//
// Copyright (c) 2002-2013 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 LIBGLESV2_MATHUTIL_H_
#define LIBGLESV2_MATHUTIL_H_
#include "common/debug.h"
#if defined(_WIN32)
#include <intrin.h>
#endif
#include <limits>
#include <algorithm>
#include <string.h>
namespace gl
{
const unsigned int Float32One = 0x3F800000;
const unsigned short Float16One = 0x3C00;
struct Vector4
{
Vector4() {}
Vector4(float x, float y, float z, float w) : x(x), y(y), z(z), w(w) {}
float x;
float y;
float z;
float w;
};
inline bool isPow2(int x)
{
return (x & (x - 1)) == 0 && (x != 0);
}
inline int log2(int x)
{
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;
}
inline int clampToInt(unsigned int x)
{
return static_cast<int>(std::min(x, static_cast<unsigned int>(std::numeric_limits<int>::max())));
}
template <typename DestT, typename SrcT>
inline DestT clampCast(SrcT value)
{
// This assumes SrcT can properly represent DestT::min/max
// Unfortunately we can't use META_ASSERT without C++11 constexpr support
ASSERT(static_cast<DestT>(static_cast<SrcT>(std::numeric_limits<DestT>::min())) == std::numeric_limits<DestT>::min());
ASSERT(static_cast<DestT>(static_cast<SrcT>(std::numeric_limits<DestT>::max())) == std::numeric_limits<DestT>::max());
SrcT lo = static_cast<SrcT>(std::numeric_limits<DestT>::min());
SrcT hi = static_cast<SrcT>(std::numeric_limits<DestT>::max());
return static_cast<DestT>(value > lo ? (value > hi ? hi : value) : lo);
}
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;
}
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(_WIN32)
static bool checked = false;
static bool supports = false;
if (checked)
{
return supports;
}
int info[4];
__cpuid(info, 0);
if (info[0] >= 1)
{
__cpuid(info, 1);
supports = (info[3] >> 26) & 1;
}
checked = true;
return supports;
#else
UNIMPLEMENTED();
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;
}
inline unsigned short float32ToFloat16(float fp32)
{
unsigned int fp32i = (unsigned int&)fp32;
unsigned int sign = (fp32i & 0x80000000) >> 16;
unsigned int abs = fp32i & 0x7FFFFFFF;
if(abs > 0x47FFEFFF) // Infinity
{
return sign | 0x7FFF;
}
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 sign | (abs + 0x00000FFF + ((abs >> 13) & 1)) >> 13;
}
else
{
return 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 float32Minfloat11 = 0x38800000;
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 < float32Minfloat11)
{
// 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);
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 float32Minfloat10 = 0x38800000;
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 float11 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 float11, set to max
return float10Max;
}
else
{
if (float32Val < float32Minfloat10)
{
// The number is too small to be represented as a normalized float11
// Convert it to a denormalized value.
const unsigned int shift = (float32ExponentBias - float10ExponentBias) - (float32Val >> float32ExponentFirstBit);
float32Val = ((1 << float32ExponentFirstBit) | (float32Val & float32MantissaMask)) >> shift;
}
else
{
// Rebias the exponent to represent the value as a normalized float11
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 = -112;
}
return bitCast<float>(((exponent + 112) << 23) | (mantissa << 17));
}
}
inline float float10ToFloat32(unsigned short fp11)
{
unsigned short exponent = (fp11 >> 5) & 0x1F;
unsigned short mantissa = fp11 & 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 = -112;
}
return bitCast<float>(((exponent + 112) << 23) | (mantissa << 18));
}
}
template <typename T>
inline float normalizedToFloat(T input)
{
META_ASSERT(std::numeric_limits<T>::is_integer);
const float inverseMax = 1.0f / std::numeric_limits<T>::max();
return input * inverseMax;
}
template <unsigned int inputBitCount, typename T>
inline float normalizedToFloat(T input)
{
META_ASSERT(std::numeric_limits<T>::is_integer);
META_ASSERT(inputBitCount < (sizeof(T) * 8));
const float inverseMax = 1.0f / ((1 << inputBitCount) - 1);
return input * inverseMax;
}
template <typename T>
inline T floatToNormalized(float input)
{
return std::numeric_limits<T>::max() * input + 0.5f;
}
template <unsigned int outputBitCount, typename T>
inline T floatToNormalized(float input)
{
META_ASSERT(outputBitCount < (sizeof(T) * 8));
return ((1 << outputBitCount) - 1) * input + 0.5f;
}
template <unsigned int inputBitCount, unsigned int inputBitStart, typename T>
inline T getShiftedData(T input)
{
META_ASSERT(inputBitCount + inputBitStart <= (sizeof(T) * 8));
const T mask = (1 << inputBitCount) - 1;
return (input >> inputBitStart) & mask;
}
template <unsigned int inputBitCount, unsigned int inputBitStart, typename T>
inline T shiftData(T input)
{
META_ASSERT(inputBitCount + inputBitStart <= (sizeof(T) * 8));
const T mask = (1 << inputBitCount) - 1;
return (input & mask) << inputBitStart;
}
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 signed int average(signed int a, signed int b)
{
return ((long long)a + (long long)b) / 2;
}
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(a) + float11ToFloat32(b)) * 0.5f);
}
inline unsigned int averageFloat10(unsigned int a, unsigned int b)
{
return float32ToFloat10((float10ToFloat32(a) + float10ToFloat32(b)) * 0.5f);
}
}
namespace rx
{
struct Range
{
Range() {}
Range(int lo, int hi) : start(lo), end(hi) { ASSERT(lo <= hi); }
int start;
int end;
};
template <typename T>
T roundUp(const T value, const T alignment)
{
return value + alignment - 1 - (value - 1) % alignment;
}
template <class T>
inline bool IsUnsignedAdditionSafe(T lhs, T rhs)
{
META_ASSERT(!std::numeric_limits<T>::is_signed);
return (rhs <= std::numeric_limits<T>::max() - lhs);
}
template <class T>
inline bool IsUnsignedMultiplicationSafe(T lhs, T rhs)
{
META_ASSERT(!std::numeric_limits<T>::is_signed);
return (lhs == T(0) || rhs == T(0) || (rhs <= std::numeric_limits<T>::max() / lhs));
}
template <class SmallIntT, class BigIntT>
inline bool IsIntegerCastSafe(BigIntT bigValue)
{
return (static_cast<BigIntT>(static_cast<SmallIntT>(bigValue)) == bigValue);
}
}
#endif // LIBGLESV2_MATHUTIL_H_