.0, -1023) / 4.0, "0x1p-1025"},
{ldexp(1.0, -1023) / 8.0, "0x1p-1026"},
{ldexp(-1.0, -1024), "-0x1p-1024"},
{ldexp(-1.0, -1024) / 2.0, "-0x1p-1025"},
{ldexp(-1.0, -1024) / 4.0, "-0x1p-1026"},
{ldexp(-1.0, -1024) / 8.0, "-0x1p-1027"},
{ldexp(1.0, -1023) + (ldexp(1.0, -1023) / 2.0), "0x1.8p-1023"},
{ldexp(1.0, -1023) / 2.0 + (ldexp(1.0, -1023) / 4.0),
"0x1.8p-1024"},
})));
INSTANTIATE_TEST_SUITE_P(
Float64NanTests, HexDoubleTest,
::testing::ValuesIn(std::vector<
std::pair<FloatProxy<double>, std::string>>({
// Various NAN and INF cases
{uint64_t(0xFFF0000000000000LL), "-0x1p+1024"}, // -inf
{uint64_t(0x7FF0000000000000LL), "0x1p+1024"}, // +inf
{uint64_t(0xFFF8000000000000LL), "-0x1.8p+1024"}, // -nan
{uint64_t(0xFFF0F00000000000LL), "-0x1.0fp+1024"}, // -nan
{uint64_t(0xFFF0000000000001LL), "-0x1.0000000000001p+1024"}, // -nan
{uint64_t(0xFFF0000300000000LL), "-0x1.00003p+1024"}, // -nan
{uint64_t(0xFFFFFFFFFFFFFFFFLL), "-0x1.fffffffffffffp+1024"}, // -nan
{uint64_t(0x7FF8000000000000LL), "0x1.8p+1024"}, // +nan
{uint64_t(0x7FF0F00000000000LL), "0x1.0fp+1024"}, // +nan
{uint64_t(0x7FF0000000000001LL), "0x1.0000000000001p+1024"}, // -nan
{uint64_t(0x7FF0000300000000LL), "0x1.00003p+1024"}, // -nan
{uint64_t(0x7FFFFFFFFFFFFFFFLL), "0x1.fffffffffffffp+1024"}, // -nan
})));
// Tests that encoding a value and decoding it again restores
// the same value.
TEST_P(RoundTripFloatTest, CanStoreAccurately) {
std::stringstream ss;
ss << FloatProxy<float>(GetParam());
ss.seekg(0);
FloatProxy<float> res;
ss >> res;
EXPECT_THAT(GetParam(), Eq(res.getAsFloat()));
}
TEST_P(RoundTripDoubleTest, CanStoreAccurately) {
std::stringstream ss;
ss << FloatProxy<double>(GetParam());
ss.seekg(0);
FloatProxy<double> res;
ss >> res;
EXPECT_THAT(GetParam(), Eq(res.getAsFloat()));
}
INSTANTIATE_TEST_SUITE_P(
Float32StoreTests, RoundTripFloatTest,
::testing::ValuesIn(std::vector<float>(
{// Value requiring more than 6 digits of precision to be
// represented accurately.
3.0000002f})));
INSTANTIATE_TEST_SUITE_P(
Float64StoreTests, RoundTripDoubleTest,
::testing::ValuesIn(std::vector<double>(
{// Value requiring more than 15 digits of precision to be
// represented accurately.
1.5000000000000002})));
TEST(HexFloatStreamTest, OperatorLeftShiftPreservesFloatAndFill) {
std::stringstream s;
s << std::setw(4) << std::oct << std::setfill('x') << 8 << " "
<< FloatProxy<float>(uint32_t(0xFF800100)) << " " << std::setw(4) << 9;
EXPECT_THAT(s.str(), Eq(std::string("xx10 -0x1.0002p+128 xx11")));
}
TEST(HexDoubleStreamTest, OperatorLeftShiftPreservesFloatAndFill) {
std::stringstream s;
s << std::setw(4) << std::oct << std::setfill('x') << 8 << " "
<< FloatProxy<double>(uint64_t(0x7FF0F00000000000LL)) << " " << std::setw(4)
<< 9;
EXPECT_THAT(s.str(), Eq(std::string("xx10 0x1.0fp+1024 xx11")));
}
TEST_P(DecodeHexFloatTest, DecodeCorrectly) {
EXPECT_THAT(Decode<float>(GetParam().first), Eq(GetParam().second));
}
TEST_P(DecodeHexDoubleTest, DecodeCorrectly) {
EXPECT_THAT(Decode<double>(GetParam().first), Eq(GetParam().second));
}
INSTANTIATE_TEST_SUITE_P(
Float32DecodeTests, DecodeHexFloatTest,
::testing::ValuesIn(std::vector<std::pair<std::string, FloatProxy<float>>>({
{"0x0p+000", 0.f},
{"0x0p0", 0.f},
{"0x0p-0", 0.f},
// flush to zero cases
{"0x1p-500", 0.f}, // Exponent underflows.
{"-0x1p-500", -0.f},
{"0x0.00000000001p-126", 0.f}, // Fraction causes underflow.
{"-0x0.0000000001p-127", -0.f},
{"-0x0.01p-142", -0.f}, // Fraction causes additional underflow.
{"0x0.01p-142", 0.f},
// Some floats that do not encode the same way as they decode.
{"0x2p+0", 2.f},
{"0xFFp+0", 255.f},
{"0x0.8p+0", 0.5f},
{"0x0.4p+0", 0.25f},
})));
INSTANTIATE_TEST_SUITE_P(
Float32DecodeInfTests, DecodeHexFloatTest,
::testing::ValuesIn(std::vector<std::pair<std::string, FloatProxy<float>>>({
// inf cases
{"-0x1p+128", uint32_t(0xFF800000)}, // -inf
{"0x32p+127", uint32_t(0x7F800000)}, // inf
{"0x32p+500", uint32_t(0x7F800000)}, // inf
{"-0x32p+127", uint32_t(0xFF800000)}, // -inf
})));
INSTANTIATE_TEST_SUITE_P(
Float64DecodeTests, DecodeHexDoubleTest,
::testing::ValuesIn(
std::vector<std::pair<std::string, FloatProxy<double>>>({
{"0x0p+000", 0.},
{"0x0p0", 0.},
{"0x0p-0", 0.},
// flush to zero cases
{"0x1p-5000", 0.}, // Exponent underflows.
{"-0x1p-5000", -0.},
{"0x0.0000000000000001p-1023", 0.}, // Fraction causes underflow.
{"-0x0.000000000000001p-1024", -0.},
{"-0x0.01p-1090", -0.f}, // Fraction causes additional underflow.
{"0x0.01p-1090", 0.},
// Some floats that do not encode the same way as they decode.
{"0x2p+0", 2.},
{"0xFFp+0", 255.},
{"0x0.8p+0", 0.5},
{"0x0.4p+0", 0.25},
})));
INSTANTIATE_TEST_SUITE_P(
Float64DecodeInfTests, DecodeHexDoubleTest,
::testing::ValuesIn(
std::vector<std::pair<std::string, FloatProxy<double>>>({
// inf cases
{"-0x1p+1024", uint64_t(0xFFF0000000000000)}, // -inf
{"0x32p+1023", uint64_t(0x7FF0000000000000)}, // inf
{"0x32p+5000", uint64_t(0x7FF0000000000000)}, // inf
{"-0x32p+1023", uint64_t(0xFFF0000000000000)}, // -inf
})));
TEST(FloatProxy, ValidConversion) {
EXPECT_THAT(FloatProxy<float>(1.f).getAsFloat(), Eq(1.0f));
EXPECT_THAT(FloatProxy<float>(32.f).getAsFloat(), Eq(32.0f));
EXPECT_THAT(FloatProxy<float>(-1.f).getAsFloat(), Eq(-1.0f));
EXPECT_THAT(FloatProxy<float>(0.f).getAsFloat(), Eq(0.0f));
EXPECT_THAT(FloatProxy<float>(-0.f).getAsFloat(), Eq(-0.0f));
EXPECT_THAT(FloatProxy<float>(1.2e32f).getAsFloat(), Eq(1.2e32f));
EXPECT_TRUE(std::isinf(FloatProxy<float>(uint32_t(0xFF800000)).getAsFloat()));
EXPECT_TRUE(std::isinf(FloatProxy<float>(uint32_t(0x7F800000)).getAsFloat()));
EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFFC00000)).getAsFloat()));
EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFF800100)).getAsFloat()));
EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFF800c00)).getAsFloat()));
EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFF80F000)).getAsFloat()));
EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFFFFFFFF)).getAsFloat()));
EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7FC00000)).getAsFloat()));
EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7F800100)).getAsFloat()));
EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7f800c00)).getAsFloat()));
EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7F80F000)).getAsFloat()));
EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7FFFFFFF)).getAsFloat()));
EXPECT_THAT(FloatProxy<float>(uint32_t(0xFF800000)).data(), Eq(0xFF800000u));
EXPECT_THAT(FloatProxy<float>(uint32_t(0x7F800000)).data(), Eq(0x7F800000u));
EXPECT_THAT(FloatProxy<float>(uint32_t(0xFFC00000)).data(), Eq(0xFFC00000u));
EXPECT_THAT(FloatProxy<float>(uint32_t(0xFF800100)).data(), Eq(0xFF800100u));
EXPECT_THAT(FloatProxy<float>(uint32_t(0xFF800c00)).data(), Eq(0xFF800c00u));
EXPECT_THAT(FloatProxy<float>(uint32_t(0xFF80F000)).data(), Eq(0xFF80F000u));
EXPECT_THAT(FloatProxy<float>(uint32_t(0xFFFFFFFF)).data(), Eq(0xFFFFFFFFu));
EXPECT_THAT(FloatProxy<float>(uint32_t(0x7FC00000)).data(), Eq(0x7FC00000u));
EXPECT_THAT(FloatProxy<float>(uint32_t(0x7F800100)).data(), Eq(0x7F800100u));
EXPECT_THAT(FloatProxy<float>(uint32_t(0x7f800c00)).data(), Eq(0x7f800c00u));
EXPECT_THAT(FloatProxy<float>(uint32_t(0x7F80F000)).data(), Eq(0x7F80F000u));
EXPECT_THAT(FloatProxy<float>(uint32_t(0x7FFFFFFF)).data(), Eq(0x7FFFFFFFu));
}
TEST(FloatProxy, Nan) {
EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFFC00000)).isNan());
EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFF800100)).isNan());
EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFF800c00)).isNan());
EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFF80F000)).isNan());
EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFFFFFFFF)).isNan());
EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7FC00000)).isNan());
EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7F800100)).isNan());
EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7f800c00)).isNan());
EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7F80F000)).isNan());
EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7FFFFFFF)).isNan());
}
TEST(FloatProxy, Negation) {
EXPECT_THAT((-FloatProxy<float>(1.f)).getAsFloat(), Eq(-1.0f));
EXPECT_THAT((-FloatProxy<float>(0.f)).getAsFloat(), Eq(-0.0f));
EXPECT_THAT((-FloatProxy<float>(-1.f)).getAsFloat(), Eq(1.0f));
EXPECT_THAT((-FloatProxy<float>(-0.f)).getAsFloat(), Eq(0.0f));
EXPECT_THAT((-FloatProxy<float>(32.f)).getAsFloat(), Eq(-32.0f));
EXPECT_THAT((-FloatProxy<float>(-32.f)).getAsFloat(), Eq(32.0f));
EXPECT_THAT((-FloatProxy<float>(1.2e32f)).getAsFloat(), Eq(-1.2e32f));
EXPECT_THAT((-FloatProxy<float>(-1.2e32f)).getAsFloat(), Eq(1.2e32f));
EXPECT_THAT(
(-FloatProxy<float>(std::numeric_limits<float>::infinity())).getAsFloat(),
Eq(-std::numeric_limits<float>::infinity()));
EXPECT_THAT((-FloatProxy<float>(-std::numeric_limits<float>::infinity()))
.getAsFloat(),
Eq(std::numeric_limits<float>::infinity()));
}
// Test conversion of FloatProxy values to strings.
//
// In previous cases, we always wrapped the FloatProxy value in a HexFloat
// before conversion to a string. In the following cases, the FloatProxy
// decides for itself whether to print as a regular number or as a hex float.
using FloatProxyFloatTest =
::testing::TestWithParam<std::pair<FloatProxy<float>, std::string>>;
using FloatProxyDoubleTest =
::testing::TestWithParam<std::pair<FloatProxy<double>, std::string>>;
// Converts a float value to a string via a FloatProxy.
template <typename T>
std::string EncodeViaFloatProxy(const T& value) {
std::stringstream ss;
ss << value;
return ss.str();
}
// Converts a floating point string so that the exponent prefix
// is 'e', and the exponent value does not have leading zeros.
// The Microsoft runtime library likes to write things like "2.5E+010".
// Convert that to "2.5e+10".
// We don't care what happens to strings that are not floating point
// strings.
std::string NormalizeExponentInFloatString(std::string in) {
std::string result;
// Reserve one spot for the terminating null, even when the sscanf fails.
std::vector<char> prefix(in.size() + 1);
char e;
char plus_or_minus;
int exponent; // in base 10
if ((4 == std::sscanf(in.c_str(), "%[-+.0123456789]%c%c%d", prefix.data(), &e,
&plus_or_minus, &exponent)) &&
(e == 'e' || e == 'E') &&
(plus_or_minus == '-' || plus_or_minus == '+')) {
// It looks like a floating point value with exponent.
std::stringstream out;
out << prefix.data() << 'e' << plus_or_minus << exponent;
result = out.str();
} else {
result = in;
}
return result;
}
TEST(NormalizeFloat, Sample) {
EXPECT_THAT(NormalizeExponentInFloatString(""), Eq(""));
EXPECT_THAT(NormalizeExponentInFloatString("1e-12"), Eq("1e-12"));
EXPECT_THAT(NormalizeExponentInFloatString("1E+14"), Eq("1e+14"));
EXPECT_THAT(NormalizeExponentInFloatString("1e-0012"), Eq("1e-12"));
EXPECT_THAT(NormalizeExponentInFloatString("1.263E+014"), Eq("1.263e+14"));
}
// The following two tests can't be DRY because they take different parameter
// types.
TEST_P(FloatProxyFloatTest, EncodeCorrectly) {
EXPECT_THAT(
NormalizeExponentInFloatString(EncodeViaFloatProxy(GetParam().first)),
Eq(GetParam().second));
}
TEST_P(FloatProxyDoubleTest, EncodeCorrectly) {
EXPECT_THAT(
NormalizeExponentInFloatString(EncodeViaFloatProxy(GetParam().first)),
Eq(GetParam().second));
}
INSTANTIATE_TEST_SUITE_P(
Float32Tests, FloatProxyFloatTest,
::testing::ValuesIn(std::vector<std::pair<FloatProxy<float>, std::string>>({
// Zero
{0.f, "0"},
// Normal numbers
{1.f, "1"},
{-0.25f, "-0.25"},
{1000.0f, "1000"},
// Still normal numbers, but with large magnitude exponents.
{float(ldexp(1.f, 126)), "8.50705917e+37"},
{float(ldexp(-1.f, -126)), "-1.17549435e-38"},
// denormalized values are printed as hex floats.
{float(ldexp(1.0f, -127)), "0x1p-127"},
{float(ldexp(1.5f, -128)), "0x1.8p-128"},
{float(ldexp(1.25, -129)), "0x1.4p-129"},
{float(ldexp(1.125, -130)), "0x1.2p-130"},
{float(ldexp(-1.0f, -127)), "-0x1p-127"},
{float(ldexp(-1.0f, -128)), "-0x1p-128"},
{float(ldexp(-1.0f, -129)), "-0x1p-129"},
{float(ldexp(-1.5f, -130)), "-0x1.8p-130"},
// NaNs
{FloatProxy<float>(uint32_t(0xFFC00000)), "-0x1.8p+128"},
{FloatProxy<float>(uint32_t(0xFF800100)), "-0x1.0002p+128"},
{std::numeric_limits<float>::infinity(), "0x1p+128"},
{-std::numeric_limits<float>::infinity(), "-0x1p+128"},
})));
INSTANTIATE_TEST_SUITE_P(
Float64Tests, FloatProxyDoubleTest,
::testing::ValuesIn(
std::vector<std::pair<FloatProxy<double>, std::string>>({
{0., "0"},
{1., "1"},
{-0.25, "-0.25"},
{1000.0, "1000"},
// Large outside the range of normal floats
{ldexp(1.0, 128), "3.4028236692093846e+38"},
{ldexp(1.5, 129), "1.0208471007628154e+39"},
{ldexp(-1.0, 128), "-3.4028236692093846e+38"},
{ldexp(-1.5, 129), "-1.0208471007628154e+39"},
// Small outside the range of normal floats
{ldexp(1.5, -129), "2.2040519077917891e-39"},
{ldexp(-1.5, -129), "-2.2040519077917891e-39"},
// lowest non-denorm
{ldexp(1.0, -1022), "2.2250738585072014e-308"},
{ldexp(-1.0, -1022), "-2.2250738585072014e-308"},
// Denormalized values
{ldexp(1.125, -1023), "0x1.2p-1023"},
{ldexp(-1.375, -1024), "-0x1.6p-1024"},
// NaNs
{uint64_t(0x7FF8000000000000LL), "0x1.8p+1024"},
{uint64_t(0xFFF0F00000000000LL), "-0x1.0fp+1024"},
// Infinity
{std::numeric_limits<double>::infinity(), "0x1p+1024"},
{-std::numeric_limits<double>::infinity(), "-0x1p+1024"},
})));
// double is used so that unbiased_exponent can be used with the output
// of ldexp directly.
int32_t unbiased_exponent(double f) {
return HexFloat<FloatProxy<float>>(static_cast<float>(f))
.getUnbiasedNormalizedExponent();
}
int16_t unbiased_half_exponent(uint16_t f) {
return HexFloat<FloatProxy<Float16>>(f).getUnbiasedNormalizedExponent();
}
TEST(HexFloatOperationTest, UnbiasedExponent) {
// Float cases
EXPECT_EQ(0, unbiased_exponent(ldexp(1.0f, 0)));
EXPECT_EQ(-32, unbiased_exponent(ldexp(1.0f, -32)));
EXPECT_EQ(42, unbiased_exponent(ldexp(1.0f, 42)));
EXPECT_EQ(125, unbiased_exponent(ldexp(1.0f, 125)));
EXPECT_EQ(128,
HexFloat<FloatProxy<float>>(std::numeric_limits<float>::infinity())
.getUnbiasedNormalizedExponent());
EXPECT_EQ(-100, unbiased_exponent(ldexp(1.0f, -100)));
EXPECT_EQ(-127, unbiased_exponent(ldexp(1.0f, -127))); // First denorm
EXPECT_EQ(-128, unbiased_exponent(ldexp(1.0f, -128)));
EXPECT_EQ(-129, unbiased_exponent(ldexp(1.0f, -129)));
EXPECT_EQ(-140, unbiased_exponent(ldexp(1.0f, -140)));
// Smallest representable number
EXPECT_EQ(-126 - 23, unbiased_exponent(ldexp(1.0f, -126 - 23)));
// Should get rounded to 0 first.
EXPECT_EQ(0, unbiased_exponent(ldexp(1.0f, -127 - 23)));
// Float16 cases
// The exponent is represented in the bits 0x7C00
// The offset is -15
EXPECT_EQ(0, unbiased_half_exponent(0x3C00));
EXPECT_EQ(3, unbiased_half_exponent(0x4800));
EXPECT_EQ(-1, unbiased_half_exponent(0x3800));
EXPECT_EQ(-14, unbiased_half_exponent(0x0400));
EXPECT_EQ(16, unbiased_half_exponent(0x7C00));
EXPECT_EQ(10, unbiased_half_exponent(0x6400));
// Smallest representable number
EXPECT_EQ(-24, unbiased_half_exponent(0x0001));
}
// Creates a float that is the sum of 1/(2 ^ fractions[i]) for i in factions
float float_fractions(const std::vector<uint32_t>& fractions) {
float f = 0;
for (int32_t i : fractions) {
f += std::ldexp(1.0f, -i);
}
return f;
}
// Returns the normalized significand of a HexFloat<FloatProxy<float>>
// that was created by calling float_fractions with the input fractions,
// raised to the power of exp.
uint32_t normalized_significand(const std::vector<uint32_t>& fractions,
uint32_t exp) {
return HexFloat<FloatProxy<float>>(
static_cast<float>(ldexp(float_fractions(fractions), exp)))
.getNormalizedSignificand();
}
// Sets the bits from MSB to LSB of the significand part of a float.
// For example 0 would set the bit 23 (counting from LSB to MSB),
// and 1 would set the 22nd bit.
uint32_t bits_set(const std::vector<uint32_t>& bits) {
const uint32_t top_bit = 1u << 22u;
uint32_t val = 0;
for (uint32_t i : bits) {
val |= top_bit >> i;
}
return val;
}
// The same as bits_set but for a Float16 value instead of 32-bit floating
// point.
uint16_t half_bits_set(const std::vector<uint32_t>& bits) {
const uint32_t top_bit = 1u << 9u;
uint32_t val = 0;
for (uint32_t i : bits) {
val |= top_bit >> i;
}
return static_cast<uint16_t>(val);
}
TEST(HexFloatOperationTest, NormalizedSignificand) {
// For normalized numbers (the following) it should be a simple matter
// of getting rid of the top implicit bit
EXPECT_EQ(bits_set({}), normalized_significand({0}, 0));
EXPECT_EQ(bits_set({0}), normalized_significand({0, 1}, 0));
EXPECT_EQ(bits_set({0, 1}), normalized_significand({0, 1, 2}, 0));
EXPECT_EQ(bits_set({1}), normalized_significand({0, 2}, 0));
EXPECT_EQ(bits_set({1}), normalized_significand({0, 2}, 32));
EXPECT_EQ(bits_set({1}), normalized_significand({0, 2}, 126));
// For denormalized numbers we expect the normalized significand to
// shift as if it were normalized. This means, in practice that the
// top_most set bit will be cut off. Looks very similar to above (on purpose)
EXPECT_EQ(bits_set({}),
normalized_significand({0}, static_cast<uint32_t>(-127)));
EXPECT_EQ(bits_set({3}),
normalized_significand({0, 4}, static_cast<uint32_t>(-128)));
EXPECT_EQ(bits_set({3}),
normalized_significand({0, 4}, static_cast<uint32_t>(-127)));
EXPECT_EQ(bits_set({}),
normalized_significand({22}, static_cast<uint32_t>(-127)));
EXPECT_EQ(bits_set({0}),
normalized_significand({21, 22}, static_cast<uint32_t>(-127)));
}
// Returns the 32-bit floating point value created by
// calling setFromSignUnbiasedExponentAndNormalizedSignificand
// on a HexFloat<FloatProxy<float>>
float set_from_sign(bool negative, int32_t unbiased_exponent,
uint32_t significand, bool round_denorm_up) {
HexFloat<FloatProxy<float>> f(0.f);
f.setFromSignUnbiasedExponentAndNormalizedSignificand(
negative, unbiased_exponent, significand, round_denorm_up);
return f.value().getAsFloat();
}
TEST(HexFloatOperationTests,
SetFromSignUnbiasedExponentAndNormalizedSignificand) {
EXPECT_EQ(1.f, set_from_sign(false, 0, 0, false));
// Tests insertion of various denormalized numbers with and without round up.
EXPECT_EQ(static_cast<float>(ldexp(1.f, -149)),
set_from_sign(false, -149, 0, false));
EXPECT_EQ(static_cast<float>(ldexp(1.f, -149)),
set_from_sign(false, -149, 0, true));
EXPECT_EQ(0.f, set_from_sign(false, -150, 1, false));
EXPECT_EQ(static_cast<float>(ldexp(1.f, -149)),
set_from_sign(false, -150, 1, true));
EXPECT_EQ(ldexp(1.0f, -127), set_from_sign(false, -127, 0, false));
EXPECT_EQ(ldexp(1.0f, -128), set_from_sign(false, -128, 0, false));
EXPECT_EQ(float_fractions({0, 1, 2, 5}),
set_from_sign(false, 0, bits_set({0, 1, 4}), false));
EXPECT_EQ(ldexp(float_fractions({0, 1, 2, 5}), -32),
set_from_sign(false, -32, bits_set({0, 1, 4}), false));
EXPECT_EQ(ldexp(float_fractions({0, 1, 2, 5}), -128),
set_from_sign(false, -128, bits_set({0, 1, 4}), false));
// The negative cases from above.
EXPECT_EQ(-1.f, set_from_sign(true, 0, 0, false));
EXPECT_EQ(-ldexp(1.0, -127), set_from_sign(true, -127, 0, false));
EXPECT_EQ(-ldexp(1.0, -128), set_from_sign(true, -128, 0, false));
EXPECT_EQ(-float_fractions({0, 1, 2, 5}),
set_from_sign(true, 0, bits_set({0, 1, 4}), false));
EXPECT_EQ(-ldexp(float_fractions({0, 1, 2, 5}), -32),
set_from_sign(true, -32, bits_set({0, 1, 4}), false));
EXPECT_EQ(-ldexp(float_fractions({0, 1, 2, 5}), -128),
set_from_sign(true, -128, bits_set({0, 1, 4}), false));
}
TEST(HexFloatOperationTests, NonRounding) {
// Rounding from 32-bit hex-float to 32-bit hex-float should be trivial,
// except in the denorm case which is a bit more complex.
using HF = HexFloat<FloatProxy<float>>;
bool carry_bit = false;
round_direction rounding[] = {round_direction::kToZero,
round_direction::kToNearestEven,
round_direction::kToPositiveInfinity,
round_direction::kToNegativeInfinity};
// Everything fits, so this should be straight-forward
for (round_direction round : rounding) {
EXPECT_EQ(bits_set({}),
HF(0.f).getRoundedNormalizedSignificand<HF>(round, &carry_bit));
EXPECT_FALSE(carry_bit);
EXPECT_EQ(bits_set({0}),
HF(float_fractions({0, 1}))
.getRoundedNormalizedSignificand<HF>(round, &carry_bit));
EXPECT_FALSE(carry_bit);
EXPECT_EQ(bits_set({1, 3}),
HF(float_fractions({0, 2, 4}))
.getRoundedNormalizedSignificand<HF>(round, &carry_bit));
EXPECT_FALSE(carry_bit);
EXPECT_EQ(
bits_set({0, 1, 4}),
HF(static_cast<float>(-ldexp(float_fractions({0, 1, 2, 5}), -128)))
.getRoundedNormalizedSignificand<HF>(round, &carry_bit));
EXPECT_FALSE(carry_bit);
EXPECT_EQ(bits_set({0, 1, 4, 22}),
HF(static_cast<float>(float_fractions({0, 1, 2, 5, 23})))
.getRoundedNormalizedSignificand<HF>(round, &carry_bit));
EXPECT_FALSE(carry_bit);
}
}
using RD = round_direction;
struct RoundSignificandCase {
float source_float;
std::pair<int16_t, bool> expected_results;
round_direction round;
};
using HexFloatRoundTest = ::testing::TestWithParam<RoundSignificandCase>;
TEST_P(HexFloatRoundTest, RoundDownToFP16) {
using HF = HexFloat<FloatProxy<float>>;
using HF16 = HexFloat<FloatProxy<Float16>>;
HF input_value(GetParam().source_float);
bool carry_bit = false;
EXPECT_EQ(GetParam().expected_results.first,
input_value.getRoundedNormalizedSignificand<HF16>(GetParam().round,
&carry_bit));
EXPECT_EQ(carry_bit, GetParam().expected_results.second);
}
// clang-format off
INSTANTIATE_TEST_SUITE_P(F32ToF16, HexFloatRoundTest,
::testing::ValuesIn(std::vector<RoundSignificandCase>(
{
{float_fractions({0}), std::make_pair(half_bits_set({}), false), RD::kToZero},
{float_fractions({0}), std::make_pair(half_bits_set({}), false), RD::kToNearestEven},
{float_fractions({0}), std::make_pair(half_bits_set({}), false), RD::kToPositiveInfinity},
{float_fractions({0}), std::make_pair(half_bits_set({}), false), RD::kToNegativeInfinity},
{float_fractions({0, 1}), std::make_pair(half_bits_set({0}), false), RD::kToZero},
{float_fractions({0, 1, 11}), std::make_pair(half_bits_set({0}), false), RD::kToZero},
{float_fractions({0, 1, 11}), std::make_pair(half_bits_set({0, 9}), false), RD::kToPositiveInfinity},
{float_fractions({0, 1, 11}), std::make_pair(half_bits_set({0}), false), RD::kToNegativeInfinity},
{float_fractions({0, 1, 11}), std::make_pair(half_bits_set({0}), false), RD::kToNearestEven},
{float_fractions({0, 1, 10, 11}), std::make_pair(half_bits_set({0, 9}), false), RD::kToZero},
{float_fractions({0, 1, 10, 11}), std::make_pair(half_bits_set({0, 8}), false), RD::kToPositiveInfinity},
{float_fractions({0, 1, 10, 11}), std::make_pair(half_bits_set({0, 9}), false), RD::kToNegativeInfinity},
{float_fractions({0, 1, 10, 11}), std::make_pair(half_bits_set({0, 8}), false), RD::kToNearestEven},
{float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0}), false), RD::kToZero},
{float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0, 9}), false), RD::kToPositiveInfinity},
{float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0}), false), RD::kToNegativeInfinity},
{float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0, 9}), false), RD::kToNearestEven},
{-float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0}), false), RD::kToZero},
{-float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0}), false), RD::kToPositiveInfinity},
{-float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0, 9}), false), RD::kToNegativeInfinity},
{-float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0, 9}), false), RD::kToNearestEven},
{float_fractions({0, 1, 11, 22}), std::make_pair(half_bits_set({0}), false), RD::kToZero},
{float_fractions({0, 1, 11, 22}), std::make_pair(half_bits_set({0, 9}), false), RD::kToPositiveInfinity},
{float_fractions({0, 1, 11, 22}), std::make_pair(half_bits_set({0}), false), RD::kToNegativeInfinity},
{float_fractions({0, 1, 11, 22}), std::make_pair(half_bits_set({0, 9}), false), RD::kToNearestEven},
// Carries
{float_fractions({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}), std::make_pair(half_bits_set({0, 1, 2, 3, 4, 5, 6, 7, 8, 9}), false), RD::kToZero},
{float_fractions({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}), std::make_pair(half_bits_set({}), true), RD::kToPositiveInfinity},
{float_fractions({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}), std::make_pair(half_bits_set({0, 1, 2, 3, 4, 5, 6, 7, 8, 9}), false), RD::kToNegativeInfinity},
{float_fractions({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}), std::make_pair(half_bits_set({}), true), RD::kToNearestEven},
// Cases where original number was denorm. Note: this should have no effect
// the number is pre-normalized.
{static_cast<float>(ldexp(float_fractions({0, 1, 11, 13}), -128)), std::make_pair(half_bits_set({0}), false), RD::kToZero},
{static_cast<float>(ldexp(float_fractions({0, 1, 11, 13}), -129)), std::make_pair(half_bits_set({0, 9}), false), RD::kToPositiveInfinity},
{static_cast<float>(ldexp(float_fractions({0, 1, 11, 13}), -131)), std::make_pair(half_bits_set({0}), false), RD::kToNegativeInfinity},
{static_cast<float>(ldexp(float_fractions({0, 1, 11, 13}), -130)), std::make_pair(half_bits_set({0, 9}), false), RD::kToNearestEven},
})));
// clang-format on
struct UpCastSignificandCase {
uint16_t source_half;
uint32_t expected_result;
};
using HexFloatRoundUpSignificandTest =
::testing::TestWithParam<UpCastSignificandCase>;
TEST_P(HexFloatRoundUpSignificandTest, Widening) {
using HF = HexFloat<FloatProxy<float>>;
using HF16 = HexFloat<FloatProxy<Float16>>;
bool carry_bit = false;
round_direction rounding[] = {round_direction::kToZero,
round_direction::kToNearestEven,
round_direction::kToPositiveInfinity,
round_direction::kToNegativeInfinity};
// Everything fits, so everything should just be bit-shifts.
for (round_direction round : rounding) {
carry_bit = false;
HF16 input_value(GetParam().source_half);
EXPECT_EQ(
GetParam().expected_result,
input_value.getRoundedNormalizedSignificand<HF>(round, &carry_bit))
<< std::hex << "0x"
<< input_value.getRoundedNormalizedSignificand<HF>(round, &carry_bit)
<< " 0x" << GetParam().expected_result;
EXPECT_FALSE(carry_bit);
}
}
INSTANTIATE_TEST_SUITE_P(
F16toF32, HexFloatRoundUpSignificandTest,
// 0xFC00 of the source 16-bit hex value cover the sign and the exponent.
// They are ignored for this test.
::testing::ValuesIn(std::vector<UpCastSignificandCase>({
{0x3F00, 0x600000},
{0x0F00, 0x600000},
{0x0F01, 0x602000},
{0x0FFF, 0x7FE000},
})));
struct DownCastTest {
float source_float;
uint16_t expected_half;
std::vector<round_direction> directions;
};
std::string get_round_text(round_direction direction) {
#define CASE(round_direction) \
case round_direction: \
return #round_direction
switch (direction) {
CASE(round_direction::kToZero);
CASE(round_direction::kToPositiveInfinity);
CASE(round_direction::kToNegativeInfinity);
CASE(round_direction::kToNearestEven);
}
#undef CASE
return "";
}
using HexFloatFP32To16Tests = ::testing::TestWithParam<DownCastTest>;
TEST_P(HexFloatFP32To16Tests, NarrowingCasts) {
using HF = HexFloat<FloatProxy<float>>;
using HF16 = HexFloat<FloatProxy<Float16>>;
HF f(GetParam().source_float);
for (auto round : GetParam().directions) {
HF16 half(0);
f.castTo(half, round);
EXPECT_EQ(GetParam().expected_half, half.value().getAsFloat().get_value())
<< get_round_text(round) << " " << std::hex
<< BitwiseCast<uint32_t>(GetParam().source_float)
<< " cast to: " << half.value().getAsFloat().get_value();
}
}
const uint16_t positive_infinity = 0x7C00;
const uint16_t negative_infinity = 0xFC00;
INSTANTIATE_TEST_SUITE_P(
F32ToF16, HexFloatFP32To16Tests,
::testing::ValuesIn(std::vector<DownCastTest>({
// Exactly representable as half.
{0.f,
0x0,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity,
RD::kToNearestEven}},
{-0.f,
0x8000,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity,
RD::kToNearestEven}},
{1.0f,
0x3C00,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity,
RD::kToNearestEven}},
{-1.0f,
0xBC00,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity,
RD::kToNearestEven}},
{float_fractions({0, 1, 10}),
0x3E01,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity,
RD::kToNearestEven}},
{-float_fractions({0, 1, 10}),
0xBE01,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity,
RD::kToNearestEven}},
{static_cast<float>(ldexp(float_fractions({0, 1, 10}), 3)),
0x4A01,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity,
RD::kToNearestEven}},
{static_cast<float>(-ldexp(float_fractions({0, 1, 10}), 3)),
0xCA01,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity,
RD::kToNearestEven}},
// Underflow
{static_cast<float>(ldexp(1.0f, -25)),
0x0,
{RD::kToZero, RD::kToNegativeInfinity, RD::kToNearestEven}},
{static_cast<float>(ldexp(1.0f, -25)), 0x1, {RD::kToPositiveInfinity}},
{static_cast<float>(-ldexp(1.0f, -25)),
0x8000,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNearestEven}},
{static_cast<float>(-ldexp(1.0f, -25)),
0x8001,
{RD::kToNegativeInfinity}},
{static_cast<float>(ldexp(1.0f, -24)),
0x1,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity,
RD::kToNearestEven}},
// Overflow
{static_cast<float>(ldexp(1.0f, 16)),
positive_infinity,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity,
RD::kToNearestEven}},
{static_cast<float>(ldexp(1.0f, 18)),
positive_infinity,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity,
RD::kToNearestEven}},
{static_cast<float>(ldexp(1.3f, 16)),
positive_infinity,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity,
RD::kToNearestEven}},
{static_cast<float>(-ldexp(1.0f, 16)),
negative_infinity,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity,
RD::kToNearestEven}},
{static_cast<float>(-ldexp(1.0f, 18)),
negative_infinity,
{RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity,
RD::kToNearestEven}},