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//
// Copyright 2002 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.h: Math and bit manipulation functions.
#ifndef COMMON_MATHUTIL_H_
#define COMMON_MATHUTIL_H_
#include <math.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <algorithm>
#include <limits>
#include <anglebase/numerics/safe_math.h>
#include "common/debug.h"
#include "common/platform.h"
namespace angle
{
using base::CheckedNumeric;
using base::IsValueInRangeForNumericType;
} // namespace angle
namespace gl
{
const unsigned int Float32One = 0x3F800000;
const unsigned short Float16One = 0x3C00;
template <typename T>
inline constexpr bool isPow2(T x)
{
static_assert(std::is_integral<T>::value, "isPow2 must be called on an integer type.");
return (x & (x - 1)) == 0 && (x != 0);
}
template <typename T>
inline int log2(T x)
{
static_assert(std::is_integral<T>::value, "log2 must be called on an integer type.");
int r = 0;
while ((x >> r) > 1)
r++;
return r;
}
inline unsigned int ceilPow2(unsigned int x)
{
if (x != 0)
x--;
x |= x >> 1;
x |= x >> 2;
x |= x >> 4;
x |= x >> 8;
x |= x >> 16;
x++;
return x;
}
template <typename DestT, typename SrcT>
inline DestT clampCast(SrcT value)
{
// For floating-point types with denormalization, min returns the minimum positive normalized
// value. To find the value that has no values less than it, use numeric_limits::lowest.
constexpr const long double destLo =
static_cast<long double>(std::numeric_limits<DestT>::lowest());
constexpr const long double destHi =
static_cast<long double>(std::numeric_limits<DestT>::max());
constexpr const long double srcLo =
static_cast<long double>(std::numeric_limits<SrcT>::lowest());
constexpr long double srcHi = static_cast<long double>(std::numeric_limits<SrcT>::max());
if (destHi < srcHi)
{
DestT destMax = std::numeric_limits<DestT>::max();
if (value >= static_cast<SrcT>(destMax))
{
return destMax;
}
}
if (destLo > srcLo)
{
DestT destLow = std::numeric_limits<DestT>::lowest();
if (value <= static_cast<SrcT>(destLow))
{
return destLow;
}
}
return static_cast<DestT>(value);
}
// Specialize clampCast for bool->int conversion to avoid MSVS 2015 performance warning when the max
// value is casted to the source type.
template <>
inline unsigned int clampCast(bool value)
{
return static_cast<unsigned int>(value);
}
template <>
inline int clampCast(bool value)
{
return static_cast<int>(value);
}
template <typename T, typename MIN, typename MAX>
inline T clamp(T x, MIN min, MAX max)
{
// Since NaNs fail all comparison tests, a NaN value will default to min
return x > min ? (x > max ? max : x) : min;
}
template <typename T>
T clampForBitCount(T value, size_t bitCount)
{
static_assert(std::numeric_limits<T>::is_integer, "T must be an integer.");
if (bitCount == 0)
{
constexpr T kZero = 0;
return kZero;
}
ASSERT(bitCount <= sizeof(T) * 8);
constexpr bool kIsSigned = std::numeric_limits<T>::is_signed;
ASSERT((bitCount > 1) || !kIsSigned);
T min = 0;
T max = 0;
if (bitCount == sizeof(T) * 8)
{
min = std::numeric_limits<T>::min();
max = std::numeric_limits<T>::max();
}
else
{
constexpr T kOne = 1;
min = (kIsSigned) ? -1 * (kOne << (bitCount - 1)) : 0;
max = (kIsSigned) ? (kOne << (bitCount - 1)) - 1 : (kOne << bitCount) - 1;
}
return gl::clamp(value, min, max);
}
inline float clamp01(float x)
{
return clamp(x, 0.0f, 1.0f);
}
template <const int n>
inline unsigned int unorm(float x)
{
const unsigned int max = 0xFFFFFFFF >> (32 - n);
if (x > 1)
{
return max;
}
else if (x < 0)
{
return 0;
}
else
{
return (unsigned int)(max * x + 0.5f);
}
}
inline bool supportsSSE2()
{
#if defined(ANGLE_USE_SSE)
static bool checked = false;
static bool supports = false;
if (checked)
{
return supports;
}
# if defined(ANGLE_PLATFORM_WINDOWS) && !defined(_M_ARM) && !defined(_M_ARM64)
{
int info[4];
__cpuid(info, 0);
if (info[0] >= 1)
{
__cpuid(info, 1);
supports = (info[3] >> 26) & 1;
}
}
# endif // defined(ANGLE_PLATFORM_WINDOWS) && !defined(_M_ARM) && !defined(_M_ARM64)
checked = true;
return supports;
#else // defined(ANGLE_USE_SSE)
return false;
#endif
}
template <typename destType, typename sourceType>
destType bitCast(const sourceType &source)
{
size_t copySize = std::min(sizeof(destType), sizeof(sourceType));
destType output;
memcpy(&output, &source, copySize);
return output;
}
template <typename T>
static constexpr double normalize(T value)
{
return value < 0 ? -static_cast<double>(value) / std::numeric_limits<T>::min()
: static_cast<double>(value) / std::numeric_limits<T>::max();
}
inline unsigned short float32ToFloat16(float fp32)
{
unsigned int fp32i = bitCast<unsigned int>(fp32);
unsigned int sign = (fp32i & 0x80000000) >> 16;
unsigned int abs = fp32i & 0x7FFFFFFF;
if (abs > 0x7F800000)
{ // NaN
return 0x7FFF;
}
else if (abs > 0x47FFEFFF)
{ // Infinity
return static_cast<uint16_t>(sign | 0x7C00);
}
else if (abs < 0x38800000) // Denormal
{
unsigned int mantissa = (abs & 0x007FFFFF) | 0x00800000;
int e = 113 - (abs >> 23);
if (e < 24)
{
abs = mantissa >> e;
}
else
{
abs = 0;
}
return static_cast<unsigned short>(sign | (abs + 0x00000FFF + ((abs >> 13) & 1)) >> 13);
}
else
{
return static_cast<unsigned short>(
sign | (abs + 0xC8000000 + 0x00000FFF + ((abs >> 13) & 1)) >> 13);
}
}
float float16ToFloat32(unsigned short h);
unsigned int convertRGBFloatsTo999E5(float red, float green, float blue);
void convert999E5toRGBFloats(unsigned int input, float *red, float *green, float *blue);
inline unsigned short float32ToFloat11(float fp32)
{
const unsigned int float32MantissaMask = 0x7FFFFF;
const unsigned int float32ExponentMask = 0x7F800000;
const unsigned int float32SignMask = 0x80000000;
const unsigned int float32ValueMask = ~float32SignMask;
const unsigned int float32ExponentFirstBit = 23;
const unsigned int float32ExponentBias = 127;
const unsigned short float11Max = 0x7BF;
const unsigned short float11MantissaMask = 0x3F;
const unsigned short float11ExponentMask = 0x7C0;
const unsigned short float11BitMask = 0x7FF;
const unsigned int float11ExponentBias = 14;
const unsigned int float32Maxfloat11 = 0x477E0000;
const unsigned int float32MinNormfloat11 = 0x38800000;
const unsigned int float32MinDenormfloat11 = 0x35000080;
const unsigned int float32Bits = bitCast<unsigned int>(fp32);
const bool float32Sign = (float32Bits & float32SignMask) == float32SignMask;
unsigned int float32Val = float32Bits & float32ValueMask;
if ((float32Val & float32ExponentMask) == float32ExponentMask)
{
// INF or NAN
if ((float32Val & float32MantissaMask) != 0)
{
return float11ExponentMask |
(((float32Val >> 17) | (float32Val >> 11) | (float32Val >> 6) | (float32Val)) &
float11MantissaMask);
}
else if (float32Sign)
{
// -INF is clamped to 0 since float11 is positive only
return 0;
}
else
{
return float11ExponentMask;
}
}
else if (float32Sign)
{
// float11 is positive only, so clamp to zero
return 0;
}
else if (float32Val > float32Maxfloat11)
{
// The number is too large to be represented as a float11, set to max
return float11Max;
}
else if (float32Val < float32MinDenormfloat11)
{
// The number is too small to be represented as a denormalized float11, set to 0
return 0;
}
else
{
if (float32Val < float32MinNormfloat11)
{
// The number is too small to be represented as a normalized float11
// Convert it to a denormalized value.
const unsigned int shift = (float32ExponentBias - float11ExponentBias) -
(float32Val >> float32ExponentFirstBit);
ASSERT(shift < 32);
float32Val =
((1 << float32ExponentFirstBit) | (float32Val & float32MantissaMask)) >> shift;
}
else
{
// Rebias the exponent to represent the value as a normalized float11
float32Val += 0xC8000000;
}
return ((float32Val + 0xFFFF + ((float32Val >> 17) & 1)) >> 17) & float11BitMask;
}
}
inline unsigned short float32ToFloat10(float fp32)
{
const unsigned int float32MantissaMask = 0x7FFFFF;
const unsigned int float32ExponentMask = 0x7F800000;
const unsigned int float32SignMask = 0x80000000;
const unsigned int float32ValueMask = ~float32SignMask;
const unsigned int float32ExponentFirstBit = 23;
const unsigned int float32ExponentBias = 127;
const unsigned short float10Max = 0x3DF;
const unsigned short float10MantissaMask = 0x1F;
const unsigned short float10ExponentMask = 0x3E0;
const unsigned short float10BitMask = 0x3FF;
const unsigned int float10ExponentBias = 14;
const unsigned int float32Maxfloat10 = 0x477C0000;
const unsigned int float32MinNormfloat10 = 0x38800000;
const unsigned int float32MinDenormfloat10 = 0x35800040;
const unsigned int float32Bits = bitCast<unsigned int>(fp32);
const bool float32Sign = (float32Bits & float32SignMask) == float32SignMask;
unsigned int float32Val = float32Bits & float32ValueMask;
if ((float32Val & float32ExponentMask) == float32ExponentMask)
{
// INF or NAN
if ((float32Val & float32MantissaMask) != 0)
{
return float10ExponentMask |
(((float32Val >> 18) | (float32Val >> 13) | (float32Val >> 3) | (float32Val)) &
float10MantissaMask);
}
else if (float32Sign)
{
// -INF is clamped to 0 since float10 is positive only
return 0;
}
else
{
return float10ExponentMask;
}
}
else if (float32Sign)
{
// float10 is positive only, so clamp to zero
return 0;
}
else if (float32Val > float32Maxfloat10)
{
// The number is too large to be represented as a float10, set to max
return float10Max;
}
else if (float32Val < float32MinDenormfloat10)
{
// The number is too small to be represented as a denormalized float10, set to 0
return 0;
}
else
{
if (float32Val < float32MinNormfloat10)
{
// The number is too small to be represented as a normalized float10
// Convert it to a denormalized value.
const unsigned int shift = (float32ExponentBias - float10ExponentBias) -
(float32Val >> float32ExponentFirstBit);
ASSERT(shift < 32);
float32Val =
((1 << float32ExponentFirstBit) | (float32Val & float32MantissaMask)) >> shift;
}
else
{
// Rebias the exponent to represent the value as a normalized float10
float32Val += 0xC8000000;
}
return ((float32Val + 0x1FFFF + ((float32Val >> 18) & 1)) >> 18) & float10BitMask;
}
}
inline float float11ToFloat32(unsigned short fp11)
{
unsigned short exponent = (fp11 >> 6) & 0x1F;
unsigned short mantissa = fp11 & 0x3F;
if (exponent == 0x1F)
{
// INF or NAN
return bitCast<float>(0x7f800000 | (mantissa << 17));
}
else
{
if (exponent != 0)
{
// normalized
}
else if (mantissa != 0)
{
// The value is denormalized
exponent = 1;
do
{
exponent--;
mantissa <<= 1;
} while ((mantissa & 0x40) == 0);
mantissa = mantissa & 0x3F;
}
else // The value is zero
{
exponent = static_cast<unsigned short>(-112);
}
return bitCast<float>(((exponent + 112) << 23) | (mantissa << 17));
}
}
inline float float10ToFloat32(unsigned short fp10)
{
unsigned short exponent = (fp10 >> 5) & 0x1F;
unsigned short mantissa = fp10 & 0x1F;
if (exponent == 0x1F)
{
// INF or NAN
return bitCast<float>(0x7f800000 | (mantissa << 17));
}
else
{
if (exponent != 0)
{
// normalized
}
else if (mantissa != 0)
{
// The value is denormalized
exponent = 1;
do
{
exponent--;
mantissa <<= 1;
} while ((mantissa & 0x20) == 0);
mantissa = mantissa & 0x1F;
}
else // The value is zero
{
exponent = static_cast<unsigned short>(-112);
}
return bitCast<float>(((exponent + 112) << 23) | (mantissa << 18));
}
}
// Converts to and from float and 16.16 fixed point format.
inline float ConvertFixedToFloat(int32_t fixedInput)
{
return static_cast<float>(fixedInput) / 65536.0f;
}
inline uint32_t ConvertFloatToFixed(float floatInput)
{
static constexpr uint32_t kHighest = 32767 * 65536 + 65535;
static constexpr uint32_t kLowest = static_cast<uint32_t>(-32768 * 65536 + 65535);
if (floatInput > 32767.65535)
{
return kHighest;
}
else if (floatInput < -32768.65535)
{
return kLowest;
}
else
{
return static_cast<uint32_t>(floatInput * 65536);
}
}
template <typename T>
inline float normalizedToFloat(T input)
{
static_assert(std::numeric_limits<T>::is_integer, "T must be an integer.");
if (sizeof(T) > 2)
{
// float has only a 23 bit mantissa, so we need to do the calculation in double precision
constexpr double inverseMax = 1.0 / std::numeric_limits<T>::max();
return static_cast<float>(input * inverseMax);
}
else
{
constexpr float inverseMax = 1.0f / std::numeric_limits<T>::max();
return input * inverseMax;
}
}
template <unsigned int inputBitCount, typename T>
inline float normalizedToFloat(T input)
{
static_assert(std::numeric_limits<T>::is_integer, "T must be an integer.");
static_assert(inputBitCount < (sizeof(T) * 8), "T must have more bits than inputBitCount.");
ASSERT((input & ~((1 << inputBitCount) - 1)) == 0);
if (inputBitCount > 23)
{
// float has only a 23 bit mantissa, so we need to do the calculation in double precision
constexpr double inverseMax = 1.0 / ((1 << inputBitCount) - 1);
return static_cast<float>(input * inverseMax);
}
else
{
constexpr float inverseMax = 1.0f / ((1 << inputBitCount) - 1);
return input * inverseMax;
}
}
template <typename T>
inline T floatToNormalized(float input)
{
if constexpr (sizeof(T) > 2)
{
// float has only a 23 bit mantissa, so we need to do the calculation in double precision
return static_cast<T>(std::numeric_limits<T>::max() * static_cast<double>(input) + 0.5);
}
else
{
return static_cast<T>(std::numeric_limits<T>::max() * input + 0.5f);
}
}
template <unsigned int outputBitCount, typename T>
inline T floatToNormalized(float input)
{
static_assert(outputBitCount < (sizeof(T) * 8), "T must have more bits than outputBitCount.");
if (outputBitCount > 23)
{
// float has only a 23 bit mantissa, so we need to do the calculation in double precision
return static_cast<T>(((1 << outputBitCount) - 1) * static_cast<double>(input) + 0.5);
}
else
{
return static_cast<T>(((1 << outputBitCount) - 1) * input + 0.5f);
}
}
template <unsigned int inputBitCount, unsigned int inputBitStart, typename T>
inline T getShiftedData(T input)
{
static_assert(inputBitCount + inputBitStart <= (sizeof(T) * 8),
"T must have at least as many bits as inputBitCount + inputBitStart.");
const T mask = (1 << inputBitCount) - 1;
return (input >> inputBitStart) & mask;
}
template <unsigned int inputBitCount, unsigned int inputBitStart, typename T>
inline T shiftData(T input)
{
static_assert(inputBitCount + inputBitStart <= (sizeof(T) * 8),
"T must have at least as many bits as inputBitCount + inputBitStart.");
const T mask = (1 << inputBitCount) - 1;
return (input & mask) << inputBitStart;
}
inline unsigned int CountLeadingZeros(uint32_t x)
{
// Use binary search to find the amount of leading zeros.
unsigned int zeros = 32u;
uint32_t y;
y = x >> 16u;
if (y != 0)
{
zeros = zeros - 16u;
x = y;
}
y = x >> 8u;
if (y != 0)
{
zeros = zeros - 8u;
x = y;
}
y = x >> 4u;
if (y != 0)
{
zeros = zeros - 4u;
x = y;
}
y = x >> 2u;
if (y != 0)
{
zeros = zeros - 2u;
x = y;
}
y = x >> 1u;
if (y != 0)
{
return zeros - 2u;
}
return zeros - x;
}
inline unsigned char average(unsigned char a, unsigned char b)
{
return ((a ^ b) >> 1) + (a & b);
}
inline signed char average(signed char a, signed char b)
{
return ((short)a + (short)b) / 2;
}
inline unsigned short average(unsigned short a, unsigned short b)
{
return ((a ^ b) >> 1) + (a & b);
}
inline signed short average(signed short a, signed short b)
{
return ((int)a + (int)b) / 2;
}
inline unsigned int average(unsigned int a, unsigned int b)
{
return ((a ^ b) >> 1) + (a & b);
}
inline int average(int a, int b)
{
long long average = (static_cast<long long>(a) + static_cast<long long>(b)) / 2LL;
return static_cast<int>(average);
}
inline float average(float a, float b)
{
return (a + b) * 0.5f;
}
inline unsigned short averageHalfFloat(unsigned short a, unsigned short b)
{
return float32ToFloat16((float16ToFloat32(a) + float16ToFloat32(b)) * 0.5f);
}
inline unsigned int averageFloat11(unsigned int a, unsigned int b)
{
return float32ToFloat11((float11ToFloat32(static_cast<unsigned short>(a)) +
float11ToFloat32(static_cast<unsigned short>(b))) *
0.5f);
}
inline unsigned int averageFloat10(unsigned int a, unsigned int b)
{
return float32ToFloat10((float10ToFloat32(static_cast<unsigned short>(a)) +
float10ToFloat32(static_cast<unsigned short>(b))) *
0.5f);
}
template <typename T>
class Range
{
public:
Range() {}
Range(T lo, T hi) : mLow(lo), mHigh(hi) {}
T length() const { return (empty() ? 0 : (mHigh - mLow)); }
bool intersects(Range<T> other)
{
if (mLow <= other.mLow)
{
return other.mLow < mHigh;
}
else
{
return mLow < other.mHigh;
}
}
// Assumes that end is non-inclusive.. for example, extending to 5 will make "end" 6.
void extend(T value)
{
mLow = value < mLow ? value : mLow;
mHigh = value >= mHigh ? (value + 1) : mHigh;
}
bool empty() const { return mHigh <= mLow; }
bool contains(T value) const { return value >= mLow && value < mHigh; }
class Iterator final
{
public:
Iterator(T value) : mCurrent(value) {}
Iterator &operator++()
{
mCurrent++;
return *this;
}
bool operator==(const Iterator &other) const { return mCurrent == other.mCurrent; }
bool operator!=(const Iterator &other) const { return mCurrent != other.mCurrent; }
T operator*() const { return mCurrent; }
private:
T mCurrent;
};
Iterator begin() const { return Iterator(mLow); }
Iterator end() const { return Iterator(mHigh); }
T low() const { return mLow; }
T high() const { return mHigh; }
void invalidate()
{
mLow = std::numeric_limits<T>::max();
mHigh = std::numeric_limits<T>::min();
}
private:
T mLow;
T mHigh;
};
typedef Range<int> RangeI;
typedef Range<unsigned int> RangeUI;
struct IndexRange
{
struct Undefined
{};
IndexRange(Undefined) {}
IndexRange() : IndexRange(0, 0, 0) {}
IndexRange(size_t start_, size_t end_, size_t vertexIndexCount_)
: start(start_), end(end_), vertexIndexCount(vertexIndexCount_)
{
ASSERT(start <= end);
}
// Number of vertices in the range.
size_t vertexCount() const { return (end - start) + 1; }
// Inclusive range of indices that are not primitive restart
size_t start;
size_t end;
// Number of non-primitive restart indices
size_t vertexIndexCount;
};
// Combine a floating-point value representing a mantissa (x) and an integer exponent (exp) into a
// floating-point value. As in GLSL ldexp() built-in.
inline float Ldexp(float x, int exp)
{
if (exp > 128)
{
return std::numeric_limits<float>::infinity();
}
if (exp < -126)
{
return 0.0f;
}
double result = static_cast<double>(x) * std::pow(2.0, static_cast<double>(exp));
return static_cast<float>(result);
}
// First, both normalized floating-point values are converted into 16-bit integer values.
// Then, the results are packed into the returned 32-bit unsigned integer.
// The first float value will be written to the least significant bits of the output;
// the last float value will be written to the most significant bits.
// The conversion of each value to fixed point is done as follows :
// packSnorm2x16 : round(clamp(c, -1, +1) * 32767.0)
inline uint32_t packSnorm2x16(float f1, float f2)
{
int16_t leastSignificantBits = static_cast<int16_t>(roundf(clamp(f1, -1.0f, 1.0f) * 32767.0f));
int16_t mostSignificantBits = static_cast<int16_t>(roundf(clamp(f2, -1.0f, 1.0f) * 32767.0f));
return static_cast<uint32_t>(mostSignificantBits) << 16 |
(static_cast<uint32_t>(leastSignificantBits) & 0xFFFF);
}
// First, unpacks a single 32-bit unsigned integer u into a pair of 16-bit unsigned integers. Then,
// each component is converted to a normalized floating-point value to generate the returned two
// float values. The first float value will be extracted from the least significant bits of the
// input; the last float value will be extracted from the most-significant bits. The conversion for
// unpacked fixed-point value to floating point is done as follows: unpackSnorm2x16 : clamp(f /
// 32767.0, -1, +1)
inline void unpackSnorm2x16(uint32_t u, float *f1, float *f2)
{
int16_t leastSignificantBits = static_cast<int16_t>(u & 0xFFFF);
int16_t mostSignificantBits = static_cast<int16_t>(u >> 16);
*f1 = clamp(static_cast<float>(leastSignificantBits) / 32767.0f, -1.0f, 1.0f);
*f2 = clamp(static_cast<float>(mostSignificantBits) / 32767.0f, -1.0f, 1.0f);
}
// First, both normalized floating-point values are converted into 16-bit integer values.
// Then, the results are packed into the returned 32-bit unsigned integer.
// The first float value will be written to the least significant bits of the output;
// the last float value will be written to the most significant bits.
// The conversion of each value to fixed point is done as follows:
// packUnorm2x16 : round(clamp(c, 0, +1) * 65535.0)
inline uint32_t packUnorm2x16(float f1, float f2)
{
uint16_t leastSignificantBits = static_cast<uint16_t>(roundf(clamp(f1, 0.0f, 1.0f) * 65535.0f));
uint16_t mostSignificantBits = static_cast<uint16_t>(roundf(clamp(f2, 0.0f, 1.0f) * 65535.0f));
return static_cast<uint32_t>(mostSignificantBits) << 16 |
static_cast<uint32_t>(leastSignificantBits);
}
// First, unpacks a single 32-bit unsigned integer u into a pair of 16-bit unsigned integers. Then,
// each component is converted to a normalized floating-point value to generate the returned two
// float values. The first float value will be extracted from the least significant bits of the
// input; the last float value will be extracted from the most-significant bits. The conversion for
// unpacked fixed-point value to floating point is done as follows: unpackUnorm2x16 : f / 65535.0
inline void unpackUnorm2x16(uint32_t u, float *f1, float *f2)
{
uint16_t leastSignificantBits = static_cast<uint16_t>(u & 0xFFFF);
uint16_t mostSignificantBits = static_cast<uint16_t>(u >> 16);
*f1 = static_cast<float>(leastSignificantBits) / 65535.0f;
*f2 = static_cast<float>(mostSignificantBits) / 65535.0f;
}
// Helper functions intended to be used only here.
namespace priv
{
inline uint8_t ToPackedUnorm8(float f)
{
return static_cast<uint8_t>(roundf(clamp(f, 0.0f, 1.0f) * 255.0f));
}
inline int8_t ToPackedSnorm8(float f)
{
return static_cast<int8_t>(roundf(clamp(f, -1.0f, 1.0f) * 127.0f));
}
} // namespace priv
// Packs 4 normalized unsigned floating-point values to a single 32-bit unsigned integer. Works
// similarly to packUnorm2x16. The floats are clamped to the range 0.0 to 1.0, and written to the
// unsigned integer starting from the least significant bits.
inline uint32_t PackUnorm4x8(float f1, float f2, float f3, float f4)
{
uint8_t bits[4];
bits[0] = priv::ToPackedUnorm8(f1);
bits[1] = priv::ToPackedUnorm8(f2);
bits[2] = priv::ToPackedUnorm8(f3);
bits[3] = priv::ToPackedUnorm8(f4);
uint32_t result = 0u;
for (int i = 0; i < 4; ++i)
{
int shift = i * 8;
result |= (static_cast<uint32_t>(bits[i]) << shift);
}
return result;
}
// Unpacks 4 normalized unsigned floating-point values from a single 32-bit unsigned integer into f.
// Works similarly to unpackUnorm2x16. The floats are unpacked starting from the least significant
// bits.
inline void UnpackUnorm4x8(uint32_t u, float *f)
{
for (int i = 0; i < 4; ++i)
{
int shift = i * 8;
uint8_t bits = static_cast<uint8_t>((u >> shift) & 0xFF);
f[i] = static_cast<float>(bits) / 255.0f;
}
}
// Packs 4 normalized signed floating-point values to a single 32-bit unsigned integer. The floats
// are clamped to the range -1.0 to 1.0, and written to the unsigned integer starting from the least
// significant bits.
inline uint32_t PackSnorm4x8(float f1, float f2, float f3, float f4)
{
int8_t bits[4];
bits[0] = priv::ToPackedSnorm8(f1);
bits[1] = priv::ToPackedSnorm8(f2);
bits[2] = priv::ToPackedSnorm8(f3);
bits[3] = priv::ToPackedSnorm8(f4);
uint32_t result = 0u;
for (int i = 0; i < 4; ++i)
{
int shift = i * 8;
result |= ((static_cast<uint32_t>(bits[i]) & 0xFF) << shift);
}
return result;
}
// Unpacks 4 normalized signed floating-point values from a single 32-bit unsigned integer into f.
// Works similarly to unpackSnorm2x16. The floats are unpacked starting from the least significant
// bits, and clamped to the range -1.0 to 1.0.
inline void UnpackSnorm4x8(uint32_t u, float *f)
{
for (int i = 0; i < 4; ++i)
{
int shift = i * 8;
int8_t bits = static_cast<int8_t>((u >> shift) & 0xFF);
f[i] = clamp(static_cast<float>(bits) / 127.0f, -1.0f, 1.0f);
}
}
// Returns an unsigned integer obtained by converting the two floating-point values to the 16-bit
// floating-point representation found in the OpenGL ES Specification, and then packing these
// two 16-bit integers into a 32-bit unsigned integer.
// f1: The 16 least-significant bits of the result;
// f2: The 16 most-significant bits.
inline uint32_t packHalf2x16(float f1, float f2)
{
uint16_t leastSignificantBits = static_cast<uint16_t>(float32ToFloat16(f1));
uint16_t mostSignificantBits = static_cast<uint16_t>(float32ToFloat16(f2));
return static_cast<uint32_t>(mostSignificantBits) << 16 |
static_cast<uint32_t>(leastSignificantBits);
}
// Returns two floating-point values obtained by unpacking a 32-bit unsigned integer into a pair of
// 16-bit values, interpreting those values as 16-bit floating-point numbers according to the OpenGL
// ES Specification, and converting them to 32-bit floating-point values. The first float value is
// obtained from the 16 least-significant bits of u; the second component is obtained from the 16
// most-significant bits of u.
inline void unpackHalf2x16(uint32_t u, float *f1, float *f2)
{
uint16_t leastSignificantBits = static_cast<uint16_t>(u & 0xFFFF);
uint16_t mostSignificantBits = static_cast<uint16_t>(u >> 16);
*f1 = float16ToFloat32(leastSignificantBits);
*f2 = float16ToFloat32(mostSignificantBits);
}
inline uint8_t sRGBToLinear(uint8_t srgbValue)
{
float value = srgbValue / 255.0f;
if (value <= 0.04045f)
{
value = value / 12.92f;
}
else
{
value = std::pow((value + 0.055f) / 1.055f, 2.4f);
}
return static_cast<uint8_t>(clamp(value * 255.0f + 0.5f, 0.0f, 255.0f));
}
inline uint8_t linearToSRGB(uint8_t linearValue)
{
float value = linearValue / 255.0f;
if (value <= 0.0f)
{
value = 0.0f;
}
else if (value < 0.0031308f)
{
value = value * 12.92f;
}
else if (value < 1.0f)
{
value = std::pow(value, 0.41666f) * 1.055f - 0.055f;
}
else
{
value = 1.0f;
}
return static_cast<uint8_t>(clamp(value * 255.0f + 0.5f, 0.0f, 255.0f));
}
// Reverse the order of the bits.
inline uint32_t BitfieldReverse(uint32_t value)
{
// TODO(oetuaho@nvidia.com): Optimize this if needed. There don't seem to be compiler intrinsics
// for this, and right now it's not used in performance-critical paths.
uint32_t result = 0u;
for (size_t j = 0u; j < 32u; ++j)
{
result |= (((value >> j) & 1u) << (31u - j));
}
return result;
}
// Count the 1 bits.
#if defined(_MSC_VER) && !defined(__clang__)
# if defined(_M_IX86) || defined(_M_X64)
namespace priv
{
// Check POPCNT instruction support and cache the result.
static const bool kHasPopcnt = [] {
int info[4];
__cpuid(&info[0], 1);
return static_cast<bool>(info[2] & 0x800000);
}();
} // namespace priv
// Polyfills for x86/x64 CPUs without POPCNT.
inline int BitCountPolyfill(uint32_t bits)
{
bits = bits - ((bits >> 1) & 0x55555555);
bits = (bits & 0x33333333) + ((bits >> 2) & 0x33333333);
bits = ((bits + (bits >> 4) & 0x0F0F0F0F) * 0x01010101) >> 24;
return static_cast<int>(bits);
}
inline int BitCountPolyfill(uint64_t bits)
{
bits = bits - ((bits >> 1) & 0x5555555555555555ull);
bits = (bits & 0x3333333333333333ull) + ((bits >> 2) & 0x3333333333333333ull);
bits = ((bits + (bits >> 4) & 0x0F0F0F0F0F0F0F0Full) * 0x0101010101010101ull) >> 56;
return static_cast<int>(bits);
}
inline int BitCount(uint32_t bits)
{
if (priv::kHasPopcnt)
{
return static_cast<int>(__popcnt(bits));
}
return BitCountPolyfill(bits);
}
inline int BitCount(uint64_t bits)
{
if (priv::kHasPopcnt)
{
# if defined(_M_X64)
return static_cast<int>(__popcnt64(bits));
# else // x86
return static_cast<int>(__popcnt(static_cast<uint32_t>(bits >> 32)) +
__popcnt(static_cast<uint32_t>(bits)));
# endif // defined(_M_X64)
}
return BitCountPolyfill(bits);
}
# elif defined(_M_ARM) || defined(_M_ARM64)
// MSVC's _CountOneBits* intrinsics are not defined for ARM64, moreover they do not use dedicated
// NEON instructions.
inline int BitCount(uint32_t bits)
{
// cast bits to 8x8 datatype and use VCNT on it
const uint8x8_t vsum = vcnt_u8(vcreate_u8(static_cast<uint64_t>(bits)));
// pairwise sums: 8x8 -> 16x4 -> 32x2
return static_cast<int>(vget_lane_u32(vpaddl_u16(vpaddl_u8(vsum)), 0));
}
inline int BitCount(uint64_t bits)
{
// cast bits to 8x8 datatype and use VCNT on it
const uint8x8_t vsum = vcnt_u8(vcreate_u8(bits));
// pairwise sums: 8x8 -> 16x4 -> 32x2 -> 64x1
return static_cast<int>(vget_lane_u64(vpaddl_u32(vpaddl_u16(vpaddl_u8(vsum))), 0));
}
# endif // defined(_M_IX86) || defined(_M_X64)
#endif // defined(_MSC_VER) && !defined(__clang__)
#if defined(ANGLE_PLATFORM_POSIX) || defined(__clang__)
inline int BitCount(uint32_t bits)
{
return __builtin_popcount(bits);
}
inline int BitCount(uint64_t bits)
{
return __builtin_popcountll(bits);
}
#endif // defined(ANGLE_PLATFORM_POSIX) || defined(__clang__)
inline int BitCount(uint8_t bits)
{
return BitCount(static_cast<uint32_t>(bits));
}
inline int BitCount(uint16_t bits)
{
return BitCount(static_cast<uint32_t>(bits));
}
#if defined(ANGLE_PLATFORM_WINDOWS)
// Return the index of the least significant bit set. Indexing is such that bit 0 is the least
// significant bit. Implemented for different bit widths on different platforms.
inline unsigned long ScanForward(uint32_t bits)
{
ASSERT(bits != 0u);
unsigned long firstBitIndex = 0ul;
unsigned char ret = _BitScanForward(&firstBitIndex, bits);
ASSERT(ret != 0u);
return firstBitIndex;
}
inline unsigned long ScanForward(uint64_t bits)
{
ASSERT(bits != 0u);
unsigned long firstBitIndex = 0ul;
# if defined(ANGLE_IS_64_BIT_CPU)
unsigned char ret = _BitScanForward64(&firstBitIndex, bits);
# else
unsigned char ret;
if (static_cast<uint32_t>(bits) == 0)
{
ret = _BitScanForward(&firstBitIndex, static_cast<uint32_t>(bits >> 32));
firstBitIndex += 32ul;
}
else
{
ret = _BitScanForward(&firstBitIndex, static_cast<uint32_t>(bits));
}
# endif // defined(ANGLE_IS_64_BIT_CPU)
ASSERT(ret != 0u);
return firstBitIndex;
}
// Return the index of the most significant bit set. Indexing is such that bit 0 is the least
// significant bit.
inline unsigned long ScanReverse(uint32_t bits)
{
ASSERT(bits != 0u);
unsigned long lastBitIndex = 0ul;
unsigned char ret = _BitScanReverse(&lastBitIndex, bits);
ASSERT(ret != 0u);
return lastBitIndex;
}
inline unsigned long ScanReverse(uint64_t bits)
{
ASSERT(bits != 0u);
unsigned long lastBitIndex = 0ul;
# if defined(ANGLE_IS_64_BIT_CPU)
unsigned char ret = _BitScanReverse64(&lastBitIndex, bits);
# else
unsigned char ret;
if (static_cast<uint32_t>(bits >> 32) == 0)
{
ret = _BitScanReverse(&lastBitIndex, static_cast<uint32_t>(bits));
}
else
{
ret = _BitScanReverse(&lastBitIndex, static_cast<uint32_t>(bits >> 32));
lastBitIndex += 32ul;
}
# endif // defined(ANGLE_IS_64_BIT_CPU)
ASSERT(ret != 0u);
return lastBitIndex;
}
#endif // defined(ANGLE_PLATFORM_WINDOWS)
#if defined(ANGLE_PLATFORM_POSIX)
inline unsigned long ScanForward(uint32_t bits)
{
ASSERT(bits != 0u);
return static_cast<unsigned long>(__builtin_ctz(bits));
}
inline unsigned long ScanForward(uint64_t bits)
{
ASSERT(bits != 0u);
# if defined(ANGLE_IS_64_BIT_CPU)
return static_cast<unsigned long>(__builtin_ctzll(bits));
# else
return static_cast<unsigned long>(static_cast<uint32_t>(bits) == 0
? __builtin_ctz(static_cast<uint32_t>(bits >> 32)) + 32
: __builtin_ctz(static_cast<uint32_t>(bits)));
# endif // defined(ANGLE_IS_64_BIT_CPU)
}
inline unsigned long ScanReverse(uint32_t bits)
{
ASSERT(bits != 0u);
return static_cast<unsigned long>(sizeof(uint32_t) * CHAR_BIT - 1 - __builtin_clz(bits));
}
inline unsigned long ScanReverse(uint64_t bits)
{
ASSERT(bits != 0u);
# if defined(ANGLE_IS_64_BIT_CPU)
return static_cast<unsigned long>(sizeof(uint64_t) * CHAR_BIT - 1 - __builtin_clzll(bits));
# else
if (static_cast<uint32_t>(bits >> 32) == 0)
{
return sizeof(uint32_t) * CHAR_BIT - 1 - __builtin_clz(static_cast<uint32_t>(bits));
}
else
{
return sizeof(uint32_t) * CHAR_BIT - 1 - __builtin_clz(static_cast<uint32_t>(bits >> 32)) +
32;
}
# endif // defined(ANGLE_IS_64_BIT_CPU)
}
#endif // defined(ANGLE_PLATFORM_POSIX)
inline unsigned long ScanForward(uint8_t bits)
{
return ScanForward(static_cast<uint32_t>(bits));
}
inline unsigned long ScanForward(uint16_t bits)
{
return ScanForward(static_cast<uint32_t>(bits));
}
inline unsigned long ScanReverse(uint8_t bits)
{
return ScanReverse(static_cast<uint32_t>(bits));
}
inline unsigned long ScanReverse(uint16_t bits)
{
return ScanReverse(static_cast<uint32_t>(bits));
}
// Returns -1 on 0, otherwise the index of the least significant 1 bit as in GLSL.
template <typename T>
int FindLSB(T bits)
{
static_assert(std::is_integral<T>::value, "must be integral type.");
if (bits == 0u)
{
return -1;
}
else
{
return static_cast<int>(ScanForward(bits));
}
}
// Returns -1 on 0, otherwise the index of the most significant 1 bit as in GLSL.
template <typename T>
int FindMSB(T bits)
{
static_assert(std::is_integral<T>::value, "must be integral type.");
if (bits == 0u)
{
return -1;
}
else
{
return static_cast<int>(ScanReverse(bits));
}
}
// Returns whether the argument is Not a Number.
// IEEE 754 single precision NaN representation: Exponent(8 bits) - 255, Mantissa(23 bits) -
// non-zero.
inline bool isNaN(float f)
{
// Exponent mask: ((1u << 8) - 1u) << 23 = 0x7f800000u
// Mantissa mask: ((1u << 23) - 1u) = 0x7fffffu
return ((bitCast<uint32_t>(f) & 0x7f800000u) == 0x7f800000u) &&
(bitCast<uint32_t>(f) & 0x7fffffu);
}
// Returns whether the argument is infinity.
// IEEE 754 single precision infinity representation: Exponent(8 bits) - 255, Mantissa(23 bits) -
// zero.
inline bool isInf(float f)
{
// Exponent mask: ((1u << 8) - 1u) << 23 = 0x7f800000u
// Mantissa mask: ((1u << 23) - 1u) = 0x7fffffu
return ((bitCast<uint32_t>(f) & 0x7f800000u) == 0x7f800000u) &&
!(bitCast<uint32_t>(f) & 0x7fffffu);
}
namespace priv
{
template <unsigned int N, unsigned int R>
struct iSquareRoot
{
static constexpr unsigned int solve()
{
return (R * R > N)
? 0
: ((R * R == N) ? R : static_cast<unsigned int>(iSquareRoot<N, R + 1>::value));
}
enum Result
{
value = iSquareRoot::solve()
};
};
template <unsigned int N>
struct iSquareRoot<N, N>
{
enum result
{
value = N
};
};
} // namespace priv
template <unsigned int N>
constexpr unsigned int iSquareRoot()
{
return priv::iSquareRoot<N, 1>::value;
}
// Sum, difference and multiplication operations for signed ints that wrap on 32-bit overflow.
//
// Unsigned types are defined to do arithmetic modulo 2^n in C++. For signed types, overflow
// behavior is undefined.
template <typename T>
inline T WrappingSum(T lhs, T rhs)
{
uint32_t lhsUnsigned = static_cast<uint32_t>(lhs);
uint32_t rhsUnsigned = static_cast<uint32_t>(rhs);
return static_cast<T>(lhsUnsigned + rhsUnsigned);
}
template <typename T>
inline T WrappingDiff(T lhs, T rhs)
{
uint32_t lhsUnsigned = static_cast<uint32_t>(lhs);
uint32_t rhsUnsigned = static_cast<uint32_t>(rhs);
return static_cast<T>(lhsUnsigned - rhsUnsigned);
}
inline int32_t WrappingMul(int32_t lhs, int32_t rhs)
{
int64_t lhsWide = static_cast<int64_t>(lhs);
int64_t rhsWide = static_cast<int64_t>(rhs);
// The multiplication is guaranteed not to overflow.
int64_t resultWide = lhsWide * rhsWide;
// Implement the desired wrapping behavior by masking out the high-order 32 bits.
resultWide = resultWide & 0xffffffffLL;
// Casting to a narrower signed type is fine since the casted value is representable in the
// narrower type.
return static_cast<int32_t>(resultWide);
}
inline float scaleScreenDimensionToNdc(float dimensionScreen, float viewportDimension)
{
return 2.0f * dimensionScreen / viewportDimension;
}
inline float scaleScreenCoordinateToNdc(float coordinateScreen, float viewportDimension)
{
float halfShifted = coordinateScreen / viewportDimension;
return 2.0f * (halfShifted - 0.5f);
}
} // namespace gl
namespace rx
{
template <typename T>
T roundUp(const T value, const T alignment)
{
auto temp = value + alignment - static_cast<T>(1);
return temp - temp % alignment;
}
template <typename T>
constexpr T roundUpPow2(const T value, const T alignment)
{
ASSERT(gl::isPow2(alignment));
return (value + alignment - 1) & ~(alignment - 1);
}
template <typename T>
constexpr T roundDownPow2(const T value, const T alignment)
{
ASSERT(gl::isPow2(alignment));
return value & ~(alignment - 1);
}
template <typename T>
angle::CheckedNumeric<T> CheckedRoundUp(const T value, const T alignment)
{
angle::CheckedNumeric<T> checkedValue(value);
angle::CheckedNumeric<T> checkedAlignment(alignment);
return roundUp(checkedValue, checkedAlignment);
}
inline constexpr unsigned int UnsignedCeilDivide(unsigned int value, unsigned int divisor)
{
unsigned int divided = value / divisor;
return (divided + ((value % divisor == 0) ? 0 : 1));
}
#if defined(__has_builtin)
# define ANGLE_HAS_BUILTIN(x) __has_builtin(x)
#else
# define ANGLE_HAS_BUILTIN(x) 0
#endif
#if defined(_MSC_VER)
# define ANGLE_ROTL(x, y) _rotl(x, y)
# define ANGLE_ROTL64(x, y) _rotl64(x, y)
# define ANGLE_ROTR16(x, y) _rotr16(x, y)
#elif defined(__clang__) && ANGLE_HAS_BUILTIN(__builtin_rotateleft32) && \
ANGLE_HAS_BUILTIN(__builtin_rotateleft64) && ANGLE_HAS_BUILTIN(__builtin_rotateright16)
# define ANGLE_ROTL(x, y) __builtin_rotateleft32(x, y)
# define ANGLE_ROTL64(x, y) __builtin_rotateleft64(x, y)
# define ANGLE_ROTR16(x, y) __builtin_rotateright16(x, y)
#else
inline uint32_t RotL(uint32_t x, int8_t r)
{
return (x << r) | (x >> (32 - r));
}
inline uint64_t RotL64(uint64_t x, int8_t r)
{
return (x << r) | (x >> (64 - r));
}
inline uint16_t RotR16(uint16_t x, int8_t r)
{
return (x >> r) | (x << (16 - r));
}
# define ANGLE_ROTL(x, y) ::rx::RotL(x, y)
# define ANGLE_ROTL64(x, y) ::rx::RotL64(x, y)
# define ANGLE_ROTR16(x, y) ::rx::RotR16(x, y)
#endif // namespace rx
constexpr unsigned int Log2(unsigned int bytes)
{
return bytes == 1 ? 0 : (1 + Log2(bytes / 2));
}
} // namespace rx
#endif // COMMON_MATHUTIL_H_