Source/ThirdParty/ANGLE/src/common/mathutil_unittest.cpp - WebKit - Git at Google

 //
 // Copyright 2015 The ANGLE Project Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 //
 // mathutil_unittest:
 //   Unit tests for the utils defined in mathutil.h
 //

 #include "mathutil.h"

 #include <gtest/gtest.h>

 using namespace gl;

 namespace
 {

 // Test the correctness of packSnorm2x16 and unpackSnorm2x16 functions.
 // For floats f1 and f2, unpackSnorm2x16(packSnorm2x16(f1, f2)) should be same as f1 and f2.
 TEST(MathUtilTest, packAndUnpackSnorm2x16)
 {
     const float input[8][2] = {
         {0.0f, 0.0f},    {1.0f, 1.0f},          {-1.0f, 1.0f},           {-1.0f, -1.0f},
         {0.875f, 0.75f}, {0.00392f, -0.99215f}, {-0.000675f, 0.004954f}, {-0.6937f, -0.02146f}};
     const float floatFaultTolerance = 0.0001f;
     float outputVal1, outputVal2;

     for (size_t i = 0; i < 8; i++)
     {
         unpackSnorm2x16(packSnorm2x16(input[i][0], input[i][1]), &outputVal1, &outputVal2);
         EXPECT_NEAR(input[i][0], outputVal1, floatFaultTolerance);
         EXPECT_NEAR(input[i][1], outputVal2, floatFaultTolerance);
     }
 }

 // Test the correctness of packSnorm2x16 and unpackSnorm2x16 functions with infinity values,
 // result should be clamped to [-1, 1].
 TEST(MathUtilTest, packAndUnpackSnorm2x16Infinity)
 {
     const float floatFaultTolerance = 0.0001f;
     float outputVal1, outputVal2;

     unpackSnorm2x16(packSnorm2x16(std::numeric_limits<float>::infinity(),
                                   std::numeric_limits<float>::infinity()),
                     &outputVal1, &outputVal2);
     EXPECT_NEAR(1.0f, outputVal1, floatFaultTolerance);
     EXPECT_NEAR(1.0f, outputVal2, floatFaultTolerance);

     unpackSnorm2x16(packSnorm2x16(std::numeric_limits<float>::infinity(),
                                   -std::numeric_limits<float>::infinity()),
                     &outputVal1, &outputVal2);
     EXPECT_NEAR(1.0f, outputVal1, floatFaultTolerance);
     EXPECT_NEAR(-1.0f, outputVal2, floatFaultTolerance);

     unpackSnorm2x16(packSnorm2x16(-std::numeric_limits<float>::infinity(),
                                   -std::numeric_limits<float>::infinity()),
                     &outputVal1, &outputVal2);
     EXPECT_NEAR(-1.0f, outputVal1, floatFaultTolerance);
     EXPECT_NEAR(-1.0f, outputVal2, floatFaultTolerance);
 }

 // Test the correctness of packUnorm2x16 and unpackUnorm2x16 functions.
 // For floats f1 and f2, unpackUnorm2x16(packUnorm2x16(f1, f2)) should be same as f1 and f2.
 TEST(MathUtilTest, packAndUnpackUnorm2x16)
 {
     const float input[8][2] = {
         {0.0f, 0.0f},    {1.0f, 1.0f},          {-1.0f, 1.0f},           {-1.0f, -1.0f},
         {0.875f, 0.75f}, {0.00392f, -0.99215f}, {-0.000675f, 0.004954f}, {-0.6937f, -0.02146f}};
     const float floatFaultTolerance = 0.0001f;
     float outputVal1, outputVal2;

     for (size_t i = 0; i < 8; i++)
     {
         unpackUnorm2x16(packUnorm2x16(input[i][0], input[i][1]), &outputVal1, &outputVal2);
         float expected = input[i][0] < 0.0f ? 0.0f : input[i][0];
         EXPECT_NEAR(expected, outputVal1, floatFaultTolerance);
         expected = input[i][1] < 0.0f ? 0.0f : input[i][1];
         EXPECT_NEAR(expected, outputVal2, floatFaultTolerance);
     }
 }

 // Test the correctness of packUnorm2x16 and unpackUnorm2x16 functions with infinity values,
 // result should be clamped to [0, 1].
 TEST(MathUtilTest, packAndUnpackUnorm2x16Infinity)
 {
     const float floatFaultTolerance = 0.0001f;
     float outputVal1, outputVal2;

     unpackUnorm2x16(packUnorm2x16(std::numeric_limits<float>::infinity(),
                                   std::numeric_limits<float>::infinity()),
                     &outputVal1, &outputVal2);
     EXPECT_NEAR(1.0f, outputVal1, floatFaultTolerance);
     EXPECT_NEAR(1.0f, outputVal2, floatFaultTolerance);

     unpackUnorm2x16(packUnorm2x16(std::numeric_limits<float>::infinity(),
                                   -std::numeric_limits<float>::infinity()),
                     &outputVal1, &outputVal2);
     EXPECT_NEAR(1.0f, outputVal1, floatFaultTolerance);
     EXPECT_NEAR(0.0f, outputVal2, floatFaultTolerance);

     unpackUnorm2x16(packUnorm2x16(-std::numeric_limits<float>::infinity(),
                                   -std::numeric_limits<float>::infinity()),
                     &outputVal1, &outputVal2);
     EXPECT_NEAR(0.0f, outputVal1, floatFaultTolerance);
     EXPECT_NEAR(0.0f, outputVal2, floatFaultTolerance);
 }

 // Test the correctness of packHalf2x16 and unpackHalf2x16 functions.
 // For floats f1 and f2, unpackHalf2x16(packHalf2x16(f1, f2)) should be same as f1 and f2.
 TEST(MathUtilTest, packAndUnpackHalf2x16)
 {
     const float input[8][2] = {
         {0.0f, 0.0f},    {1.0f, 1.0f},          {-1.0f, 1.0f},           {-1.0f, -1.0f},
         {0.875f, 0.75f}, {0.00392f, -0.99215f}, {-0.000675f, 0.004954f}, {-0.6937f, -0.02146f},
     };
     const float floatFaultTolerance = 0.0005f;
     float outputVal1, outputVal2;

     for (size_t i = 0; i < 8; i++)
     {
         unpackHalf2x16(packHalf2x16(input[i][0], input[i][1]), &outputVal1, &outputVal2);
         EXPECT_NEAR(input[i][0], outputVal1, floatFaultTolerance);
         EXPECT_NEAR(input[i][1], outputVal2, floatFaultTolerance);
     }
 }

 // Test the correctness of packUnorm4x8 and unpackUnorm4x8 functions.
 // For floats f1 to f4, unpackUnorm4x8(packUnorm4x8(f1, f2, f3, f4)) should be same as f1 to f4.
 TEST(MathUtilTest, packAndUnpackUnorm4x8)
 {
     const float input[5][4] = {{0.0f, 0.0f, 0.0f, 0.0f},
                                {1.0f, 1.0f, 1.0f, 1.0f},
                                {-1.0f, 1.0f, -1.0f, 1.0f},
                                {-1.0f, -1.0f, -1.0f, -1.0f},
                                {64.0f / 255.0f, 128.0f / 255.0f, 32.0f / 255.0f, 16.0f / 255.0f}};

     const float floatFaultTolerance = 0.005f;
     float outputVals[4];

     for (size_t i = 0; i < 5; i++)
     {
         UnpackUnorm4x8(PackUnorm4x8(input[i][0], input[i][1], input[i][2], input[i][3]),
                        outputVals);
         for (size_t j = 0; j < 4; j++)
         {
             float expected = input[i][j] < 0.0f ? 0.0f : input[i][j];
             EXPECT_NEAR(expected, outputVals[j], floatFaultTolerance);
         }
     }
 }

 // Test the correctness of packSnorm4x8 and unpackSnorm4x8 functions.
 // For floats f1 to f4, unpackSnorm4x8(packSnorm4x8(f1, f2, f3, f4)) should be same as f1 to f4.
 TEST(MathUtilTest, packAndUnpackSnorm4x8)
 {
     const float input[5][4] = {{0.0f, 0.0f, 0.0f, 0.0f},
                                {1.0f, 1.0f, 1.0f, 1.0f},
                                {-1.0f, 1.0f, -1.0f, 1.0f},
                                {-1.0f, -1.0f, -1.0f, -1.0f},
                                {64.0f / 127.0f, -8.0f / 127.0f, 32.0f / 127.0f, 16.0f / 127.0f}};

     const float floatFaultTolerance = 0.01f;
     float outputVals[4];

     for (size_t i = 0; i < 5; i++)
     {
         UnpackSnorm4x8(PackSnorm4x8(input[i][0], input[i][1], input[i][2], input[i][3]),
                        outputVals);
         for (size_t j = 0; j < 4; j++)
         {
             float expected = input[i][j];
             EXPECT_NEAR(expected, outputVals[j], floatFaultTolerance);
         }
     }
 }

 // Test the correctness of gl::isNaN function.
 TEST(MathUtilTest, isNaN)
 {
     EXPECT_TRUE(isNaN(bitCast<float>(0xffu << 23 | 1u)));
     EXPECT_TRUE(isNaN(bitCast<float>(1u << 31 | 0xffu << 23 | 1u)));
     EXPECT_TRUE(isNaN(bitCast<float>(1u << 31 | 0xffu << 23 | 0x400000u)));
     EXPECT_TRUE(isNaN(bitCast<float>(1u << 31 | 0xffu << 23 | 0x7fffffu)));
     EXPECT_FALSE(isNaN(0.0f));
     EXPECT_FALSE(isNaN(bitCast<float>(1u << 31 | 0xffu << 23)));
     EXPECT_FALSE(isNaN(bitCast<float>(0xffu << 23)));
 }

 // Test the correctness of gl::isInf function.
 TEST(MathUtilTest, isInf)
 {
     EXPECT_TRUE(isInf(bitCast<float>(0xffu << 23)));
     EXPECT_TRUE(isInf(bitCast<float>(1u << 31 | 0xffu << 23)));
     EXPECT_FALSE(isInf(0.0f));
     EXPECT_FALSE(isInf(bitCast<float>(0xffu << 23 | 1u)));
     EXPECT_FALSE(isInf(bitCast<float>(1u << 31 | 0xffu << 23 | 1u)));
     EXPECT_FALSE(isInf(bitCast<float>(1u << 31 | 0xffu << 23 | 0x400000u)));
     EXPECT_FALSE(isInf(bitCast<float>(1u << 31 | 0xffu << 23 | 0x7fffffu)));
     EXPECT_FALSE(isInf(bitCast<float>(0xfeu << 23 | 0x7fffffu)));
     EXPECT_FALSE(isInf(bitCast<float>(1u << 31 | 0xfeu << 23 | 0x7fffffu)));
 }

 TEST(MathUtilTest, CountLeadingZeros)
 {
     for (unsigned int i = 0; i < 32u; ++i)
     {
         uint32_t iLeadingZeros = 1u << (31u - i);
         EXPECT_EQ(i, CountLeadingZeros(iLeadingZeros));
     }
     EXPECT_EQ(32u, CountLeadingZeros(0));
 }

 // Some basic tests. Tests that rounding up zero produces zero.
 TEST(MathUtilTest, BasicRoundUp)
 {
     EXPECT_EQ(0u, rx::roundUp(0u, 4u));
     EXPECT_EQ(4u, rx::roundUp(1u, 4u));
     EXPECT_EQ(4u, rx::roundUp(4u, 4u));
 }

 // Test that rounding up zero produces zero for checked ints.
 TEST(MathUtilTest, CheckedRoundUpZero)
 {
     auto checkedValue = rx::CheckedRoundUp(0u, 4u);
     ASSERT_TRUE(checkedValue.IsValid());
     ASSERT_EQ(0u, checkedValue.ValueOrDie());
 }

 // Test out-of-bounds with CheckedRoundUp
 TEST(MathUtilTest, CheckedRoundUpInvalid)
 {
     // The answer to this query is out of bounds.
     auto limit        = std::numeric_limits<unsigned int>::max();
     auto checkedValue = rx::CheckedRoundUp(limit, limit - 1);
     ASSERT_FALSE(checkedValue.IsValid());

     // Our implementation can't handle this query, despite the parameters being in range.
     auto checkedLimit = rx::CheckedRoundUp(limit - 1, limit);
     ASSERT_FALSE(checkedLimit.IsValid());
 }

 // Test BitfieldReverse which reverses the order of the bits in an integer.
 TEST(MathUtilTest, BitfieldReverse)
 {
     EXPECT_EQ(0u, gl::BitfieldReverse(0u));
     EXPECT_EQ(0x80000000u, gl::BitfieldReverse(1u));
     EXPECT_EQ(0x1u, gl::BitfieldReverse(0x80000000u));
     uint32_t bits     = (1u << 4u) | (1u << 7u);
     uint32_t reversed = (1u << (31u - 4u)) | (1u << (31u - 7u));
     EXPECT_EQ(reversed, gl::BitfieldReverse(bits));
 }

 // Test BitCount, which counts 1 bits in an integer.
 TEST(MathUtilTest, BitCount)
 {
     EXPECT_EQ(0, gl::BitCount(0u));
     EXPECT_EQ(32, gl::BitCount(0xFFFFFFFFu));
     EXPECT_EQ(10, gl::BitCount(0x17103121u));

 #if defined(ANGLE_IS_64_BIT_CPU)
     EXPECT_EQ(0, gl::BitCount(static_cast<uint64_t>(0ull)));
     EXPECT_EQ(32, gl::BitCount(static_cast<uint64_t>(0xFFFFFFFFull)));
     EXPECT_EQ(10, gl::BitCount(static_cast<uint64_t>(0x17103121ull)));
 #endif  // defined(ANGLE_IS_64_BIT_CPU)
 }

 // Test ScanForward, which scans for the least significant 1 bit from a non-zero integer.
 TEST(MathUtilTest, ScanForward)
 {
     EXPECT_EQ(0ul, gl::ScanForward(1u));
     EXPECT_EQ(16ul, gl::ScanForward(0x80010000u));
     EXPECT_EQ(31ul, gl::ScanForward(0x80000000u));

 #if defined(ANGLE_IS_64_BIT_CPU)
     EXPECT_EQ(0ul, gl::ScanForward(static_cast<uint64_t>(1ull)));
     EXPECT_EQ(16ul, gl::ScanForward(static_cast<uint64_t>(0x80010000ull)));
     EXPECT_EQ(31ul, gl::ScanForward(static_cast<uint64_t>(0x80000000ull)));
 #endif  // defined(ANGLE_IS_64_BIT_CPU)
 }

 // Test ScanReverse, which scans for the most significant 1 bit from a non-zero integer.
 TEST(MathUtilTest, ScanReverse)
 {
     EXPECT_EQ(0ul, gl::ScanReverse(1ul));
     EXPECT_EQ(16ul, gl::ScanReverse(0x00010030ul));
     EXPECT_EQ(31ul, gl::ScanReverse(0x80000000ul));
 }

 // Test FindLSB, which finds the least significant 1 bit.
 TEST(MathUtilTest, FindLSB)
 {
     EXPECT_EQ(-1, gl::FindLSB(0u));
     EXPECT_EQ(0, gl::FindLSB(1u));
     EXPECT_EQ(16, gl::FindLSB(0x80010000u));
     EXPECT_EQ(31, gl::FindLSB(0x80000000u));
 }

 // Test FindMSB, which finds the most significant 1 bit.
 TEST(MathUtilTest, FindMSB)
 {
     EXPECT_EQ(-1, gl::FindMSB(0u));
     EXPECT_EQ(0, gl::FindMSB(1u));
     EXPECT_EQ(16, gl::FindMSB(0x00010030u));
     EXPECT_EQ(31, gl::FindMSB(0x80000000u));
 }

 // Test Ldexp, which combines mantissa and exponent into a floating-point number.
 TEST(MathUtilTest, Ldexp)
 {
     EXPECT_EQ(2.5f, Ldexp(0.625f, 2));
     EXPECT_EQ(-5.0f, Ldexp(-0.625f, 3));
     EXPECT_EQ(std::numeric_limits<float>::infinity(), Ldexp(0.625f, 129));
     EXPECT_EQ(0.0f, Ldexp(1.0f, -129));
 }

 // Test that Range::extend works as expected.
 TEST(MathUtilTest, RangeExtend)
 {
     RangeI range(0, 0);

     range.extend(5);
     EXPECT_EQ(0, range.low());
     EXPECT_EQ(6, range.high());
     EXPECT_EQ(6, range.length());

     range.extend(-1);
     EXPECT_EQ(-1, range.low());
     EXPECT_EQ(6, range.high());
     EXPECT_EQ(7, range.length());

     range.extend(10);
     EXPECT_EQ(-1, range.low());
     EXPECT_EQ(11, range.high());
     EXPECT_EQ(12, range.length());
 }

 // Test that Range iteration works as expected.
 TEST(MathUtilTest, RangeIteration)
 {
     RangeI range(0, 10);
     int expected = 0;
     for (int value : range)
     {
         EXPECT_EQ(expected, value);
         expected++;
     }
     EXPECT_EQ(range.length(), expected);
 }

 // Tests for float32 to float16 conversion
 TEST(MathUtilTest, Float32ToFloat16)
 {
     ASSERT_EQ(float32ToFloat16(0.0f), 0x0000);
     ASSERT_EQ(float32ToFloat16(-0.0f), 0x8000);

     float inf = std::numeric_limits<float>::infinity();

     ASSERT_EQ(float32ToFloat16(inf), 0x7C00);
     ASSERT_EQ(float32ToFloat16(-inf), 0xFC00);

     // Check that NaN is converted to a value in one of the float16 NaN ranges
     float nan      = std::numeric_limits<float>::quiet_NaN();
     uint16_t nan16 = float32ToFloat16(nan);
     ASSERT_TRUE(nan16 > 0xFC00 || (nan16 < 0x8000 && nan16 > 0x7C00));

     ASSERT_EQ(float32ToFloat16(1.0f), 0x3C00);
 }

 }  // anonymous namespace
	//
	// Copyright 2015 The ANGLE Project Authors. All rights reserved.
	// Use of this source code is governed by a BSD-style license that can be
	// found in the LICENSE file.
	//
	// mathutil_unittest:
	// Unit tests for the utils defined in mathutil.h
	//

	#include "mathutil.h"

	#include <gtest/gtest.h>

	using namespace gl;

	namespace
	{

	// Test the correctness of packSnorm2x16 and unpackSnorm2x16 functions.
	// For floats f1 and f2, unpackSnorm2x16(packSnorm2x16(f1, f2)) should be same as f1 and f2.
	TEST(MathUtilTest, packAndUnpackSnorm2x16)
	{
	const float input[8][2] = {
	{0.0f, 0.0f}, {1.0f, 1.0f}, {-1.0f, 1.0f}, {-1.0f, -1.0f},
	{0.875f, 0.75f}, {0.00392f, -0.99215f}, {-0.000675f, 0.004954f}, {-0.6937f, -0.02146f}};
	const float floatFaultTolerance = 0.0001f;
	float outputVal1, outputVal2;

	for (size_t i = 0; i < 8; i++)
	{
	unpackSnorm2x16(packSnorm2x16(input[i][0], input[i][1]), &outputVal1, &outputVal2);
	EXPECT_NEAR(input[i][0], outputVal1, floatFaultTolerance);
	EXPECT_NEAR(input[i][1], outputVal2, floatFaultTolerance);
	}
	}

	// Test the correctness of packSnorm2x16 and unpackSnorm2x16 functions with infinity values,
	// result should be clamped to [-1, 1].
	TEST(MathUtilTest, packAndUnpackSnorm2x16Infinity)
	{
	const float floatFaultTolerance = 0.0001f;
	float outputVal1, outputVal2;

	unpackSnorm2x16(packSnorm2x16(std::numeric_limits<float>::infinity(),
	std::numeric_limits<float>::infinity()),
	&outputVal1, &outputVal2);
	EXPECT_NEAR(1.0f, outputVal1, floatFaultTolerance);
	EXPECT_NEAR(1.0f, outputVal2, floatFaultTolerance);

	unpackSnorm2x16(packSnorm2x16(std::numeric_limits<float>::infinity(),
	-std::numeric_limits<float>::infinity()),
	&outputVal1, &outputVal2);
	EXPECT_NEAR(1.0f, outputVal1, floatFaultTolerance);
	EXPECT_NEAR(-1.0f, outputVal2, floatFaultTolerance);

	unpackSnorm2x16(packSnorm2x16(-std::numeric_limits<float>::infinity(),
	-std::numeric_limits<float>::infinity()),
	&outputVal1, &outputVal2);
	EXPECT_NEAR(-1.0f, outputVal1, floatFaultTolerance);
	EXPECT_NEAR(-1.0f, outputVal2, floatFaultTolerance);
	}

	// Test the correctness of packUnorm2x16 and unpackUnorm2x16 functions.
	// For floats f1 and f2, unpackUnorm2x16(packUnorm2x16(f1, f2)) should be same as f1 and f2.
	TEST(MathUtilTest, packAndUnpackUnorm2x16)
	{
	const float input[8][2] = {
	{0.0f, 0.0f}, {1.0f, 1.0f}, {-1.0f, 1.0f}, {-1.0f, -1.0f},
	{0.875f, 0.75f}, {0.00392f, -0.99215f}, {-0.000675f, 0.004954f}, {-0.6937f, -0.02146f}};
	const float floatFaultTolerance = 0.0001f;
	float outputVal1, outputVal2;

	for (size_t i = 0; i < 8; i++)
	{
	unpackUnorm2x16(packUnorm2x16(input[i][0], input[i][1]), &outputVal1, &outputVal2);
	float expected = input[i][0] < 0.0f ? 0.0f : input[i][0];
	EXPECT_NEAR(expected, outputVal1, floatFaultTolerance);
	expected = input[i][1] < 0.0f ? 0.0f : input[i][1];
	EXPECT_NEAR(expected, outputVal2, floatFaultTolerance);
	}
	}

	// Test the correctness of packUnorm2x16 and unpackUnorm2x16 functions with infinity values,
	// result should be clamped to [0, 1].
	TEST(MathUtilTest, packAndUnpackUnorm2x16Infinity)
	{
	const float floatFaultTolerance = 0.0001f;
	float outputVal1, outputVal2;

	unpackUnorm2x16(packUnorm2x16(std::numeric_limits<float>::infinity(),
	std::numeric_limits<float>::infinity()),
	&outputVal1, &outputVal2);
	EXPECT_NEAR(1.0f, outputVal1, floatFaultTolerance);
	EXPECT_NEAR(1.0f, outputVal2, floatFaultTolerance);

	unpackUnorm2x16(packUnorm2x16(std::numeric_limits<float>::infinity(),
	-std::numeric_limits<float>::infinity()),
	&outputVal1, &outputVal2);
	EXPECT_NEAR(1.0f, outputVal1, floatFaultTolerance);
	EXPECT_NEAR(0.0f, outputVal2, floatFaultTolerance);

	unpackUnorm2x16(packUnorm2x16(-std::numeric_limits<float>::infinity(),
	-std::numeric_limits<float>::infinity()),
	&outputVal1, &outputVal2);
	EXPECT_NEAR(0.0f, outputVal1, floatFaultTolerance);
	EXPECT_NEAR(0.0f, outputVal2, floatFaultTolerance);
	}

	// Test the correctness of packHalf2x16 and unpackHalf2x16 functions.
	// For floats f1 and f2, unpackHalf2x16(packHalf2x16(f1, f2)) should be same as f1 and f2.
	TEST(MathUtilTest, packAndUnpackHalf2x16)
	{
	const float input[8][2] = {
	{0.0f, 0.0f}, {1.0f, 1.0f}, {-1.0f, 1.0f}, {-1.0f, -1.0f},
	{0.875f, 0.75f}, {0.00392f, -0.99215f}, {-0.000675f, 0.004954f}, {-0.6937f, -0.02146f},
	};
	const float floatFaultTolerance = 0.0005f;
	float outputVal1, outputVal2;

	for (size_t i = 0; i < 8; i++)
	{
	unpackHalf2x16(packHalf2x16(input[i][0], input[i][1]), &outputVal1, &outputVal2);
	EXPECT_NEAR(input[i][0], outputVal1, floatFaultTolerance);
	EXPECT_NEAR(input[i][1], outputVal2, floatFaultTolerance);
	}
	}

	// Test the correctness of packUnorm4x8 and unpackUnorm4x8 functions.
	// For floats f1 to f4, unpackUnorm4x8(packUnorm4x8(f1, f2, f3, f4)) should be same as f1 to f4.
	TEST(MathUtilTest, packAndUnpackUnorm4x8)
	{
	const float input[5][4] = {{0.0f, 0.0f, 0.0f, 0.0f},
	{1.0f, 1.0f, 1.0f, 1.0f},
	{-1.0f, 1.0f, -1.0f, 1.0f},
	{-1.0f, -1.0f, -1.0f, -1.0f},
	{64.0f / 255.0f, 128.0f / 255.0f, 32.0f / 255.0f, 16.0f / 255.0f}};

	const float floatFaultTolerance = 0.005f;
	float outputVals[4];

	for (size_t i = 0; i < 5; i++)
	{
	UnpackUnorm4x8(PackUnorm4x8(input[i][0], input[i][1], input[i][2], input[i][3]),
	outputVals);
	for (size_t j = 0; j < 4; j++)
	{
	float expected = input[i][j] < 0.0f ? 0.0f : input[i][j];
	EXPECT_NEAR(expected, outputVals[j], floatFaultTolerance);
	}
	}
	}

	// Test the correctness of packSnorm4x8 and unpackSnorm4x8 functions.
	// For floats f1 to f4, unpackSnorm4x8(packSnorm4x8(f1, f2, f3, f4)) should be same as f1 to f4.
	TEST(MathUtilTest, packAndUnpackSnorm4x8)
	{
	const float input[5][4] = {{0.0f, 0.0f, 0.0f, 0.0f},
	{1.0f, 1.0f, 1.0f, 1.0f},
	{-1.0f, 1.0f, -1.0f, 1.0f},
	{-1.0f, -1.0f, -1.0f, -1.0f},
	{64.0f / 127.0f, -8.0f / 127.0f, 32.0f / 127.0f, 16.0f / 127.0f}};

	const float floatFaultTolerance = 0.01f;
	float outputVals[4];

	for (size_t i = 0; i < 5; i++)
	{
	UnpackSnorm4x8(PackSnorm4x8(input[i][0], input[i][1], input[i][2], input[i][3]),
	outputVals);
	for (size_t j = 0; j < 4; j++)
	{
	float expected = input[i][j];
	EXPECT_NEAR(expected, outputVals[j], floatFaultTolerance);
	}
	}
	}

	// Test the correctness of gl::isNaN function.
	TEST(MathUtilTest, isNaN)
	{
	EXPECT_TRUE(isNaN(bitCast<float>(0xffu << 23 \| 1u)));
	EXPECT_TRUE(isNaN(bitCast<float>(1u << 31 \| 0xffu << 23 \| 1u)));
	EXPECT_TRUE(isNaN(bitCast<float>(1u << 31 \| 0xffu << 23 \| 0x400000u)));
	EXPECT_TRUE(isNaN(bitCast<float>(1u << 31 \| 0xffu << 23 \| 0x7fffffu)));
	EXPECT_FALSE(isNaN(0.0f));
	EXPECT_FALSE(isNaN(bitCast<float>(1u << 31 \| 0xffu << 23)));
	EXPECT_FALSE(isNaN(bitCast<float>(0xffu << 23)));
	}

	// Test the correctness of gl::isInf function.
	TEST(MathUtilTest, isInf)
	{
	EXPECT_TRUE(isInf(bitCast<float>(0xffu << 23)));
	EXPECT_TRUE(isInf(bitCast<float>(1u << 31 \| 0xffu << 23)));
	EXPECT_FALSE(isInf(0.0f));
	EXPECT_FALSE(isInf(bitCast<float>(0xffu << 23 \| 1u)));
	EXPECT_FALSE(isInf(bitCast<float>(1u << 31 \| 0xffu << 23 \| 1u)));
	EXPECT_FALSE(isInf(bitCast<float>(1u << 31 \| 0xffu << 23 \| 0x400000u)));
	EXPECT_FALSE(isInf(bitCast<float>(1u << 31 \| 0xffu << 23 \| 0x7fffffu)));
	EXPECT_FALSE(isInf(bitCast<float>(0xfeu << 23 \| 0x7fffffu)));
	EXPECT_FALSE(isInf(bitCast<float>(1u << 31 \| 0xfeu << 23 \| 0x7fffffu)));
	}

	TEST(MathUtilTest, CountLeadingZeros)
	{
	for (unsigned int i = 0; i < 32u; ++i)
	{
	uint32_t iLeadingZeros = 1u << (31u - i);
	EXPECT_EQ(i, CountLeadingZeros(iLeadingZeros));
	}
	EXPECT_EQ(32u, CountLeadingZeros(0));
	}

	// Some basic tests. Tests that rounding up zero produces zero.
	TEST(MathUtilTest, BasicRoundUp)
	{
	EXPECT_EQ(0u, rx::roundUp(0u, 4u));
	EXPECT_EQ(4u, rx::roundUp(1u, 4u));
	EXPECT_EQ(4u, rx::roundUp(4u, 4u));
	}

	// Test that rounding up zero produces zero for checked ints.
	TEST(MathUtilTest, CheckedRoundUpZero)
	{
	auto checkedValue = rx::CheckedRoundUp(0u, 4u);
	ASSERT_TRUE(checkedValue.IsValid());
	ASSERT_EQ(0u, checkedValue.ValueOrDie());
	}

	// Test out-of-bounds with CheckedRoundUp
	TEST(MathUtilTest, CheckedRoundUpInvalid)
	{
	// The answer to this query is out of bounds.
	auto limit = std::numeric_limits<unsigned int>::max();
	auto checkedValue = rx::CheckedRoundUp(limit, limit - 1);
	ASSERT_FALSE(checkedValue.IsValid());

	// Our implementation can't handle this query, despite the parameters being in range.
	auto checkedLimit = rx::CheckedRoundUp(limit - 1, limit);
	ASSERT_FALSE(checkedLimit.IsValid());
	}

	// Test BitfieldReverse which reverses the order of the bits in an integer.
	TEST(MathUtilTest, BitfieldReverse)
	{
	EXPECT_EQ(0u, gl::BitfieldReverse(0u));
	EXPECT_EQ(0x80000000u, gl::BitfieldReverse(1u));
	EXPECT_EQ(0x1u, gl::BitfieldReverse(0x80000000u));
	uint32_t bits = (1u << 4u) \| (1u << 7u);
	uint32_t reversed = (1u << (31u - 4u)) \| (1u << (31u - 7u));
	EXPECT_EQ(reversed, gl::BitfieldReverse(bits));
	}

	// Test BitCount, which counts 1 bits in an integer.
	TEST(MathUtilTest, BitCount)
	{
	EXPECT_EQ(0, gl::BitCount(0u));
	EXPECT_EQ(32, gl::BitCount(0xFFFFFFFFu));
	EXPECT_EQ(10, gl::BitCount(0x17103121u));

	#if defined(ANGLE_IS_64_BIT_CPU)
	EXPECT_EQ(0, gl::BitCount(static_cast<uint64_t>(0ull)));
	EXPECT_EQ(32, gl::BitCount(static_cast<uint64_t>(0xFFFFFFFFull)));
	EXPECT_EQ(10, gl::BitCount(static_cast<uint64_t>(0x17103121ull)));
	#endif // defined(ANGLE_IS_64_BIT_CPU)
	}

	// Test ScanForward, which scans for the least significant 1 bit from a non-zero integer.
	TEST(MathUtilTest, ScanForward)
	{
	EXPECT_EQ(0ul, gl::ScanForward(1u));
	EXPECT_EQ(16ul, gl::ScanForward(0x80010000u));
	EXPECT_EQ(31ul, gl::ScanForward(0x80000000u));

	#if defined(ANGLE_IS_64_BIT_CPU)
	EXPECT_EQ(0ul, gl::ScanForward(static_cast<uint64_t>(1ull)));
	EXPECT_EQ(16ul, gl::ScanForward(static_cast<uint64_t>(0x80010000ull)));
	EXPECT_EQ(31ul, gl::ScanForward(static_cast<uint64_t>(0x80000000ull)));
	#endif // defined(ANGLE_IS_64_BIT_CPU)
	}

	// Test ScanReverse, which scans for the most significant 1 bit from a non-zero integer.
	TEST(MathUtilTest, ScanReverse)
	{
	EXPECT_EQ(0ul, gl::ScanReverse(1ul));
	EXPECT_EQ(16ul, gl::ScanReverse(0x00010030ul));
	EXPECT_EQ(31ul, gl::ScanReverse(0x80000000ul));
	}

	// Test FindLSB, which finds the least significant 1 bit.
	TEST(MathUtilTest, FindLSB)
	{
	EXPECT_EQ(-1, gl::FindLSB(0u));
	EXPECT_EQ(0, gl::FindLSB(1u));
	EXPECT_EQ(16, gl::FindLSB(0x80010000u));
	EXPECT_EQ(31, gl::FindLSB(0x80000000u));
	}

	// Test FindMSB, which finds the most significant 1 bit.
	TEST(MathUtilTest, FindMSB)
	{
	EXPECT_EQ(-1, gl::FindMSB(0u));
	EXPECT_EQ(0, gl::FindMSB(1u));
	EXPECT_EQ(16, gl::FindMSB(0x00010030u));
	EXPECT_EQ(31, gl::FindMSB(0x80000000u));
	}

	// Test Ldexp, which combines mantissa and exponent into a floating-point number.
	TEST(MathUtilTest, Ldexp)
	{
	EXPECT_EQ(2.5f, Ldexp(0.625f, 2));
	EXPECT_EQ(-5.0f, Ldexp(-0.625f, 3));
	EXPECT_EQ(std::numeric_limits<float>::infinity(), Ldexp(0.625f, 129));
	EXPECT_EQ(0.0f, Ldexp(1.0f, -129));
	}

	// Test that Range::extend works as expected.
	TEST(MathUtilTest, RangeExtend)
	{
	RangeI range(0, 0);

	range.extend(5);
	EXPECT_EQ(0, range.low());
	EXPECT_EQ(6, range.high());
	EXPECT_EQ(6, range.length());

	range.extend(-1);
	EXPECT_EQ(-1, range.low());
	EXPECT_EQ(6, range.high());
	EXPECT_EQ(7, range.length());

	range.extend(10);
	EXPECT_EQ(-1, range.low());
	EXPECT_EQ(11, range.high());
	EXPECT_EQ(12, range.length());
	}

	// Test that Range iteration works as expected.
	TEST(MathUtilTest, RangeIteration)
	{
	RangeI range(0, 10);
	int expected = 0;
	for (int value : range)
	{
	EXPECT_EQ(expected, value);
	expected++;
	}
	EXPECT_EQ(range.length(), expected);
	}

	// Tests for float32 to float16 conversion
	TEST(MathUtilTest, Float32ToFloat16)
	{
	ASSERT_EQ(float32ToFloat16(0.0f), 0x0000);
	ASSERT_EQ(float32ToFloat16(-0.0f), 0x8000);

	float inf = std::numeric_limits<float>::infinity();

	ASSERT_EQ(float32ToFloat16(inf), 0x7C00);
	ASSERT_EQ(float32ToFloat16(-inf), 0xFC00);

	// Check that NaN is converted to a value in one of the float16 NaN ranges
	float nan = std::numeric_limits<float>::quiet_NaN();
	uint16_t nan16 = float32ToFloat16(nan);
	ASSERT_TRUE(nan16 > 0xFC00 \|\| (nan16 < 0x8000 && nan16 > 0x7C00));

	ASSERT_EQ(float32ToFloat16(1.0f), 0x3C00);
	}

	} // anonymous namespace